Universality for shape dependence of Casimir effects from Weyl anomaly

NASA Astrophysics Data System (ADS)

Miao, Rong-Xin; Chu, Chong-Sun

2018-03-01

We reveal elegant relations between the shape dependence of the Casimir effects and Weyl anomaly in boundary conformal field theories (BCFT). We show that for any BCFT which has a description in terms of an effective action, the near boundary divergent behavior of the renormalized stress tensor is completely determined by the central charges of the theory. These relations are verified by free BCFTs. We also test them with holographic models of BCFT and find exact agreement. We propose that these relations between Casimir coefficients and central charges hold for any BCFT. With the holographic models, we reproduce not only the precise form of the near boundary divergent behavior of the stress tensor, but also the surface counter term that is needed to make the total energy finite. As they are proportional to the central charges, the near boundary divergence of the stress tensor must be physical and cannot be dropped by further artificial renormalization. Our results thus provide affirmative support on the physical nature of the divergent energy density near the boundary, whose reality has been a long-standing controversy in the literature.

An anisotropic elastoplastic constitutive formulation generalised for orthotropic materials

NASA Astrophysics Data System (ADS)

Mohd Nor, M. K.; Ma'at, N.; Ho, C. S.

2018-03-01

This paper presents a finite strain constitutive model to predict a complex elastoplastic deformation behaviour that involves very high pressures and shockwaves in orthotropic materials using an anisotropic Hill's yield criterion by means of the evolving structural tensors. The yield surface of this hyperelastic-plastic constitutive model is aligned uniquely within the principal stress space due to the combination of Mandel stress tensor and a new generalised orthotropic pressure. The formulation is developed in the isoclinic configuration and allows for a unique treatment for elastic and plastic orthotropy. An isotropic hardening is adopted to define the evolution of plastic orthotropy. The important feature of the proposed hyperelastic-plastic constitutive model is the introduction of anisotropic effect in the Mie-Gruneisen equation of state (EOS). The formulation is further combined with Grady spall failure model to predict spall failure in the materials. The proposed constitutive model is implemented as a new material model in the Lawrence Livermore National Laboratory (LLNL)-DYNA3D code of UTHM's version, named Material Type 92 (Mat92). The combination of the proposed stress tensor decomposition and the Mie-Gruneisen EOS requires some modifications in the code to reflect the formulation of the generalised orthotropic pressure. The validation approach is also presented in this paper for guidance purpose. The \\varvec{ψ} tensor used to define the alignment of the adopted yield surface is first validated. This is continued with an internal validation related to elastic isotropic, elastic orthotropic and elastic-plastic orthotropic of the proposed formulation before a comparison against range of plate impact test data at 234, 450 and {895 ms}^{-1} impact velocities is performed. A good agreement is obtained in each test.

Influence of seismic anisotropy on the cross correlation tensor: numerical investigations

NASA Astrophysics Data System (ADS)

Saade, M.; Montagner, J. P.; Roux, P.; Cupillard, P.; Durand, S.; Brenguier, F.

2015-05-01

Temporal changes in seismic anisotropy can be interpreted as variations in the orientation of cracks in seismogenic zones, and thus as variations in the stress field. Such temporal changes have been observed in seismogenic zones before and after earthquakes, although they are still not well understood. In this study, we investigate the azimuthal polarization of surface waves in anisotropic media with respect to the orientation of anisotropy, from a numerical point of view. This technique is based on the observation of the signature of anisotropy on the nine-component cross-correlation tensor (CCT) computed from seismic ambient noise recorded on pairs of three-component sensors. If noise sources are spatially distributed in a homogeneous medium, the CCT allows the reconstruction of the surface wave Green's tensor between the station pairs. In homogeneous, isotropic medium, four off-diagonal terms of the surface wave Green's tensor are null, but not in anisotropic medium. This technique is applied to three-component synthetic seismograms computed in a transversely isotropic medium with a horizontal symmetry axis, using a spectral element code. The CCT is computed between each pair of stations and then rotated, to approximate the surface wave Green's tensor by minimizing the off-diagonal components. This procedure allows the calculation of the azimuthal variation of quasi-Rayleigh and quasi-Love waves. In an anisotropic medium, in some cases, the azimuth of seismic anisotropy can induce a large variation in the horizontal polarization of surface waves. This variation depends on the relative angle between a pair of stations and the direction of anisotropy, the amplitude of the anisotropy, the frequency band of the signal and the depth of the anisotropic layer.

Conservation laws and stress-energy-momentum tensors for systems with background fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gratus, Jonathan, E-mail: j.gratus@lancaster.ac.uk; The Cockcroft Institute, Daresbury Laboratory, Warrington WA4 4AD; Obukhov, Yuri N., E-mail: yo@thp.uni-koeln.de

2012-10-15

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics inmore » media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields. - Highlights: Black-Right-Pointing-Pointer The role of background fields in diffeomorphism invariant actions is demonstrated. Black-Right-Pointing-Pointer Interrelations between different stress-energy-momentum tensors are emphasised. Black-Right-Pointing-Pointer The Abraham and Minkowski electromagnetic tensors are discussed in this context. Black-Right-Pointing-Pointer Conservation laws in the presence of nondynamic background fields are formulated. Black-Right-Pointing-Pointer The discussion is facilitated by the development of a new variational calculus.« less

Mechanics of couple-stress fluid coatings

NASA Technical Reports Server (NTRS)

Waxman, A. M.

1982-01-01

The formal development of a theory of viscoelastic surface fluids with bending resistance - their kinematics, dynamics, and rheology are discussed. It is relevant to the mechanics of fluid drops and jets coated by a thin layer of immiscible fluid with rather general rheology. This approach unifies the hydrodynamics of two-dimensional fluids with the mechanics of an elastic shell in the spirit of a Cosserat continuum. There are three distinct facets to the formulation of surface continuum mechanics. Outlined are the important ideas and results associated with each: the kinematics of evolving surface geometries, the conservation laws governing the mechanics of surface continua, and the rheological equations of state governing the surface stress and moment tensors.

Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levashov, V. A.

2016-03-07

It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids’ structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectorsmore » of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ{sub 1} ≥ λ{sub 2} ≥ λ{sub 3} ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ{sub 2}/λ{sub 1}) and (λ{sub 3}/λ{sub 2}) are essentially identical to each other in the liquids state. We also found that λ{sub 2} tends to be equal to the geometric average of λ{sub 1} and λ{sub 3}. In our view, correlations between the eigenvalues may represent “the Poisson ratio effect” at the atomic scale.« less

Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors.

PubMed

Levashov, V A

2016-03-07

It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids' structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ1 ≥ λ2 ≥ λ3 ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ2/λ1) and (λ3/λ2) are essentially identical to each other in the liquids state. We also found that λ2 tends to be equal to the geometric average of λ1 and λ3. In our view, correlations between the eigenvalues may represent "the Poisson ratio effect" at the atomic scale.

Irreducible Representations of Oscillatory and Swirling Flows in Active Soft Matter

NASA Astrophysics Data System (ADS)

Ghose, Somdeb; Adhikari, R.

2014-03-01

Recent experiments imaging fluid flow around swimming microorganisms have revealed complex time-dependent velocity fields that differ qualitatively from the stresslet flow commonly employed in theoretical descriptions of active matter. Here we obtain the most general flow around a finite sized active particle by expanding the surface stress in irreducible Cartesian tensors. This expansion, whose first term is the stresslet, must include, respectively, third-rank polar and axial tensors to minimally capture crucial features of the active oscillatory flow around translating Chlamydomonas and the active swirling flow around rotating Volvox. The representation provides explicit expressions for the irreducible symmetric, antisymmetric, and isotropic parts of the continuum active stress. Antisymmetric active stresses do not conserve orbital angular momentum and our work thus shows that spin angular momentum is necessary to restore angular momentum conservation in continuum hydrodynamic descriptions of active soft matter.

Micro-Stress Bound Estimate Enabled Optimization of Structural Composite Repair for the Next Generation Aircraft

DTIC Science & Technology

2007-02-28

where they exhibited the maximum values, which were the midsurface and 0/-0 surface for two laminates with 0=150 and 0=400. a) 50000 40000 - 0 30000...the first and second invariants of the strain tensor calculated at the midsurface in the x=O cross section as a function of distance from the hole edge...Y Figure 7. Comparison of the distributions of strain tensor invariants predicted in the matrix phase at the midsurface at x=0 as a function of

Quantum electromagnetic stress tensor in an inhomogeneous medium

NASA Astrophysics Data System (ADS)

Parashar, Prachi; Milton, Kimball A.; Li, Yang; Day, Hannah; Guo, Xin; Fulling, Stephen A.; Cavero-Peláez, Inés

2018-06-01

Continuing a program of examining the behavior of the vacuum expectation value of the stress tensor in a background which varies only in a single direction, we here study the electromagnetic stress tensor in a medium with permittivity depending on a single spatial coordinate, specifically, a planar dielectric half-space facing a vacuum region. There are divergences occurring that are regulated by temporal and spatial point splitting, which have a universal character for both transverse electric and transverse magnetic modes. The nature of the divergences depends on the model of dispersion adopted. And there are singularities occurring at the edge between the dielectric and vacuum regions, which also have a universal character, depending on the structure of the discontinuities in the material properties there. Remarks are offered concerning renormalization of such models, and the significance of the stress tensor. The ambiguity in separating "bulk" and "scattering" parts of the stress tensor is discussed.

Simplified derivation of the gravitational wave stress tensor from the linearized Einstein field equations.

PubMed

Balbus, Steven A

2016-10-18

A conserved stress energy tensor for weak field gravitational waves propagating in vacuum is derived directly from the linearized general relativistic wave equation alone, for an arbitrary gauge. In any harmonic gauge, the form of the tensor leads directly to the classical expression for the outgoing wave energy. The method described here, however, is a much simpler, shorter, and more physically motivated approach than is the customary procedure, which involves a lengthy and cumbersome second-order (in wave-amplitude) calculation starting with the Einstein tensor. Our method has the added advantage of exhibiting the direct coupling between the outgoing wave energy flux and the work done by the gravitational field on the sources. For nonharmonic gauges, the directly derived wave stress tensor has an apparent index asymmetry. This coordinate artifact may be straightforwardly removed, and the symmetrized (still gauge-invariant) tensor then takes on its widely used form. Angular momentum conservation follows immediately. For any harmonic gauge, however, the stress tensor found is manifestly symmetric from the start, and its derivation depends, in its entirety, on the structure of the linearized wave equation.

Surface thermodynamics, surface stress, equations at surfaces and triple lines for deformable bodies.

PubMed

Olives, Juan

2010-03-03

The thermodynamics and mechanics of the surface of a deformable body are studied here, following and refining the general approach of Gibbs. It is first shown that the 'local' thermodynamic variables of the state of the surface are only the temperature, the chemical potentials and the surface strain tensor (true thermodynamic variables, for a viscoelastic solid or a viscous fluid). A new definition of the surface stress is given and the corresponding surface thermodynamics equations are presented. The mechanical equilibrium equation at the surface is then obtained. It involves the surface stress and is similar to the Cauchy equation for the volume. Its normal component is a generalization of the Laplace equation. At a (body-fluid-fluid) triple contact line, two equations are obtained, which represent: (i) the equilibrium of the forces (surface stresses) for a triple line fixed on the body; (ii) the equilibrium relative to the motion of the line with respect to the body. This last equation leads to a strong modification of Young's classical capillary equation.

The influence of open fracture anisotropy on CO2 movement within geological storage complexes

NASA Astrophysics Data System (ADS)

Bond, C. E.; Wightman, R.; Ringrose, P. S.

2012-12-01

Carbon mitigation through the geological storage of carbon dioxide is dependent on the ability of geological formations to store CO2 trapping it within a geological storage complex. Secure long-term containment needs to be demonstrated, due to both political and social drivers, meaning that this containment must be verifiable over periods of 100-105 years. The effectiveness of sub-surface geological storage systems is dependent on trapping CO2 within a volume of rock and is reliant on the integrity of the surrounding rocks, including their chemical and physical properties, to inhibit migration to the surface. Oil and gas reservoir production data, and field evidence show that fracture networks have the potential to act as focused pathways for fluid movement. Fracture networks can allow large volumes of fluid to migrate to the surface within the time scales of interest. In this paper we demonstrate the importance of predicting the effects of fracture networks in storage, using a case study from the In Salah CO2 storage site, and show how the fracture permeability is closely controlled by the stress regime that determines the open fracture network. Our workflow combines well data of imaged fractures, with a discrete fracture network (DFN) model of tectonically induced fractures, within the horizon of interest. The modelled and observed fractures have been compared and combined with present day stress data to predict the open fracture network and its implications for anisotropic movement of CO2 in the sub-surface. The created fracture network model has been used to calculate the 2D permeability tensor for the reservoir for two scenarios: 1) a model in which all fractures are permeable, based on the whole DFN model and 2) those fractures determined to be in dilatational failure under the present day stress regime, a sub-set of the DFN. The resulting permeability anisotropy tensors show distinct anisotropies for the predicted CO2 movement within the reservoir. These predictions have been compared with InSAR imagery of surface uplift, used as an indicator of fluid pressure and movement in the sub-surface, around the CO2 injection wells. The analysis shows that the permeability tensor with the greatest anisotropy, that for the DFN sub-set of open fractures, matches well with the anisotropy in surface uplift imaged by InSAR. We demonstrate that predicting fracture networks alone does not predict fluid movement in the sub-surface, and that fracture permeability is closely controlled by the stress regime that determines the open fracture network. Our results show that a workflow of fracture network prediction combined with present day stress analysis can be used to successfully predict CO2 movement in the sub-surface at an active injection site.

On the dual variable of the Cauchy stress tensor in isotropic finite hyperelasticity

NASA Astrophysics Data System (ADS)

Vallée, Claude; Fortuné, Danielle; Lerintiu, Camelia

2008-11-01

Elastic materials are governed by a constitutive law relating the second Piola-Kirchhoff stress tensor Σ and the right Cauchy-Green strain tensor C=FF. Isotropic elastic materials are the special cases for which the Cauchy stress tensor σ depends solely on the left Cauchy-Green strain tensor B=FF. In this Note we revisit the following property of isotropic hyperelastic materials: if the constitutive law relating Σ and C is derivable from a potential ϕ, then σ and lnB are related by a constitutive law derived from the compound potential ϕ○exp. We give a new and concise proof which is based on an explicit integral formula expressing the derivative of the exponential of a tensor. To cite this article: C. Vallée et al., C. R. Mecanique 336 (2008).

Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

NASA Technical Reports Server (NTRS)

Jongen, T.; Gatski, T. B.

1997-01-01

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

NIED seismic moment tensor catalogue for regional earthquakes around Japan: quality test and application

NASA Astrophysics Data System (ADS)

Kubo, Atsuki; Fukuyama, Eiichi; Kawai, Hiroyuki; Nonomura, Ken'ichi

2002-10-01

We have examined the quality of the National Research Institute for Earth Science and Disaster Prevention (NIED) seismic moment tensor (MT) catalogue obtained using a regional broadband seismic network (FREESIA). First, we examined using synthetic waveforms the robustness of the solutions with regard to data noise as well as to errors in the velocity structure and focal location. Then, to estimate the reliability, robustness and validity of the catalogue, we compared it with the Harvard centroid moment tensor (CMT) catalogue as well as the Japan Meteorological Agency (JMA) focal mechanism catalogue. We found out that the NIED catalogue is consistent with Harvard and JMA catalogues within the uncertainty of 0.1 in moment magnitude, 10 km in depth, and 15° in direction of the stress axes. The NIED MT catalogue succeeded in reducing to 3.5 the lower limit of moment magnitude above which the moment tensor could be reliably estimated. Finally, we estimated the stress tensors in several different regions by using the NIED MT catalogue. This enables us to elucidate the stress/deformation field in and around the Japanese islands to understand the mode of deformation and applied stress. Moreover, we identified a region of abnormal stress in a swarm area from stress tensor estimates.

Reversible and dissipative macroscopic contributions to the stress tensor: active or passive?

PubMed

Brand, H R; Pleiner, H; Svenšek, D

2014-09-01

The issue of dynamic contributions to the macroscopic stress tensor has been of high interest in the field of bio-inspired active systems over the last few years. Of particular interest is a direct coupling ("active term") of the stress tensor with the order parameter, the latter describing orientational order induced by active processes. Here we analyze more generally possible reversible and irreversible dynamic contributions to the stress tensor for various passive and active macroscopic systems. This includes systems with tetrahedral/octupolar order, polar and non-polar (chiral) nematic and smectic liquid crystals, as well as active fluids with a dynamic preferred (polar or non-polar) direction. We show that it cannot a priori be seen, neither from the symmetry properties of the macroscopic variables involved, nor from the structure of the cross-coupling contributions to the stress tensor, whether the system studied is active or passive. Rather, that depends on whether the variables that give rise to those cross-couplings in the stress tensor are driven or not. We demonstrate that several simplified descriptions of active systems in the literature that neglect the necessary counter term to the active term violate linear irreversible thermodynamics and lead to an unphysical contribution to the entropy production.

Spatial distribution of F-net moment tensors for the 2005 West Off Fukuoka Prefecture Earthquake determined by the extended method of the NIED F-net routine

NASA Astrophysics Data System (ADS)

Matsumoto, Takumi; Ito, Yoshihiro; Matsubayashi, Hirotoshi; Sekiguchi, Shoji

2006-01-01

The 2005 West Off Fukuoka Prefecture Earthquake with a Japan Meteorological Agency (JMA) magnitude (MJMA) of 7.0 occurred on March 20, 2005. We determined moment tensor solutions, using a surface wave with an extended method of the NIED F-net routine processing. The horizontal distance to the station is rounded to the nearest interval of 1 km, and the variance reduction approach is applied to a focal depth from 2 km with an interval of 1 km. We obtain the moment tensors of 101 events with (MJMA) exceeding 3.0 and spatial distribution of these moment tensors. The focal mechanism of aftershocks is mainly of the strike-slip type. The alignment of the epicenters in the rupture zone of the main-shock is oriented between N110°E and N130°E, which is close to the strike of the main-shock's moment tensor solutions (N122°E). These moment tensor solutions of intermediatesized aftershocks around the focal region represent basic and important information concerning earthquakes in investigating regional tectonic stress fields, source mechanisms and so on.

Inversion of calcite twin data for paleostress (1) : improved Etchecopar technique tested on numerically-generated and natural data

NASA Astrophysics Data System (ADS)

Parlangeau, Camille; Lacombe, Olivier; Daniel, Jean-Marc; Schueller, Sylvie

2015-04-01

Inversion of calcite twin data are known to be a powerful tool to reconstruct the past-state of stress in carbonate rocks of the crust, especially in fold-and-thrust belts and sedimentary basins. This is of key importance to constrain results of geomechanical modelling. Without proposing a new inversion scheme, this contribution reports some recent improvements of the most efficient stress inversion technique to date (Etchecopar, 1984) that allows to reconstruct the 5 parameters of the deviatoric paleostress tensors (principal stress orientations and differential stress magnitudes) from monophase and polyphase twin data sets. The improvements consist in the search of the possible tensors that account for the twin data (twinned and untwinned planes) and the aid to the user to define the best stress tensor solution, among others. We perform a systematic exploration of an hypersphere in 4 dimensions by varying different parameters, Euler's angles and the stress ratio. We first record all tensors with a minimum penalization function accounting for 20% of the twinned planes. We then define clusters of tensors following a dissimilarity criterion based on the stress distance between the 4 parameters of the reduced stress tensors and a degree of disjunction of the related sets of twinned planes. The percentage of twinned data to be explained by each tensor is then progressively increased and tested using the standard Etchecopar procedure until the best solution that explains the maximum number of twinned planes and the whole set of untwinned planes is reached. This new inversion procedure is tested on monophase and polyphase numerically-generated as well as natural calcite twin data in order to more accurately define the ability of the technique to separate more or less similar deviatoric stress tensors applied in sequence on the samples, to test the impact of strain hardening through the change of the critical resolved shear stress for twinning as well as to evaluate the possible bias due to measurement uncertainties or clustering of grain optical axes in the samples.

Scalewise invariant analysis of the anisotropic Reynolds stress tensor for atmospheric surface layer and canopy sublayer turbulent flows

NASA Astrophysics Data System (ADS)

Brugger, Peter; Katul, Gabriel G.; De Roo, Frederik; Kröniger, Konstantin; Rotenberg, Eyal; Rohatyn, Shani; Mauder, Matthias

2018-05-01

Anisotropy in the turbulent stress tensor, which forms the basis of invariant analysis, is conducted using velocity time series measurements collected in the canopy sublayer (CSL) and the atmospheric surface layer (ASL). The goal is to assess how thermal stratification and surface roughness conditions simultaneously distort the scalewise relaxation towards isotropic state from large to small scales when referenced to homogeneous turbulence. To achieve this goal, conventional invariant analysis is extended to allow scalewise information about relaxation to isotropy in physical (instead of Fourier) space to be incorporated. The proposed analysis shows that the CSL is more isotropic than its ASL counterpart at large, intermediate, and small (or inertial) scales irrespective of the thermal stratification. Moreover, the small (or inertial) scale anisotropy is more prevalent in the ASL when compared to the CSL, a finding that cannot be fully explained by the intensity of the mean velocity gradient acting on all scales. Implications to the validity of scalewise Rotta and Lumley models for return to isotropy as well as advantages to using barycentric instead of anisotropy invariant maps for such scalewise analysis are discussed.

On the curvature effect of thin membranes

NASA Astrophysics Data System (ADS)

Wang, Duo; Jiao, Xiangmin; Conley, Rebecca; Glimm, James

2013-01-01

We investigate the curvature effect of a thin, curved elastic interface that separates two subdomains and exerts a pressure due to a curvature effect. This pressure, which we refer to as interface pressure, is similar to the surface tension in fluid mechanics. It is important in some applications, such as the canopy of parachutes, biological membranes of cells, balloons, airbags, etc., as it partially balances a pressure jump between the two sides of an interface. In this paper, we show that the interface pressure is equal to the trace of the matrix product of the curvature tensor and the Cauchy stress tensor in the tangent plane. We derive the theory for interfaces in both 2-D and 3-D, and present numerical discretizations for computing the quality over triangulated surfaces.

Spatio-temporal changes of seismic anisotropy in seismogenic zones

NASA Astrophysics Data System (ADS)

Saade, M.; Montagner, J.; Roux, P.; Paul, C.; Brenguier, F.; Enescu, B.; Shiomi, K.

2013-12-01

Seismic anisotropy plays a key role in the study of stress and strain fields in the earth. Potential temporal change of seismic anisotropy can be interpreted as change of the orientation of cracks in seismogenic zones and thus change of the stress field. Such temporal changes have been observed in seismogenic zones before and after earthquakes (Durand et al. , 2011) but are still not well understood. In this study, from a numerical point of view, we investigate the variations of the polarization of surface waves in anisotropic media. These variations are related to the elastic properties of the medium, in particular to anisotropy. The technique used is based on the calculation of the whole cross-correlation tensor (CCT) of ambient seismic noise. If the sources are randomly distributed in homogeneous medium, it allows us to reconstruct the Green's tensor between two stations continuously and to monitor the region through the use of its fluctuations. Therefore, the temporal change of the Green's cross-correlation tensor enables the monitoring of stress and strain fields. This technique is applied to synthetic seismograms computed in a transversally isotropic medium with horizontal symmetry axis (hereafter referred to an HTI medium) using a code RegSEM (Cupillard et al. , 2012) based on the spectral element method. We designed an experiment in order to investigate the influence of anisotropy on the CCT. In homogeneous, isotropic medium the off-diagonal terms of the Green's tensor are null. The CCT is computed between each pair of stations and then rotated in order to approximate the Green's tensor by minimizing the off-diagonal components. This procedure permits the calculation of the polarization angle of quasi-Rayleigh and quasi-Love waves, and to observe the azimuthal variation of their polarization. The results show that even a small variation of the azimuth of seismic anisotropy with respect to a certain pair of stations can induce, in some cases, a large variation in the horizontal polarization of surface waves along the direction of this pair of stations. It depends on the relative azimuth angle between the pair of stations and the direction of anisotropy, on the amplitude of anisotropy and the frequency band of the signal. Therefore, it is now possible to explain the large, rapid and very localized variations of surface waves horizontal polarization observed by Durand et al. (2011) during the Parkfield earthquake of 2004. Furthermore, some preliminary results about the investigation of seismic anisotropy change caused by the June 13, 2008 Iwate-Miyagi Nairiku earthquake (Mw = 6.9) will be presented.

Stresses in curved nematic membranes.

PubMed

Santiago, J A

2018-05-01

Ordering configurations of a director field on a curved membrane induces stress. In this work, we present a theoretical framework to calculate the stress tensor and the torque as a consequence of the nematic ordering; we use the variational principle and invariance of the energy under Euclidean motions. Euler-Lagrange equations of the membrane as well as the corresponding boundary conditions also appear as natural results. The stress tensor found includes attraction-repulsion forces between defects; likewise, defects are attracted to patches with the same sign in Gaussian curvature. These forces are mediated by the Green function of the Laplace-Beltrami operator of the surface. In addition, we find nonisotropic forces that involve derivatives of the Green function and the Gaussian curvature, even in the normal direction to the membrane. We examine the case of axial membranes to analyze the spherical one. For spherical vesicles we find the modified Young-Laplace law as a consequence of the nematic texture. In the case of spherical cap with defect at the north pole, we find that the force is repulsive with respect to the north pole, indicating that it is an unstable equilibrium point.

Stresses in curved nematic membranes

NASA Astrophysics Data System (ADS)

Santiago, J. A.

2018-05-01

Ordering configurations of a director field on a curved membrane induces stress. In this work, we present a theoretical framework to calculate the stress tensor and the torque as a consequence of the nematic ordering; we use the variational principle and invariance of the energy under Euclidean motions. Euler-Lagrange equations of the membrane as well as the corresponding boundary conditions also appear as natural results. The stress tensor found includes attraction-repulsion forces between defects; likewise, defects are attracted to patches with the same sign in Gaussian curvature. These forces are mediated by the Green function of the Laplace-Beltrami operator of the surface. In addition, we find nonisotropic forces that involve derivatives of the Green function and the Gaussian curvature, even in the normal direction to the membrane. We examine the case of axial membranes to analyze the spherical one. For spherical vesicles we find the modified Young-Laplace law as a consequence of the nematic texture. In the case of spherical cap with defect at the north pole, we find that the force is repulsive with respect to the north pole, indicating that it is an unstable equilibrium point.

A contribution toward rational modeling of the pressure-strain-rate correlation

NASA Technical Reports Server (NTRS)

Lee, Moon Joo

1990-01-01

A novel method of obtaining an analytical expression of the 'linear part' of the pressure-strain-rate tensor in terms of the anisotropy tensor of the Reynolds stresses has been developed, where the coefficients of the seven independent tensor terms are functions of the invariants of the Reynolds-stress anisotropy. The coefficients are evaluated up to fourth order in the anisotropy of the Reynolds stresses to provide guidance for development of a turbulence model.

Holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole

NASA Astrophysics Data System (ADS)

Ishibashi, Akihiro; Maeda, Kengo; Mefford, Eric

2017-07-01

We investigate a stress-energy tensor for a conformal field theory (CFT) at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the "derivative expansion" method, generalizing the work of Haddad [Classical Quantum Gravity 29, 245001 (2012), 10.1088/0264-9381/29/24/245001] and analytically compute the holographic stress-energy tensor for our solution. We find that the stress-energy tensor is finite at both the future and past outer (event) horizons and that the energy density is negative just outside the event horizons due to the Hawking effect. Furthermore, we apply the holographic method to the question of quantum instability of the Cauchy horizon since, by construction, our black droplet solution also admits a Cauchy horizon inside. We analytically show that the null-null component of the holographic stress-energy tensor negatively diverges at the Cauchy horizon, suggesting that a singularity appears there, in favor of strong cosmic censorship.

On deriving the Maxwell stress tensor method for calculating the optical force and torque on an object in harmonic electromagnetic fields

NASA Astrophysics Data System (ADS)

Ye, Qian; Lin, Haoze

2017-07-01

Though extensively used in calculating optical force and torque acting on a material object illuminated by laser, the Maxwell stress tensor (MST) method follows the electromagnetic linear and angular momentum balance that is usually derived in most textbooks for a continuous volume charge distribution in free space, if not resorting to the application of Noether’s theorem in electrodynamics. To cast the conservation laws into a physically appealing form involving the current densities of linear and angular momentum, on which the MST method is based, the divergence theorem is employed to transform a volume integral into a surface integral. When a material object of finite volume is put into the field, it brings about a discontinuity of field across its surface, due to the presence of induced surface charge and surface current. Ambiguity arises among students in whether the divergence theorem can still be directly used without any justification. By taking into account the effect of the induced surface charge and current, we present a simple pedagogical derivation for the MST method for calculating the optical force and torque on an object immersed in monochromatic optical field, without resorting to Noether’s theorem. Although the results turn out to be identical to those given in the standard textbooks, our derivation avoids the direct use of the divergence theorem on a discontinuous function.

Minimum-dissipation scalar transport model for large-eddy simulation of turbulent flows

NASA Astrophysics Data System (ADS)

Abkar, Mahdi; Bae, Hyun J.; Moin, Parviz

2016-08-01

Minimum-dissipation models are a simple alternative to the Smagorinsky-type approaches to parametrize the subfilter turbulent fluxes in large-eddy simulation. A recently derived model of this type for subfilter stress tensor is the anisotropic minimum-dissipation (AMD) model [Rozema et al., Phys. Fluids 27, 085107 (2015), 10.1063/1.4928700], which has many desirable properties. It is more cost effective than the dynamic Smagorinsky model, it appropriately switches off in laminar and transitional flows, and it is consistent with the exact subfilter stress tensor on both isotropic and anisotropic grids. In this study, an extension of this approach to modeling the subfilter scalar flux is proposed. The performance of the AMD model is tested in the simulation of a high-Reynolds-number rough-wall boundary-layer flow with a constant and uniform surface scalar flux. The simulation results obtained from the AMD model show good agreement with well-established empirical correlations and theoretical predictions of the resolved flow statistics. In particular, the AMD model is capable of accurately predicting the expected surface-layer similarity profiles and power spectra for both velocity and scalar concentration.

Polymer stress tensor in turbulent shear flows.

PubMed

L'vov, Victor S; Pomyalov, Anna; Procaccia, Itamar; Tiberkevich, Vasil

2005-01-01

The interaction of polymers with turbulent shear flows is examined. We focus on the structure of the elastic stress tensor, which is proportional to the polymer conformation tensor. We examine this object in turbulent flows of increasing complexity. First is isotropic turbulence, then anisotropic (but homogenous) shear turbulence, and finally wall bounded turbulence. The main result of this paper is that for all these flows the polymer stress tensor attains a universal structure in the limit of large Deborah number De > 1. We present analytic results for the suppression of the coil-stretch transition at large Deborah numbers. Above the transition the turbulent velocity fluctuations are strongly correlated with the polymer's elongation: there appear high-quality "hydroelastic" waves in which turbulent kinetic energy turns into polymer potential energy and vice versa. These waves determine the trace of the elastic stress tensor but practically do not modify its universal structure. We demonstrate that the influence of the polymers on the balance of energy and momentum can be accurately described by an effective polymer viscosity that is proportional to the cross-stream component of the elastic stress tensor. This component is smaller than the streamwise component by a factor proportional to De2. Finally we tie our results to wall bounded turbulence and clarify some puzzling facts observed in the problem of drag reduction by polymers.

Tensorial analysis of Eshelby stresses in 3D supercooled liquids

NASA Astrophysics Data System (ADS)

Lemaître, Anaël

2015-10-01

It was recently proposed that the local rearrangements governing relaxation in supercooled liquids impress on the liquid medium long-ranged (Eshelby) stress fluctuations that accumulate over time. From this viewpoint, events must be characterized by elastic dipoles, which are second order tensors, and Eshelby fields are expected to show up in stress and stress increment correlations, which are fourth order tensor fields. We construct here an analytical framework that permits analyzing such tensorial correlations in isotropic media in view of accessing Eshelby fields. Two spherical bases are introduced, which correspond to Cartesian and spherical coordinates for tensors. We show how they can be used to decompose stress correlations and thus test such properties as isotropy and power-law scalings. Eshelby fields and the predicted stress correlations in an infinite medium are shown to belong to an algebra that can conveniently be described using the spherical tensor bases. Using this formalism, we demonstrate that the inherent stress field of 3D supercooled liquids is power law correlated and carries the signature of Eshelby fields, thus supporting the idea that relaxation events give rise to Eshelby stresses that accumulate over time.

The incompressible Rindler fluid versus the Schwarzschild-AdS fluid

NASA Astrophysics Data System (ADS)

Matsuo, Yoshinori; Natsuume, Makoto; Ohta, Masahiro; Okamura, Takashi

2013-02-01

We study the proposal by Bredberg et al. [J. High Energy Phys. 1103, 141 (2011)], where the fluid is defined by the Brown-York tensor on a timelike surface at r = rc in black hole backgrounds. We consider both Rindler space and the Schwarzschild-AdS (SAdS) black hole. The former describes an incompressible fluid, whereas the latter describes the vanishing bulk viscosity at arbitrary rc. Although the near-horizon limit of the SAdS black hole is Rindler space, these two results do not contradict each other. We also find an interesting "coincidence" with the black hole membrane paradigm that gives a negative bulk viscosity. In order to show these results, we rewrite the hydrodynamic stress tensor via metric perturbations using the conservation equation. The resulting expressions are suitable to compare with the Brown-York tensor.

Software Tool for Computing Maximum Von Mises Stress

NASA Technical Reports Server (NTRS)

Chen, Long Y.; Knutson, Kurt; Martin, Eric

2007-01-01

The maximum Van Mises stress and stress direction are of interest far analyzing launch accelerations such as with the Mass Acceleration Curves developed by JPL. Maximum launch stresses can be combined with appropriate load cases at consistent locations with resulting stress tensors. Maximum Van Mises stress is also of interest for understanding maximum operational loading such as traverse events. - For example, planetary traversing simulations may prescribe bounding acceleration values during traverse for a rover such as Mars Science Lab (MSL) in (X,Y,Z) of the rover. - Such accelerations can be really in any directions for many parts such as a mast or head mounted components which can be in numerous configurations and orientations when traversing a planet surface.

The method of planes pressure tensor for a spherical subvolume

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heyes, D. M., E-mail: d.heyes@imperial.ac.uk; Smith, E. R., E-mail: edward.smith05@imperial.ac.uk; Dini, D., E-mail: d.dini@imperial.ac.uk

2014-02-07

Various formulas for the local pressure tensor based on a spherical subvolume of radius, R, are considered. An extension of the Method of Planes (MOP) formula of Todd et al. [Phys. Rev. E 52, 1627 (1995)] for a spherical geometry is derived using the recently proposed Control Volume formulation [E. R. Smith, D. M. Heyes, D. Dini, and T. A. Zaki, Phys. Rev. E 85, 056705 (2012)]. The MOP formula for the purely radial component of the pressure tensor is shown to be mathematically identical to the Radial Irving-Kirkwood formula. Novel offdiagonal elements which are important for momentum conservation emergemore » naturally from this treatment. The local pressure tensor formulas for a plane are shown to be the large radius limits of those for spherical surfaces. The radial-dependence of the pressure tensor computed by Molecular Dynamics simulation is reported for virtual spheres in a model bulk liquid where the sphere is positioned randomly or whose center is also that of a molecule in the liquid. The probability distributions of angles relating to pairs of atoms which cross the surface of the sphere, and the center of the sphere, are presented as a function of R. The variance in the shear stress calculated from the spherical Volume Averaging method is shown to converge slowly to the limiting values with increasing radius, and to be a strong function of the number of molecules in the simulation cell.« less

Description of plastic deformation of structural materials in triaxial loading

NASA Astrophysics Data System (ADS)

Lagzdins, A.; Zilaucs, A.

2008-03-01

A model of nonassociated plasticity is put forward for initially isotropic materials deforming with residual changes in volume under the action of triaxial normal stresses. The model is based on novel plastic loading and plastic potential functions, which define closed, convex, every where smooth surfaces in the 6D space of symmetric second-rank stress tensors. By way of example, the plastic deformation of a cylindrical concrete specimen wrapped with a CFRP tape and loaded in axial compression is described.

Simple Derivation of the Maxwell Stress Tensor and Electrostrictive Effects in Crystals

ERIC Educational Resources Information Center

Juretschke, H. J.

1977-01-01

Shows that local equilibrium and energy considerations in an elastic dielectric crystal lead to a simple derivation of the Maxwell stress tensor in anisotropic dielectric solids. The resulting equilibrium stress-strain relations are applied to determine the deformations of a charged parallel plate capacitor. (MLH)

Vacuum quantum stress tensor fluctuations: A diagonalization approach

NASA Astrophysics Data System (ADS)

Schiappacasse, Enrico D.; Fewster, Christopher J.; Ford, L. H.

2018-01-01

Large vacuum fluctuations of a quantum stress tensor can be described by the asymptotic behavior of its probability distribution. Here we focus on stress tensor operators which have been averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability distribution for obtaining a given value in a measurement of the time-averaged operator taken in the vacuum state. In these calculations, we study a specific operator that contributes to the stress-energy tensor of a massless scalar field in Minkowski spacetime, namely, the normal ordered square of the time derivative of the field. We analyze the rate of decrease of the tail of the probability distribution for different temporal sampling functions, such as compactly supported functions and the Lorentzian function. We find that the tails decrease relatively slowly, as exponentials of fractional powers, in agreement with previous work using the moments of the distribution. Our results lend additional support to the conclusion that large vacuum stress tensor fluctuations are more probable than large thermal fluctuations, and may have observable effects.

Present-day stress tensors along the southern Caribbean plate boundary zone from inversion of focal mechanism solutions: A successful trial

NASA Astrophysics Data System (ADS)

Audemard M., Franck A.; Castilla, Raymi

2016-11-01

This paper presents a compilation of 16 present-day stress tensors along the southern Caribbean plate boundary zone (PBZ), and particularly in western and along northern Venezuela. As a trial, these new stress tensors along PBZ have been calculated from inversion of 125 focal mechanism solutions (FMS) by applying the Angelier & Mechler's dihedral method, which were originally gathered by the first author and published in 2005. These new tensors are compared to those 59 tensors inverted from fault-slip data measured only in Plio-Quaternary sedimentary rocks, compiled in Audemard et al. (2005), which were originally calculated by several researchers through the inversion methods developed by Angelier and Mechler or Etchecopar et al. The two sets of stress tensors, one derived from geological data and the other one from seismological data, compare very well throughout the PBZ in terms of both stress orientation and shape of the stress tensor. This region is characterized by a compressive strike-slip (transpressional senso lato), occasionally compressional, regime from the southern Mérida Andes on the southwest to the gulf of Paria in the east. Significant changes in direction of the maximum horizontal stress (σH = σ1) can be established along it though. The σ1 direction varies progressively from nearly east-west in the southern Andes (SW Venezuela) to between NW-SE and NNW-SSE in northwestern Venezuela; this direction remaining constant across northern Venezuela, from Colombia to Trinidad. In addition, the σV defined by inversion of focal mechanisms or by the shape of the stress ellipsoid derived from the Etchecopar et al.'s method better characterize whether the stress regime is transpressional or compressional, or even very rarely trantensional at local scale. The orientation and space variation of this regional stress field in western Venezuela results from the addition of the two major neighbouring interplate maximum horizontal stress orientations (σH): roughly east-west trending stress across the Nazca-South America type-B subduction along the pacific coast of Colombia and NNW-SSE oriented one across the southern Caribbean PBZ. Meanwhile, northern Venezuela, although dextral strike-slip (SS) is the dominant process, NW-SE to NNW-SSE compression is also taking place, which are both also supported by recent GPS results.

Elliptic Relaxation of a Tensor Representation for the Redistribution Terms in a Reynolds Stress Turbulence Model

NASA Technical Reports Server (NTRS)

Carlson, J. R.; Gatski, T. B.

2002-01-01

A formulation to include the effects of wall proximity in a second-moment closure model that utilizes a tensor representation for the redistribution terms in the Reynolds stress equations is presented. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. Direct numerical simulation data and Reynolds stress solutions using a full differential approach are compared for the case of fully developed channel flow.

Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Padmanabhan, T.

2011-02-15

It has been known for several decades that Einstein's field equations, when projected onto a null surface, exhibit a structure very similar to the nonrelativistic Navier-Stokes equation. I show that this result arises quite naturally when gravitational dynamics is viewed as an emergent phenomenon. Extremizing the spacetime entropy density associated with the null surfaces leads to a set of equations which, when viewed in the local inertial frame, becomes identical to the Navier-Stokes equation. This is in contrast to the usual description of the Damour-Navier-Stokes equation in a general coordinate system, in which there appears a Lie derivative rather thanmore » a convective derivative. I discuss this difference, its importance, and why it is more appropriate to view the equation in a local inertial frame. The viscous force on fluid, arising from the gradient of the viscous stress-tensor, involves the second derivatives of the metric and does not vanish in the local inertial frame, while the viscous stress-tensor itself vanishes so that inertial observers detect no dissipation. We thus provide an entropy extremization principle that leads to the Damour-Navier-Stokes equation, which makes the hydrodynamical analogy with gravity completely natural and obvious. Several implications of these results are discussed.« less

Mesoscopic model for the viscosities of nematic liquid crystals.

PubMed

Chrzanowska, A; Kröger, M; Sellers, S

1999-10-01

Based on the definition of the mesoscopic concept by Blenk et al. [Physica A 174, 119 (1991); J. Noneq. Therm. 16, 67 (1991); Mol. Cryst. Liq. Cryst. 204, 133 (1991)] an approach to calculate the Leslie viscosity coefficients for nematic liquid crystals is presented. The approach rests upon the mesoscopic stress tensor, whose structure is assumed similar to the macroscopic Leslie viscous stress. The proposed form is also the main dissipation part of the mesoscopic Navier-Stokes equation. On the basis of the correspondence between microscopic and mesoscopic scales a mean-field mesoscopic potential is introduced. It allows us to obtain the stress tensor angular velocity of the free rotating molecules with the help of the orientational Fokker-Planck equation. The macroscopic stress tensor is calculated as an average of the mesoscopic counterpart. Appropriate relations among mesoscopic viscosities have been found. The mesoscopic analysis results are shown to be consistent with the diffusional model of Kuzuu-Doi and Osipov-Terentjev with the exception of the shear viscosity alpha(4). In the nematic phase alpha(4) is shown to have two contributions: isotropic and nematic. There exists an indication that the influence of the isotropic part is dominant over the nematic part. The so-called microscopic stress tensor used in the microscopic theories is shown to be the mean-field potential-dependent representation of the mesoscopic stress tensor. In the limiting case of total alignment the Leslie coefficients are estimated for the diffusional and mesoscopic models. They are compared to the results of the affine transformation model of the perfectly ordered systems. This comparison shows disagreement concerning the rotational viscosity, whereas the coefficients characteristic for the symmetric part of the viscous stress tensor remain the same. The difference is caused by the hindered diffusion in the affine model case.

A Review of Tensors and Tensor Signal Processing

NASA Astrophysics Data System (ADS)

Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.

Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.

Geomechanical simulation of the stress tensor rotation caused by injection of cold water in a deep geothermal reservoir

DOE PAGES

Jeanne, Pierre; Rutqvist, Jonny; Dobson, Patrick F.; ...

2015-11-12

We present a three-dimensional thermohydromechanical numerical study of the evolution and distribution of the stress tensor within the northwest part of The Geysers geothermal reservoir (in California), including a detailed study of the region around one injection well from 2003 to 2012. Initially, after imposing a normal faulting stress regime, we calculated local changes in the stress regime around injection wells. Our results were compared with previously published studies in which the stress state was inferred from inverting the focal plane mechanism of seismic events. Our main finding is that changes in stress tensor orientation are caused by injection-induced progressivemore » cooling of the reservoir, as well as by the seasonal variations in injection rate. Because of the gravity flow and cooling around a liquid zone formed by the injection, the vertical stress reduction is larger and propagates far below the injection well. At the same time, the horizontal stress increases, mostly because of stress redistribution below and above the cooling area. These two phenomena cause the rotation of the stress tensor and the appearance of a strike-slip regime above, inside, and below the cooling area. The cooling and the associated rotation of the stress regime can play a significant role in the observed long-term deepening of the microseismicity below active injection wells.« less

Dense lower crust elevates long-term earthquake rates in the New Madrid seismic zone

USGS Publications Warehouse

Levandowski, William Brower; Boyd, Oliver; Ramirez-Guzman, Leonardo

2016-01-01

Knowledge of the local state of stress is critical in appraising intraplate seismic hazard. Inverting earthquake moment tensors, we demonstrate that principal stress directions in the New Madrid seismic zone (NMSZ) differ significantly from those in the surrounding region. Faults in the NMSZ that are incompatible with slip in the regional stress field are favorably oriented relative to local stress. We jointly analyze seismic velocity, gravity, and topography to develop a 3-D crustal and upper mantle density model, revealing uniquely dense lower crust beneath the NMSZ. Finite element simulations then estimate the stress tensor due to gravitational body forces, which sums with regional stress. The anomalous lower crust both elevates gravity-derived stress at seismogenic depths in the NMSZ and rotates it to interfere more constructively with far-field stress, producing a regionally maximal deviatoric stress coincident with the highest concentration of modern seismicity. Moreover, predicted principal stress directions mirror variations (observed independently in moment tensors) at the NMSZ and across the region.

Polymer Fluid Dynamics: Continuum and Molecular Approaches.

PubMed

Bird, R B; Giacomin, A J

2016-06-07

To solve problems in polymer fluid dynamics, one needs the equations of continuity, motion, and energy. The last two equations contain the stress tensor and the heat-flux vector for the material. There are two ways to formulate the stress tensor: (a) One can write a continuum expression for the stress tensor in terms of kinematic tensors, or (b) one can select a molecular model that represents the polymer molecule and then develop an expression for the stress tensor from kinetic theory. The advantage of the kinetic theory approach is that one gets information about the relation between the molecular structure of the polymers and the rheological properties. We restrict the discussion primarily to the simplest stress tensor expressions or constitutive equations containing from two to four adjustable parameters, although we do indicate how these formulations may be extended to give more complicated expressions. We also explore how these simplest expressions are recovered as special cases of a more general framework, the Oldroyd 8-constant model. Studying the simplest models allows us to discover which types of empiricisms or molecular models seem to be worth investigating further. We also explore equivalences between continuum and molecular approaches. We restrict the discussion to several types of simple flows, such as shearing flows and extensional flows, which are of greatest importance in industrial operations. Furthermore, if these simple flows cannot be well described by continuum or molecular models, then it is not necessary to lavish time and energy to apply them to more complex flow problems.

Membrane paradigm of black holes in Chern-Simons modified gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Tian-Yi; Wang, Towe, E-mail: zhaotianyi5566@foxmail.com, E-mail: twang@phy.ecnu.edu.cn

2016-06-01

The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress tensor, if related to the bulk stress tensor in a special form, obeys the low-dimensional fluid continuity equation and the Navier-Stokes equation. This paradigm is applied to spherically symmetric static geometries, and in particular, the Schwarzschild black hole, which is a solution of a large class of dynamical Chern-Simons gravity.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klima, Matej; Kucharik, MIlan; Shashkov, Mikhail Jurievich

We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables.more » We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J 2 invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J 2 invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.« less

Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias

DOE PAGES

Levine, Lyle E.; Okoro, Chukwudi A.; Xu, Ruqing

2015-09-30

We report non-destructive measurements of the full elastic strain and stress tensors from individual dislocation cells distributed along the full extent of a 50 mm-long polycrystalline copper via in Si is reported. Determining all of the components of these tensors from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positionsmore » were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain tensor and stress tensor components.« less

8 January 2013 Mw=5.7 North Aegean Sea Earthquake Sequence

NASA Astrophysics Data System (ADS)

Kürçer, Akın; Yalçın, Hilal; Gülen, Levent; Kalafat, Doǧan

2014-05-01

The deformation of the North Aegean Sea is mainly controlled by the westernmost segments of North Anatolian Fault Zone (NAFZ). On January 8, 2013, a moderate earthquake (Mw= 5.7) occurred in the North Aegean Sea, which may be considered to be a part of westernmost splay of the NAFZ. A series of aftershocks were occurred within four months following the mainschock, which have magnitudes varying from 1.9 to 5.0. In this study, a total of 23 earthquake moment tensor solutions that belong to the 2013 earthquake sequence have been obtained by using KOERI and AFAD seismic data. The most widely used Gephart & Forsyth (1984) and Michael (1987) methods have been used to carry out stress tensor inversions. Based on the earthquake moment tensor solutions, distribution of epicenters and seismotectonic setting, the source of this earthquake sequence is a N75°E trending pure dextral strike-slip fault. The temporal and spatial distribution of earthquakes indicate that the rupture unilaterally propagated from SW to NE. The length of the fault has been calculated as approximately 12 km. using the afterschock distribution and empirical equations, suggested by Wells and Coppersmith (1994). The stress tensor analysis indicate that the dominant faulting type in the region is strike-slip and the direction of the regional compressive stress is WNW-ESE. The 1968 Aghios earthquake (Ms=7.3; Ambraseys and Jackson, 1998) and 2013 North Aegean Sea earthquake sequences clearly show that the regional stress has been transferred from SW to NE in this region. The last historical earthquake, the Bozcaada earthquake (M=7.05) had been occurred in the northeast of the 2013 earthquake sequence in 1672. The elapsed time (342 year) and regional stress transfer point out that the 1672 earthquake segment is probably a seismic gap. According to the empirical equations, the surface rupture length of the 1672 Earthquake segment was about 47 km, with a maximum displacement of 170 cm and average displacement of 107 cm. These values indicate that the 1672 earthquake segment is a potential earthquake hazard for this region.

Identification of a constitutive law for trabecular bone samples under remodeling in the framework of irreversible thermodynamics

NASA Astrophysics Data System (ADS)

Louna, Zineeddine; Goda, Ibrahim; Ganghoffer, Jean-François

2018-01-01

We construct in the present paper constitutive models for bone remodeling based on micromechanical analyses at the scale of a representative unit cell (RUC) including a porous trabecular microstructure. The time evolution of the microstructure is simulated as a surface remodeling process by relating the surface growth remodeling velocity to a surface driving force incorporating a (surface) Eshelby tensor. Adopting the framework of irreversible thermodynamics, a 2D constitutive model based on the setting up of the free energy density and a dissipation potential is identified from FE simulations performed over a unit cell representative of the trabecular architecture obtained from real bone microstructures. The static and evolutive effective properties of bone at the scale of the RUC are obtained by combining a methodology for the evaluation of the average kinematic and static variables over a prototype unit cell and numerical simulations with controlled imposed first gradient rates. The formulated effective growth constitutive law at the scale of the homogenized set of trabeculae within the RUC is of viscoplastic type and relates the average growth strain rate to the homogenized stress tensor. The postulated model includes a power law function of an effective stress chosen to depend on the first and second stress invariants. The model coefficients are calibrated from a set of virtual testing performed over the RUC subjected to a sequence of loadings. Numerical simulations show that overall bone growth does not show any growth kinematic hardening. The obtained results quantify the strength and importance of different types of external loads (uniaxial tension, simple shear, and biaxial loading) on the overall remodeling process and the development of elastic deformations within the RUC.

Probing Earth's State of Stress

NASA Astrophysics Data System (ADS)

Delorey, A. A.; Maceira, M.; Johnson, P. A.; Coblentz, D. D.

2016-12-01

The state of stress in the Earth's crust is a fundamental physical property that controls both engineered and natural systems. Engineered environments including those for hydrocarbon, geothermal energy, and mineral extraction, as well those for storage of wastewater, carbon dioxide, and nuclear fuel are as important as ever to our economy and environment. Yet, it is at spatial scales relevant to these activities where stress is least understood. Additionally, in engineered environments the rate of change in the stress field can be much higher than that of natural systems. In order to use subsurface resources more safely and effectively, we need to understand stress at the relevant temporal and spatial scales. We will present our latest results characterizing the state of stress in the Earth at scales relevant to engineered environments. Two important components of the state of stress are the orientation and magnitude of the stress tensor, and a measure of how close faults are to failure. The stress tensor at any point in a reservoir or repository has contributions from both far-field tectonic stress and local density heterogeneity. We jointly invert seismic (body and surface waves) and gravity data for a self-consistent model of elastic moduli and density and use the model to calculate the contribution of local heterogeneity to the total stress field. We then combine local and plate-scale contributions, using local indicators for calibration and ground-truth. In addition, we will present results from an analysis of the quantity and pattern of microseismicity as an indicator of critically stressed faults. Faults are triggered by transient stresses only when critically stressed (near failure). We show that tidal stresses can trigger earthquakes in both tectonic and reservoir environments and can reveal both stress and poroelastic conditions.

Stress Fields Along Okinawa Trough and Ryukyu Arc Inferred From Regional Broadband Moment Tensors

NASA Astrophysics Data System (ADS)

Kubo, A.; Fukuyama, E.

2001-12-01

Most shallow earthquakes along Okinawa trough and Ryukyu arc are relatively small (M<5.5). Focal mechanism estimations for such events were difficult due to insufficient dataset. However, this situation is improved by regional broadband network (FREESIA). Lower limit of magnitude of the earthquakes determined becomes 1.5 smaller in M{}w than that of Harvard moment tensors. As a result, we could examine the stress field in more detail than Fournier et al.(2001, JGR, 106, 13751-) did based on surface geology and teleseismic moment tensors. In the NE Okinawa trough, extension axes are oblique to the trough strike, while in SW Okinawa trough, they are perpendicular to the trough. Fault type in SW is normal fault and gradually changes to mixture of normal and strike slip toward NE. In the Ryukyu arc, extension axes are parallel to the arc. Although this feature is not clear in the NW Ryukyu arc, arc parallel extension may be a major property of entire arc. Dominant fault type is normal fault and several strike slips with the same extensional component are included. The volcanic train is located at the edge of arc parallel extension field faced A simple explanation of the arc parallel extension is the response to the opening motion of the Okinawa trough. Another possible mechanism is forearc movement due to oblique subduction which is enhanced in SW. We consider that the Okinawa trough and the Ryukyu arc are independent stress provinces.

Normal stress differences and beyond-Navier-Stokes hydrodynamics

NASA Astrophysics Data System (ADS)

Alam, Meheboob; Saha, Saikat

2017-06-01

A recently proposed beyond-Navier-Stokes order hydrodynamic theory for dry granular fluids is revisited by focussing on the behaviour of the stress tensor and the scaling of related transport coefficients in the dense limit. For the homogeneous shear flow, it is shown that the eigen-directions of the second-moment tensor and those of the shear tensor become co-axial, thus making the first normal stress difference (N1) to zero in the same limit. In contrast, the origin of the second normal stress difference (N2) is tied to the `excess' temperature along the mean-vorticity direction and the imposed shear field, respectively, in the dilute and dense flows. The scaling relations for transport coefficients are suggested based on the present theory.

Matrix exponential-based closures for the turbulent subgrid-scale stress tensor.

PubMed

Li, Yi; Chevillard, Laurent; Eyink, Gregory; Meneveau, Charles

2009-01-01

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy.

Computer simulation of ledge formation and ledge interaction for the silicon (111) free surface

NASA Technical Reports Server (NTRS)

Balamane, H.; Halicioglu, T.; Tiller, W. A.

1987-01-01

Both strip and triangular clusters, composed of 2 -1 -1 line ledges, have been simulated on the Si (111) surface. The long-range ledge-ledge interaction and the surface stress tensor distribution have been evaluated for these two pill-box geometries using a semiempirical potential-energy function that incorporates both two-body and three-body contributions. The consequences of the ledge-ledge interaction on two-dimensional nucleation for Si (111) has been evaluated as a function of Si adatom supersaturation and shown to differ significantly from conventional theory, where such interaction is neglected.

Features of Relaxation of a Stress Tensor in the Microscopic Volume of Nematic Phase under the Action of a Strong Electric Field

NASA Astrophysics Data System (ADS)

Zakharov, A. V.

2018-02-01

A numerical study of new regimes of reorientation of director field n̂, velocity v, and components of stress tensor σ ij ( ij = x, y, z) of nematic liquid crystal (LC) encapsulated in a rectangular channel under the action of a strong electric field E directed at angle α ( {˜{π }/{2}} ) to the horizontal surfaces bounding the LC channel is proposed. The numerical calculations performed in the framework of nonlinear generalization of the classical Eriksen-Leslie theory have shown that at certain relations between the torques and momenta affecting the unit LC volume and E ≫ E th, transition periodic structures can emerge during reorientation of n̂, if the corresponding distortion mode has the fastest response, and, thus, suppress all other modes. Rotating domains originating within this process decrease the energy dissipation rate and create more favorable regimes of the director field reorientation, as compared with the uniform rotational displacement.

Crista egregia: a geometrical model of the crista ampullaris, a sensory surface that detects head rotations.

PubMed

Marianelli, Prisca; Berthoz, Alain; Bennequin, Daniel

2015-02-01

The crista ampullaris is the epithelium at the end of the semicircular canals in the inner ear of vertebrates, which contains the sensory cells involved in the transduction of the rotational head movements into neuronal activity. The crista surface has the form of a saddle, or a pair of saddles separated by a crux, depending on the species and the canal considered. In birds, it was described as a catenoid by Landolt et al. (J Comp Neurol 159(2):257-287, doi: 10.1002/cne.901590207 , 1972). In the present work, we establish that this particular form results from principles of invariance maximization and energy minimization. The formulation of the invariance principle was inspired by Takumida (Biol Sci Space 15(4):356-358, 2001). More precisely, we suppose that in functional conditions, the equations of linear elasticity are valid, and we assume that in a certain domain of the cupula, in proximity of the crista surface, (1) the stress tensor of the deformed cupula is invariant under the gradient of the pressure, (2) the dissipation of energy is minimum. Then, we deduce that in this domain the crista surface is a minimal surface and that it must be either a planar, or helicoidal Scherk surface, or a piece of catenoid, which is the unique minimal surface of revolution. If we add the hypothesis that the direction of invariance of the stress tensor is unique and that a bilateral symmetry of the crista exists, only the catenoid subsists. This finding has important consequences for further functional modeling of the role of the vestibular system in head motion detection and spatial orientation.

Radiation Forces and Torques without Stress (Tensors)

ERIC Educational Resources Information Center

Bohren, Craig F.

2011-01-01

To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce…

SGS Closure Methodology for Surface-layer Rough-wall Turbulence.

NASA Astrophysics Data System (ADS)

Brasseur, James G.; Juneja, Anurag

1998-11-01

As reported in another abstract, necessary under-resolution and anisotropy of integral scales near the surface in LES of rough-wall boundary layers cause errors in the statistical structure of the modeled subgrid-scale (SGS) acceleration using eddy viscosity and similarity closures. The essential difficulty is an overly strong coupling between the modeled SGS stress tensor and predicted resolved velocity u^r. Specific to this problem, we propose a class of SGS closures in which subgrid scale velocities u^s1 between an explicit filter scale Δ and the grid scale δ are estimated from the solution to a separate prognostic equation, and the SGS stress tensor is formed using u^s1 as a surrogate for subgrid velocity u^s. The method is currently under development for pseudo-spectral LES where a filter at scales δ < Δ is explicit. The exact evolution equation for u^s1 contains dynamical interactions between u^r and u^s1 which can be calculated directly, and a term which is modeled to capture energy flux from the s1 scales without altering u^s1 structure. Three levels of closure for SGS stress are possible at different levels of accuracy and computational expense. The cheapest model has been tested with DNS and LES of anisotropic buoyancy-driven turbulence. Preliminary results show major improvement in the structure of the predicted SGS acceleration with much of the spurious coupling between u^r and SGS stress removed. Performance, predictions and cost of the three levels of closure are under analysis.

Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.

PubMed

Liu, Haofei; Sun, Wei

2017-08-01

Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.

Octupolar tensors for liquid crystals

NASA Astrophysics Data System (ADS)

Chen, Yannan; Qi, Liqun; Virga, Epifanio G.

2018-01-01

A third-rank three-dimensional symmetric traceless tensor, called the octupolar tensor, has been introduced to study tetrahedratic nematic phases in liquid crystals. The octupolar potential, a scalar-valued function generated on the unit sphere by that tensor, should ideally have four maxima (on the vertices of a tetrahedron), but it was recently found to possess an equally generic variant with three maxima instead of four. It was also shown that the irreducible admissible region for the octupolar tensor in a three-dimensional parameter space is bounded by a dome-shaped surface, beneath which is a separatrix surface connecting the two generic octupolar states. The latter surface, which was obtained through numerical continuation, may be physically interpreted as marking a possible intra-octupolar transition. In this paper, by using the resultant theory of algebraic geometry and the E-characteristic polynomial of spectral theory of tensors, we give a closed-form, algebraic expression for both the dome-shaped surface and the separatrix surface. This turns the envisaged intra-octupolar transition into a quantitative, possibly observable prediction.

Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration

NASA Astrophysics Data System (ADS)

Becattini, F.; Grossi, E.

2015-08-01

We show that the stress-energy tensor has additional terms with respect to the ideal form in states of global thermodynamic equilibrium in flat spacetime with nonvanishing acceleration and vorticity. These corrections are of quantum origin and their leading terms are second order in the gradients of the thermodynamic fields. Their relevant coefficients can be expressed in terms of correlators of the stress-energy tensor operator and the generators of the Lorentz group. With respect to previous assessments, we find that there are more second-order coefficients and that all thermodynamic functions including energy density receive acceleration and vorticity dependent corrections. Notably, also the relation between ρ and p , that is, the equation of state, is affected by acceleration and vorticity. We have calculated the corrections for a free real scalar field—both massive and massless—and we have found that they increase, particularly for a massive field, at very high acceleration and vorticity and very low temperature. Finally, these nonideal terms depend on the explicit form of the stress-energy operator, implying that different stress-energy tensors of the scalar field—canonical or improved—are thermodynamically inequivalent.

Analysis of Multi-Layered Materials Under High Velocity Impact Using CTH

DTIC Science & Technology

2008-03-01

of state . The other relationship deals with the deviatoric stress and is taken care of by the constitutive equations which are discussed in the next...models in CTH decompose the total stress tensor into the spherical and deviatoric parts. The spherical part of the stress tensor is the equation of state ...investigate the effects of wave propagation. Waves in rods are considered to create a state of

Stress regularity in quasi-static perfect plasticity with a pressure dependent yield criterion

NASA Astrophysics Data System (ADS)

Babadjian, Jean-François; Mora, Maria Giovanna

2018-04-01

This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic - perfectly plastic materials obeying a Drucker-Prager or Mohr-Coulomb yield criterion. Under suitable assumptions on the data, it is proved that the stress tensor has a spatial gradient that is locally squared integrable. As a corollary, the usual measure theoretical flow rule is expressed in a strong form using the quasi-continuous representative of the stress.

In Silico Investigation of Intracranial Blast Mitigation with Relevance to Military Traumatic Brain Injury

DTIC Science & Technology

2010-09-01

how personal protective equipment affects the brain’s response to blasts. In this study we investigated the effect of the Advanced Combat...analyzing stress wave propagation, which is the main dynamic effect loading the brain tissue during a blast event. We consider two key metrics of stress ...Cauchy stress tensor, and sij ¼ σij − 13σkkδij are the compo- nents of the deviatoric stress tensor (24). Fig. 1 shows snapshots of the pressure

Two formalisms, one renormalized stress-energy tensor

NASA Astrophysics Data System (ADS)

Barceló, C.; Carballo, R.; Garay, L. J.

2012-04-01

We explicitly compare the structure of the renormalized stress-energy tensor of a massless scalar field in a (1+1) curved spacetime as obtained by two different strategies: normal-mode construction of the field operator and one-loop effective action. We pay special attention to where and how the information related to the choice of vacuum state in both formalisms is encoded. By establishing a clear translation map between both procedures, we show that these two potentially different renormalized stress-energy tensors are actually equal, when using vacuum-state choices related by this map. One specific aim of the analysis is to facilitate the comparison of results regarding semiclassical effects in gravitational collapse as obtained within these different formalisms.

Use of non-fault fractures in stress tensor reconstruction using the Mohr Circle with the Win-tensor program

NASA Astrophysics Data System (ADS)

Delvaux, Damien

2016-04-01

Paleostress inversion of geological fault-slip data is usually done using the directional part of the applied stress tensor on a slip plane and comparing it with the observed slip lines. However, this method do not fully exploit the brittle data sets as those are composed of shear and tension fractures, in addition to faults. Brittle deformation can be decomposed in two steps. An initial fracture/failure in previously intact rock generate extension/tensile fractures or shear fractures, both without visible opening or displacement. This first step may or not be followed by fracture opening to form tension joints, frictional shearing to form shear faults, or a combination of opening and shearing which produces hybrid fractures. Fractured rock outcrop contain information of the stress conditions that acted during both brittle deformation steps. The purpose here is to investigate how the fracture pattern generated during the initial fracture/failure step might be used in paleostress reconstruction. Each fracture is represented on the Mohr Circle by its resolved normal and shear stress magnitudes. We consider the typical domains on the Mohr circle where the different types de fractures nucleate (tension, hybrid, shear and compression fractures), as well the domain which contain reactivated fractures (faults reactivating an initial fracture plane). In function of the fracture type defined in the field, a "distance" is computed on the Mohr circle between each point and its expected corresponding nucleation/reactivation domain. This "Mohr Distance" is then used as function to minimize during the inversion. We implemented this new function in the Win-Tensor program, and tested it with natural and synthetic data sets from different stress regimes. It can be used alone using only the Mohr Distance on each plane (function F10), or combined with the angular misfit between observed striae and resolved shear directions (composite function F11). When used alone (F10), only the 3 stress axes can be determined and the stress ratio R (sigma 2-3)/sigma1-3) has to be pre-determined. With the combined function (F11), it provide an additional constrain to the classical angular misfit. With data sets composed of a majority of neoformed fractures, stress inversion using the Mohr Distance F10 function provide a good approximation of the 3 stress axes (using only the fracture data) as compared with the results of the F11 composite function (using also the observed slip lines). Tensor program is available at (http://www.damiendelvaux.be/Tensor/tensor-index.html).

Unified Stress Tensor of the Hydration Water Layer

NASA Astrophysics Data System (ADS)

Kim, Bongsu; Kim, QHwan; Kwon, Soyoung; An, Sangmin; Lee, Kunyoung; Lee, Manhee; Jhe, Wonho

2013-12-01

We present the general stress tensor of the ubiquitous hydration water layer (HWL), based on the empirical hydration force, by combining the elasticity and hydrodynamics theories. The tapping and shear component of the tensor describe the elastic and damping properties of the HWL, respectively, in good agreement with experiments. In particular, a unified understanding of HWL dynamics provides the otherwise unavailable intrinsic parameters of the HWL, which offer additional but unexplored aspects to the supercooled liquidity of the confined HWL. Our results may allow deeper insight on systems where the HWL is critical.

Unified stress tensor of the hydration water layer.

PubMed

Kim, Bongsu; Kim, Qhwan; Kwon, Soyoung; An, Sangmin; Lee, Kunyoung; Lee, Manhee; Jhe, Wonho

2013-12-13

We present the general stress tensor of the ubiquitous hydration water layer (HWL), based on the empirical hydration force, by combining the elasticity and hydrodynamics theories. The tapping and shear component of the tensor describe the elastic and damping properties of the HWL, respectively, in good agreement with experiments. In particular, a unified understanding of HWL dynamics provides the otherwise unavailable intrinsic parameters of the HWL, which offer additional but unexplored aspects to the supercooled liquidity of the confined HWL. Our results may allow deeper insight on systems where the HWL is critical.

Elliptic Relaxation of a Tensor Representation of the Pressure-Strain and Dissipation Rate

NASA Technical Reports Server (NTRS)

Carlson, John R.; Gatski, Thomas B.

2002-01-01

A formulation to include the effects of wall-proximity in a second moment closure model is presented that utilizes a tensor representation for the redistribution term in the Reynolds stress equations. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. DNS data and Reynolds stress solutions using a full differential approach at channel Reynolds number of 590 are compared to the new model.

Distinguishing and quantifying the torquoselectivity in competitive ring-opening reactions using the stress tensor and QTAIM.

PubMed

Guo, Huan; Morales-Bayuelo, Alejandro; Xu, Tianlv; Momen, Roya; Wang, Lingling; Yang, Ping; Kirk, Steven R; Jenkins, Samantha

2016-12-05

Currently the theories to explain and predict the classification of the electronic reorganization due to the torquoselectivity of a ring-opening reaction cannot accommodate the directional character of the reaction pathway; the torquoselectivity is a type of stereoselectivity and therefore is dependent on the pathway. Therefore, in this investigation we introduced new measures from quantum theory of atoms in molecules and the stress tensor to clearly distinguish and quantify the transition states of the inward (TSIC) and outward (TSOC) conrotations of competitive ring-opening reactions of 3-(trifluoromethyl)cyclobut-1-ene and 1-cyano-1-methylcyclobutene. We find the metallicity ξ(r b ) of the ring-opening bond does not occur exactly at the transition state in agreement with transition state theory. The vector-based stress tensor response β σ was used to distinguish the effect of the CN, CH 3 , and CF 3 groups on the TSIC and TSOC paths that was consistent with the ellipticity ε, the total local energy density H(r b ) and the stress tensor stiffness S σ . We determine the directional properties of the TSIC and TSOC ring-opening reactions by constructing a stress tensor UσTS space with trajectories TσTS (s) with length l in real space, longer l correlated with the lowest density functional theory-evaluated total energy barrier and hence will be more thermodynamically favored. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Importance of Force Decomposition for Local Stress Calculations in Biomembrane Molecular Simulations.

PubMed

Vanegas, Juan M; Torres-Sánchez, Alejandro; Arroyo, Marino

2014-02-11

Local stress fields are routinely computed from molecular dynamics trajectories to understand the structure and mechanical properties of lipid bilayers. These calculations can be systematically understood with the Irving-Kirkwood-Noll theory. In identifying the stress tensor, a crucial step is the decomposition of the forces on the particles into pairwise contributions. However, such a decomposition is not unique in general, leading to an ambiguity in the definition of the stress tensor, particularly for multibody potentials. Furthermore, a theoretical treatment of constraints in local stress calculations has been lacking. Here, we present a new implementation of local stress calculations that systematically treats constraints and considers a privileged decomposition, the central force decomposition, that leads to a symmetric stress tensor by construction. We focus on biomembranes, although the methodology presented here is widely applicable. Our results show that some unphysical behavior obtained with previous implementations (e.g. nonconstant normal stress profiles along an isotropic bilayer in equilibrium) is a consequence of an improper treatment of constraints. Furthermore, other valid force decompositions produce significantly different stress profiles, particularly in the presence of dihedral potentials. Our methodology reveals the striking effect of unsaturations on the bilayer mechanics, missed by previous stress calculation implementations.

A tensorial description of particle perception in black-hole physics

NASA Astrophysics Data System (ADS)

Barbado, Luis C.; Barceló, Carlos; Garay, Luis J.; Jannes, G.

2016-09-01

In quantum field theory in curved backgrounds, one typically distinguishes between objective, tensorial quantities such as the renormalized stress-energy tensor (RSET) and subjective, nontensorial quantities such as Bogoliubov coefficients which encode perception effects associated with the specific trajectory of a detector. In this work, we propose a way to treat both objective and subjective notions on an equal tensorial footing. For that purpose, we define a new tensor which we will call the perception renormalized stress-energy tensor (PeRSET). The PeRSET is defined as the subtraction of the RSET corresponding to two different vacuum states. Based on this tensor, we can define perceived energy densities and fluxes. The PeRSET helps us to have a more organized and systematic understanding of various results in the literature regarding quantum field theory in black hole spacetimes. We illustrate the physics encoded in this tensor by working out various examples of special relevance.

Constraints on behaviour of a mining‐induced earthquake inferred from laboratory rock mechanics experiments

USGS Publications Warehouse

McGarr, Arthur F.; Johnston, Malcolm J.; Boettcher, M.; Heesakkers, V.; Reches, Z.

2013-01-01

On December 12, 2004, an earthquake of magnitude 2.2, located in the TauTona Gold Mine at a depth of about 3.65 km in the ancient Pretorius fault zone, was recorded by the in-mine borehole seismic network, yielding an excellent set of ground motion data recorded at hypocentral distances of several km. From these data, the seismic moment tensor, indicating mostly normal faulting with a small implosive component, and the radiated energy were measured; the deviatoric component of the moment tensor was estimated to be M0 = 2.3×1012 N·m and the radiated energy ER = 5.4×108 J. This event caused extensive damage along tunnels within the Pretorius fault zone. What rendered this earthquake of particular interest was the underground investigation of the complex pattern of exposed rupture surfaces combined with laboratory testing of rock samples retrieved from the ancient fault zone (Heesakkers et al.2011a, 2011b). Event 12/12 2004 was the result of fault slip across at least four nonparallel fault surfaces; 25 mm of slip was measured at one location on the rupture segment that is most parallel with a fault plane inferred from the seismic moment tensor, suggesting that this segment accounted for much of the total seismic deformation. By applying a recently developed technique based on biaxial stick-slip friction experiments (McGarr2012, 2013) to the seismic results, together with the 25 mm slip observed underground, we estimated a maximum slip rate of at least 6.6 m/s, which is consistent with the observed damage to tunnels in the rupture zone. Similarly, the stress drop and apparent stress were found to be correspondingly high at 21.9 MPa and 6.6 MPa, respectively. The ambient state of stress, measured at the approximate depth of the earthquake but away from the influence of mining, in conjunction with laboratory measurements of the strength of the fault zone cataclasites, indicates that during rupture of the M 2.2 event, the normal stress acting on the large-slip fault segment was about 260 MPa, the yield stress was 172 MPa and the seismic efficiency was 0.05. Thus, for event 12/12 2004, 5% of the energy released by the earthquake was radiated and the remaining 95% was consumed in overcoming fault friction and expanding the zone of rupture.

Surface energy and surface stress on vicinals by revisiting the Shuttleworth relation

NASA Astrophysics Data System (ADS)

Hecquet, Pascal

2018-04-01

In 1998 [Surf. Sci. 412/413, 639 (1998)], we showed that the step stress on vicinals varies as 1/L, L being the distance between steps, while the inter-step interaction energy primarily follows the law as 1/L2 from the well-known Marchenko-Parshin model. In this paper, we give a better understanding of the interaction term of the step stress. The step stress is calculated with respect to the nominal surface stress. Consequently, we calculate the diagonal surface stresses in both the vicinal system (x, y, z) where z is normal to the vicinal and the projected system (x, b, c) where b is normal to the nominal terrace. Moreover, we calculate the surface stresses by using two methods: the first called the 'Zero' method, from the surface pressure forces and the second called the 'One' method, by homogeneously deforming the vicinal in the parallel direction, x or y, and by calculating the surface energy excess proportional to the deformation. By using the 'One' method on the vicinal Cu(0 1 M), we find that the step deformations, due to the applied deformation, vary as 1/L by the same factor for the tensor directions bb and cb, and by twice the same factor for the parallel direction yy. Due to the vanishing of the surface stress normal to the vicinal, the variation of the step stress in the direction yy is better described by using only the step deformation in the same direction. We revisit the Shuttleworth formula, for while the variation of the step stress in the direction xx is the same between the two methods, the variation in the direction yy is higher by 76% for the 'Zero' method with respect to the 'One' method. In addition to the step energy, we confirm that the variation of the step stress must be taken into account for the understanding of the equilibrium of vicinals when they are not deformed.

Energy Flux Positivity and Unitarity in Conformal Field Theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kulaxizi, Manuela; Parnachev, Andrei

2011-01-07

We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop light like poles. The residues of the poles can be computed, as long as the only spin-two conserved current, which appears in the stress energy tensor operator-product expansion and acquires a nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost-freemore » is equivalent to the condition of positivity of energy flux.« less

Inversion of calcite twin data for paleostress orientations and magnitudes: A new technique tested and calibrated on numerically-generated and natural data

NASA Astrophysics Data System (ADS)

Parlangeau, Camille; Lacombe, Olivier; Schueller, Sylvie; Daniel, Jean-Marc

2018-01-01

The inversion of calcite twin data is a powerful tool to reconstruct paleostresses sustained by carbonate rocks during their geological history. Following Etchecopar's (1984) pioneering work, this study presents a new technique for the inversion of calcite twin data that reconstructs the 5 parameters of the deviatoric stress tensors from both monophase and polyphase twin datasets. The uncertainties in the parameters of the stress tensors reconstructed by this new technique are evaluated on numerically-generated datasets. The technique not only reliably defines the 5 parameters of the deviatoric stress tensor, but also reliably separates very close superimposed stress tensors (30° of difference in maximum principal stress orientation or switch between σ3 and σ2 axes). The technique is further shown to be robust to sampling bias and to slight variability in the critical resolved shear stress. Due to our still incomplete knowledge of the evolution of the critical resolved shear stress with grain size, our results show that it is recommended to analyze twin data subsets of homogeneous grain size to minimize possible errors, mainly those concerning differential stress values. The methodological uncertainty in principal stress orientations is about ± 10°; it is about ± 0.1 for the stress ratio. For differential stresses, the uncertainty is lower than ± 30%. Applying the technique to vein samples within Mesozoic limestones from the Monte Nero anticline (northern Apennines, Italy) demonstrates its ability to reliably detect and separate tectonically significant paleostress orientations and magnitudes from naturally deformed polyphase samples, hence to fingerprint the regional paleostresses of interest in tectonic studies.

On the role of the transformation eigenstrain in the growth or shrinkage of spheroidal isotropic precipitations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fischer, F.D.; Boehm, H.J.

The jumps of the strain and stress tensors on the surface of elastic homogeneous or inhomogeneous ellipsoidal inclusions embedded in an elastic matrix are obtained from results reported in the literature. They are used to derive closed-form expressions for the thermodynamic force in such matrix-inclusion systems that are subjected to a generally defined homogeneous transformation eigenstrain. A detailed study is presented for an isotropic spheroidal inclusion in an isotropic matrix in which the most important parameters are the inclusion's aspect ratio {alpha} and an eigenstrain triaxiality parameter d-bar. The fluctuations of the thermodynamic force are investigated for a set ofmore » specific transformation eigenstrain tensors and are presented for inclusion shapes ranging from disk-like to fiber-like spheroids.« less

Single-shot full strain tensor determination with microbeam X-ray Laue diffraction and a two-dimensional energy-dispersive detector.

PubMed

Abboud, A; Kirchlechner, C; Keckes, J; Conka Nurdan, T; Send, S; Micha, J S; Ulrich, O; Hartmann, R; Strüder, L; Pietsch, U

2017-06-01

The full strain and stress tensor determination in a triaxially stressed single crystal using X-ray diffraction requires a series of lattice spacing measurements at different crystal orientations. This can be achieved using a tunable X-ray source. This article reports on a novel experimental procedure for single-shot full strain tensor determination using polychromatic synchrotron radiation with an energy range from 5 to 23 keV. Microbeam X-ray Laue diffraction patterns were collected from a copper micro-bending beam along the central axis (centroid of the cross section). Taking advantage of a two-dimensional energy-dispersive X-ray detector (pnCCD), the position and energy of the collected Laue spots were measured for multiple positions on the sample, allowing the measurement of variations in the local microstructure. At the same time, both the deviatoric and hydrostatic components of the elastic strain and stress tensors were calculated.

The Kummer tensor density in electrodynamics and in gravity

NASA Astrophysics Data System (ADS)

Baekler, Peter; Favaro, Alberto; Itin, Yakov; Hehl, Friedrich W.

2014-10-01

Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T, which is antisymmetric in its first two and its last two indices: T=-T=-T. Thus, K∼T3, see Eq. (46). (i) If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R of a Riemann-Cartan spacetime, then K∼R3 and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4,R) and, subsequently, under the Lorentz group SO(1,3).

Detailed fault structure of the 2000 Western Tottori, Japan, earthquake sequence

USGS Publications Warehouse

Fukuyama, E.; Ellsworth, W.L.; Waldhauser, F.; Kubo, A.

2003-01-01

We investigate the faulting process of the aftershock region of the 2000 western Tottori earthquake (Mw 6.6) by combining aftershock hypocenters and moment tensor solutions. Aftershock locations were precisely determined by the double difference method using P- and S-phase arrival data of the Japan Meteorological Agency unified catalog. By combining the relocated hypocenters and moment tensor solutions of aftershocks by broadband waveform inversion of FREESIA (F-net), we successfully resolved very detailed fault structures activated by the mainshock. The estimated fault model resolves 15 individual fault segments that are consistent with both aftershock distribution and focal mechanism solutions. Rupture in the mainshock was principally confined to the three fault elements in the southern half of the zone, which is also where the earliest aftershocks concentrate. With time, the northern part of the zone becomes activated, which is also reflected in the postseismic deformation field. From the stress tensor analysis of aftershock focal mechanisms, we found a rather uniform stress field in the aftershock region, although fault strikes were scattered. The maximum stress direction is N107??E, which is consistent with the tectonic stress field in this region. In the northern part of the fault, where no slip occurred during the mainshock but postseismic slip was observed, the maximum stress direction of N130??E was possible as an alternative solution of stress tensor inversion.

Synchrotron X-ray microbeam diffraction measurements of full elastic long range internal strain and stress tensors in commercial-purity aluminum processed by multiple passes of equal-channel angular pressing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Phan, Thien Q.; Levine, Lyle E.; Lee, I-Fang

Synchrotron X-ray microbeam diffraction was used to measure the full elastic long range internal strain and stress tensors of low dislocation density regions within the submicrometer grain/subgrain structure of equal-channel angular pressed (ECAP) aluminum alloy AA1050 after 1, 2, and 8 passes using route B C. This is the first time that full tensors were measured in plastically deformed metals at this length scale. The maximum (most tensile or least compressive) principal elastic strain directions for the unloaded 1 pass sample for the grain/subgrain interiors align well with the pressing direction, and are more random for the 2 and 8more » pass samples. The measurements reported here indicate that the local stresses and strains become increasingly isotropic (homogenized) with increasing ECAP passes using route BC. The average maximum (in magnitude) LRISs are -0.43 σ a for 1 pass, -0.44 σ a for 2 pass, and 0.14 σ a for the 8 pass sample. Furthermore, these LRISs are larger than those reported previously because those earlier measurements were unable to measure the full stress tensor. Significantly, the measured stresses are inconsistent with the two-component composite model.« less

Synchrotron X-ray microbeam diffraction measurements of full elastic long range internal strain and stress tensors in commercial-purity aluminum processed by multiple passes of equal-channel angular pressing

DOE PAGES

Phan, Thien Q.; Levine, Lyle E.; Lee, I-Fang; ...

2016-04-23

Synchrotron X-ray microbeam diffraction was used to measure the full elastic long range internal strain and stress tensors of low dislocation density regions within the submicrometer grain/subgrain structure of equal-channel angular pressed (ECAP) aluminum alloy AA1050 after 1, 2, and 8 passes using route B C. This is the first time that full tensors were measured in plastically deformed metals at this length scale. The maximum (most tensile or least compressive) principal elastic strain directions for the unloaded 1 pass sample for the grain/subgrain interiors align well with the pressing direction, and are more random for the 2 and 8more » pass samples. The measurements reported here indicate that the local stresses and strains become increasingly isotropic (homogenized) with increasing ECAP passes using route BC. The average maximum (in magnitude) LRISs are -0.43 σ a for 1 pass, -0.44 σ a for 2 pass, and 0.14 σ a for the 8 pass sample. Furthermore, these LRISs are larger than those reported previously because those earlier measurements were unable to measure the full stress tensor. Significantly, the measured stresses are inconsistent with the two-component composite model.« less

Nonlocal elasticity tensors in dislocation and disclination cores

DOE PAGES

Taupin, V.; Gbemou, K.; Fressengeas, C.; ...

2017-01-07

We introduced nonlocal elastic constitutive laws for crystals containing defects such as dislocations and disclinations. Additionally, the pointwise elastic moduli tensors adequately reflect the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum andmore » moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. Here, the convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.« less

Parameterization of subgrid-scale stress by the velocity gradient tensor

NASA Technical Reports Server (NTRS)

Lund, Thomas S.; Novikov, E. A.

1993-01-01

The objective of this work is to construct and evaluate subgrid-scale models that depend on both the strain rate and the vorticity. This will be accomplished by first assuming that the subgrid-scale stress is a function of the strain and rotation rate tensors. Extensions of the Caley-Hamilton theorem can then be used to write the assumed functional dependence explicitly in the form of a tensor polynomial involving products of the strain and rotation rates. Finally, use of this explicit expression as a subgrid-scale model will be evaluated using direct numerical simulation data for homogeneous, isotropic turbulence.

Effect of thermal exposure on the residual stress relaxation in a hardened cylindrical sample under creep conditions

NASA Astrophysics Data System (ADS)

Radchenko, V. P.; Saushkin, M. N.; Tsvetkov, V. V.

2016-05-01

This paper describes the effect of thermal exposure (high-temperature exposure) ( T = 675°C) on the residual creep stress relaxation in a surface hardened solid cylindrical sample made of ZhS6UVI alloy. The analysis is carried out with the use of experimental data for residual stresses after micro-shot peening and exposures to temperatures equal to T = 675°C during 50, 150, and 300 h. The paper presents the technique for solving the boundary-value creep problem for the hardened cylindrical sample with the initial stress-strain state under the condition of thermal exposure. The uniaxial experimental creep curves obtained under constant stresses of 500, 530, 570, and 600 MPa are used to construct the models describing the primary and secondary stages of creep. The calculated and experimental data for the longitudinal (axial) tensor components of residual stresses are compared, and their satisfactory agreement is determined.

Einstein gravity 3-point functions from conformal field theory

NASA Astrophysics Data System (ADS)

Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein

2017-12-01

We study stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter suggests that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions 〈 T T T 〉, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy a ≈ c as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.

A priori testing of subgrid-scale models for large-eddy simulation of the atmospheric boundary layer

NASA Astrophysics Data System (ADS)

Juneja, Anurag; Brasseur, James G.

1996-11-01

Subgrid-scale models are generally developed assuming homogeneous isotropic turbulence with the filter cutoff lying in the inertial range. In the surface layer and capping inversion regions of the atmospheric boundary layer, the turbulence is strongly anisotropic and, in general, influenced by both buoyancy and shear. Furthermore, the integral scale motions are under-resolved in these regions. Herein we perform direct numerical simulations of shear and buoyancy-generated homogeneous anisotropic turbulence to compute and analyze the actual subgrid-resolved-scale (SGS-RS) dynamics as the filter cutoff moves into the energy-containing scales. These are compared with the SGS-RS dynamics predicted by Smagorinsky-based models with a focus on motivating improved closures. We find that, in general, the underlying assumption of such models, that the anisotropic part of the subgrid stress tensor be aligned with the resolved strain rate tensor, is a poor approximation. Similarly, we find poor alignment between the actual and predicted stress divergence, and find low correlations between the actual and modeled subgrid-scale contribution to the pressure and pressure gradient. Details will be given in the talk.

X-Ray Microdiffraction as a Probe to Reveal Flux Divergences in Interconnects

NASA Astrophysics Data System (ADS)

Spolenak, R.; Tamura, N.; Patel, J. R.

2006-02-01

Most reliability issues in interconnect systems occur at a local scale and many of them include the local build-up of stresses. Typical failure mechanisms are electromigration and stress voiding in interconnect lines and fatigue in surface acoustic wave devices. Thus a local probe is required for the investigation of these phenomena. In this paper the application of the Laue microdiffraction technique to investigate flux divergences in interconnect systems will be described. The deviatoric strain tensor of single grains can be correlated with the local microstructure, orientation and defect density. Especially the latter led to recent results about the correlation of stress build-up and orientation in Cu lines and electromigration-induced grain rotation in Cu and Al lines.

Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

NASA Astrophysics Data System (ADS)

Bogdanov, Alexander; Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Yulia

2018-02-01

Stages of direct computational experiments in hydromechanics based on tensor mathematics tools are represented by conditionally independent mathematical models for calculations separation in accordance with physical processes. Continual stage of numerical modeling is constructed on a small time interval in a stationary grid space. Here coordination of continuity conditions and energy conservation is carried out. Then, at the subsequent corpuscular stage of the computational experiment, kinematic parameters of mass centers and surface stresses at the boundaries of the grid cells are used in modeling of free unsteady motions of volume cells that are considered as independent particles. These particles can be subject to vortex and discontinuous interactions, when restructuring of free boundaries and internal rheological states has place. Transition from one stage to another is provided by interpolation operations of tensor mathematics. Such interpolation environment formalizes the use of physical laws for mechanics of continuous media modeling, provides control of rheological state and conditions for existence of discontinuous solutions: rigid and free boundaries, vortex layers, their turbulent or empirical generalizations.

A space-time tensor formulation for continuum mechanics in general curvilinear, moving, and deforming coordinate systems

NASA Technical Reports Server (NTRS)

Avis, L. M.

1976-01-01

Tensor methods are used to express the continuum equations of motion in general curvilinear, moving, and deforming coordinate systems. The space-time tensor formulation is applicable to situations in which, for example, the boundaries move and deform. Placing a coordinate surface on such a boundary simplifies the boundary condition treatment. The space-time tensor formulation is also applicable to coordinate systems with coordinate surfaces defined as surfaces of constant pressure, density, temperature, or any other scalar continuum field function. The vanishing of the function gradient components along the coordinate surfaces may simplify the set of governing equations. In numerical integration of the equations of motion, the freedom of motion of the coordinate surfaces provides a potential for enhanced resolution of the continuum field function. An example problem of an incompressible, inviscid fluid with a top free surface is considered, where the surfaces of constant pressure (including the top free surface) are coordinate surfaces.

Nonlinear temperature dependent failure analysis of finite width composite laminates

NASA Technical Reports Server (NTRS)

Nagarkar, A. P.; Herakovich, C. T.

1979-01-01

A quasi-three dimensional, nonlinear elastic finite element stress analysis of finite width composite laminates including curing stresses is presented. Cross-ply, angle-ply, and two quasi-isotropic graphite/epoxy laminates are studied. Curing stresses are calculated using temperature dependent elastic properties that are input as percent retention curves, and stresses due to mechanical loading in the form of an axial strain are calculated using tangent modulii obtained by Ramberg-Osgood parameters. It is shown that curing stresses and stresses due to tensile loading are significant as edge effects in all types of laminate studies. The tensor polynomial failure criterion is used to predict the initiation of failure. The mode of failure is predicted by examining individual stress contributions to the tensor polynomial.

The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results

PubMed Central

Seppecher, P.

2015-01-01

In order to found continuum mechanics, two different postulations have been used. The first, introduced by Lagrange and Piola, starts by postulating how the work expended by internal interactions in a body depends on the virtual velocity field and its gradients. Then, by using the divergence theorem, a representation theorem is found for the volume and contact interactions which can be exerted at the boundary of the considered body. This method assumes an a priori notion of internal work, regards stress tensors as dual of virtual displacements and their gradients, deduces the concept of contact interactions and produces their representation in terms of stresses using integration by parts. The second method, conceived by Cauchy and based on the celebrated tetrahedron argument, starts by postulating the type of contact interactions which can be exerted on the boundary of every (suitably) regular part of a body. Then it proceeds by proving the existence of stress tensors from a balance-type postulate. In this paper, we review some relevant literature on the subject, discussing how the two postulations can be reconciled in the case of higher gradient theories. Finally, we underline the importance of the concept of contact surface, edge and wedge s-order forces. PMID:26730215

Symmetry breaking in tensor models

NASA Astrophysics Data System (ADS)

Benedetti, Dario; Gurau, Razvan

2015-11-01

In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical point corresponds to a phase transition in the tensor model associated to a breaking of the unitary symmetry. We analyze the model in the two phases and prove that, in a double scaling limit, the symmetric phase corresponds to a theory of infinitely refined random surfaces, while the broken phase corresponds to a theory of infinitely refined random nodal surfaces. At leading order in the double scaling limit planar surfaces dominate in the symmetric phase, and planar nodal surfaces dominate in the broken phase.

Correlation Between Fracture Network Properties and Stress Variability in Geological Media

NASA Astrophysics Data System (ADS)

Lei, Qinghua; Gao, Ke

2018-05-01

We quantitatively investigate the stress variability in fractured geological media under tectonic stresses. The fracture systems studied include synthetic fracture networks following power law length scaling and natural fracture patterns based on outcrop mapping. The stress field is derived from a finite-discrete element model, and its variability is analyzed using a set of mathematical formulations that honor the tensorial nature of stress data. We show that local stress perturbation, quantified by the Euclidean distance of a local stress tensor to the mean stress tensor, has a positive, linear correlation with local fracture intensity, defined as the total fracture length per unit area within a local sampling window. We also evaluate the stress dispersion of the entire stress field using the effective variance, that is, a scalar-valued measure of the overall stress variability. The results show that a well-connected fracture system under a critically stressed state exhibits strong local and global stress variabilities.

Physical process first law and increase of horizon entropy for black holes in Einstein-Gauss-Bonnet gravity.

PubMed

Chatterjee, Ayan; Sarkar, Sudipta

2012-03-02

We establish the physical process version of the first law by studying small perturbations of a stationary black hole with a regular bifurcation surface in Einstein-Gauss-Bonnet gravity. Our result shows that when the stationary black hole is perturbed by a matter stress energy tensor and finally settles down to a new stationary state, the Wald entropy increases as long as the matter satisfies the null energy condition.

Mysteries of R ik = 0: A novel paradigm in Einstein's theory of gravitation

NASA Astrophysics Data System (ADS)

Vishwakarma, Ram Gopal

2014-02-01

Despite a century-long effort, a proper energy-stress tensor of the gravitational field, could not have been discovered. Furthermore, it has been discovered recently that the standard formulation of the energy-stress tensor of matter, suffers from various inconsistencies and paradoxes, concluding that the tensor is not consistent with the geometric formulation of gravitation [Astrophys. Space Sci., 2009, 321: 151; Astrophys. Space Sci., 2012, 340: 373]. This perhaps hints that a consistent theory of gravitation should not have any bearing on the energy-stress tensor. It is shown here that the so-called "vacuum" field equations R ik = 0 do not represent an empty spacetime, and the energy, momenta and angular momenta of the gravitational and the matter fields are revealed through the geometry, without including any formulation thereof in the field equations. Though, this novel discovery appears baffling and orthogonal to the usual understanding, is consistent with the observations at all scales, without requiring the hypothetical dark matter, dark energy or inflation. Moreover, the resulting theory circumvents the long-standing problems of the standard cosmology, besides explaining some unexplained puzzles.

Stress field models from Maxwell stress functions: southern California

NASA Astrophysics Data System (ADS)

Bird, Peter

2017-08-01

The lithospheric stress field is formally divided into three components: a standard pressure which is a function of elevation (only), a topographic stress anomaly (3-D tensor field) and a tectonic stress anomaly (3-D tensor field). The boundary between topographic and tectonic stress anomalies is somewhat arbitrary, and here is based on the modeling tools available. The topographic stress anomaly is computed by numerical convolution of density anomalies with three tensor Green's functions provided by Boussinesq, Cerruti and Mindlin. By assuming either a seismically estimated or isostatic Moho depth, and by using Poisson ratio of either 0.25 or 0.5, I obtain four alternative topographic stress models. The tectonic stress field, which satisfies the homogeneous quasi-static momentum equation, is obtained from particular second derivatives of Maxwell vector potential fields which are weighted sums of basis functions representing constant tectonic stress components, linearly varying tectonic stress components and tectonic stress components that vary harmonically in one, two and three dimensions. Boundary conditions include zero traction due to tectonic stress anomaly at sea level, and zero traction due to the total stress anomaly on model boundaries at depths within the asthenosphere. The total stress anomaly is fit by least squares to both World Stress Map data and to a previous faulted-lithosphere, realistic-rheology dynamic model of the region computed with finite-element program Shells. No conflict is seen between the two target data sets, and the best-fitting model (using an isostatic Moho and Poisson ratio 0.5) gives minimum directional misfits relative to both targets. Constraints of computer memory, execution time and ill-conditioning of the linear system (which requires damping) limit harmonically varying tectonic stress to no more than six cycles along each axis of the model. The primary limitation on close fitting is that the Shells model predicts very sharp shallow stress maxima and discontinuous horizontal compression at the Moho, which the new model can only approximate. The new model also lacks the spatial resolution to portray the localized stress states that may occur near the central surfaces of weak faults; instead, the model portrays the regional or background stress field which provides boundary conditions for weak faults. Peak shear stresses in one registered model and one alternate model are 120 and 150 MPa, respectively, while peak vertically integrated shear stresses are 2.9 × 1012 and 4.1 × 1012 N m-1. Channeling of deviatoric stress along the strong Great Valley and the western slope of the Peninsular Ranges is evident. In the neotectonics of southern California, it appears that deviatoric stress and long-term strain rate have a negative correlation, because regions of low heat flow are strong and act as stress guides, while undergoing very little internal deformation. In contrast, active faults lie preferentially in areas with higher heat flow, and their low strength keeps deviatoric stresses locally modest.

FAST TRACK COMMUNICATION The Bel-Robinson tensor for topologically massive gravity

NASA Astrophysics Data System (ADS)

Deser, S.; Franklin, J.

2011-02-01

We construct, and establish the (covariant) conservation of, a 4-index 'super stress tensor' for topologically massive gravity. Separately, we discuss its invalidity in quadratic curvature models and suggest a generalization.

Visualization of geologic stress perturbations using Mohr diagrams.

PubMed

Crossno, Patricia; Rogers, David H; Brannon, Rebecca M; Coblentz, David; Fredrich, Joanne T

2005-01-01

Huge salt formations, trapping large untapped oil and gas reservoirs, lie in the deepwater region of the Gulf of Mexico. Drilling in this region is high-risk and drilling failures have led to well abandonments, with each costing tens of millions of dollars. Salt tectonics plays a central role in these failures. To explore the geomechanical interactions between salt and the surrounding sand and shale formations, scientists have simulated the stresses in and around salt diapirs in the Gulf of Mexico using nonlinear finite element geomechanical modeling. In this paper, we describe novel techniques developed to visualize the simulated subsurface stress field. We present an adaptation of the Mohr diagram, a traditional paper-and-pencil graphical method long used by the material mechanics community for estimating coordinate transformations for stress tensors, as a new tensor glyph for dynamically exploring tensor variables within three-dimensional finite element models. This interactive glyph can be used as either a probe or a filter through brushing and linking.

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

NASA Astrophysics Data System (ADS)

Shi, Peidong; Angus, Doug; Nowacki, Andy; Yuan, Sanyi; Wang, Yanyan

2018-03-01

Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green's function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

NASA Astrophysics Data System (ADS)

Shi, Peidong; Angus, Doug; Nowacki, Andy; Yuan, Sanyi; Wang, Yanyan

2018-07-01

Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green's function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.

Moment Tensor Analysis of Shallow Sources

NASA Astrophysics Data System (ADS)

Chiang, A.; Dreger, D. S.; Ford, S. R.; Walter, W. R.; Yoo, S. H.

2015-12-01

A potential issue for moment tensor inversion of shallow seismic sources is that some moment tensor components have vanishing amplitudes at the free surface, which can result in bias in the moment tensor solution. The effects of the free-surface on the stability of the moment tensor method becomes important as we continue to investigate and improve the capabilities of regional full moment tensor inversion for source-type identification and discrimination. It is important to understand these free surface effects on discriminating shallow explosive sources for nuclear monitoring purposes. It may also be important in natural systems that have shallow seismicity such as volcanoes and geothermal systems. In this study, we apply the moment tensor based discrimination method to the HUMMING ALBATROSS quarry blasts. These shallow chemical explosions at approximately 10 m depth and recorded up to several kilometers distance represent rather severe source-station geometry in terms of vanishing traction issues. We show that the method is capable of recovering a predominantly explosive source mechanism, and the combined waveform and first motion method enables the unique discrimination of these events. Recovering the correct yield using seismic moment estimates from moment tensor inversion remains challenging but we can begin to put error bounds on our moment estimates using the NSS technique.

Simulation of Anisotropic Rock Damage for Geologic Fracturing

NASA Astrophysics Data System (ADS)

Busetti, S.; Xu, H.; Arson, C. F.

2014-12-01

A continuum damage model for differential stress-induced anisotropic crack formation and stiffness degradation is used to study geologic fracturing in rocks. The finite element-based model solves for deformation in the quasi-linear elastic domain and determines the six component damage tensor at each deformation increment. The model permits an isotropic or anisotropic intact or pre-damaged reference state, and the elasticity tensor evolves depending on the stress path. The damage variable, similar to Oda's fabric tensor, grows when the surface energy dissipated by three-dimensional opened cracks exceeds a threshold defined at the appropriate scale of the representative elementary volume (REV). At the laboratory or wellbore scale (<1m) brittle continuum damage reflects microcracking, grain boundary separation, grain crushing, or fine delamination, such as in shale. At outcrop (1m-100m), seismic (10m-1000m), and tectonic (>1000m) scales the damaged REV reflects early natural fracturing (background or tectonic fracturing) or shear strain localization (fault process zone, fault-tip damage, etc.). The numerical model was recently benchmarked against triaxial stress-strain data from laboratory rock mechanics tests. However, the utility of the model to predict geologic fabric such as natural fracturing in hydrocarbon reservoirs was not fully explored. To test the ability of the model to predict geological fracturing, finite element simulations (Abaqus) of common geologic scenarios with known fracture patterns (borehole pressurization, folding, faulting) are simulated and the modeled damage tensor is compared against physical fracture observations. Simulated damage anisotropy is similar to that derived using fractured rock-mass upscaling techniques for pre-determined fracture patterns. This suggests that if model parameters are constrained with local data (e.g., lab, wellbore, or reservoir domain), forward modeling could be used to predict mechanical fabric at the relevant REV scale. This reference fabric also can be used as the starting material property to pre-condition subsequent deformation or fluid flow. Continuing efforts are to expand the present damage model to couple damage evolution with plasticity and with permeability for more geologically realistic simulation.

Lithospheric Stress Tensor from Gravity and Lithospheric Structure Models

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi; Tenzer, Robert

2017-07-01

In this study we investigate the lithospheric stresses computed from the gravity and lithospheric structure models. The functional relation between the lithospheric stress tensor and the gravity field parameters is formulated based on solving the boundary-value problem of elasticity in order to determine the propagation of stresses inside the lithosphere, while assuming the horizontal shear stress components (computed at the base of the lithosphere) as lower boundary values for solving this problem. We further suppress the signature of global mantle flow in the stress spectrum by subtracting the long-wavelength harmonics (below the degree of 13). This numerical scheme is applied to compute the normal and shear stress tensor components globally at the Moho interface. The results reveal that most of the lithospheric stresses are accumulated along active convergent tectonic margins of oceanic subductions and along continent-to-continent tectonic plate collisions. These results indicate that, aside from a frictional drag caused by mantle convection, the largest stresses within the lithosphere are induced by subduction slab pull forces on the side of subducted lithosphere, which are coupled by slightly less pronounced stresses (on the side of overriding lithospheric plate) possibly attributed to trench suction. Our results also show the presence of (intra-plate) lithospheric loading stresses along Hawaii islands. The signature of ridge push (along divergent tectonic margins) and basal shear traction resistive forces is not clearly manifested at the investigated stress spectrum (between the degrees from 13 to 180).

Rotational relaxation time as unifying time scale for polymer and fiber drag reduction

NASA Astrophysics Data System (ADS)

Boelens, A. M. P.; Muthukumar, M.

2016-05-01

Using hybrid direct numerical simulation plus Langevin dynamics, a comparison is performed between polymer and fiber stress tensors in turbulent flow. The stress tensors are found to be similar, suggesting a common drag reducing mechanism in the onset regime for both flexible polymers and rigid fibers. Since fibers do not have an elastic backbone, this must be a viscous effect. Analysis of the viscosity tensor reveals that all terms are negligible, except the off-diagonal shear viscosity associated with rotation. Based on this analysis, we identify the rotational orientation time as the unifying time scale setting a new time criterion for drag reduction by both flexible polymers and rigid fibers.

Rotational relaxation time as unifying time scale for polymer and fiber drag reduction.

PubMed

Boelens, A M P; Muthukumar, M

2016-05-01

Using hybrid direct numerical simulation plus Langevin dynamics, a comparison is performed between polymer and fiber stress tensors in turbulent flow. The stress tensors are found to be similar, suggesting a common drag reducing mechanism in the onset regime for both flexible polymers and rigid fibers. Since fibers do not have an elastic backbone, this must be a viscous effect. Analysis of the viscosity tensor reveals that all terms are negligible, except the off-diagonal shear viscosity associated with rotation. Based on this analysis, we identify the rotational orientation time as the unifying time scale setting a new time criterion for drag reduction by both flexible polymers and rigid fibers.

Vacuum polarization of the quantized massive fields in Friedman-Robertson-Walker spacetime

NASA Astrophysics Data System (ADS)

Matyjasek, Jerzy; Sadurski, Paweł; Telecka, Małgorzata

2014-04-01

The stress-energy tensor of the quantized massive fields in a spatially open, flat, and closed Friedman-Robertson-Walker universe is constructed using the adiabatic regularization (for the scalar field) and the Schwinger-DeWitt approach (for the scalar, spinor, and vector fields). It is shown that the stress-energy tensor calculated in the sixth adiabatic order coincides with the result obtained from the regularized effective action, constructed from the heat kernel coefficient a3. The behavior of the tensor is examined in the power-law cosmological models, and the semiclassical Einstein field equations are solved exactly in a few physically interesting cases, such as the generalized Starobinsky models.

A Note on the Application of the Extended Bernoulli Equation

DTIC Science & Technology

1999-02-01

as OV s ... - Vp „ _ = -±L L + VO , (2) Dt p where DIDt denotes the material derivative (discussed in following section); V is the vector...force potential; V is the vector gradient operator; s (J is the deviatoric-stress tensor arising from any type of elasto-viscoplastic constitutive...behavior; and s ^j is index notation for dsy/dxp denoting the following vector condensation of the deviatoric-stress tensor: ds ds ds

Electrostatic forces in the Poisson-Boltzmann systems

NASA Astrophysics Data System (ADS)

Xiao, Li; Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2013-09-01

Continuum modeling of electrostatic interactions based upon numerical solutions of the Poisson-Boltzmann equation has been widely used in structural and functional analyses of biomolecules. A limitation of the numerical strategies is that it is conceptually difficult to incorporate these types of models into molecular mechanics simulations, mainly because of the issue in assigning atomic forces. In this theoretical study, we first derived the Maxwell stress tensor for molecular systems obeying the full nonlinear Poisson-Boltzmann equation. We further derived formulations of analytical electrostatic forces given the Maxwell stress tensor and discussed the relations of the formulations with those published in the literature. We showed that the formulations derived from the Maxwell stress tensor require a weaker condition for its validity, applicable to nonlinear Poisson-Boltzmann systems with a finite number of singularities such as atomic point charges and the existence of discontinuous dielectric as in the widely used classical piece-wise constant dielectric models.

The Constantine (Algeria) seismic sequence of 27 October 1985: a new rupture model from aftershock relocation, focal mechanisms, and stress tensors

NASA Astrophysics Data System (ADS)

Ousadou, F.; Dorbath, L.; Dorbath, C.; Bounif, M. A.; Benhallou, H.

2013-04-01

The October 27, 1985 Constantine earthquake of magnitude MS 5.9 (NEIC) although moderate is the strongest earthquake recorded in the eastern Tellian Atlas (northeast Algeria) since the beginning of instrumental seismology. The main shock locations given by different institutions are scattered and up to 10 km away northwest from the NE-SW 30 km long elongated aftershocks cloud localized by a dedicated temporary portable network. The focal mechanism indicates left-lateral strike-slip on an almost vertical fault with a small reverse component on the northwest dipping plane. This paper presents relocations of the main shock and aftershocks using TomoDD. One hundred thirty-eight individual focal mechanisms have been built allowing the determination of the stress tensor at different scales. A rupture model has been suggested, which explains the different observations of aftershock distribution and stress tensor rotation.

Intrinsic Viscosity of Dendrimers via Equilibrium Molecular Dynamics

NASA Astrophysics Data System (ADS)

Drew, Phil; Adolf, David

2004-03-01

Equilibrium molecular dynamics simulations of dendrimers in dilute solution have been performed using dl-poly. Analysis of the system stress tensor via the Green-Kubo formula produces the viscosity of the dendrimer solution which, when coupled with that of a solvent only system leads to the intrinsic viscosity of the dendrimer solute. Particular attention has been paid to error analysis as the auto-correlation of the stress tensor exhibits a long time tail, potentially leading to large uncertainties in the solution, and hence intrinsic, viscosities. In order to counter this effect and provide reliable statistical averaging, simulations have been run spanning very many times the longest system relaxation. Comparison is made to previous studies, using different techniques, which suggest a peak in the intrinsic viscosity of dendrimers at around generation four. Results are also presented from investigations in to the individual contributions to the system stress tensor from the solvent and the solute.

The influence of topographic stresses on faulting, emphasizing the 2008 Wenchuan, China earthquake rupture

NASA Astrophysics Data System (ADS)

Styron, R. H.; Hetland, E. A.; Zhang, G.

2013-12-01

The weight of large mountains produces stresses in the crust that locally may be on the order of tectonic stresses (10-100 MPa). These stresses have a significant and spatially-variable deviatoric component that may be resolved as strong normal and shear stresses on range-bounding faults. In areas of high relief, the shear stress on faults can be comparable to inferred stress drops in earthquakes, and fault-normal stresses may be greater than 50 MPa, and thus may potentially influence fault rupture. Additionally, these stresses may be used to make inferences about the orientation and magnitude of tectonic stresses, for example by indicating a minimum stress needed to be overcome by tectonic stress. We are studying these effects in several tectonic environments, such as the Longmen Shan (China), the Denali fault (Alaska, USA) and the Wasatch Fault Zone (Utah, USA). We calculate the full topographic stress tensor field in the crust in a study region by convolution of topography with Green's functions approximating stresses from a point load on the surface of an elastic halfspace, using the solution proposed by Liu and Zoback [1992]. The Green's functions are constructed from Boussinesq's solutions for a vertical point load on an elastic halfspace, as well as Cerruti's solutions for a horizontal surface point load, accounting for irregular surface boundary and topographic spreading forces. The stress tensor field is then projected onto points embedded in the halfspace representing the faults, and the fault normal and shear stresses at each point are calculated. Our primary focus has been on the 2008 Wenchuan earthquake, as this event occurred at the base of one of Earth's highest and steepest topographic fronts and had a complex and well-studied coseismic slip distribution, making it an ideal case study to evaluate topographic influence on faulting. We calculate the topographic stresses on the Beichuan and Pengguan faults, and compare the results to the coseismic slip distribution, considering several published fault models. These models differ primarily in slip magnitude and planar vs. listric fault geometry at depth. Preliminary results indicate that topographic stresses are generally resistive to tectonic deformation, especially above ~10 km depth, where the faults are steep in all models. Down-dip topographic shear stresses on the fault are normal sense where the faults dip steeply, and reach 20 MPa on the fault beneath the Pengguan massif. Reverse-sense shear up to ~15 MPa is present on gently-dipping thrust flats at depth on listric fault models. Strike-slip shear stresses are sinistral on the steep, upper portions of faults but may be dextral on thrust flats. Topographic normal stress on the faults reaches ~80 MPa on thrust ramps and may be higher on flats. Coseismic slip magnitude is negatively correlated with topographic normal and down-dip shear stresses. The spatial patterns of topographic stresses and slip suggest that topographic stresses have significantly suppressed slip in certain areas: slip maxima occur in areas of locally lower topographic stresses, while areas of higher down-dip shear and normal stress show less slip than adjacent regions.

Tensor calculus: unlearning vector calculus

NASA Astrophysics Data System (ADS)

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-02-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can serve as a bridge for vector calculus into tensor calculus.

Design and Implementation of a Numerical Technique to Inform Anisotropic Hyperelastic Finite Element Models using Diffusion-Weighted Imaging

DTIC Science & Technology

2011-10-01

the deviatoric part of a tensor in the reference configuration and p = −∂Ψ ∂J is the hydrostatic pressure. Using the chain 4 rule, equation 13 can be...Kirchoff stress tensor S to the current configuration, and a scaling with the inverse of the volume ratio, transforms equation 16 to the Cauchy stress ...a characteristic of most soft tissues. Then, similar to equation 13, the second Piola-Kirchoff stress is given by: S = 2J−2/3DEV [ ∂Ψisoc ( C ) ∂C

Mechanics of deformations in terms of scalar variables

NASA Astrophysics Data System (ADS)

Ryabov, Valeriy A.

2017-05-01

Theory of particle and continuous mechanics is developed which allows a treatment of pure deformation in terms of the set of variables "coordinate-momentum-force" instead of the standard treatment in terms of tensor-valued variables "strain-stress." This approach is quite natural for a microscopic description of atomic system, according to which only pointwise forces caused by the stress act to atoms making a body deform. The new concept starts from affine transformation of spatial to material coordinates in terms of the stretch tensor or its analogs. Thus, three principal stretches and three angles related to their orientation form a set of six scalar variables to describe deformation. Instead of volume-dependent potential used in the standard theory, which requires conditions of equilibrium for surface and body forces acting to a volume element, a potential dependent on scalar variables is introduced. A consistent introduction of generalized force associated with this potential becomes possible if a deformed body is considered to be confined on the surface of torus having six genuine dimensions. Strain, constitutive equations and other fundamental laws of the continuum and particle mechanics may be neatly rewritten in terms of scalar variables. Giving a new presentation for finite deformation new approach provides a full treatment of hyperelasticity including anisotropic case. Derived equations of motion generate a new kind of thermodynamical ensemble in terms of constant tension forces. In this ensemble, six internal deformation forces proportional to the components of Irving-Kirkwood stress are controlled by applied external forces. In thermodynamical limit, instead of the pressure and volume as state variables, this ensemble employs deformation force measured in kelvin unit and stretch ratio.

Nonlinear fluid dynamics of nanoscale hydration water layer

NASA Astrophysics Data System (ADS)

Jhe, Wonho; Kim, Bongsu; Kim, Qhwan; An, Sangmin

In nature, the hydration water layer (HWL) ubiquitously exists in ambient conditions or aqueous solutions, where water molecules are tightly bound to ions or hydrophilic surfaces. It plays an important role in various mechanisms such as biological processes, abiotic materials, colloidal interaction, and friction. The HWL, for example, can be easily formed between biomaterials since most biomaterials are covered by hydrophilic molecules such as lipid bilayers, and this HWL is expected to be significant to biological and physiological functions. Here (1) we present the general stress tensor of the hydration water layer. The hydration stress tensor provided the platform form for holistic understanding of the dynamic behaviors of the confined HWL including tapping and shear dynamics which are until now individually studied. And, (2) through fast shear velocity ( 1mm/s) experiments, the elastic turbulence caused by elastic property of the HWL is indirectly observed. Our results may contribute to a deeper study of systems where the HWL plays an important role such as biomolecules, colloidal particles, and the MEMS. This work was supported by the National Research Foundation of Korea(NRF) Grant funded by the Korea government(MSIP) (2016R1A3B1908660).

QTAIM and Stress Tensor Characterization of Intramolecular Interactions Along Dynamics Trajectories of a Light-Driven Rotary Molecular Motor.

PubMed

Wang, Lingling; Huan, Guo; Momen, Roya; Azizi, Alireza; Xu, Tianlv; Kirk, Steven R; Filatov, Michael; Jenkins, Samantha

2017-06-29

A quantum theory of atoms in molecules (QTAIM) and stress tensor analysis was applied to analyze intramolecular interactions influencing the photoisomerization dynamics of a light-driven rotary molecular motor. For selected nonadiabatic molecular dynamics trajectories characterized by markedly different S 1 state lifetimes, the electron densities were obtained using the ensemble density functional theory method. The analysis revealed that torsional motion of the molecular motor blades from the Franck-Condon point to the S 1 energy minimum and the S 1 /S 0 conical intersection is controlled by two factors: greater numbers of intramolecular bonds before the hop-time and unusually strongly coupled bonds between the atoms of the rotor and the stator blades. This results in the effective stalling of the progress along the torsional path for an extended period of time. This finding suggests a possibility of chemical tuning of the speed of photoisomerization of molecular motors and related molecular switches by reshaping their molecular backbones to decrease or increase the degree of coupling and numbers of intramolecular bond critical points as revealed by the QTAIM/stress tensor analysis of the electron density. Additionally, the stress tensor scalar and vector analysis was found to provide new methods to follow the trajectories, and from this, new insight was gained into the behavior of the S 1 state in the vicinity of the conical intersection.

Highly efficient all-dielectric optical tensor impedance metasurfaces for chiral polarization control.

PubMed

Kim, Minseok; Eleftheriades, George V

2016-10-15

We propose a highly efficient (nearly lossless and impedance-matched) all-dielectric optical tensor impedance metasurface that mimics chiral effects at optical wavelengths. By cascading an array of rotated crossed silicon nanoblocks, we realize chiral optical tensor impedance metasurfaces that operate as circular polarization selective surfaces. Their efficiencies are maximized through a nonlinear numerical optimization process in which the tensor impedance metasurfaces are modeled via multi-conductor transmission line theory. From rigorous full-wave simulations that include all material losses, we show field transmission efficiencies of 94% for right- and left-handed circular polarization selective surfaces at 800 nm.

Refraction of the principal stress trajectories and the stress jumps on faults and contact surfaces: Part 1. Non-constrained regular trajectories

NASA Astrophysics Data System (ADS)

Mukhamediev, Sh. A.

2014-09-01

Rock masses contain ubiquitous multiscale heterogeneities, which (or whose boundaries) serve as the surfaces of discontinuity for some characteristics of the stress state, e.g., for the orientation of principal stress axes. Revealing the regularities that control these discontinuities is a key to understanding the processes taking place at the boundaries of the heterogeneities and for designing the correct procedures for reconstructing and theoretical modeling of tectonic stresses. In the present study, the local laws describing the refraction of the axes of extreme principal stresses T 1 (maximal tension in the deviatoric sense) and T 3 (maximal compression) of the Cauchy stress tensor at the transition over the elementary area n of discontinuity whose orientation is specified by the unit normal n are derived. It is assumed that on the area n of discontinuity, frictional contact takes place. No hypotheses are made on the constitutive equations, and a priori constraints are not posed on the orientation on the stress axes. Two domains, which adjoin area n on the opposite sides and are conventionally marked + and -, are distinguished. In the case of the two-dimensional (2D) stress state, any principal stress axis on passing from domain - to domain + remains in the same quadrant of the plane as the continuation of this axis in domain +. The sign and size of the refraction angle depend on the sign and amplitude of the jump of the normal stress, which is tangential to the surface of discontinuity. In the three-dimensional (3D) case, the refraction of axes T 1 and T 3 should be analyzed simultaneously. For each side, + and -, the projections of the T 1 and T 3 axes on the generally oriented plane n form the shear sectors S + and S -, which are determined unambiguously and to whose angular domains the possible directions p + and p - of the shear stress vectors belong. In order for the extreme stress axes T {1/+}, T {3/+} and T {1/-}, T {3/-} to be statically compatible on the generally oriented plane n, it is required that sectors S + and S - had a nonempty intersection. The direction vectors p + and p - are determined uniquely if, besides axes T {1/-}, T {3/-} and T {1/+}, T {3/+}, also the ratios of differential stresses R + and R - (0 ≤ R ± ≤ 1) are known. This is equivalent to specifying the reduced stress tensors T {/R +} and T {/R -} The necessary condition for tensors T {/R +} and T {/R -} being statically compatible on plane n is the equality p + = p -. In this paper, simple methods are suggested for solving the inverse problem of constructing the set of the orientations of the extreme stress axes from the known direction p of the shear stress vector on plane n and from the data on the shear sector. Based on these methods and using the necessary conditions of local equilibrium on plane n formulated above, all the possible orientations of axes T {1/+}, T {3/+} are determined if the projections of axes T {1/-}, T {3/-} axes on side — are given. The angle between the projections of axes T {1/+}, T {1/-} and/or T {3/+}, T {3/-} on the plane can attain 90°. Besides the general case, also the particular cases of the contact between the degenerate stress states and the special position of plane n relative to the principal stress axes are thoroughly examined. Generalization of the obtained results makes it possible to plot the local diagram of the orientations of axes T {1/+}, T {3/+} for a given sector S -. This diagram is a so-called stress orientation sphere, which is subdivided into three pairs of areas (compression, tension, and compression-extension). The tension and compression zones cannot contain the poles of T {3/+} and T {1/+} axes, respectively. The compression-extension zones can contain the poles of either T {1/+} or T {3/+} axis but not both poles simultaneously. In the particular case when the shear stress vector has a unique direction p - on side -, the areas of compression-extension disappear and the diagram is reduced to a beach-ball plot, which visualizes the focal mechanism solution of an earthquake. If area n is a generally oriented plane and if the orientation of the pairs of the statically compatible axes T {1/-}, T {3/-} and T {1/+}, T {3/+} is specified, then, the stress values on side + are uniquely determined from the known stress values on side -. From the value of differential stress ratio R -, one can calculate the value of R +, and using the values of the principal stresses on side -, determine the total stress tensor T + on side +. The obtained results are supported by the laboratory experiments and drilling data. In particular, these results disclose the drawbacks of some established notions and methods in which the possible refraction of the stress axes is unreasonably ignored or taken into account improperly. For example, it is generally misleading to associate the slip on the preexisting fault with the orientation of any particular trihedron of the principal stress axes. The reconstruction should address the potentially statically compatible principal stress axes, which are differently oriented on opposite sides of the fault plane. The fact that, based on the orientation of the intraplate principal stresses at the base of the lithosphere, one cannot make a conclusion on the active or passive influence of the mantle flows on the lithospheric plate motion is another example. The present relationships linking the stress values on the opposite sides of the fault plane on which the orientations of the principal stress axes are known demonstrate the incorrectness of the existing methods, in which the reduced stress tensors within the material domains are reconstructed without allowance for the dynamic interaction of these domains with their neighbors. In addition, using the obtained results, one can generalize the notion of the zone of dynamical control of a fault onto the case of the existence of discontinuities in this region and analyze the stress transfer across the system of the faults.

Influences of granular constraints and surface effects on the heterogeneity of elastic, superelastic, and plastic responses of polycrystalline shape memory alloys

DOE PAGES

Paranjape, Harshad M.; Paul, Partha P.; Sharma, Hemant; ...

2017-02-16

Deformation heterogeneities at the microstructural length-scale developed in polycrystalline shape memory alloys (SMAs) during superelastic loading are studied using both experiments and simulations. In situ X-ray diffraction, specifically the far-field high energy diffraction microscopy (ff-HEDM) technique, was used to non-destructively measure the grain-averaged statistics of position, crystal orientation, elastic strain tensor, and volume for hundreds of austenite grains in a superelastically loaded nickel-titanium (NiTi) SMA. These experimental data were also used to create a synthetic microstructure within a finite element model. The development of intragranular stresses were then simulated during tensile loading of the model using anisotropic elasticity. Driving forcesmore » for phase transformation and slip were calculated from these stresses. The grain-average responses of individual austenite crystals examined before and after multiple stress-induced transformation events showed that grains in the specimen interior carry more axial stress than the surface grains as the superelastic response "shakes down". Examination of the heterogeneity within individual grains showed that regions near grain boundaries exhibit larger stress variation compared to the grain interiors. As a result, this intragranular heterogeneity is more strongly driven by the constraints of neighboring grains than the initial stress state and orientation of the individual grains.« less

Influences of granular constraints and surface effects on the heterogeneity of elastic, superelastic, and plastic responses of polycrystalline shape memory alloys

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paranjape, Harshad M.; Paul, Partha P.; Sharma, Hemant

Deformation heterogeneities at the microstructural length-scale developed in polycrystalline shape memory alloys (SMAs) during superelastic loading are studied using both experiments and simulations. In situ X-ray diffraction, specifically the far-field high energy diffraction microscopy (ff-HEDM) technique, was used to non-destructively measure the grain-averaged statistics of position, crystal orientation, elastic strain tensor, and volume for hundreds of austenite grains in a superelastically loaded nickel-titanium (NiTi) SMA. These experimental data were also used to create a synthetic microstructure within a finite element model. The development of intragranular stresses were then simulated during tensile loading of the model using anisotropic elasticity. Driving forcesmore » for phase transformation and slip were calculated from these stresses. The grain-average responses of individual austenite crystals examined before and after multiple stress-induced transformation events showed that grains in the specimen interior carry more axial stress than the surface grains as the superelastic response "shakes down". Examination of the heterogeneity within individual grains showed that regions near grain boundaries exhibit larger stress variation compared to the grain interiors. As a result, this intragranular heterogeneity is more strongly driven by the constraints of neighboring grains than the initial stress state and orientation of the individual grains.« less

An investigation of the flow characteristics in the blade endwall corner region

NASA Technical Reports Server (NTRS)

Hazarika, Birinchi K.; Raj, Rishi S.

1987-01-01

Studies were undertaken to determine the structure of the flow in the blade end wall corner region simulated by attaching two uncambered airfoils on either side of a flat plate with a semicircular leading edge. Detailed measurements of the corner flow were obtained with conventional pressure probes, hot wire anemometry, and flow visualization. The mean velocity profiles and six components of the Reynolds stress tensor were obtained with an inclined single sensor hot wire probe whereas power spectra were obtained with a single sensor oriented normal to the flow. Three streamwise vortices were identified based on the surface streamlines, distortion of total pressure profiles, and variation of mean velocity components in the corner. A horseshoe vortex formed near the leading edge of the airfoil. Within a short distance downstream, a corner vortex was detected between the horseshoe vortex and the surfaces forming the corner. A third vortex was formed at the rear portion of the corner between the corner vortex and the surface of the flat plate. Turbulent shear stress and production of turbulence are negligibly small. A region of negative turbulent shear stress was also observed near the region of low turbulence intensity from the vicinity of the flat plate.

Tensor Calculus: Unlearning Vector Calculus

ERIC Educational Resources Information Center

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Detailed stress tensor measurements in a centrifugal compressor vaneless diffuser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pinarbasi, A.; Johnson, M.W.

1996-04-01

Detailed flow measurements have been made in the vaneless diffuser of a large low-speed centrifugal compressor using hot-wire anemometry. The three time mean velocity components and full stress tensor distributions have been determined on eight measurement plans within the diffuser. High levels of Reynolds stress result in the rapid mixing out of the blade wake. Although high levels of turbulent kinetic energy are found in the passage wake, they are not associated with strong Reynolds stresses and hence the passage wake mixes out only slowly. Low-frequency meandering of the wake position is therefore likely to be responsible for the highmore » kinetic energy levels. The anisotropic nature of the turbulence suggests that Reynolds stress turbulence models are required for CFD modeling of diffuser flows.« less

Implicit constitutive models with a thermodynamic basis: a study of stress concentration

NASA Astrophysics Data System (ADS)

Bridges, C.; Rajagopal, K. R.

2015-02-01

Motivated by the recent generalization of the class of elastic bodies by Rajagopal (Appl Math 48:279-319, 2003), there have been several recent studies that have been carried out within the context of this new class. Rajagopal and Srinivasa (Proc R Soc Ser A 463:357-367, 2007, Proc R Soc Ser A: Math Phys Eng Sci 465:493-500, 2009) provided a thermodynamic basis for such models and appealing to the idea that rate of entropy production ought to be maximized they developed nonlinear rate equations of the form where T is the Cauchy stress and D is the stretching tensor as well as , where S is the Piola-Kirchhoff stress tensor and E is the Green-St. Venant strain tensor. We follow a similar procedure by utilizing the Gibb's potential and the left stretch tensor V from the Polar Decomposition of the deformation gradient, and we show that when the displacement gradient is small one arrives at constitutive relations of the form . This is, of course, in stark contrast to traditional elasticity wherein one obtains a single model, Hooke's law, when the displacement gradient is small. By solving a classical boundary value problem, with a particular form for f( T), we show that when the stresses are small, the strains are also small which is in agreement with traditional elasticity. However, within the context of our model, when the stress blows up the strains remain small, unlike the implications of Hooke's law. We use this model to study boundary value problems in annular domains to illustrate its efficacy.

Magnification effect of Kerr metric by configurations of collisionless particles in non-isotropic kinetic equilibria

NASA Astrophysics Data System (ADS)

Cremaschini, Claudio; Stuchlík, Zdeněk

2018-05-01

A test fluid composed of relativistic collisionless neutral particles in the background of Kerr metric is expected to generate non-isotropic equilibrium configurations in which the corresponding stress-energy tensor exhibits pressure and temperature anisotropies. This arises as a consequence of the constraints placed on single-particle dynamics by Killing tensor symmetries, leading to a peculiar non-Maxwellian functional form of the kinetic distribution function describing the continuum system. Based on this outcome, in this paper the generation of Kerr-like metric by collisionless N -body systems of neutral matter orbiting in the field of a rotating black hole is reported. The result is obtained in the framework of covariant kinetic theory by solving the Einstein equations in terms of an analytical perturbative treatment whereby the gravitational field is decomposed as a prescribed background metric tensor described by the Kerr solution plus a self-field correction. The latter one is generated by the uncharged fluid at equilibrium and satisfies the linearized Einstein equations having the non-isotropic stress-energy tensor as source term. It is shown that the resulting self-metric is again of Kerr type, providing a mechanism of magnification of the background metric tensor and its qualitative features.

Implementation and Testing of Advanced Surface Boundary Conditions Over Complex Terrain in A Semi-idealized Model

NASA Astrophysics Data System (ADS)

Li, Y.; Epifanio, C.

2017-12-01

In numerical prediction models, the interaction between the Earth's surface and the atmosphere is typically accounted for in terms of surface layer parameterizations, whose main job is to specify turbulent fluxes of heat, moisture and momentum across the lower boundary of the model domain. In the case of a domain with complex geometry, implementing the flux conditions (particularly the tensor stress condition) at the boundary can be somewhat subtle, and there has been a notable history of confusion in the CFD community over how to formulate and impose such conditions generally. In the atmospheric case, modelers have largely been able to avoid these complications, at least until recently, by assuming that the terrain resolved at typical model resolutions is fairly gentle, in the sense of having relatively shallow slopes. This in turn allows the flux conditions to be imposed as if the lower boundary were essentially flat. Unfortunately, while this flat-boundary assumption is acceptable for coarse resolutions, as grids become more refined and the geometry of the resolved terrain becomes more complex, the appproach is less justified. With this in mind, the goal of our present study is to explore the implementation and usage of the full, unapproximated version of the turbulent flux/stress conditions in atmospheric models, thus taking full account of the complex geometry of the resolved terrain. We propose to implement the conditions using a semi-idealized model developed by Epifanio (2007), in which the discretized boundary conditions are reduced to a large, sparse-matrix problem. The emphasis will be on fluxes of momentum, as the tensor nature of this flux makes the associated stress condition more difficult to impose, although the flux conditions for heat and moisture will be considered as well. With the resulotion of 90 meters, some of the results show that the typical differences between flat-boundary cases and full/stress cases are on the order of 10%, with extreme cases reaching as high as 30% based on typical disturbance wind speeds. And this difference dropping by a factor of six between grid spacings of 90 meters and 240 meters. It would thus appear that the need to apply the full stress condition is limited to relatively high-resolution modeling, with grid spacings on the order of 250 meters or less.

Generalized Rainich conditions, generalized stress-energy conditions, and the Hawking-Ellis classification

NASA Astrophysics Data System (ADS)

Martín–Moruno, Prado; Visser, Matt

2017-11-01

The (generalized) Rainich conditions are algebraic conditions which are polynomial in the (mixed-component) stress-energy tensor. As such they are logically distinct from the usual classical energy conditions (NEC, WEC, SEC, DEC), and logically distinct from the usual Hawking-Ellis (Segré-Plebański) classification of stress-energy tensors (type I, type II, type III, type IV). There will of course be significant inter-connections between these classification schemes, which we explore in the current article. Overall, we shall argue that it is best to view the (generalized) Rainich conditions as a refinement of the classical energy conditions and the usual Hawking-Ellis classification.

The calculation of the viscosity from the autocorrelation function using molecular and atomic stress tensors

NASA Astrophysics Data System (ADS)

Cui, S. T.

The stress-stress correlation function and the viscosity of a united-atom model of liquid decane are studied by equilibrium molecular dynamics simulation using two different formalisms for the stress tensor: the atomic and the molecular formalisms. The atomic and molecular correlation functions show dramatic difference in short-time behaviour. The integrals of the two correlation functions, however, become identical after a short transient period whichis significantly shorter than the rotational relaxation time of the molecule. Both reach the same plateau value in a time period corresponding to this relaxation time. These results provide a convenient guide for the choice of the upper integral time limit in calculating the viscosity by the Green-Kubo formula.

Asymmetric Yield Function Based on the Stress Invariants for Pressure Sensitive Metals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeong Wahn Yoon; Yanshan Lou; Jong Hun Yoon

A general asymmetric yield function is proposed with dependence on the stress invariants for pressure sensitive metals. The pressure sensitivity of the proposed yield function is consistent with the experimental result of Spitzig and Richmond (1984) for steel and aluminum alloys while the asymmetry of the third invariant is preserved to model strength differential (SD) effect of pressure insensitive materials. The proposed yield function is transformed in the space of the stress triaxaility, the von Mises stress and the normalized invariant to theoretically investigate the possible reason of the SD effect. The proposed plasticity model is further extended to characterizemore » the anisotropic behavior of metals both in tension and compression. The extension of the yield function is realized by introducing two distinct fourth-order linear transformation tensors of the stress tensor for the second and third invariants, respectively. The extended yield function reasonably models the evolution of yield surfaces for a zirconium clock-rolled plate during in-plane and through-thickness compression reported by Plunkett et al. (2007). The extended yield function is also applied to describe the orthotropic behavior of a face-centered cubic metal of AA 2008-T4 and two hexagonal close-packed metals of high-purity-titanium and AZ31 magnesium alloy. The orthotropic behavior predicted by the generalized model is compared with experimental results of these metals. The comparison validates that the proposed yield function provides sufficient predictability on SD effect and anisotropic behavior both in tension and compression. When it is necessary to consider r-value anisotropy, the proposed function is efficient to be used with nonassociated flow plasticity by introducing a separate plastic potential for the consideration of r-values as shown in Stoughton & Yoon (2004, 2009).« less

BOOK REVIEW: Nonlinear Continuum Mechanics for Finite Element Analysis

NASA Astrophysics Data System (ADS)

Bialek, James M.

1998-05-01

Nonlinear continuum mechanics of solids is a fascinating subject. All the assumptions inherited from an overexposure to linear behaviour and analysis must be re-examined. The standard definitions of strain designed for small deformation linear problems may be totally misleading when finite motion or large deformations are considered. Nonlinear behaviour includes phenomena like `snap-through', where bifurcation theory is applied to engineering design. Capabilities in this field are growing at a fantastic speed; for example, modern automobiles are presently being designed to crumple in the most energy absorbing manner in order to protect the occupants. The combination of nonlinear mechanics and the finite element method is a very important field. Most engineering designs encountered in the fusion effort are strictly limited to small deformation linear theory. In fact, fusion devices are usually kept in the low stress, long life regime that avoids large deformations, nonlinearity and any plastic behaviour. The only aspect of nonlinear continuum solid mechanics about which the fusion community now worries is that rare case where details of the metal forming process must be considered. This text is divided into nine sections: introduction, mathematical preliminaries, kinematics, stress and equilibrium, hyperelasticity, linearized equilibrium equations, discretization and solution, computer implementation and an appendix covering an introduction to large inelastic deformations. The authors have decided to use vector and tensor notation almost exclusively. This means that the usual maze of indicial equations is avoided, but most readers will therefore be stretched considerably to follow the presentation, which quickly proceeds to the heart of nonlinear behaviour in solids. With great speed the reader is led through the material (Lagrangian) and spatial (Eulerian) co-ordinates, the deformation gradient tensor (an example of a two point tensor), the right and left Cauchy-Green tensors, the Eulerian or Almansi strain tensor, distortional components, strain rate tensors, rate of deformation tensors, spin tensors and objectivity. The standard Cauchy stress tensor is mentioned in passing, and then virtual work and work conjugacy lead to alternative stress representations such as the Piola-Kirchoff representation. Chapter 5 concentrates on hyperelasticity (where stresses are derived from a stored energy function) and its subvarieties. Chapter 6 proceeds by linearizing the virtual work statement prior to discretization and Chapter 7 deals with approaches to solving the formulation. In Chapter 8 the FORTRAN finite element code written by Bonet (available via the world wide web) is described. In summary this book is written by experts, for future experts, and provides a very fast review of the field for people who already know the topic. The authors assume the reader is familiar with `elementary stress analysis' and has had some exposure to `the principle of the finite element method'. Their goals are summarized by the statement, `If the reader is prepared not to get too hung up on details, it is possible to use the book to obtain a reasonable overview of the subject'. This is a very nice summary of what is going on in the field but as a stand-alone text it is much too terse. The total bibliography is a page and a half. It would be an improvement if there were that much reference material for each chapter.

Close-range photogrammetry in underground mining ground control

NASA Astrophysics Data System (ADS)

Benton, Donovan J.; Chambers, Amy J.; Raffaldi, Michael J.; Finley, Seth A.; Powers, Mark J.

2016-09-01

Monitoring underground mine deformation and support conditions has traditionally involved visual inspection and geotechnical instrumentation. Monitoring displacements with conventional instrumentation can be expensive and time-consuming, and the number of locations that can be effectively monitored is generally limited. Moreover, conventional methods typically produce vector rather than tensor descriptions of geometry changes. Tensor descriptions can provide greater insight into hazardous ground movements, particularly in recently excavated openings and in older workings that have been negatively impacted by high stress concentrations, time-dependent deformation, or corrosion of ground support elements. To address these issues, researchers with the National Institute for Occupational Safety and Health, Spokane Mining Research Division are developing and evaluating photogrammetric systems for ground control monitoring applications in underground mines. This research has demonstrated that photogrammetric systems can produce millimeter-level measurements that are comparable to conventional displacement-measuring instruments. This paper provides an overview of the beneficial use of close-range photogrammetry for the following three ground control applications in underground mines: monitoring the deformation of surface support, monitoring rock mass movement, and monitoring the corrosion of surface support. Preliminary field analyses, case studies, limitations, and best practices for these applications are also discussed.

Seismicity and stress transfer studies in eastern California and Nevada: Implications for earthquake sources and tectonics

NASA Astrophysics Data System (ADS)

Ichinose, Gene Aaron

The source parameters for eastern California and western Nevada earthquakes are estimated from regionally recorded seismograms using a moment tensor inversion. We use the point source approximation and fit the seismograms, at long periods. We generated a moment tensor catalog for Mw > 4.0 since 1997 and Mw > 5.0 since 1990. The catalog includes centroid depths, seismic moments, and focal mechanisms. The regions with the most moderate sized earthquakes in the last decade were in aftershock zones located in Eureka Valley, Double Spring Flat, Coso, Ridgecrest, Fish Lake Valley, and Scotty's Junction. The remaining moderate size earthquakes were distributed across the region. The 1993 (Mw 6.0) Eureka Valley earthquake occurred in the Eastern California Shear Zone. Careful aftershock relocations were used to resolve structure from aftershock clusters. The mainshock appears to rupture along the western side of the Last Change Range along a 30° to 60° west dipping fault plane, consistent with previous geodetic modeling. We estimate the source parameters for aftershocks at source-receiver distances less than 20 km using waveform modeling. The relocated aftershocks and waveform modeling results do not indicate any significant evidence of low angle faulting (dips > 30°. The results did reveal deformation along vertical faults within the hanging-wall block, consistent with observed surface rupture along the Saline Range above the dipping fault plane. The 1994 (Mw 5.8) Double Spring Flat earthquake occurred along the eastern Sierra Nevada between overlapping normal faults. Aftershock migration and cross fault triggering occurred in the following two years, producing seventeen Mw > 4 aftershocks The source parameters for the largest aftershocks were estimated from regionally recorded seismograms using moment tensor inversion. We estimate the source parameters for two moderate sized earthquakes which occurred near Reno, Nevada, the 1995 (Mw 4.4) Border Town, and the 1998 (Mw 4.7) Incline Village Earthquakes. We test to see how such stress interactions affected a cluster of six large earthquakes (Mw 6.6 to 7.5) between 1915 to 1954 within the Central Nevada Seismic Belt. We compute the static stress changes for these earthquake using dislocation models based on the location and amount of surface rupture. (Abstract shortened by UMI.)

Seismotectonics and crustal stress across the northern Arabian plate

NASA Astrophysics Data System (ADS)

yassminh, R.; Gomez, F. G.; Sandvol, E. A.; Ghalib, H. A.; Daoud, M.

2013-12-01

The region encompassing the collision of northern Arabia with Eurasia is a tectonically heterogeneous region of distributed deformation. The northern Arabia plate is bounded to the west by the subducting Sinai plate and the left-lateral Dead Sea transform. This complexity suggests that there are, multiple competing processes that may influence regional tectonics in northern Arabia and adjacent areas. Earthquake mechanisms provide insight into crustal kinematics and stress; however, reliable determination of earthquake source parameters can be challenging in a complex geological region, such as the continental collision zone between the Arabian and Eurasian plates. The goal of this study is to investigate spatial patterns of the crustal stress in the northern Arabian plate and surrounding area. The focal mechanisms used in this study are based on (1) first-motion polarities for earthquakes recorded by Syrian earthquake center during 2000-2011, and (2) regional moment tensors from broadband seismic data, from Turkey and Iraq. First motion focal mechanisms were assigned quality classifications based on the variation of both nodal planes. Regional moment tensor analysis can be significantly influenced by seismic velocity structure; thus, we have divided the study area into regions based on tectonic units. For each region, a specific velocity model is defined using waveform-modeling technique prior to the regional moment tensor inversion. The resulting focal mechanisms, combined with other previously published focal mechanisms for the study area, provide a basis for stress inversion analysis. The resulting deviatoric stress tensors show the spatial distribution of the maximum horizontal stress varies from NW-SE along the Dead Sea Fault to the N-S toward the east. We interpret this to reflect the eastward change from the transform to collision processes in northern Arabia. Along the Dead Sea Fault, transposition of the sigma-1 and sigma-2 to vertical and horizontal, respectively, may relate to influences from the subducted part of the Sinai plate. This change in regional stress is also consistent with extensional strains observed from GPS velocities.

An Integrated Tensorial Approach for Quantifying Porous, Fractured Rocks

NASA Astrophysics Data System (ADS)

Healy, David; Rizzo, Roberto; Harland, Sophie; Farrell, Natalie; Browning, John; Meredith, Phil; Mitchell, Tom; Bubeck, Alodie; Walker, Richard

2017-04-01

The patterns of fractures in deformed rocks are rarely uniform or random. Fracture orientations, sizes, shapes and spatial distributions often exhibit some kind of order. In detail, there may be relationships among the different fracture attributes e.g. small fractures dominated by one orientation, and larger fractures by another. These relationships are important because the mechanical (e.g. strength, anisotropy) and transport (e.g. fluids, heat) properties of rock depend on these fracture patterns and fracture attributes. Based on previously published work (Oda, Cowin, Sayers & Kachanov) this presentation describes an integrated tensorial approach to quantifying fracture networks and predicting the key properties of fractured rock: permeability and elasticity (and in turn, seismic velocities). Each of these properties can be represented as tensors, and these entities capture the essential 'directionality', or anisotropy of the property. In structural geology, we are familiar with using tensors for stress and strain, where these concepts incorporate volume averaging of many forces (in the case of the stress tensor), or many displacements (for the strain tensor), to produce more tractable and more computationally efficient quantities. It is conceptually attractive to formulate both the structure (the fracture network) and the structure-dependent properties (permeability, elasticity) in a consistent way with tensors of 2nd and 4th rank, as appropriate. Examples are provided to highlight the interdependence of the property tensors with the geometry of the fracture network. The fabric tensor (or orientation tensor of Scheidegger, Woodcock) describes the orientation distribution of fractures in the network. The crack tensor combines the fabric tensor (orientation distribution) with information about the fracture density and fracture size distribution. Changes to the fracture network, manifested in the values of the fabric and crack tensors, translate into changes in predicted permeability and elasticity (seismic velocity). Conversely, this implies that measured changes in any of the in situ properties or responses in the subsurface (e.g. permeability, seismic velocity) could be used to predict, or at least constrain, the fracture network. Explicitly linking the fracture network geometry to the permeability and elasticity (seismic velocity) through a tensorial formulation provides an exciting and efficient alternative to existing approaches.

Reynolds stress flow shear and turbulent energy transfer in reversed field pinch configuration

NASA Astrophysics Data System (ADS)

Vianello, Nicola; Spolaore, Monica; Serianni, Gianluigi; Regnoli, Giorgio; Spada, Emanuele; Antoni, Vanni; Bergsåker, Henric; Drake, James R.

2003-10-01

The role of Reynolds Stress tensor on flow generation in turbulent fluids and plasmas is still an open question and the comprehension of its behavior may assist the understanding of improved confinement scenario. It is generally believed that shear flow generation may occur by an interaction of the turbulent Reynolds stress with the shear flow. It is also generally believed that this mechanism may influence the generation of zonal flow shears. The evaluation of the complete Reynolds Stress tensor requires contemporary measurements of its electrostatic and magnetic part: this requirement is more restrictive for Reversed Field Pinch configuration where magnetic fluctuations are larger than in tokamak . A new diagnostic system which combines electrostatic and magnetic probes has been installed in the edge region of Extrap-T2R reversed field pinch. With this new probe the Reynolds stress tensor has been deduced and its radial profile has been reconstructed on a shot to shot basis exploring differen plasma conditions. These profiles have been compared with the naturally occurring velocity flow profile, in particular during Pulsed Poloidal Current Drive experiment, where a strong variation of ExB flow radial profile has been registered. The study of the temporal evolution of Reynolds stress reveals the appearance of strong localized bursts: these are considered in relation with global MHD relaxation phenomena, which naturally occur in the core of an RFP plasma sustaining its configuration.

Contemporary Crustal Deformation Within the Pamir Plateau Constrained by Geodetic Observations and Focal Mechanism Solutions

NASA Astrophysics Data System (ADS)

Pan, Zhengyang; He, Jiankun; Li, Jun

2018-04-01

We used an updated data set of 192 GPS-derived surface velocities and 393 earthquake focal mechanisms (Mw > 3.0, hypocenter depths < 30 km) to evaluate the spatial variations in the surface strain rate and crustal stress regime throughout the Pamir Plateau and its surrounding regions. The strain rate field was estimated using the spline in tension approach that solves for the surface velocity in a rectangular grid and the stress field was predicted from focal mechanism solutions using the damped regional-scale stress inversion (DRSSI) method of Hardebeck and Michael (Journal of Geophysical Research, https://doi.org/10.1029/2005jb004144, 2006). The results show that the crustal stress field around the Pamir Plateau is predominantly characterized by NNW-SSE compression and E-W extension, which is consistent with the principal orientations of the two-dimensional surface strain rate tensor. This agreement supports the notion that the Pamir and southwestern Tien Shan are uniformly strained blocks. In particular, the fan-shaped rotational pattern between {Shmax} and the strain rate from the western Pamir to the Tajik Basin shows that the counterclockwise rotation of the {Shmax} orientation is associated with vertical deformation, which is consistent with the idea of Schurr et al. (Tectonics 33(8):2014TC003576, 2014) concerning the gravitational collapse and westward extrusion of the crust in the western Pamir. We propose that such a stress-strain pattern, dominated by NNW-ESE oriented compression and E-W trending extension, originated from a combination of the northward push of the Indian continent and the southward subduction of the Tien Shan.

Nanoscale multiphase phase field approach for stress- and temperature-induced martensitic phase transformations with interfacial stresses at finite strains

NASA Astrophysics Data System (ADS)

Basak, Anup; Levitas, Valery I.

2018-04-01

A thermodynamically consistent, novel multiphase phase field approach for stress- and temperature-induced martensitic phase transformations at finite strains and with interfacial stresses has been developed. The model considers a single order parameter to describe the austenite↔martensitic transformations, and another N order parameters describing N variants and constrained to a plane in an N-dimensional order parameter space. In the free energy model coexistence of three or more phases at a single material point (multiphase junction), and deviation of each variant-variant transformation path from a straight line have been penalized. Some shortcomings of the existing models are resolved. Three different kinematic models (KMs) for the transformation deformation gradient tensors are assumed: (i) In KM-I the transformation deformation gradient tensor is a linear function of the Bain tensors for the variants. (ii) In KM-II the natural logarithms of the transformation deformation gradient is taken as a linear combination of the natural logarithm of the Bain tensors multiplied with the interpolation functions. (iii) In KM-III it is derived using the twinning equation from the crystallographic theory. The instability criteria for all the phase transformations have been derived for all the kinematic models, and their comparative study is presented. A large strain finite element procedure has been developed and used for studying the evolution of some complex microstructures in nanoscale samples under various loading conditions. Also, the stresses within variant-variant boundaries, the sample size effect, effect of penalizing the triple junctions, and twinned microstructures have been studied. The present approach can be extended for studying grain growth, solidifications, para↔ferro electric transformations, and diffusive phase transformations.

Einstein Revisited - Gravity in Curved Spacetime Without Event Horizons

NASA Astrophysics Data System (ADS)

Leiter, Darryl

2000-04-01

In terms of covariant derivatives with respect to flat background spacetimes upon which the physical curved spacetime is imposed (1), covariant conservation of energy momentum requires, via the Bianchi Identity, that the Einstein tensor be equated to the matter energy momentum tensor. However the Einstein tensor covariantly splits (2) into two tensor parts: (a) a term proportional to the gravitational stress energy momentum tensor, and (b) an anti-symmetric tensor which obeys a covariant 4-divergence identity called the Freud Identity. Hence covariant conservation of energy momentum requires, via the Freud Identity, that the Freud tensor be equal to a constant times the matter energy momentum tensor. The resultant field equations (3) agree with the Einstein equations to first order, but differ in higher orders (4) such that black holes are replaced by "red holes" i.e., dense objects collapsed inside of their photon orbits with no event horizons. (1) Rosen, N., (1963), Ann. Phys. v22, 1; (2) Rund, H., (1991), Alg. Grps. & Geom. v8, 267; (3) Yilmaz, Hl, (1992), Nuo. Cim. v107B, 946; (4) Roberstson, S., (1999),Ap.J. v515, 365.

Generalized recursion relations for correlators in the gauge-gravity correspondence.

PubMed

Raju, Suvrat

2011-03-04

We show that a generalization of the Britto-Cachazo-Feng-Witten recursion relations gives a new and efficient method of computing correlation functions of the stress tensor or conserved currents in conformal field theories with an (d+1)-dimensional anti-de Sitter space dual, for d≥4, in the limit where the bulk theory is approximated by tree-level Yang-Mills theory or gravity. In supersymmetric theories, additional correlators of operators that live in the same multiplet as a conserved current or stress tensor can be computed by these means.

Stress Energy tensor in LCFT and the Logarithmic Sugawara construction

NASA Astrophysics Data System (ADS)

Kogan, Ian I.; Nichols, Alexander

2002-01-01

We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. However they are both characterised by at least two independent parameters. We show how, by using a generalised Sugawara construction, one can calculate the logarithmic partner of T. We show that such a construction works in the c = -2 theory using the conformal dimension one primary currents which generate a logarithmic extension of the Kac-Moody algebra.

Altimetry data and the elastic stress tensor of subduction zones

NASA Technical Reports Server (NTRS)

Caputo, Michele

1987-01-01

The maximum shear stress (mss) field due to mass anomalies is estimated in the Apennines, the Kermadec-Tonga Trench, and the Rio Grande Rift areas and the results for each area are compared to observed seismicity. A maximum mss of 420 bar was calculated in the Kermadec-Tonga Trench region at a depth of 28 km. Two additional zones with more than 300 bar mss were also observed in the Kermadec-Tonga Trench study. Comparison of the calculated mss field with the observed seismicity in the Kermadec-Tonga showed two zones of well correlated activity. The Rio Grande Rift results showed a maximum mss of 700 bar occurring east of the rift and at a depth of 6 km. Recorded seismicity in the region was primarily constrained to a depth of approximately 5 km, correlating well to the results of the stress calculations. Two areas of high mss are found in the Apennine region: 120 bar at a depth of 55 km, and 149 bar at the surface. Seismic events observed in the Apennine area compare favorably with the mss field calculated, exhibiting two zones of activity. The case of loading by seamounts and icecaps are also simulated. Results for this study show that the mss reaches a maximum of about 1/3 that of the applied surface stress for both cases, and is located at a depth related to the diameter of the surface mass anomaly.

Coulomb stress change of crustal faults in Japan for 21 years, estimated from GNSS displacement

NASA Astrophysics Data System (ADS)

Nishimura, T.

2017-12-01

Coulomb stress is one of the simplest index to show how the fault is close to a brittle failure (e.g., earthquake). Many previous studies used the Coulomb stress change (ΔCFS) to evaluate whether the fault approaches failure and successfully explained an earthquake triggered by previous earthquakes and volcanic sources. Most studies use a model of a half-space medium with given rheological properties, boundary conditions, dislocation, etc. to calculate ΔCFS. However, Ueda and Takahashi (2005) proposed to calculate DCFS directly from surface displacement observed by GNSS. There are 6 independent components of stress tensor in an isotropic elastic medium. On the surface of the half-space medium, 3 components should be zero because of no traction on the surface. This means the stress change on the surface is calculated from the surface strain change using Hooke's law. Although an earthquake does not occur on surface, the stress change on the surface may approximate that at a depth of a shallow crustal earthquake (e.g., 10 km) if the source is far from the point at which we calculate the stress change. We tested it by comparing ΔCFS from the surface displacement and that from elastic fault models for past earthquakes. We first estimate a strain change with a method of Shen et al.(1996 JGR) from surface displacement and then calculate ΔCFS for a targeted focal mechanism. Although ΔCFS in the vicinity of the source fault cannot be reproduced from the surface displacement, surface displacement gives a good approximation of ΔCFS in a region 50 km away from the source if the target mechanism is a vertical strike-slip fault. It suggests that GNSS observation can give useful information on a recent change of earthquake potential. We, therefore, calculate the temporal evolution of ΔCFS on active faults in southwest Japan from April 1996 using surface displacement at GNSS stations. We used parameters for the active faults used for evaluation of strong motion by the Earthquake Research Committee. When we use 0.4 for an effective frictional coefficient, ΔCFS increased at most active faults in the Kyushu region by up to 50 KPa for 21 years. On the other hand, ΔCFS did not always increase at active faults in the Kinki region.

Transversely Isotropic Hyperelastic Constitutive Model of Short Fiber Reinforced EPDM Based on Tensor Function

NASA Astrophysics Data System (ADS)

Feng, Q. L.; Li, C.; Liao, Y. F.

2017-12-01

Short fiber reinforced EPDM is a new kind of composite material used in solid rocket motor winding and coating. It has relatively large deformation under the small stress condition, and the physical non-linear characteristic is obvious. Due to the addition of fiber in the specific direction of the rubber, the macroscopic mechanical properties are expressed as transversely isotropic properties. In order to describe the mechanical behavior under the impact and vibration, the transversely isotropic hyperelastic constitutive model based on tensor function is proposed. The symmetry of the transversely isotropic incompressible material limits the stress tensor ‘ K ’ to be characterized as a function of 5 tensor invariants and 4 scalar invariants. The third power constitutive equations of the model give 12 independent elastic constants of the transversely isotropic nonlinear elastic material. The experimental results show that the non-zero elastic constants are different in the fiber direction and at the different strain rate. Number and value of adiabatic layer and related products R & D has a reference value.

Killing approximation for vacuum and thermal stress-energy tensor in static space-times

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frolov, V.P.; Zel'nikov, A.I.

1987-05-15

The problem of the vacuum polarization of conformal massless fields in static space-times is considered. A tensor T/sub ..mu..//sub ..nu../ constructed from the curvature, the Killing vector, and their covariant derivatives is proposed which can be used to approximate the average value of the stress-energy tensor /sup ren/ in such spaces. It is shown that if (i) its trace T /sub epsilon//sup epsilon/ coincides with the trace anomaly /sup ren/, (ii) it satisfies the conservation law T/sup ..mu..//sup epsilon/ /sub ;//sub epsilon/ = 0, and (iii) it has the correct behavior under the scale transformations, then it is uniquely definedmore » up to a few arbitrary constants. These constants must be chosen to satisfy the boundary conditions. In the case of a static black hole in a vacuum these conditions single out the unique tensor T/sub ..mu..//sub ..nu../ which provides a good approximation for /sup ren/ in the Hartle-Hawking vacuum. The relation between this approach and the Page-Brown-Ottewill approach is discussed.« less

Physical stress, mass, and energy for non-relativistic matter

NASA Astrophysics Data System (ADS)

Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.

2017-06-01

For theories of relativistic matter fields there exist two possible definitions of the stress-energy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two stress-energy tensors do not necessarily coincide and it is the latter that corresponds to the Cauchy stress measured in the lab. In this note we discuss the corresponding issue for non-relativistic matter theories. We point out that while the physical non-relativistic stress, momentum, and mass currents are defined by a variation of the action at fixed torsion, the energy current does not admit such a description and is naturally defined at fixed connection. Any attempt to define an energy current at fixed torsion results in an ambiguity which cannot be resolved from the background spacetime data or conservation laws. We also provide computations of these quantities for some simple non-relativistic actions.

Stochastic Gravity: Theory and Applications.

PubMed

Hu, Bei Lok; Verdaguer, Enric

2004-01-01

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operatorvalued) stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole (enclosed in a box). We derive a fluctuation-dissipation relation between the fluctuations in the radiation and the dissipative dynamics of metric fluctuations.

Experimental Measurement of In Situ Stress

NASA Astrophysics Data System (ADS)

Tibbo, Maria; Milkereit, Bernd; Nasseri, Farzine; Schmitt, Douglas; Young, Paul

2016-04-01

The World Stress Map data is determined by stress indicators including earthquake focal mechanisms, in situ measurement in mining, oil and gas boreholes as well as the borehole cores, and geologic data. Unfortunately, these measurements are not only infrequent but sometimes infeasible, and do not provide nearly enough data points with high accuracy to correctly infer stress fields in deep mines around the world. Improvements in stress measurements of Earth's crust is fundamental to several industries such as oil and gas, mining, nuclear waste management, and enhanced geothermal systems. Quantifying the state of stress and the geophysical properties of different rock types is a major complication in geophysical monitoring of deep mines. Most stress measurement techniques involve either the boreholes or their cores, however these measurements usually only give stress along one axis, not the complete stress tensor. The goal of this project is to investigate a new method of acquiring a complete stress tensor of the in situ stress in the Earth's crust. This project is part of a comprehensive, exploration geophysical study in a deep, highly stressed mine located in Sudbury, Ontario, Canada, and focuses on two boreholes located in this mine. These boreholes are approximately 400 m long with NQ diameters and are located at depths of about 1300 - 1600 m and 1700 - 2000 m. Two borehole logging surveys were performed on both boreholes, October 2013 and July 2015, in order to perform a time-lapse analysis of the geophysical changes in the mine. These multi-parameter surveys include caliper, full waveform sonic, televiewer, chargeability (IP), and resistivity. Laboratory experiments have been performed on borehole core samples of varying geologies from each borehole. These experiments have measured the geophysical properties including elastic modulus, bulk modulus, P- and S-wave velocities, and density. The apparatus' used for this project are geophysical imaging cells capable of hydrostatic stress (σ1 = σ2 = σ3), differential stress (σ1 > σ2 = σ3), and the unique true triaxial stress (σ1 > σ2 > σ3). Velocity surveys can be acquired along all three axes, and therefore the effects of σ1,σ2,σ3 on the velocity-stress curve can be obtained. These geophysical cells are being used to reproduce the borehole P- and S-wave velocities by altering the differential stress, allowing for the unique position of determining the stress tensor. Currently, results have been obtained for differential stress (σ1 > σ2 = σ3), and true triaxial experiments will determine if σ3 is the missing factor to reproducing the borehole velocities. This project is the first to combine time - lapse borehole logging data and experimental laboratory data to infer a complete stress tensor.

Mechanical signals in plant development: a new method for single cell studies

NASA Technical Reports Server (NTRS)

Lynch, T. M.; Lintilhac, P. M.

1997-01-01

Cell division, which is critical to plant development and morphology, requires the orchestration of hundreds of intracellular processes. In the end, however, cells must make critical decisions, based on a discrete set of mechanical signals such as stress, strain, and shear, to divide in such a way that they will survive the mechanical loads generated by turgor pressure and cell enlargement within the growing tissues. Here we report on a method whereby tobacco protoplasts swirled into a 1.5% agarose entrapment medium will survive and divide. The application of a controlled mechanical load to agarose blocks containing protoplasts orients the primary division plane of the embedded cells. Photoelastic analysis of the agarose entrapment medium can identify the lines of principal stress within the agarose, confirming the hypothesis that cells divide either parallel or perpendicular to the principal stress tensors. The coincidence between the orientation of the new division wall and the orientation of the principal stress tensors suggests that the perception of mechanical stress is a characteristic of individual plant cells. The ability of a cell to determine a shear-free orientation for a new partition wall may be related to the applied load through the deformation of the matrix material. In an isotropic matrix a uniaxial load will produce a rotationally symmetric strain field, which will define a shear-free plane. Where high stress intensities combine with the loading geometry to produce multiaxial loads there will be no axis of rotational symmetry and hence no shear free plane. This suggests that two mechanisms may be orienting the division plane, one a mechanism that works in rotationally symmetrical fields, yielding divisions perpendicular to the compressive tensor, parallel to the long axis of the cell, and one in asymmetric fields, yielding divisions parallel to the short axis of the cell and the compressive tensor.

A thickness-weighted average perspective of force balance in an idealized circumpolar current

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ringler, Todd Darwin; Saenz, Juan Antonio; Wolfram, Jr., Phillip Justin

The exact, three-dimensional thickness-weighted averaged (TWA) Boussinesq equations are used to diagnose eddy-mean flow interaction in an idealized circumpolar current (ICC). The force exerted by mesoscale eddies on the TWA velocity is expressed as the divergence of the Eliassen-Palm flux tensor. Consistent with previous findings, the analysis indicates that the dynamically relevant definition of the ocean surface layer is comprised of the set of buoyancy coordinates that ever reside at the ocean surface at a given horizontal position. The surface layer is found to be a physically distinct object with a diabatic- and force-balance that is largely isolated from themore » underlying adiabatic region in the interior. Within the ICC surface layer, the TWA meridional velocity is southward/northward in the top/bottom half, and has a value near zero at the bottom. In the top half of the surface layer, the zonal forces due to wind stress and meridional advection of potential vorticity act to accelerate the TWA zonal velocity; equilibrium is obtained by eddies decelerating the zonal flow via a downward flux of eastward momentum that increases with depth. In the bottom half of the surface layer, the accelerating force of the wind stress is balanced by the eddy force and meridional advection of potential vorticity. The bottom of the surface layer coincides with the location where the zonal eddy force, meridional advection of potential vorticity and zonal wind stress force are all zero. The net meridional transport, S f, within the surface layer is a small residual of its southward and northward TWA meridional flows. Furthermore, the mean meridional gradient of surface-layer buoyancy is advected by S f to balance the surface buoyancy fluxs.« less

A thickness-weighted average perspective of force balance in an idealized circumpolar current

DOE PAGES

Ringler, Todd Darwin; Saenz, Juan Antonio; Wolfram, Jr., Phillip Justin; ...

2016-11-22

The exact, three-dimensional thickness-weighted averaged (TWA) Boussinesq equations are used to diagnose eddy-mean flow interaction in an idealized circumpolar current (ICC). The force exerted by mesoscale eddies on the TWA velocity is expressed as the divergence of the Eliassen-Palm flux tensor. Consistent with previous findings, the analysis indicates that the dynamically relevant definition of the ocean surface layer is comprised of the set of buoyancy coordinates that ever reside at the ocean surface at a given horizontal position. The surface layer is found to be a physically distinct object with a diabatic- and force-balance that is largely isolated from themore » underlying adiabatic region in the interior. Within the ICC surface layer, the TWA meridional velocity is southward/northward in the top/bottom half, and has a value near zero at the bottom. In the top half of the surface layer, the zonal forces due to wind stress and meridional advection of potential vorticity act to accelerate the TWA zonal velocity; equilibrium is obtained by eddies decelerating the zonal flow via a downward flux of eastward momentum that increases with depth. In the bottom half of the surface layer, the accelerating force of the wind stress is balanced by the eddy force and meridional advection of potential vorticity. The bottom of the surface layer coincides with the location where the zonal eddy force, meridional advection of potential vorticity and zonal wind stress force are all zero. The net meridional transport, S f, within the surface layer is a small residual of its southward and northward TWA meridional flows. Furthermore, the mean meridional gradient of surface-layer buoyancy is advected by S f to balance the surface buoyancy fluxs.« less

Nonzero Ideal Gas Contribution to the Surface Tension of Water.

PubMed

Sega, Marcello; Fábián, Balázs; Jedlovszky, Pál

2017-06-15

Surface tension, the tendency of fluid interfaces to behave elastically and minimize their surface, is routinely calculated as the difference between the lateral and normal components of the pressure or, invoking isotropy in momentum space, of the virial tensor. Here we show that the anisotropy of the kinetic energy tensor close to a liquid-vapor interface can be responsible for a large part of its surface tension (about 15% for water, independent from temperature).

From orientation to magnitudes in paleostress determinations using fault slip data

NASA Astrophysics Data System (ADS)

Angelier, Jacques

Determinations of reduced stress tensors using fault slip data yield the orientation of principal stress axes and the ratio Φ of the differences between principal stress magnitudes. The use of rupture and friction laws allows determination of the two remaining unknowns, that is, the reconstruction of the complete stress tensor. Taking into account the depth of overburden brings an additional constraint. The method is applied and discussed in the case of the Hoover Dam site (western U.S.A.), where large data sets and rock mechanics information are available. Differences between intact sample and rock mass properties account for apparent disagreements between paleostress levels determined in similar tectonic environments. Pore pressure plays an important role; where information about pore pressure is absent, zero and hydrostatic pore pressure cases should be considered as limits.

Complex brittle deformation pattern along the Southern Patagonian Andes (Argentina)

NASA Astrophysics Data System (ADS)

Barberón, Vanesa; Sue, Christian; Ronda, Gonzalo; Ghiglione, Matías

2016-04-01

The Southern Patagonian Andes is located in the southern extreme of the Pacific subduction zone, where the Antartic oceanic plate sinks underneath South America. The history of the area begins with compression during Paleozoic, Jurassic extension associated to the rift and opening of the South Atlantic Ocean, then a sag stage in the Lower Cretaceous followed by a foreland phase as a result of plate tectonics (Ghiglione et al., 2016). The kinematic study is concentrated in the Argentinean foothills, between 46°40' and 48° SL. We measured around 800 fault planes and their striaes with the sense of movement in order to characterize the stress field. The software used to make the stress inversion were Tensor (Delvaux, 2011) and Multiple Inverse Method MIM (Yamaji et al., 2011). The stress field map was built with the results of the MIM. We present new data from 48 sites located in the northern sector of the Southern Patagonian Andes. The measurements were made in several rocks from Paleozoic to Lower Cretaceous, even though most were taken in pyroclastic jurassic rocks from El Quemado Complex. Paleostress tensors obtained are mostly strike-slip, although a 25% is normal and there are a few compresional. The pattern of faults found is complex. In some sites the tensor can be locally linked to satellite images and observations from the field or be related to a major thrust front. There is no clear correlation between the age and/or lithology with the tensor since the youngest rocks measured are Lower Cretaceous. Probably there are several generations of family faults connected to different and recent tectonic phases then the paleostress tensors might correspond to the latest tectonic events.

Averaging problem in general relativity, macroscopic gravity and using Einstein's equations in cosmology.

NASA Astrophysics Data System (ADS)

Zalaletdinov, R. M.

1998-04-01

The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the geometry of macroscopic space-time, which follows from averaging Cartan's structure equations, is described and the correlation tensors present in the theory are discussed. The macroscopic field equations (averaged Einstein's equations) derived in the framework of the approach are presented and their structure is analysed. The correspondence principle for macroscopic gravity is formulated and a definition of the stress-energy tensor for the macroscopic gravitational field is proposed. It is shown that the physical meaning of using Einstein's equations with a hydrodynamic stress-energy tensor in looking for cosmological models means neglecting all gravitational field correlations. The system of macroscopic gravity equations to be solved when the correlations are taken into consideration is given and described.

Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

DOE PAGES

Ling, Julia; Kurzawski, Andrew; Templeton, Jeremy

2016-10-18

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property.more » Furthermore, the Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.« less

Vector and tensor contributions to the curvature perturbation at second order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carrilho, Pedro; Malik, Karim A., E-mail: p.gregoriocarrilho@qmul.ac.uk, E-mail: k.malik@qmul.ac.uk

2016-02-01

We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from different splits of the spatial metric, and compare the expressions. The results are valid at all scales and include all contributions from scalar, vector and tensor perturbations, as well as anisotropic stress, with all our results written purely in terms of gauge invariant quantities. Taking the large-scale approximation, we find that a conserved quantity exists only if, in addition to the non-adiabatic pressure, the transverse traceless part ofmore » the anisotropic stress tensor is also negligible. We also find that the version of the gauge invariant curvature perturbation which is exactly conserved is the one defined with the determinant of the spatial part of the inverse metric.« less

Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ling, Julia; Kurzawski, Andrew; Templeton, Jeremy

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property.more » Furthermore, the Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.« less

Instability of enclosed horizons

NASA Astrophysics Data System (ADS)

Kay, Bernard S.

2015-03-01

We point out that there are solutions to the scalar wave equation on dimensional Minkowski space with finite energy tails which, if they reflect off a uniformly accelerated mirror due to (say) Dirichlet boundary conditions on it, develop an infinite stress-energy tensor on the mirror's Rindler horizon. We also show that, in the presence of an image mirror in the opposite Rindler wedge, suitable compactly supported arbitrarily small initial data on a suitable initial surface will develop an arbitrarily large stress-energy scalar near where the two horizons cross. Also, while there is a regular Hartle-Hawking-Israel-like state for the quantum theory between these two mirrors, there are coherent states built on it for which there are similar singularities in the expectation value of the renormalized stress-energy tensor. We conjecture that in other situations with analogous enclosed horizons such as a (maximally extended) Schwarzschild black hole in equilibrium in a (stationary spherical) box or the (maximally extended) Schwarzschild-AdS spacetime, there will be similar stress-energy singularities and almost-singularities—leading to instability of the horizons when gravity is switched on and matter and gravity perturbations are allowed for. All this suggests it is incorrect to picture a black hole in equilibrium in a box or a Schwarzschild-AdS black hole as extending beyond the past and future horizons of a single Schwarzschild (/Schwarzschild-AdS) wedge. It would thus provide new evidence for 't Hooft's brick wall model while seeming to invalidate the picture in Maldacena's ` Eternal black holes in AdS'. It would thereby also support the validity of the author's matter-gravity entanglement hypothesis and of the paper ` Brick walls and AdS/CFT' by the author and Ortíz.

New Views on Dark Matter from Emergent Gravity

NASA Astrophysics Data System (ADS)

Sun, Sichun; Zhang, Yun-Long

2018-01-01

We discuss a scenario that apparent dark matter comes from the induced gravity in the (3+1)- dimensional spacetime, which can be embedded into one higher dimensional flat spacetime. The stress tensor of dark energy and dark matter is identified with the Brown-York stress tensor on the hypersurface, and we find an interesting constraint relation between the dark matter and dark energy density parameter and baryonic density parameter. Our approach may show a new understanding for Verlinde's emergent gravity from higher dimensions. We also comment on some phenomenological implications, including gravitational wave solutions and MOND limit.

The nonlocal elastomagnetoelectrostatics of disordered micropolar media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kabychenkov, A. F.; Lisiovskii, F. V., E-mail: lisf@rambler.ru

The interactions of electric, magnetic, and elastic subsystems in nonlinear disordered micropolar media that possess a bending–torsion tensor and an nonsymmetric strain tensor have been studied in the framework of phenomenological elastomagnetoelectrostatics. A system of nonlinear equations for determining the ground state of these media has been obtained by the variational method. It is shown that nonuniform external and internal rotations not only create elastic stresses, but also generate additional electric and magnetic fields, while nonuniform elastic stresses and external fields induce internal rotations. The nonlocal character of the micropolar media significantly influences elementary excitations and nonlinear dynamic processes.

Anisotropy of the Reynolds stress tensor in the wakes of wind turbine arrays in Cartesian arrangements with counter-rotating rotors

NASA Astrophysics Data System (ADS)

Hamilton, Nicholas; Cal, Raúl Bayoán

2015-01-01

A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear stress - v w ¯ . The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds stress anisotropy tensor (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy tensor are composed with the eigenvalues yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates trends in the streamwise coordinate following the rotors, especially trailing the top-tip of the rotor and below the hub. Direction of rotation of rotor blades is shown by the orientation of characteristic spheroids according to principle axes. In the inflows of exit row turbines, the normalized Reynolds stress anisotropy tensor shows cumulative effects of the upstream turbines, tending toward prolate shapes for uniform rotational sense, oblate spheroids for streamwise organization of rotational senses, and a mixture of characteristic shapes when the rotation varies by row. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean mechanical energy equation indicate correlation between the degree of anisotropy and the regions of the wind turbine wakes where turbulence kinetic energy is produced. The flux of kinetic energy into the momentum-deficit area of the wake from above the canopy is associated with prolate characteristic spheroids. Flux upward into the wake from below the rotor area is associated with oblate characteristic spheroids. Turbulence in the region of the flow directly following the nacelle of the wind turbines demonstrates greater isotropy than regions following the rotor blades. The power and power coefficients for wind turbines indicate that flow structures on the order of magnitude of the spanwise turbine spacing that increase turbine efficiency depending on particular array configuration.

Trapping of a micro-bubble by non-paraxial Gaussian beam: computation using the FDTD method.

PubMed

Sung, Seung-Yong; Lee, Yong-Gu

2008-03-03

Optical forces on a micro-bubble were computed using the Finite Difference Time Domain method. Non-paraxial Gaussian beam equation was used to represent the incident laser with high numerical aperture, common in optical tweezers. The electromagnetic field distribution around a micro-bubble was computed using FDTD method and the electromagnetic stress tensor on the surface of a micro-bubble was used to compute the optical forces. By the analysis of the computational results, interesting relations between the radius of the circular trapping ring and the corresponding stability of the trap were found.

Crustal stress across the northern Arabian plate and the relationship with the plate boundary forces

NASA Astrophysics Data System (ADS)

Yassminh, Rayan

The region encompassing the collision of northern Arabia with Eurasia is a tectonically heterogeneous region of distributed deformation. The northern Arabia plate is bounded to the west by the subducting Sinai plate and the left-lateral Dead Sea transform. This complexity suggests that there are multiple competing processes that may influence regional tectonics in northern Arabia and adjacent areas. Earthquake mechanisms provide insight into crustal kinematics and stress; however, reliable determination of earthquake source parameters can be challenging in a complex geological region, such as the continental collision zone between the Arabian and Eurasian plates. The goal of this study is to investigate spatial patterns of the crustal stress in the northern Arabian plate and surrounding area. The focal mechanisms used in this study are based on (1) first-motion polarities for earthquakes recorded by Syrian earthquake center during 2000-2011, and (2) regional moment tensors from broadband seismic data, from Turkey and Iraq. First motion focal mechanisms were assigned quality classifications based on the variation of both nodal planes. Regional moment tensor analysis can be significantly influenced by seismic velocity structure; thus, we have divided the study area into regions based on tectonic units. For each region, the velocity model is described using a waveform-modeling technique prior to the regional moment tensor inversion. The resulting focal mechanisms, combined with other previously published focal mechanisms for the study area, provide a basis for stress inversion analysis. The resulting deviatoric stress tensors show the spatial distribution of the maximum horizontal stress varies from NW-SE along the Dead Sea Fault to the N-S toward the east. We interpret this to reflect the eastward change from the transform to collision processes in northern Arabia. Along the Dead Sea Fault, transposition of the sigma-1 and sigma-2 to vertical and horizontal, respectively, may relate to influences from the subducted part of the Sinai plate. This change in regional stress is also consistent with extensional strains observed from GPS velocities.

Spatial and Temporal Variations in the Moment Tensor Solutions of the 2008 Wenchuan Earthquake Aftershocks and Their Tectonic Implications

NASA Astrophysics Data System (ADS)

Lin, X.; Dreger, D.; Ge, H.; Xu, P.; Wu, M.; Chiang, A.; Zhao, G.; Yuan, H.

2018-03-01

Following the mainshock of the 2008 M8 Wenchuan Earthquake, there were more than 300 ML ≥ 4.0 aftershocks that occurred between 12 May 2008 and 8 September 2010. We analyzed the broadband waveforms for these events and found 160 events with sufficient signal-to-noise levels to invert for seismic moment tensors. Considering the length of the activated fault and the distances to the recording stations, four velocity models were employed to account for variability in crustal structure. The moment tensor solutions show considerable variations with a mixture of mainly reverse and strike-slip mechanisms and a small number of normal events and ambiguous events. We analyzed the spatial and temporal distribution of the aftershocks and their mechanism types to characterize the structure and the deformation occurring in the Longmen Shan fold and thrust belt. Our results suggest that the stress is very complex at the Longmen Shan fault zone. The moment tensors have both a spatial segmentation with two major categories of the moment tensor of thrust and strike slip; and a temporal pattern that the majority of the aftershocks gradually migrated to thrust-type events. The variability of aftershock mechanisms is a strong indication of significant tectonic release and stress reorganization that activated numerous small faults in the system.

Seismic moment tensor for anisotropic media: implication for Non-double-couple earthquakes

NASA Astrophysics Data System (ADS)

Cai, X.; Chen, X.; Chen, Y.; Cai, M.

2008-12-01

It is often found that the inversion results of seismic moment tensor from real seismic recorded data show the trace of seismic moment tensor M is not zero, a phenomenon called non-double-couple earthquake sources mechanism. Recently we have derived the analytical expressions of M in transversely isotropic media with the titled axis of symmetry and the results shows even only pure shear-motion of fault can lead to the implosive components determined by several combined anisotropic elastic constants. Many non-double-couple earthquakes from observations often appear in volcanic and geothermal areas (Julian, 1998), where there exist a mount of stress-aligned fluid-saturated parallel vertical micro-cracks identical to transversely isotropic media (Crampin, 2008), this stress-aligned crack will modify the seismic moment tensor. In another word, non-double-couple earthquakes don't mean to have a seismic failure movement perpendicular to the fault plane, while traditional research of seismic moment tensor focus on the case of isotropy, which cannot provide correct interpretation of seismic source mechanism. Reference: Julian, B.R., Miller, A.D. and Foulger, G.R., 1998. Non-double-couple earthquakes,1. Theory, Rev. Geophys., 36, 525¨C549. Crampin,S., Peacock,S., 2008, A review of the current understanding of seismic shear-wave splitting in the Earth's crust and common fallacies in interpretation, wave motion, 45,675-722

Complete stress tensor determination by microearthquake analysis

NASA Astrophysics Data System (ADS)

Slunga, R.

2010-12-01

Jones 1984 found that half of the shallow strike-slip EQ in California had at least one M>2 foreshock. By the Gutenberg law this means at least 3-20 M>0 (low b-value 0.4-0.8). deformations within the crust. This was confirmed by observations in Iceland after 1990 when anew seismic network in Iceland operated by IMO started. Like the Parkfield project in California the SIL network in Iceland was established in an area predicted (Einarsson et al 1981, Stefansson and Halldorsson 1988) to be struck by major EQs within decades of years. The area of main interest have a detection threshold of M=0. A physical approach was chosen to the earthquake warning problem (Stefansson et al 1993) and therefore all microearthquakes were analyzed for FPS by the spectral amplitude method (Slunga 1981). As the shear slip is caused by the in situ stress it is logical to investigate what bounds the FPS puts on the stress tensor. McKenzie 1969 assumed that the earthquake takes place in a crust containing only one fracture, the fault plane. He found that in s uch a case only very weak constraints could be put on the stress. This was widely accepted t o be valid also for microearthquakes in the real crust and lead to methods (Angelier 1978, G ephart and Forsythe 1984 etc) to put four constraints on the stress tensor by assuming that the same stress tensor is causing the slip on four or more different fractures. Another and more realistic approach is to assume that the crust have frequent fractures with almost all orientations. In such a case one can rely on Coulomb's failure criterion for isotropic mat erial (gives four constraints) instead of the weaker Bolt's criterion (giving only one const raint). One obvious fifth constraint is to require the vertical stress to equal the lithosta tic pressure. A sixth constraint is achieved by requiring that the deviatoric elastic energy is minimized. The water pressure is also needed for the fourth constraint by Coulomb (CFS=0 ). It can be related to the depth based on the assumptions of a fractured crust, widely vary ing stress field, and a general closeness to instability as found by stress measurements (Jamison and Cook 1976). Wheather this approach is working or not is best answered by applying it to real data. This was provided by the IMO network in Iceland. Along Southern Iceland Seismic Zone (SISZ) more than 200,000 microearthquakes and a few M 5 EQs and 2 M=6.6 EQs have been recorded. The results will be presented it is obvious that the use of the stresses determined from the microearthquake recordings may significa ntly improve earthquake warnings and will make it possible to use the absolute C FS method for more deterministic predictions. Note that the microearthquake meth od only shows the part of the stress field that has caused slip. Volumes with st able stress will not show up. However stress measurements (Brown and Hoek 1978, Slunga 1988) have shown that the crustal stresses in general are close to instabi lity and microearthquake source analysis has shown that a large number of differ ent fractures become unstable within longer time windows. This may explain the e xcellent results given by the Icelandic tests of the absolute stress tensor fiel d as given by the microearthquakes. However I prefer to call this stress apparen t.

Moment tensor inversion of ground motion from mining-induced earthquakes, Trail Mountain, Utah

USGS Publications Warehouse

Fletcher, Joe B.; McGarr, A.

2005-01-01

A seismic network was operated in the vicinity of the Trail Mountain mine, central Utah, from the summer of 2000 to the spring of 2001 to investigate the seismic hazard to a local dam from mining-induced events that we expect to be triggered by future coal mining in this area. In support of efforts to develop groundmotion prediction relations for this situation, we inverted ground-motion recordings for six mining-induced events to determine seismic moment tensors and then to estimate moment magnitudes M for comparison with the network coda magnitudes Mc. Six components of the tensor were determined, for an assumed point source, following the inversion method of McGarr (1992a), which uses key measurements of amplitude from obvious features of the displacement waveforms. When the resulting moment tensors were decomposed into implosive and deviatoric components, we found that four of the six events showed a substantial volume reduction, presumably due to coseismic closure of the adjacent mine openings. For these four events, the volume reduction ranges from 27% to 55% of the shear component (fault area times average slip). Radiated seismic energy, computed from attenuation-corrected body-wave spectra, ranged from 2.4 ?? 105 to 2.4 ?? 106 J for events with M from 1.3 to 1.8, yielding apparent stresses from 0.02 to 0.06 MPa. The energy released for each event, approximated as the product of volume reduction and overburden stress, when compared with the corresponding seismic energies, revealed seismic efficiencies ranging from 0.5% to 7%. The low apparent stresses are consistent with the shallow focal depths of 0.2 to 0.6 km and rupture in a low stress/low strength regime compared with typical earthquake source regions at midcrustal depths.

Symmetry classes of the anisotropy tensors of quasielastic materials and a generalized Kelvin approach

NASA Astrophysics Data System (ADS)

Ostrosablin, N. I.

2017-05-01

The anisotropy matrices (tensors) of quasielastic (Cauchy-elastic) materials were obtained for all classes of crystallographic symmetries in explicit form. The fourth-rank anisotropy tensors of such materials do not have the main symmetry, in which case the anisotropy matrix is not symmetric. As a result of introducing various bases in the space of symmetric stress and strain tensors, the linear relationship between stresses and strains is represented in invariant form similar to the form in which generalized Hooke's law is written for the case of anisotropic hyperelastic materials and contains six positive Kelvin eigen moduli. It is shown that the introduction of modified rotation-induced deformation in the strain space can cause a transition to the symmetric anisotropy matrix observed in the case of hyperelasticity. For the case of transverse isotropy, there are examples of determination of the Kelvin eigen moduli and eigen bases and the rotation matrix in the strain space. It is shown that there is a possibility of existence of quasielastic media with a skew-symmetric anisotropy matrix with no symmetric part. Some techniques for the experimental testing of the quasielasticity model are proposed.

What Is Better Than Coulomb Failure Stress? A Ranking of Scalar Static Stress Triggering Mechanisms from 105 Mainshock-Aftershock Pairs

NASA Astrophysics Data System (ADS)

Meade, Brendan J.; DeVries, Phoebe M. R.; Faller, Jeremy; Viegas, Fernanda; Wattenberg, Martin

2017-11-01

Aftershocks may be triggered by the stresses generated by preceding mainshocks. The temporal frequency and maximum size of aftershocks are well described by the empirical Omori and Bath laws, but spatial patterns are more difficult to forecast. Coulomb failure stress is perhaps the most common criterion invoked to explain spatial distributions of aftershocks. Here we consider the spatial relationship between patterns of aftershocks and a comprehensive list of 38 static elastic scalar metrics of stress (including stress tensor invariants, maximum shear stress, and Coulomb failure stress) from 213 coseismic slip distributions worldwide. The rates of true-positive and false-positive classification of regions with and without aftershocks are assessed with receiver operating characteristic analysis. We infer that the stress metrics that are most consistent with observed aftershock locations are maximum shear stress and the magnitude of the second and third invariants of the stress tensor. These metrics are significantly better than random assignment at a significance level of 0.005 in over 80% of the slip distributions. In contrast, the widely used Coulomb failure stress criterion is distinguishable from random assignment in only 51-64% of the slip distributions. These results suggest that a number of alternative scalar metrics are better predictors of aftershock locations than classic Coulomb failure stress change.

The Topology of Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

1997-01-01

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Micromechanical analysis of volumetric growth in the context of open systems thermodynamics and configurational mechanics. Application to tumor growth

NASA Astrophysics Data System (ADS)

Ganghoffer, J. F.; Boubaker, M. B.

2017-03-01

We adopt in this paper the physically and micromechanically motivated point of view that growth (resp. resorption) occurs as the expansion (resp. contraction) of initially small tissue elements distributed within a host surrounding matrix, due to the interfacial motion of their boundary. The interface motion is controlled by the availability of nutrients and mechanical driving forces resulting from the internal stresses that built in during the growth. A general extremum principle of the zero potential for open systems witnessing a change of their mass due to the diffusion of nutrients is constructed, considering the framework of open systems thermodynamics. We postulate that the shape of the tissue element evolves in such a way as to minimize the zero potential among all possible admissible shapes of the growing tissue elements. The resulting driving force for the motion of the interface sets a surface growth models at the scale of the growing tissue elements, and is conjugated to a driving force identified as the interfacial jump of the normal component of an energy momentum tensor, in line with Hadamard's structure theorem. The balance laws associated with volumetric growth at the mesoscopic level result as the averaging of surface growth mechanisms occurring at the microscopic scale of the growing tissue elements. The average kinematics has been formulated in terms of the effective growth velocity gradient and elastic rate of deformation tensor, both functions of time. This formalism is exemplified by the simulation of the avascular growth of multicell spheroids in the presence of diffusion of nutrients, showing the respective influence of mechanical and chemical driving forces in relation to generation of internal stresses.

The mathematical formulation of a generalized Hooke's law for blood vessels.

PubMed

Zhang, Wei; Wang, Chong; Kassab, Ghassan S

2007-08-01

It is well known that the stress-strain relationship of blood vessels is highly nonlinear. To linearize the relationship, the Hencky strain tensor is generalized to a logarithmic-exponential (log-exp) strain tensor to absorb the nonlinearity. A quadratic nominal strain potential is proposed to derive the second Piola-Kirchhoff stresses by differentiating the potential with respect to the log-exp strains. The resulting constitutive equation is a generalized Hooke's law. Ten material constants are needed for the three-dimensional orthotropic model. The nondimensional constant used in the log-exp strain definition is interpreted as a nonlinearity parameter. The other nine constants are the elastic moduli with respect to the log-exp strains. In this paper, the proposed linear stress-strain relation is shown to represent the pseudoelastic Fung model very well.

Investigation of low-speed turbulent separated flow around airfoils

NASA Technical Reports Server (NTRS)

Wadcock, Alan J.

1987-01-01

Described is a low-speed wind tunnel experiment to measure the flowfield around a two-dimensional airfoil operating close to maximum lift. Boundary layer separation occurs on the upper surface at x/c=0.85. A three-component laser velocimeter, coupled with a computer-controlled data acquisition system, was used to obtain three orthogonal mean velocity components and three components of the Reynolds stress tensor in both the boundary layer and wake of the airfoil. Pressure distributions on the airfoil, skin friction distribution on the upper surface of the airfoil, and integral properties of the airfoil boudary layer are also documented. In addition to these near-field flow properties, static pressure distributions, both upstream and downstream from the airfoil and on the walls of the wind tunnel, are also presented.

ON THE DECOMPOSITION OF STRESS AND STRAIN TENSORS INTO SPHERICAL AND DEVIATORIC PARTS

PubMed Central

Augusti, G.; Martin, J. B.; Prager, W.

1969-01-01

It is well known that Hooke's law for a linearly elastic, isotropic solid may be written in the form of two relations that involve only the spherical or only the deviatoric parts of the tensors of stress and strain. The example of the linearly elastic, transversely isotropic solid is used to show that this decomposition is not, in general, feasible for linearly elastic, anisotropic solids. The discussion is extended to a large class of work-hardening rigid, plastic solids, and it is shown that the considered decomposition can only be achieved for the incompressible solids of this class. PMID:16591754

Analytical Summary. Part 1. The Physical Properties of STS under Triaxial Stress

DTIC Science & Technology

1946-06-01

between Octahedral Shear Stress and Octahedral Shear Strain for Zero Mean Hydrostatic Tension. Data for SIS of 115000 (lb)/(in)2 Tensile Strength. Figure (5...the specimen and the twist by the equation a4• S The tensors I + VAr and (I + VAr)-1 have the matrices Ii 0 0 0 00 0 i O and 0 1 0 0 s 1 jO- si The...given in terms of s by the equations = - + V. + ’s + ___ Sis + + =. 2 ’ = - i + i+ 1s2 is 44 e/ l+ 44S2 The rate of strain tensor X has the components

Thin films structural properties: results of the full-atomistic supercomputer simulation

NASA Astrophysics Data System (ADS)

Grigoriev, F. V.; Sulimov, V. B.; Tikhonravov, A. V.

2017-12-01

The previously developed full-atomistic approach to the thin film growth simulation is applied for the investigation of the dependence of silicon dioxide films properties on deposition conditions. It is shown that the surface roughness and porosity are essentially reduced with the growth of energy of deposited silicon atoms. The growth of energy from 0.1 eV to 10 eV results in the increase of the film density for 0.2 - 0.4 g/cm3 and of the refractive index for 0.04-0.08. The compressive stress in films structures is observed for all deposition conditions. Absolute values of the stress tensor components increase with the growth of e energy of deposited atoms. The increase of the substrate temperature results in smoothing of the density profiles of the deposited films.

Complex conductivity of organic-rich shales

NASA Astrophysics Data System (ADS)

Woodruff, W. F.; Revil, A.; Torres-Verdin, C.

2013-12-01

We can accurately determine the intrinsic anisotropy and material properties in the laboratory, providing empirical evidence of transverse isotropy and the polarization of the organic and metallic fractions in saturated and unsaturated shales. We develop two distinct approaches to obtain the complex conductivity tensor from spectral induced polarization (SIP) measurements. Experimental results indicate clear anisotropy, and characterize the effects of thermal maturation, TOC, and pyrite, aiding in the calibration and interpretation of geophysical data. SIP is a non-intrusive measurement, sensitive to the surface conductance of mineral grains, frequency-dependent polarization of the electrical double layer, and bulk conductivity of the pore water. The in-phase and quadrature components depend upon parameters of principal importance in unconventional shale formation evaluation (e.g., the distribution of pore throat sizes, formation factor, permeability, salinity and cation exchange capacity (CEC), fluid saturation and wettability). In addition to the contribution of the electrical double layer of non-conducting minerals to surface conductivity, we have observed a clear relaxation associated with kerogen pyrolysis, pyrite distribution, and evidence that the CEC of the kerogen fraction may also contribute, depending on thermal maturation history. We utilize a recent model for anisotropic complex conductivity, and rigorous experimental protocols to quantify the role of kerogen and pyrolysis on surface and quadrature conductivity in mudrocks. The complex conductivity tensor σ* describes the directional dependence of electrical conduction in a porous medium, and accounts for both conduction and polarization. The complex-valued tensor components are given as σ*ij , where σ'ij represents in-phase and σ"ij denotes quadrature conductivities. The directional dependence of the complex conductivity tensor is relegated to the textural properties of the material. The components of the formation factor and connectivity (tortuosity) tensors Fij and Tij (affecting the bulk and surface conductivity, respectively) are correlated as Fij=TijΦ. Both conductivity and connectivity tensors share the same eigenvectors; the anisotropy ratio is equivalent in TI media. At high pore water salinity, surface and quadrature conductivity share the same bulk tortuosity; when surface conductivity dominates (low salinity), conductivity is controlled by the surface conductance, and the tortuosity of electrical current along mineral surfaces usually higher than that of the pore water. We developed two distinct SIP measurement protocols to obtain the tensor: (1) azimuthal sampling and inversion of phasor potentials through the full-field solution of the Laplace equation; (2) direct measurement of complex conductivity eigenvalues by polarized, single-component stimulus current. Experiments also include unsaturated and saturated measurements with three brines of known salinity and pH, at log-distributed frequencies ranging 1 mHz to 45 kHz. Both azimuthal spectra and eigenvalue spectra validate the theoretical model and illustrate the effectiveness of the protocols themselves. We obtain the textural tensors and invert key parameters including Archie exponents and CEC, and characterize the relaxation phenomena associated with kerogen content and maturity for multiphase fluid systems.

Constitutive equations of a tensorial model for strain-induced damage of metals based on three invariants

NASA Astrophysics Data System (ADS)

Tutyshkin, Nikolai D.; Lofink, Paul; Müller, Wolfgang H.; Wille, Ralf; Stahn, Oliver

2017-01-01

On the basis of the physical concepts of void formation, nucleation, and growth, generalized constitutive equations are formulated for a tensorial model of plastic damage in metals based on three invariants. The multiplicative decomposition of the metric transformation tensor and a thermodynamically consistent formulation of constitutive relations leads to a symmetric second-order damage tensor with a clear physical meaning. Its first invariant determines the damage related to plastic dilatation of the material due to growth of the voids. The second invariant of the deviatoric damage tensor is related to the change in void shape. The third invariant of the deviatoric tensor describes the impact of the stress state on damage (Lode angle), including the effect of rotating the principal axes of the stress tensor (Lode angle change). The introduction of three measures with related physical meaning allows for the description of kinetic processes of strain-induced damage with an equivalent parameter in a three-dimensional vector space, including the critical condition of ductile failure. Calculations were performed by using experimentally determined material functions for plastic dilatation and deviatoric strain at the mesoscale, as well as three-dimensional graphs for plastic damage of steel DC01. The constitutive parameter was determined from tests in tension, compression, and shear by using scanning electron microscopy, which allowed to vary the Lode angle over the full range of its values [InlineEquation not available: see fulltext.]. In order to construct the three-dimensional plastic damage curve for a range of triaxiality parameters -1 ≤ ST ≤ 1 and of Lode angles [InlineEquation not available: see fulltext.], we used our own, as well as systematized published experimental data. A comparison of calculations shows a significant effect of the third invariant (Lode angle) on equivalent damage. The measure of plastic damage, based on three invariants, can be useful for assessing the quality of metal mesostructure produced during metal forming processes. In many processes of metal sheet forming the material experiences, a non-proportional loading accompanied by rotating the principal axes of the stress tensor and a corresponding change of Lode angle.

Mechanical behaviour of the human atria.

PubMed

Bellini, Chiara; Di Martino, Elena S; Federico, Salvatore

2013-07-01

This work was aimed at providing a local mechanical characterisation of tissues from the healthy human atria. Thirty-two tissue specimens were harvested from nine adult subjects whose death was not directly related to cardiovascular diseases. Tissues were kept in Tyrode's solution and tested using a planar biaxial device. Results showed that tissues from healthy human atria undergo large deformations under in-plane distributed tensions roughly corresponding to an in vivo pressure of 15 mmHg. The material was modelled as hyperelastic and a Fung-type elastic strain energy potential was chosen. This class of potentials is based on a function of a quadratic form in the components of the Green-Lagrange strain tensor, and it has been previously proved that the fourth-order tensor of this quadratic form is proportional to the linear elasticity tensor of the linearised theory. This has three important consequences: (i) the coefficients in Fung-type potentials have a precise physical meaning; (ii) whenever a microstructural description for the linear elasticity tensor is available, this is automatically inherited by the Fung-type potential; (iii) because of the presence of the linear elasticity tensor in the definition of a Fung-type potential, each of the three normal stresses is coupled with all three normal strains.We propose to include information on the microstructure of the atrium by writing the linear elasticity tensor as the volumetric-fraction-weighed sum of the linear elasticity tensors of the three constituents of the tissue: the ground matrix, the main fibre family and the secondary fibre family. To the best of our knowledge, this is the first time that a Fung-type potential is given a precise structural meaning, based on the directions and the material properties of the fibres. Because of the coupling between normal strains and normal stresses, this structurally-based Fung-type potential allows for discriminating among all testing protocols in planar biaxial stretch.

Robotic Online Path Planning on Point Cloud.

PubMed

Liu, Ming

2016-05-01

This paper deals with the path-planning problem for mobile wheeled- or tracked-robot which drive in 2.5-D environments, where the traversable surface is usually considered as a 2-D-manifold embedded in a 3-D ambient space. Specially, we aim at solving the 2.5-D navigation problem using raw point cloud as input. The proposed method is independent of traditional surface parametrization or reconstruction methods, such as a meshing process, which generally has high-computational complexity. Instead, we utilize the output of 3-D tensor voting framework on the raw point clouds. The computation of tensor voting is accelerated by optimized implementation on graphics computation unit. Based on the tensor voting results, a novel local Riemannian metric is defined using the saliency components, which helps the modeling of the latent traversable surface. Using the proposed metric, we prove that the geodesic in the 3-D tensor space leads to rational path-planning results by experiments. Compared to traditional methods, the results reveal the advantages of the proposed method in terms of smoothing the robot maneuver while considering the minimum travel distance.

Damped regional-scale stress inversions: Methodology and examples for southern California and the Coalinga aftershock sequence

USGS Publications Warehouse

Hardebeck, J.L.; Michael, A.J.

2006-01-01

We present a new focal mechanism stress inversion technique to produce regional-scale models of stress orientation containing the minimum complexity necessary to fit the data. Current practice is to divide a region into small subareas and to independently fit a stress tensor to the focal mechanisms of each subarea. This procedure may lead to apparent spatial variability that is actually an artifact of overfitting noisy data or nonuniquely fitting data that does not completely constrain the stress tensor. To remove these artifacts while retaining any stress variations that are strongly required by the data, we devise a damped inversion method to simultaneously invert for stress in all subareas while minimizing the difference in stress between adjacent subareas. This method is conceptually similar to other geophysical inverse techniques that incorporate damping, such as seismic tomography. In checkerboard tests, the damped inversion removes the stress rotation artifacts exhibited by an undamped inversion, while resolving sharper true stress rotations than a simple smoothed model or a moving-window inversion. We show an example of a spatially damped stress field for southern California. The methodology can also be used to study temporal stress changes, and an example for the Coalinga, California, aftershock sequence is shown. We recommend use of the damped inversion technique for any study examining spatial or temporal variations in the stress field.

Deformation Behavior and TExture Evolution of Steel Alloys under Axial-Torsional Loading

DOE Office of Scientific and Technical Information (OSTI.GOV)

Siriruk, A.; Kant, M.; Penumadu, D.

2011-06-01

Using hollow cylinder samples with suitable geometry obtained from round bar stock, the deformation behavior of bcc Fe based 12L14 steel alloy is evaluated under multi-axial conditions. A stacked strain gage rosette and extensometer mounted on the cylindrical surface at the mid height of the specimen provided strain tensor as a function of applied stress for pure tensile and torsion tests prior to yielding. This study examines elastic and yield behavior and effects of these with respect to texture evolution. Hollow cylinder specimen geometry (tubes) with small wall thickness and relatively (to its thickness) large inner diameter is used. Themore » variation of observed yield surface in deviatoric plane and the effect on mode of deformation (tension versus torsion versus its combination) on stress-strain behavior is discussed. Bulk texture was studied using neutron time-of-flight diffractometer at High-Pressure-Preferred Orientation (HIPPO) - Los Alamos Neutron Science Center (LANSCE) instrument and the evolution of texture and related anisotropy for pure tension versus torsion are also included.« less

Growth, stress, and defects of heteroepitaxial diamond on Ir/YSZ/Si(111)

NASA Astrophysics Data System (ADS)

Gallheber, B.-C.; Fischer, M.; Mayr, M.; Straub, J.; Schreck, M.

2018-06-01

Basic understanding of the fundamental processes in crystal growth as well as the structural quality of diamond synthesized by chemical vapour deposition on iridium surfaces has reached a high level for samples with (001) orientation. Diamond deposition on the alternative (111) surface is generally more challenging but of appreciable technological interest, too. In the present work, heteroepitaxy of diamond on Ir/YSZ/Si(111) with different off-axis angles and directions has been studied. During the growth of the first microns, strong and complex intrinsic stress states were rapidly formed. They restricted the range of suitable temperatures in this study to values between 830 °C and 970 °C. At low-stress conditions, the maximum growth rates were about 1 μm/h. They facilitated long-time processes which yielded pronounced structural improvements with minimum values of 0.08° for the azimuthal mosaic spread, 4 × 107 cm-2 for the dislocation density and 1.8 cm-1 for the Raman line width. This refinement is even faster than on (001) growth surfaces. It indicates substantial differences between the two crystal directions in terms of merging of mosaic blocks and annihilation of dislocations. Crystals with a thickness of up to 330 μm have been grown. The correlation of photoluminescence and μ-Raman tomograms with topography data also revealed fundamental differences in the off-axis growth between (001) and (111) orientation. Finally, the analysis of the microscopic structures at the growth surface provided the base for a model that can conclusively explain the intriguing reversal of stress tensor anisotropy caused by a simple inversion in sign of the off-axis angle.

Full paleostress tensor reconstruction: case study of the Panasqueira Mine, Portugal.

NASA Astrophysics Data System (ADS)

Pascal, C.; Jaques Ribeiro, L. M.

2017-12-01

Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal 3D exposures of mineralised quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To further constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of 300 MPa and formation depths of 10 km. As a second step, we measured 600 subhorizontal quartz veins in all the levels of the mine. The inversion of the attitudes of the veins allowed for reconstructing the orientations of the principal axes of stress, the unscaled Mohr circle and the relative pore pressure. After merging these results with the previously obtained absolute pore pressure we reconstructed the six parameters of the paleostress tensor.

Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation.

PubMed

Freistühler, Heinrich; Temple, Blake

2014-06-08

CURRENT THEORIES OF DISSIPATION IN THE RELATIVISTIC REGIME SUFFER FROM ONE OF TWO DEFICITS: either their dissipation is not causal or no profiles for strong shock waves exist. This paper proposes a relativistic Navier-Stokes-Fourier-type viscosity and heat conduction tensor such that the resulting second-order system of partial differential equations for the fluid dynamics of pure radiation is symmetric hyperbolic. This system has causal dissipation as well as the property that all shock waves of arbitrary strength have smooth profiles. Entropy production is positive both on gradients near those of solutions to the dissipation-free equations and on gradients of shock profiles. This shows that the new dissipation stress tensor complies to leading order with the principles of thermodynamics. Whether higher order modifications of the ansatz are required to obtain full compatibility with the second law far from the zero-dissipation equilibrium is left to further investigations. The system has exactly three a priori free parameters χ , η , ζ , corresponding physically to heat conductivity, shear viscosity and bulk viscosity. If the bulk viscosity is zero (as is stated in the literature) and the total stress-energy tensor is trace free, the entire viscosity and heat conduction tensor is determined to within a constant factor.

Analysis of spatial correlations in a model two-dimensional liquid through eigenvalues and eigenvectors of atomic-level stress matrices.

PubMed

Levashov, V A; Stepanov, M G

2016-01-01

Considerations of local atomic-level stresses associated with each atom represent a particular approach to address structures of disordered materials at the atomic level. We studied structural correlations in a two-dimensional model liquid using molecular dynamics simulations in the following way. We diagonalized the atomic-level stress tensor of every atom and investigated correlations between the eigenvalues and orientations of the eigenvectors of different atoms as a function of distance between them. It is demonstrated that the suggested approach can be used to characterize structural correlations in disordered materials. In particular, we found that changes in the stress correlation functions on decrease of temperature are the most pronounced for the pairs of atoms with separation distance that corresponds to the first minimum in the pair density function. We also show that the angular dependencies of the stress correlation functions previously reported by Wu et al. [Phys. Rev. E 91, 032301 (2015)10.1103/PhysRevE.91.032301] do not represent the anisotropic Eshelby's stress fields, as it is suggested, but originate in the rotational properties of the stress tensors.

Tensorial Minkowski functionals of triply periodic minimal surfaces

PubMed Central

Mickel, Walter; Schröder-Turk, Gerd E.; Mecke, Klaus

2012-01-01

A fundamental understanding of the formation and properties of a complex spatial structure relies on robust quantitative tools to characterize morphology. A systematic approach to the characterization of average properties of anisotropic complex interfacial geometries is provided by integral geometry which furnishes a family of morphological descriptors known as tensorial Minkowski functionals. These functionals are curvature-weighted integrals of tensor products of position vectors and surface normal vectors over the interfacial surface. We here demonstrate their use by application to non-cubic triply periodic minimal surface model geometries, whose Weierstrass parametrizations allow for accurate numerical computation of the Minkowski tensors. PMID:24098847

Renormalized stress-energy tensor for stationary black holes

NASA Astrophysics Data System (ADS)

Levi, Adam

2017-01-01

We continue the presentation of the pragmatic mode-sum regularization (PMR) method for computing the renormalized stress-energy tensor (RSET). We show in detail how to employ the t -splitting variant of the method, which was first presented for ⟨ϕ2⟩ren , to compute the RSET in a stationary, asymptotically flat background. This variant of the PMR method was recently used to compute the RSET for an evaporating spinning black hole. As an example for regularization, we demonstrate here the computation of the RSET for a minimally coupled, massless scalar field on Schwarzschild background in all three vacuum states. We discuss future work and possible improvements of the regularization schemes in the PMR method.

Method to compute the stress-energy tensor for a quantum field outside a black hole that forms from collapse

NASA Astrophysics Data System (ADS)

Anderson, Paul; Evans, Charles

2017-01-01

A method to compute the stress-energy tensor for a quantized massless minimally coupled scalar field outside the event horizon of a 4-D black hole that forms from the collapse of a spherically symmetric null shell is given. The method is illustrated in the corresponding 2-D case which is mathematically similar but is simple enough that the calculations can be done analytically. The approach to the Unruh state at late times is discussed. National Science Foundation Grant No. PHY-1505875 to Wake Forest University and National Science Foundation Grant No. PHY-1506182 to the University of North Carolina, Chapel Hill

Bridging scales of crustal stress patterns using the new World Stress Map

NASA Astrophysics Data System (ADS)

Heidbach, O.; Rajabi, M.; Cui, X.; Fuchs, K. W.; Mueller, B.; Reinecker, J.; Reiter, K.; Tingay, M. R. P.; Wenzel, F.; Xie, F.; Ziegler, M.; Zoback, M. D.; Zoback, M. L.

2017-12-01

Knowledge of the contemporary crustal stress field is a key parameter for the understanding of geodynamic processes such as global plate tectonics and the earthquake cycle. It is also an essential parameter for our sustainable and safe usage of Earth's resources, which is a major challenge for energy security in the 21st century. Since 1986, the World Stress Map (WSM) project has systematically compiled present-day stress information and provides a unique public domain global database. It is a long-term project based on an international network of partners from academia and industry. All data are public and available on the project website at world-stress-map.org. For the 30th anniversary of the project a new database has been compiled, containing double the amount of data records (n=42,870) including new data records from almost 4,000 deep boreholes. The new compilation focused on areas with previously sparse data coverage in order to resolve the stress pattern on different spatial scales. The significantly higher data density can now be used to resolve stress pattern heterogeneities on regional and local scales, as well as with depth in some regions. We present three results derived from the new WSM compilation: 1.) The global comparison between absolute plate motion and the mean of the orientation of maximum horizontal stress SHmax on a regular grid shows that there is still a correlation for the North and South America plate, but deviations from this general trend are now also clearly resolved. 2.) The variability of the crustal stress pattern changes when zooming in from plate-wide scale down to basin scale at 100 km. We show examples for Eastern Australia, Oklahoma and Central Europe. This regional and local variability of the stress pattern can be used as a proxy to identify and quantify regional and local stress sources by means of geomechanical-numerical models of the 3D stress tensor. 3.) Finally we present briefly the general concept of a multi-stage 3D geomechanical-numerical model workflow based on the WSM data to describe the in situ stress tensor. 3D Geomechanical-numerical modelling of the in situ stress state is essential to derive a continuous description of the stress tensor e.g. in order to estimate the distance to a critical stress state.

Progress in turbulence modeling for complex flow fields including effects of compressibility

NASA Technical Reports Server (NTRS)

Wilcox, D. C.; Rubesin, M. W.

1980-01-01

Two second-order-closure turbulence models were devised that are suitable for predicting properties of complex turbulent flow fields in both incompressible and compressible fluids. One model is of the "two-equation" variety in which closure is accomplished by introducing an eddy viscosity which depends on both a turbulent mixing energy and a dissipation rate per unit energy, that is, a specific dissipation rate. The other model is a "Reynolds stress equation" (RSE) formulation in which all components of the Reynolds stress tensor and turbulent heat-flux vector are computed directly and are scaled by the specific dissipation rate. Computations based on these models are compared with measurements for the following flow fields: (a) low speed, high Reynolds number channel flows with plane strain or uniform shear; (b) equilibrium turbulent boundary layers with and without pressure gradients or effects of compressibility; and (c) flow over a convex surface with and without a pressure gradient.

Failure analysis of composite laminates including biaxial compression

NASA Technical Reports Server (NTRS)

Tennyson, R. C.; Elliott, W. G.

1983-01-01

This report describes a continued effort on the development and application of the tensor polynomial failure criterion for composite laminate analysis. In particular, emphasis is given to the design, construction and testing of a cross-beam laminate configuration to obtain "pure' biaxial compression failure. The purpose of this test case was to provide to permit "closure' of the cubic form of the failure surface in the 1-2 compression-compression quadrant. This resulted in a revised set of interaction strength parameters and the construction of a failure surface which can be used with confidence for strength predictions, assuming a plane stress state exists. Furthermore, the problem of complex conjugate roots which can occur in some failure regions is addressed and an "engineering' interpretation is provided. Results are presented illustrating this behavior and the methodology for overcoming this problem is discussed.

Propagation of Axisymmetric Electroelastic Waves in a Hollow Layered Cylinder Under Mechanical Excitation

NASA Astrophysics Data System (ADS)

Grigorenko, A. Ya.; Loza, I. A.

2017-09-01

The problem on propagation of axisymmetric electroelastic waves in a hollow layered cylinder made of metallic and radially polarized piezoceramic layers is solved. The lateral surfaces of the cylinder are free of electrodes. The outside surface is free of mechanical loads, while the inside one undergoes harmonically varying pressure Pe. The problem was solved with a numerical-analytical method. By representing the components of the stress tensor, displacement vectors, electric-flux density, and electrostatic potential by traveling waves, the original electroelastic problem in partial derivatives is reduced to an inhomogeneous boundary-value problem for ordinary differential equations. To solve the problem, the stable numerical discrete-orthogonalization method is used. The results of the kinematic analysis of the layered cylinder both with metallic and piezoceramic (PZT 4) layers are presented. The numerical results are analyzed.

Theoretical and numerical aspects of fluid-saturated elasto-plastic soils

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ehlers, W.

1995-12-31

The theoretical and numerical treatment of fluid-saturated porous solid materials generally falls into the category of porous media models, which are described within the framework of the classical theory of mixtures extended by the concept of volume fractions (porous media theories). In particular, this concept allows for the description of saturated, unsaturated and empty porous matrix materials, thus offering a well-founded theoretical background for a lot of engineering problems occurring, for instance, in the fields of geomechanics (soil and rock mechanics as well as glacier and rock ice mechanics), oil producing industries, sintering technologies, biomechanics, etc. In the present contribution,more » theoretical and numerical studies are outlined to describe a two-phase material composed of an incompressible elasto-plastic soil matrix saturated by an incompressible viscous pore fluid. In this context, the phenomenon of phase incompressibility is well known as a microscopic effect not implying bulk incompressibility in the macro regime. This is seen from the fact that even if the material density functions of the individual constituents are constant during deformation, the corresponding bulk densities can still change through changes in the volume fractions. Within the framework of a pure mechanical theory, constitutive equations are given for both the solid and the fluid partial stress tensors and for the interaction force acting between the two materials. Concerning the porous soil matrix, the elastic properties are described by an elasticity law of Hookean type, while the plastic range is governed by a {open_quote}single surface{close_quote} yield function exhibiting a smooth and closed shape in the principal stress space together with a non-associated flow rule. The viscosity effects of the pore fluid are included in the fluid stress tensor and in the drag force.« less

Pragmatic mode-sum regularization method for semiclassical black-hole spacetimes

NASA Astrophysics Data System (ADS)

Levi, Adam; Ori, Amos

2015-05-01

Computation of the renormalized stress-energy tensor is the most serious obstacle in studying the dynamical, self-consistent, semiclassical evaporation of a black hole in 4D. The difficulty arises from the delicate regularization procedure for the stress-energy tensor, combined with the fact that in practice the modes of the field need to be computed numerically. We have developed a new method for numerical implementation of the point-splitting regularization in 4D, applicable to the renormalized stress-energy tensor as well as to ⟨ϕ2⟩ren , namely the renormalized ⟨ϕ2⟩. So far we have formulated two variants of this method: t -splitting (aimed for stationary backgrounds) and angular splitting (for spherically symmetric backgrounds). In this paper we introduce our basic approach, and then focus on the t -splitting variant, which is the simplest of the two (deferring the angular-splitting variant to a forthcoming paper). We then use this variant, as a first stage, to calculate ⟨ϕ2⟩ren in Schwarzschild spacetime, for a massless scalar field in the Boulware state. We compare our results to previous ones, obtained by a different method, and find full agreement. We discuss how this approach can be applied (using the angular-splitting variant) to analyze the dynamical self-consistent evaporation of black holes.

Wrinkle ridges, reverse faulting, and the depth penetration of lithospheric stress in lunae planum, Mars

NASA Technical Reports Server (NTRS)

Zuber, M. T.

1993-01-01

Tectonic features on a planetary surface are commonly used as constraints on models to determine the state of stress at the time the features formed. Quantitative global stress models applied to understand the formation of the Tharsis province on Mars constrained by observed tectonics have calculated stresses at the surface of a thin elastic shell and have neglected the role of vertical structure in influencing the predicted pattern of surface deformation. Wrinkle ridges in the Lunae Planum region of Mars form a conentric pattern of regularly spaced features in the eastern and southeastern part of Tharsis; they are formed due to compressional stresses related to the response of the Martian lithosphere to the Tharsis bulge. As observed in the exposures of valley walls in areas such as the Kasei Valles, the surface plains unit is underlain by an unconsolidated impact-generated megaregolith that grades with depth into structurally competent lithospheric basement. The ridges have alternatively been hypothesized to reflect deformation restricted to the surface plains unit ('thin skinned deformation') and deformation that includes the surface unit, megaregolith and basement lithosphere ('thick skinned deformation'). We have adopted a finite element approach to quantify the nature of deformation associated with the development of wrinkle ridges in a vertically stratified elastic lithosphere. We used the program TECTON, which contains a slippery node capability that allowed us to explicitly take into account the presence of reverse faults believed to be associated with the ridges. In this study we focused on the strain field in the vicinity of a single ridge when slip occurs along the fault. We considered two initial model geometries. In the first, the reverse fault was assumed to be in the surface plains unit, and in the second the initial fault was located in lithospheric basement, immediately beneath the weak megaregolith. We are interested in the conditions underwhich strain in the surface layer and basement either penetrates or fails to penetrate through the megaregolith. We thus address the conditions required for an initial basement fault to propagate through the megaregolith to the surface, as well as the effect of the megareolith on the strain tensor in the vicinity of a fault that nucleates in the surface plains unit.

Wrinkle ridges, reverse faulting, and the depth penetration of lithospheric stress in lunae planum, Mars

NASA Astrophysics Data System (ADS)

Zuber, M. T.

1993-03-01

Tectonic features on a planetary surface are commonly used as constraints on models to determine the state of stress at the time the features formed. Quantitative global stress models applied to understand the formation of the Tharsis province on Mars constrained by observed tectonics have calculated stresses at the surface of a thin elastic shell and have neglected the role of vertical structure in influencing the predicted pattern of surface deformation. Wrinkle ridges in the Lunae Planum region of Mars form a conentric pattern of regularly spaced features in the eastern and southeastern part of Tharsis; they are formed due to compressional stresses related to the response of the Martian lithosphere to the Tharsis bulge. As observed in the exposures of valley walls in areas such as the Kasei Valles, the surface plains unit is underlain by an unconsolidated impact-generated megaregolith that grades with depth into structurally competent lithospheric basement. The ridges have alternatively been hypothesized to reflect deformation restricted to the surface plains unit ('thin skinned deformation') and deformation that includes the surface unit, megaregolith and basement lithosphere ('thick skinned deformation'). We have adopted a finite element approach to quantify the nature of deformation associated with the development of wrinkle ridges in a vertically stratified elastic lithosphere. We used the program TECTON, which contains a slippery node capability that allowed us to explicitly take into account the presence of reverse faults believed to be associated with the ridges. In this study we focused on the strain field in the vicinity of a single ridge when slip occurs along the fault. We considered two initial model geometries. In the first, the reverse fault was assumed to be in the surface plains unit, and in the second the initial fault was located in lithospheric basement, immediately beneath the weak megaregolith. We are interested in the conditions under which strain in the surface layer and basement either penetrates or fails to penetrate through the megaregolith. We thus address the conditions required for an initial basement fault to propagate through the megaregolith to the surface, as well as the effect of the megareolith on the strain tensor in the vicinity of a fault that nucleates in the surface plains unit.

Multivariate Tensor-based Morphometry on Surfaces: Application to Mapping Ventricular Abnormalities in HIV/AIDS

PubMed Central

Wang, Yalin; Zhang, Jie; Gutman, Boris; Chan, Tony F.; Becker, James T.; Aizenstein, Howard J.; Lopez, Oscar L.; Tamburo, Robert J.; Toga, Arthur W.; Thompson, Paul M.

2010-01-01

Here we developed a new method, called multivariate tensor-based surface morphometry (TBM), and applied it to study lateral ventricular surface differences associated with HIV/AIDS. Using concepts from differential geometry and the theory of differential forms, we created mathematical structures known as holomorphic one-forms, to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain. The new meshing approach also provides a natural way to register anatomical surfaces across subjects, and improves on prior methods as it handles surfaces that branch and join at complex 3D junctions. To analyze anatomical differences, we computed new statistics from the Riemannian surface metrics - these retain multivariate information on local surface geometry. We applied this framework to analyze lateral ventricular surface morphometry in 3D MRI data from 11 subjects with HIV/AIDS and 8 healthy controls. Our method detected a 3D profile of surface abnormalities even in this small sample. Multivariate statistics on the local tensors gave better effect sizes for detecting group differences, relative to other TBM-based methods including analysis of the Jacobian determinant, the largest and smallest eigenvalues of the surface metric, and the pair of eigenvalues of the Jacobian matrix. The resulting analysis pipeline may improve the power of surface-based morphometry studies of the brain. PMID:19900560

A Three-Dimensional Eulerian Code for Simulation of High-Speed Multimaterial Interactions

DTIC Science & Technology

2011-08-01

PDE -based extension. The extension process is done on only the host cells on a particular processor. After extension the parallel communication is...condensation shocks, explosive debris transport, detonation in heterogeneous media and so on. In these flows complex interactions occur between the...A.22] and ijΩ is the spin tensor. The Jaumann derivative is used to ensure objectivity of the stress tensor with respect to rotation

Experimental Validation of a Coupled Fluid-Multibody Dynamics Model for Tanker Trucks

DTIC Science & Technology

2007-11-08

order to accurately predict the dynamic response of tanker trucks, the model must accurately account for the following effects : • Incompressible...computational code which uses a time- accurate explicit solution procedure is used to solve both the solid and fluid equations of motion. Many commercial...position vector, τ is the deviatoric stress tensor, D is the rate of deformation tensor, f r is the body force vector, r is the artificial

Quantum field theory in spaces with closed timelike curves

NASA Astrophysics Data System (ADS)

Boulware, David G.

1992-11-01

Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

Elastic constants of hcp 4He: Path-integral Monte Carlo results versus experiment

NASA Astrophysics Data System (ADS)

Ardila, Luis Aldemar Peña; Vitiello, Silvio A.; de Koning, Maurice

2011-09-01

The elastic constants of hcp 4He are computed using the path-integral Monte Carlo (PIMC) method. The stiffness coefficients are obtained by imposing different distortions to a periodic cell containing 180 atoms, followed by measurement of the elements of the corresponding stress tensor. For this purpose an appropriate path-integral expression for the stress tensor observable is derived and implemented into the pimc++ package. In addition to allowing the determination of the elastic stiffness constants, this development also opens the way to an explicit atomistic determination of the Peierls stress for dislocation motion using the PIMC technique. A comparison of the results to available experimental data shows an overall good agreement of the density dependence of the elastic constants, with the single exception of C13. Additional calculations for the bcc phase, on the other hand, show good agreement for all elastic constants.

Current crustal deformation of the Taiwan orogen reassessed by cGPS strain-rate estimation and focal mechanism stress inversion

NASA Astrophysics Data System (ADS)

Chen, Sean Kuanhsiang; Wu, Yih-Min; Hsu, Ya-Ju; Chan, Yu-Chang

2017-07-01

We study internal deformation of the Taiwan orogen, a young arc-continental collision belt, which the spatial heterogeneity remains unclear. We aim to ascertain heterogeneity of the orogenic crust in depth when specifying general mechanisms of the Taiwan orogeny. To reach this goal, we used updated data of continuous GPS (cGPS) and earthquake focal mechanisms to reassess geodetic strain-rate and seismic stress fields of Taiwan, respectively. We updated the both data sets from 1990 to 2015 to provide large amount of constraints on surficial and internal deformation of the crust for a better understanding. We estimated strain-rate tensors by calculating gradient tensors of cGPS station velocities in horizontal 0.1°-spacing grids via Delaunay triangulation. We determined stress tensors within a given horizontal and vertical grid cell of 0.1° and 10 km, respectively, by employing the spatial and temporal stress inversion. To minimize effects of the 1999 Mw 7.6 Chi-Chi earthquake on trends of the strain and stress, we modified observational possible bias of the cGPS velocities after the earthquake and removed the first 15-month focal mechanisms within the fault rupture zone. We also calculated the Anderson fault parameter (Aϕ) based on stress ratios and rake angles to quantitatively describe tectonic regimes of Taiwan. By examining directions of seismic compressive axes and styles of faulting, our results indicate that internal deformation of the crust is presently heterogeneous in the horizontal and vertical spaces. Directions of the compressive axes are fan-shaped oriented between N10°W and N110°W in the western and mid-eastern Taiwan at the depths of 0-20 km and near parallel to orientations of geodetic compressional axes. The orientations agreed with predominantly reverse faulting in the western Taiwan at the same depth range, implying a brittle deformation regime against the Peikang Basement High. Orientations of the compressive axes most rotated counter-clockwise at the depths of 20-40 km, coinciding with transition of styles of faulting from reverse to strike-slip faulting along the depths as revealed by variation of the Aϕ values. The features indicate that internal deformation of the upper crust is primarily driven by the same compressional mechanism. It implies that geodetic strains could detect the deformation from surface down to a maximal depth of 20 km in most regimes of Taiwan. We find that heterogeneity in orientations of compressive axes and styles of faulting is strong in two regimes at the northern and southern Central Range, coinciding to areas of the orogenic thinned/thickened crust. Conversely, the heterogeneity is weak in the central Western Foothills at surrounding area of root of the overthickened crust. This observation, coupled with regional seismological observations, may imply that vertical deformation from crustal thickening and thinning and thinning-related dynamics from mantle flows may have joint influence on degree of stress heterogeneity.

The Spacetime Between Einstein and Kaluza-Klein: Further Explorations

NASA Astrophysics Data System (ADS)

Vuille, Chris

2017-01-01

Tensor multinomials can be used to create a generalization of Einstein's general relativity that in a mathematical sense falls between Einstein's original theory in four dimensions and the Kaluza-Klein theory in five dimensions. In the extended theory there are only four physical dimensions, but the tensor multinomials are expanded operators that can accommodate other forces of nature. The equivalent Ricci tensor of this geometry yields vacuum general relativity and electromagnetism, as well as a Klein-Gordon-like quantum scalar field. With a generalization of the stress-energy tensor, an exact solution for a plane-symmetric dust can be found where the scalar portion of the field drives early universe inflation, levels off for a period, then causes a later continued universal acceleration, a possible geometric mechanism for the inflaton or dark energy. Some new explorations of the equations, the problems, and possibilities will be presented and discussed.

Nonlinear interaction of strong S-waves with the rupture front in the shallow subsurface

NASA Astrophysics Data System (ADS)

Sleep, N. H.

2017-12-01

Shallow deformation in moderate to large earthquakes is sometimes distributed rather than being concentrated on a single fault plane. Strong high-frequency S-waves interact with the rupture front to produce this effect. For strike-slip faults, the rupture propagation velocity is a fraction of the S-wave velocity. The rupture propagation vector refracts essentially vertically in the low (S-wave) velocity shallow subsurface. So does the propagation direction of S-waves. The shallow rupture front is essentially mode 3 near the surface. Strong S-waves arrive before the rupture front. They continue to arrive for several seconds in a large event. There are simple scaling relationships. The dynamic Coulomb stress ratio of horizontal stress on horizontal planes from S-waves is the normalized acceleration in g's. For fractured rock and gravel, frictional failure occurs when the normalized acceleration exceeds the effective coefficient of friction. Acceleration tends to saturate at that level as the anelastic strain rate increases rapidly with stress. For muddy materials, failure begins at a low normalized acceleration but increases slowly with dynamic stress. Dynamic accelerations sometimes exceed 1 g. In both cases, the rupture tip finds the shallow subsurface already in nonlinear failure down to a few to tens of meters depth. The material does not distinguish between S-wave and rupture tip stresses. Both stresses add to the stress invariant and hence to the anelastic strain rate tensor. Surface anelastic strain from fault slip is thus distributed laterally over a distance scaling to the depth of nonlinearity from S-waves. The environs of the fault anelastically accommodate the fault slip at depth. This process differs from blind faults where the shallow coseismic strain is mostly elastic and interseismic anelastic processes accommodate the long-term shallow deformation.

Focal mechanisms and tidal modulation for tectonic tremors in Taiwan

NASA Astrophysics Data System (ADS)

Ide, S.; Yabe, S.; Tai, H. J.; Chen, K. H.

2015-12-01

Tectonic tremors in Taiwan have been discovered beneath the southern Central Range, but their hosting structure has been unknown. Here we constrain the focal mechanism of underground deformation related to tremors, using moment tensor inversion in the very low frequency band and tidal stress analysis. Three types of seismic data are used for two analysis steps: detection of tremors and the moment tensor inversion. Short-period seismograms from CWBSN are used for tremor detection. Broadband seismograms from BATS and the TAIGER project are used for both steps. About 1000 tremors were detected using an envelope correlation method in the high frequency band (2-8 Hz). Broadband seismograms are stacked relative to the tremor timing, and inverted for a moment tensor in the low frequency band (0.02-0.05 Hz). The best solution was obtained at 32 km depth, as a double-couple consistent with a low-angle thrust fault dipping to the east-southeast, or a high-angle thrust with a south-southwest strike. Almost all tremors occur when tidal shear stress is positive and normal stress is negative (clamping). Since the clamping stress is high for a high-angle thrust fault, the low-angle thrust fault is more likely to be the fault plane. Tremor rate increases non-linearly with increasing shear stress, suggesting a velocity strengthening friction law. The high tidal sensitivity is inconsistent with horizontal slip motion suggested by previous studies, and normal faults that dominates regional shallow earthquakes. Our results favor thrust slip on a low-angle fault dipping to the east-southeast, consistent with the subduction of the Eurasian plate. The tremor region is characterized by a deep thermal anomaly with decrease normal stress. This region has also experienced enough subduction to produce metamorphic fluids. A large amount of fluid and low vertical stress may explain the high tidal sensitivity.

Spatially Resolved Measurement of the Stress Tensor in Thin Membranes Using Bending Waves

NASA Astrophysics Data System (ADS)

Waitz, Reimar; Lutz, Carolin; Nößner, Stephan; Hertkorn, Michael; Scheer, Elke

2015-04-01

The mode shape of bending waves in thin silicon and silicon-carbide membranes is measured as a function of space and time, using a phase-shift interferometer with stroboscopic light. The mode shapes hold information about all the relevant mechanical parameters of the samples, including the spatial distribution of static prestress. We present a simple algorithm to obtain a map of the lateral tensor components of the prestress, with a spatial resolution much better than the wavelength of the bending waves. The method is not limited to measuring the stress of bending waves. It is applicable in almost any situation, where the fields determining the state of the system can be measured as a function of space and time.

Vacuum polarization of the electromagnetic field near a rotating black hole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frolov, V.P.; Zel'nikov, A.I.

1985-12-15

The electromagnetic field contribution to the vacuum polarization near a rotating black hole is considered. It is shown that the problem of calculating the renormalized average value of the stress-energy tensor /sup ren/ for the Hartle-Hawking vacuum state at the pole of the event horizon can be reduced to the problem of electro- and magnetostatics in the Kerr spacetime. An explicit expression for /sup ren/ at the pole of the event horizon is obtained and its properties are discussed. It is shown that in the case of a nonrotating black hole the Page-Brown approximation for the electromagnetic stress-energy tensor givesmore » a result which coincides at the event horizon with the exact value of /sup ren/. .AE« less

Stress Energy Tensor in LCFT and LOGARITHMIC Sugawara Construction

NASA Astrophysics Data System (ADS)

Kogan, Ian I.; Nichols, Alexander

We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. However they are both characterised by at least two independent parameters. We show how, by using a generalised Sugawara construction, one can calculate the logarithmic partner of T. We show that such a construction works in the c=-2 theory using the conformal dimension one primary currents which generate a logarithmic extension of the Kac-Moody algebra. This is an expanded version of a talk presented by A. Nichols at the conference on Logarithmic Conformal Field Theory and its Applications in Tehran Iran, 2001.

Renormalized Stress-Energy Tensor of an Evaporating Spinning Black Hole.

PubMed

Levi, Adam; Eilon, Ehud; Ori, Amos; van de Meent, Maarten

2017-04-07

We provide the first calculation of the renormalized stress-energy tensor (RSET) of a quantum field in Kerr spacetime (describing a stationary spinning black hole). More specifically, we employ a recently developed mode-sum regularization method to compute the RSET of a minimally coupled massless scalar field in the Unruh vacuum state, the quantum state corresponding to an evaporating black hole. The computation is done here for the case a=0.7M, using two different variants of the method: t splitting and φ splitting, yielding good agreement between the two (in the domain where both are applicable). We briefly discuss possible implications of the results for computing semiclassical corrections to certain quantities, and also for simulating dynamical evaporation of a spinning black hole.

Bespoke analogue space-times: meta-material mimics

NASA Astrophysics Data System (ADS)

Schuster, Sebastian; Visser, Matt

2018-06-01

Modern meta-materials allow one to construct electromagnetic media with almost arbitrary bespoke permittivity, permeability, and magneto-electric tensors. If (and only if) the permittivity, permeability, and magneto-electric tensors satisfy certain stringent compatibility conditions, can the meta-material be fully described (at the wave optics level) in terms of an effective Lorentzian metric—an analogue spacetime. We shall consider some of the standard black-hole spacetimes of primary interest in general relativity, in various coordinate systems, and determine the equivalent meta-material susceptibility tensors in a laboratory setting. In static black hole spacetimes (Schwarzschild and the like) certain eigenvalues of the susceptibility tensors will be seen to diverge on the horizon. In stationary black hole spacetimes (Kerr and the like) certain eigenvalues of the susceptibility tensors will be seen to diverge on the ergo-surface.

Numerical Estimation of the Elastic Properties of Thin-Walled Structures Manufactured from Short-Fiber-Reinforced Thermoplastics

NASA Astrophysics Data System (ADS)

Altenbach, H.; Naumenko, K.; L'vov, G. I.; Pilipenko, S. N.

2003-05-01

A model which allows us to estimate the elastic properties of thin-walled structures manufactured by injection molding is presented. The starting step is the numerical prediction of the microstructure of a short-fiber-reinforced composite developed during the filling stage of the manufacturing process. For this purpose, the Moldflow Plastic Insight® commercial program is used. As a result of simulating the filling process, a second-rank orientation tensor characterizing the microstructure of the material is obtained. The elastic properties of the prepared material locally depend on the orientational distribution of fibers. The constitutive equation is formulated by means of orientational averaging for a given orientation tensor. The tensor of elastic material properties is computed and translated into the format for a stress-strain analysis based on the ANSYSÒ finite-element code. The numerical procedure and the convergence of results are discussed for a thin strip, a rectangular plate, and a shell of revolution. The influence of manufacturing conditions on the stress-strain state of statically loaded thin-walled elements is illustrated.

Derivation of the Schwartzchild Metric From the ``Self Censorship'' of the ZPF (Zero Point Energy) in the GEM Theory

NASA Astrophysics Data System (ADS)

Brandenburg, John

2012-10-01

The GEM theory (1) links the EM stress tensor directly to the metric tensor by the principle of ``self censorship'' of the ZPF (2) where the definition of guv = FuwF^wv/ 4 for Planck scale fields makes the stress tensor vanish even when fields are present. The first order form of the metric is recovered as Lorentzian due to alternating regions of strong electric and magnetic fields similar to that seen in models of spacetime in ``Loop Gravity,'' where the model admits perturbations. The GEM ExB drift models of gravity is used The first order perturbations on the fields are considered to be of the order of the fine structure constant alpha. Radiation fields due to a single charged particle of mass M fall off as 1/r and give the values (G=c=1) gtt = 1-2M/r and grr = (1-2M/r). (1) Brandenburg, J.E. (2012)., (2) STAIF II Conference Albuquerque NM 2.Brandenburg, J.E. (2007). IEEE Transactions On Plasma Science, Vol. 35, No. 4., p845.

Spinorial characterizations of surfaces into three-dimensional homogeneous manifolds

NASA Astrophysics Data System (ADS)

Roth, Julien

2010-06-01

We give spinorial characterizations of isometrically immersed surfaces into three-dimensional homogeneous manifolds with four-dimensional isometry group in terms of the existence of a particular spinor field. This generalizes works by Friedrich for R3 and Morel for S3 and H3. The main argument is the interpretation of the energy-momentum tensor of such a spinor field as the second fundamental form up to a tensor depending on the structure of the ambient space.

Possibilities and limitations of rod-beam theories. [nonlinear distortion tensor and nonlinear stress tensors

NASA Technical Reports Server (NTRS)

Peterson, D.

1979-01-01

Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.

Anisotropic Poroelasticity in a Rock With Cracks

NASA Astrophysics Data System (ADS)

Wong, Teng-Fong

2017-10-01

Deformation of a saturated rock in the field and laboratory may occur in a broad range of conditions, ranging from undrained to drained. The poromechanical response is often anisotropic, and in a brittle rock, closely related to preexisting and stress-induced cracks. This can be modeled as a rock matrix embedded with an anisotropic system of cracks. Assuming microisotropy, expressions for three of the poroelastic coefficients of a transversely isotropic rock were derived in terms of the crack density tensor. Together with published results for the five effective elastic moduli, this provides a complete micromechanical description of the eight independent poroelastic coefficients of such a cracked rock. Relatively simple expressions were obtained for the Skempton pore pressure tensor, which allow one to infer the crack density tensor from undrained measurement in the laboratory, and also to infer the Biot-Willis effective stress coefficients. The model assumes a dilute concentration of noninteractive penny-shaped cracks, and it shows good agreement with experimental data for Berea sandstone, with crack density values up to 0.6. Whereas predictions on the storage coefficient and normal components of the elastic stiffness tensor also seem reasonable, significant discrepancy between model and measurement was observed regarding the off-diagonal and shear components of the stiffness. A plausible model had been proposed for development of very strong anisotropy in the undrained response of a fault zone, and the model here placed geometric constraints on the associated fracture system.

Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows

NASA Technical Reports Server (NTRS)

Zhao, C. Y.; So, R. M. C.; Gatski, T. B.

2001-01-01

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.

Simultaneous determination of mean pressure and deviatoric stress based on numerical tensor analysis: a case study for polycrystalline x-ray diffraction of gold enclosed in a methanol-ethanol mixture.

PubMed

Yoneda, A; Kubo, A

2006-06-28

It is known that the {100} and {111} planes of cubic crystals subjected to uniaxial deviatoric stress conditions have strain responses that are free from the effect of lattice preferred orientation. By utilizing this special character, one can unambiguously and simultaneously determine the mean pressure and deviatoric stress from polycrystalline diffraction data of the cubic sample. Here we introduce a numerical tensor calculation method based on the generalized Hooke's law to simultaneously determine the hydrostatic component of the stress (mean pressure) and deviatoric stress in the sample. The feasibility of this method has been tested by examining the experimental data of the Au pressure marker enclosed in a diamond anvil cell using a pressure medium of methanol-ethanol mixture. The results demonstrated that the magnitude of the deviatoric stress is ∼0.07 GPa at the mean pressure of 10.5 GPa, which is consistent with previous results of Au strength under high pressure. Our results also showed that even a small deviatoric stress (∼0.07 GPa) could yield a ∼0.3 GPa mean pressure error at ∼10 GPa.

An Assessment of the Seismicity of the Bursa Region from a Temporary Seismic Network

NASA Astrophysics Data System (ADS)

Gok, Elcin; Polat, Orhan

2012-04-01

A temporary earthquake station network of 11 seismological recorders was operated in the Bursa region, south of the Marmara Sea in the northwest of Turkey, which is located at the southern strand of the North Anatolian Fault Zone (NAFZ). We located 384 earthquakes out of a total of 582 recorded events that span the study area between 28.50-30.00°E longitudes and 39.75-40.75°N latitudes. The depth of most events was found to be less than 29 km, and the magnitude interval ranges were between 0.3 ≤ ML ≤ 5.4, with RMS less than or equal to 0.2. Seismic activities were concentrated southeast of Uludag Mountain (UM), in the Kestel-Igdir area and along the Gemlik Fault (GF). In the study, we computed 10 focal mechanisms from temporary and permanents networks. The predominant feature of the computed focal mechanisms is the relatively widespread near horizontal northwest-southeast (NW-SE) T-axis orientation. These fault planes have been used to obtain the orientation and shape factor (R, magnitude stress ratio) of the principal stress tensors (σ1, σ2, σ3). The resulting stress tensors reveal σ1 closer to the vertical (oriented NE-SW) and σ2, σ3 horizontal with R = 0.5. These results confirm that Bursa and its vicinity could be defined by an extensional regime showing a primarily normal to oblique-slip motion character. It differs from what might be expected from the stress tensor inversion for the NAFZ. Different fault patterns related to structural heterogeneity from the north to the south in the study area caused a change in the stress regime from strike-slip to normal faulting.

Characterizing heterogeneous properties of cerebral aneurysms with unknown stress-free geometry: a precursor to in vivo identification.

PubMed

Zhao, Xuefeng; Raghavan, Madhavan L; Lu, Jia

2011-05-01

Knowledge of elastic properties of cerebral aneurysms is crucial for understanding the biomechanical behavior of the lesion. However, characterizing tissue properties using in vivo motion data presents a tremendous challenge. Aside from the limitation of data accuracy, a pressing issue is that the in vivo motion does not expose the stress-free geometry. This is compounded by the nonlinearity, anisotropy, and heterogeneity of the tissue behavior. This article introduces a method for identifying the heterogeneous properties of aneurysm wall tissue under unknown stress-free configuration. In the proposed approach, an accessible configuration is taken as the reference; the unknown stress-free configuration is represented locally by a metric tensor describing the prestrain from the stress-free configuration to the reference configuration. Material parameters are identified together with the metric tensor pointwisely. The paradigm is tested numerically using a forward-inverse analysis loop. An image-derived sac is considered. The aneurysm tissue is modeled as an eightply laminate whose constitutive behavior is described by an anisotropic hyperelastic strain-energy function containing four material parameters. The parameters are assumed to vary continuously in two assigned patterns to represent two types of material heterogeneity. Nine configurations between the diastolic and systolic pressures are generated by forward quasi-static finite element analyses. These configurations are fed to the inverse analysis to delineate the material parameters and the metric tensor. The recovered and the assigned distributions are in good agreement. A forward verification is conducted by comparing the displacement solutions obtained from the recovered and the assigned material parameters at a different pressure. The nodal displacements are found in excellent agreement.

Evidence for Nuclear Tensor Polarization of Deuterium Molecules in Storage Cells

DOE Office of Scientific and Technical Information (OSTI.GOV)

van den Brand, J.; Bulten, H.; Zhou, Z.

1997-02-01

Deuterium molecules were obtained by recombination, on a copper surface, of deuterium atoms prepared in specific hyperfine states. The molecules were stored for about 5ms in an open-ended cylindrical cell, placed in a 23mT magnetic field, and their tensor polarization was measured by elastic scattering of 704MeV electrons. The results of the measurements are consistent with the deuterium molecules retaining the tensor polarization of the initial atoms. {copyright} {ital 1997} {ital The American Physical Society}

On improving the efficiency of tensor voting.

PubMed

Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim

2011-11-01

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.

Traction patterns of tumor cells.

PubMed

Ambrosi, D; Duperray, A; Peschetola, V; Verdier, C

2009-01-01

The traction exerted by a cell on a planar deformable substrate can be indirectly obtained on the basis of the displacement field of the underlying layer. The usual methodology used to address this inverse problem is based on the exploitation of the Green tensor of the linear elasticity problem in a half space (Boussinesq problem), coupled with a minimization algorithm under force penalization. A possible alternative strategy is to exploit an adjoint equation, obtained on the basis of a suitable minimization requirement. The resulting system of coupled elliptic partial differential equations is applied here to determine the force field per unit surface generated by T24 tumor cells on a polyacrylamide substrate. The shear stress obtained by numerical integration provides quantitative insight of the traction field and is a promising tool to investigate the spatial pattern of force per unit surface generated in cell motion, particularly in the case of such cancer cells.

Two-point function of a quantum scalar field in the interior region of a Reissner-Nordstrom black hole

NASA Astrophysics Data System (ADS)

Lanir, Assaf; Levi, Adam; Ori, Amos; Sela, Orr

2018-01-01

We derive explicit expressions for the two-point function of a massless scalar field in the interior region of a Reissner-Nordstrom black hole, in both the Unruh and the Hartle-Hawking quantum states. The two-point function is expressed in terms of the standard l m ω modes of the scalar field (those associated with a spherical harmonic Yl m and a temporal mode e-i ω t), which can be conveniently obtained by solving an ordinary differential equation, the radial equation. These explicit expressions are the internal analogs of the well-known results in the external region (originally derived by Christensen and Fulling), in which the two-point function outside the black hole is written in terms of the external l m ω modes of the field. They allow the computation of ⟨Φ2⟩ren and the renormalized stress-energy tensor inside the black hole, after the radial equation has been solved (usually numerically). In the second part of the paper, we provide an explicit expression for the trace of the renormalized stress-energy tensor of a minimally coupled massless scalar field (which is nonconformal), relating it to the d'Alembertian of ⟨Φ2⟩ren . This expression proves itself useful in various calculations of the renormalized stress-energy tensor.

Hawking radiation, covariant boundary conditions, and vacuum states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, Rabin; Kulkarni, Shailesh

2009-04-15

The basic characteristics of the covariant chiral current and the covariant chiral energy-momentum tensor are obtained from a chiral effective action. These results are used to justify the covariant boundary condition used in recent approaches of computing the Hawking flux from chiral gauge and gravitational anomalies. We also discuss a connection of our results with the conventional calculation of nonchiral currents and stress tensors in different (Unruh, Hartle-Hawking and Boulware) states.

Seismic sensitivity of normal-mode coupling to Lorentz stresses in the Sun

NASA Astrophysics Data System (ADS)

Hanasoge, Shravan M.

2017-09-01

Understanding the governing mechanism of solar magnetism remains an outstanding challenge in astrophysics. Seismology is the most compelling technique to infer the internal properties of the Sun and stars. Waves in the Sun, nominally acoustic, are sensitive to the emergence and cyclical strengthening of magnetic field, evidenced by measured changes in resonant oscillation frequencies that are correlated with the solar cycle. The inference of internal Lorentz stresses from these measurements has the potential to significantly advance our appreciation of the dynamo. Indeed, seismological inverse theory for the Sun is well understood for perturbations in composition, thermal structure and flows but, is not fully developed for magnetism, owing to the complexity of the ideal magnetohydrodynamic (MHD) equation. Invoking first-Born perturbation theory to characterize departures from spherically symmetric hydrostatic models of the Sun and applying the notation of generalized spherical harmonics, we calculate sensitivity functions of seismic measurements to the general time-varying Lorentz stress tensor. We find that eigenstates of isotropic (I.e. acoustic only) background models are dominantly sensitive to isotropic deviations in the stress tensor and much more weakly than anisotropic stresses (and therefore challenging to infer). The apple cannot fall far from the tree.

Stress field estimation based on focal mechanisms and back projected imaging in the Eastern Llanos Basin (Colombia)

NASA Astrophysics Data System (ADS)

Gómez-Alba, Sebastián; Fajardo-Zarate, Carlos Eduardo; Vargas, Carlos Alberto

2016-11-01

At least 156 earthquakes (Mw 2.8-4.4) were detected in Puerto Gaitán, Colombia (Eastern Llanos Basin) between April 2013 and December 2014. Out of context, this figure is not surprising. However, from its inception in 1993, the Colombian National Seismological Network (CNSN) found no evidence of significant seismic events in this region. In this study, we used CNSN data to model the rupture front and orientation of the highest-energy events. For these earthquakes, we relied on a joint inversion method to estimate focal mechanisms and, in turn, determine the area's fault trends and stress tensor. While the stress tensor defines maximum stress with normal tendency, focal mechanisms generally represent normal faults with NW orientation, an orientation which lines up with the tracking rupture achieved via Back Projection Imaging for the study area. We ought to bear in mind that this anomalous earthquake activity has taken place within oil fields. In short, the present paper argues that, based on the spatiotemporal distribution of seismic events, hydrocarbon operations may induce the study area's seismicity.

Finite element implementation of a thermo-damage-viscoelastic constitutive model for hydroxyl-terminated polybutadiene composite propellant

NASA Astrophysics Data System (ADS)

Xu, Jinsheng; Han, Long; Zheng, Jian; Chen, Xiong; Zhou, Changsheng

2017-11-01

A thermo-damage-viscoelastic model for hydroxyl-terminated polybutadiene (HTPB) composite propellant with consideration for the effect of temperature was implemented in ABAQUS. The damage evolution law of the model has the same form as the crack growth equation for viscoelastic materials, and only a single damage variable S is considered. The HTPB propellant was considered as an isotropic material, and the deviatoric and volumetric strain-stress relations are decoupled and described by the bulk and shear relaxation moduli, respectively. The stress update equations were expressed by the principal stresses σ_{ii}R and the rotation tensor M, the Jacobian matrix in the global coordinate system J_{ijkl} was obtained according to the fourth-order tensor transformation rules. Two models having complex stress states were used to verify the accuracy of the constitutive model. The test results showed good agreement with the strain responses of characteristic points measured by a contactless optical deformation test system, which illustrates that the thermo-damage-viscoelastic model perform well at describing the mechanical properties of an HTPB propellant.

Finite-temperature stress calculations in atomic models using moments of position.

PubMed

Parthasarathy, Ranganathan; Misra, Anil; Ouyang, Lizhi

2018-07-04

Continuum modeling of finite temperature mechanical behavior of atomic systems requires refined description of atomic motions. In this paper, we identify additional kinematical quantities that are relevant for a more accurate continuum description as the system is subjected to step-wise loading. The presented formalism avoids the necessity for atomic trajectory mapping with deformation, provides the definitions of the kinematic variables and their conjugates in real space, and simplifies local work conjugacy. The total work done on an atom under deformation is decomposed into the work corresponding to changing its equilibrium position and work corresponding to changing its second moment about equilibrium position. Correspondingly, we define two kinematic variables: a deformation gradient tensor and a vibration tensor, and derive their stress conjugates, termed here as static and vibration stresses, respectively. The proposed approach is validated using MD simulation in NVT ensembles for fcc aluminum subjected to uniaxial extension. The observed evolution of second moments in the MD simulation with macroscopic deformation is not directly related to the transformation of atomic trajectories through the deformation gradient using generator functions. However, it is noteworthy that deformation leads to a change in the second moment of the trajectories. Correspondingly, the vibration part of the Piola stress becomes particularly significant at high temperature and high tensile strain as the crystal approaches the softening limit. In contrast to the eigenvectors of the deformation gradient, the eigenvectors of the vibration tensor show strong spatial heterogeneity in the vicinity of softening. More importantly, the elliptic distribution of local atomic density transitions to a dumbbell shape, before significant non-affinity in equilibrium positions has occurred.

Finite-temperature stress calculations in atomic models using moments of position

NASA Astrophysics Data System (ADS)

Parthasarathy, Ranganathan; Misra, Anil; Ouyang, Lizhi

2018-07-01

Continuum modeling of finite temperature mechanical behavior of atomic systems requires refined description of atomic motions. In this paper, we identify additional kinematical quantities that are relevant for a more accurate continuum description as the system is subjected to step-wise loading. The presented formalism avoids the necessity for atomic trajectory mapping with deformation, provides the definitions of the kinematic variables and their conjugates in real space, and simplifies local work conjugacy. The total work done on an atom under deformation is decomposed into the work corresponding to changing its equilibrium position and work corresponding to changing its second moment about equilibrium position. Correspondingly, we define two kinematic variables: a deformation gradient tensor and a vibration tensor, and derive their stress conjugates, termed here as static and vibration stresses, respectively. The proposed approach is validated using MD simulation in NVT ensembles for fcc aluminum subjected to uniaxial extension. The observed evolution of second moments in the MD simulation with macroscopic deformation is not directly related to the transformation of atomic trajectories through the deformation gradient using generator functions. However, it is noteworthy that deformation leads to a change in the second moment of the trajectories. Correspondingly, the vibration part of the Piola stress becomes particularly significant at high temperature and high tensile strain as the crystal approaches the softening limit. In contrast to the eigenvectors of the deformation gradient, the eigenvectors of the vibration tensor show strong spatial heterogeneity in the vicinity of softening. More importantly, the elliptic distribution of local atomic density transitions to a dumbbell shape, before significant non-affinity in equilibrium positions has occurred.

Multiple seismogenic processes for high-frequency earthquakes at Katmai National Park, Alaska: Evidence from stress tensor inversions of fault-plane solutions

USGS Publications Warehouse

Moran, S.C.

2003-01-01

The volcanological significance of seismicity within Katmai National Park has been debated since the first seismograph was installed in 1963, in part because Katmai seismicity consists almost entirely of high-frequency earthquakes that can be caused by a wide range of processes. I investigate this issue by determining 140 well-constrained first-motion fault-plane solutions for shallow (depth < 9 km) earthquakes occuring between 1995 and 2001 and inverting these solutions for the stress tensor in different regions within the park. Earthquakes removed by several kilometers from the volcanic axis occur in a stress field characterized by horizontally oriented ??1 and ??3 axes, with ??1 rotated slightly (12??) relative to the NUVELIA subduction vector, indicating that these earthquakes are occurring in response to regional tectonic forces. On the other hand, stress tensors for earthquake clusters beneath several Katmai cluster volcanoes have vertically oriented ??1 axes, indicating that these events are occuring in response to local, not regional, processes. At Martin-Mageik, vertically oriented ??1 is most consistent with failure under edifice loading conditions in conjunction with localized pore pressure increases associated with hydrothermal circulation cells. At Trident-Novarupta, it is consistent with a number of possible models, including occurence along fractures formed during the 1912 eruption that now serve as horizontal conduits for migrating fluids and/or volatiles from nearby degassing and cooling magma bodies. At Mount Katmai, it is most consistent with continued seismicity along ring-fracture systems created in the 1912 eruption, perhaps enhanced by circulating hydrothermal fluids and/or seepage from the caldera-filling lake.

Global seasonal strain and stress models derived from GRACE loading, and their impact on seismicity

NASA Astrophysics Data System (ADS)

Chanard, K.; Fleitout, L.; Calais, E.; Craig, T. J.; Rebischung, P.; Avouac, J. P.

2017-12-01

Loading by continental water, atmosphere and oceans deforms the Earth at various spatio-temporal scales, inducing crustal and mantelic stress perturbations that may play a role in earthquake triggering.Deformation of the Earth by this surface loading is observed in GNSS position time series. While various models predict well vertical observations, explaining horizontal displacements remains challenging. We model the elastic deformation induced by loading derived from GRACE for coefficients 2 and higher. We estimate the degree-1 deformation field by comparison between predictions of our model and IGS-repro2 solutions at a globally distributed network of 700 GNSS sites, separating the horizontal and vertical components to avoid biases between components. The misfit between model and data is reduced compared to previous studies, particularly on the horizontal component. The associated geocenter motion time series are consistent with results derived from other datasets. We also discuss the impact on our results of systematic errors in GNSS geodetic products, in particular of the draconitic error.We then compute stress tensors time series induced by GRACE loads and discuss the potential link between large scale seasonal mass redistributions and seismicity. Within the crust, we estimate hydrologically induced stresses in the intraplate New Madrid Seismic Zone, where secular stressing rates are unmeasurably low. We show that a significant variation in the rate of micro-earthquakes at annual and multi-annual timescales coincides with stresses induced by hydrological loading in the upper Mississippi embayment, with no significant phase-lag, directly modulating regional seismicity. We also investigate pressure variations in the mantle transition zone and discuss potential correlations between the statistically significant observed seasonality of deep-focus earthquakes, most likely due to mineralogical transformations, and surface hydrological loading.

Assessment of Reynolds stress components and turbulent pressure loss using 4D flow MRI with extended motion encoding.

PubMed

Haraldsson, Henrik; Kefayati, Sarah; Ahn, Sinyeob; Dyverfeldt, Petter; Lantz, Jonas; Karlsson, Matts; Laub, Gerhard; Ebbers, Tino; Saloner, David

2018-04-01

To measure the Reynolds stress tensor using 4D flow MRI, and to evaluate its contribution to computed pressure maps. A method to assess both velocity and Reynolds stress using 4D flow MRI is presented and evaluated. The Reynolds stress is compared by cross-sectional integrals of the Reynolds stress invariants. Pressure maps are computed using the pressure Poisson equation-both including and neglecting the Reynolds stress. Good agreement is seen for Reynolds stress between computational fluid dynamics, simulated MRI, and MRI experiment. The Reynolds stress can significantly influence the computed pressure loss for simulated (eg, -0.52% vs -15.34% error; P < 0.001) and experimental (eg, 306 ± 11 vs 203 ± 6 Pa; P < 0.001) data. A 54% greater pressure loss is seen at the highest experimental flow rate when accounting for Reynolds stress (P < 0.001). 4D flow MRI with extended motion-encoding enables quantification of both the velocity and the Reynolds stress tensor. The additional information provided by this method improves the assessment of pressure gradients across a stenosis in the presence of turbulence. Unlike conventional methods, which are only valid if the flow is laminar, the proposed method is valid for both laminar and disturbed flow, a common presentation in diseased vessels. Magn Reson Med 79:1962-1971, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Smoothed Particle Hydrodynamics: A consistent model for interfacial multiphase fluid flow simulations

NASA Astrophysics Data System (ADS)

Krimi, Abdelkader; Rezoug, Mehdi; Khelladi, Sofiane; Nogueira, Xesús; Deligant, Michael; Ramírez, Luis

2018-04-01

In this work, a consistent Smoothed Particle Hydrodynamics (SPH) model to deal with interfacial multiphase fluid flows simulation is proposed. A modification to the Continuum Stress Surface formulation (CSS) [1] to enhance the stability near the fluid interface is developed in the framework of the SPH method. A non-conservative first-order consistency operator is used to compute the divergence of stress surface tensor. This formulation benefits of all the advantages of the one proposed by Adami et al. [2] and, in addition, it can be applied to more than two phases fluid flow simulations. Moreover, the generalized wall boundary conditions [3] are modified in order to be well adapted to multiphase fluid flows with different density and viscosity. In order to allow the application of this technique to wall-bounded multiphase flows, a modification of generalized wall boundary conditions is presented here for using the SPH method. In this work we also present a particle redistribution strategy as an extension of the damping technique presented in [3] to smooth the initial transient phase of gravitational multiphase fluid flow simulations. Several computational tests are investigated to show the accuracy, convergence and applicability of the proposed SPH interfacial multiphase model.

BRST Exactness of Stress-Energy Tensors

NASA Astrophysics Data System (ADS)

Miyata, Hideo; Sugimoto, Hiroshi

BRST commutators in the topological conformal field theories obtained by twisting N=2 theories are evaluated explicitly. By our systematic calculations of the multiple integrals which contain screening operators, the BRST exactness of the twisted stress-energy tensors is deduced for classical simple Lie algebras and general level k. We can see that the paths of integrations do not affect the result, and further, the N=2 coset theories are obtained by deleting two simple roots with Kac-label 1 from the extended Dynkin diagram; in other words, by not performing the integrations over the variables corresponding to the two simple roots of Kac-Moody algebras. It is also shown that a series of N=1 theories are generated in the same way by deleting one simple root with Kac-label 2.

Consequences of theory level choice evaluated with new tools from QTAIM and the stress tensor for a dipeptide conformer

NASA Astrophysics Data System (ADS)

Li, Jiahui; Xu, Tianlv; Ping, Yang; van Mourik, Tanja; Früchtl, Herbert; Kirk, Steven R.; Jenkins, Samantha

2018-03-01

QTAIM and the stress tensor were used to provide a detailed analysis of the topology of the molecular graph, BCP and bond-path properties, including the new introduced helicity length H, of a Tyr-Gly dipeptide conformer subjected to a torsion with four levels of theory; MP2, M06-2X, B3LYP-D3 and B3LYP and a modest-sized basis set, 6-31+G(d). Structural effects and bonding properties are quantified and reflect differences in the BSSE and lack of inclusion of dispersion effects in the B3LYP calculations. The helicity length H demonstrated that MP2 produced a unique response to the torsion suggesting future use as a diagnostic tool.

Exact example of backreaction of small scale inhomogeneities in cosmology

NASA Astrophysics Data System (ADS)

Green, Stephen; Wald, Robert

2013-04-01

We construct a one-parameter family of polarized vacuum Gowdy spacetimes on a torus. In the limit as the parameter N goes to infinity, the metric uniformly approaches a smooth ``background metric.'' However, spacetime derivatives of the metric do not approach a limit. As a result, we find that the background metric itself is not a solution of the vacuum Einstein equation. Rather, it is a solution of the Einstein equation with an ``effective stress-energy tensor,'' which is traceless and satisfies the weak energy condition. This is an explicit example of backreaction due to small scale inhomogeneities. We comment on the non-vacuum case, where we have proven in previous work that, provided the matter stress-energy tensor satisfies the weak energy condition, no additional backreaction is possible.

Quantum corrections in thermal states of fermions on anti-de Sitter space-time

NASA Astrophysics Data System (ADS)

Ambruş, Victor E.; Winstanley, Elizabeth

2017-12-01

We study the energy density and pressure of a relativistic thermal gas of massless fermions on four-dimensional Minkowski and anti-de Sitter space-times using relativistic kinetic theory. The corresponding quantum field theory quantities are given by components of the renormalized expectation value of the stress-energy tensor operator acting on a thermal state. On Minkowski space-time, the renormalized vacuum expectation value of the stress-energy tensor is by definition zero, while on anti-de Sitter space-time the vacuum contribution to this expectation value is in general nonzero. We compare the properties of the vacuum and thermal expectation values of the energy density and pressure for massless fermions and discuss the circumstances in which the thermal contribution dominates over the vacuum one.

An Orthotropic Model for Composite Materials in EPIC

DTIC Science & Technology

2014-06-06

directions, and fails the material by eliminating the deviatoric stresses when any of the plastic strain components reaches its user-supplied critical...the directions of the fibers, especially in comparison to the non-linear stress -strain curves obtained from off-axis tensile tests. A somewhat...increment in Cauchy stress ; and is the tensor of elastic moduli. In EPIC, this equation is implemented via central differences because the velocity

SORTAN: a Unix program for calculation and graphical presentation of fault slip as induced by stresses

NASA Astrophysics Data System (ADS)

Pascal, Christophe

2004-04-01

Stress inversion programs are nowadays frequently used in tectonic analysis. The purpose of this family of programs is to reconstruct the stress tensor characteristics from fault slip data acquired in the field or derived from earthquake focal mechanisms (i.e. inverse methods). Until now, little attention has been paid to direct methods (i.e. to determine fault slip directions from an inferred stress tensor). During the 1990s, the fast increase in resolution in 3D seismic reflection techniques made it possible to determine the geometry of subsurface faults with a satisfactory accuracy but not to determine precisely their kinematics. This recent improvement allows the use of direct methods. A computer program, namely SORTAN, is introduced. The program is highly portable on Unix platforms, straightforward to install and user-friendly. The computation is based on classical stress-fault slip relationships and allows for fast treatment of a set of faults and graphical presentation of the results (i.e. slip directions). In addition, the SORTAN program permits one to test the sensitivity of the results to input uncertainties. It is a complementary tool to classical stress inversion methods and can be used to check the mechanical consistency and the limits of structural interpretations based upon 3D seismic reflection surveys.

A stress-dependent model for reservoir stimulation in enhanced geothermal systems

NASA Astrophysics Data System (ADS)

Troiano, Antonio; Giulia Di Giuseppe, Maria; Troise, Claudia; De Natale, Giuseppe

2015-04-01

We present a procedure for testing the interpretation of the induced seismicity. The procedure is based on Coulomb stress changes induced by deep fluid injection during well stimulation, providing a way to estimate how the potential for seismic failure in different volumes of a geothermal reservoir might change due to the water injection. Coulomb stress changes appear to be the main cause for the induced seismicity during the water injection. These stress changes do not only result from changes in the pore pressure, but also from the whole change in the stress tensor at any point in the medium, which results from the pressure perturbations. The numerical procedure presented takes into account the permeability increase that is due to the induced stress changes. A conceptual model that links the induced stress tensor and the permeability modifications is considered to estimate the permeability change induced during the water injection. In this way, we can adapt the medium behavior to mechanical changes, in order to better evaluate the effectiveness of the stimulation process for the enhancement of the reservoir permeability, while also refining the reconstruction of the Coulomb stress change patterns. Numerical tests have been developed that consider a physical medium and a geometry of the system comparable with that of Soultz EGS site (Alsace, France). Tests considering a fixed permeability, both isotropic and anisotropic, indicate a general decrease in the pressure changes when an anisotropic permeability was considered, with respect to the isotropic case. A marked elongation of the coulomb stress change patterns in the regional load direction was retrieved. This effect is enforced when a stress-dependent permeability is taken into account. Permeability enhancement progressively enlarges the seismic volume in turns, while decreasing the pressure in the neighborhood of the bottom of the well. The use of stress-dependent permeability also improves the reconstruction of the observed seismicity pattern. In particular, the large maximum of the coulomb stress changes at the point of injection, which was already mitigated by the consideration of anisotropic permeability, appears further decreased in the new data. The improving of the correlation between the coulomb stress changes and the induced seismicity distribution supports the reliability and robustness of the main hypothesis of this study of the relationship between the induced stress tensor variation and the permeability enhancement. The use of stress-dependent permeability constitutes an important step towards the theoretical planning of stimulation procedures, and towards interpretation and mitigation of the induced seismicity.

Plate convergence at the westernmost Philippine Sea Plate

NASA Astrophysics Data System (ADS)

Wu, Wen-Nan; Hsu, Shu-Kun; Lo, Chung-Liang; Chen, How-Wei; Ma, Kuo-Fong

2009-03-01

To understand the convergent characteristics of the westernmost plate boundary between the Philippine Sea Plate (PSP) and Eurasian Plate (EP), we have calculated the stress states of plate motion by focal mechanisms. Cataloged by the Harvard centroid moment tensor solutions (Harvard CMT) and the Broadband Array in Taiwan (BATS) moment tensor, 251 focal mechanisms are used to determine the azimuths of the principal stress axes. We first used all the data to derive the mean stress tensor of the study area. The inversion result shows that the stress regime has a maximum compression along the direction of azimuth N299°. This result is consistent with the general direction of the rigid plate motion between the PSP and EP in the study area. In order to understand the spatial variation of the regional stress pattern, we divided the study area into six sub-areas (blocks A to F) based on the feature of the free-air gravity anomaly. We compare the compressive directions obtained from the stress inversion with the plate motions calculated by the Euler pole and the Global Positioning System (GPS) analysis. As a result, the azimuth of the maximum stress axis, σ1, generally agrees with the directions of the theoretical plate motion and GPS velocity vectors except block C (Lanhsu region) and block F (Ilan plain region). The discrepancy of convergent direction near the Ilan plain region is probably caused by the rifting of the Okinawa Trough. The deviation of the σ1 azimuth in the Lanhsu region could be attributed to a southwestward extrusion of the Luzon Arc (LA) block between 21°N and 22°N whose northern boundary may be associated with the right-lateral NE-SW trending fault (i.e. Huatung Fault, HF) along the Taitung Canyon. Comparing the σ1 stress patterns between block C and block D, great strain energy along HF may not be completely released yet. Alternatively, the upper crust of block C may significantly have decoupled from its lower crust or uppermost mantle.

Coseismic temporal changes of slip direction: the effect of absolute stress on dynamic rupture

USGS Publications Warehouse

Guatteri, Mariagiovanna; Spudich, P.

1998-01-01

We investigate the dynamics of rupture at low-stress level. We show that one main difference between the dynamics of high- and low-stress events is the amount of coseismic temporal rake rotation occurring at given points on the fault. Curved striations on exposed fault surfaces and earthquake dislocation models derived from ground-motion inversion indicate that the slip direction may change with time at a point on the fault during dynamic rupture. We use a 3D boundary integral method to model temporal rake variations during dynamic rupture propagation assuming a slip-weakening friction law and isotropic friction. The points at which the slip rotates most are characterized by an initial shear stress direction substantially different from the average stress direction over the fault plane. We show that for a given value of stress drop, the level of initial shear stress (i.e., the fractional stress drop) determines the amount of rotation in slip direction. We infer that seismic events that show evidence of temporal rake rotations are characterized by a low initial shear-stress level with spatially variable direction on the fault (possibly due to changes in fault surface geometry) and an almost complete stress drop.Our models motivate a new interpretation of curved and cross-cutting striations and put new constraints on their analysis. The initial rake is in general collinear with the initial stress at the hypocentral zone, supporting the assumptions made in stress-tensor inversion from first-motion analysis. At other points on the fault, especially away from the hypocenter, the initial slip rake may not be collinear with the initial shear stress, contradicting a common assumption of structural geology. On the other hand, the later part of slip in our models is systematically more aligned with the average stress direction than the early slip. Our modeling suggests that the length of the straight part of curved striations is usually an upper bound of the slip-weakening distance if this parameter is uniform over the fault plane, and the direction of the late part of slip of curved striations should have more weight in the estimate of initial stress direction.

Influence of Tidal Forces on the Triggering of Seismic Events

NASA Astrophysics Data System (ADS)

Varga, Péter; Grafarend, Erik

2018-05-01

Tidal stresses are generated in any three-dimensional body influenced by an external inhomogeneous gravity field of rotating planets or moons. In this paper, as a special case, stresses caused within the solid Earth by the body tides are discussed from viewpoint of their influence on seismic activity. The earthquake triggering effects of the Moon and Sun are usually investigated by statistical comparison of tidal variations and temporal distribution of earthquake activity, or with the use of mathematical or experimental modelling of physical processes in earthquake prone structures. In this study, the magnitude of the lunisolar stress tensor in terms of its components along the latitude of the spherical surface of the Earth as well as inside the Earth (up to the core-mantle boundary) were calculated for the PREM (Dziewonski and Anderson in Phys Earth Planet Inter 25(4):297-356, 1981). Results of calculations prove that stress increases as a function of depth reaching a value around some kPa at the depth of 900-1500 km, well below the zone of deep earthquakes. At the depth of the overwhelming part of seismic energy accumulation (around 50 km) the stresses of lunisolar origin are only (0.0-1.0)·103 Pa. Despite the fact that these values are much smaller than the earthquake stress drops (1-30 MPa) (Kanamori in Annu Rev Earth Planet Sci 22:207-237, 1994) this does not exclude the possibility of an impact of tidal forces on outbreak of seismic events. Since the tidal potential and its derivatives are coordinate dependent and the zonal, tesseral and sectorial tides have different distributions from the surface down to the CMB, the lunisolar stress cannot influence the break-out of every seismological event in the same degree. The influencing lunisolar effect of the solid earth tides on earthquake occurrences is connected first of all with stress components acting parallel to the surface of the Earth. The influence of load tides is limited to the loaded area and its immediate vicinity.

Influence of Tidal Forces on the Triggering of Seismic Events

NASA Astrophysics Data System (ADS)

Varga, Péter; Grafarend, Erik

2017-05-01

Tidal stresses are generated in any three-dimensional body influenced by an external inhomogeneous gravity field of rotating planets or moons. In this paper, as a special case, stresses caused within the solid Earth by the body tides are discussed from viewpoint of their influence on seismic activity. The earthquake triggering effects of the Moon and Sun are usually investigated by statistical comparison of tidal variations and temporal distribution of earthquake activity, or with the use of mathematical or experimental modelling of physical processes in earthquake prone structures. In this study, the magnitude of the lunisolar stress tensor in terms of its components along the latitude of the spherical surface of the Earth as well as inside the Earth (up to the core-mantle boundary) were calculated for the PREM (Dziewonski and Anderson in Phys Earth Planet Inter 25(4):297-356, 1981). Results of calculations prove that stress increases as a function of depth reaching a value around some kPa at the depth of 900-1500 km, well below the zone of deep earthquakes. At the depth of the overwhelming part of seismic energy accumulation (around 50 km) the stresses of lunisolar origin are only (0.0-1.0)·103 Pa. Despite the fact that these values are much smaller than the earthquake stress drops (1-30 MPa) (Kanamori in Annu Rev Earth Planet Sci 22:207-237, 1994) this does not exclude the possibility of an impact of tidal forces on outbreak of seismic events. Since the tidal potential and its derivatives are coordinate dependent and the zonal, tesseral and sectorial tides have different distributions from the surface down to the CMB, the lunisolar stress cannot influence the break-out of every seismological event in the same degree. The influencing lunisolar effect of the solid earth tides on earthquake occurrences is connected first of all with stress components acting parallel to the surface of the Earth. The influence of load tides is limited to the loaded area and its immediate vicinity.

A Mass Diffusion Model for Dry Snow Utilizing a Fabric Tensor to Characterize Anisotropy

NASA Astrophysics Data System (ADS)

Shertzer, Richard H.; Adams, Edward E.

2018-03-01

A homogenization algorithm for randomly distributed microstructures is applied to develop a mass diffusion model for dry snow. Homogenization is a multiscale approach linking constituent behavior at the microscopic level—among ice and air—to the macroscopic material—snow. Principles of continuum mechanics at the microscopic scale describe water vapor diffusion across an ice grain's surface to the air-filled pore space. Volume averaging and a localization assumption scale up and down, respectively, between microscopic and macroscopic scales. The model yields a mass diffusivity expression at the macroscopic scale that is, in general, a second-order tensor parameterized by both bulk and microstructural variables. The model predicts a mass diffusivity of water vapor through snow that is less than that through air. Mass diffusivity is expected to decrease linearly with ice volume fraction. Potential anisotropy in snow's mass diffusivity is captured due to the tensor representation. The tensor is built from directional data assigned to specific, idealized microstructural features. Such anisotropy has been observed in the field and laboratories in snow morphologies of interest such as weak layers of depth hoar and near-surface facets.

Generalized Boussinesq-Scriven surface fluid model with curvature dissipation for liquid surfaces and membranes.

PubMed

Aguilar Gutierrez, Oscar F; Herrera Valencia, Edtson E; Rey, Alejandro D

2017-10-01

Curvature dissipation is relevant in synthetic and biological processes, from fluctuations in semi-flexible polymer solutions, to buckling of liquid columns, tomembrane cell wall functioning. We present a micromechanical model of curvature dissipation relevant to fluid membranes and liquid surfaces based on a parallel surface parameterization and a stress constitutive equation appropriate for anisotropic fluids and fluid membranes.The derived model, aimed at high curvature and high rate of change of curvature in liquid surfaces and membranes, introduces additional viscous modes not included in the widely used 2D Boussinesq-Scriven rheological constitutive equation for surface fluids.The kinematic tensors that emerge from theparallel surface parameterization are the interfacial rate of deformation and the surface co-rotational Zaremba-Jaumann derivative of the curvature, which are used to classify all possibledissipative planar and non-planar modes. The curvature dissipation function that accounts for bending, torsion and twist rates is derived and analyzed under several constraints, including the important inextensional bending mode.A representative application of the curvature dissipation model to the periodic oscillation in nano-wrinkled outer hair cells show how and why curvature dissipation decreases with frequency, and why the 100kHz frequency range is selected. These results contribute to characterize curvature dissipation in membranes and liquid surfaces. Copyright © 2017 Elsevier Inc. All rights reserved.

Physics behind the oscillation of pressure tensor autocorrelation function for nanocolloidal dispersions.

PubMed

Wang, Tao; Wang, Xinwei; Luo, Zhongyang; Cen, Kefa

2008-08-01

In this work, extensive equilibrium molecular dynamics simulations are conducted to explore the physics behind the oscillation of pressure tensor autocorrelation function (PTACF) for nanocolloidal dispersions, which leads to strong instability in viscosity calculation. By reducing the particle size and density, we find the intensity of the oscillation decreases while the frequency of the oscillation becomes higher. Careful analysis of the relationship between the oscillation and nanoparticle characteristics reveals that the stress wave scattering/reflection at the particle-liquid interface plays a critical role in PTACF oscillation while the Brownian motion/vibration of solid particles has little effect. Our modeling proves that it is practical to eliminate the PTACF oscillation through suppressing the acoustic mismatch at the solid-liquid interface by designing special nanoparticle materials. It is also found when the particle size is comparable with the wavelength of the stress wave, diffraction of stress wave happens at the interface. Such effect substantially reduces the PTACF oscillation and improves the stability of viscosity calculation.

Quantum field theory in spaces with closed time-like curves

NASA Astrophysics Data System (ADS)

Boulware, D. G.

Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27(pi). A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

Neotectonic activity and parameters of seismotectonic deformations of seismic belts in Northeast Asia

NASA Astrophysics Data System (ADS)

Imaeva, Lyudmila; Gusev, Georgy; Imaev, Valerii; Mel'nikova, Valentina

2017-10-01

The Arctic-Asian and Okhotsk-Chukotka seismic belts bordering the Kolyma-Chukotka crustal plate are the subject of our study aimed at reconstructing the stress-strain state of the crust and defining the types of seismotectonic deformation (STD) in the region. Based on the degrees of activity of geodynamic processes, the regional principles for ranking neotectonic structures were constrained, and the corresponding classes of the discussed neotectonic structures were substantiated. We analyzed the structural tectonic positions of the modern structures, their deep structure parameters, and the systems of active faults in the Laptev, Kharaulakh, Koryak, and Chukotka segments and Chersky seismotectonic zone, as well as the tectonic stress fields revealed by tectonophysical analysis of the Late Cenozoic faults and folds. From the earthquake focal mechanisms, the average seismotectonic strain tensors were estimated. Using the geological, geostructural, geophysical and GPS data, and corresponding average tensors, the directions of the principal stress axes were determined. A regularity in the changes of tectonic settings in the Northeast Arctic was revealed.

A note on stress-driven anisotropic diffusion and its role in active deformable media.

PubMed

Cherubini, Christian; Filippi, Simonetta; Gizzi, Alessio; Ruiz-Baier, Ricardo

2017-10-07

We introduce a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to employ diffusion tensors directly influenced by the coupling with mechanical stress. The proposed generalised reaction-diffusion-mechanics model reveals that initially isotropic and homogeneous diffusion tensors turn into inhomogeneous and anisotropic quantities due to the intrinsic structure of the nonlinear coupling. We study the physical properties leading to these effects, and investigate mathematical conditions for its occurrence. Together, the mathematical model and the numerical results obtained using a mixed-primal finite element method, clearly support relevant consequences of stress-driven diffusion into anisotropy patterns, drifting, and conduction velocity of the resulting excitation waves. Our findings also indicate the applicability of this novel approach in the description of mechano-electric feedback in actively deforming bio-materials such as the cardiac tissue. Copyright © 2017. Published by Elsevier Ltd.

A representation for the turbulent mass flux contribution to Reynolds-stress and two-equation closures for compressible turbulence

NASA Technical Reports Server (NTRS)

Ristorcelli, J. R.

1993-01-01

The turbulent mass flux, or equivalently the fluctuating Favre velocity mean, appears in the first and second moment equations of compressible kappa-epsilon and Reynolds stress closures. Mathematically it is the difference between the unweighted and density-weighted averages of the velocity field and is therefore a measure of the effects of compressibility through variations in density. It appears to be fundamental to an inhomogeneous compressible turbulence, in which it characterizes the effects of the mean density gradients, in the same way the anisotropy tensor characterizes the effects of the mean velocity gradients. An evolution equation for the turbulent mass flux is derived. A truncation of this equation produces an algebraic expression for the mass flux. The mass flux is found to be proportional to the mean density gradients with a tensor eddy-viscosity that depends on both the mean deformation and the Reynolds stresses. The model is tested in a wall bounded DNS at Mach 4.5 with notable results.

The Reynolds-stress tensor in diffusion flames; An experimental and theoretical investigation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schneider, F.; Janicka, J.

1990-07-01

The authors present measurements and predictions of Reynolds-stress components and mean velocities in a CH{sub 4}-air diffusion flame. A reference beam LDA technique is applied for measuring all Reynolds-stress components. A hologram with dichromated gelatine as recording medium generates strictly coherent reference beams. The theoretical part describes a Reynolds-stress model based on Favre-averaged quantities, paying special attention to modeling the pressure-shear correlation and the dissipation equation in flames. Finally, measurement/prediction comparisons are presented.

Propagation of threading dislocations in heteroepitaxial diamond films with (111) orientation and their role in the formation of intrinsic stress

NASA Astrophysics Data System (ADS)

Gallheber, B.-C.; Klein, O.; Fischer, M.; Schreck, M.

2017-06-01

In the present study, systematic correlations were revealed between the propagation direction of threading dislocations, the off-axis growth conditions, and the stress state of heteroepitaxial diamond on Ir/YSZ/Si(111). Measurements of the strain tensor ɛ ⃡ by X-ray diffraction and the subsequent calculation of the tensor of intrinsic stress σ ⃡ showed stress-free samples as well as symmetric biaxial stress states for on-axis samples. Transmission electron microscopy (TEM) lamellas were prepared for plan-view studies along the [ 1 ¯ 1 ¯ 1 ¯ ] direction and for cross-section investigations along the [11 2 ¯ ] and [1 1 ¯ 0] zone axes. For samples grown on-axis with parameters which avoid the formation of intrinsic stress, the majority of dislocations have line vectors clearly aligned along [111]. A sudden change to conditions that promote stress formation is correlated with an abrupt bending of the dislocations away from [111]. This behaviour is in nice agreement with the predictions of a model that attributes formation of intrinsic stress to an effective climb of dislocations. Further growth experiments under off-axis conditions revealed the generation of stress states with pronounced in-plane anisotropy of several Gigapascal. Their formation is attributed to the combined action of two basic processes, i.e., the step flow driven dislocation tilting and the temperature dependent effective climb of dislocations. Again, our interpretation is supported by the dislocation propagation derived from TEM observations.

Dynamic rupture modeling of the transition from thrust to strike-slip motion in the 2002 Denali fault earthquake, Alaska

USGS Publications Warehouse

Aagaard, Brad T.; Anderson, G.; Hudnut, K.W.

2004-01-01

We use three-dimensional dynamic (spontaneous) rupture models to investigate the nearly simultaneous ruptures of the Susitna Glacier thrust fault and the Denali strike-slip fault. With the 1957 Mw 8.3 Gobi-Altay, Mongolia, earthquake as the only other well-documented case of significant, nearly simultaneous rupture of both thrust and strike-slip faults, this feature of the 2002 Denali fault earthquake provides a unique opportunity to investigate the mechanisms responsible for development of these large, complex events. We find that the geometry of the faults and the orientation of the regional stress field caused slip on the Susitna Glacier fault to load the Denali fault. Several different stress orientations with oblique right-lateral motion on the Susitna Glacier fault replicate the triggering of rupture on the Denali fault about 10 sec after the rupture nucleates on the Susitna Glacier fault. However, generating slip directions compatible with measured surface offsets and kinematic source inversions requires perturbing the stress orientation from that determined with focal mechanisms of regional events. Adjusting the vertical component of the principal stress tensor for the regional stress field so that it is more consistent with a mixture of strike-slip and reverse faulting significantly improves the fit of the slip-rake angles to the data. Rotating the maximum horizontal compressive stress direction westward appears to improve the fit even further.

New insights on the matter-gravity coupling paradigm.

PubMed

Delsate, Térence; Steinhoff, Jan

2012-07-13

The coupling between matter and gravity in general relativity is given by a proportionality relation between the stress tensor and the geometry. This is an oriented assumption driven by the fact that both the stress tensor and the Einstein tensor are divergenceless. However, general relativity is in essence a nonlinear theory, so there is no obvious reason why the coupling to matter should be linear. On another hand, modified theories of gravity usually affect the vacuum dynamics, yet keep the coupling to matter linear. In this Letter, we address the implications of consistent nonlinear gravity-matter coupling. The Eddington-inspired Born-Infeld theory recently introduced by Bañados and Ferreira provides an enlightening realization of such coupling modifications. We find that this theory coupled to a perfect fluid reduces to general relativity coupled to a nonlinearly modified perfect fluid, leading to an ambiguity between modified coupling and modified equation of state. We discuss observational consequences of this degeneracy and argue that such a completion of general relativity is viable from both an experimental and theoretical point of view through energy conditions, consistency, and singularity-avoidance perspectives. We use these results to discuss the impact of changing the coupling paradigm.

Why fibers are better turbulent drag reducing agents than polymers

NASA Astrophysics Data System (ADS)

Boelens, Arnout; Muthukumar, Murugappan

2016-11-01

It is typically found in literature that fibers are not as effective as drag reducing agents as polymers. However, for low concentrations, when adding charged polymers to either distilled or salt water, it is found that polymers showing rod-like behavior are better drag reducing agents than polymers showing coil-like behavior. In this study, using hybrid Direct Numerical Simulation with Langevin dynamics, a comparison is performed between polymer and fiber stress tensors in turbulent flow. The stress tensors are found to be similar, suggesting a common drag reducing mechanism in the onset regime. Since fibers do not have an elastic backbone, this must be a viscous effect. Analysis of the viscosity tensor reveals that all terms are negligible, except the off-diagonal shear viscosity associated with rotation. Based on this analysis, we are able to explain why charged polymers showing rod-like behavior are better drag reducing agents than polymers showing coil-like behavior. Additionally, we identify the rotational orientation time as the unifying time scale setting a new time criterion for drag reduction by both flexible polymers and rigid fibers. This research was supported by NSF Grant No. DMR-1404940 and AFOSR Grant No. FA9550-14-1-0164.

Projector Augmented-Wave formulation of response to strain and electric field perturbation within the density-functional perturbation theory

NASA Astrophysics Data System (ADS)

Martin, Alexandre; Torrent, Marc; Caracas, Razvan

2015-03-01

A formulation of the response of a system to strain and electric field perturbations in the pseudopotential-based density functional perturbation theory (DFPT) has been proposed by D.R Hamman and co-workers. It uses an elegant formalism based on the expression of DFT total energy in reduced coordinates, the key quantity being the metric tensor and its first and second derivatives. We propose to extend this formulation to the Projector Augmented-Wave approach (PAW). In this context, we express the full elastic tensor including the clamped-atom tensor, the atomic-relaxation contributions (internal stresses) and the response to electric field change (piezoelectric tensor and effective charges). With this we are able to compute the elastic tensor for all materials (metals and insulators) within a fully analytical formulation. The comparison with finite differences calculations on simple systems shows an excellent agreement. This formalism has been implemented in the plane-wave based DFT ABINIT code. We apply it to the computation of elastic properties and seismic-wave velocities of iron with impurity elements. By analogy with the materials contained in meteorites, tested impurities are light elements (H, O, C, S, Si).

Investigation of Thermal Stress Convection in Nonisothermal Gases Under Microgravity Conditions

NASA Technical Reports Server (NTRS)

Mackowski, Daniel W.; Knight, Roy W.

1996-01-01

Microgravity conditions offer an environment in which convection in a nonisothermal gas could be driven primarily by thermal stress. A direct examination of thermal stress flows would be invaluable in assessing the accuracy of the Burnett terms in the fluid stress tensor. We present a preliminary numerical investigation of the competing effects of thermal stress, thermal creep at the side walls, and buoyancy on gas convection in nonuniformly heated containers under normal and reduced gravity levels. Conditions in which thermal stress convection becomes dominant are identified, and issues regarding the experimental measurement of the flows are discussed.

Three-dimensional wave-induced current model equations and radiation stresses

NASA Astrophysics Data System (ADS)

Xia, Hua-yong

2017-08-01

After the approach by Mellor (2003, 2008), the present paper reports on a repeated effort to derive the equations for three-dimensional wave-induced current. Via the vertical momentum equation and a proper coordinate transformation, the phase-averaged wave dynamic pressure is well treated, and a continuous and depth-dependent radiation stress tensor, rather than the controversial delta Dirac function at the surface shown in Mellor (2008), is provided. Besides, a phase-averaged vertical momentum flux over a sloping bottom is introduced. All the inconsistencies in Mellor (2003, 2008), pointed out by Ardhuin et al. (2008) and Bennis and Ardhuin (2011), are overcome in the presently revised equations. In a test case with a sloping sea bed, as shown in Ardhuin et al. (2008), the wave-driving forces derived in the present equations are in good balance, and no spurious vertical circulation occurs outside the surf zone, indicating that Airy's wave theory and the approach of Mellor (2003, 2008) are applicable for the derivation of the wave-induced current model.

Moment tensor clustering: a tool to monitor mining induced seismicity

NASA Astrophysics Data System (ADS)

Cesca, Simone; Dahm, Torsten; Tolga Sen, Ali

2013-04-01

Automated moment tensor inversion routines have been setup in the last decades for the analysis of global and regional seismicity. Recent developments could be used to analyse smaller events and larger datasets. In particular, applications to microseismicity, e.g. in mining environments, have then led to the generation of large moment tensor catalogues. Moment tensor catalogues provide a valuable information about the earthquake source and details of rupturing processes taking place in the seismogenic region. Earthquake focal mechanisms can be used to discuss the local stress field, possible orientations of the fault system or to evaluate the presence of shear and/or tensile cracks. Focal mechanism and moment tensor solutions are typically analysed for selected events, and quick and robust tools for the automated analysis of larger catalogues are needed. We propose here a method to perform cluster analysis for large moment tensor catalogues and identify families of events which characterize the studied microseismicity. Clusters include events with similar focal mechanisms, first requiring the definition of distance between focal mechanisms. Different metrics are here proposed, both for the case of pure double couple, constrained moment tensor and full moment tensor catalogues. Different clustering approaches are implemented and discussed. The method is here applied to synthetic and real datasets from mining environments to demonstrate its potential: the proposed cluserting techniques prove to be able to automatically recognise major clusters. An important application for mining monitoring concerns the early identification of anomalous rupture processes, which is relevant for the hazard assessment. This study is funded by the project MINE, which is part of the R&D-Programme GEOTECHNOLOGIEN. The project MINE is funded by the German Ministry of Education and Research (BMBF), Grant of project BMBF03G0737.

Application of boundary element method to Stokes flows over a striped superhydrophobic surface with trapped gas bubbles

NASA Astrophysics Data System (ADS)

Ageev, A. I.; Golubkina, I. V.; Osiptsov, A. N.

2018-01-01

A slow steady flow of a viscous fluid over a superhydrophobic surface with a periodic striped system of 2D rectangular microcavities is considered. The microcavities contain small gas bubbles on the curved surface of which the shear stress vanishes. The general case is analyzed when the bubble occupies only a part of the cavity, and the flow velocity far from the surface is directed at an arbitrary angle to the cavity edge. Due to the linearity of the Stokes flow problem, the solution is split into two parts, corresponding to the flows perpendicular and along the cavities. Two variants of a boundary element method are developed and used to construct numerical solutions on the scale of a single cavity with periodic boundary conditions. By averaging these solutions, the average slip velocity and the slip length tensor components are calculated over a wide range of variation of governing parameters for the cases of a shear-driven flow and a pressure-driven channel flow. For a sufficiently high pressure drop in a microchannel of finite length, the variation of the bubble surface shift into the cavities induced by the streamwise pressure variation is estimated from numerical calculations.

A dynamic regularized gradient model of the subgrid-scale stress tensor for large-eddy simulation

NASA Astrophysics Data System (ADS)

Vollant, A.; Balarac, G.; Corre, C.

2016-02-01

Large-eddy simulation (LES) solves only the large scales part of turbulent flows by using a scales separation based on a filtering operation. The solution of the filtered Navier-Stokes equations requires then to model the subgrid-scale (SGS) stress tensor to take into account the effect of scales smaller than the filter size. In this work, a new model is proposed for the SGS stress model. The model formulation is based on a regularization procedure of the gradient model to correct its unstable behavior. The model is developed based on a priori tests to improve the accuracy of the modeling for both structural and functional performances, i.e., the model ability to locally approximate the SGS unknown term and to reproduce enough global SGS dissipation, respectively. LES is then performed for a posteriori validation. This work is an extension to the SGS stress tensor of the regularization procedure proposed by Balarac et al. ["A dynamic regularized gradient model of the subgrid-scale scalar flux for large eddy simulations," Phys. Fluids 25(7), 075107 (2013)] to model the SGS scalar flux. A set of dynamic regularized gradient (DRG) models is thus made available for both the momentum and the scalar equations. The second objective of this work is to compare this new set of DRG models with direct numerical simulations (DNS), filtered DNS in the case of classic flows simulated with a pseudo-spectral solver and with the standard set of models based on the dynamic Smagorinsky model. Various flow configurations are considered: decaying homogeneous isotropic turbulence, turbulent plane jet, and turbulent channel flows. These tests demonstrate the stable behavior provided by the regularization procedure, along with substantial improvement for velocity and scalar statistics predictions.

Model for quantum effects in stellar collapse

NASA Astrophysics Data System (ADS)

Arderucio-Costa, Bruno; Unruh, William G.

2018-01-01

We present a simple model for stellar collapse and evaluate the quantum mechanical stress-energy tensor to argue that quantum effects do not play an important role for the collapse of astrophysical objects.

Microstructural Rearrangements and their Rheological Implications in a Model Thixotropic Elastoviscoplastic Fluid

NASA Astrophysics Data System (ADS)

Jamali, Safa; McKinley, Gareth H.; Armstrong, Robert C.

2017-01-01

We identify the sequence of microstructural changes that characterize the evolution of an attractive particulate gel under flow and discuss their implications on macroscopic rheology. Dissipative particle dynamics is used to monitor shear-driven evolution of a fabric tensor constructed from the ensemble spatial configuration of individual attractive constituents within the gel. By decomposing this tensor into isotropic and nonisotropic components we show that the average coordination number correlates directly with the flow curve of the shear stress versus shear rate, consistent with theoretical predictions for attractive systems. We show that the evolution in nonisotropic local particle rearrangements are primarily responsible for stress overshoots (strain-hardening) at the inception of steady shear flow and also lead, at larger times and longer scales, to microstructural localization phenomena such as shear banding flow-induced structure formation in the vorticity direction.

A Hydraulic Stress Measurement System for Investigations at Depth in Slim Boreholes

NASA Astrophysics Data System (ADS)

Ask, M. V. S.; Ask, D.; Cornet, F. H.; Nilsson, T.; Talib, M.; Sundberg, J.

2017-12-01

Knowledge of the state of stress is essential to most underground work in rock mechanics as it provides means to analyze the mechanical behavior of a rock mass, serve as boundary condition in rock engineering problems, and help understand rock mass stability and groundwater flow. Luleå University of Technology (LTU) has developed and built a wire-line system for hydraulic rock stress measurements in slim boreholes together with the University of Strasbourg and Geosigma AB. The system consists of a downhole- and a surface unit. The downhole unit consists of hydraulic fracturing equipment (straddle packers and downhole imaging tool) and their associated data acquisition systems. The surface unit comprises of a 40-foot container permanently mounted on a trailer, which is equipped with a tripod, wire-line winches, water hydraulics, and a generator. The surface unit serves as a climate-independent on-site operations center, as well as a self-supporting transport vessel for the entire system. Three hydraulic stress testing methods can be applied: hydraulic fracturing, sleeve fracturing and hydraulic testing of pre-existing fractures. The three-dimensional stress tensor and its variation with depth within a continuous rock mass can be determined in a scientific unambiguously way by integrating results from the three test methods. The testing system is state of the art in several aspects including: (1) Large depth range (3 km), (2) Ability to test three borehole dimensions, (3) Resistivity imager maps the orientation of tested fracture (which is highlighted); (4) Highly stiff and resistive to corrosion downhole testing equipment; and (5) Very detailed control on the injection flow rate and cumulative volume is obtained by a hydraulic injection pump with variable piston rate, and a highly sensitive flow-meter. These aspects highly reduce measurement-related uncertainties of stress determination. Commissioning testing and initial field tests are scheduled to occur in a 1200 m long borehole in crystalline rock during the autumn of 2017. We aim at presenting this new and unique stress measurement system and some test results from the initial field tests.

Defects in Nonlinear Elastic Crystals: Differential Geometry, Finite Kinematics, and Second-Order Analytical Solutions

DTIC Science & Technology

2015-04-01

of unit length: da = F L a αδ α Ad A , da = F L−1αaδ A α dA . (2.12) The metric tensor associated with the deformed... A spatial density tensor θ and Frank vector ω̂ of the following forms are consistent with geometry of the problem: θ = θzzgz ⊗ gz = ω̂δ(r)gz ⊗ gz = δ...stress depends quadratically on strain, with the elastic potential cubic in strain and including elastic constants of

Nonlinear Viscoelastic Analysis of Orthotropic Beams Using a General Third-Order Theory

DTIC Science & Technology

2012-06-20

Kirchhoff stress tensor, denoted by r and reduced strain tensor E e is given by rxx rzz rxz 8><>: 9>=>;¼ Q11ð0Þ Q13ð0Þ 0 Q13ð0Þ Q33ð0Þ 0 0 0 Q55ð0Þ...0.5 1 −0.5 0 0.5 1 (a) (b) Fig. 1. Graphs of (a) equi-spaced and (b) spectral lagrange interpolation functions for polynomial order of p = 11. 3762 V

Investigating source processes of isotropic events

NASA Astrophysics Data System (ADS)

Chiang, Andrea

This dissertation demonstrates the utility of the complete waveform regional moment tensor inversion for nuclear event discrimination. I explore the source processes and associated uncertainties for explosions and earthquakes under the effects of limited station coverage, compound seismic sources, assumptions in velocity models and the corresponding Green's functions, and the effects of shallow source depth and free-surface conditions. The motivation to develop better techniques to obtain reliable source mechanism and assess uncertainties is not limited to nuclear monitoring, but they also provide quantitative information about the characteristics of seismic hazards, local and regional tectonics and in-situ stress fields of the region . This dissertation begins with the analysis of three sparsely recorded events: the 14 September 1988 US-Soviet Joint Verification Experiment (JVE) nuclear test at the Semipalatinsk test site in Eastern Kazakhstan, and two nuclear explosions at the Chinese Lop Nor test site. We utilize a regional distance seismic waveform method fitting long-period, complete, three-component waveforms jointly with first-motion observations from regional stations and teleseismic arrays. The combination of long period waveforms and first motion observations provides unique discrimination of these sparsely recorded events in the context of the Hudson et al. (1989) source-type diagram. We examine the effects of the free surface on the moment tensor via synthetic testing, and apply the moment tensor based discrimination method to well-recorded chemical explosions. These shallow chemical explosions represent rather severe source-station geometry in terms of the vanishing traction issues. We show that the combined waveform and first motion method enables the unique discrimination of these events, even though the data include unmodeled single force components resulting from the collapse and blowout of the quarry face immediately following the initial explosion. In contrast, recovering the announced explosive yield using seismic moment estimates from moment tensor inversion remains challenging but we can begin to put error bounds on our moment estimates using the NSS technique. The estimation of seismic source parameters is dependent upon having a well-calibrated velocity model to compute the Green's functions for the inverse problem. Ideally, seismic velocity models are calibrated through broadband waveform modeling, however in regions of low seismicity velocity models derived from body or surface wave tomography may be employed. Whether a velocity model is 1D or 3D, or based on broadband seismic waveform modeling or the various tomographic techniques, the uncertainty in the velocity model can be the greatest source of error in moment tensor inversion. These errors have not been fully investigated for the nuclear discrimination problem. To study the effects of unmodeled structures on the moment tensor inversion, we set up a synthetic experiment where we produce synthetic seismograms for a 3D model (Moschetti et al., 2010) and invert these data using Green's functions computed with a 1D velocity mode (Song et al., 1996) to evaluate the recoverability of input solutions, paying particular attention to biases in the isotropic component. The synthetic experiment results indicate that the 1D model assumption is valid for moment tensor inversions at periods as short as 10 seconds for the 1D western U.S. model (Song et al., 1996). The correct earthquake mechanisms and source depth are recovered with statistically insignificant isotropic components as determined by the F-test. Shallow explosions are biased by the theoretical ISO-CLVD tradeoff but the tectonic release component remains low, and the tradeoff can be eliminated with constraints from P wave first motion. Path-calibration to the 1D model can reduce non-double-couple components in earthquakes, non-isotropic components in explosions and composite sources and improve the fit to the data. When we apply the 3D model to real data, at long periods (20-50 seconds), we see good agreement in the solutions between the 1D and 3D models and slight improvement in waveform fits when using the 3D velocity model Green's functions. (Abstract shortened by ProQuest.).

Rupture model based on non-associated plasticity

NASA Astrophysics Data System (ADS)

Pradeau, Adrien; Yoon, Jeong Whan; Thuillier, Sandrine; Lou, Yanshan; Zhang, Shunying

2018-05-01

This research work is about modeling the mechanical behavior of metallic sheets of AA6016 up to rupture using non-associated flow rule. Experiments were performed at room temperature in uniaxial tension and simple shear in different directions according to the rolling direction and an additional hydraulic bulge test. The anisotropy of the material is described by a Yld2000-2d yield surface [1], calibrated by stress ratios, and a plastic potential represented by Hill1948 [2], calibrated using Lankford coefficients. That way, the former is able to reproduce the yield stresses in different directions and the latter is able to reproduce the deformations in different directions as well [3], [4]. Indeed, the non-associated flow rule allows for the direction of the plastic flow not to be necessarily normal to the yield surface. Concerning the rupture, the macroscopic ductile fracture criterion DF2014 was used [5]. It indirectly uses the three invariants of the stress tensor by using the three following parameters: the stress triaxiality η, the Lode parameter L and the equivalent plastic strain to fracture ∈f-p . In order to be consistent with the plastic model and to add more flexibility to the p criterion, the equivalent stress σ ¯ and the equivalent strain to fracture ∈f-p have been substituted respectively as Yld2000-2d and Hill1948 in the DF2014 fracture criterion. The parameters for the fracture criterion were obtained by optimization and the fracture locus can be plotted in the (η ,L ,∈-p) space. The damage indicator D is then numerically predicted with respect of average strain values. A good correlation with the experimental results is obtained.

Relating Residual Stress and Substructural Evolution During Tensile Deformation of an Aluminum-Manganese Alloy

NASA Astrophysics Data System (ADS)

Lodh, Arijit; Tak, Tawqeer Nasir; Prakash, Aditya; Guruprasad, P. J.; Hutchinson, Christopher; Samajdar, Indradev

2017-11-01

Interrupted tensile tests were coupled with ex situ measurements of residual stress and microtexture. The residual stress quantification involved measurements of six independent Laue spots and conversion of the interplanar spacings to the residual stress tensor. A clear orientation-dependent residual stress evolution emerged from the experiments and the numerical simulations. For the orientations undergoing negligible changes in ρ GND (density of geometrically necessary dislocation), the residual stress developments appeared to be governed by the elastic stiffness of the grain clusters. For the others, the evolution of the residual stress and ρ GND exhibited a clear orientation-dependent scaling.

The cancellous bone multiscale morphology-elasticity relationship.

PubMed

Agić, Ante; Nikolić, Vasilije; Mijović, Budimir

2006-06-01

The cancellous bone effective properties relations are analysed on multiscale across two aspects; properties of representative volume element on micro scale and statistical measure of trabecular trajectory orientation on mesoscale. Anisotropy of the microstructure is described across fabric tensor measure with trajectory orientation tensor as bridging scale connection. The scatter measured data (elastic modulus, trajectory orientation, apparent density) from compression test are fitted by stochastic interpolation procedure. The engineering constants of the elasticity tensor are estimated by last square fitt procedure in multidimensional space by Nelder-Mead simplex. The multiaxial failure surface in strain space is constructed and interpolated by modified super-ellipsoid.

Mesh Denoising based on Normal Voting Tensor and Binary Optimization.

PubMed

Yadav, Sunil Kumar; Reitebuch, Ulrich; Polthier, Konrad

2017-08-17

This paper presents a two-stage mesh denoising algorithm. Unlike other traditional averaging approaches, our approach uses an element-based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a local binary neighborhood concept, our algorithm better retains sharp features and produces smoother umbilical regions than previous approaches. On top of that, we provide a stochastic analysis on the different kinds of noise based on the average edge length. The quantitative results demonstrate that the performance of our method is better compared to state-of-the-art smoothing approaches.

Stress-stress correlator in ϕ 4 theory: poles or a cut?

NASA Astrophysics Data System (ADS)

Moore, Guy D.

2018-05-01

We explore the analytical properties of the traceless stress tensor 2-point function at zero momentum and small frequency (relevant for shear viscosity and hydrodynamic response) in hot, weakly coupled λ ϕ 4 theory. We show that, rather than one or a small number of poles, the correlator has a cut along the negative imaginary frequency axis. We briefly discuss this result's relevance for constructing 2'nd order hydrodynamic models of hot relativistic field theories.

Stress formulation in the all-electron full-potential linearized augmented plane wave method

NASA Astrophysics Data System (ADS)

Nagasako, Naoyuki; Oguchi, Tamio

2012-02-01

Stress formulation in the linearlized augmented plane wave (LAPW) method has been proposed in 2002 [1] as an extension of the force formulation in the LAPW method [2]. However, pressure calculations only for Al and Si were reported in Ref.[1] and even now stress calculations have not yet been fully established in the LAPW method. In order to make it possible to efficiently relax lattice shape and atomic positions simultaneously and to precisely evaluate the elastic constants in the LAPW method, we reformulate stress formula in the LAPW method with the Soler-Williams representation [3]. Validity of the formulation is tested by comparing the pressure obtained as the trace of stress tensor with that estimated from total energies for a wide variety of material systems. Results show that pressure is estimated within the accuracy of less than 0.1 GPa. Calculations of the shear elastic constant show that the shear components of the stress tensor are also precisely computed with the present formulation [4].[4pt] [1] T. Thonhauser et al., Solid State Commun. 124, 275 (2002).[0pt] [2] R. Yu et al., Phys. Rev. B 43, 6411 (1991).[0pt] [3] J. M. Soler and A. R. Williams, Phys. Rev. B 40, 1560 (1989).[0pt] [4] N. Nagasako and T. Oguchi, J. Phys. Soc. Jpn. 80, 024701 (2011).

Search for subgrid scale parameterization by projection pursuit regression

NASA Technical Reports Server (NTRS)

Meneveau, C.; Lund, T. S.; Moin, Parviz

1992-01-01

The dependence of subgrid-scale stresses on variables of the resolved field is studied using direct numerical simulations of isotropic turbulence, homogeneous shear flow, and channel flow. The projection pursuit algorithm, a promising new regression tool for high-dimensional data, is used to systematically search through a large collection of resolved variables, such as components of the strain rate, vorticity, velocity gradients at neighboring grid points, etc. For the case of isotropic turbulence, the search algorithm recovers the linear dependence on the rate of strain (which is necessary to transfer energy to subgrid scales) but is unable to determine any other more complex relationship. For shear flows, however, new systematic relations beyond eddy viscosity are found. For the homogeneous shear flow, the results suggest that products of the mean rotation rate tensor with both the fluctuating strain rate and fluctuating rotation rate tensors are important quantities in parameterizing the subgrid-scale stresses. A model incorporating these terms is proposed. When evaluated with direct numerical simulation data, this model significantly increases the correlation between the modeled and exact stresses, as compared with the Smagorinsky model. In the case of channel flow, the stresses are found to correlate with products of the fluctuating strain and rotation rate tensors. The mean rates of rotation or strain do not appear to be important in this case, and the model determined for homogeneous shear flow does not perform well when tested with channel flow data. Many questions remain about the physical mechanisms underlying these findings, about possible Reynolds number dependence, and, given the low level of correlations, about their impact on modeling. Nevertheless, demonstration of the existence of causal relations between sgs stresses and large-scale characteristics of turbulent shear flows, in addition to those necessary for energy transfer, provides important insight into the relation between scales in turbulent flows.

Seismotectonics of the Armutlu peninsula (Marmara Sea, NW Turkey) from geological field observation and regional moment tensor inversion

NASA Astrophysics Data System (ADS)

Kinscher, J.; Krüger, F.; Woith, H.; Lühr, B. G.; Hintersberger, E.; Irmak, T. S.; Baris, S.

2013-11-01

The Armutlu peninsula, located in the eastern Marmara Sea, coincides with the western end of the rupture of the 17 August 1999, İzmit MW 7.6 earthquake which is the penultimate event of an apparently westward migrating series of strong and disastrous earthquakes along the NAFZ during the past century. We present new seismotectonic data of this key region in order to evaluate previous seismotectonic models and their implications for seismic hazard assessment in the eastern Marmara Sea. Long term kinematics were investigated by performing paleo strain reconstruction from geological field investigations by morphotectonic and kinematic analysis of exposed brittle faults. Short term kinematics were investigated by inverting for the moment tensor of 13 small to moderate recent earthquakes using surface wave amplitude spectra. Our results confirm previous models interpreting the eastern Marmara Sea Region as an active transtensional pull-apart environment associated with significant NNE-SSW extension and vertical displacement. At the northern peninsula, long term deformation pattern did not change significantly since Pliocene times contradicting regional tectonic models which postulate a newly formed single dextral strike slip fault in the Marmara Sea Region. This area is interpreted as a horsetail splay fault structure associated with a major normal fault segment that we call the Waterfall Fault. Apart from the Waterfall Fault, the stress strain relation appears complex associated with a complicated internal fault geometry, strain partitioning, and reactivation of pre-existing plane structures. At the southern peninsula, recent deformation indicates active pull-apart tectonics constituted by NE-SW trending dextral strike slip faults. Earthquakes generated by stress release along large rupture zones seem to be less probable at the northern, but more probable at the southern peninsula. Additionally, regional seismicity appears predominantly driven by plate boundary stresses as transtensional faulting is consistent with the southwest directed far field deformation of the Anatolian plate.

Stress as an order parameter for the glass transition

NASA Astrophysics Data System (ADS)

Visscher, P. B.; Logan, W. T.

1990-09-01

The stress tensor has been considered as a possible order parameter for the liquid-glass transition, and its autocorrelation matrix (elements of which are the integrands in the Green-Kubo formulas for bulk and shear viscosity) have been measured in simulations. However, only the k=0 spatial Fourier component has apparently been previously measured. We have measured four Fourier components of all matrix elements of the stress-stress correlation function, and we find that some of those with nonzero wave vector are significantly more persistent (slower decaying) than the k=0 component.

Analysis of Lithospheric Stresses Using Satellite Gravimetry: Hypotheses and Applications to North Atlantic

NASA Astrophysics Data System (ADS)

Minakov, A.; Medvedev, S.

2017-12-01

Analysis of lithospheric stresses is necessary to gain understanding of the forces that drive plate tectonics and intraplate deformations and the structure and strength of the lithosphere. A major source of lithospheric stresses is believed to be in variations of surface topography and lithospheric density. The traditional approach to stress estimation is based on direct calculations of the Gravitational Potential Energy (GPE), the depth integrated density moment of the lithosphere column. GPE is highly sensitive to density structure which, however, is often poorly constrained. Density structure of the lithosphere may be refined using methods of gravity modeling. However, the resulted density models suffer from non-uniqueness of the inverse problem. An alternative approach is to directly estimate lithospheric stresses (depth integrated) from satellite gravimetry data. Satellite gravity gradient measurements by the ESA GOCE mission ensures a wealth of data for mapping lithospheric stresses if a link between data and stresses or GPE can be established theoretically. The non-uniqueness of interpretation of sources of the gravity signal holds in this case as well. Therefore, the data analysis was tested for the North Atlantic region where reliable additional constraints are supplied by both controlled-source and earthquake seismology. The study involves comparison of three methods of stress modeling: (1) the traditional modeling approach using a thin sheet approximation; (2) the filtered geoid approach; and (3) the direct utilization of the gravity gradient tensor. Whereas the first two approaches (1)-(2) calculate GPE and utilize a computationally expensive finite element mechanical modeling to calculate stresses, the approach (3) uses a much simpler numerical treatment but requires simplifying assumptions that yet to be tested. The modeled orientation of principal stresses and stress magnitudes by each of the three methods are compared with the World Stress Map.

Analytical structure, dynamics, and coarse graining of a kinetic model of an active fluid

NASA Astrophysics Data System (ADS)

Gao, Tong; Betterton, Meredith D.; Jhang, An-Sheng; Shelley, Michael J.

2017-09-01

We analyze one of the simplest active suspensions with complex dynamics: a suspension of immotile "extensor" particles that exert active extensile dipolar stresses on the fluid in which they are immersed. This is relevant to several experimental systems, such as recently studied tripartite rods that create extensile flows by consuming a chemical fuel. We first describe the system through a Doi-Onsager kinetic theory based on microscopic modeling. This theory captures the active stresses produced by the particles that can drive hydrodynamic instabilities, as well as the steric interactions of rodlike particles that lead to nematic alignment. This active nematic system yields complex flows and disclination defect dynamics very similar to phenomenological Landau-deGennes Q -tensor theories for active nematic fluids, as well as by more complex Doi-Onsager theories for polar microtubule-motor-protein systems. We apply the quasiequilibrium Bingham closure, used to study suspensions of passive microscopic rods, to develop a nonstandard Q -tensor theory. We demonstrate through simulation that this B Q -tensor theory gives an excellent analytical and statistical accounting of the suspension's complex dynamics, at a far reduced computational cost. Finally, we apply the B Q -tensor model to study the dynamics of extensor suspensions in circular and biconcave domains. In circular domains, we reproduce previous results for systems with weak nematic alignment, but for strong alignment we find unusual dynamics with activity-controlled defect production and absorption at the boundaries of the domain. In biconcave domains, a Fredericks-like transition occurs as the width of the neck connecting the two disks is varied.

Micromechanics based simulation of ductile fracture in structural steels

NASA Astrophysics Data System (ADS)

Yellavajjala, Ravi Kiran

The broader aim of this research is to develop fundamental understanding of ductile fracture process in structural steels, propose robust computational models to quantify the associated damage, and provide numerical tools to simplify the implementation of these computational models into general finite element framework. Mechanical testing on different geometries of test specimens made of ASTM A992 steels is conducted to experimentally characterize the ductile fracture at different stress states under monotonic and ultra-low cycle fatigue (ULCF) loading. Scanning electron microscopy studies of the fractured surfaces is conducted to decipher the underlying microscopic damage mechanisms that cause fracture in ASTM A992 steels. Detailed micromechanical analyses for monotonic and cyclic loading are conducted to understand the influence of stress triaxiality and Lode parameter on the void growth phase of ductile fracture. Based on monotonic analyses, an uncoupled micromechanical void growth model is proposed to predict ductile fracture. This model is then incorporated in to finite element program as a weakly coupled model to simulate the loss of load carrying capacity in the post microvoid coalescence regime for high triaxialities. Based on the cyclic analyses, an uncoupled micromechanics based cyclic void growth model is developed to predict the ULCF life of ASTM A992 steels subjected to high stress triaxialities. Furthermore, a computational fracture locus for ASTM A992 steels is developed and incorporated in to finite element program as an uncoupled ductile fracture model. This model can be used to predict the ductile fracture initiation under monotonic loading in a wide range of triaxiality and Lode parameters. Finally, a coupled microvoid elongation and dilation based continuum damage model is proposed, implemented, calibrated and validated. This model is capable of simulating the local softening caused by the various phases of ductile fracture process under monotonic loading for a wide range of stress states. Novel differentiation procedures based on complex analyses along with existing finite difference methods and automatic differentiation are extended using perturbation techniques to evaluate tensor derivatives. These tensor differentiation techniques are then used to automate nonlinear constitutive models into implicit finite element framework. Finally, the efficiency of these automation procedures is demonstrated using benchmark problems.

Drilling into seismogenic zones of M2.0 - M5.5 earthquakes in deep South African gold mines (DSeis)

NASA Astrophysics Data System (ADS)

Ogasawara, Hiroshi; Durrheim, Raymond; Yabe, Yasuo; Ito, Takatoshi; van Aswegen, Gerrie; Cichowicz, Artur; Onstott, Tullis; Kieft, Tom; Boettcher, Margaret; Wiemer, Stefan; Ziegler, Martin; Janssen, Christoph; Shapiro, Serge; Gupta, Harsh; Dight, Phil

2016-04-01

Several times a year, mining-induced earthquakes with magnitudes equal to or larger than 2 take place only a few tens of meters away from active workings in South African gold mines at depths of up to 3.4 km. The largest event recorded in mining regions, a M5.5 earthquake, took place near Orkney, South Africa on 5 August 2014, with the upper edge of the activated fault being only some hundred meters below the nearest mine workings (3.0 km depth). This is one of the rare events for which detailed seismological data are available, both from surface and underground seismometers and strainmeters, allowing for a detailed seismological analysis and comparison with in-situ observed data. Therefore, this earthquake calls for drilling to investigate the seismogenic zones before aftershocks diminish. Such a project will have a significantly better spatial coverage (including nuclei of ruptures, strong motion sources, asperities, and rupture edges) than drilling in seismogenic zones of natural large earthquakes and will be possible with a lower risk and at much smaller costs. In seismogenic zones in a critical state of stress, it is difficult to delineate reliably the local spatial variation in both directions and magnitudes of principal stresses (3D full stress tensor) reliably. However, we have overcome this problem. We are able to numerically model stress better than before, enabling us to orient boreholes so that the chance of stress-induced damage during stress measurement is minimized, and enabling us to measure the full 3D stress tensor successively in a hole within reasonable time even when stresses are as large as those expected in seismogenic zones. Better recovery of cores with less stress-induced damage during drilling is also feasible. These will allow us to address key scientific questions in earthquake science and associated deep biosphere activities which have remained elusive. We held a 4-day workshop sponsored by ICDP and Ritsumeikan University in October/November 2015, which confirmed the great scientific value as well as technical feasibility, flexibility, and cost-effectiveness of drilling into the targets which have already been well seismologically probed. The value will be maximized if we combine outcomes from a limited number of holes drilled from 3 km depth into the M5.5 seismogenic zones (~ 4 km depth) with larger number of boreholes from mining horizons into the other targets (M~2 faults) already extensively exhumed by mining or which will be in future. We could have additional inputs during the 2015 AGU Fall Meeting period. We intend to start drilling before the M5.5 aftershocks diminish or mining around the M2.8 fault starts to alter stress considerably.

An enhanced structure tensor method for sea ice ridge detection from GF-3 SAR imagery

NASA Astrophysics Data System (ADS)

Zhu, T.; Li, F.; Zhang, Y.; Zhang, S.; Spreen, G.; Dierking, W.; Heygster, G.

2017-12-01

In SAR imagery, ridges or leads are shown as the curvilinear features. The proposed ridge detection method is facilitated by their curvilinear shapes. The bright curvilinear features are recognized as the ridges while the dark curvilinear features are classified as the leads. In dual-polarization HH or HV channel of C-band SAR imagery, the bright curvilinear feature may be false alarm because the frost flowers of young leads may show as bright pixels associated with changes in the surface salinity under calm surface conditions. Wind roughened leads also trigger the backscatter increasing that can be misclassified as ridges [1]. Thus the width limitation is considered in this proposed structure tensor method [2], since only shape feature based method is not enough for detecting ridges. The ridge detection algorithm is based on the hypothesis that the bright pixels are ridges with curvilinear shapes and the ridge width is less 30 meters. Benefited from GF-3 with high spatial resolution of 3 meters, we provide an enhanced structure tensor method for detecting the significant ridge. The preprocessing procedures including the calibration and incidence angle normalization are also investigated. The bright pixels will have strong response to the bandpass filtering. The ridge training samples are delineated from the SAR imagery in the Log-Gabor filters to construct structure tensor. From the tensor, the dominant orientation of the pixel representing the ridge is determined by the dominant eigenvector. For the post-processing of structure tensor, the elongated kernel is desired to enhance the ridge curvilinear shape. Since ridge presents along a certain direction, the ratio of the dominant eigenvector will be used to measure the intensity of local anisotropy. The convolution filter has been utilized in the constructed structure tensor is used to model spatial contextual information. Ridge detection results from GF-3 show the proposed method performs better compared to the direct threshold method.

Relaxation approximation in the theory of shear turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, Robert

1995-01-01

Leslie's perturbative treatment of the direct interaction approximation for shear turbulence (Modern Developments in the Theory of Turbulence, 1972) is applied to derive a time dependent model for the Reynolds stresses. The stresses are decomposed into tensor components which satisfy coupled linear relaxation equations; the present theory therefore differs from phenomenological Reynolds stress closures in which the time derivatives of the stresses are expressed in terms of the stresses themselves. The theory accounts naturally for the time dependence of the Reynolds normal stress ratios in simple shear flow. The distortion of wavenumber space by the mean shear plays a crucial role in this theory.

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

NASA Astrophysics Data System (ADS)

Caputa, Pawel; Kundu, Nilay; Miyaji, Masamichi; Takayanagi, Tadashi; Watanabe, Kento

2017-11-01

We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.

General equilibrium second-order hydrodynamic coefficients for free quantum fields

NASA Astrophysics Data System (ADS)

Buzzegoli, M.; Grossi, E.; Becattini, F.

2017-10-01

We present a systematic calculation of the corrections of the stress-energy tensor and currents of the free boson and Dirac fields up to second order in thermal vorticity, which is relevant for relativistic hydrodynamics. These corrections are non-dissipative because they survive at general thermodynamic equilibrium with non vanishing mean values of the conserved generators of the Lorentz group, i.e. angular momenta and boosts. Their equilibrium nature makes it possible to express the relevant coefficients by means of correlators of the angular-momentum and boost operators with stress-energy tensor and current, thus making simpler to determine their so-called "Kubo formulae". We show that, at least for free fields, the corrections are of quantum origin and we study several limiting cases and compare our results with previous calculations. We find that the axial current of the free Dirac field receives corrections proportional to the vorticity independently of the anomalous term.

Tectonic analysis of mine tremor mechanisms from the Upper Silesian Coal Basin

NASA Astrophysics Data System (ADS)

Sagan, Grzegorz; Teper, Lesław; Zuberek, Waclaw M.

1996-07-01

Fault network of the Upper Silesian Coal Basin (USCB) is built of sets of strike-slip, oblique-slip and dip-slip faults. It is a typical product of force couple which acts evenly with the parallel of latitude, causing horizontal and anti-clockwise movement of rock-mass. Earlier research of focal mechanisms of mine tremors, using a standard fault plane solution, has shown that some events are related to tectonic directions in main structural units of the USCB. An attempt was undertaken to analyze the records of mine tremors from the period 1992 1994 in the selected coal fields. The digital records of about 200 mine tremors with energy larger than 1×104 J ( M L >1.23) were analyzed with SMT software for seismic moment tensor inversion. The decomposition of seismic moment tensor of mine tremors was segmented into isotropic (I) part, compensated linear vector dipole (CLVD) part and double-couple (DC) part. The DC part is prevalent (up to 70%) in the majority of quakes from the central region of the USCB. A group of mine tremors with large I element (up to 50%) can also be observed. The spatial orientation of the fault and auxiliary planes were obtained from the computations for the seismic moment DC part. Study of the DC part of the seismic moment tensor made it possible for us to separate the group of events which might be acknowledged to have their origin in unstable energy release on surfaces of faults forming a regional structural pattern. The possible influence of the Cainozoic tectonic history of the USCB on the recent shape of stress field is discussed.

Boundary Element Method in a Self-Gravitating Elastic Half-Space and Its Application to Deformation Induced by Magma Chambers

NASA Astrophysics Data System (ADS)

Fang, M.; Hager, B. H.

2014-12-01

In geophysical applications the boundary element method (BEM) often carries the essential physics in addition to being an efficient numerical scheme. For use of the BEM in a self-gravitating uniform half-space, we made extra effort and succeeded in deriving the fundamental solution analytically in closed-form. A problem that goes deep into the heart of the classic BEM is encountered when we try to apply the new fundamental solution in BEM for deformation field induced by a magma chamber or a fluid-filled reservoir. The central issue of the BEM is the singular integral arising from determination of the boundary values. A widely employed technique is to rescale the singular boundary point into a small finite volume and then shrink it to extract the limits. This operation boils down to the calculation of the so-called C-matrix. Authors in the past take the liberty of either adding or subtracting a small volume. By subtracting a small volume, the C-matrix is (1/2)I on a smooth surface, where I is the identity matrix; by adding a small volume, we arrive at the same C-matrix in the form of I - (1/2)I. This evenness is a result of the spherical symmetry of Kelvin's fundamental solution employed. When the spherical symmetry is broken by gravity, the C-matrix is polarized. And we face the choice between right and wrong, for adding and subtracting a small volume yield different C-matrices. Close examination reveals that both derivations, addition and subtraction of a small volume, are ad hoc. To resolve the issue we revisit the Somigliana identity with a new derivation and careful step-by-step anatomy. The result proves that even though both adding and subtracting a small volume appear to twist the original boundary, only addition essentially modifies the original boundary and consequently modifies the physics of the original problem in a subtle way. The correct procedure is subtraction. We complete a new BEM theory by introducing in full analytical form what we call the singular stress tensor for the fundamental solution. We partition the stress tensor of the fundamental solution into a singular part and a regular part. In this way all singular integrals systematically shift into the easy singular stress tensor. Applications of this new BEM to deformation and gravitational perturbation induced by magma chambers of finite volume will be presented.

Assessing the Uncertainties on Seismic Source Parameters: Towards Realistic Estimates of Moment Tensor Determinations

NASA Astrophysics Data System (ADS)

Magnoni, F.; Scognamiglio, L.; Tinti, E.; Casarotti, E.

2014-12-01

Seismic moment tensor is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Moment tensor catalogues are ordinarily used by geoscientists, however, few attempts have been done to assess possible impacts of moment magnitude uncertainties upon their own analysis. The 2012 May 20 Emilia mainshock is a representative event since it is defined in literature with a moment magnitude value (Mw) spanning between 5.63 and 6.12. An uncertainty of ~0.5 units in magnitude leads to a controversial knowledge of the real size of the event. The possible uncertainty associated to this estimate could be critical for the inference of other seismological parameters, suggesting caution for seismic hazard assessment, coulomb stress transfer determination and other analyses where self-consistency is important. In this work, we focus on the variability of the moment tensor solution, highlighting the effect of four different velocity models, different types and ranges of filtering, and two different methodologies. Using a larger dataset, to better quantify the source parameter uncertainty, we also analyze the variability of the moment tensor solutions depending on the number, the epicentral distance and the azimuth of used stations. We endorse that the estimate of seismic moment from moment tensor solutions, as well as the estimate of the other kinematic source parameters, cannot be considered an absolute value and requires to come out with the related uncertainties and in a reproducible framework characterized by disclosed assumptions and explicit processing workflows.

Proposal for a biometrics of the cortical surface: a statistical method for relative surface distance metrics

NASA Astrophysics Data System (ADS)

Bookstein, Fred L.

1995-08-01

Recent advances in computational geometry have greatly extended the range of neuroanatomical questions that can be approached by rigorous quantitative methods. One of the major current challenges in this area is to describe the variability of human cortical surface form and its implications for individual differences in neurophysiological functioning. Existing techniques for representation of stochastically invaginated surfaces do not conduce to the necessary parametric statistical summaries. In this paper, following a hint from David Van Essen and Heather Drury, I sketch a statistical method customized for the constraints of this complex data type. Cortical surface form is represented by its Riemannian metric tensor and averaged according to parameters of a smooth averaged surface. Sulci are represented by integral trajectories of the smaller principal strains of this metric, and their statistics follow the statistics of that relative metric. The diagrams visualizing this tensor analysis look like alligator leather but summarize all aspects of cortical surface form in between the principal sulci, the reliable ones; no flattening is required.

Tensor veli palatini electromyography for monitoring Eustachian tube rehabilitation in otitis media.

PubMed

Picciotti, P M; Della Marca, G; D'Alatri, L; Lucidi, D; Rigante, M; Scarano, E

2017-05-01

The pathogenesis of otitis media is related to Eustachian tube dysfunction. The tensor veli palatini muscle actively opens the Eustachian tube and promotes middle-ear ventilation. This study describes a technique for paratubal electromyography that uses a surface, non-invasive electrode able to record tensor veli palatini muscle activity during swallowing. Twenty otitis media patients and 10 healthy patients underwent tensor veli palatini electromyography. Activity of this muscle before and after Eustachian tube rehabilitation was also assessed. In 78.5 per cent of patients, the electromyography duration phase and/or amplitude were reduced in the affected side. The muscle action potential was impaired in all patients who underwent Eustachian tube rehabilitation. This study confirmed that Eustachian tube muscle dysfunction has a role in otitis media pathogenesis and showed that muscle activity increases after Eustachian tube rehabilitation therapy.

Diffusion of phonons through (along and across) the ultrathin crystalline films

NASA Astrophysics Data System (ADS)

Šetrajčić, J. P.; Jaćimovski, S. K.; Vučenović, S. M.

2017-11-01

Instead of usual approach, applying displacement-displacement Green's functions, the momentum-momentum Green's functions will be used to calculate the diffusion tensor. With this type of Green's function we have calculated and analyzed dispersion law in film-structures. A small number of phonon energy levels along the direction of boundary surfaces joint of the film are discrete-ones and in this case standing waves could occur. This is consequence of quantum size effects. These Green's functions enter into Kubo's formula defining diffusion properties of the system and possible heat transfer direction through observed structures. Calculation of the diffusion tensor for phonons in film-structure requires solving of the system of difference equations. Boundary conditions are included into mentioned system through the Hamiltonian of the film-structure. It has been shown that the diagonal elements of the diffusion tensor express discrete behavior of the dispersion law of elementary excitations. More important result is-that they are temperature independent and that their values are much higher comparing with bulk structures. This result favors better heat conduction of the film, but in direction which is perpendicular to boundary film surface. In the same time this significantly favors appearance 2D superconducting surfaces inside the ultra-thin crystal structure, which are parallel to the boundary surface.

Modular Hamiltonians on the null plane and the Markov property of the vacuum state

NASA Astrophysics Data System (ADS)

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2017-09-01

We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with a boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non-locally outside the null plane. We regain this result in greater generality using more abstract tools on the algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.

Corner entanglement as a probe of quantum criticality

NASA Astrophysics Data System (ADS)

Witczak-Krempa, William; Bueno, Pablo; Myers, Robert C.

The entanglement entropy in many gapless quantum systems in 2+1D receives a contribution from corners in the entangling surface. It is characterized by a universal function a (θ) that depends non-trivially on the corner opening angle θ. Focusing on a large family of quantum critical theories with emergent Lorentz invariance (CFTs), we argue that the smooth limit a (θ ~ π) is entirely determined by the energy-density or stress tensor 2-point function coefficient. This explains recent results obtained via cutting edge simulations on the quantum critical Ising, XY and Heisenberg models. We also show how to extract the full thermal entropy of the quantum critical system using corner entanglement of the groundstate alone. ** Bueno, Myers, WK, Phys. Rev. Lett. (2015) Work supported by Perimeter Institute and NSERC.

Remarks on turbulent constitutive relations

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Lumley, John L.

1993-01-01

The paper demonstrates that the concept of turbulent constitutive relations can be used to construct general models for various turbulent correlations. Some of the Generalized Cayley-Hamilton formulas for relating tensor products of higher extension to tensor products of lower extension are introduced. The combination of dimensional analysis and invariant theory can lead to 'turbulent constitutive relations' (or general turbulence models) for, in principle, any turbulent correlations. As examples, the constitutive relations for Reynolds stresses and scalar fluxes are derived. The results are consistent with ones from Renormalization Group (RNG) theory and two-scale Direct-Interaction Approximation (DIA) method, but with a more general form.

Scale-invariant curvature fluctuations from an extended semiclassical gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pinamonti, Nicola, E-mail: pinamont@dima.unige.it, E-mail: siemssen@dima.unige.it; INFN Sezione di Genova, Via Dodecaneso 33, 16146 Genova; Siemssen, Daniel, E-mail: pinamont@dima.unige.it, E-mail: siemssen@dima.unige.it

2015-02-15

We present an extension of the semiclassical Einstein equations which couple n-point correlation functions of a stochastic Einstein tensor to the n-point functions of the quantum stress-energy tensor. We apply this extension to calculate the quantum fluctuations during an inflationary period, where we take as a model a massive conformally coupled scalar field on a perturbed de Sitter space and describe how a renormalization independent, almost-scale-invariant power spectrum of the scalar metric perturbation is produced. Furthermore, we discuss how this model yields a natural basis for the calculation of non-Gaussianities of the considered metric fluctuations.

Acoustoelastic effect of textured (Ba,Sr)TiO{sub 3} thin films under an initial mechanical stress

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamel, Marwa; Mseddi, Souhir; Njeh, Anouar

Acoustoelastic (AE) analysis of initial stresses plays an important role as a nondestructive tool in current engineering. Two textured BST (Ba{sub 0.65}Sr{sub 0.35}TiO{sub 3}) thin films, with different substrate to target distance, were grown on Pt(111)/TiO{sub 2}/SiO{sub 2}/Si(001) substrate by rf-magnetron sputtering deposition techniques. A conventional “sin{sup 2} ψ” method to determine residual stress and strain in BST films by X-ray diffraction is applied. A laser acoustic waves (LA-waves) technique is used to generate surface acoustic waves (SAW) propagating in both samples. Young's modulus E and Poisson ratio ν of BST films in different propagation directions are derived from the measuredmore » dispersion curves. Estimation of effective second-order elastic constants of BST thin films in stressed states is served in SAW study. This paper presents an original investigation of AE effect in prestressed Ba{sub 0.65}Sr{sub 0.35}TiO{sub 3} films, where the effective elastic constants and the effect of texture on second and third order elastic tensor are considered and used. The propagation behavior of Rayleigh and Love waves in BST thin films under residual stress is explored and discussed. The guiding velocities affected by residual stresses, reveal some shifts which do not exceed four percent mainly in the low frequency range.« less

Analytic non-Maxwellian electron velocity distribution function in a Hall discharge plasma

NASA Astrophysics Data System (ADS)

Shagayda, Andrey; Tarasov, Alexey

2017-10-01

The electron velocity distribution function in the low-pressure discharges with the crossed electric and magnetic fields, which occur in magnetrons, plasma accelerators, and Hall thrusters with a closed electron drift, is not Maxwellian. A deviation from equilibrium is caused by a large electron mean free path relative to the Larmor radius and the size of the discharge channel. In this study, we derived in the relaxation approximation the analytical expression of the electron velocity distribution function in a weakly ionized Lorentz plasma with the crossed electric and magnetic fields in the presence of the electron density and temperature gradients in the direction of the electric field. The solution was obtained in the stationary approximation far from boundary surfaces, when diffusion and mobility are determined by the classical effective collision frequency of electrons with ions and atoms. The moments of the distribution function including the average velocity, the stress tensor, and the heat flux were calculated and compared with the classical hydrodynamic expressions. It was shown that a kinetic correction to the drift velocity stems from a contribution of the off-diagonal component of the stress tensor. This correction becomes essential if the drift velocity in the crossed electric and magnetic fields would be comparable to the thermal velocity of electrons. The electron temperature has three different components at a nonzero effective collision frequency and two different components in the limit when the collision frequency tends to zero. It is shown that, in the presence of ionization collisions, the components of the heat flux have additives that are not related to the temperature gradient, and arise because of the electron drift.

Seismic velocity structure and microearthquake source properties at The Geysers, California, geothermal area

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Connell, D.R.

1986-12-01

The method of progressive hypocenter-velocity inversion has been extended to incorporate S-wave arrival time data and to estimate S-wave velocities in addition to P-wave velocities. S-wave data to progressive inversion does not completely eliminate hypocenter-velocity tradeoffs, but they are substantially reduced. Results of a P and S-wave progressive hypocenter-velocity inversion at The Geysers show that the top of the steam reservoir is clearly defined by a large decrease of V/sub p//V/sub s/ at the condensation zone-production zone contact. The depth interval of maximum steam production coincides with minimum observed V/sub p//V/sub s/, and V/sub p//V/sub s/ increses below the shallowmore » primary production zone suggesting that reservoir rock becomes more fluid saturated. The moment tensor inversion method was applied to three microearthquakes at The Geysers. Estimated principal stress orientations were comparable to those estimated using P-wave firstmotions as constraints. Well constrained principal stress orientations were obtained for one event for which the 17 P-first motions could not distinguish between normal-slip and strike-slip mechanisms. The moment tensor estimates of principal stress orientations were obtained using far fewer stations than required for first-motion focal mechanism solutions. The three focal mechanisms obtained here support the hypothesis that focal mechanisms are a function of depth at The Geysers. Progressive inversion as developed here and the moment tensor inversion method provide a complete approach for determining earthquake locations, P and S-wave velocity structure, and earthquake source mechanisms.« less

Turbulent Kinetic Energy (TKE) Budgets Using 5-beam Doppler Profilers

NASA Astrophysics Data System (ADS)

Guerra, M. A.; Thomson, J. M.

2016-12-01

Field observations of turbulence parameters are important for the development of hydrodynamic models, understanding contaminant mixing, and predicting sediment transport. The turbulent kinetic energy (TKE) budget quantifies where turbulence is being produced, dissipated or transported at a specific site. The Nortek Signature 5-beam AD2CP was used to measure velocities at high sampling rates (up to 8 Hz) at Admiralty Inlet and Rich Passage in Puget Sound, WA, USA. Raw along-beam velocity data is quality controlled and is used to estimate TKE spectra, spatial structure functions, and Reynolds stress tensors. Exceptionally low Doppler noise in the data enables clear observations of the inertial sub-range of isotropic turbulence in both the frequency TKE spectra and the spatial structure functions. From these, TKE dissipation rates are estimated following Kolmogorov's theory of turbulence. The TKE production rates are estimated using Reynolds stress tensors together with the vertical shear in the mean flow. The Reynolds stress tensors are estimated following the methodology of Dewey and Stinger (2007), which is significantly improved by inclusion of the 5th beam (as opposed to the conventional 4). These turbulence parameters are used to study the TKE budget along the water column at the two sites. Ebb and flood production and dissipation rates are compared through the water column at both sites. At Admiralty Inlet, dissipation exceeds production during ebb while the opposite occurs during flood because the proximity to a lateral headland. At Rich Passage, production exceeds dissipation through the water column for all tidal conditions due to a vertical sill in the vicinity of the measurement site.

Topological regularization and self-duality in four-dimensional anti-de Sitter gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miskovic, Olivera; Olea, Rodrigo; Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso

2009-06-15

It is shown that the addition of a topological invariant (Gauss-Bonnet term) to the anti-de Sitter gravity action in four dimensions recovers the standard regularization given by the holographic renormalization procedure. This crucial step makes possible the inclusion of an odd parity invariant (Pontryagin term) whose coupling is fixed by demanding an asymptotic (anti) self-dual condition on the Weyl tensor. This argument allows one to find the dual point of the theory where the holographic stress tensor is related to the boundary Cotton tensor as T{sub j}{sup i}={+-}(l{sup 2}/8{pi}G)C{sub j}{sup i}, which has been observed in recent literature in solitonicmore » solutions and hydrodynamic models. A general procedure to generate the counterterm series for anti-de Sitter gravity in any even dimension from the corresponding Euler term is also briefly discussed.« less

Full moment tensors with uncertainties for the 2017 North Korea declared nuclear test and for a collocated, subsequent event

NASA Astrophysics Data System (ADS)

Alvizuri, C. R.; Tape, C.

2017-12-01

A seismic moment tensor is a 3×3 symmetric matrix that characterizes the far-field seismic radiation from a source, whether it be an earthquake, volcanic event, explosion. We estimate full moment tensors and their uncertainties for the North Korea declared nuclear test and for a collocated event that occurred eight minutes later. The nuclear test and the subsequent event occurred on September 3, 2017 at around 03:30 and 03:38 UTC time. We perform a grid search over the six-dimensional space of moment tensors, generating synthetic waveforms at each moment tensor grid point and then evaluating a misfit function between the observed and synthetic waveforms. The synthetic waveforms are computed using a 1-D structure model for the region; this approximation requires careful assessment of time shifts between data and synthetics, as well as careful choice of the bandpass for filtering. For each moment tensor we characterize its uncertainty in terms of waveform misfit, a probability function, and a confidence curve for the probability that the true moment tensor lies within the neighborhood of the optimal moment tensor. For each event we estimate its moment tensor using observed waveforms from all available seismic stations within a 2000-km radius. We use as much of the waveform as possible, including surface waves for all stations, and body waves above 1 Hz for some of the closest stations. Our preliminary magnitude estimates are Mw 5.1-5.3 for the first event and Mw 4.7 for the second event. Our results show a dominantly positive isotropic moment tensor for the first event, and a dominantly negative isotropic moment tensor for the subsequent event. As expected, the details of the probability density, waveform fit, and confidence curves are influenced by the structural model, the choice of filter frequencies, and the selection of stations.

Polarized-cathodoluminescence study of uniaxial and biaxial stress in GaAs/Si

NASA Technical Reports Server (NTRS)

Rich, D. H.; Ksendzov, A.; Terhune, R. W.; Grunthaner, F. J.; Wilson, B. A.; Shen, H.; Dutta, M.; Vernon, S. M.; Dixon, T. M.

1991-01-01

The strain-induced splitting of the heavy-hole (hh) and light-hole (lh) valence bands for 4-microns thick GaAs/Si is examined on a microscopic scale using linear polarized-cathodoluminescence imaging and spectroscopy. The energies and intensities of the hh- and lh-exciton luminescence are quantitatively analyzed to determine spatial variations in the stress tensor. The results indicate that regions near and far from the microcracks are primarily subject to uniaxial and biaxial tensile stresses, respectively. The transition region where biaxial stress gradually converts to uniaxial stress is analyzed, and reveals a mixing of lh and hh characters in the strain-split bands.

Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Patnaik, Surya N.; Hopkins, Dale A.

1996-01-01

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.

Stress pattern of the Shanxi rift system, North China, inferred from the inversion of new focal mechanisms

NASA Astrophysics Data System (ADS)

Li, Bin; Atakan, Kuvvet; Sørensen, Mathilde Bøttger; Havskov, Jens

2015-05-01

Earthquake focal mechanisms of the Shanxi rift system, North China, are investigated for the time period 1965-April 2014. A total of 143 focal mechanisms of ML ≥ 3.0 earthquakes were compiled. Among them, 105 solutions are newly determined in this study by combining the P-wave first motions and full waveform inversion, and 38 solutions are from available published data. Stress tensor inversion was then performed based on the new database. The results show that most solutions in the Shanxi rift system exhibit normal or strike-slip faulting, and the regional stress field is transtensional and dominated by NNW-SSE extension. This correlates well with results from GPS data, geological field observations and levelling measurements across the faults. Heterogeneity exists in the regional stress field, as indicated by individual stress tensor inversions conducted for five subzones. While the minimum stress axis (σ3) appears to be consistent and stable, the orientations, especially the plunges, of the maximum and intermediate stresses (σ1 and σ2) vary significantly along the strike of the different subzones. Based on our results and combining multidisciplinary observations from geological surveys, GPS and cross-fault monitoring, a kinematic model is proposed for the Shanxi rift system, in which the rift is situated between two opposite rotating crustal blocks, exhibiting a transtensional stress regimes. This model illustrates the present-day stress field and its correlation to the regional tectonics, as well as the current crustal deformation of the Shanxi rift system. Results obtained in this study, may help to understand the geodynamics, neotectonic activity, active seismicity and potential seismic hazard in this region.

Spatial profile reconstruction of individual componentsof the nonlinear susceptibility tensors {chi}-circumflex {sup (3)}(z, {omega}', {omega}' -{omega}, {omega}) and {chi}-circumflex {sup (3)}(z, 2{omega}{+-}{omega}', {+-}{omega}', {omega}, {omega}) of a one-dimensionally inhomogeneous medium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golubkov, A A; Makarov, Vladimir A

We have proved for the first time and proposed an algorithm of unique spatial profile reconstruction of the components {chi}-circumflex {sup (3)}{sub yyyy} of complex tensors {chi}-circumflex {sup (3)}(z, {omega}', {omega}', -{omega}, {omega}) and {chi}-circumflex {sup (3)}(z, 2{omega}{+-}{omega}', {+-}{omega}', {omega}, {omega}), describing four-photon interaction of light waves in a one-dimensionally inhomogeneous plate, whose medium has a symmetry plane m{sub y} that is perpendicular to its surface. For the media with an additional symmetry axis 2{sub z}, 4{sub z}, 6{sub z} or {infinity}{sub z} that is perpendicular to the plate surface, the proposed method can be used to reconstruct about one-fifthmore » of all independent components of the above tensors. (nonlinear optical phenomena)« less

Shape-from-focus by tensor voting.

PubMed

Hariharan, R; Rajagopalan, A N

2012-07-01

In this correspondence, we address the task of recovering shape-from-focus (SFF) as a perceptual organization problem in 3-D. Using tensor voting, depth hypotheses from different focus operators are validated based on their likelihood to be part of a coherent 3-D surface, thereby exploiting scene geometry and focus information to generate reliable depth estimates. The proposed method is fast and yields significantly better results compared with existing SFF methods.

Nonexistence of extremal de Sitter black rings

NASA Astrophysics Data System (ADS)

Khuri, Marcus; Woolgar, Eric

2017-11-01

We show that near-horizon geometries in the presence of a positive cosmological constant cannot exist with ring topology. In particular, de Sitter black rings with vanishing surface gravity do not exist. Our result relies on a known mathematical theorem which is a straightforward consequence of a type of energy condition for a modified Ricci tensor, similar to the curvature-dimension conditions for the m-Bakry-Émery-Ricci tensor.

A generalized electro-elastic theory of polymer networks

NASA Astrophysics Data System (ADS)

Cohen, Noy

2018-01-01

A rigorous multi-scale analysis of the electromechanical coupling in dielectric polymers is conducted. The body couples stemming from a misalignment between the electric field and the electric-dipole density vector are studied and the conservation laws for polymer networks are derived. Using variational principles, expressions for the polarization and the stress are determined. Interestingly, it is found that the stress tensor resulting from coupled loadings in which the electric field is misaligned with the principal stretch directions is not symmetric and the asymmetry arises from the body couples. Next, the electro-mechanical response of a chain is analyzed. The deformations of the individual polymer chains are related to the macroscopic deformation via two highly non-linear constraints - the first pertaining to the compatibility of the local deformations with the imposed macroscopic one and the second stems from the symmetric part of the stress at equilibrium. In accord with the proposed framework, an amended three-chains model is introduced. The predictions of this model are found to be in excellent agreement with experimental findings. Lastly, the behavior of a polymer subjected to a simple shear and an electric field is studied. The offset between the electric field and the principal directions gives rise to body couples, a polarization that is not aligned with the electric field, and an asymmetric stress tensor.

Thermodynamic stability in elastic systems: Hard spheres embedded in a finite spherical elastic solid.

PubMed

Solano-Altamirano, J M; Goldman, Saul

2015-12-01

We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another.

A new unified theory of electromagnetic and gravitational interactions

NASA Astrophysics Data System (ADS)

Li, Li-Xin

2016-12-01

In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations in the four-dimensional spacetime from the fivedimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is obtained: ∇a F ab - ξ R b a A a = -4π J b with ξ = -2, where F ab is the antisymmetric electromagnetic field tensor defined by the potential vector A a , R ab is the Ricci curvature tensor of the hypersurface, and J a is the electric current density vector. The electromagnetic field equation differs from the Einstein-Maxwell equation by a curvature-coupled term ξ R b a A a , whose presence addresses the problem of incompatibility of the Einstein-Maxwell equation with a universe containing a uniformly distributed net charge, as discussed in a previous paper by the author [L.-X. Li, Gen. Relativ. Gravit. 48, 28 (2016)]. Hence, the new unified theory is physically different from Kaluza-Klein theory and its variants in which the Einstein-Maxwell equation is derived. In the four-dimensional Einstein field equation derived in the new theory, the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter. Under certain conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime. We argue that, the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density, e.g., inside a neutron star or a white dwarf, and in the early epoch of the universe.

Stress field modeling of the Carpathian Basin based on compiled tectonic maps

NASA Astrophysics Data System (ADS)

Albert, Gáspár; Ungvári, Zsuzsanna; Szentpéteri, Krisztián

2014-05-01

The estimation of the stress field in the Carpathian Basin is tackled by several authors. Their modeling methods usually based on measurements (borehole-, focal mechanism- and geodesic data) and the result is a possible structural pattern of the region. Our method works indirectly: the analysis is aimed to project a possible 2D stress field over the already mapped/known/compiled lineament pattern. This includes a component-wise interpolation of the tensor-field, which is based on the generated irregular point cloud in the puffer zone of the mapped lineaments. The interpolated values appear on contour and tensor maps, and show the relative stress field of the area. In 2006 Horváth et al. compiled the 'Atlas of the present-day geodynamics of the Pannonian basin'. To test our method we processed the lineaments of the 1:1 500 000 scale 'Map of neotectonic (active) structures' published in this atlas. The geodynamic parameters (i.e. normal, reverse, right- and left lateral strike-slip faults, etc.) of the lines on this map were mostly explained in the legend. We classified the linear elements according to these parameters and created a geo-referenced mapping database. This database contains the polyline sections of the map lineaments as vectors (i.e. line sections), and the directions of the stress field as attributes of these vectors. The directions of the dip-parallel-, strike-parallel- and vertical stress-vectors are calculated from the geodynamical parameters of the line section. Since we created relative stress field properties, the eigenvalues of the vectors were maximized to one. Each point in the point cloud inherits the stress property of the line section, from which it was derived. During the modeling we tried several point-cloud generating- and interpolation methods. The analysis of the interpolated tensor fields revealed that the model was able to reproduce a geodynamic synthesis of the Carpathian Basin, which can be correlated with the synthesis of the Atlas published in 2006. The method was primarily aimed to reconstruct paleo-stress fields. References Horváth, F., Bada, G., Windhoffer, G., Csontos, L., Dombrádi, E., Dövényi, P., Fodor, L., Grenerczy, G., Síkhegyi, F., Szafián, P., Székely, B., Timár, G., Tóth, L., Tóth, T. 2006: Atlas of the present-day geodynamics of the Pannonian basin: Euroconform maps with explanatory text. Magyar Geofizika 47, 133-137.

Topology in colored tensor models via crystallization theory

NASA Astrophysics Data System (ADS)

Casali, Maria Rita; Cristofori, Paola; Dartois, Stéphane; Grasselli, Luigi

2018-07-01

The aim of this paper is twofold. On the one hand, it provides a review of the links between random tensor models, seen as quantum gravity theories, and the PL-manifolds representation by means of edge-colored graphs (crystallization theory). On the other hand, the core of the paper is to establish results about the topological and geometrical properties of the Gurau-degree (or G-degree) of the represented manifolds, in relation with the motivations coming from physics. In fact, the G-degree appears naturally in higher dimensional tensor models as the quantity driving their 1 / N expansion, exactly as it happens for the genus of surfaces in the two-dimensional matrix model setting. In particular, the G-degree of PL-manifolds is proved to be finite-to-one in any dimension, while in dimension 3 and 4 a series of classification theorems are obtained for PL-manifolds represented by graphs with a fixed G-degree. All these properties have specific relevance in the tensor models framework, showing a direct fruitful interaction between tensor models and discrete geometry, via crystallization theory.

Scale Properties of Anisotropic and Isotropic Turbulence in the Urban Surface Layer

NASA Astrophysics Data System (ADS)

Liu, Hao; Yuan, Renmin; Mei, Jie; Sun, Jianning; Liu, Qi; Wang, Yu

2017-11-01

The scale properties of anisotropic and isotropic turbulence in the urban surface layer are investigated. A dimensionless anisotropic tensor is introduced and the turbulent tensor anisotropic coefficient, defined as C, where C = 3d3 + 1 (d3 is the minimum eigenvalue of the tensor) is used to characterize the turbulence anisotropy or isotropy. Turbulence is isotropic when C ≈ 1, and anisotropic when C ≪ 1. Three-dimensional velocity data collected using a sonic anemometer are analyzed to obtain the anisotropic characteristics of atmospheric turbulence in the urban surface layer, and the tensor anisotropic coefficient of turbulent eddies at different spatial scales calculated. The analysis shows that C is strongly dependent on atmospheric stability ξ = (z-zd)/L_{{it{MO}}}, where z is the measurement height, zd is the displacement height, and L_{{it{MO}}} is the Obukhov length. The turbulence at a specific scale in unstable conditions (i.e., ξ < 0) is closer to isotropic than that at the same scale under stable conditions. The maximum isotropic scale of turbulence is determined based on the characteristics of the power spectrum in three directions. Turbulence does not behave isotropically when the eddy scale is greater than the maximum isotropic scale, whereas it is horizontally isotropic at relatively large scales. The maximum isotropic scale of turbulence is compared to the outer scale of temperature, which is obtained by fitting the temperature fluctuation spectrum using the von Karman turbulent model. The results show that the outer scale of temperature is greater than the maximum isotropic scale of turbulence.

A direct numerical simulation-based re-examination of coefficients in the pressure-strain models in second-moment closures

NASA Astrophysics Data System (ADS)

Jakirlić, S.; Hanjalić, K.

2013-10-01

The most challenging task in closing the Reynolds-averaged Navier-Stokes equations at the second-moment closure (SMC) level is to model the pressure-rate-of-strain correlation in the transport equation for the Reynolds-stress tensor. The accurate modelling of this term, commonly denoted as Φij, is the key prerequisite for the correct capturing of the stress anisotropy, which potentially gives SMCs a decisive advantage over the ‘anisotropy-blind’ eddy-viscosity models. A variety of models for Φij proposed in the literature can all be expressed as a function of the stress-anisotropy-, rate-of-strain- and rate-of-rotation second-rank tensors, so that the modelling task is reduced to determining the model coefficients. It is, thus, the coefficients, associated with various terms in the expression, which differ from one model to another. The model coefficients have been traditionally determined with reference to the available data for sets of generic flows while being forced to satisfying the known values at flow boundaries. We evaluated the coefficients up to the second-order terms (in stress-anisotropy aij) directly from the DNS database for Φij and the turbulence variables involved in its modelling. The variations of the coefficients across the flow in a plane channel over a range of Reynolds numbers are compared with several popular models. The analysis provided a reasonable support for the common tensor-expansion representation of both the slow and rapid terms. Apart from the near-wall region and the channel centre, most coefficients for higher Re numbers showed themselves to be reasonably uniform, with the values closest to those proposed by Sarkar et al (1991 J. Fluid Mech. 227 245-72). An illustration of the coefficient variation for the ‘quasi-linear’ model is also presented for flow over a backward-facing step.

Triple-material stress-strain resistivity gage

DOEpatents

Stout, R.B.

1987-05-19

A triple material piezoresistive gage provides multi-component elastic stress or strain measurements. Thin foils of three piezoresistive materials, e.g., ytterbium, manganin, and constantan, are configured in a nested serpentine rectilinear grind or other grind arrangement and embedded in a medium, preferably normal to the direction of shock wave propagation. The output of the gage is a resistivity change history for each material of gage. Each resistivity change is independent of the others so that three diagonal components of the elastic stress or strain tensor can be calculated form the resistivity measurements. 4 figs.

Triple-material stress-strain resistivity gage

DOEpatents

Stout, R.B.

1988-05-17

A triple material piezoresistive gage provides multi-component elastic stress measurements is disclosed. Thin foils of three piezoresistive materials, e.g. ytterbium, manganin, and constantan, are configured in a nested serpentine rectilinear grid or other grid arrangement and embedded in a medium, preferably normal to the direction of shock wave propagation. The output of the gage is a resistivity change history for each material of the gage. Each resistivity change is independent of the others so that three diagonal components of the elastic stress or strain tensor can be calculated from the resistivity measurements. 4 figs.

Triple-material stress-strain resistivity gage

DOEpatents

Stout, Ray B.

1988-01-01

A triple material piezoresistive gage provides multi-component elastic stress or measurements. Thin foils of three piezoresistive materials, e.g. ytterbium, manganin, and constantan, are configured in a nested serpentine rectilinear grid or other grid arrangement and embedded in a medium, preferably normal to the direction of shock wave propagation. The output of the gage is a resistivity change history for each material of the gage. Each resistivity change is independent of the others so that three diagonal components of the elastic stress or strain tensor can be calculated from the resistivity measurements.

Effect of microstructural damage on ply stresses in laminated composites

NASA Technical Reports Server (NTRS)

Allen, D. H.; Nottorf, E. W.; Harris, C. E.

1988-01-01

The mechanisms involved in damage and failure of laminated orthotropic composites are investigated theoretically. The continuum model developed accounts for both matrix cracks and interply delamination using second-order tensor-valued internal-state variables based on the locally averaged microcrack dynamics. The derivation of the model is given in detail, and numerical results for sample problems are presented in extensive graphs and tables. The model is shown to be effective in predicting stresses at the ply level, and significant damage-induced decreases in laminate stress states are found.

Fluid-Structure Interaction in Continuum Models of Bacterial Biofilms

NASA Astrophysics Data System (ADS)

Hicks, Jared A.

Bacterial biofilms are aggregates of cells that adhere to nearly any solid-fluid interface. While many have harmful effects, such as industrial damage and nosocomial infections, certain biofilm species are now generating renewable energy as the fundamental components of Microbial Fuel Cells (MFCs). In an MFC, bacteria consume organic waste and, as they respire, produce free electrons. To do so efficiently, the bacteria must operate at peak metabolic activity, and so require an ample supply of nutrients. But existing MFC systems face several nutrient delivery problems, including clogging and downstream depletion. Ameliorating these problems will require a better understanding of the interplay between structural development and the surrounding fluid flow. In addition to delivering nutrients that affect biofilm growth, the fluid also exerts stresses that cause erosion, detachment, and deformation. These structural changes, in turn, affect the flow and alter the nutrient distribution. To account for this feedback effect, I have developed a continuum model that couples the growth and deformation processes. My model augments an existing growth model with evolution equations derived from Morphoelasticity Theory, by showing that the growth tensor can be directly related to the biofilm velocity potential. This result helps overcome one of the major practical limitations of Morphoelasticity--there is no physical framework for specifying the growth tensor. Through further analysis of the growth tensor, I define the related adjugate and anisotropic growth tensors, which can be more meaningful measures of growth for some models. Under the assumption of small strain, I show that there exists a small correction to the biofilm growth velocity (the accommodation velocity) that represents the effect of the elastic response on the evolution of the biofilm shape. I derive a solvability condition for the accommodation velocity, and show that it leads to a novel evolution equation for stress and strain in the biofilm, which couples the growth and deformation processes. Furthermore, I show that the introduction of a vorticity allows the accommodation velocity to be described by a system of Poisson equations, and that this vorticity arises naturally from Morphoelasticity theory and is related to the velocity solvability condition. I apply the modeling approach to a one-dimensional biofilm, and show that (a) the coupled growth process affects the evolution of the biofilm shape as expected, and (b) a non-coupled approach to biofilm strain introduces an error that grows over time. Numerical analysis of the one-dimensional strain evolution equation leads to several insights that inform the development of numerical methods for the two-dimensional case, including a split-step approach that reduces the fifth-order PDE to an advection equation for strain and a biharmonic equation for stress. Finally, I discuss some useful numerical methods for the simulation of elastic biofilm growth, particularly the discretization of the strain evolution equation(s). My overall approach is to track the evolving biofilm surface using a combination of the level-set method coupled with the eXtended Finite Element Method (XFEM). The major result is a novel mixed-XFEM discretization of the clamped-plate biharmonic equation, which I show to be first-order accurate for the trace of the solution on the interface.

Full paleostress tensor reconstruction using quartz veins of Panasqueira Mine, central Portugal; part I: Paleopressure determination

NASA Astrophysics Data System (ADS)

Jaques, Luís; Pascal, Christophe

2017-09-01

Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal exposures of mineralized quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. The present contribution focuses specifically on the determination of pore pressure. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of ∼300 MPa and formation depths of ∼10 km. Such formation depths are in good agreement with the regional geological evolution. The obtained pore pressure will be merged with vein inversion results, in order to achieve full paleostress tensor restoration, in a forthcoming companion paper.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

Dilational processes accompanying earthquakes in the Long Valley Caldera

USGS Publications Warehouse

Dreger, Douglas S.; Tkalcic, Hrvoje; Johnston, M.

2000-01-01

Regional distance seismic moment tensor determinations and broadband waveforms of moment magnitude 4.6 to 4.9 earthquakes from a November 1997 Long Valley Caldera swarm, during an inflation episode, display evidence of anomalous seismic radiation characterized by non-double couple (NDC) moment tensors with significant volumetric components. Observed coseismic dilation suggests that hydrothermal or magmatic processes are directly triggering some of the seismicity in the region. Similarity in the NDC solutions implies a common source process, and the anomalous events may have been triggered by net fault-normal stress reduction due to high-pressure fluid injection or pressurization of fluid-saturated faults due to magmatic heating.

Design of a multi-axis implantable MEMS sensor for intraosseous bone stress monitoring

NASA Astrophysics Data System (ADS)

Alfaro, Fernando; Weiss, Lee; Campbell, Phil; Miller, Mark; Fedder, Gary K.

2009-08-01

The capability to assess the biomechanical properties of living bone is important for basic research as well as the clinical management of skeletal trauma and disease. Even though radiodensitometric imaging is commonly used to infer bone quality, bone strength does not necessarily correlate well with these non-invasive measurements. This paper reports on the design, fabrication and initial testing of an implantable ultra-miniature multi-axis sensor for directly measuring bone stresses at a micro-scale. The device, which is fabricated with CMOS-MEMS processes, is intended to be permanently implanted within open fractures, or embedded in bone grafts, or placed on implants at the interfaces between bone and prosthetics. The stress sensor comprises an array of piezoresistive pixels to detect a stress tensor at the interfacial area between the MEMS chip and bone, with a resolution to 100 Pa, in 1 s averaging. The sensor system design and manufacture is also compatible with the integration of wireless RF telemetry, for power and data retrieval, all within a 3 mm × 3 mm × 0.3 mm footprint. The piezoresistive elements are integrated within a textured surface to enhance sensor integration with bone. Finite element analysis led to a sensor design for normal and shear stress detection. A wired sensor was fabricated in the Jazz 0.35 µm BiCMOS process and then embedded in mock bone material to characterize its response to tensile and bending loads up to 250 kPa.

Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

NASA Technical Reports Server (NTRS)

Leone, Frank A., Jr.

2015-01-01

A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

Stationary black holes with stringy hair

NASA Astrophysics Data System (ADS)

Boos, Jens; Frolov, Valeri P.

2018-01-01

We discuss properties of black holes which are pierced by special configurations of cosmic strings. For static black holes, we consider radial strings in the limit when the number of strings grows to infinity while the tension of each single string tends to zero. In a properly taken limit, the stress-energy tensor of the string distribution is finite. We call such matter stringy matter. We present a solution of the Einstein equations for an electrically charged static black hole with the stringy matter, with and without a cosmological constant. This solution is a warped product of two metrics. One of them is a deformed 2-sphere, whose Gaussian curvature is determined by the energy density of the stringy matter. We discuss the embedding of a corresponding distorted sphere into a three-dimensional Euclidean space and formulate consistency conditions. We also found a relation between the square of the Weyl tensor invariant of the four-dimensional spacetime of the stringy black holes and the energy density of the stringy matter. In the second part of the paper, we discuss test stationary strings in the Kerr geometry and in its Kerr-NUT-(anti-)de Sitter generalizations. Explicit solutions for strings that are regular at the event horizon are obtained. Using these solutions, the stress-energy tensor of the stringy matter in these geometries is calculated. Extraction of the angular momentum from rotating black holes by such strings is also discussed.

Seismic source study of the Racha-Dzhava (Georgia) earthquake from aftershocks and broad-band teleseismic body-wave records: An example of active nappe tectonics

USGS Publications Warehouse

Fuenzalida, H.; Rivera, L.; Haessler, H.; Legrand, D.; Philip, H.; Dorbath, L.; McCormack, D.; Arefiev, S.; Langer, C.; Cisternas, A.

1997-01-01

The Racha-Dzhava earthquake (Ms = 7.0) that occurred on 1991 April 29 at 09:12:48.1 GMT in the southern border of the Great Caucasus is the biggest event ever recorded in the region, stronger than the Spitak earthquake (Ms = 6.9) of 1988. A field expedition to the epicentral area was organised and a temporary seismic network of 37 stations was deployed to record the aftershock activity. A very precise image of the aftershock distribution is obtained, showing an elongated cloud oriented N105??, with one branch trending N310?? in the western part. The southernmost part extends over 80 km, with the depth ranging from 0 to 15 km, and dips north. The northern branch, which is about 30 km long, shows activity that ranges in depth from 5 to 15 km. The complex thrust dips northwards. A stress-tensor inversion from P-wave first-motion polarities shows a state of triaxial compression, with the major principal axis oriented roughly N-S, the minor principal axis being vertical. Body-waveform inversion of teleseismic seismograms was performed for the main shock, which can be divided into four subevents with a total rupture-time duration of 22 s. The most important part of the seismic moment was released by a gentle northerly dipping thrust. The model is consistent with the compressive tectonics of the region and is in agreement with the aftershock distribution and the stress tensor deduced from the aftershocks. The focal mechanisms of the three largest aftershocks were also inverted from body-wave records. The April 29th (Ms = 6.1) and May 5th (Ms = 5.4) aftershocks have thrust mechanisms on roughly E-W-oriented planes, similar to the main shock. Surprisingly, the June 15th (Ms = 6.2) aftershock shows a thrust fault striking N-S. This mechanism is explained by the structural control of the rupture along the east-dipping geometry of the Dzirula Massif close to the Borzhomi-Kazbeg strike-slip fault. In fact, the orientation and shape of the stress tensor produce a thrust on a N-S oriented plane. Nappe tectonics has been identified as an important feature in the Caucasus, and the source mechanism is consistent with this observation. A hidden fault is present below the nappe, and no large surface breaks were observed due to the main shock. The epicentral region is characterized by sediments that are trapped between two crystalline basements: the Dzirula Massif, which crops out south of Chiatoura, and the Caucasus Main Range north of Oni. Most, if not all, of the rupture is controlled by the thrusting of overlapping, deformed and folded sediments over the Dzirula Massif. This event is another example of blind active faults, with the distinctive feature that the fault plane dips at a gentle angle. The Racha Range is one of the surface expressions of this blind thrust, and its growth is the consequence and evidence of similar earthquakes in the past.

Modeling the Proterozoic Basement's Effective Stress Field, Assessing Fault Reactivation Potential Related to Increased Fluid Pressures, and Improved 3D Structural Interpretation of Faulting within Wellington and Anson-Bates Fields, Sumner County, Kansas

NASA Astrophysics Data System (ADS)

Keast, R. T.; Lacroix, B.; Raef, A. E.; Adam, C.; Bidgoli, T. S.; Leclere, H.; Daniel, G.

2017-12-01

South-central Kansas has experienced an increase in seismic activity within the Proterozoic basement. Since 2013, United States Geological Survey (USGS) seismograph stations have recorded 3414 earthquakes. Fluid pressure increases associated with recent high-rate wastewater injection into the dolomitic Arbuckle disposal zone is the hypothesized cause of reactivation of the faulted study region's Proterozoic basement. Although the magnitude of the pressure change required for reactivation of these faults is likely low given failure equilibrium conditions in the midcontinent, heterogeneities in the basement could allow for a range of fluid pressure changes associated with injection. This research aims to quantify the fluid pressure changes responsible for fault reactivation of the Proterozoic basement. To address this issue, we use 103 focal mechanisms and 3,414 seismic events, from the USGS catalog, within an area encompassing 4,000 km2. Three major fault populations have been identified using the dense seismicity and focal mechanism datasets. Win-Tensor paleostress reconstruction software was used to identify effective stress ratios, R = (σ'1/σ'3), and stress tensors for twelve 22 km by 17 km grid squares covering the study area. One fault population strikes parallel with the Nemaha Ridge basement structure ( 030˚). Another reoccurring fault population is oriented 310˚, closely parallel to the Central Kansas Uplift, a subtle anticlinal structure subjected to repeated movement during the Paleozoic. The third population of faults is parallel to the regional maximum compressive stress oriented 265˚ as determined by previous researchers using borehole image logs and shear wave anisotropy. A 3D stress modeling Matlab script was used to analyze fault reactivation potential based on results obtained from Win-Tensor to better understand fault orientations and their susceptibility to reactivation related to pore fluid pressure increases. In addition, the orientations of these normal and strike-slip fault populations suggest the development of a transtensional basin, not yet identified.

Background Stress State Before the 2008 Wenchuan Earthquake and the Dynamics of the Longmen Shan Thrust Belt

NASA Astrophysics Data System (ADS)

Wang, Kaiying; Rebetsky, Yu. L.; Feng, Xiangdong; Ma, Shengli

2018-02-01

A stress reconstruction was performed based on focal mechanisms around the Longmen Shan region prior to the 2008 M s 8.0 Wenchuan earthquake using a newly developed algorithm (known as MCA). The method determines the stress tensor, including principal axes orientations, and quantitative stress values, such as the effective confining pressure and maximum shear stress. The results of the MCA application using data recorded by the regional network from 1989 to April 2008 show the background stress state around the Longmen Shan belt before the Wenchuan earthquake. The characteristics of the stress orientation reveal that the Longmen Shan region is primarily under the eastward extrusion of the eastern Tibetan plateau. Non-uniform quantitative stress distributions show low stress levels in the upper crust of the middle Longmen Shan segment, which is consistent with the observed high-angle reverse faulting associated with the 2008 Wenchuan earthquake. In contrast, other study areas, such as the Bayankela block and the NW strip extending to the Sichuan basin, show high stress intensity. This feature coincides with heterogeneity in the wave speed image of the upper crust in this region, which shows high S-wave speed in the high stress areas and comparatively low S-wave speed in low stress areas. Deformation features across the Longmen Shan belt with the slow rates of convergence determined by GPS and the distribution of surface deformation rates also are in keeping with our stress results. We propose a dynamic model in which sloping uplift under the Longmen Shan, which partly counteracts the pushing force from the eastern plateau, causes the low-quantitative stresses in the upper crust beneath the Longmen Shan. The decreasing gravitational potential energy beneath the Longmen Shan leads to earthquake thrust faulting and plays an important role in the geodynamics of the area that results from ductile thickening of the deep crust behind the Sichuan basin, creating a narrow, steep margin.

A geometric exploration of stress in deformed liquid foams

NASA Astrophysics Data System (ADS)

Evans, Myfanwy E.; Schröder-Turk, Gerd E.; Kraynik, Andrew M.

2017-03-01

We explore an alternate way of looking at the rheological response of a yield stress fluid: using discrete geometry to probe the heterogeneous distribution of stress in soap froth. We present quasi-static, uniaxial, isochoric compression and extension of three-dimensional random monodisperse soap froth in periodic boundary conditions and examine the stress and geometry that result. The stress and shape anisotropy of individual cells is quantified by Q, a scalar measure derived from the interface tensor that gauges each cell’s contribution to the global stress. Cumulatively, the spatial distribution of highly deformed cells allows us to examine how stress is internally distributed. The topology of highly deformed cells, how they arrange relative to one another in space, gives insight into the heterogeneous distribution of stress.

An integrated workflow for stress and flow modelling using outcrop-derived discrete fracture networks

NASA Astrophysics Data System (ADS)

Bisdom, K.; Nick, H. M.; Bertotti, G.

2017-06-01

Fluid flow in naturally fractured reservoirs is often controlled by subseismic-scale fracture networks. Although the fracture network can be partly sampled in the direct vicinity of wells, the inter-well scale network is poorly constrained in fractured reservoir models. Outcrop analogues can provide data for populating domains of the reservoir model where no direct measurements are available. However, extracting relevant statistics from large outcrops representative of inter-well scale fracture networks remains challenging. Recent advances in outcrop imaging provide high-resolution datasets that can cover areas of several hundred by several hundred meters, i.e. the domain between adjacent wells, but even then, data from the high-resolution models is often upscaled to reservoir flow grids, resulting in loss of accuracy. We present a workflow that uses photorealistic georeferenced outcrop models to construct geomechanical and fluid flow models containing thousands of discrete fractures covering sufficiently large areas, that does not require upscaling to model permeability. This workflow seamlessly integrates geomechanical Finite Element models with flow models that take into account stress-sensitive fracture permeability and matrix flow to determine the full permeability tensor. The applicability of this workflow is illustrated using an outcropping carbonate pavement in the Potiguar basin in Brazil, from which 1082 fractures are digitised. The permeability tensor for a range of matrix permeabilities shows that conventional upscaling to effective grid properties leads to potential underestimation of the true permeability and the orientation of principal permeabilities. The presented workflow yields the full permeability tensor model of discrete fracture networks with stress-induced apertures, instead of relying on effective properties as most conventional flow models do.

A curious explanation of some cosmological phenomena

NASA Astrophysics Data System (ADS)

Gopal Vishwakarma, Ram

2013-05-01

Although observational cosmology has shown tremendous growth over the last decade, deep mysteries continue to haunt our theoretical understanding of the ingredients of the concordance cosmological model, which are mainly ‘dark’. More than 95% of the content of the energy-stress tensor has to be in the form of the inflaton field, dark matter and dark energy, which do not have any non-gravitational or laboratory evidence and remain unidentified. Moreover, the dark energy poses a serious confrontation between fundamental physics and cosmology. This makes a strong case to discover alternative theories that do not require the dark sectors of the standard approach to explain the observations. In the present situation, it would be important to gain insight about the requirements of the ‘would-be’ final theory from all possible means. In this context, this paper highlights some, hitherto unnoticed, interesting coincidences that may prove useful to develop insight about the ‘holy grail’ of gravitation. It appears that the requirement of the speculative dark sectors by the energy-stress tensor is indicative of a possible way out of the present crisis appearing in the standard cosmology, in terms of a theory wherein the energy-stress tensor does not play a direct role in the dynamics. It is shown that various cosmological observations can be explained satisfactorily in the framework of one such theory—the Milne model, without requiring the dark sectors of the standard approach. Moreover, the model evades the horizon, flatness and the cosmological constant problems afflicting the standard cosmology. Although Milne's theory is an incomplete, phenomenological theory, and cannot be the final theory of gravitation, nevertheless, it would be worthwhile to study these coincidences, which may help us develop insight about the would-be final theory.

Characteristics of global strong earthquakes and their implications for the present-day stress pattern

NASA Astrophysics Data System (ADS)

Wei, Ju; Weifeng, Sun; Jinhui, Luo

2017-10-01

Earthquakes occurred on the surface of the Earth contain comprehensive and abundant geodynamic connotations, and can serve as important sources for describing the present-day stress field and regime. An important advantage of the earthquake focal mechanism solution is the ability to obtain the stress pattern information at depth in the lithosphere. During the past several decades, an increasing number of focal mechanisms were available for estimating the present-day stress field and regime. In the present study, altogether 553 focal mechanism data ranging from the year 1976 to 2017 with Mw ≥ 7.0 were compiled in the Global/Harvard centroid moment tensor (CMT) catalogue, the characteristics of global strong earthquakes and the present-day stress pattern were analyzed based on these data. The majority of global strong earthquakes are located around the plate boundaries, shallow-focus, and thrust faulting (TF) regime. We grouped 518 of them into 12 regions (Boxes) based on their geographical proximity and tectonic setting. For each box, the present-day stress field and regime were obtained by formal stress inversion. The results indicated that the maximum horizontal principal stress direction was ˜ N-S-trending in western North America continent and southwestern Indonesia, ˜ NNE-SSW-trending in western Middle America and central Asia, ˜ NE-SW in southeastern South America continent and northeastern Australia, ˜ NEE-SWW-trending in western South America continent and southeastern Asia, ˜ E-W-trending in southeastern Australia, and ˜ NW-SE-trending in eastern Asia. The results can provide additional constraints to the driving forces and geodynamic models, allowing them to explain the current plate interactions and crustal tectonic complexities better.

Ordered rate constitutive theories for thermoviscoelastic solids with memory in Lagrangian description using Gibbs potential

NASA Astrophysics Data System (ADS)

Surana, K. S.; Reddy, J. N.; Nunez, Daniel

2015-11-01

This paper presents ordered rate constitutive theories of orders m and n, i.e., ( m, n) for finite deformation of homogeneous, isotropic, compressible and incompressible thermoviscoelastic solids with memory in Lagrangian description using entropy inequality in Gibbs potential Ψ as an alternate approach of deriving constitutive theories using entropy inequality in terms of Helmholtz free energy density Φ. Second Piola-Kirchhoff stress σ [0] and Green's strain tensor ɛ [0] are used as conjugate pair. We consider Ψ, heat vector q, entropy density η and rates of upto orders m and n of σ [0] and ɛ [0], i.e., σ [ i]; i = 0, 1, . . . , m and ɛ [ j]; j = 0, 1, . . . , n. We choose Ψ, ɛ [ n], q and η as dependent variables in the constitutive theories with ɛ [ j]; j = 0, 1, . . . , n - 1, σ [ i]; i = 0, 1, . . . , m, temperature gradient g and temperature θ as their argument tensors. Rationale for this choice is explained in the paper. Entropy inequality, decomposition of σ [0] into equilibrium and deviatoric stresses, the conditions resulting from entropy inequality and the theory of generators and invariants are used in the derivations of ordered rate constitutive theories of orders m and n in stress and strain tensors. Constitutive theories for the heat vector q (of up to orders m and n - 1) that are consistent (in terms of the argument tensors) with the constitutive theories for ɛ [ n] (of up to orders m and n) are also derived. Many simplified forms of the rate theories of orders ( m, n) are presented. Material coefficients are derived by considering Taylor series expansions of the coefficients in the linear combinations representing ɛ [ n] and q using the combined generators of the argument tensors about a known configuration {{\\underline{\\varOmega}}} in the combined invariants of the argument tensors and temperature. It is shown that the rate constitutive theories of order one ( m = 1, n = 1) when further simplified result in constitutive theories that resemble currently used theories but are in fact different. The solid continua characterized by these theories have mechanisms of elasticity, dissipation and memory, i.e., relaxation behavior or rheology. Fourier heat conduction law is shown to be an over simplified case of the rate theory of order one ( m = 1, n = 1) for q. The paper establishes when there is equivalence between the constitutive theories derived here using Ψ and those presented in reference Surana et al. (Acta Mech. doi:10.1007/s00707-014-1173-6, 2014) that are derived using Helmholtz free energy density Φ. The fundamental differences between the two constitutive theories in terms of physics and their explicit forms using Φ and Ψ are difficult to distinguish from the ordered theories of orders ( m, n) due to complexity of expressions. However, by choosing lower ordered theories, the difference between the two approaches can be clearly seen.

Numerical simulation of a compressible homogeneous, turbulent shear flow. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Feiereisen, W. J.; Reynolds, W. C.; Ferziger, J. H.

1981-01-01

A direct, low Reynolds number, numerical simulation was performed on a homogeneous turbulent shear flow. The full compressible Navier-Stokes equations were used in a simulation on the ILLIAC IV computer with a 64,000 mesh. The flow fields generated by the code are used as an experimental data base, to examine the behavior of the Reynols stresses in this simple, compressible flow. The variation of the structure of the stresses and their dynamic equations as the character of the flow changed is emphasized. The structure of the tress tensor is more heavily dependent on the shear number and less on the fluctuating Mach number. The pressure-strain correlation tensor in the dynamic uations is directly calculated in this simulation. These correlations are decomposed into several parts, as contrasted with the traditional incompressible decomposition into two parts. The performance of existing models for the conventional terms is examined, and a model is proposed for the 'mean fluctuating' part.

On the equivalence among stress tensors in a gauge-fluid system

NASA Astrophysics Data System (ADS)

Mitra, Arpan Krishna; Banerjee, Rabin; Ghosh, Subir

2017-12-01

In this paper, we bring out the subtleties involved in the study of a first-order relativistic field theory with auxiliary field variables playing an essential role. In particular, we discuss the nonisentropic Eulerian (or Hamiltonian) fluid model. Interactions are introduced by coupling the fluid to a dynamical Maxwell (U(1)) gauge field. This dynamical nature of the gauge field is crucial in showing the equivalence, on the physical subspace, of the stress tensor derived from two definitions, i.e. the canonical (Noether) one and the symmetric one. In the conventional equal-time formalism, we have shown that the generators of the space-time transformations obtained from these two definitions agree modulo the Gauss constraint. This equivalence in the physical sector has been achieved only because of the dynamical nature of the gauge fields. Subsequently, we have explicitly demonstrated the validity of the Schwinger condition. A detailed analysis of the model in lightcone formalism has also been done where several interesting features are revealed.

Effective Tolman temperature induced by trace anomaly

NASA Astrophysics Data System (ADS)

Eune, Myungseok; Gim, Yongwan; Kim, Wontae

2017-04-01

Despite the finiteness of stress tensor for a scalar field on the four-dimensional Schwarzschild black hole in the Israel-Hartle-Hawking vacuum, the Tolman temperature in thermal equilibrium is certainly divergent on the horizon due to the infinite blue-shift of the Hawking temperature. The origin of this conflict is due to the fact that the conventional Tolman temperature was based on the assumption of a traceless stress tensor, which is, however, incompatible with the presence of the trace anomaly responsible for the Hawking radiation. Here, we present an effective Tolman temperature which is compatible with the presence of the trace anomaly by using the modified Stefan-Boltzmann law. Eventually, the effective Tolman temperature turns out to be finite everywhere outside the horizon, and so an infinite blue-shift of the Hawking temperature at the event horizon does not appear any more. In particular, it is vanishing on the horizon, so that the equivalence principle is exactly recovered at the horizon.

Evaluating Small Sphere Limit of the Wang-Yau Quasi-Local Energy

NASA Astrophysics Data System (ADS)

Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung

2018-01-01

In this article, we study the small sphere limit of the Wang-Yau quasi-local energy defined in Wang and Yau (Phys Rev Lett 102(2):021101, 2009, Commun Math Phys 288(3):919-942, 2009). Given a point p in a spacetime N, we consider a canonical family of surfaces approaching p along its future null cone and evaluate the limit of the Wang-Yau quasi-local energy. The evaluation relies on solving an "optimal embedding equation" whose solutions represent critical points of the quasi-local energy. For a spacetime with matter fields, the scenario is similar to that of the large sphere limit found in Chen et al. (Commun Math Phys 308(3):845-863, 2011). Namely, there is a natural solution which is a local minimum, and the limit of its quasi-local energy recovers the stress-energy tensor at p. For a vacuum spacetime, the quasi-local energy vanishes to higher order and the solution of the optimal embedding equation is more complicated. Nevertheless, we are able to show that there exists a solution that is a local minimum and that the limit of its quasi-local energy is related to the Bel-Robinson tensor. Together with earlier work (Chen et al. 2011), this completes the consistency verification of the Wang-Yau quasi-local energy with all classical limits.

Multiscale properties of unconventional reservoir rocks

NASA Astrophysics Data System (ADS)

Woodruff, W. F.

A multidisciplinary study of unconventional reservoir rocks is presented, providing the theory, forward modeling and Bayesian inverse modeling approaches, and laboratory protocols to characterize clay-rich, low porosity and permeability shales and mudstones within an anisotropic framework. Several physical models characterizing oil and gas shales are developed across multiple length scales, ranging from microscale phenomena, e.g. the effect of the cation exchange capacity of reactive clay mineral surfaces on water adsorption isotherms, and the effects of infinitesimal porosity compaction on elastic and electrical properties, to meso-scale phenomena, e.g. the role of mineral foliations, tortuosity of conduction pathways and the effects of organic matter (kerogen and hydrocarbon fractions) on complex conductivity and their connections to intrinsic electrical anisotropy, as well as the macro-scale electrical and elastic properties including formulations for the complex conductivity tensor and undrained stiffness tensor within the context of effective stress and poroelasticity. Detailed laboratory protocols are described for sample preparation and measurement of these properties using spectral induced polarization (SIP) and ultrasonics for the anisotropic characterization of shales for both unjacketed samples under benchtop conditions and jacketed samples under differential loading. An ongoing study of the effects of kerogen maturation through hydrous pyrolysis on the complex conductivity is also provided in review. Experimental results are catalogued and presented for various unconventional formations in North America including the Haynesville, Bakken, and Woodford shales.

AnisoVis: a MATLAB™ toolbox for the visualisation of elastic anisotropy

NASA Astrophysics Data System (ADS)

Healy, D.; Timms, N.; Pearce, M. A.

2016-12-01

The elastic properties of rocks and minerals vary with direction, and this has significant consequences for their physical response to acoustic waves and natural or imposed stresses. This anisotropy of elasticity is well described mathematically by 4th rank tensors of stiffness or compliance. These tensors are not easy to visualise in a single diagram or graphic, and visualising Poisson's ratio and shear modulus presents a further challenge in that their anisotropy depends on two principal directions. Students and researchers can easily underestimate the importance of elastic anisotropy. This presentation describes an open source toolbox of MATLAB scripts that aims to visualise elastic anisotropy in rocks and minerals. The code produces linked 2-D and 3-D representations of the standard elastic constants, such as Young's modulus, Poisson's ratio and shear modulus, all from a simple GUI. The 3-D plots can be manipulated by the user (rotated, panned, zoomed), to encourage investigation and a deeper understanding of directional variations in the fundamental properties. Examples are presented of common rock forming minerals, including those with negative Poisson's ratio (auxetic behaviour). We hope that an open source code base will encourage further enhancements from the rock physics and wider geoscience communities. Eventually, we hope to generate 3-D prints of these complex and beautiful natural surfaces to provide a tactile link to the underlying physics of elastic anisotropy.

A chemo-mechanical free-energy-based approach to model durotaxis and extracellular stiffness-dependent contraction and polarization of cells.

PubMed

Shenoy, Vivek B; Wang, Hailong; Wang, Xiao

2016-02-06

We propose a chemo-mechanical model based on stress-dependent recruitment of myosin motors to describe how the contractility, polarization and strain in cells vary with the stiffness of their surroundings and their shape. A contractility tensor, which depends on the distribution of myosin motors, is introduced to describe the chemical free energy of the cell due to myosin recruitment. We explicitly include the contributions to the free energy that arise from mechanosensitive signalling pathways (such as the SFX, Rho-Rock and MLCK pathways) through chemo-mechanical coupling parameters. Taking the variations of the total free energy, which consists of the chemical and mechanical components, in accordance with the second law of thermodynamics provides equations for the temporal evolution of the active stress and the contractility tensor. Following this approach, we are able to recover the well-known Hill relation for active stresses, based on the fundamental principles of irreversible thermodynamics rather than phenomenology. We have numerically implemented our free energy-based approach to model spatial distribution of strain and contractility in (i) cells supported by flexible microposts, (ii) cells on two-dimensional substrates, and (iii) cells in three-dimensional matrices. We demonstrate how the polarization of the cells and the orientation of stress fibres can be deduced from the eigenvalues and eigenvectors of the contractility tensor. Our calculations suggest that the chemical free energy of the cell decreases with the stiffness of the extracellular environment as the cytoskeleton polarizes in response to stress-dependent recruitment of molecular motors. The mechanical energy, which includes the strain energy and motor potential energy, however, increases with stiffness, but the overall energy is lower for cells in stiffer environments. This provides a thermodynamic basis for durotaxis, whereby cells preferentially migrate towards stiffer regions of the extracellular environment. Our models also explain, from an energetic perspective, why the shape of the cells can change in response to stiffness of the surroundings. The effect of the stiffness of the nucleus on its shape and the orientation of the stress fibres is also studied for all the above geometries. Along with making testable predictions, we have estimated the magnitudes of the chemo-mechanical coupling parameters for myofibroblasts based on data reported in the literature.

A chemo-mechanical free-energy-based approach to model durotaxis and extracellular stiffness-dependent contraction and polarization of cells

PubMed Central

Shenoy, Vivek B.; Wang, Hailong; Wang, Xiao

2016-01-01

We propose a chemo-mechanical model based on stress-dependent recruitment of myosin motors to describe how the contractility, polarization and strain in cells vary with the stiffness of their surroundings and their shape. A contractility tensor, which depends on the distribution of myosin motors, is introduced to describe the chemical free energy of the cell due to myosin recruitment. We explicitly include the contributions to the free energy that arise from mechanosensitive signalling pathways (such as the SFX, Rho-Rock and MLCK pathways) through chemo-mechanical coupling parameters. Taking the variations of the total free energy, which consists of the chemical and mechanical components, in accordance with the second law of thermodynamics provides equations for the temporal evolution of the active stress and the contractility tensor. Following this approach, we are able to recover the well-known Hill relation for active stresses, based on the fundamental principles of irreversible thermodynamics rather than phenomenology. We have numerically implemented our free energy-based approach to model spatial distribution of strain and contractility in (i) cells supported by flexible microposts, (ii) cells on two-dimensional substrates, and (iii) cells in three-dimensional matrices. We demonstrate how the polarization of the cells and the orientation of stress fibres can be deduced from the eigenvalues and eigenvectors of the contractility tensor. Our calculations suggest that the chemical free energy of the cell decreases with the stiffness of the extracellular environment as the cytoskeleton polarizes in response to stress-dependent recruitment of molecular motors. The mechanical energy, which includes the strain energy and motor potential energy, however, increases with stiffness, but the overall energy is lower for cells in stiffer environments. This provides a thermodynamic basis for durotaxis, whereby cells preferentially migrate towards stiffer regions of the extracellular environment. Our models also explain, from an energetic perspective, why the shape of the cells can change in response to stiffness of the surroundings. The effect of the stiffness of the nucleus on its shape and the orientation of the stress fibres is also studied for all the above geometries. Along with making testable predictions, we have estimated the magnitudes of the chemo-mechanical coupling parameters for myofibroblasts based on data reported in the literature. PMID:26855753

Tensors and Differential Geometry Applied to Analytic and Numerical Coordinate Generation

DTIC Science & Technology

1981-01-01

or surfaces. Since the writing of the first memoir on the subject of tensor analysis by Ricci and Levi - Civita [11 in 1901 some very significant...available in the standard texts, such as, Levi - Civita [2], Weatherburn [3), McConnell [41, Eisenhart [51, [6], Tolman [7], Graustein [8], Synge and...Equations (216) have been used in Ref. [29] to compute the coordinates for arbitrary shaped two -dimensional bodies . §7. Miscellaneous Derivations. In this

Microseismic Monitoring Using Sparse Surface Network of Broadband Instruments: Western Canada Shale Play Case Study

NASA Astrophysics Data System (ADS)

Yenier, E.; Baturan, D.; Karimi, S.

2016-12-01

Monitoring of seismicity related to oil and gas operations is routinely performed nowadays using a number of different surface and downhole seismic array configurations and technologies. Here, we provide a hydraulic fracture (HF) monitoring case study that compares the data set generated by a sparse local surface network of broadband seismometers to a data set generated by a single downhole geophone string. Our data was collected during a 5-day single-well HF operation, by a temporary surface network consisting of 10 stations deployed within 5 km of the production well. The downhole data was recorded by a 20 geophone string deployed in an observation well located 15 m from the production well. Surface network data processing included standard STA/LTA event triggering enhanced by template-matching subspace detection, grid search locations which was improved using the double-differencing re-location technique, as well as Richter (ML) and moment (Mw) magnitude computations for all detected events. In addition, moment tensors were computed from first motion polarities and amplitudes for the subset of highest SNR events. The resulting surface event catalog shows a very weak spatio-temporal correlation to HF operations with only 43% of recorded seismicity occurring during HF stages times. This along with source mechanisms shows that the surface-recorded seismicity delineates the activation of several pre-existing structures striking NNE-SSW and consistent with regional stress conditions as indicated by the orientation of SHmax. Comparison of the sparse-surface and single downhole string datasets allows us to perform a cost-benefit analysis of the two monitoring methods. Our findings show that although the downhole array recorded ten times as many events, the surface network provides a more coherent delineation of the underlying structure and more accurate magnitudes for larger magnitude events. We attribute this to the enhanced focal coverage provided by the surface network and the use of broadband instrumentation. The results indicate that sparse surface networks of high quality instruments can provide rich and reliable datasets for evaluation of the impact and effectiveness of hydraulic fracture operations in regions with favorable surface noise, local stress and attenuation characteristics.

Thermodynamics of viscoelastic rate-type fluids with stress diffusion

NASA Astrophysics Data System (ADS)

Málek, Josef; Průša, Vít; Skřivan, Tomáš; Süli, Endre

2018-02-01

We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution equation for the extra stress tensor. It is shown that the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism, while different interpretations of the stress diffusion mechanism lead to different evolution equations for the temperature. The benefits of the knowledge of the thermodynamical background of the derived models are documented in the study of nonlinear stability of equilibrium rest states. The derived models open up the possibility to study fully coupled thermomechanical problems involving viscoelastic rate-type fluids with stress diffusion.

Closed system of coupling effects in generalized thermo-elastoplasticity

NASA Astrophysics Data System (ADS)

Śloderbach, Z.

2016-05-01

In this paper, the field equations of the generalized coupled thermoplasticity theory are derived using the postulates of classical thermodynamics of irreversible processses. Using the Legendre transformations two new thermodynamics potentials P and S depending upon internal thermodynamic forces Π are introduced. The most general form for all the thermodynamics potentials are assumed instead of the usually used additive form. Due to this assumption, it is possible to describe all the effects of thermomechanical couples and also the elastic-plastic coupling effects observed in such materials as rocks, soils, concretes and in some metalic materials. In this paper not only the usual postulate of existence of a dissipation qupotential (the Gyarmati postulate) is used to derive the velocity equation. The plastic flow constitutive equations have the character of non-associated flow laws even when the Gyarmati postulate is assumed. In general formulation, the plastic strain rate tensor is normal to the surface of the generalized function of plastic flow defined in the the space of internal thermodynamic forces Π but is not normal to the yield surface. However, in general formulation and after the use the Gyarmati postulate, the direction of the sum of the plastic strain rate tensor and the coupled elastic strain rate tensor is normal to the yield surface.

Calculation and Analysis of Magnetic Gradient Tensor Components of Global Magnetic Models

NASA Astrophysics Data System (ADS)

Schiffler, M.; Queitsch, M.; Schneider, M.; Goepel, A.; Stolz, R.; Krech, W.; Meyer, H. G.; Kukowski, N.

2014-12-01

Global Earth's magnetic field models like the International Geomagnetic Reference Field (IGRF), the World Magnetic Model (WMM) or the High Definition Geomagnetic Model (HDGM) are harmonic analysis regressions to available magnetic observations stored as spherical harmonic coefficients. Input data combine recordings from magnetic observatories, airborne magnetic surveys and satellite data. The advance of recent magnetic satellite missions like SWARM and its predecessors like CHAMP offer high resolution measurements while providing a full global coverage. This deserves expansion of the theoretical framework of harmonic synthesis to magnetic gradient tensor components. Measurement setups for Full Tensor Magnetic Gradiometry equipped with high sensitive gradiometers like the JeSSY STAR system can directly measure the gradient tensor components, which requires precise knowledge about the background regional gradients which can be calculated with this extension. In this study we develop the theoretical framework for calculation of the magnetic gradient tensor components from the harmonic series expansion and apply our approach to the IGRF and HDGM. The gradient tensor component maps for entire Earth's surface produced for the IGRF show low gradients reflecting the variation from the dipolar character, whereas maps for the HDGM (up to degree N=729) reveal new information about crustal structure, especially across the oceans, and deeply situated ore bodies. From the gradient tensor components, the rotational invariants, the Eigenvalues, and the normalized source strength (NSS) are calculated. The NSS focuses on shallower and stronger anomalies. Euler deconvolution using either the tensor components or the NSS applied to the HDGM reveals an estimate of the average source depth for the entire magnetic crust as well as individual plutons and ore bodies. The NSS reveals the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European Craton.

The instantaneous apparent resistivity tensor: a visualization scheme for LOTEM electric field measurements

NASA Astrophysics Data System (ADS)

Caldwell, T. Grant; Bibby, Hugh M.

1998-12-01

Long-offset transient electromagnetic (LOTEM) data have traditionally been represented as early- and late-time apparent resistivities. Time-varying electric field data recorded in a LOTEM survey made with multiple sources can be represented by an `instantaneous apparent resistivity tensor'. Three independent, coordinate-invariant, time-varying apparent resistivities can be derived from this tensor. For dipolar sources, the invariants are also independent of source orientation. In a uniform-resistivity half-space, the invariant given by the square root of the tensor determinant remains almost constant with time, deviating from the half-space resistivity by a maximum of 6 per cent. For a layered half-space, a distance-time pseudo-section of the determinant apparent resistivity produces an image of the layering beneath the measurement profile. As time increases, the instantaneous apparent resistivity tensor approaches the direct current apparent resistivity tensor. An approximate time-to-depth conversion can be achieved by integrating the diffusion depth formula with time, using the determinant apparent resistivity at each instant to represent the resistivity of the conductive medium. Localized near-surface inhomogeneities produce shifts in the time-domain apparent resistivity sounding curves that preserve the gradient, analogous to static shifts seen in magnetotelluric soundings. Instantaneous apparent resistivity tensors calculated for 3-D resistivity models suggest that profiles of LOTEM measurements across a simple 3-D structure can be used to create an image that reproduces the main features of the subsurface resistivity. Where measurements are distributed over an area, maps of the tensor invariants can be made into a sequence of images, which provides a way of `time slicing' down through the target structure.

Phase transformations in nanograin materials under high pressure and plastic shear: nanoscale mechanisms.

PubMed

Levitas, Valery I; Javanbakht, Mahdi

2014-01-07

There are two main challenges in the discovery of new high pressure phases (HPPs) and transforming this discovery into technologies: finding conditions to synthesize new HPPs and finding ways to reduce the phase transformation (PT) pressure to an economically reasonable level. Based on the results of pressure-shear experiments in the rotational diamond anvil cell (RDAC), superposition of plastic shear on high pressure is a promising way to resolve these problems. However, physical mechanisms behind these phenomena are not yet understood. Here, we elucidate generic mechanisms of coupled nucleation and evolution of dislocation and HPP structures in the nanograin material under pressure and shear utilizing the developed advanced phase field approach (PFA). Dislocations are generated at the grain boundaries and are densely piled up near them, creating a strong concentrator of the stress tensor. Averaged shear stress is essentially larger in the nanograin material due to grain boundary strengthening. This leads to the increase in the local thermodynamic driving force for PT, which allows one to significantly reduce the applied pressure. For all cases, the applied pressure is 3-20 times lower than the PT pressure and 2-12.5 times smaller than the phase equilibrium pressure. Interaction between nuclei leads sometimes to their coalescence and growth of the HPP away from stress concentrators. Plasticity plays a dual role: in addition to creating stress concentrators, it may relax stresses at other concentrators, thus competing with PT. Some ways to optimize the loading parameters have been found that lead to methods for controlling PT. Since such a local stress tensor with high shear stress component cannot be created without plastic deformations, this may lead to new transformation paths and phases, which are hidden during pressure induced PTs.

New seismogenic stress fields for southern Italy from a Bayesian approach

NASA Astrophysics Data System (ADS)

Totaro, Cristina; Orecchio, Barbara; Presti, Debora; Scolaro, Silvia; Neri, Giancarlo

2017-04-01

A new database of high-quality waveform inversion focal mechanism has been compiled for southern Italy by integrating the highest quality solutions, available from literature and catalogues, and 146 newly-computed ones. All the selected focal mechanisms are (i) coming from the Italian CMT, Regional CMT and TDMT catalogues (Pondrelli et al., PEPI 2006, PEPI 2011; http://www.ingv.it), or (ii) computed by using the Cut And Paste (CAP) method (Zhao & Helmberger, BSSA 1994; Zhu & Helmberger, BSSA 1996). Specific tests have been carried out in order to evaluate the robustness of the obtained solutions (e.g., by varying both seismic network configuration and Earth structure parameters) and to estimate uncertainties on the focal mechanism parameters. Only the resulting highest-quality solutions have been enclosed in the database, that has then been used for computation of posterior density distributions of stress tensor components by a Bayesian method (Arnold & Townend, GJI 2007). This algorithm furnishes the posterior density function of the principal components of stress tensor (maximum σ1, intermediate σ2, and minimum σ3 compressive stress, respectively) and the stress-magnitude ratio (R). Before stress computation, we applied the k-means clustering algorithm to subdivide the focal mechanism catalog on the basis of earthquake locations. This approach allows identifying the sectors to be investigated without any "a priori" constraint from faulting type distribution. The large amount of data and the application of the Bayesian algorithm allowed us to provide a more accurate local-to-regional scale stress distribution that has shed new light on the kinematics and dynamics of this very complex area, where lithospheric unit configuration and geodynamic engines are still strongly debated. The new high-quality information here furnished will then represent very useful tools and constraints for future geophysical analyses and geodynamic modeling.

Constraining primordial vector mode from B-mode polarization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saga, Shohei; Ichiki, Kiyotomo; Shiraishi, Maresuke, E-mail: saga.shohei@nagoya-u.jp, E-mail: maresuke.shiraishi@pd.infn.it, E-mail: ichiki@a.phys.nagoya-u.ac.jp

The B-mode polarization spectrum of the Cosmic Microwave Background (CMB) may be the smoking gun of not only the primordial tensor mode but also of the primordial vector mode. If there exist nonzero vector-mode metric perturbations in the early Universe, they are known to be supported by anisotropic stress fluctuations of free-streaming particles such as neutrinos, and to create characteristic signatures on both the CMB temperature, E-mode, and B-mode polarization anisotropies. We place constraints on the properties of the primordial vector mode characterized by the vector-to-scalar ratio r{sub v} and the spectral index n{sub v} of the vector-shear power spectrum,more » from the Planck and BICEP2 B-mode data. We find that, for scale-invariant initial spectra, the ΛCDM model including the vector mode fits the data better than the model including the tensor mode. The difference in χ{sup 2} between the vector and tensor models is Δχ{sup 2} = 3.294, because, on large scales the vector mode generates smaller temperature fluctuations than the tensor mode, which is preferred for the data. In contrast, the tensor mode can fit the data set equally well if we allow a significantly blue-tilted spectrum. We find that the best-fitting tensor mode has a large blue tilt and leads to an indistinct reionization bump on larger angular scales. The slightly red-tilted vector mode supported by the current data set can also create O(10{sup -22})-Gauss magnetic fields at cosmological recombination. Our constraints should motivate research that considers models of the early Universe that involve the vector mode.« less

Rheological Predictions of Network Systems Swollen with Entangled Solvent

DTIC Science & Technology

2014-04-01

represent binary entanglements and the crosses represent cross-links. Both of which are fixed in space for Green– Kubo calculations or moved affinely for...Two types of calculations can be performed, equilibrium (or Green– Kubo ) calculations in which the rate of deformation tensor21,22 is set to zero and the...autocorrelation function of stress at equilibrium is followed; or flow calculations in which a specific flow field is applied and the stress as a

Modeling Slip System Strength Evolution in Ti 7Al Informed by In situ Grain Stress Measurements (Postprint)

DTIC Science & Technology

2017-02-17

time for the tomography and diffraction sweeps was approximately 42 min. In a typical quasi -static in-situ experiment, loading is halted and the...data is used to extract individual grain- average stress tensors in a large aggregate of Ti-7Al grains (z500) over a time series of prescribed states...for public release: distribution unlimited. © 2017 ELSEVIER LTD (STINFO COPY) AIR FORCE RESEARCH LABORATORY MATERIALS AND MANUFACTURING

Forces in General Relativity

ERIC Educational Resources Information Center

Ridgely, Charles T.

2010-01-01

Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress-energy-momentum tensor is used to derive a general expression of the force experienced…

The simplicial Ricci tensor

NASA Astrophysics Data System (ADS)

Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.

2011-08-01

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.

On curve and surface stretching in turbulent flow

NASA Technical Reports Server (NTRS)

Etemadi, Nassrollah

1989-01-01

Cocke (1969) proved that in incompressible, isotropic turbulence the average material line (material surface) elements increase in comparison with their initial values. Good estimates of how much they increase in terms of the eigenvalues of the Green deformation tensor were rigorously obtained.

Earthquakes of Garhwal Himalaya region of NW Himalaya, India: A study of relocated earthquakes and their seismogenic source and stress

NASA Astrophysics Data System (ADS)

R, A. P.; Paul, A.; Singh, S.

2017-12-01

Since the continent-continent collision 55 Ma, the Himalaya has accommodated 2000 km of convergence along its arc. The strain energy is being accumulated at a rate of 37-44 mm/yr and releases at time as earthquakes. The Garhwal Himalaya is located at the western side of a Seismic Gap, where a great earthquake is overdue atleast since 200 years. This seismic gap (Central Seismic Gap: CSG) with 52% probability for a future great earthquake is located between the rupture zones of two significant/great earthquakes, viz. the 1905 Kangra earthquake of M 7.8 and the 1934 Bihar-Nepal earthquake of M 8.0; and the most recent one, the 2015 Gorkha earthquake of M 7.8 is in the eastern side of this seismic gap (CSG). The Garhwal Himalaya is one of the ideal locations of the Himalaya where all the major Himalayan structures and the Himalayan Seimsicity Belt (HSB) can ably be described and studied. In the present study, we are presenting the spatio-temporal analysis of the relocated local micro-moderate earthquakes, recorded by a seismicity monitoring network, which is operational since, 2007. The earthquake locations are relocated using the HypoDD (double difference hypocenter method for earthquake relocations) program. The dataset from July, 2007- September, 2015 have been used in this study to estimate their spatio-temporal relationships, moment tensor (MT) solutions for the earthquakes of M>3.0, stress tensors and their interactions. We have also used the composite focal mechanism solutions for small earthquakes. The majority of the MT solutions show thrust type mechanism and located near the mid-crustal-ramp (MCR) structure of the detachment surface at 8-15 km depth beneath the outer lesser Himalaya and higher Himalaya regions. The prevailing stress has been identified to be compressional towards NNE-SSW, which is the direction of relative plate motion between the India and Eurasia continental plates. The low friction coefficient estimated along with the stress inversions suggests the presence of fluids around the chamoli region. Although the epicentral locations of these earthquakes are located near the Main Central Thrust Zone, and based on the faulting mechanisms suggest that, these earthquakes are indeed related to the detachment/Main Himalayan Thrust (MHT), hence we suggest that the detachment/MHT is seismogenic.

Anisotropic Developments for Homogeneous Shear Flows

NASA Technical Reports Server (NTRS)

Cambon, Claude; Rubinstein, Robert

2006-01-01

The general decomposition of the spectral correlation tensor R(sub ij)(k) by Cambon et al. (J. Fluid Mech., 202, 295; J. Fluid Mech., 337, 303) into directional and polarization components is applied to the representation of R(sub ij)(k) by spherically averaged quantities. The decomposition splits the deviatoric part H(sub ij)(k) of the spherical average of R(sub ij)(k) into directional and polarization components H(sub ij)(sup e)(k) and H(sub ij)(sup z)(k). A self-consistent representation of the spectral tensor in the limit of weak anisotropy is constructed in terms of these spherically averaged quantities. The directional polarization components must be treated independently: models that attempt the same representation of the spectral tensor using the spherical average H(sub ij)(k) alone prove to be inconsistent with Navier-Stokes dynamics. In particular, a spectral tensor consistent with a prescribed Reynolds stress is not unique. The degree of anisotropy permitted by this theory is restricted by realizability requirements. Since these requirements will be less severe in a more accurate theory, a preliminary account is given of how to generalize the formalism of spherical averages to higher expansion of the spectral tensor. Directionality is described by a conventional expansion in spherical harmonics, but polarization requires an expansion in tensorial spherical harmonics generated by irreducible representations of the spatial rotation group SO(exp 3). These expansions are considered in more detail in the special case of axial symmetry.

Moment tensor inversion with three-dimensional sensor configuration of mining induced seismicity (Kiruna mine, Sweden)

NASA Astrophysics Data System (ADS)

Ma, Ju; Dineva, Savka; Cesca, Simone; Heimann, Sebastian

2018-06-01

Mining induced seismicity is an undesired consequence of mining operations, which poses significant hazard to miners and infrastructures and requires an accurate analysis of the rupture process. Seismic moment tensors of mining-induced events help to understand the nature of mining-induced seismicity by providing information about the relationship between the mining, stress redistribution and instabilities in the rock mass. In this work, we adapt and test a waveform-based inversion method on high frequency data recorded by a dense underground seismic system in one of the largest underground mines in the world (Kiruna mine, Sweden). A stable algorithm for moment tensor inversion for comparatively small mining induced earthquakes, resolving both the double-couple and full moment tensor with high frequency data, is very challenging. Moreover, the application to underground mining system requires accounting for the 3-D geometry of the monitoring system. We construct a Green's function database using a homogeneous velocity model, but assuming a 3-D distribution of potential sources and receivers. We first perform a set of moment tensor inversions using synthetic data to test the effects of different factors on moment tensor inversion stability and source parameters accuracy, including the network spatial coverage, the number of sensors and the signal-to-noise ratio. The influence of the accuracy of the input source parameters on the inversion results is also tested. Those tests show that an accurate selection of the inversion parameters allows resolving the moment tensor also in the presence of realistic seismic noise conditions. Finally, the moment tensor inversion methodology is applied to eight events chosen from mining block #33/34 at Kiruna mine. Source parameters including scalar moment, magnitude, double-couple, compensated linear vector dipole and isotropic contributions as well as the strike, dip and rake configurations of the double-couple term were obtained. The orientations of the nodal planes of the double-couple component in most cases vary from NNW to NNE with a dip along the ore body or in the opposite direction.

Moment Tensor Inversion with 3D sensor configuration of Mining Induced Seismicity (Kiruna mine, Sweden)

NASA Astrophysics Data System (ADS)

Ma, Ju; Dineva, Savka; Cesca, Simone; Heimann, Sebastian

2018-03-01

Mining induced seismicity is an undesired consequence of mining operations, which poses significant hazard to miners and infrastructures and requires an accurate analysis of the rupture process. Seismic moment tensors of mining-induced events help to understand the nature of mining-induced seismicity by providing information about the relationship between the mining, stress redistribution and instabilities in the rock mass. In this work, we adapt and test a waveform-based inversion method on high frequency data recorded by a dense underground seismic system in one of the largest underground mines in the world (Kiruna mine, Sweden). Stable algorithm for moment tensor inversion for comparatively small mining induced earthquakes, resolving both the double couple and full moment tensor with high frequency data is very challenging. Moreover, the application to underground mining system requires accounting for the 3D geometry of the monitoring system. We construct a Green's function database using a homogeneous velocity model, but assuming a 3D distribution of potential sources and receivers. We first perform a set of moment tensor inversions using synthetic data to test the effects of different factors on moment tensor inversion stability and source parameters accuracy, including the network spatial coverage, the number of sensors and the signal-to-noise ratio. The influence of the accuracy of the input source parameters on the inversion results is also tested. Those tests show that an accurate selection of the inversion parameters allows resolving the moment tensor also in presence of realistic seismic noise conditions. Finally, the moment tensor inversion methodology is applied to 8 events chosen from mining block #33/34 at Kiruna mine. Source parameters including scalar moment, magnitude, double couple, compensated linear vector dipole and isotropic contributions as well as the strike, dip, rake configurations of the double couple term were obtained. The orientations of the nodal planes of the double-couple component in most cases vary from NNW to NNE with a dip along the ore body or in the opposite direction.

Tidal disruption of solid bodies

NASA Technical Reports Server (NTRS)

Dobrovolskis, Anthony R.

1990-01-01

The problem of stress, strain, and breakup in solid satellites and stray bodies subject to tidal perturbations is presently addressed in view of three novel considerations. After presenting a new analytic solution for the stress tensor in a homogeneous and compressible elastic sphere, where the inclusion of compressibility alters stresses by several percent, realistic failure criteria are noted to demonstrate the general failure of such ductile bodies as iron meteoroids by plastic shear, while brittle ice bodies fail by either tensile or shear fracture. A reexamination of crack propagation after initial failure allows the diverse breakup criteria to be reconciled.

Precursory, Nucleation and Propagation of Ruptures Along Heterogeneously Loaded, Circular Experimental Faults

NASA Astrophysics Data System (ADS)

Reches, Z.; Zu, X.; Jeffers, J.

2017-12-01

We explored the evolution of dynamic rupture along a circular experimental fault composed of clear acrylic blocks. The ring-shaped fault surface has inner and outer diameters of 7.72 and 10.16 cm, respectively. An array of ten rossette strain-gauges is attached to the outer rim of one block that provide the 2D strain tensor in a plane normal to the fault. The 30 components of the gauges are monitored at 10^6 samples/second. One 3D miniature accelerometer is attached to the fault block. The initial asperities of the fault surface generated a non-uniform strain (=stress) distribution that was recorded, and indicated local deviations of ±30% from the mean stress. The mean normal stress was up to 3.5 MPa, the remotely applied velocity was up to .002 m/s, and the slip velocities during rupture were not measured. The rupture characteristics, namely propagation velocity and rupture front strain-field, were determined from strain-gauge outputs. The analysis of tens of stick-slip events revealed the following preliminary results: (1) The ruptures consistently nucleated at sites of high local strains (=stresses) that were formed by the pre-shear, normal stress loading. (2) The pre-rupture nucleation process was recognized a by temporal (< 0.1 s), local (<20 mm) reduction of the shear strain. (3) Commonly, the initiation of nucleation was associated with micro acoustic emissions, whereas the initiation of rupture was associated with intense acoustic activity. (4) Nucleation could occur quasi-simultaneously at two, highly stressed sites. (5) From the nucleation site, the ruptures propagated in two directions along the ring-shaped fault, and the collision between the two fronts led to rupture `shut-off'. (5) The strain-field of rupture fronts was well-recognized for ruptures propagating faster than 50 m/s, and the fastest fronts propagated at 1000 m/s. (7) It appears that the rupture front strain-field close to the nucleation site differs from the front strain-field far from nucleation site. (8) Post-shear examination of the fault surfaces revealed evidence of brittle wear of the acrylic including gouge formation, ploughing, and powder smearing. (9) Work in progress includes attempts to achieve faster dynamic ruptures, and the utilization of the existing monitoring system to rupture granite faults.

How to use retarded Green's functions in de Sitter spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Higuchi, Atsushi; Cheong, Lee Yen

2008-10-15

We demonstrate in examples that the covariant retarded Green's functions in electromagnetism and linearized gravity work as expected in de Sitter spacetime. We first clarify how retarded Green's functions should be used in spacetimes with spacelike past infinity such as de Sitter spacetime. In particular, we remind the reader of a general formula which gives the field for given initial data on a Cauchy surface and a given source (a charge or stress-energy tensor distribution) in its future. We then apply this formula to three examples: (i) electromagnetism in the future of a Cauchy surface in Minkowski spacetime, (ii) electromagnetismmore » in de Sitter spacetime, and (iii) linearized gravity in de Sitter spacetime. In each example the field is reproduced correctly as predicted by the general argument. In the third example we construct a linearized gravitational field from two equal point masses located at the 'North and South Poles' which is nonsingular on the cosmological horizon and satisfies a covariant gauge condition and show that this field is reproduced by the retarded Green's function with corresponding gauge parameters.« less

Tensor Analysis Reveals Distinct Population Structure that Parallels the Different Computational Roles of Areas M1 and V1

PubMed Central

Ryu, Stephen I.; Shenoy, Krishna V.; Cunningham, John P.; Churchland, Mark M.

2016-01-01

Cortical firing rates frequently display elaborate and heterogeneous temporal structure. One often wishes to compute quantitative summaries of such structure—a basic example is the frequency spectrum—and compare with model-based predictions. The advent of large-scale population recordings affords the opportunity to do so in new ways, with the hope of distinguishing between potential explanations for why responses vary with time. We introduce a method that assesses a basic but previously unexplored form of population-level structure: when data contain responses across multiple neurons, conditions, and times, they are naturally expressed as a third-order tensor. We examined tensor structure for multiple datasets from primary visual cortex (V1) and primary motor cortex (M1). All V1 datasets were ‘simplest’ (there were relatively few degrees of freedom) along the neuron mode, while all M1 datasets were simplest along the condition mode. These differences could not be inferred from surface-level response features. Formal considerations suggest why tensor structure might differ across modes. For idealized linear models, structure is simplest across the neuron mode when responses reflect external variables, and simplest across the condition mode when responses reflect population dynamics. This same pattern was present for existing models that seek to explain motor cortex responses. Critically, only dynamical models displayed tensor structure that agreed with the empirical M1 data. These results illustrate that tensor structure is a basic feature of the data. For M1 the tensor structure was compatible with only a subset of existing models. PMID:27814353

Strength Analysis of Glass-Fiber-Reinforced Plastic during Buckling,

DTIC Science & Technology

An algorithm is developed for calculating and analyzing the stress tensor by the experimental function of deflections during the buckling of glass ... fiber -reinforced plastic shells loaded with a hydrostatic load. Malmeyster’s theory of strength is used to qualitatively establish the possible points of shell failure. (Author-PL)

A fast and robust method for moment tensor and depth determination of shallow seismic events in CTBT related studies.

NASA Astrophysics Data System (ADS)

Baker, Ben; Stachnik, Joshua; Rozhkov, Mikhail

2017-04-01

International Data Center is required to conduct expert technical analysis and special studies to improve event parameters and assist State Parties in identifying the source of specific event according to the protocol to the Protocol to the Comprehensive Nuclear Test Ban Treaty. Determination of seismic event source mechanism and its depth is closely related to these tasks. It is typically done through a strategic linearized inversion of the waveforms for a complete or subset of source parameters, or similarly defined grid search through precomputed Greens Functions created for particular source models. In this presentation we demonstrate preliminary results obtained with the latter approach from an improved software design. In this development we tried to be compliant with different modes of CTBT monitoring regime and cover wide range of source-receiver distances (regional to teleseismic), resolve shallow source depths, provide full moment tensor solution based on body and surface waves recordings, be fast to satisfy both on-demand studies and automatic processing and properly incorporate observed waveforms and any uncertainties a priori as well as accurately estimate posteriori uncertainties. Posterior distributions of moment tensor parameters show narrow peaks where a significant number of reliable surface wave observations are available. For earthquake examples, fault orientation (strike, dip, and rake) posterior distributions also provide results consistent with published catalogues. Inclusion of observations on horizontal components will provide further constraints. In addition, the calculation of teleseismic P wave Green's Functions are improved through prior analysis to determine an appropriate attenuation parameter for each source-receiver path. Implemented HDF5 based Green's Functions pre-packaging allows much greater flexibility in utilizing different software packages and methods for computation. Further additions will have the rapid use of Instaseis/AXISEM full waveform synthetics added to a pre-computed GF archive. Along with traditional post processing analysis of waveform misfits through several objective functions and variance reduction, we follow a probabilistic approach to assess the robustness of moment tensor solution. In a course of this project full moment tensor and depth estimates are determined for DPRK events and shallow earthquakes using a new implementation of teleseismic P waves waveform fitting. A full grid search over the entire moment tensor space is used to appropriately sample all possible solutions. A recent method by Tape & Tape (2012) to discretize the complete moment tensor space from a geometric perspective is used. Probabilistic uncertainty estimates on the moment tensor parameters provide robustness to solution.

Non-equilibrium surface tension of the vapour-liquid interface of active Lennard-Jones particles

NASA Astrophysics Data System (ADS)

Paliwal, Siddharth; Prymidis, Vasileios; Filion, Laura; Dijkstra, Marjolein

2017-08-01

We study a three-dimensional system of self-propelled Brownian particles interacting via the Lennard-Jones potential. Using Brownian dynamics simulations in an elongated simulation box, we investigate the steady states of vapour-liquid phase coexistence of active Lennard-Jones particles with planar interfaces. We measure the normal and tangential components of the pressure tensor along the direction perpendicular to the interface and verify mechanical equilibrium of the two coexisting phases. In addition, we determine the non-equilibrium interfacial tension by integrating the difference of the normal and tangential components of the pressure tensor and show that the surface tension as a function of strength of particle attractions is well fitted by simple power laws. Finally, we measure the interfacial stiffness using capillary wave theory and the equipartition theorem and find a simple linear relation between surface tension and interfacial stiffness with a proportionality constant characterized by an effective temperature.

Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation

PubMed Central

Freistühler, Heinrich; Temple, Blake

2014-01-01

Current theories of dissipation in the relativistic regime suffer from one of two deficits: either their dissipation is not causal or no profiles for strong shock waves exist. This paper proposes a relativistic Navier–Stokes–Fourier-type viscosity and heat conduction tensor such that the resulting second-order system of partial differential equations for the fluid dynamics of pure radiation is symmetric hyperbolic. This system has causal dissipation as well as the property that all shock waves of arbitrary strength have smooth profiles. Entropy production is positive both on gradients near those of solutions to the dissipation-free equations and on gradients of shock profiles. This shows that the new dissipation stress tensor complies to leading order with the principles of thermodynamics. Whether higher order modifications of the ansatz are required to obtain full compatibility with the second law far from the zero-dissipation equilibrium is left to further investigations. The system has exactly three a priori free parameters χ,η,ζ, corresponding physically to heat conductivity, shear viscosity and bulk viscosity. If the bulk viscosity is zero (as is stated in the literature) and the total stress–energy tensor is trace free, the entire viscosity and heat conduction tensor is determined to within a constant factor. PMID:24910526

Stress before and after the 2002 Denali fault earthquake

USGS Publications Warehouse

Wesson, R.L.; Boyd, O.S.

2007-01-01

Spatially averaged, absolute deviatoric stress tensors along the faults ruptured during the 2002 Denali fault earthquake, both before and after the event, are derived, using a new method, from estimates of the orientations of the principal stresses and the stress change associated with the earthquake. Stresses are estimated in three regions along the Denali fault, one of which also includes the Susitna Glacier fault, and one region along the Totschunda fault. Estimates of the spatially averaged shear stress before the earthquake resolved onto the faults that ruptured during the event range from near 1 MPa to near 4 MPa. Shear stresses estimated along the faults in all these regions after the event are near zero (0 ?? 1 MPa). These results suggest that deviatoric stresses averaged over a few tens of km along strike are low, and that the stress drop during the earthquake was complete or nearly so.

Future Directions of Nonlinear Dynamics in PhysicaL and Biological Systems,

DTIC Science & Technology

1992-01-01

ACKNOWLEDGEMENT This work has been supported in part by the Air Force Office of Scientific Research through Grant No. AFOSR-89-0510 and by NWSC, Crane ...Biological Systemr Edied by PL. Cbhsius et a., Plenu= Press, New York, 1993 121 with the stress tensor (TMm,) having components TMrm ` SYM nNtnN + I...transparent. This also implies that Nt= N, - N where N = N1=1 is the usual boson number operator. It is worth stressing that the notion of q-hermiticity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun Dongsheng; Wang Hongcai; Ma Yinsheng

In-situ stress change near the fault before and after a great earthquake is a key issue in the geosciences field. In this work, based on the 2008 Great Wenchuan earthquake fault slip dislocation model, the co-seismic stress tensor change due to the Wenchuan earthquake and the distribution functions around the Longmen Shan fault are given. Our calculated results are almost consistent with the before and after great Wenchuan earthquake in-situ measuring results. The quantitative assessment results provide a reference for the study of the mechanism of earthquakes.

Efficient 3-D finite element failure analysis of compression loaded angle-ply plates with holes

NASA Technical Reports Server (NTRS)

Burns, S. W.; Herakovich, C. T.; Williams, J. G.

1987-01-01

Finite element stress analysis and the tensor polynomial failure criterion predict that failure always initiates at the interface between layers on the hole edge for notched angle-ply laminates loaded in compression. The angular location of initial failure is a function of the fiber orientation in the laminate. The dominant stress components initiating failure are shear. It is shown that approximate symmetry can be used to reduce the computer resources required for the case of unaxial loading.

Stress-dependence of kinetic transitions at atomistic defects

NASA Astrophysics Data System (ADS)

Ball, S. L.; Alexander, K. C.; Schuh, C. A.

2018-01-01

The full second-rank activation volume tensors associated with vacancy migration in FCC copper and HCP titanium as well as transition events in the Σ5 (2 1 0) grain boundary in copper are calculated and analyzed. The full tensorial results quantitatively illustrate how the conventional use of an activation volume scalar in atomistic studies of the kinetic processes of complex defects can miss important stress dependencies, in that neither hydrostatic pressure nor deviatoric stress dependencies can be considered alone as dominating the response. The results speak to the importance of anisotropies in the stress-dependence of atomistic kinetics, including crystal structure anisotropy, elastic anisotropy, and defect structure or migration-path anisotropies.

Normal-faulting stress state associated with low differential stress in an overriding plate in northeast Japan prior to the 2011 Mw 9.0 Tohoku earthquake

NASA Astrophysics Data System (ADS)

Otsubo, Makoto; Miyakawa, Ayumu; Imanishi, Kazutoshi

2018-03-01

Spatial and temporal variations in inland crustal stress prior to the 2011 Mw 9.0 Tohoku earthquake are investigated using focal mechanism solutions for shallow seismicity in Iwaki City, Japan. The multiple inverse method of stress tensor inversion detected two normal-faulting stress states that dominate in different regions. The stress field around Iwaki City changed from a NNW-SSE-trending triaxial extensional stress (stress regime A) to a NW-SE-trending axial tension (stress regime B) between 2005 and 2008. These stress changes may be the result of accumulated extensional stress associated with co- and post-seismic deformation due to the M7 class earthquakes. In this study we suggest that the stress state around Iwaki City prior to the 2011 Tohoku earthquake may have been extensional with a low differential stress. High pore pressure is required to cause earthquakes under such small differential stresses.

Separation of specular and diffuse components using tensor voting in color images.

PubMed

Nguyen, Tam; Vo, Quang Nhat; Yang, Hyung-Jeong; Kim, Soo-Hyung; Lee, Guee-Sang

2014-11-20

Most methods for the detection and removal of specular reflections suffer from nonuniform highlight regions and/or nonconverged artifacts induced by discontinuities in the surface colors, especially when dealing with highly textured, multicolored images. In this paper, a novel noniterative and predefined constraint-free method based on tensor voting is proposed to detect and remove the highlight components of a single color image. The distribution of diffuse and specular pixels in the original image is determined using tensors' saliency analysis, instead of comparing color information among neighbor pixels. The achieved diffuse reflectance distribution is used to remove specularity components. The proposed method is evaluated quantitatively and qualitatively over a dataset of highly textured, multicolor images. The experimental results show that our result outperforms other state-of-the-art techniques.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar

Here, we study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on R 1,d--1. We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We also show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, andmore » proportional to the coefficient C T appearing in the two-point function of stress tensors in that CFT. As applications of our result, we prove the conjectured universality of the corner term coefficient σ/CT=π 2/24 in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.« less

Shape dependence of holographic Rényi entropy in general dimensions

DOE PAGES

Bianchi, Lorenzo; Chapman, Shira; Dong, Xi; ...

2016-11-29

We present a holographic method for computing the response of Rényi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our strategy employs the stress tensor one-point function in a deformed hyperboloid background and relates it to the coefficient in the two-point function of the displacement operator. We obtain explicit numerical results for d = 3, · · · , 6 spacetime dimensions, and also evaluate analytically the limits where the Rényi index approaches 1 and 0 in general dimensions. We use our results to extend the work of 1602.08493 and disprove amore » set of conjectures in the literature regarding the relation between the Rényi shape dependence and the conformal weight of the twist operator. As a result, we also extend our analysis beyond leading order in derivatives in the bulk theory by studying Gauss-Bonnet gravity.« less

A Hydraulic Stress Measurement System for Deep Borehole Investigations

NASA Astrophysics Data System (ADS)

Ask, Maria; Ask, Daniel; Cornet, Francois; Nilsson, Tommy

2017-04-01

Luleå University of Technology (LTU) is developing and building a wire-line system for hydraulic rock stress measurements, with funding from the Swedish Research Council and Luleå University of Technology. In this project, LTU is collaborating with University of Strasbourg and Geosigma AB. The stress state influences drilling and drillability, as well as rock mass stability and permeability. Therefore, knowledge about the state of in-situ stress (stress magnitudes, and orientations) and its spatial variation with depth is essential for many underground rock engineering projects, for example for underground storage of hazardous material (e.g. nuclear waste, carbon dioxide), deep geothermal exploration, and underground infrastructure (e.g. tunneling, hydropower dams). The system is designed to conduct hydraulic stress testing in slim boreholes. There are three types of test methods: (1) hydraulic fracturing, (2) sleeve fracturing and (3) hydraulic testing of pre-existing fractures. These are robust methods for determining in situ stresses from boreholes. Integration of the three methods allows determination of the three-dimensional stress tensor and its spatial variation with depth in a scientific unambiguously way. The stress system is composed of a downhole and a surface unit. The downhole unit consists of hydraulic fracturing equipment (straddle packers and downhole imaging tool) and their associated data acquisition systems. The testing system is state of the art in several aspects including: (1) Large depth range (3 km), (2) Ability to test three borehole dimensions (N=76 mm, H=96 mm, and P=122 mm), (3) Resistivity imager maps the orientation of tested fracture; (4) Highly stiff and resistive to corrosion downhole testing equipment; and (5) Very detailed control on the injection flow rate and cumulative volume is obtained by a hydraulic injection pump with variable piston rate, and a highly sensitive flow-meter. At EGU General Assembly 2017, we would like to present this new and unique stress measurement system and some initial test results from a 1200 m long borehole in crystalline rock.

Dynamic shear-stress-enhanced rates of nutrient consumption in gas-liquid semi-continuous-flow suspensions

NASA Astrophysics Data System (ADS)

Belfiore, Laurence A.; Volpato, Fabio Z.; Paulino, Alexandre T.; Belfiore, Carol J.

2011-12-01

The primary objective of this investigation is to establish guidelines for generating significant mammalian cell density in suspension bioreactors when stress-sensitive kinetics enhance the rate of nutrient consumption. Ultra-low-frequency dynamic modulations of the impeller (i.e., 35104 Hz) introduce time-dependent oscillatory shear into this transient analysis of cell proliferation under semi-continuous creeping flow conditions. Greater nutrient consumption is predicted when the amplitude A of modulated impeller rotation increases, and stress-kinetic contributions to nutrient consumption rates increase linearly at higher modulation frequency via an application of fluctuation-dissipation response. Interphase mass transfer is required to replace dissolved oxygen as it is consumed by aerobic nutrient consumption in the liquid phase. The theory and predictions described herein could be important at small length scales in the creeping flow regime where viscous shear is significant at the interface between the nutrient medium and isolated cells in suspension. Two-dimensional flow around spherically shaped mammalian cells, suspended in a Newtonian culture medium, is analyzed to calculate the surface-averaged magnitude of the velocity gradient tensor and modify homogeneous rates of nutrient consumption that are stimulated by viscous shear, via the formalism of stress-kinetic reciprocal relations that obey Curie's theorem in non-equilibrium thermodynamics. Time constants for stress-free free and stress-sensitive stress nutrient consumption are defined and quantified to identify the threshold (i.e., stress,threshold) below which the effect of stress cannot be neglected in accurate predictions of bioreactor performance. Parametric studies reveal that the threshold time constant for stress-sensitive nutrient consumption stress,threshold decreases when the time constant for stress-free nutrient consumption free is shorter. Hence, stress,threshold depends directly on free. In other words, the threshold rate of stress-sensitive nutrient consumption is higher when the stress-free rate of nutrient consumption increases. Modulated rotation of the impeller, superimposed on steady shear, increases stress,threshold when free is constant, and stress,threshold depends directly on the amplitude A of these angular velocity modulations.

Estimation of full moment tensors, including uncertainties, for earthquakes, volcanic events, and nuclear explosions

NASA Astrophysics Data System (ADS)

Alvizuri, Celso R.

We present a catalog of full seismic moment tensors for 63 events from Uturuncu volcano in Bolivia. The events were recorded during 2011-2012 in the PLUTONS seismic array of 24 broadband stations. Most events had magnitudes between 0.5 and 2.0 and did not generate discernible surface waves; the largest event was Mw 2.8. For each event we computed the misfit between observed and synthetic waveforms, and we used first-motion polarity measurements to reduce the number of possible solutions. Each moment tensor solution was obtained using a grid search over the six-dimensional space of moment tensors. For each event we show the misfit function in eigenvalue space, represented by a lune. We identify three subsets of the catalog: (1) 6 isotropic events, (2) 5 tensional crack events, and (3) a swarm of 14 events southeast of the volcanic center that appear to be double couples. The occurrence of positively isotropic events is consistent with other published results from volcanic and geothermal regions. Several of these previous results, as well as our results, cannot be interpreted within the context of either an oblique opening crack or a crack-plus-double-couple model. Proper characterization of uncertainties for full moment tensors is critical for distinguishing among physical models of source processes. A seismic moment tensor is a 3x3 symmetric matrix that provides a compact representation of a seismic source. We develop an algorithm to estimate moment tensors and their uncertainties from observed seismic data. For a given event, the algorithm performs a grid search over the six-dimensional space of moment tensors by generating synthetic waveforms for each moment tensor and then evaluating a misfit function between the observed and synthetic waveforms. 'The' moment tensor M0 for the event is then the moment tensor with minimum misfit. To describe the uncertainty associated with M0, we first convert the misfit function to a probability function. The uncertainty, or rather the confidence, is then given by the 'confidence curve' P( V), where P(V) is the probability that the true moment tensor for the event lies within the neighborhood of M that has fractional volume V. The area under the confidence curve provides a single, abbreviated 'confidence parameter' for M0. We apply the method to data from events in different regions and tectonic settings: 63 small (M w 4) earthquakes in the southern Alaska subduction zone, and 12 earthquakes and 17 nuclear explosions at the Nevada Test Site. Characterization of moment tensor uncertainties puts us in better position to discriminate among moment tensor source types and to assign physical processes to the events.

Influence of fault geometry and tectonic driving stress orientation on the mechanics of multifault earthquakes

NASA Astrophysics Data System (ADS)

Madden, E. H.; Maerten, F.; Pollard, D. D.

2012-12-01

The M 7.3 28 June 1992 Landers, California earthquake was a well-documented event that highlighted the complex relationship between the earthquake and the multiple faults on which it occurred. Not only was fault slip data mapped in the field in detail, due to good exposure in the arid conditions of the Mojave Desert, but also it was one of the first earthquakes for which the surface displacement field was captured by satellite technology. In addition, precise aftershock relocations and fault plane solutions provide information about stress and fault behavior at depth. Study of fault interactions leading to the linkage of five right-lateral, strike-slip faults at Landers is aided by this abundance of available surface and subsurface data. While mapped near-field surface data often are restricted to the realm of the geologist, and subsurface data, such as aftershocks, often are restricted to the realm of the geophysicist, we find that integrating these data in mechanical forward models provides good constraint on the three-dimensional structures of the faults involved. Mechanical models also reveal that fault geometry and the orientation of the tectonic driving stress greatly influence whether or not slip is promoted across the extensional step between two of the faults along the southern-central rupture and elucidate the role of a crossing fault located within the step. Unfortunately, the orientation of the principal stresses are not well constrained near Landers or in many regions around the world. Previous determinations of the tectonic driving stress at Landers range from 7 degrees to 45 degrees, measured clockwise from North. We introduce a new stress inversion method that honors mechanical relationships among the remote stress state that is being inverted for, mainshock fault slip, the resulting total stress field following fault slip, and aftershocks. Use of the principal of superposition in this new algorithm obviates the need for the prohibitive computation times associated with running successive forward models. We apply the inverse method using aftershock, Interferometric Synthetic Aperture Radar (InSAR) and Global Positioning System (GPS) data associated with the Landers earthquake and address how fault geometry and aftershock size, timing, and focal mechanism quality influence inversion results. The advantages of this new method are that: (1) coseismic displacement data can be used, (2) the underlying model is better constrained to find a solution in the parameter space in the presence of fault slip perturbations, (3) absolute magnitudes can be recovered when using data with magnitude information such as GPS, InSAR and stress tensors inferred from aftershocks with known magnitudes. In addition, while one can choose to invert for an Andersonian fault regime, the method is not restricted to that particular case with one vertical principal stress.

Renormalized stress-energy tensor near the horizon of a slowly evolving, rotating black hole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frolov, V.P.; Thorne, K.S.

1989-04-15

The renormalized expectation value of the stress-energy tensor /sup ren/ of a quantum field in an arbitrary quantum state near the future horizon of a rotating (Kerr) black hole is derived in two very different ways: One derivation (restricted for simplicity to a massless scalar field) makes use of traditional techniques of quantum field theory in curved spacetime, augmented by a variant of the ''eta formalism'' for handling superradiant modes. The other derivation (valid for any quantum field) uses the equivalence principle to infer, from /sup ren/ in flat spacetime, what must be /sup ren/ near the hole's horizon. Themore » two derivations give the same result: a result in accord with a previous conjecture by Zurek and Thorne: /sup ren/, in any quantum state, is equal to that, /sup ZAMO/, which zero-angular-momentum observers (ZAMO's) would compute from their own physical measurements near the horizon, plus a vacuum-polarization contribution T/sub ..mu..//sub ..nu..//sup vac pol/, which is the negative of the stress-energy of a rigidly rotating thermal reservoir with angular velocity equal to that of the horizon ..cap omega../sub H/, and (red-shifted) temperature equal to that of the Hawking temperature T/sub H/.« less

Quantifying Anderson's fault types

USGS Publications Warehouse

Simpson, R.W.

1997-01-01

Anderson [1905] explained three basic types of faulting (normal, strike-slip, and reverse) in terms of the shape of the causative stress tensor and its orientation relative to the Earth's surface. Quantitative parameters can be defined which contain information about both shape and orientation [Ce??le??rier, 1995], thereby offering a way to distinguish fault-type domains on plots of regional stress fields and to quantify, for example, the degree of normal-faulting tendencies within strike-slip domains. This paper offers a geometrically motivated generalization of Angelier's [1979, 1984, 1990] shape parameters ?? and ?? to new quantities named A?? and A??. In their simple forms, A?? varies from 0 to 1 for normal, 1 to 2 for strike-slip, and 2 to 3 for reverse faulting, and A?? ranges from 0?? to 60??, 60?? to 120??, and 120?? to 180??, respectively. After scaling, A?? and A?? agree to within 2% (or 1??), a difference of little practical significance, although A?? has smoother analytical properties. A formulation distinguishing horizontal axes as well as the vertical axis is also possible, yielding an A?? ranging from -3 to +3 and A?? from -180?? to +180??. The geometrically motivated derivation in three-dimensional stress space presented here may aid intuition and offers a natural link with traditional ways of plotting yield and failure criteria. Examples are given, based on models of Bird [1996] and Bird and Kong [1994], of the use of Anderson fault parameters A?? and A?? for visualizing tectonic regimes defined by regional stress fields. Copyright 1997 by the American Geophysical Union.

Rheologic effects of crystal preferred orientation in upper mantle flow near plate boundaries

NASA Astrophysics Data System (ADS)

Blackman, Donna; Castelnau, Olivier; Dawson, Paul; Boyce, Donald

2016-04-01

Observations of anisotropy provide insight into upper mantle processes. Flow-induced mineral alignment provides a link between mantle deformation patterns and seismic anisotropy. Our study focuses on the rheologic effects of crystal preferred orientation (CPO), which develops during mantle flow, in order to assess whether corresponding anisotropic viscosity could significantly impact the pattern of flow. We employ a coupled nonlinear numerical method to link CPO and the flow model via a local viscosity tensor field that quantifies the stress/strain-rate response of a textured mineral aggregate. For a given flow field, the CPO is computed along streamlines using a self-consistent texture model and is then used to update the viscosity tensor field. The new viscosity tensor field defines the local properties for the next flow computation. This iteration produces a coupled nonlinear model for which seismic signatures can be predicted. Results thus far confirm that CPO can impact flow pattern by altering rheology in directionally-dependent ways, particularly in regions of high flow gradient. Multiple iterations run for an initial, linear stress/strain-rate case (power law exponent n=1) converge to a flow field and CPO distribution that are modestly different from the reference, scalar viscosity case. Upwelling rates directly below the spreading axis are slightly reduced and flow is focused somewhat toward the axis. Predicted seismic anisotropy differences are modest. P-wave anisotropy is a few percent greater in the flow 'corner', near the spreading axis, below the lithosphere and extending 40-100 km off axis. Predicted S-wave splitting differences would be below seafloor measurement limits. Calculations with non-linear stress/strain-rate relation, which is more realistic for olivine, indicate that effects are stronger than for the linear case. For n=2-3, the distribution and strength of CPO for the first iteration are greater than for n=1, although the fast seismic axis directions are similar. The greatest difference in CPO for the nonlinear cases develop at the flow 'corner' at depths of 10-30 km and 20-100 km off-axis. J index values up to 10% greater than the linear case are predicted near the lithosphere base in that region. Viscosity tensor components are notably altered in the nonlinear cases. Iterations between the texture and flow calculations for the non-linear cases are underway this winter; results will be reported in the presentation.

Moment Tensor Inversion of the 1998 Aiquile Earthquake Using Long-period surface waves

NASA Astrophysics Data System (ADS)

Wang, H.

2016-12-01

On 22nd May 1998 at 04:49(GMT), an earthquake of magnitude Mw = 6.6 struck the Aiquile region of Bolivia, causing 105 deaths and significant damage to the nearby towns of Hoyadas and Pampa Grande. This was the largest shallow earthquake (15 km depth) in Bolivia in over 50 years, and was felt as far Sucre, approximately 100 km away. In this report, a centroid moment tensor (CMT) inversion is carried using body waves and surface waves from 1998 Aiquile earthquake with 1-D and 3-D earth models to obtain the source model parameters and moment tensor, which are the values will be subsequently compared against the Global Centroid Moment Tensor Catalog(GCMT). Also, the excitation kernels could be gained and synthetic data can be created with different earth models. The two method for calculating synthetic seismograms are SPECFEM3D Globe which is based on shear wave mantle model S40RTS and crustal model CRUST 2.0, and AxiSEM which is based on PREM 1-D earth Model. Within the report, the theory behind the CMT inversion was explained and the source parameters gained from the inversion can be used to reveal the tectonics of the source of this earthquake, these information could be helpful in assessing seismic hazard and overall tectonic regime of this region. Furthermore, results of synthetic seismograms and the solution of inversion are going to be used to assess two models.

On computing stress in polymer systems involving multi-body potentials from molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Fu, Yao; Song, Jeong-Hoon

2014-08-01

Hardy stress definition has been restricted to pair potentials and embedded-atom method potentials due to the basic assumptions in the derivation of a symmetric microscopic stress tensor. Force decomposition required in the Hardy stress expression becomes obscure for multi-body potentials. In this work, we demonstrate the invariance of the Hardy stress expression for a polymer system modeled with multi-body interatomic potentials including up to four atoms interaction, by applying central force decomposition of the atomic force. The balance of momentum has been demonstrated to be valid theoretically and tested under various numerical simulation conditions. The validity of momentum conservation justifies the extension of Hardy stress expression to multi-body potential systems. Computed Hardy stress has been observed to converge to the virial stress of the system with increasing spatial averaging volume. This work provides a feasible and reliable linkage between the atomistic and continuum scales for multi-body potential systems.

Simulation of Two-Fluid Flows by the Least-Squares Finite Element Method Using a Continuum Surface Tension Model

NASA Technical Reports Server (NTRS)

Wu, Jie; Yu, Sheng-Tao; Jiang, Bo-nan

1996-01-01

In this paper a numerical procedure for simulating two-fluid flows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols and the continuum surface force (CSF) model developed by Brackbill, et al. In the VOF method fluids of different properties are identified through the use of a continuous field variable (color function). The color function assigns a unique constant (color) to each fluid. The interfaces between different fluids are distinct due to sharp gradients of the color function. The evolution of the interfaces is captured by solving the convective equation of the color function. The CSF model is used as a means to treat surface tension effect at the interfaces. Here a modified version of the CSF model, proposed by Jacqmin, is used to calculate the tension force. In the modified version, the force term is obtained by calculating the divergence of a stress tensor defined by the gradient of the color function. In its analytical form, this stress formulation is equivalent to the original CSF model. Numerically, however, the use of the stress formulation has some advantages over the original CSF model, as it bypasses the difficulty in approximating the curvatures of the interfaces. The least-squares finite element method (LSFEM) is used to discretize the governing equation systems. The LSFEM has proven to be effective in solving incompressible Navier-Stokes equations and pure convection equations, making it an ideal candidate for the present applications. The LSFEM handles all the equations in a unified manner without any additional special treatment such as upwinding or artificial dissipation. Various bench mark tests have been carried out for both two dimensional planar and axisymmetric flows, including a dam breaking, oscillating and stationary bubbles and a conical liquid sheet in a pressure swirl atomizer.

Full moment tensors for small events (Mw < 3) at Uturuncu volcano, Bolivia

NASA Astrophysics Data System (ADS)

Alvizuri, Celso; Tape, Carl

2016-09-01

We present a catalogue of full seismic moment tensors for 63 events from Uturuncu volcano in Bolivia. The events were recorded during 2011-2012 in the PLUTONS seismic array of 24 broad-band stations. Most events had magnitudes between 0.5 and 2.0 and did not generate discernible surface waves; the largest event was Mw 2.8. For each event we computed the misfit between observed and synthetic waveforms, and we used first-motion polarity measurements to reduce the number of possible solutions. Each moment tensor solution was obtained using a grid search over the 6-D space of moment tensors. For each event, we show the misfit function in eigenvalue space, represented by a lune. We identify three subsets of the catalogue: (1) six isotropic events, (2) five tensional crack events, and (3) a swarm of 14 events southeast of the volcanic centre that appear to be double couples. The occurrence of positively isotropic events is consistent with other published results from volcanic and geothermal regions. Several of these previous results, as well as our results, cannot be interpreted within the context of either an oblique opening crack or a crack-plus-double-couple model. Proper characterization of uncertainties for full moment tensors is critical for distinguishing among physical models of source processes.

Spherocylindrical microplane constitutive model for shale and other anisotropic rocks

NASA Astrophysics Data System (ADS)

Li, Cunbao; Caner, Ferhun C.; Chau, Viet T.; Bažant, Zdeněk P.

2017-06-01

Constitutive equations for inelastic behavior of anisotropic materials have been a challenge for decades. Presented is a new spherocylindrical microplane constitutive model that meets this challenge for the inelastic fracturing behavior of orthotropic materials, and particularly the shale, which is transversely isotropic and is important for hydraulic fracturing (aka fracking) as well as many geotechnical structures. The basic idea is to couple a cylindrical microplane system to the classical spherical microplane system. Each system is subjected to the same strain tensor while their stress tensors are superposed. The spherical phase is similar to the previous microplane models for concrete and isotropic rock. The integration of stresses over spherical microplanes of all spatial orientations relies on the previously developed optimal Gaussian integration over a spherical surface. The cylindrical phase, which is what creates the transverse isotropy, involves only microplanes that are normal to plane of isotropy, or the bedding layers, and enhance the stiffness and strength in that plane. Unlike all the microplane models except the spectral one, the present one can reproduce all the five independent elastic constants of transversely isotropic shales. Vice versa, from these constants, one can easily calculate all the microplane elastic moduli, which are all positive if the elastic in-to-out-of plane moduli ratio is not too big (usually less than 3.75, which applies to all shales). Oriented micro-crack openings, frictional micro-slips and bedding plane behavior can be modeled more intuitively than with the spectral approach. Data fitting shows that the microplane resistance depends on the angle with the bedding layers non-monotonically, and compressive resistance reaches a minimum at 60°. A robust algorithm for explicit step-by-step structural analysis is formulated. Like all microplane models, there are many material parameters, but they can be identified sequentially. Finally, comparisons with extensive test data for shale validate the model.

The structure and Gel'fand patterns inherent in the Heisenberg supergenerator algebra of dual Liouville-space ||kq{K-tilde.}(k1 - kn)[lambda- tilde],scriptn>> tensors and the Cayley algebra of scalar invariants over a (k1 - kn) field

NASA Astrophysics Data System (ADS)

Temme, F. P.

1991-06-01

For many-body spin cluster problems, dual-symmetry recoupled tensors over Liouville space provide suitable bases for a generalized torque formalism using the Sn-adapted density operator in which to discuss NMR and related techniques. The explicit structure of such tensors is considered in the context of the Cayley algebra of scalar invariants over a field, specified by the inner ki rank labels of the Tkq(kl-kn)s. The pertinence of both lexical combinatorial architectures over inner rank sets and SU2 propagative topologies in specifying the structure of dual recoupling tensors is considered in the context of the Sn partitional aspects of spin clusters. The form of Heisenberg superoperator generators whose algebra underlies the Gel'fand pattern algebra of SU(2) and SU(2)×Sn tensor bases over Liouville space is presented together with both the related s-boson algebras and a description of the associated {||2k 0>>} pattern sets of CF29H carrier space under the appropriate symmetry. These concepts are correlated with recent work on SU(2)×Sn induced symmetry hierarchies over Liouville spin space. The pertinence of this theoretical work to an understanding of multiquantum NMR in Liouville space formalisms is stressed in a discussion of the nature of pathways for intracluster J coupling, which also gives a valuable physical insight into the nature of coherence transfer in more general spin-1/2 systems.

Evaluation of mechanical deformation and distributive magnetic loads with different mechanical constraints in two parallel conducting bars

NASA Astrophysics Data System (ADS)

Lee, Ho-Young; Lee, Se-Hee

2017-08-01

Mechanical deformation, bending deformation, and distributive magnetic loads were evaluated numerically and experimentally for conducting materials excited with high current. Until now, many research works have extensively studied the area of magnetic force and mechanical deformation by using coupled approaches such as multiphysics solvers. In coupled analysis for magnetoelastic problems, some articles and commercial software have presented the resultant mechanical deformation and stress on the body. To evaluate the mechanical deformation, the Lorentz force density method (LZ) and the Maxwell stress tensor method (MX) have been widely used for conducting materials. However, it is difficult to find any experimental verification regarding mechanical deformation or bending deformation due to magnetic force density. Therefore, we compared our numerical results to those from experiments with two parallel conducting bars to verify our numerical setup for bending deformation. Before showing this, the basic and interesting coupled simulation was conducted to test the mechanical deformations by the LZ (body force density) and the MX (surface force density) methods. This resulted in MX gave the same total force as LZ, but the local force distribution in MX introduced an incorrect mechanical deformation in the simulation of a solid conductor.

Eulerian adaptive finite-difference method for high-velocity impact and penetration problems

NASA Astrophysics Data System (ADS)

Barton, P. T.; Deiterding, R.; Meiron, D.; Pullin, D.

2013-05-01

Owing to the complex processes involved, faithful prediction of high-velocity impact events demands a simulation method delivering efficient calculations based on comprehensively formulated constitutive models. Such an approach is presented herein, employing a weighted essentially non-oscillatory (WENO) method within an adaptive mesh refinement (AMR) framework for the numerical solution of hyperbolic partial differential equations. Applied widely in computational fluid dynamics, these methods are well suited to the involved locally non-smooth finite deformations, circumventing any requirement for artificial viscosity functions for shock capturing. Application of the methods is facilitated through using a model of solid dynamics based upon hyper-elastic theory comprising kinematic evolution equations for the elastic distortion tensor. The model for finite inelastic deformations is phenomenologically equivalent to Maxwell's model of tangential stress relaxation. Closure relations tailored to the expected high-pressure states are proposed and calibrated for the materials of interest. Sharp interface resolution is achieved by employing level-set functions to track boundary motion, along with a ghost material method to capture the necessary internal boundary conditions for material interactions and stress-free surfaces. The approach is demonstrated for the simulation of high velocity impacts of steel projectiles on aluminium target plates in two and three dimensions.

Calculation and Analysis of magnetic gradient tensor components of global magnetic models

NASA Astrophysics Data System (ADS)

Schiffler, Markus; Queitsch, Matthias; Schneider, Michael; Stolz, Ronny; Krech, Wolfram; Meyer, Hans-Georg; Kukowski, Nina

2014-05-01

Magnetic mapping missions like SWARM and its predecessors, e.g. the CHAMP and MAGSAT programs, offer high resolution Earth's magnetic field data. These datasets are usually combined with magnetic observatory and survey data, and subject to harmonic analysis. The derived spherical harmonic coefficients enable magnetic field modelling using a potential series expansion. Recently, new instruments like the JeSSY STAR Full Tensor Magnetic Gradiometry system equipped with very high sensitive sensors can directly measure the magnetic field gradient tensor components. The full understanding of the quality of the measured data requires the extension of magnetic field models to gradient tensor components. In this study, we focus on the extension of the derivation of the magnetic field out of the potential series magnetic field gradient tensor components and apply the new theoretical framework to the International Geomagnetic Reference Field (IGRF) and the High Definition Magnetic Model (HDGM). The gradient tensor component maps for entire Earth's surface produced for the IGRF show low values and smooth variations reflecting the core and mantle contributions whereas those for the HDGM gives a novel tool to unravel crustal structure and deep-situated ore bodies. For example, the Thor Suture and the Sorgenfrei-Thornquist Zone in Europe are delineated by a strong northward gradient. Derived from Eigenvalue decomposition of the magnetic gradient tensor, the scaled magnetic moment, normalized source strength (NSS) and the bearing of the lithospheric sources are presented. The NSS serves as a tool for estimating the lithosphere-asthenosphere boundary as well as the depth of plutons and ore bodies. Furthermore changes in magnetization direction parallel to the mid-ocean ridges can be obtained from the scaled magnetic moment and the normalized source strength discriminates the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European Craton.

Four Poynting Theorems

ERIC Educational Resources Information Center

Kinsler, Paul; Favaro, Alberto; McCall, Martin W.

2009-01-01

The Poynting vector is an invaluable tool for analysing electromagnetic problems. However, even a rigorous stress-energy tensor approach can still leave us with the question: is it best defined as E x H or as D x B? Typical electromagnetic treatments provide yet another perspective: they regard E x B as the appropriate definition, because E and B…

Archimedes' Principle in General Coordinates

ERIC Educational Resources Information Center

Ridgely, Charles T.

2010-01-01

Archimedes' principle is well known to state that a body submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body. Herein, Archimedes' principle is derived from first principles by using conservation of the stress-energy-momentum tensor in general coordinates. The resulting expression for the force is…

The excitation of long period seismic waves by a source spanning a structural discontinuity

NASA Astrophysics Data System (ADS)

Woodhouse, J. H.

Simple theoretical results are obtained for the excitation of seismic waves by an indigenous seismic source in the case that the source volume is intersected by a structural discontinuity. In the long wavelength approximation the seismic radiation is identical to that of a point source placed on one side of the discontinuity or of a different point source placed on the other side. The moment tensors of these two equivalent sources are related by a specific linear transformation and may differ appreciably both in magnitude and geometry. Either of these sources could be obtained by linear inversion of seismic data but the physical interpretation is more complicated than in the usual case. A source which involved no volume change would, for example, yield an isotropic component if, during inversion, it were assumed to lie on the wrong side of the discontinuity. The problem of determining the true moment tensor of the source is indeterminate unless further assumptions are made about the stress glut distribution; one way to resolve this indeterminancy is to assume proportionality between the integrated stress glut on each side of the discontinuity.

Characterizing Atomistic Geometries and Potential Functions Using Strain Functionals

NASA Astrophysics Data System (ADS)

Kober, Edward; Mathew, Nithin; Rudin, Sven

2017-06-01

We demonstrate the use of strain tensor functionals for characterizing arbitrarily ordered atomistic structures. This approach defines a Gaussian-weighted neighborhood around each atom and characterizes that local geometry in terms of n-th order strain tensors, which are equivalent to the n-th order moments/derivatives of the neighborhood. Fourth order expansions can distinguish the cubic structures (and deformations thereof), but sixth order expansions are required to fully characterize hexagonal structures. These functions are continuous and smooth and much less sensitive to thermal fluctuations than other descriptors based on discrete neighborhoods. Reducing these metrics to rotational invariant descriptors allows a large number of defect structures to be readily identified and forms the basis of a classification scheme that allows molecular dynamics simulations to be readily analyzed. Applications to the analysis of shock waves impinging on samples of Cu, Ta and Ti will be presented. The method has been extended to vector fields as well, enabling the local stress to be cast in terms of rotationally invariant functions as well. The stress-strain correlations can then be used as the basis for developing and analyzing potential functions.

Modulated Hawking radiation and a nonviolent channel for information release

NASA Astrophysics Data System (ADS)

Giddings, Steven B.

2014-11-01

Unitarization of black hole evaporation requires that quantum information escapes a black hole; an important question is to identify the mechanism or channel by which it does so. Accurate counting of black hole states via the Bekenstein-Hawking entropy would indicate this information should be encoded in radiation with average energy flux matching Hawking's. Information can be encoded with no change in net flux via fine-grained modulation of the Hawking radiation. In an approximate effective field theory description, couplings to the stress tensor of the black hole atmosphere that depend on the internal state of the black hole are a promising alternative for inducing such modulation. These can be picturesquely thought of as due to state-dependent metric fluctuations in the vicinity of the horizon. Such couplings offer the prospect of emitting information without extra energy flux, and can be shown to do so at linear order in the couplings, with motivation given for possible extension of this result to higher orders. The potential advantages of such couplings to the stress tensor thus extend beyond their universality, which is helpful in addressing constraints from black hole mining.

Quantum heating as an alternative of reheating

NASA Astrophysics Data System (ADS)

Akhmedov, Emil T.; Bascone, Francesco

2018-02-01

To model a realistic situation for the beginning we consider massive real scalar ϕ4 theory in a (1 +1 )-dimensional asymptotically static Minkowski spacetime with an intermediate stage of expansion. To have an analytic headway we assume that scalars have a big mass. At past and future infinities of the background we have flat Minkowski regions which are joint by the inflationary expansion region. We use the tree-level Keldysh propagator in the theory in question to calculate the expectation value of the stress-energy tensor which is, thus, due to the excitations of the zero-point fluctuations. Then we show that even for large mass, if the de Sitter expansion stage is long enough, the quantum loop corrections to the expectation value of the stress-energy tensor are not negligible in comparison with the tree-level contribution. That is revealed itself via the excitation of the higher-point fluctuations of the exact modes: during the expansion stage a nonzero particle number density for the exact modes is generated. This density is not Planckian and serves as a quench which leads to a thermalization in the out Minkowski stage.

The relationship between a deformation-based eddy parameterization and the LANS-α turbulence model

NASA Astrophysics Data System (ADS)

Bachman, Scott D.; Anstey, James A.; Zanna, Laure

2018-06-01

A recent class of ocean eddy parameterizations proposed by Porta Mana and Zanna (2014) and Anstey and Zanna (2017) modeled the large-scale flow as a non-Newtonian fluid whose subgridscale eddy stress is a nonlinear function of the deformation. This idea, while largely new to ocean modeling, has a history in turbulence modeling dating at least back to Rivlin (1957). The new class of parameterizations results in equations that resemble the Lagrangian-averaged Navier-Stokes-α model (LANS-α, e.g., Holm et al., 1998a). In this note we employ basic tensor mathematics to highlight the similarities between these turbulence models using component-free notation. We extend the Anstey and Zanna (2017) parameterization, which was originally presented in 2D, to 3D, and derive variants of this closure that arise when the full non-Newtonian stress tensor is used. Despite the mathematical similarities between the non-Newtonian and LANS-α models which might provide insight into numerical implementation, the input and dissipation of kinetic energy between these two turbulent models differ.

On a viable first-order formulation of relativistic viscous fluids and its applications to cosmology

NASA Astrophysics Data System (ADS)

Disconzi, Marcelo M.; Kephart, Thomas W.; Scherrer, Robert J.

We consider a first-order formulation of relativistic fluids with bulk viscosity based on a stress-energy tensor introduced by Lichnerowicz. Choosing a barotropic equation-of-state, we show that this theory satisfies basic physical requirements and, under the further assumption of vanishing vorticity, that the equations of motion are causal, both in the case of a fixed background and when the equations are coupled to Einstein's equations. Furthermore, Lichnerowicz's proposal does not fit into the general framework of first-order theories studied by Hiscock and Lindblom, and hence their instability results do not apply. These conclusions apply to the full-fledged nonlinear theory, without any equilibrium or near equilibrium assumptions. Similarities and differences between the approach explored here and other theories of relativistic viscosity, including the Mueller-Israel-Stewart formulation, are addressed. Cosmological models based on the Lichnerowicz stress-energy tensor are studied. As the topic of (relativistic) viscous fluids is also of interest outside the general relativity and cosmology communities, such as, for instance, in applications involving heavy-ion collisions, we make our presentation largely self-contained.

A new hybrid turbulence modelling strategy for industrial CFD

NASA Astrophysics Data System (ADS)

Basara, B.; Jakirlic, S.

2003-05-01

This paper presents a new strategy for turbulence model employment with emphasis on the model's applicability for industrial computational fluid dynamics (CFD). In the hybrid modelling strategy proposed here, the Reynolds stress and mean rate of strain tensors are coupled via Boussinesq's formula as in the standard k-model. However, the turbulent kinetic energy is calculated as the sum of the normal Reynolds-stress components, representing the solutions of the appropriate transport equations. The equations governing the Reynolds-stress tensor and dissipation rate have been solved in the framework of a background second-moment closure model. Furthermore, the structure parameter C-? has been re-calculated from a newly proposed functional dependency rather than kept constant. This new definition of C-? has been assessed by using direct numerical simulation (DNS) results of several generic flow configurations featuring different phenomena such as separation, reattachment and rotation. Comparisons show a large departure of C-? from the commonly used value of 0.09. The model proposed is computationally validated in a number of well-proven fluid flow benchmarks, e.g. backward-facing step, 180° turn-around duct, rotating pipe, impinging jet and three-dimensional (3D) Ahmed body. The obtained results confirm that the present hybrid model delivers a robust solution procedure while preserving most of the physical advantages of the Reynolds-stress model over simple k-models. A low Reynolds number version of the hybrid model is also proposed and discussed.

Mass Function of Galaxy Clusters in Relativistic Inhomogeneous Cosmology

NASA Astrophysics Data System (ADS)

Ostrowski, Jan J.; Buchert, Thomas; Roukema, Boudewijn F.

The current cosmological model (ΛCDM) with the underlying FLRW metric relies on the assumption of local isotropy, hence homogeneity of the Universe. Difficulties arise when one attempts to justify this model as an average description of the Universe from first principles of general relativity, since in general, the Einstein tensor built from the averaged metric is not equal to the averaged stress-energy tensor. In this context, the discrepancy between these quantities is called "cosmological backreaction" and has been the subject of scientific debate among cosmologists and relativists for more than 20 years. Here we present one of the methods to tackle this problem, i.e. averaging the scalar parts of the Einstein equations, together with its application, the cosmological mass function of galaxy clusters.

Mapping residual stress fields from Vickers hardness indents using Raman microprobe spectroscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sparks, R.G.; Enloe, W.S.; Paesler, M.A.

Micro-Raman spectroscopy is used to map the residual stress fields in the vicinity of Vickers hardness indents. Both 514.5 and 488.0 nm, light is used to excite the effect and the resulting shifted and broadened Raman peaks are analyzed using computer deconvolution. Half-wave plates are used to vary the orientation of the incident later light`s polarization state with respect to crystal orientation. The Raman scattered light is then analyzed for polarization dependences which are indicative of the various components of the Raman scattering tensor. Such studies can yield valuable information about the orientation of stress components in a well knownmore » stress field. The results can then be applied to the determination of stress components in machined semiconductor materials.« less

Molecular Eigensolution Symmetry Analysis and Fine Structure

PubMed Central

Harter, William G.; Mitchell, Justin C.

2013-01-01

Spectra of high-symmetry molecules contain fine and superfine level cluster structure related to J-tunneling between hills and valleys on rovibronic energy surfaces (RES). Such graphic visualizations help disentangle multi-level dynamics, selection rules, and state mixing effects including widespread violation of nuclear spin symmetry species. A review of RES analysis compares it to that of potential energy surfaces (PES) used in Born–Oppenheimer approximations. Both take advantage of adiabatic coupling in order to visualize Hamiltonian eigensolutions. RES of symmetric and D2 asymmetric top rank-2-tensor Hamiltonians are compared with Oh spherical top rank-4-tensor fine-structure clusters of 6-fold and 8-fold tunneling multiplets. Then extreme 12-fold and 24-fold multiplets are analyzed by RES plots of higher rank tensor Hamiltonians. Such extreme clustering is rare in fundamental bands but prevalent in hot bands, and analysis of its superfine structure requires more efficient labeling and a more powerful group theory. This is introduced using elementary examples involving two groups of order-6 (C6 and D3~C3v), then applied to families of Oh clusters in SF6 spectra and to extreme clusters. PMID:23344041

Mapping Earth's electromagnetic dimensionality

NASA Astrophysics Data System (ADS)

Love, J. J.; Kelbert, A.; Bedrosian, P.

2017-12-01

The form of a magnetotelluric impedance tensor, obtained for a given geographic site through simultaneous measurement of geomagnetic and geoelectric field variation, is affected by electrical conductivity structure beneath the measurement site. Building on existing methods for characterizing the symmetry of magnetotelluric impedance tensors, a simple scalar measure is developed for measuring the (frequency dependent) proportion of the impedance tensor that is not just a one-dimensional (1D) function of depth ("non-1D-ness"). These measures are applied to nearly 1000 impedance tensors obtained during magnetotelluric surveys, those for the continental United States and obtained principally through the National Science Foundation's EarthScope project. Across geomagnetic/geoelectric variational periods ranging from 30 s to 3,000 s, corresponding to crustal and upper mantle depths, it is shown that local Earth structure is very often not simply 1D-depth-dependent - often less than 50% of magnetotelluric impedance is 1D. For selected variational frequencies, non-1D-ness is mapped and the relationship between electromagnetic dimensionality and known geological and tectonic structures is discussed. The importance of using realistic surface impedances to accurately evaluate magnetic-storm geoelectric hazards is emphasized.

Frictionless bead packs have macroscopic friction, but no dilatancy.

PubMed

Peyneau, Pierre-Emmanuel; Roux, Jean-Noël

2008-07-01

The statement of the title is shown by numerical simulation of homogeneously sheared assemblies of frictionless, nearly rigid beads in the quasistatic limit. Results coincide for steady flows at constant shear rate gamma[over ] in the limit of small gamma[over ] and static approaches, in which packings are equilibrated under growing deviator stresses. The internal friction angle phi , equal to 5.76 degrees +/-0.22 degrees in simple shear, is independent of average pressure P in the rigid limit and stems from the ability of stable frictionless contact networks to form stress-induced anisotropic fabrics. No enduring strain localization is observed. Dissipation at the macroscopic level results from repeated network rearrangements, similar to the effective friction of a frictionless slider on a bumpy surface. Solid fraction Phi remains equal to the random close packing value approximately 0.64 in slowly or statically sheared systems. Fluctuations of stresses and volume are observed to regress in the large system limit. Defining the inertial number as I=gamma radical m/(aP), with m the grain mass and a its diameter, both internal friction coefficient mu*=tan phi and volume 1/Phi increase as powers of I in the quasistatic limit of vanishing I , in which all mechanical properties are determined by contact network geometry. The microstructure of the sheared material is characterized with a suitable parametrization of the fabric tensor and measurements of coordination numbers.

Study of grain-level deformation and residual stresses in Ti-7Al under combined bending and tension using high energy diffraction microscopy (HEDM)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chatterjee, K.; Venkataraman, A.; Garbaciak, T.

In-situ high energy diffraction microscopy (HEDM) experiments are carried out to analyze the state of combined bending and tension in a Ti-7Al alloy under room temperature creep. Grain-level elastic strain tensors are evaluated from HEDM data. Atomistic calculations are used to predict elastic constants of Ti-7Al, to be used in determination of stress from strain. The stress gradient and residual stresses are successfully determined, which allows the demarcation between macro-/micro-level residual stresses. A cluster of three neighboring grains are identified that highlight the variation of mean and effective stress between grains. Crystallographic orientations and slip characteristics are analyzed for themore » selected grains. It is inferred that the interfaces between loaded grains with markedly different stress triaxiality and slip tendency are potential spots for material damage.« less

Analysis of stress fields and elastic energies in the vicinity of nanograin boundaries using the disclination approach

NASA Astrophysics Data System (ADS)

Sukhanov, Ivan I.; Ditenberg, Ivan A.

2017-12-01

The paper provides a theoretical analysis of elastic stresses and elastic energy distribution in nanostructured metal materials in the vicinity of nanograin boundaries with a high partial disclination density. The analysis demonstrates the stress field distribution in disclination grain boundary configurations as a function of nanograin size, taking into account the superposition of these stresses in screening the disclination pile-ups. It is found that the principal stress tensor components reach maximum values only in disclination planes P ≈ E/25 and that the stress gradients peak at nodal points ∂P/∂x ≈ 0.08E nm-1. The shear stress components are localized within the physical grain size, and the specific elastic energy distribution for such configurations reveals characteristic local maxima which can be the cause for physical broadening of nanograin boundaries.

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

DOE PAGES

Song, Chenchen; Martinez, Todd J.

2017-08-29

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. Furthermore, the resulting energy conservation in micro-canonical AIMD demonstrates that the implementationmore » provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.« less

Generalized minimal principle for rotor filaments.

PubMed

Dierckx, Hans; Wellner, Marcel; Bernus, Olivier; Verschelde, Henri

2015-05-01

To a reaction-diffusion medium with an inhomogeneous anisotropic diffusion tensor D, we add a fourth spatial dimension such that the determinant of the diffusion tensor is constant in four dimensions. We propose a generalized minimal principle for rotor filaments, stating that the scroll wave filament strives to minimize its surface area in the higher-dimensional space. As a consequence, stationary scroll wave filaments in the original 3D medium are geodesic curves with respect to the metric tensor G=det(D)D(-1). The theory is confirmed by numerical simulations for positive and negative filament tension and a model with a non-stationary spiral core. We conclude that filaments in cardiac tissue with positive tension preferentially reside or anchor in regions where cardiac cells are less interconnected, such as portions of the cardiac wall with a large number of cleavage planes.

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

NASA Astrophysics Data System (ADS)

Song, Chenchen; Martínez, Todd J.

2017-10-01

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. The resulting energy conservation in micro-canonical AIMD demonstrates that the implementation provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Chenchen; Martinez, Todd J.

Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. Furthermore, the resulting energy conservation in micro-canonical AIMD demonstrates that the implementationmore » provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.« less

Density functional theory of gas-liquid phase separation in dilute binary mixtures

NASA Astrophysics Data System (ADS)

Okamoto, Ryuichi; Onuki, Akira

2016-06-01

We examine statics and dynamics of phase-separated states of dilute binary mixtures using density functional theory. In our systems, the difference of the solvation chemical potential between liquid and gas Δ {μ\\text{s}} (the Gibbs energy of transfer) is considerably larger than the thermal energy {{k}\\text{B}}T for each solute particle and the attractive interaction among the solute particles is weaker than that among the solvent particles. In these conditions, the saturated vapor pressure increases by {{k}\\text{B}}Tn2\\ell\\exp ≤ft(Δ {μ\\text{s}}/{{k}\\text{B}}T\\right) , where n2\\ell is the solute density added in liquid. For \\exp ≤ft(Δ {μ\\text{s}}/{{k}\\text{B}}T\\right)\\gg 1 , phase separation is induced at low solute densities in liquid and the new phase remains in gaseous states, even when the liquid pressure is outside the coexistence curve of the solvent. This explains the widely observed formation of stable nanobubbles in ambient water with a dissolved gas. We calculate the density and stress profiles across planar and spherical interfaces, where the surface tension decreases with increasing interfacial solute adsorption. We realize stable solute-rich bubbles with radius about 30 nm, which minimize the free energy functional. We then study dynamics around such a bubble after a decompression of the surrounding liquid, where the bubble undergoes a damped oscillation. In addition, we present some exact and approximate expressions for the surface tension and the interfacial stress tensor.

Performance of Smagorinsky and dynamic models in near surface turbulence

NASA Astrophysics Data System (ADS)

Brasseur, James G.; Juneja, Anurag

1997-11-01

In LES of high-Reynolds-number wall bounded turbulence such as the atmospheric boundary layer (ABL), a viscous sublayer either does not exist or is within the first grid cell, and some integral scale motions are necessarily under-resolved at the first few grid locations. Here the subgrid terms dominate the evolution of resolved velocity and the SGS model performance becomes crucial. To develop improved closures for surface layer turbulence (under-resolved and anisotropic), we explore (a) why current SGS closures fail and (b) what needs to be fixed. We evaluate the performance of the Smagorinsky and dynamic models using DNS data from shear- and buoyancy-driven turbulence as a function of filter cutoff location. We find that the underlying assumption of good alignment between the subgrid stress and resolved strain-rate tensors is not correct in general. More importantly, the Smagorinsky model incorrectly predicts a strong preference in the direction of the SGS stress divergence vector, a spurious prediction that is directly related to the anisotropic structure of the resolved turbulence field. This, and its under-estimation of the SGS pressure gradient, are likely sources of the errors observed in LES of the ABL. Whereas the dynamic formulations do a better job predicting some SGS dynamics, the model fails when the filter cutoff is near an integral scale, and predicts unreasonable fluctuation levels-- although performance is sensitive to type of averaging. *supported by ARO grant DAAL03-92-0117.

Regional flow simulation in fractured aquifers using stress-dependent parameters.

PubMed

Preisig, Giona; Joel Cornaton, Fabien; Perrochet, Pierre

2012-01-01

A model function relating effective stress to fracture permeability is developed from Hooke's law, implemented in the tensorial form of Darcy's law, and used to evaluate discharge rates and pressure distributions at regional scales. The model takes into account elastic and statistical fracture parameters, and is able to simulate real stress-dependent permeabilities from laboratory to field studies. This modeling approach gains in phenomenology in comparison to the classical ones because the permeability tensors may vary in both strength and principal directions according to effective stresses. Moreover this method allows evaluation of the fracture porosity changes, which are then translated into consolidation of the medium. © 2011, The Author(s). Ground Water © 2011, National Ground Water Association.

Conformal and Nearly Conformal Theories at Large N

NASA Astrophysics Data System (ADS)

Tarnoplskiy, Grigory M.

In this thesis we present new results in conformal and nearly conformal field theories in various dimensions. In chapter two, we study different properties of the conformal Quantum Electrodynamics (QED) in continuous dimension d. At first we study conformal QED using large Nf methods, where Nf is the number of massless fermions. We compute its sphere free energy as a function of d, ignoring the terms of order 1/Nf and higher. For finite Nf we use the epsilon-expansion. Next we use a large Nf diagrammatic approach to calculate the leading corrections to CT, the coefficient of the two-point function of the stress-energy tensor, and CJ, the coefficient of the two-point function of the global symmetry current. We present explicit formulae as a function of d and check them versus the expectations in 2 and 4 - epsilon dimensions. In chapter three, we discuss vacuum stability in 1 + 1 dimensional conformal field theories with external background fields. We show that the vacuum decay rate is given by a non-local two-form. This two-form is a boundary term that must be added to the effective in/out Lagrangian. The two-form is expressed in terms of a Riemann-Hilbert decomposition for background gauge fields, and is given by its novel "functional'' version in the gravitational case. In chapter four, we explore Tensor models. Such models possess the large N limit dominated by the melon diagrams. The quantum mechanics of a real anti-commuting rank-3 tensor has a large N limit similar to the Sachdev-Ye-Kitaev (SYK) model. We also discuss the quantum mechanics of a complex 3-index anti-commuting tensor and argue that it is equivalent in the large N limit to a version of SYK model with complex fermions. Finally, we discuss models of a commuting tensor in dimension d. We study the spectrum of the large N quantum field theory of bosonic rank-3 tensors using the Schwinger-Dyson equations. We compare some of these results with the 4 - epsilon expansion, finding perfect agreement. We also study the spectra of bosonic theories of rank q - 1 tensors with φq interactions.

Monitoring the Earthquake source process in North America

USGS Publications Warehouse

Herrmann, Robert B.; Benz, H.; Ammon, C.J.

2011-01-01

With the implementation of the USGS National Earthquake Information Center Prompt Assessment of Global Earthquakes for Response system (PAGER), rapid determination of earthquake moment magnitude is essential, especially for earthquakes that are felt within the contiguous United States. We report an implementation of moment tensor processing for application to broad, seismically active areas of North America. This effort focuses on the selection of regional crustal velocity models, codification of data quality tests, and the development of procedures for rapid computation of the seismic moment tensor. We systematically apply these techniques to earthquakes with reported magnitude greater than 3.5 in continental North America that are not associated with a tectonic plate boundary. Using the 0.02-0.10 Hz passband, we can usually determine, with few exceptions, moment tensor solutions for earthquakes with M w as small as 3.7. The threshold is significantly influenced by the density of stations, the location of the earthquake relative to the seismic stations and, of course, the signal-to-noise ratio. With the existing permanent broadband stations in North America operated for rapid earthquake response, the seismic moment tensor of most earthquakes that are M w 4 or larger can be routinely computed. As expected the nonuniform spatial pattern of these solutions reflects the seismicity pattern. However, the orientation of the direction of maximum compressive stress and the predominant style of faulting is spatially coherent across large regions of the continent.

Distribution, origin and implications of seismic stress release in shallow and intermediate-depth subduction systems

NASA Astrophysics Data System (ADS)

Chen, Po-Fei

A characterization of focal mechanisms is developed for shallow and intermediate-depth earthquakes in the context of the local geometry of subduction systems. Its application to the Ryukyu-Taiwan-Luzon system is used to refine the spatial distribution of characteristic groups of earthquakes in the framework of local tectonic processes, such as flipping of the polarity of subduction and the nascent processes of arc-continent collision. The Harvard catalogue of Centroid Moment Tensor solutions is expanded to include intermediate-depth earthquakes from the WWSSN-HGLP era (1962--1975). Seventy-six new solutions are obtained, with the resulting dataset estimated to be complete for M0 ≥ 1026 dyn-cm. While source mechanisms from our new dataset are generally similar to those previously compiled in the Harvard catalogue, seismic moment release rates are found to be significantly smaller for the WWSSN era. The intermediate-depth seismicity of South America is compiled from the Harvard catalogue, using projection along local slab coordinates, to determine along-strike variations in the distribution of earthquakes and in the geometry of their stress release. Slab geometry is investigated in relation to slab stresses and the presence or absence of arc volcanism. Steeper-dipping slabs are found to exhibit consistent down-dip extension, a higher rate of seismic moment release and surface volcanism. Visualization using slab coordinate projections is extended systematically to a global survey of the geometry of stress release in intermediate-depth earthquakes. Various proposed models for all subduction zones are appraised, as contributors to stress regimes, based on global data compilations. Down-dip stresses, where prominent, are found to be consistent with the thermo-mechanical and petrological force models. Slab-normal conjugate stresses generally support the concept of earthquake reactivation of fossil faults. Patterns of lateral stresses support the predictions of the so-called "punctured-ping-pong-ball" model.

Determining the coordinate dependence of some components of the cubic susceptibility tensor {chi}-hat{sub yyyy}{sup (3)}(z, {omega}, -{omega}, {omega}, {omega}) of a one-dimensionally inhomogeneous absorbing plate at an arbitrary frequency dispersion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golubkov, A A; Makarov, Vladimir A

The possibility of unique reconstruction of the spatial profile of the cubic nonlinear susceptibility tensor component {chi}-hat{sub yyyy}{sup (3)}(z, {omega}, -{omega}, {omega}, {omega}) of a one-dimensionally inhomogeneous plate whose medium has a symmetry plane m{sub y} perpendicular to its surface is proved for the first time and the unique reconstruction algorithm is proposed. The amplitude complex coefficients of reflection and transmission (measured in some range of angles of incidence) as well as of conversion of an s-polarised plane signal monochromatic wave into two waves propagating on both sides of the plate make it possible to reconstruct the profile. These twomore » waves result from nonlinear interaction of a signal wave with an intense plane wave incident normally on the plate. All the waves under consideration have the same frequency {omega}, and so its variation helps study the frequency dispersion of the cubic nonlinear susceptibility tensor component {chi}-hat{sub yyyy}{sup (3)}(z, {omega}, -{omega}, {omega}, {omega}). For media with additional symmetry axes 2{sub z}, 4{sub z}, 6{sub z}, or {infinity}{sub z} that are perpendicular to the plate surface, the proposed method can be used to reconstruct the profile and to examine the frequency dispersion of about one third of all independent complex components of the tensor {chi}-hat{sup (3)}. (nonlinear-optics phenomena)« less

Boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Panaras, Argyris G.

1987-01-01

A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations.

Composite Fermi surface in the half-filled Landau level with anisotropic electron mass

NASA Astrophysics Data System (ADS)

Ippoliti, Matteo; Geraedts, Scott; Bhatt, Ravindra

We study the problem of interacting electrons in the lowest Landau level at half filling in the quantum Hall regime, when the electron dispersion is given by an anisotropic mass tensor. Based on experimental observations and theoretical arguments, the ground state of the system is expected to consist of composite Fermions filling an elliptical Fermi sea, with the anisotropy of the ellipse determined by the competing effects of the isotropic Coulomb interaction and anisotropic electron mass tensor. We test this idea quantitatively by using a numerical density matrix renormalization group method for quantum Hall systems on an infinitely long cylinder. Singularities in the structure factor allow us to map the Fermi surface of the composite Fermions. We compute the composite Fermi surface anisotropy for several values of the electron mass anisotropy which allow us to deduce the functional dependence of the former on the latter. This research was supported by Department of Energy Office of Basic Energy Sciences through Grant No. DE-SC0002140.

Normal stresses in semiflexible polymer hydrogels

NASA Astrophysics Data System (ADS)

Vahabi, M.; Vos, Bart E.; de Cagny, Henri C. G.; Bonn, Daniel; Koenderink, Gijsje H.; MacKintosh, F. C.

2018-03-01

Biopolymer gels such as fibrin and collagen networks are known to develop tensile axial stress when subject to torsion. This negative normal stress is opposite to the classical Poynting effect observed for most elastic solids including synthetic polymer gels, where torsion provokes a positive normal stress. As shown recently, this anomalous behavior in fibrin gels depends on the open, porous network structure of biopolymer gels, which facilitates interstitial fluid flow during shear and can be described by a phenomenological two-fluid model with viscous coupling between network and solvent. Here we extend this model and develop a microscopic model for the individual diagonal components of the stress tensor that determine the axial response of semiflexible polymer hydrogels. This microscopic model predicts that the magnitude of these stress components depends inversely on the characteristic strain for the onset of nonlinear shear stress, which we confirm experimentally by shear rheometry on fibrin gels. Moreover, our model predicts a transient behavior of the normal stress, which is in excellent agreement with the full time-dependent normal stress we measure.

Stress field modelling from digital geological map data

NASA Astrophysics Data System (ADS)

Albert, Gáspár; Barancsuk, Ádám; Szentpéteri, Krisztián

2016-04-01

To create a model for the lithospheric stress a functional geodatabase is required which contains spatial and geodynamic parameters. A digital structural-geological map is a geodatabase, which usually contains enough attributes to create a stress field model. Such a model is not accurate enough for engineering-geological purposes because simplifications are always present in a map, but in many cases maps are the only sources for a tectonic analysis. The here presented method is designed for field geologist, who are interested to see the possible realization of the stress field over the area, on which they are working. This study presents an application which can produce a map of 3D stress vectors from a kml-file. The core application logic is implemented on top of a spatially aware relational database management system. This allows rapid and geographically accurate analysis of the imported geological features, taking advantage of standardized spatial algorithms and indexing. After pre-processing the map features in a GIS, according to the Type-Property-Orientation naming system, which was described in a previous study (Albert et al. 2014), the first stage of the algorithm generates an irregularly spaced point cloud by emitting a pattern of points within a user-defined buffer zone around each feature. For each point generated, a component-wise approximation of the tensor field at the point's position is computed, derived from the original feature's geodynamic properties. In a second stage a weighted moving average method calculates the stress vectors in a regular grid. Results can be exported as geospatial data for further analysis or cartographic visualization. Computation of the tensor field's components is based on the implementation of the Mohr diagram of a compressional model, which uses a Coulomb fracture criterion. Using a general assumption that the main principal stress must be greater than the stress from the overburden, the differential stress is calculated from the fracture criterion. The calculation includes the gravitational acceleration, the average density of rocks and the experimental 60 degree of the fracture angle from the normal of the fault plane. This way, the stress tensors are calculated as absolute pressure values per square meters on both sides of the faults. If the stress from the overburden is greater than 1 bar (i.e. the faults are buried), a confined compression would be present. Modelling this state of stress may result a confusing pattern of vectors, because in a confined position the horizontal stress vectors may point towards structures primarily associated with extension. To step over this, and to highlight the variability in the stress-field, the model calculates the vectors directly from the differential stress (practically subtracting the minimum principal stress from the critical stress). The result of the modelling is a vector map, which theoretically represents the minimum tectonic pressure in the moment, when the rock body breaks from an initial state. This map - together with the original fault-map - is suitable for determining those areas where unrevealed tectonic, sedimentary and lithological structures are possibly present (e.g. faults, sub-basins and intrusions). With modelling different deformational phases on the same area, change of the stress vectors can be detected which reveals not only the varying directions of the principal stresses, but the tectonic-driven sedimentation patterns too. The decrease of necessary critical stress in the case of a possible reactivation of a fault in subsequent deformation phase can be managed with the down-ranking of the concerning structural elements. Reference: Albert G., Ungvári ZS., Szentpéteri K. 2014: Modeling the present day stress field of the Pannonian Basin from neotectonic maps - In: Beqiraj A, Ionescu C, Christofides G, Uta A, Beqiraj Goga E, Marku S (eds.) Proceedings XX Congress of the Carpathian-Balkan Geological Association. Tirana: p. 2.

Surface integral analogy approaches for predicting noise from 3D high-lift low-noise wings

NASA Astrophysics Data System (ADS)

Yao, Hua-Dong; Davidson, Lars; Eriksson, Lars-Erik; Peng, Shia-Hui; Grundestam, Olof; Eliasson, Peter E.

2014-06-01

Three surface integral approaches of the acoustic analogies are studied to predict the noise from three conceptual configurations of three-dimensional high-lift low-noise wings. The approaches refer to the Kirchhoff method, the Ffowcs Williams and Hawkings (FW-H) method of the permeable integral surface and the Curle method that is known as a special case of the FW-H method. The first two approaches are used to compute the noise generated by the core flow region where the energetic structures exist. The last approach is adopted to predict the noise specially from the pressure perturbation on the wall. A new way to construct the integral surface that encloses the core region is proposed for the first two methods. Considering the local properties of the flow around the complex object-the actual wing with high-lift devices-the integral surface based on the vorticity is constructed to follow the flow structures. The surface location is discussed for the Kirchhoff method and the FW-H method because a common surface is used for them. The noise from the core flow region is studied on the basis of the dependent integral quantities, which are indicated by the Kirchhoff formulation and by the FW-H formulation. The role of each wall component on noise contribution is analyzed using the Curle formulation. Effects of the volume integral terms of Lighthill's stress tensors on the noise prediction are then evaluated by comparing the results of the Curle method with the other two methods.

Stress tensor and focal mechanisms in the Dead Sea basin

NASA Astrophysics Data System (ADS)

Hofstetter, A.; Dorbath, C.; Dorbath, L.; Braeuer, B.; Weber, M. H.

2015-12-01

We use the recorded seismicity, confined to the Dead Sea basin and its boundaries, by the Dead Sea Integrated Research (DESIRE) portable seismic network and the Israel and Jordan permanent seismic networks for studying the mechanisms of earthquakes that occurred in the Dead Sea basin. The observed seismicity in the Dead Sea basin was divided into 9 regions according to the spatial distribution of the earthquakes and the known tectonic features. The large number of recording stations and the good station distribution allowed the reliable determinations of 494 earthquake focal mechanisms. For each region, based on the inversion of the observed polarities of the earthquakes, we determine the focal mechanisms and the associated stress tensor. For 159 earthquakes out of the 494 mechanisms we could determine compatible fault planes. On the eastern side, the focal mechanisms are mainly strike-slip mechanism with nodal planes in the N-S and E-W directions. The azimuths of the stress axes are well constrained presenting minimal variability in the inversion of the data, which is in good agreement with the Arava fault on the eastern side of the Dead Sea basin and what we had expected from the regional geodynamics. However, larger variabilities of the azimuthal and dip angles are observed on the western side of the basin. Due to the wider range of azimuths of the fault planes, we observe the switching of sigma1 and sigma2 or the switching of sigma2 and sigma3as major horizontal stress directions. This observed switching of stress axes allows having dip-slip and normal mechanisms in a region that is dominated by strike-slip motion.

A Catalog of Moment Tensors and Source-type Characterization for Small Events at Uturuncu Volcano, Bolivia

NASA Astrophysics Data System (ADS)

Alvizuri, C. R.; Tape, C.

2015-12-01

We present a catalog of full seismic moment tensors for 63 events from Uturuncu volcano in Bolivia. The events were recorded during 2011-2012 in the PLUTONS seismic array of 24 broadband stations. Most events had magnitudes between 0.5 and 2.0 and did not generate discernible surface waves; the largest event was Mw 2.8. For each event we computed the misfit between observed and synthetic waveforms, and we also used first-motion polarity measurements to reduce the number of possible solutions. Each moment tensor solution was obtained using a grid search over the six-dimensional space of moment tensors. For each event we characterize the variation of moment tensor source type by plotting the misfit function in eigenvalue space, represented by a lune. We plot the optimal solutions for the 63 events on the lune in order to identify three subsets of the catalog: (1) a set of isotropic events, (2) a set of tensional crack events, and (3) a swarm of events southeast of the volcanic center that appear to be double couples. The occurrence of positively isotropic events is consistent with other published results from volcanic and geothermal regions. Several of these previous results, as well as our results, cannot be interpreted within the context of either an oblique opening crack or a crack-plus-double-couple model; instead they require a multiple-process source model. Our study emphasizes the importance of characterizing uncertainties for full moment tensors, and it provides strong support for isotropic events at Uturuncu volcano.

Gravitational radiation theory. M.A. Thesis - Rice Univ.; [survey of current research

NASA Technical Reports Server (NTRS)

Wilson, T. L.

1973-01-01

A survey is presented of current research in the theory of gravitational radiation. The mathematical structure of gravitational radiation is stressed. Furthermore, the radiation problem is treated independently from other problems in gravitation. The development proceeds candidly through three points of view - scalar, rector, and tensor radiation theory - and the corresponding results are stated.

Dynamic properties of interfaces in soft matter: Experiments and theory

NASA Astrophysics Data System (ADS)

Sagis, Leonard M. C.

2011-10-01

The dynamic properties of interfaces often play a crucial role in the macroscopic dynamics of multiphase soft condensed matter systems. These properties affect the dynamics of emulsions, of dispersions of vesicles, of biological fluids, of coatings, of free surface flows, of immiscible polymer blends, and of many other complex systems. The study of interfacial dynamic properties, surface rheology, is therefore a relevant discipline for many branches of physics, chemistry, engineering, and life sciences. In the past three to four decades a vast amount of literature has been produced dealing with the rheological properties of interfaces stabilized by low molecular weight surfactants, proteins, (bio)polymers, lipids, colloidal particles, and various mixtures of these surface active components. In this paper recent experiments are reviewed in the field of surface rheology, with particular emphasis on the models used to analyze surface rheological data. Most of the models currently used are straightforward generalizations of models developed for the analysis of rheological data of bulk phases. In general the limits on the validity of these generalizations are not discussed. Not much use is being made of recent advances in nonequilibrium thermodynamic formalisms for multiphase systems, to construct admissible models for the stress-deformation behavior of interfaces. These formalisms are ideally suited to construct thermodynamically admissible constitutive equations for rheological behavior that include the often relevant couplings to other fluxes in the interface (heat and mass), and couplings to the transfer of mass from the bulk phase to the interface. In this review recent advances in the application of classical irreversible thermodynamics, extended irreversible thermodynamics, rational thermodynamics, extended rational thermodynamics, and the general equation for the nonequilibrium reversible-irreversible coupling formalism to multiphase systems are also discussed, and shown how these formalisms can be used to generate a wide range of thermodynamically admissible constitutive models for the surface stress tensor. Some of the generalizations currently in use are shown to have only limited validity. The aim of this review is to stimulate new developments in the fields of experimental surface rheology and constitutive modeling of multiphase systems using nonequilibrium thermodynamic formalisms and to promote a closer integration of these disciplines.

Scale-Similar Models for Large-Eddy Simulations

NASA Technical Reports Server (NTRS)

Sarghini, F.

1999-01-01

Scale-similar models employ multiple filtering operations to identify the smallest resolved scales, which have been shown to be the most active in the interaction with the unresolved subgrid scales. They do not assume that the principal axes of the strain-rate tensor are aligned with those of the subgrid-scale stress (SGS) tensor, and allow the explicit calculation of the SGS energy. They can provide backscatter in a numerically stable and physically realistic manner, and predict SGS stresses in regions that are well correlated with the locations where large Reynolds stress occurs. In this paper, eddy viscosity and mixed models, which include an eddy-viscosity part as well as a scale-similar contribution, are applied to the simulation of two flows, a high Reynolds number plane channel flow, and a three-dimensional, nonequilibrium flow. The results show that simulations without models or with the Smagorinsky model are unable to predict nonequilibrium effects. Dynamic models provide an improvement of the results: the adjustment of the coefficient results in more accurate prediction of the perturbation from equilibrium. The Lagrangian-ensemble approach [Meneveau et al., J. Fluid Mech. 319, 353 (1996)] is found to be very beneficial. Models that included a scale-similar term and a dissipative one, as well as the Lagrangian ensemble averaging, gave results in the best agreement with the direct simulation and experimental data.

Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings

NASA Astrophysics Data System (ADS)

Hu, Haiping; Hou, Junpeng; Zhang, Fan; Zhang, Chuanwei

2018-06-01

The recent discovery of triply degenerate points (TDPs) in topological materials has opened a new perspective toward the realization of novel quasiparticles without counterparts in quantum field theory. The emergence of such protected nodes is often attributed to spin-vector-momentum couplings. We show that the interplay between spin-tensor- and spin-vector-momentum couplings can induce three types of TDPs, classified by different monopole charges (C =±2 , ±1 , 0). A Zeeman field can lift them into Weyl points with distinct numbers and charges. Different TDPs of the same type are connected by intriguing Fermi arcs at surfaces, and transitions between different types are accompanied by level crossings along high-symmetry lines. We further propose an experimental scheme to realize such TDPs in cold-atom optical lattices. Our results provide a framework for studying spin-tensor-momentum coupling-induced TDPs and other exotic quasiparticles.

Paleostress analysis of the upper-plate rocks of Anafi Island (Cyclades, Greece)

NASA Astrophysics Data System (ADS)

Soukis, Konstantinos; Lozios, Stylianos

2017-04-01

The Attic Cycladic complex (Aegean Sea, Greece) is an area where profound extension, as a result of the Hellenic trench retreat due to slab-rollback, has exhumed mid-crustal rocks to the surface. The remnants of the upper plate are observed in the form of clippen scattered throughout the complex, occupying a very small percentage of the area. Anafi Island, located at the southeastern rim of the Attic-Cycladic complex, represents one of the few areas where a significant part of the upper plate units can be observed and studied. The complex tectonostratigraphy of Anafi Island is characterized by inverted metamorphism and includes a series of medium to high-grade metamorphic rocks that are thrusted onto a non-metamorphosed Paleogene flysch. The uppermost amphibolitic-facies thrust sheets were intruded in the late Cretaceous by intermediate to felsic magmatic rocks. The nappe pile was later destroyed in the late Miocene - Pliocene through successive stages of normal faulting that included both low- and high-angle normal faults. During that stage, supra-detachment syn-extensional sedimentation has taken place thus giving the opportunity to put some age constraints on the fault activity. Paleostress analysis with the separation and stress inversion method TRM revealed two stress tensors that can explain the fault-slip data-set of Anafi Island related to NE-SW and N-S extension, respectively. The older NE-SW trend is related to the late Miocene stress field whereas the N-S is likely related to the present day stress field. These results show that there was a gradual rotation to the trend of least principal stress axis (σ3), that could be associated with regional events such as the escape of Anatolia towards the Aegean and fastest retreat of the Hellenic subduction zone.

Orbiting naked singularities in large-ω Brans-Dicke gravity

NASA Astrophysics Data System (ADS)

Chauvineau, Bertrand

2017-11-01

Brans-Dicke gravity admits spherical solutions describing naked singularities rather than black holes. Depending on some parameters entering such a solution, stable circular orbits exist for all radii. One shows that, despite the fact a naked singularity is an infinite redshift location, the far observed orbital motion frequency is unbounded for an adiabatically decreasing radius. We then argue that this feature remains true in a wide set of scalar(s)-tensor theories if gravity. This is a salient difference with general relativity, and the repercussion on the gravitational radiation by EMRI systems is stressed. Since this behaviour survives the ω \\longrightarrow ∞ limit, the possibility of such solutions is of utmost interest in the new gravitational wave astronomy context, despite the current constraints on scalar-tensor gravity.

Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories

NASA Astrophysics Data System (ADS)

Dong, Xi

2016-06-01

We develop a framework for studying the well-known universal term in the Rényi entropy for an arbitrary entangling region in four-dimensional conformal field theories that are holographically dual to gravitational theories. The shape dependence of the Rényi entropy Sn is described by two coefficients: fb(n ) for traceless extrinsic curvature deformations and fc(n ) for Weyl tensor deformations. We provide the first calculation of the coefficient fb(n ) in interacting theories by relating it to the stress tensor one-point function in a deformed hyperboloid background. The latter is then determined by a straightforward holographic calculation. Our results show that a previous conjecture fb(n )=fc(n ), motivated by surprising evidence from a variety of free field theories and studies of conical defects, fails holographically.

Stereo using monocular cues within the tensor voting framework.

PubMed

Mordohai, Philippos; Medioni, Gérard

2006-06-01

We address the fundamental problem of matching in two static images. The remaining challenges are related to occlusion and lack of texture. Our approach addresses these difficulties within a perceptual organization framework, considering both binocular and monocular cues. Initially, matching candidates for all pixels are generated by a combination of matching techniques. The matching candidates are then embedded in disparity space, where perceptual organization takes place in 3D neighborhoods and, thus, does not suffer from problems associated with scanline or image neighborhoods. The assumption is that correct matches produce salient, coherent surfaces, while wrong ones do not. Matching candidates that are consistent with the surfaces are kept and grouped into smooth layers. Thus, we achieve surface segmentation based on geometric and not photometric properties. Surface overextensions, which are due to occlusion, can be corrected by removing matches whose projections are not consistent in color with their neighbors of the same surface in both images. Finally, the projections of the refined surfaces on both images are used to obtain disparity hypotheses for unmatched pixels. The final disparities are selected after a second tensor voting stage, during which information is propagated from more reliable pixels to less reliable ones. We present results on widely used benchmark stereo pairs.

The 3 + 1 decomposition of conformal Yano-Killing tensors and ‘momentary’ charges for the spin-2 field

NASA Astrophysics Data System (ADS)

Jezierski, Jacek; Migacz, Szymon

2015-02-01

The ‘fully charged’ spin-2 field solution is presented. This is an analog of the Coulomb solution in electrodynamics and represents the ‘non-waving’ part of the spin-2 field theory. Basic facts and definitions of the spin-2 field and conformal Yano-Killing tensors are introduced. Application of those two objects provides a precise definition of quasi-local gravitational charge. Next, the 3 + 1 decomposition leads to the construction of the momentary gravitational charges on the initial surface, which is applicable for Schwarzschild-like spacetimes.

On computing stress in polymer systems involving multi-body potentials from molecular dynamics simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu, Yao, E-mail: fu5@mailbox.sc.edu, E-mail: jhsong@cec.sc.edu; Song, Jeong-Hoon, E-mail: fu5@mailbox.sc.edu, E-mail: jhsong@cec.sc.edu

2014-08-07

Hardy stress definition has been restricted to pair potentials and embedded-atom method potentials due to the basic assumptions in the derivation of a symmetric microscopic stress tensor. Force decomposition required in the Hardy stress expression becomes obscure for multi-body potentials. In this work, we demonstrate the invariance of the Hardy stress expression for a polymer system modeled with multi-body interatomic potentials including up to four atoms interaction, by applying central force decomposition of the atomic force. The balance of momentum has been demonstrated to be valid theoretically and tested under various numerical simulation conditions. The validity of momentum conservation justifiesmore » the extension of Hardy stress expression to multi-body potential systems. Computed Hardy stress has been observed to converge to the virial stress of the system with increasing spatial averaging volume. This work provides a feasible and reliable linkage between the atomistic and continuum scales for multi-body potential systems.« less

Stress regime in the Philippine Sea slab beneath Kanto, Japan

NASA Astrophysics Data System (ADS)

Nakajima, Junichi; Hasegawa, Akira; Hirose, Fuyuki

2011-08-01

We determine the focal mechanisms of earthquakes within the Philippine Sea slab beneath the Tokyo metropolitan area, and perform stress tensor inversions to investigate the detailed stress field within the slab. The results show a characteristic spatial variation in earthquake-generating stress. Slab stress in northeastern part of the PHS slab is characterized by down-dip tension (DDT), except for the uppermost tip of the seismic portion of the slab where down-dip compression (DDC) stress is dominant. We interpret that DDT is caused by the net slab pull and DDC is attributable to local resistance to subduction at the tip of the slab. In southwestern part of the PHS slab, σ1 and σ3 are generally rotated oblique to the dip of the slab, suggesting that earthquakes occur under stress conditions of neither DDC nor DDT. The rotations in σ1 and σ3 may be related to stress accumulation by the slip deficit along the asperity of the 1923 Kanto earthquake (M7.9).

Investigation of Magnetotelluric Source Effect Based on Twenty Years of Telluric and Geomagnetic Observation

NASA Astrophysics Data System (ADS)

Kis, A.; Lemperger, I.; Wesztergom, V.; Menvielle, M.; Szalai, S.; Novák, A.; Hada, T.; Matsukiyo, S.; Lethy, A. M.

2016-12-01

Magnetotelluric method is widely applied for investigation of subsurface structures by imaging the spatial distribution of electric conductivity. The method is based on the experimental determination of surface electromagnetic impedance tensor (Z) by surface geomagnetic and telluric registrations in two perpendicular orientation. In practical explorations the accurate estimation of Z necessitates the application of robust statistical methods for two reasons:1) the geomagnetic and telluric time series' are contaminated by man-made noise components and2) the non-homogeneous behavior of ionospheric current systems in the period range of interest (ELF-ULF and longer periods) results in systematic deviation of the impedance of individual time windows.Robust statistics manage both load of Z for the purpose of subsurface investigations. However, accurate analysis of the long term temporal variation of the first and second statistical moments of Z may provide valuable information about the characteristics of the ionospheric source current systems. Temporal variation of extent, spatial variability and orientation of the ionospheric source currents has specific effects on the surface impedance tensor. Twenty year long geomagnetic and telluric recordings of the Nagycenk Geophysical Observatory provides unique opportunity to reconstruct the so called magnetotelluric source effect and obtain information about the spatial and temporal behavior of ionospheric source currents at mid-latitudes. Detailed investigation of time series of surface electromagnetic impedance tensor has been carried out in different frequency classes of the ULF range. The presentation aims to provide a brief review of our results related to long term periodic modulations, up to solar cycle scale and about eventual deviations of the electromagnetic impedance and so the reconstructed equivalent ionospheric source effects.

Electromagnetic δ -function sphere

NASA Astrophysics Data System (ADS)

Parashar, Prachi; Milton, Kimball A.; Shajesh, K. V.; Brevik, Iver

2017-10-01

We develop a formalism to extend our previous work on the electromagnetic δ -function plates to a spherical surface. The electric (λe) and magnetic (λg) couplings to the surface are through δ -function potentials defining the dielectric permittivity and the diamagnetic permeability, with two anisotropic coupling tensors. The formalism incorporates dispersion. The electromagnetic Green's dyadic breaks up into transverse electric and transverse magnetic parts. We derive the Casimir interaction energy between two concentric δ -function spheres in this formalism and show that it has the correct asymptotic flat-plate limit. We systematically derive expressions for the Casimir self-energy and the total stress on a spherical shell using a δ -function potential, properly regulated by temporal and spatial point splitting, which are different from the conventional temporal point splitting. In the strong-coupling limit, we recover the usual result for the perfectly conducting spherical shell but in addition there is an integrated curvature-squared divergent contribution. For finite coupling, there are additional divergent contributions; in particular, there is a familiar logarithmic divergence occurring in the third order of the uniform asymptotic expansion that renders it impossible to extract a unique finite energy except in the case of an isorefractive sphere, which translates into λg=-λe.

New constraints on micro-seismicity and stress state in the western part of the North Anatolian Fault Zone: Observations from a dense seismic array

NASA Astrophysics Data System (ADS)

Altuncu Poyraz, Selda; Teoman, M. Uğur; Türkelli, Niyazi; Kahraman, Metin; Cambaz, Didem; Mutlu, Ahu; Rost, Sebastian; Houseman, Gregory A.; Thompson, David A.; Cornwell, David; Utkucu, Murat; Gülen, Levent

2015-08-01

With the aim of extensively investigating the crustal structure beneath the western segment of the North Anatolian Fault Zone where it splays into northern and southern branches, a temporary seismic network (dense array for North Anatolia-DANA) consisting of 70 stations was deployed in early May 2012 and operated for 18 months in the Sakarya region during the FaultLab experiment. Out of 2437 events contaminated by explosions, we extracted 1371 well located earthquakes. The enhanced station coverage having a nominal station spacing of 7 km, lead to a minimum magnitude calculation of 0.1. Horizontal and vertical location uncertainties within the array do not exceed 0.8 km and 0.9 km, respectively. We observe considerable seismic activity along both branches of the fault where the depth of the seismogenic zone was mostly confined to 15 km. Using our current earthquake catalog we obtained a b-value of 1. We also mapped the b-value variation with depth and observed a gradual decrease. Furthermore, we determined the source parameters of 41 earthquakes with magnitudes greater than 1.8 using P-wave first motion polarity method. Regional Moment Tensor Inversion method was also applied to earthquakes with magnitudes greater than 3.0. Focal mechanism solutions confirm that Sakarya and its vicinity is stressed by a compressional regime showing a primarily oblique-slip motion character. Stress tensor analysis indicates that the maximum principal stress is aligned in WNW-ESE direction and the tensional axis is aligned in NNE-SSW direction.

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

NASA Astrophysics Data System (ADS)

Rai, Prashant; Sargsyan, Khachik; Najm, Habib; Hermes, Matthew R.; Hirata, So

2017-09-01

A new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss-Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm-1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martínez-Ruiz, F. J.; Blas, F. J., E-mail: felipe@uhu.es; Centro de Investigación de Física Teórica y Matemática, Universidad de Huelva, 21071 Huelva

We propose an extension of the improved version of the inhomogeneous long-range corrections of Janeček [J. Phys. Chem. B 110, 6264–6269 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] to account for the intermolecular potential energy of spherical, rigid, and flexible molecular systems, to deal with the contributions to the microscopic components of the pressure tensor due to the dispersive long-range corrections. We have performed Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of spherical Lennard-Jones molecules with different cutoff distances, r{sub c} = 2.5, 3, 4, and 5σ. In addition,more » we have also considered cutoff distances r{sub c} = 2.5 and 3σ in combination with the inhomogeneous long-range corrections proposed in this work. The normal and tangential microscopic components of the pressure tensor are obtained using the mechanical or virial route in combination with the recipe of Irving and Kirkwood, while the macroscopic components are calculated using the Volume Perturbation thermodynamic route proposed by de Miguel and Jackson [J. Chem. Phys. 125, 164109 (2006)]. The vapour-liquid interfacial tension is evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the Test-Area methodology. In addition to the pressure tensor and the surface tension, we also obtain density profiles, coexistence densities, vapour pressure, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the cutoff distance and the long-range corrections on these properties. According to our results, the main effect of increasing the cutoff distance (at fixed temperature) is to sharpen the vapour-liquid interface, to decrease the vapour pressure, and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases, the width of the tangential microscopic component of the pressure tensor profile increases, and the surface tension increases as the cutoff distance is larger. We have also checked the effect of the impulsive contribution to the pressure due to the discontinuity of the intermolecular interaction potential when it is cut. If this contribution is not accounted for in the calculation of the microscopic components of the pressure tensor, incorrect values of both components as well as a wrong structure along the vapour-liquid interface are obtained.« less

An Improved Method for Seismic Event Depth and Moment Tensor Determination: CTBT Related Application

NASA Astrophysics Data System (ADS)

Stachnik, J.; Rozhkov, M.; Baker, B.

2016-12-01

According to the Protocol to CTBT, International Data Center is required to conduct expert technical analysis and special studies to improve event parameters and assist State Parties in identifying the source of specific event. Determination of seismic event source mechanism and its depth is a part of these tasks. It is typically done through a strategic linearized inversion of the waveforms for a complete or subset of source parameters, or similarly defined grid search through precomputed Greens Functions created for particular source models. We show preliminary results using the latter approach from an improved software design and applied on a moderately powered computer. In this development we tried to be compliant with different modes of CTBT monitoring regime and cover wide range of source-receiver distances (regional to teleseismic), resolve shallow source depths, provide full moment tensor solution based on body and surface waves recordings, be fast to satisfy both on-demand studies and automatic processing and properly incorporate observed waveforms and any uncertainties a priori as well as accurately estimate posteriori uncertainties. Implemented HDF5 based Green's Functions pre-packaging allows much greater flexibility in utilizing different software packages and methods for computation. Further additions will have the rapid use of Instaseis/AXISEM full waveform synthetics added to a pre-computed GF archive. Along with traditional post processing analysis of waveform misfits through several objective functions and variance reduction, we follow a probabilistic approach to assess the robustness of moment tensor solution. In a course of this project full moment tensor and depth estimates are determined for DPRK 2009, 2013 and 2016 events and shallow earthquakes using a new implementation of waveform fitting of teleseismic P waves. A full grid search over the entire moment tensor space is used to appropriately sample all possible solutions. A recent method by Tape & Tape (2012) to discretize the complete moment tensor space from a geometric perspective is used. Moment tensors for DPRK events show isotropic percentages greater than 50%. Depth estimates for the DPRK events range from 1.0-1.4 km. Probabilistic uncertainty estimates on the moment tensor parameters provide robustness to solution.

Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts

NASA Astrophysics Data System (ADS)

Ren, Zhengyong; Zhong, Yiyuan; Chen, Chaojian; Tang, Jingtian; Kalscheuer, Thomas; Maurer, Hansruedi; Li, Yang

2018-03-01

During the last 20 years, geophysicists have developed great interest in using gravity gradient tensor signals to study bodies of anomalous density in the Earth. Deriving exact solutions of the gravity gradient tensor signals has become a dominating task in exploration geophysics or geodetic fields. In this study, we developed a compact and simple framework to derive exact solutions of gravity gradient tensor measurements for polyhedral bodies, in which the density contrast is represented by a general polynomial function. The polynomial mass contrast can continuously vary in both horizontal and vertical directions. In our framework, the original three-dimensional volume integral of gravity gradient tensor signals is transformed into a set of one-dimensional line integrals along edges of the polyhedral body by sequentially invoking the volume and surface gradient (divergence) theorems. In terms of an orthogonal local coordinate system defined on these edges, exact solutions are derived for these line integrals. We successfully derived a set of unified exact solutions of gravity gradient tensors for constant, linear, quadratic and cubic polynomial orders. The exact solutions for constant and linear cases cover all previously published vertex-type exact solutions of the gravity gradient tensor for a polygonal body, though the associated algorithms may differ in numerical stability. In addition, to our best knowledge, it is the first time that exact solutions of gravity gradient tensor signals are derived for a polyhedral body with a polynomial mass contrast of order higher than one (that is quadratic and cubic orders). Three synthetic models (a prismatic body with depth-dependent density contrasts, an irregular polyhedron with linear density contrast and a tetrahedral body with horizontally and vertically varying density contrasts) are used to verify the correctness and the efficiency of our newly developed closed-form solutions. Excellent agreements are obtained between our solutions and other published exact solutions. In addition, stability tests are performed to demonstrate that our exact solutions can safely be used to detect shallow subsurface targets.

Gluing operation and form factors of local operators in N = 4 Super Yang-Mills theory

NASA Astrophysics Data System (ADS)

Bolshov, A. E.

2018-04-01

The gluing operation is an effective way to get form factors of both local and non-local operators starting from different representations of on-shell scattering amplitudes. In this paper it is shown how it works on the example of form factors of operators from stress-tensor operator supermultiplet in Grassmannian and spinor helicity representations.

Finsler-Geometric Continuum Mechanics

DTIC Science & Technology

2016-05-01

gravitation and astrophysical applications. Physical Review D. 1977;16:1643–1663. 50. Ozakin A, Yavari A. A geometric theory of thermal stresses...to physical problems of tensile fracture, shear localization, and cavitation in solid bodies. The pseudo-Finsler approach is demonstrated to be more...Weyl-type transformation of the fundamental tensor, analytical and numerical solutions of representative example problems offer new physical insight

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brizard, Alain J.; Tronci, Cesare

The variational formulations of guiding-center Vlasov-Maxwell theory based on Lagrange, Euler, and Euler-Poincaré variational principles are presented. Each variational principle yields a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric.

Modulated Hawking radiation and a nonviolent channel for information release

DOE PAGES

Giddings, Steven B.

2014-09-16

The unitarization of black hole evaporation requires that quantum information escapes a black hole; an important question is to identify the mechanism or channel by which it does so. Accurate counting of black hole states via the Bekenstein–Hawking entropy would indicate this information should be encoded in radiation with average energy flux matching Hawking’s. Information can be encoded with no change in net flux via fine-grained modulation of the Hawking radiation. In an approximate effective field theory description, couplings to the stress tensor of the black hole atmosphere that depend on the internal state of the black hole are amore » promising alternative for inducing such modulation. These can be picturesquely thought of as due to state-dependent metric fluctuations in the vicinity of the horizon. Such couplings offer the prospect of emitting information without extra energy flux, and can be shown to do so at linear order in the couplings, with motivation given for possible extension of this result to higher orders. The potential advantages of such couplings to the stress tensor thus extend beyond their universality, which is helpful in addressing constraints from black hole mining.« less

A Comprehensive Overview of the Duvernay Induced Seismicity near Fox Creek, Alberta

NASA Astrophysics Data System (ADS)

Schultz, R.; Wang, R.; Gu, Y. J.; Haug, K.; Atkinson, G. M.

2016-12-01

In this work we summarize the current state of understanding regarding the induced seismicity related to Duvernay hydraulic fracturing operations in central Alberta, near the town of Fox Creek. Earthquakes in this region cluster into distinct sequences in time, space, and focal mechanism. To corroborate this point, we use cross-correlation detection methods to delineate transient temporal relationships, double-difference relocations to confirm spatial clustering, and moment tensor determinations to show fault motion consistency. The spatiotemporal clustering of sequences is strongly related to nearby hydraulic fracturing operations. In addition, we identify a strong preference for subvertical strike-slip motion with a roughly 45º P-axis orientation, consistent with ambient stress field considerations. The hypocentral geometry in two red traffic light protocol cases, that are robustly constrained by local array data, provide compelling evidence for planar features starting at Duvernay Formation depths and extending into the shallow Precambrian basement. We interpret these features as faults orientated approximately north-south and subvertically, consistent with moment tensor determinations. Finally, we conclude that the primary sequences are best explained as induced events in response to effective stress changes as a result of pore-pressure increase along previously existing faults due to hydraulic fracturing stimulations.

Statistics of fully turbulent impinging jets

NASA Astrophysics Data System (ADS)

Wilke, Robert; Sesterhenn, Jörn

2017-08-01

Direct numerical simulations of sub- and supersonic impinging jets with Reynolds numbers of 3300 and 8000 are carried out to analyse their statistical properties. The influence of the parameters Mach number, Reynolds number and ambient temperature on the mean velocity and temperature fields are studied. For the compressible subsonic cold impinging jets into a heated environment, different Reynolds analogies are assesses. It is shown, that the (original) Reynolds analogy as well as the Chilton Colburn analogy are in good agreement with the DNS data outside the impinging area. The generalised Reynolds analogy (GRA) and the Crocco-Busemann relation are not suited for the estimation of the mean temperature field based on the mean velocity field of impinging jets. Furthermore, the prediction of fluctuating temperatures according to the GRA fails. On the contrary, the linear relation between thermodynamic fluctuations of entropy, density and temperature as suggested by Lechner et al. (2001) can be confirmed for the entire wall jet. The turbulent heat flux and Reynolds stress tensor are analysed and brought into coherence with the primary and secondary ring vortices of the wall jet. Budget terms of the Reynolds stress tensor are given as data base for the improvement of turbulence models.

Boundary stress tensor and asymptotically AdS3 non-Einstein spaces at the chiral point

NASA Astrophysics Data System (ADS)

Giribet, Gaston; Goya, Andrés; Leston, Mauricio

2011-09-01

Chiral gravity admits asymptotically AdS3 solutions that are not locally equivalent to AdS3; meaning that solutions do exist which, while obeying the strong boundary conditions usually imposed in general relativity, happen not to be Einstein spaces. In topologically massive gravity (TMG), the existence of non-Einstein solutions is particularly connected to the question about the role played by complex saddle points in the Euclidean path integral. Consequently, studying (the existence of) nonlocally AdS3 solutions to chiral gravity is relevant to understanding the quantum theory. Here, we discuss a special family of nonlocally AdS3 solutions to chiral gravity. In particular, we show that such solutions persist when one deforms the theory by adding the higher-curvature terms of the so-called new massive gravity. Moreover, the addition of higher-curvature terms to the gravity action introduces new nonlocally AdS3 solutions that have no analogues in TMG. Both stationary and time-dependent, axially symmetric solutions that asymptote AdS3 space without being locally equivalent to it appear. Defining the boundary stress tensor for the full theory, we show that these non-Einstein geometries have associated vanishing conserved charges.

A strain energy filter for 3D vessel enhancement with application to pulmonary CT images.

PubMed

Xiao, Changyan; Staring, Marius; Shamonin, Denis; Reiber, Johan H C; Stolk, Jan; Stoel, Berend C

2011-02-01

The traditional Hessian-related vessel filters often suffer from detecting complex structures like bifurcations due to an over-simplified cylindrical model. To solve this problem, we present a shape-tuned strain energy density function to measure vessel likelihood in 3D medical images. This method is initially inspired by established stress-strain principles in mechanics. By considering the Hessian matrix as a stress tensor, the three invariants from orthogonal tensor decomposition are used independently or combined to formulate distinctive functions for vascular shape discrimination, brightness contrast and structure strength measuring. Moreover, a mathematical description of Hessian eigenvalues for general vessel shapes is obtained, based on an intensity continuity assumption, and a relative Hessian strength term is presented to ensure the dominance of second-order derivatives as well as suppress undesired step-edges. Finally, we adopt the multi-scale scheme to find an optimal solution through scale space. The proposed method is validated in experiments with a digital phantom and non-contrast-enhanced pulmonary CT data. It is shown that our model performed more effectively in enhancing vessel bifurcations and preserving details, compared to three existing filters. Copyright © 2010 Elsevier B.V. All rights reserved.

Experimental investigation of turbulent flow through a circular-to-rectangular transition duct. Ph.D. Thesis - Washington Univ.

NASA Technical Reports Server (NTRS)

Davis, David O.

1991-01-01

Steady, incompressible, turbulent, swirl-free flow through a circular-to-rectangular transition duck was studied experimentally. The cross-sectional area remains the same at the exit as at the inlet, but varies through the transition section to a maximum value approximately 15 percent above the inlet value. The cross-sectional geometry everywhere along the duct is defined by the equation of a superellipse. Mean and turbulence data were accumulated utilizing pressure and hot-wire instrumentation at five stations along the test section. Data are presented for operating bulk Reynolds numbers of 88,000 and 390,000. Measured quantities include total and static pressure, the three components of the mean velocity vector, and the six components of the Reynolds stress tensor. In addition to the transition duct measurements, a hot-wire technique which relies on the sequential use of single rotatable normal and slant-wire probes was proposed. The technique is applicable for measurement of the total mean velocity vector and the complete Reynolds stress tensor when the primary flow is arbitrarily skewed relative to a plane which lies normal to the probe axis of rotation.

Multi-scale properties of large eddy simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities

NASA Astrophysics Data System (ADS)

Linkmann, Moritz; Buzzicotti, Michele; Biferale, Luca

2018-06-01

We provide analytical and numerical results concerning multi-scale correlations between the resolved velocity field and the subgrid-scale (SGS) stress-tensor in large eddy simulations (LES). Following previous studies for Navier-Stokes equations, we derive the exact hierarchy of LES equations governing the spatio-temporal evolution of velocity structure functions of any order. The aim is to assess the influence of the subgrid model on the inertial range intermittency. We provide a series of predictions, within the multifractal theory, for the scaling of correlation involving the SGS stress and we compare them against numerical results from high-resolution Smagorinsky LES and from a-priori filtered data generated from direct numerical simulations (DNS). We find that LES data generally agree very well with filtered DNS results and with the multifractal prediction for all leading terms in the balance equations. Discrepancies are measured for some of the sub-leading terms involving cross-correlation between resolved velocity increments and the SGS tensor or the SGS energy transfer, suggesting that there must be room to improve the SGS modelisation to further extend the inertial range properties for any fixed LES resolution.

Stress tensor and viscosity of water: Molecular dynamics and generalized hydrodynamics results

NASA Astrophysics Data System (ADS)

Bertolini, Davide; Tani, Alessandro

1995-08-01

The time correlation functions (CF's) of diagonal and off-diagonal components of the stress tensor of water have been calculated at 245 and 298 K in a molecular dynamics (MD) study on 343 molecules in the microcanonical ensemble. We present results obtained at wave number k=0 and at a few finite values of k, in the atomic and molecular formalism. In all cases, more than 98% of these functions are due to the potential term of the stress tensor. At k=0, their main features are a fast oscillatory initial decay, followed by a long-time tail more apparent in the supercooled region. Bulk and shear viscosities, calculated via Green-Kubo integration of the relevant CF at k=0, are underestimated with respect to experimental data, mainly at low temperature, but their ratio (~=2) is correctly reproduced. Both shear and bulk viscosity decrease as a function of k, the latter more rapidly, so that they become almost equal at ~=1 Å-1. Also, both viscosities drop rapidly from their maximum at ω=0. This behavior has been related to the large narrowing observed in the acoustic band, mainly in the supercooled region. The infinite frequency bulk and shear rigidity moduli have been shown to be in fair agreement with the experimental data, provided the MD value used for comparison is that corresponding to the frequency range relevant to ultrasonic measurements. The MD results of stress-stress CF's compare well with those predicted by Bertolini and Tani [Phys. Rev. E 51, 1091 (1995)] at k=0, by an application of generalized hydrodynamics [de Schepper et al., Phys. Rev. A 38, 271 (1988)] in the molecular formalism, to the same model of water (TIP4P) [Jorgensen et al., J. Chem. Phys. 79, 926 (1983)]. These CF's are essentially equal in the atomic and molecular formalism, the only minor difference being restricted to the high frequency librational region of the shear function. By a comparison of atomic and molecular results, we show here that neglecting libration has no effect on the density-density and longitudinal current CF's and very little effect on transverse properties. On the other hand, this study points out the importance of including the oscillation in the nearest-neighbor cage in the memory function of the longitudinal and transverse current CF. The oscillatory local motion turns out to play an important role in all CF's and hence contributes significantly to the value of viscosity and of rigidity moduli.

BOOK REVIEW: Introduction to Computational Plasticity

NASA Astrophysics Data System (ADS)

Hartley, P.

2006-04-01

The use of computational modelling in all areas of science and engineering has in recent years escalated to the point where it underpins much of current research. However, the distinction must be made between computer systems in which no knowledge of the underlying computer technology or computational theory is required and those areas of research where the mastery of computational techniques is of great value, almost essential, for final year undergraduates or masters students planning to pursue a career in research. Such a field of research in the latter category is continuum mechanics, and in particular non-linear material behaviour, which is the core topic of this book. The focus of the book on computational plasticity embodies techniques of relevance not only to academic researchers, but also of interest to industrialists engaged in the production of components using bulk or sheet forming processes. Of particular interest is the guidance on how to create modules for use with the commercial system Abaqus for specific types of material behaviour. The book is in two parts, the first of which contains six chapters, starting with microplasticity, but predominantly on continuum plasticity. The first chapter on microplasticty gives a brief description of the grain structure of metals and the existence of slip systems within the grains. This provides an introduction to the concept of incompressibility during plastic deformation, the nature of plastic yield and the importance of the critically resolved shear stress on the slip planes (Schmid's law). Some knowledge of the notation commonly used to describe slip systems is assumed, which will be familiar to students of metallurgy, but anyone with a more general engineering background may need to undertake additional reading to understand the various descriptions. Any lack of knowledge in this area however, is of no disadvantage as it serves only as an introduction and the book moves on quickly to continuum plasticity. Chapter two introduces one of several yield criteria, that normally attributed to von Mises (though historians of mechanics might argue over who was first to develop the theory of yielding associated with strain energy density), and its two or three-dimensional representation as a yield surface. The expansion of the yield surface during plastic deformation, its translation due to kinematic hardening and the Bauschinger effect in reversed loading are described with a direct link to the material stress-strain curve. The assumption, that the increment of strain is normal to the yield surface, the normality principle, is introduced. Uniaxial loading of an elastic-plastic material is used as an example in which to develop expressions to describe increments in stress and strain. The full presentation of numerous expressions, tensors and matrices with a clear explanation of their development, is a recurring, and commendable, feature of the book, which provides an invaluable introduction for those new to the subject. The chapter moves on from time-independent behaviour to introduce viscoplasticity and creep. Chapter three takes the theories of deformation another stage further to consider the problems associated with large deformation in which an important concept is the separation of the phenomenon into material stretch and rotation. The latter is crucial to allow correct measures of strain and stress to be developed in which the effects of rigid body rotation do not contribute to these variables. Hence, the introduction of 'objective' measures for stress and strain. These are described with reference to deformation gradients, which are clearly explained; however, the introduction of displacement gradients passes with little comment, although velocity gradients appear later in the chapter. The interpretation of different strain measures, e.g. Green--Lagrange and Almansi, is covered briefly, followed by a description of the spin tensor and its use in developing the objective Jaumann rate of stress. It is tempting here to suggest that a more complete description should be given together with other measures of strain and stress, of which there are several, but there would be a danger of changing the book from an `introduction' to a more comprehensive text, and examples of such exist already. Chapter four begins the process of developing the plasticity theories into a form suitable for inclusion in the finite-element method. The starting point is Hamilton's principle for equilibrium of a dynamic system. A very brief introduction to the finite-element method is then given, followed by the finite-element equilibrium equations and a description of how they are incorporated into Hamilton's principle. A useful clarification is provided by comparing tensor notation and the form normally used in finite-element expressions, i.e. Voigt notation. The chapter concludes with a brief overview of implicit integration methods, i.e. tangent stiffness, initial tangent stiffness and Newton Raphson. Chapter five deals with the more specialized topic of implicit and explicit integration of von Mises plasticity. One of the techniques described is the radial-return method which ensures that the stresses at the end of an increment of deformation always lie on the expanded yield surface. Although this method guarantees a solution it may not always be the most accurate for large deformation, this is one area where reference to alternative methods would have been a helpful addition. Chapter six continues with further detail of how the plasticity models may be incorporated into finite-element codes, with particular reference to the Abaqus package and the use of user-defined subroutines, introduced via a `UMAT' subroutine. This completes part I of the book. Part II focuses on plasticity models, each chapter dealing with a particular process or material model. For example, chapter seven deals with superplasticity, chapter eight with porous plasticity, chapter nine with creep and chapter ten with cyclic plasticity, creep and TMF. Examples of deep drawing, forming of titanium metal-matrix composites and creep damage are provided, together with further guidelines on the use of Abaqus to model these processes. Overall, the book is organised in a very logical and readable form. The use of simple one-dimensional examples, with full descriptions of tensors and vectors throughout the book, is particularly useful. It provides a good introduction to the topic, covering much of the theory and with applications to give a good grounding that can be taken further with more comprehensive advanced texts. An excellent starting point for anyone involved in research in computational plasticity.

The algorithms for rational spline interpolation of surfaces

NASA Technical Reports Server (NTRS)

Schiess, J. R.

1986-01-01

Two algorithms for interpolating surfaces with spline functions containing tension parameters are discussed. Both algorithms are based on the tensor products of univariate rational spline functions. The simpler algorithm uses a single tension parameter for the entire surface. This algorithm is generalized to use separate tension parameters for each rectangular subregion. The new algorithm allows for local control of tension on the interpolating surface. Both algorithms are illustrated and the results are compared with the results of bicubic spline and bilinear interpolation of terrain elevation data.

Hydraulic Fracturing Induced Seismicity at Preese Hall, UK: Moment Tensors, Uncertainties and Implications for Microseismic Monitoring Strategies

NASA Astrophysics Data System (ADS)

O'toole, T. B.; Woodhouse, J. H.; Verdon, J.; Kendall, J.

2012-12-01

Hydraulic fracturing operations carried out in April and May 2011 by Cuadrilla Resources Ltd. during the exploration of a shale gas reservoir at Preese Hall, near Blackpool, UK, induced a series of microseismic events. The largest of these, with magnitude ML = 2.3, was felt at the surface and recorded by the British Geological Survey regional seismic network. Subsequently, two local seismic stations were installed, which continued to detect seismicity with ML ≤ 1.5 until the hydraulic fracture treatment was suspended due to the anomalously large magnitudes of the induced earthquakes. Here, we present the results of moment tensor inversions of seismic waveforms recorded by these two near-field stations. We determine the best point source description of an event by minimising the least-squares difference between observed and synthetic waveforms. In contrast to source mechanisms obtained from body wave polarity and amplitude picks, which require a good sampling of the focal sphere and typically assume a pure double-couple mechanism, using the whole waveform allows us to place good constraints on the moment tensor even when only a few seismograms are available, and also enables the investigation of possible non-double-couple components and volume changes associated with a source. We discuss our results in the context of the studies commissioned by Cuadrilla after the suspension of hydraulic fracturing operations at Preese Hall. Using synthetic waveform data, we investigate how different monitoring geometries can be used to reduce uncertainties in source parameters of induced microseisms. While our focus is on the monitoring of hydraulic fracturing operations, the methods developed here are general and could equally be applied to determine moment tensors from surface and borehole observations of seismicity induced by other activities.

Brain structural changes in spasmodic dysphonia: A multimodal magnetic resonance imaging study.

PubMed

Kostic, Vladimir S; Agosta, Federica; Sarro, Lidia; Tomić, Aleksandra; Kresojević, Nikola; Galantucci, Sebastiano; Svetel, Marina; Valsasina, Paola; Filippi, Massimo

2016-04-01

The pathophysiology of spasmodic dysphonia is poorly understood. This study evaluated patterns of cortical morphology, basal ganglia, and white matter microstructural alterations in patients with spasmodic dysphonia relative to healthy controls. T1-weighted and diffusion tensor magnetic resonance imaging (MRI) scans were obtained from 13 spasmodic dysphonia patients and 30 controls. Tract-based spatial statistics was applied to compare diffusion tensor MRI indices (i.e., mean, radial and axial diffusivities, and fractional anisotropy) between groups on a voxel-by-voxel basis. Cortical measures were analyzed using surface-based morphometry. Basal ganglia were segmented on T1-weighted images, and volumes and diffusion tensor MRI metrics of nuclei were measured. Relative to controls, patients with spasmodic dysphonia showed increased cortical surface area of the primary somatosensory cortex bilaterally in a region consistent with the buccal sensory representation, as well as right primary motor cortex, left superior temporal, supramarginal and superior frontal gyri. A decreased cortical area was found in the rolandic operculum bilaterally, left superior/inferior parietal and lingual gyri, as well as in the right angular gyrus. Compared to controls, spasmodic dysphonia patients showed increased diffusivities and decreased fractional anisotropy of the corpus callosum and major white matter tracts, in the right hemisphere. Altered diffusion tensor MRI measures were found in the right caudate and putamen nuclei with no volumetric changes. Multi-level alterations in voice-controlling networks, that included regions devoted not only to sensorimotor integration, motor preparation and motor execution, but also processing of auditory and visual information during speech, might have a role in the pathophysiology of spasmodic dysphonia. Copyright © 2016 Elsevier Ltd. All rights reserved.

Analysis of Seismic Moment Tensor and Finite-Source Scaling During EGS Resource Development at The Geysers, CA

NASA Astrophysics Data System (ADS)

Boyd, O. S.; Dreger, D. S.; Gritto, R.

2015-12-01

Enhanced Geothermal Systems (EGS) resource development requires knowledge of subsurface physical parameters to quantify the evolution of fracture networks. We investigate seismicity in the vicinity of the EGS development at The Geysers Prati-32 injection well to determine moment magnitude, focal mechanism, and kinematic finite-source models with the goal of developing a rupture area scaling relationship for the Geysers and specifically for the Prati-32 EGS injection experiment. Thus far we have analyzed moment tensors of M ≥ 2 events, and are developing the capability to analyze the large numbers of events occurring as a result of the fluid injection and to push the analysis to smaller magnitude earthquakes. We have also determined finite-source models for five events ranging in magnitude from M 3.7 to 4.5. The scaling relationship between rupture area and moment magnitude of these events resembles that of a published empirical relationship derived for events from M 4.5 to 8.3. We plan to develop a scaling relationship in which moment magnitude and corner frequency are predictor variables for source rupture area constrained by the finite-source modeling. Inclusion of corner frequency in the empirical scaling relationship is proposed to account for possible variations in stress drop. If successful, we will use this relationship to extrapolate to the large numbers of events in the EGS seismicity cloud to estimate the coseismic fracture density. We will present the moment tensor and corner frequency results for the micro earthquakes, and for select events, finite-source models. Stress drop inferred from corner frequencies and from finite-source modeling will be compared.

Earthquake focal mechanism forecasting in Italy for PSHA purposes

NASA Astrophysics Data System (ADS)

Roselli, Pamela; Marzocchi, Warner; Mariucci, Maria Teresa; Montone, Paola

2018-01-01

In this paper, we put forward a procedure that aims to forecast focal mechanism of future earthquakes. One of the primary uses of such forecasts is in probabilistic seismic hazard analysis (PSHA); in fact, aiming at reducing the epistemic uncertainty, most of the newer ground motion prediction equations consider, besides the seismicity rates, the forecast of the focal mechanism of the next large earthquakes as input data. The data set used to this purpose is relative to focal mechanisms taken from the latest stress map release for Italy containing 392 well-constrained solutions of events, from 1908 to 2015, with Mw ≥ 4 and depths from 0 down to 40 km. The data set considers polarity focal mechanism solutions until to 1975 (23 events), whereas for 1976-2015, it takes into account only the Centroid Moment Tensor (CMT)-like earthquake focal solutions for data homogeneity. The forecasting model is rooted in the Total Weighted Moment Tensor concept that weighs information of past focal mechanisms evenly distributed in space, according to their distance from the spatial cells and magnitude. Specifically, for each cell of a regular 0.1° × 0.1° spatial grid, the model estimates the probability to observe a normal, reverse, or strike-slip fault plane solution for the next large earthquakes, the expected moment tensor and the related maximum horizontal stress orientation. These results will be available for the new PSHA model for Italy under development. Finally, to evaluate the reliability of the forecasts, we test them with an independent data set that consists of some of the strongest earthquakes with Mw ≥ 3.9 occurred during 2016 in different Italian tectonic provinces.

Enhancement of surface definition and gridding in the EAGLE code

NASA Technical Reports Server (NTRS)

Thompson, Joe F.

1991-01-01

Algorithms for smoothing of curves and surfaces for the EAGLE grid generation program are presented. The method uses an existing automated technique which detects undesirable geometric characteristics by using a local fairness criterion. The geometry entity is then smoothed by repeated removal and insertion of spline knots in the vicinity of the geometric irregularity. The smoothing algorithm is formulated for use with curves in Beta spline form and tensor product B-spline surfaces.

Transformations of the dislocation structure of nickel single crystals

NASA Astrophysics Data System (ADS)

Alfyorova, E. A.; Lychagin, D. V.; Lychagina, L. L.; Tsvetkov, N. A.

2017-12-01

A relationship between different-scale deformations of crystals has not been established yet. In order to solve this task, we investigate the development of a deformation relief and dislocation structure in nickel single crystals after deformation. The stress tensor, crystallography, and geometry of specimens affect the organization of some shear along corresponding systems of sliding. The organization of shear shows some features of self-organization. It is associated with the self-organization in the dislocation subsystem analyzed previously. The effectiveness of reducing external and internal stresses determines patterns of deformation processes at different scale levels.

A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations

NASA Technical Reports Server (NTRS)

Shay, R. M., Jr.; Caruthers, J. M.

1987-01-01

Yield stress predictions of a nonlinear viscoelastic constitutive equation for amorphous polymer solids have been obtained and are compared with the phenomenological von Mises yield criterion. Linear viscoelasticity theory has been extended to include finite strains and a material timescale that depends on the instantaneous temperature, volume, and pressure. Results are presented for yield and the correct temperature and strain-rate dependence in a variety of multiaxial deformations. The present nonlinear viscoelastic constitutive equation can be formulated in terms of either a Cauchy or second Piola-Kirchhoff stress tensor, and in terms of either atmospheric or hydrostatic pressure.

Influences of the Darrieus-Landau instability on premixed turbulent flames

NASA Astrophysics Data System (ADS)

Patyal, Advitya; Matalon, Moshe

2017-11-01

The propagation of turbulent flames in three-dimensional turbulent flows is studied within the context of the hydrodynamic theory. The flame is treated as a surface of density discontinuity with the flow modified by gas expansion resulting from heat released during combustion. The flame is tracked using a level-set method with a propagation speed that depends on the local flame stretch, modulated by a Markstein length. Impact of the Darrieus-Landau instability on the topology of the flame surface is studied. It is shown that similar to passive interfaces, flames under the influence of the hydrodynamic instability resort to cylindrical structures with increasing turbulence intensity, even in 3D. The mechanism of modification of vortical structures in the burned gas is identified in terms of the alignments between the vorticity vector, flame surface normal and eigenvectors of the strain rate tensor. The results indicate that the strain rate tensor is intricately coupled with the normal to the flame surface and creates anisotropy in the orientation of vortical structures, which begins to weaken as the turbulent intensity increases. Furthermore, vorticity budgets are used to highlight the relative importance of baroclinic torque due to Darrieus-Landau instability.

A resolvable subfilter-scale model specific to large-eddy simulation of under-resolved turbulence

NASA Astrophysics Data System (ADS)

Zhou, Yong; Brasseur, James G.; Juneja, Anurag

2001-09-01

Large-eddy simulation (LES) of boundary-layer flows has serious deficiencies near the surface when a viscous sublayer either does not exist (rough walls) or is not practical to resolve (high Reynolds numbers). In previous work, we have shown that the near-surface errors arise from the poor performance of algebraic subfilter-scale (SFS) models at the first several grid levels, where integral scales are necessarily under-resolved and the turbulence is highly anisotropic. In under-resolved turbulence, eddy viscosity and similarity SFS models create a spurious feedback loop between predicted resolved-scale (RS) velocity and modeled SFS acceleration, and are unable to simultaneously capture SFS acceleration and RS-SFS energy flux. To break the spurious coupling in a dynamically meaningful manner, we introduce a new modeling strategy in which the grid-resolved subfilter velocity is estimated from a separate dynamical equation containing the essential inertial interactions between SFS and RS velocity. This resolved SFS (RSFS) velocity is then used as a surrogate for the complete SFS velocity in the SFS stress tensor. We test the RSFS model by comparing LES of highly under-resolved anisotropic buoyancy-generated homogeneous turbulence with a corresponding direct numerical simulation (DNS). The new model successfully suppresses the spurious feedback loop between RS velocity and SFS acceleration, and greatly improves model predictions of the anisotropic structure of SFS acceleration and resolved velocity fields. Unlike algebraic models, the RSFS model accurately captures SFS acceleration intensity and RS-SFS energy flux, even during the nonequilibrium transient, and properly partitions SFS acceleration between SFS stress divergence and SFS pressure force.

New insights into Kilauea's volcano dynamics brought by large-scale relative relocation of microearthquakes

USGS Publications Warehouse

Got, J.-L.; Okubo, P.

2003-01-01

We investigated the microseismicity recorded in an active volcano to infer information concerning the volcano structure and long-term dynamics, by using relative relocations and focal mechanisms of microearthquakes. There were 32,000 earthquakes of the Mauna Loa and Kilauea volcanoes recorded by more than eight stations of the Hawaiian Volcano Observatory seismic network between 1988 and 1999. We studied 17,000 of these events and relocated more than 70%, with an accuracy ranging from 10 to 500 m. About 75% of these relocated events are located in the vicinity of subhorizontal decollement planes, at a depth of 8-11 km. However, the striking features revealed by these relocation results are steep southeast dipping fault planes working as reverse faults, clearly located below the decollement plane and which intersect it. If this decollement plane coincides with the pre-Mauna Loa seafloor, as hypothesized by numerous authors, such reverse faults rupture the pre-Mauna Loa oceanic crust. The weight of the volcano and pressure in the magma storage system are possible causes of these ruptures, fully compatible with the local stress tensor computed by Gillard et al. [1996]. Reverse faults are suspected of producing scarps revealed by kilometer-long horizontal slip-perpendicular lineations along the decollement surface and therefore large-scale roughness, asperities, and normal stress variations. These are capable of generating stick-slip, large-magnitude earthquakes, the spatial microseismic pattern observed in the south flank of Kilauea volcano, and Hilina-type instabilities. Rupture intersecting the decollement surface, causing its large-scale roughness, may be an important parameter controlling the growth of Hawaiian volcanoes.

Shape dependence of entanglement entropy in conformal field theories

DOE PAGES

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar

2016-04-14

Here, we study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on R 1,d--1. We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We also show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, andmore » proportional to the coefficient C T appearing in the two-point function of stress tensors in that CFT. As applications of our result, we prove the conjectured universality of the corner term coefficient σ/CT=π 2/24 in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.« less

Efficient Brownian Dynamics of rigid colloids in linear flow fields based on the grand mobility matrix

NASA Astrophysics Data System (ADS)

Palanisamy, Duraivelan; den Otter, Wouter K.

2018-05-01

We present an efficient general method to simulate in the Stokesian limit the coupled translational and rotational dynamics of arbitrarily shaped colloids subject to external potential forces and torques, linear flow fields, and Brownian motion. The colloid's surface is represented by a collection of spherical primary particles. The hydrodynamic interactions between these particles, here approximated at the Rotne-Prager-Yamakawa level, are evaluated only once to generate the body's (11 × 11) grand mobility matrix. The constancy of this matrix in the body frame, combined with the convenient properties of quaternions in rotational Brownian Dynamics, enables an efficient simulation of the body's motion. Simulations in quiescent fluids yield correct translational and rotational diffusion behaviour and sample Boltzmann's equilibrium distribution. Simulations of ellipsoids and spherical caps under shear, in the absence of thermal fluctuations, yield periodic orbits in excellent agreement with the theories by Jeffery and Dorrepaal. The time-varying stress tensors provide the Einstein coefficient and viscosity of dilute suspensions of these bodies.

An efficient numerical method for the solution of the problem of elasticity for 3D-homogeneous elastic medium with cracks and inclusions

NASA Astrophysics Data System (ADS)

Kanaun, S.; Markov, A.

2017-06-01

An efficient numerical method for solution of static problems of elasticity for an infinite homogeneous medium containing inhomogeneities (cracks and inclusions) is developed. Finite number of heterogeneous inclusions and planar parallel cracks of arbitrary shapes is considered. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for stress tensors inside the inclusions. For the numerical solution of these equations, a class of Gaussian approximating functions is used. The method based on these functions is mesh free. For such functions, the elements of the matrix of the discretized system are combinations of explicit analytical functions and five standard 1D-integrals that can be tabulated. Thus, the numerical integration is excluded from the construction of the matrix of the discretized problem. For regular node grids, the matrix of the discretized system has Toeplitz's properties, and Fast Fourier Transform technique can be used for calculation matrix-vector products of such matrices.

Subsurface structure imaging of the Sembalun-Propok area, West Nusa Tenggara, Indonesia by using the audio-frequency magnetotelluric data

NASA Astrophysics Data System (ADS)

Febriani, F.; Widarto, D. S.; Gaffar, E.; Nasution, A.; Grandis, H.

2017-07-01

We have investigated the subsurface structure of the Sembalun-Propok Area, West Nusa Tenggara, by using the audio-frequency magnetotelluric (AMT) method. This area is one of the geothermal prospect areas in eastern Indonesia. There are 38 AMT observation points, which were deployed along three profiles. We applied the phase tensor analysis on all observation points to determine both the dimensionality of and the regional strike of the study area. The results of the phase tensor analysis show that the study area can be assumed as 2-D and the regional strike of the study area is about N330°E. Then, after rotating the impedance tensor data to the regional strike, we carried out the 2-D inversion modeling to know more detail the subsurface structure of the study area. The results of the 2-D MT inversion are consistent with the geology of the study area. The near surface along all profiles is dominated by the higher resistivity layer (> 500 Ωm). It is highly associated with the surface geology of the study area which is characterized by the volcanic rock and mostly consist of andesitic to dacitic rocks of a calc-alkaline suite. Below the resistive layer at the near surface, the modelings show the layer which has the lower-moderate resistivity layer. It is possibly a cap rock layer of geothermal system of the Sembalun-Propok area. Lastly, the third layer is the very conductive layer and possibly associated with the presence of thermal fluids in the study area.

Vaidya spacetime in the diagonal coordinates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berezin, V. A., E-mail: berezin@inr.ac.ru; Dokuchaev, V. I., E-mail: dokuchaev@inr.ac.ru; Eroshenko, Yu. N., E-mail: eroshenko@inr.ac.ru

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric andmore » cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g{sub 00} = 0 or g{sub 00} = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.« less

3D polarisation speckle as a demonstration of tensor version of the van Cittert-Zernike theorem for stochastic electromagnetic beams

NASA Astrophysics Data System (ADS)

Ma, Ning; Zhao, Juan; Hanson, Steen G.; Takeda, Mitsuo; Wang, Wei

2016-10-01

Laser speckle has received extensive studies of its basic properties and associated applications. In the majority of research on speckle phenomena, the random optical field has been treated as a scalar optical field, and the main interest has been concentrated on their statistical properties and applications of its intensity distribution. Recently, statistical properties of random electric vector fields referred to as Polarization Speckle have come to attract new interest because of their importance in a variety of areas with practical applications such as biomedical optics and optical metrology. Statistical phenomena of random electric vector fields have close relevance to the theories of speckles, polarization and coherence theory. In this paper, we investigate the correlation tensor for stochastic electromagnetic fields modulated by a depolarizer consisting of a rough-surfaced retardation plate. Under the assumption that the microstructure of the scattering surface on the depolarizer is as fine as to be unresolvable in our observation region, we have derived a relationship between the polarization matrix/coherency matrix for the modulated electric fields behind the rough-surfaced retardation plate and the coherence matrix under the free space geometry. This relation is regarded as entirely analogous to the van Cittert-Zernike theorem of classical coherence theory. Within the paraxial approximation as represented by the ABCD-matrix formalism, the three-dimensional structure of the generated polarization speckle is investigated based on the correlation tensor, indicating a typical carrot structure with a much longer axial dimension than the extent in its transverse dimension.

Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories.

PubMed

Dong, Xi

2016-06-24

We develop a framework for studying the well-known universal term in the Rényi entropy for an arbitrary entangling region in four-dimensional conformal field theories that are holographically dual to gravitational theories. The shape dependence of the Rényi entropy S_{n} is described by two coefficients: f_{b}(n) for traceless extrinsic curvature deformations and f_{c}(n) for Weyl tensor deformations. We provide the first calculation of the coefficient f_{b}(n) in interacting theories by relating it to the stress tensor one-point function in a deformed hyperboloid background. The latter is then determined by a straightforward holographic calculation. Our results show that a previous conjecture f_{b}(n)=f_{c}(n), motivated by surprising evidence from a variety of free field theories and studies of conical defects, fails holographically.

Particle-based solid for nonsmooth multidomain dynamics

NASA Astrophysics Data System (ADS)

Nordberg, John; Servin, Martin

2018-04-01

A method for simulation of elastoplastic solids in multibody systems with nonsmooth and multidomain dynamics is developed. The solid is discretised into pseudo-particles using the meshfree moving least squares method for computing the strain tensor. The particle's strain and stress tensor variables are mapped to a compliant deformation constraint. The discretised solid model thus fit a unified framework for nonsmooth multidomain dynamics simulations including rigid multibodies with complex kinematic constraints such as articulation joints, unilateral contacts with dry friction, drivelines, and hydraulics. The nonsmooth formulation allows for impact impulses to propagate instantly between the rigid multibody and the solid. Plasticity is introduced through an associative perfectly plastic modified Drucker-Prager model. The elastic and plastic dynamics are verified for simple test systems, and the capability of simulating tracked terrain vehicles driving on a deformable terrain is demonstrated.

Reactivated faulting near Cushing, Oklahoma: Increased potential for a triggered earthquake in an area of United States strategic infrastructure

USGS Publications Warehouse

McNamara, Daniel E.; Hayes, Gavin; Benz, Harley M.; Williams, Robert; McMahon, Nicole D; Aster, R.C.; Holland, Austin F.; Sickbert, T; Herrmann, Robert B.; Briggs, Richard; Smoczyk, Gregory M.; Bergman, Eric; Earle, Paul S.

2015-01-01

In October 2014 two moderate-sized earthquakes (Mw 4.0 and 4.3) struck south of Cushing, Oklahoma, below the largest crude oil storage facility in the world. Combined analysis of the spatial distribution of earthquakes and regional moment tensor focal mechanisms indicate reactivation of a subsurface unnamed and unmapped left-lateral strike-slip fault. Coulomb failure stress change calculations using the relocated seismicity and slip distribution determined from regional moment tensors, allow for the possibility that the Wilzetta-Whitetail fault zone south of Cushing, Oklahoma, could produce a large, damaging earthquake comparable to the 2011 Prague event. Resultant very strong shaking levels (MMI VII) in the epicentral region present the possibility of this potential earthquake causing moderate to heavy damage to national strategic infrastructure and local communities.

Heat Transfer in Complex Fluids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mehrdad Massoudi

Amongst the most important constitutive relations in Mechanics, when characterizing the behavior of complex materials, one can identify the stress tensor T, the heat flux vector q (related to heat conduction) and the radiant heating (related to the radiation term in the energy equation). Of course, the expression 'complex materials' is not new. In fact, at least since the publication of the paper by Rivlin & Ericksen (1955), who discussed fluids of complexity (Truesdell & Noll, 1992), to the recently published books (Deshpande et al., 2010), the term complex fluids refers in general to fluid-like materials whose response, namely themore » stress tensor, is 'non-linear' in some fashion. This non-linearity can manifest itself in variety of forms such as memory effects, yield stress, creep or relaxation, normal-stress differences, etc. The emphasis in this chapter, while focusing on the constitutive modeling of complex fluids, is on granular materials (such as coal) and non-linear fluids (such as coal-slurries). One of the main areas of interest in energy related processes, such as power plants, atomization, alternative fuels, etc., is the use of slurries, specifically coal-water or coal-oil slurries, as the primary fuel. Some studies indicate that the viscosity of coal-water mixtures depends not only on the volume fraction of solids, and the mean size and the size distribution of the coal, but also on the shear rate, since the slurry behaves as shear-rate dependent fluid. There are also studies which indicate that preheating the fuel results in better performance, and as a result of such heating, the viscosity changes. Constitutive modeling of these non-linear fluids, commonly referred to as non-Newtonian fluids, has received much attention. Most of the naturally occurring and synthetic fluids are non-linear fluids, for example, polymer melts, suspensions, blood, coal-water slurries, drilling fluids, mud, etc. It should be noted that sometimes these fluids show Newtonian (linear) behavior for a given range of parameters or geometries; there are many empirical or semi-empirical constitutive equations suggested for these fluids. There have also been many non-linear constitutive relations which have been derived based on the techniques of continuum mechanics. The non-linearities oftentimes appear due to higher gradient terms or time derivatives. When thermal and or chemical effects are also important, the (coupled) momentum and energy equations can give rise to a variety of interesting problems, such as instability, for example the phenomenon of double-diffusive convection in a fluid layer. In Conclusion, we have studied the flow of a compressible (density gradient type) non-linear fluid down an inclined plane, subject to radiation boundary condition. The heat transfer is also considered where a source term, similar to the Arrhenius type reaction, is included. The non-dimensional forms of the equations are solved numerically and the competing effects of conduction, dissipation, heat generation and radiation are discussed. It is observed that the velocity increases rapidly in the region near the inclined surface and is slower in the region near the free surface. Since R{sub 7} is a measure of the heat generation due to chemical reaction, when the reaction is frozen (R{sub 7}=0.0) the temperature distributions would depend only on R{sub 1}, and R{sub 2}, representing the effects of the pressure force developed in the material due to the distribution, R{sub 3} and R{sub 4} viscous dissipation, R{sub 5} the normal stress coefficient, R{sub 6} the measure of the emissivity of the particles to the thermal conductivity, etc. When the flow is not frozen (RP{sub 7} > 0) the temperature inside the flow domain is much higher than those at the inclined and free surfaces. As a result, heat is transferred away from the flow toward both the inclined surface and the free surface with a rate that increases as R{sub 7} increases. For a given temperature, an increase in {zeta} implies that the activation energy is smaller and thus, the reaction rate is increased leading to an increase in the heat of the reaction. As a result the flow is chemically heated and its temperature increase. The results shown here indicate that for all values of {zeta} used the chemical effects are significant and the temperature is always higher than both the surface temperature and the free surface temperature. The heat transfer is always from the flow toward both the inclined surface and the free stream. It is also noticed that for all values of m chosen in this study, the temperature is higher than the surface and the free stream temperature. The heat transfer at the inclined surface and at the free stream increase slowly for negative values of m to about m=0.5, but it begins to significantly increase for m greater than 0.5.« less

The complexity of non-Schmid behavior in the CuZnAl shape memory alloy

NASA Astrophysics Data System (ADS)

Alkan, S.; Ojha, A.; Sehitoglu, H.

2018-05-01

The paper addresses one of the most important yet overlooked phenomenon in shape memory research- the plastic slip response. We show that the slip response is highly crystal orientation dependent and we demonstrate the precise reasons behind such complex response. The fractional dislocations on <111> {112} or <111> {011} systems can be activated depending on the sample orientation and solutions are derived for the variations in disregistries and dislocation core spreadings. This leads to the calculation of critical resolved shear stress in close agreement with experimental trends. The results show considerable dependence of the flow behavior on the non-Schmid stress components and the proposed yield criterion captures the role of stress tensor components.