Hydrogen Burning in Low Mass Stars Constrains Scalar-Tensor Theories of Gravity.

PubMed

Sakstein, Jeremy

2015-11-13

The most general scalar-tensor theories of gravity predict a weakening of the gravitational force inside astrophysical bodies. There is a minimum mass for hydrogen burning in stars that is set by the interplay of plasma physics and the theory of gravity. We calculate this for alternative theories of gravity and find that it is always significantly larger than the general relativity prediction. The observation of several low mass red dwarf stars therefore rules out a large class of scalar-tensor gravity theories and places strong constraints on the cosmological parameters appearing in the effective field theory of dark energy.

Somatosensory attunement to the rigid body laws.

PubMed

Shockley, K; Grocki, M; Carello, C; Turvey, M T

2001-01-01

In the most general case, haptic perception of an object's heaviness is most likely the perception of the object's resistance to movement, determined jointly by the object's mass and mass distribution. In two experiments with occluded objects wielded freely in three dimensions, we showed additive effects on perceived heaviness of mass and the inertia tensor. Our manipulations of the inertia tensor were directed specifically at the volume and symmetry of the inertia ellipsoid, quantities that can be understood as important to controlling the level and patterning of muscular forces, respectively. Ellipsoid volume and symmetry were found to have separate effects on perceptual reports of heaviness that were invariant over different tensors. Independent sensitivities to translational inertia and particular characterizations of rotational inertia suggest specialized somatosensory attunement to the rigid body laws.

An introduction to tensor calculus, relativity and cosmology /3rd edition/

NASA Astrophysics Data System (ADS)

Lawden, D. F.

This textbook introduction to the principles of special relativity proceeds within the context of cartesian tensors. Newton's laws of motion are reviewed, as are the Lorentz transformations, Minkowski space-time, and the Fitzgerald contraction. Orthogonal transformations are described, and invariants, gradients, tensor derivatives, contraction, scalar products, divergence, pseudotensors, vector products, and curl are defined. Special relativity mechanics are explored in terms of mass, momentum, the force vector, the Lorentz transformation equations for force, calculations for photons and neutrinos, the development of the Lagrange and Hamilton equations, and the energy-momentum tensor. Electrodynamics is investigated, together with general tensor calculus and Riemmanian space. The General Theory of Relativity is presented, along with applications to astrophysical phenomena such as black holes and gravitational waves. Finally, analytical discussions of cosmological problems are reviewed, particularly Einstein, de Sitter, and Friedmann universes, redshifts, event horizons, and the redshift.

Casimir Effect in de Sitter Spacetime

NASA Astrophysics Data System (ADS)

Saharian, A. A.

2011-06-01

The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background spacetime decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the field mass.

Erratum to Surface‐wave green’s tensors in the near field

USGS Publications Warehouse

Haney, Matthew M.; Hisashi Nakahara,

2016-01-01

Haney and Nakahara (2014) derived expressions for surface‐wave Green’s tensors that included near‐field behavior. Building on the result for a force source, Haney and Nakahara (2014) further derived expressions for a general point moment tensor source using the exact Green’s tensors. However, it has come to our attention that, although the Green’s tensors were correct, the resulting expressions for a general point moment tensor source were missing some terms. In this erratum, we provide updated expressions with these missing terms. The inclusion of the missing terms changes the example given in Haney and Nakahara (2014).

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.

Derivation of revised formulae for eddy viscous forces used in the ocean general circulation model

NASA Technical Reports Server (NTRS)

Chou, Ru Ling

1988-01-01

Presented is a re-derivation of the eddy viscous dissipation tensor commonly used in present oceanographic general circulation models. When isotropy is imposed, the currently-used form of the tensor fails to return to the laplacian operator. In this paper, the source of this error is identified in a consistent derivation of the tensor in both rectangular and earth spherical coordinates, and the correct form of the eddy viscous tensor is presented.

Casimir forces on a bi-anisotropic absorbing magneto-dielectric slab between two parallel conducting plates

NASA Astrophysics Data System (ADS)

Amooshahi, Majid; Shoughi, Ali

2018-05-01

A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is demonstrated. The electric and the magnetic polarization densities of the magneto-dielectric slab are defined in terms of the dynamical variables modeling the slab and the coupling tensors that couple the electromagnetic field to the slab. The four susceptibility tensors of the bi-anisotropic magneto-dielectric slab are expressed in terms of the coupling tensors that couple an electromagnetic field to the slab. It is shown that the four susceptibility tensors of the bi-anisotropic magneto-dielectric slab satisfy Kramers-Kronig relations. The Maxwell’s equations are exactly solved in the presence of the bi-anisotropic magneto-dielectric slab. The tangential and the normal components of the Casimir forces exerted on the bi-anisotropic magnet-dielectric slab exactly are calculated in the vacuum state and thermal state of the total system. It is shown that the tangential components of the Casimir forces vanish when the bi-anisotropic slab is converted to an isotropic slab.

BRIEF COMMUNICATION: A note on the Coulomb collision operator in curvilinear coordinates

NASA Astrophysics Data System (ADS)

Goncharov, P. R.

2010-10-01

The dynamic friction force, diffusion tensor, flux density in velocity space and Coulomb collision term are expressed in curvilinear coordinates via Trubnikov potential functions corresponding to each species of a background plasma. For comparison, explicit formulae are given for the dynamic friction force, diffusion tensor and collisional flux density in velocity space in curvilinear coordinates via Rosenbluth potential functions summed over all species of the background plasma.

No fifth force in a scale invariant universe

DOE PAGES

Ferreira, Pedro G.; Hill, Christopher T.; Ross, Graham G.

2017-03-15

We revisit the possibility that the Planck mass is spontaneously generated in scale-invariant scalar-tensor theories of gravity, typically leading to a “dilaton.” The fifth force, arising from the dilaton, is severely constrained by astrophysical measurements. We explore the possibility that nature is fundamentally scale invariant and argue that, as a consequence, the fifth-force effects are dramatically suppressed and such models are viable. Finally, we discuss possible obstructions to maintaining scale invariance and how these might be resolved.

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.

Monitoring the refinement of crystal structures with {sup 15}N solid-state NMR shift tensor data

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

Kalakewich, Keyton; Eloranta, Harriet; Harper, James K.

The {sup 15}N chemical shift tensor is shown to be extremely sensitive to lattice structure and a powerful metric for monitoring density functional theory refinements of crystal structures. These refinements include lattice effects and are applied here to five crystal structures. All structures improve based on a better agreement between experimental and calculated {sup 15}N tensors, with an average improvement of 47.0 ppm. Structural improvement is further indicated by a decrease in forces on the atoms by 2–3 orders of magnitude and a greater similarity in atom positions to neutron diffraction structures. These refinements change bond lengths by more thanmore » the diffraction errors including adjustments to X–Y and X–H bonds (X, Y = C, N, and O) of 0.028 ± 0.002 Å and 0.144 ± 0.036 Å, respectively. The acquisition of {sup 15}N tensors at natural abundance is challenging and this limitation is overcome by improved {sup 1}H decoupling in the FIREMAT method. This decoupling dramatically narrows linewidths, improves signal-to-noise by up to 317%, and significantly improves the accuracy of measured tensors. A total of 39 tensors are measured with shifts distributed over a range of more than 400 ppm. Overall, experimental {sup 15}N tensors are at least 5 times more sensitive to crystal structure than {sup 13}C tensors due to nitrogen’s greater polarizability and larger range of chemical shifts.« less

The Topology of Three-Dimensional Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.

Gravitoelectromagnetic analogy based on tidal tensors

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

Costa, L. Filipe O.; Herdeiro, Carlos A. R.

2008-07-15

We propose a new approach to a physical analogy between general relativity and electromagnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations, which makes transparent both the similarities and key differences between the two interactions. The following realizations of the analogy are given. The first one matches linearized gravitational tidal tensors to exact electromagnetic tidal tensors in Minkowski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultrastationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third wemore » show that our approach leads to a two-step exact derivation of Papapetrou's equation describing the force exerted on a spinning test particle. Analogous scalar invariants built from tidal tensors of both theories are also discussed.« less

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

Ferreira, Pedro G.; Hill, Christopher T.; Ross, Graham G.

We revisit the possibility that the Planck mass is spontaneously generated in scale-invariant scalar-tensor theories of gravity, typically leading to a “dilaton.” The fifth force, arising from the dilaton, is severely constrained by astrophysical measurements. We explore the possibility that nature is fundamentally scale invariant and argue that, as a consequence, the fifth-force effects are dramatically suppressed and such models are viable. Finally, we discuss possible obstructions to maintaining scale invariance and how these might be resolved.

Efficient Computation of Anharmonic Force Constants via q-space, with Application to Graphene

NASA Astrophysics Data System (ADS)

Kornbluth, Mordechai; Marianetti, Chris

We present a new approach for extracting anharmonic force constants from a sparse sampling of the anharmonic dynamical tensor. We calculate the derivative of the energy with respect to q-space displacements (phonons) and strain, which guarantees the absence of supercell image errors. Central finite differences provide a well-converged quadratic error tail for each derivative, separating the contribution of each anharmonic order. These derivatives populate the anharmonic dynamical tensor in a sparse mesh that bounds the Brillouin Zone, which ensures comprehensive sampling of q-space while exploiting small-cell calculations for efficient, high-throughput computation. This produces a well-converged and precisely-defined dataset, suitable for big-data approaches. We transform this sparsely-sampled anharmonic dynamical tensor to real-space anharmonic force constants that obey full space-group symmetries by construction. Machine-learning techniques identify the range of real-space interactions. We show the entire process executed for graphene, up to and including the fifth-order anharmonic force constants. This method successfully calculates strain-based phonon renormalization in graphene, even under large strains, which solves a major shortcoming of previous potentials.

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

Park, Jong-Kyu; Logan, Nikolas C.

Toroidal torque is one of the most important consequences of non-axisymmetric fields in tokamaks. The well-known neoclassical toroidal viscosity (NTV) is due to the second-order toroidal force from anisotropic pressure tensor in the presence of these asymmetries. This work shows that the first-order toroidal force originating from the same anisotropic pressure tensor, despite having no flux surface average, can significantly modify the local perturbed force balance and thus must be included in perturbed equilibrium self-consistent with NTV. The force operator with an anisotropic pressure tensor is not self-adjoint when the NTV torque is finite and thus is solved directly formore » each component. This approach yields a modified, non-self-adjoint Euler-Lagrange equation that can be solved using a variety of common drift-kinetic models in generalized tokamak geometry. The resulting energy and torque integral provides a unique way to construct a torque response matrix, which contains all the information of self-consistent NTV torque profiles obtainable by applying non-axisymmetric fields to the plasma. This torque response matrix can then be used to systematically optimize non-axisymmetric field distributions for desired NTV profiles. Published by AIP Publishing.« less

Physics of Gravitational Interaction: Geometry of Space or Quantum Field in Space

NASA Astrophysics Data System (ADS)

Baryshev, Yurij

2006-03-01

Thirring-Feynman's tensor field approach to gravitation opens new understanding on the physics of gravitational interaction and stimulates novel experiments on the nature of gravity. According to Field Gravity, the universal gravity force is caused by exchange of gravitons - the quanta of gravity field. Energy of this field is well-defined and excludes the singularity. All classical relativistic effects are the same as in General Relativity. The intrinsic scalar (spin 0) part of gravity field corresponds to ``antigravity'' and only together with the pure tensor (spin 2) part gives the usual Newtonian force. Laboratory and astrophysical experiments which may test the predictions of FG, will be performed in near future. In particular, observations at gravity observatories with bar and interferometric detectors, like Explorer, Nautilus, LIGO and VIRGO, will check the predicted scalar gravitational waves from supernova explosions. New types of cosmological models in Minkowski space are possible too.

Calculation of the Maxwell stress tensor and the Poisson-Boltzmann force on a solvated molecular surface using hypersingular boundary integrals

NASA Astrophysics Data System (ADS)

Lu, Benzhuo; Cheng, Xiaolin; Hou, Tingjun; McCammon, J. Andrew

2005-08-01

The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress tensor. Compared with the variational method (also in a BEM frame) that we proposed recently, this method provides an even more efficient way to calculate the full intermolecular electrostatic interaction force, especially for macromolecular systems. Thus, it may be more suitable for the application of Brownian dynamics methods to study the dynamics of protein/protein docking as well as the assembly of large 3D architectures involving many diffusing subunits. The method has been tested on two simple cases to demonstrate its reliability and efficiency, and also compared with our previous variational method used in BEM.

Non-double-couple earthquakes. 1. Theory

USGS Publications Warehouse

Julian, B.R.; Miller, A.D.; Foulger, G.R.

1998-01-01

Historically, most quantitative seismological analyses have been based on the assumption that earthquakes are caused by shear faulting, for which the equivalent force system in an isotropic medium is a pair of force couples with no net torque (a 'double couple,' or DC). Observations of increasing quality and coverage, however, now resolve departures from the DC model for many earthquakes and find some earthquakes, especially in volcanic and geothermal areas, that have strongly non-DC mechanisms. Understanding non-DC earthquakes is important both for studying the process of faulting in detail and for identifying nonshear-faulting processes that apparently occur in some earthquakes. This paper summarizes the theory of 'moment tensor' expansions of equivalent-force systems and analyzes many possible physical non-DC earthquake processes. Contrary to long-standing assumption, sources within the Earth can sometimes have net force and torque components, described by first-rank and asymmetric second-rank moment tensors, which must be included in analyses of landslides and some volcanic phenomena. Non-DC processes that lead to conventional (symmetric second-rank) moment tensors include geometrically complex shear faulting, tensile faulting, shear faulting in an anisotropic medium, shear faulting in a heterogeneous region (e.g., near an interface), and polymorphic phase transformations. Undoubtedly, many non-DC earthquake processes remain to be discovered. Progress will be facilitated by experimental studies that use wave amplitudes, amplitude ratios, and complete waveforms in addition to wave polarities and thus avoid arbitrary assumptions such as the absence of volume changes or the temporal similarity of different moment tensor components.

Advanced Computational Techniques in Regional Wave Studies

DTIC Science & Technology

1990-01-03

UiNCL.ASSIriEDIUNLIMITED C SAME AS RPT. C DTIC USERS CUNCLASSIFIED ; a 𔃾AM OF RE.;PONSIBL- E INOIVIDIJAL 22D. TELEPHCNE NUMBER 22c. OFFICE SYMBOL...this system is right We define the components of the time dependent force handed). Then, e ,, e ., and e , are the unit vectors moment tensor as towards...are constants representing the components of the 1 , ,( ,, - second order seismic moment tensor M, usually termed , M,- "(x,/,,t ,( E ,’ the moment tensor

Casimir effect in presence of spontaneous Lorentz symmetry breaking

NASA Astrophysics Data System (ADS)

Escobar, C. A.

2018-01-01

The Casimir effect is one of the most remarkable consequences of the nonzero vacuum energy predicted by quantum field theory. In this contribution we study the Lorentz-violation effects of the minimal standard-model extension on the Casimir force between two parallel conducting plates in the vacuum. Using a perturbative method, we compute the relevant Green’s function which satisfies given boundary conditions. The standard point-splitting technique allow us to express the vacuum expectation value of the stress-energy tensor in terms of this Green’s function. Finally, we study the Casimir energy and the Casimir force paying particular attention to the quantum effects as approaching the plates.

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…

Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks

DOE PAGES

Park, Jong-Kyu; Logan, Nikolas C.

2017-03-01

Toroidal torque is one of the most important consequences of non-axisymmetric fields in tokamaks. The well-known neoclassical toroidal viscosity (NTV) is due to the second-order toroidal force from anisotropic pressure tensor in the presence of these asymmetries. This work shows that the first-order toroidal force originating from the same anisotropic pressure tensor, despite having no flux surface average, can significantly modify the local perturbed force balance and thus must be included in perturbed equilibrium self-consistent with NTV. The force operator with an anisotropic pressure tensor is not self-adjoint when the NTV torque is finite and thus is solved directly formore » each component. This approach yields a modified, non-self-adjoint Euler-Lagrange equation that can be solved using a variety of common drift-kinetic models in generalized tokamak geometry. The resulting energy and torque integral provides a unique way to construct a torque response matrix, which contains all the information of self-consistent NTV torque profiles obtainable by applying non-axisymmetric fields to the plasma. This torque response matrix can then be used to systematically optimize non-axisymmetric field distributions for desired NTV profiles. Published by AIP Publishing.« 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

Source characterization for an explosion during the 2009 eruption of Redoubt Volcano from very-long-period seismic waves

USGS Publications Warehouse

Haney, Matthew M.; Chouet, Bernard A.; Dawson, Phillip B.; Power, John A.

2013-01-01

The 2009 eruption of Redoubt produced several very-long-period (VLP) signals associated with explosions. We invert for the source location and mechanism of an explosion at Redoubt volcano using waveform methods applied to broadband recordings. Such characterization of the source carries information on the geometry of the conduit and the physics of the explosion process. Inversions are carried out assuming the volcanic source can be modeled as a point source, with mechanisms described by a) a set of 3 orthogonal forces, b) a moment tensor consisting of force couples, and c) both forces and moment tensor components. We find that the source of the VLP seismic waves during the explosion is well-described by either a combined moment/force source located northeast of the crater and at an elevation of 1.6 km ASL or a moment source at an elevation of 800 m to the southwest of the crater. The moment tensors for the solutions with moment and force and moment-only share similar characteristics. The source time functions for both moment tensors begin with inflation (pressurization) and execute two cycles of deflation-reinflation (depressurization–repressurization). Although the moment/force source provides a better fit to the data, we find that owing to the limited coverage of the broadband stations at Redoubt the moment-only source is the more robust and reliable solution. Based on the moment-only solution, we estimate a volume change of 19,000 m3 and a pressure change of 7 MPa in a dominant sill and an out-of-phase volume change of 5000 m3 and pressure change of 1.8 MPa in a subdominant dike at the source location. These results shed new light on the magmatic plumbing system beneath Redoubt and complement previous studies on Vulcanian explosions at other volcanoes.

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.

Ponderomotive forces in electrodynamics of moving media: The Minkowski and Abraham approaches

NASA Astrophysics Data System (ADS)

Nesterenko, V. V.; Nesterenko, A. V.

2016-09-01

In the general setting of the problem, the explicit compact formulae are derived for the ponderomotive forces in the macroscopic electrodynamics of moving media in the Minkowski and Abraham approaches. Taking account of the Minkowski constitutive relations and making use of a special representation for the Abraham energy-momentum tensor enable one to obtain a compact expression for the Abraham force in the case of arbitrary dependence of the medium velocity on spatial coordinates and the time and for nonstationary external electromagnetic field. We term the difference between the ponderomotive forces in the Abraham and Minkowski approaches as the Abraham force not only under consideration of media at rest but also in the case of moving media. The Lorentz force is found which is exerted by external electromagnetic field on the conduction current in a medium, the covariant Ohm law, and the constitutive Minkowski relations being taken into account. The physical argumentation is traced for the definition of the 4-vector of the ponderomotive force as the 4-divergence of the energy-momentum tensor of electromagnetic field in a medium.

Metric-affine f (R ,T ) theories of gravity and their applications

NASA Astrophysics Data System (ADS)

Barrientos, E.; Lobo, Francisco S. N.; Mendoza, S.; Olmo, Gonzalo J.; Rubiera-Garcia, D.

2018-05-01

We study f (R ,T ) theories of gravity, where T is the trace of the energy-momentum tensor Tμ ν, with independent metric and affine connection (metric-affine theories). We find that the resulting field equations share a close resemblance with their metric-affine f (R ) relatives once an effective energy-momentum tensor is introduced. As a result, the metric field equations are second-order and no new propagating degrees of freedom arise as compared to GR, which contrasts with the metric formulation of these theories, where a dynamical scalar degree of freedom is present. Analogously to its metric counterpart, the field equations impose the nonconservation of the energy-momentum tensor, which implies nongeodesic motion and consequently leads to the appearance of an extra force. The weak field limit leads to a modified Poisson equation formally identical to that found in Eddington-inspired Born-Infeld gravity. Furthermore, the coupling of these gravity theories to perfect fluids, electromagnetic, and scalar fields, and their potential applications are discussed.

Newton-Cartan Gravity in Noninertial Reference Frames

NASA Astrophysics Data System (ADS)

Rodriguez, Leo; St. Germaine-Fuller, James; Wickramasekara, Sujeev

2015-03-01

We study Newton-Cartan gravity under transformations into all noninertial, nonrelativistic reference frames. These transformations form an infinite dimensional Lie group, called the Galilean line group, which contains as a subgroup the Galilei group. The fictitious forces of noninertial reference frames are encoded in the Cartan connection transformed under the Galilean line group. These fictitious forces, which are coordinate effects, do not contribute to the Ricci tensor. Only the 00-component of the Ricci tensor is non-zero and equals (4 π times) the matter density in all reference frames. While the Ricci field equation and Gauss' law are fulfilled by the physical matter density in inertial and linearly accelerating reference frames, in rotating reference frames Gauss' law holds for an effective mass density that differs from the physical matter density. This effective density has its origin in the simulated magnetic field of rotating frames, highlighting a striking difference between linearly and rotationally accelerating frames. The equations governing the simulated fields have the same form as Maxwell's equations, a surprising result given that these equations obey special relativity (and U (1) -gauge symmetry), rather than Galilean symmetry. This work was supported in part by the HHMI Undergraduate Science Education Award 52006298 and the Grinnell College Academic Affairs' CSFS and MAP programs.

Mass effects and internal space geometry in triatomic reaction dynamics

NASA Astrophysics Data System (ADS)

Yanao, Tomohiro; Koon, Wang S.; Marsden, Jerrold E.

2006-05-01

The effect of the distribution of mass in triatomic reaction dynamics is analyzed using the geometry of the associated internal space. Atomic masses are appropriately incorporated into internal coordinates as well as the associated non-Euclidean internal space metric tensor after a separation of the rotational degrees of freedom. Because of the non-Euclidean nature of the metric in the internal space, terms such as connection coefficients arise in the internal equations of motion, which act as velocity-dependent forces in a coordinate chart. By statistically averaging these terms, an effective force field is deduced, which accounts for the statistical tendency of geodesics in the internal space. This force field is shown to play a crucial role in determining mass-related branching ratios of isomerization and dissociation dynamics of a triatomic molecule. The methodology presented can be useful for qualitatively predicting branching ratios in general triatomic reactions, and may be applied to the study of isotope effects.

Geometrization of the Dirac theory of the electron

NASA Technical Reports Server (NTRS)

Fock, V.

1977-01-01

Using the concept of parallel displacement of a half vector, the Dirac equations are generally written in invariant form. The energy tensor is formed and both the macroscopic and quantum mechanic equations of motion are set up. The former have the usual form: divergence of the energy tensor equals the Lorentz force and the latter are essentially identical with those of the geodesic line.

Scalar Casimir densities and forces for parallel plates in cosmic string spacetime

NASA Astrophysics Data System (ADS)

Bezerra de Mello, E. R.; Saharian, A. A.; Abajyan, S. V.

2018-04-01

We analyze the Green function, the Casimir densities and forces associated with a massive scalar quantum field confined between two parallel plates in a higher dimensional cosmic string spacetime. The plates are placed orthogonal to the string, and the field obeys the Robin boundary conditions on them. The boundary-induced contributions are explicitly extracted in the vacuum expectation values (VEVs) of the field squared and of the energy-momentum tensor for both the single plate and two plates geometries. The VEV of the energy-momentum tensor, in additional to the diagonal components, contains an off diagonal component corresponding to the shear stress. The latter vanishes on the plates in special cases of Dirichlet and Neumann boundary conditions. For points outside the string core the topological contributions in the VEVs are finite on the plates. Near the string the VEVs are dominated by the boundary-free part, whereas at large distances the boundary-induced contributions dominate. Due to the nonzero off diagonal component of the vacuum energy-momentum tensor, in addition to the normal component, the Casimir forces have nonzero component parallel to the boundary (shear force). Unlike the problem on the Minkowski bulk, the normal forces acting on the separate plates, in general, do not coincide if the corresponding Robin coefficients are different. Another difference is that in the presence of the cosmic string the Casimir forces for Dirichlet and Neumann boundary conditions differ. For Dirichlet boundary condition the normal Casimir force does not depend on the curvature coupling parameter. This is not the case for other boundary conditions. A new qualitative feature induced by the cosmic string is the appearance of the shear stress acting on the plates. The corresponding force is directed along the radial coordinate and vanishes for Dirichlet and Neumann boundary conditions. Depending on the parameters of the problem, the radial component of the shear force can be either positive or negative.

Forces exerted by a correlated fluid on embedded inclusions.

PubMed

Bitbol, Anne-Florence; Fournier, Jean-Baptiste

2011-06-01

We investigate the forces exerted on embedded inclusions by a fluid medium with long-range correlations, described by an effective scalar field theory. Such forces are the basis for the medium-mediated Casimir-like force. To study these forces beyond thermal average, it is necessary to define them in each microstate of the medium. Two different definitions of these forces are currently used in the literature. We study the assumptions underlying them. We show that only the definition that uses the stress tensor of the medium gives the sought-after force exerted by the medium on an embedded inclusion. If a second inclusion is embedded in the medium, the thermal average of this force gives the usual Casimir-like force between the two inclusions. The other definition can be used in the different physical case of an object that interacts with the medium without being embedded in it. We show in a simple example that the two definitions yield different results for the variance of the Casimir-like force.

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

Unified tensor model for space-frequency spreading-multiplexing (SFSM) MIMO communication systems

NASA Astrophysics Data System (ADS)

de Almeida, André LF; Favier, Gérard

2013-12-01

This paper presents a unified tensor model for space-frequency spreading-multiplexing (SFSM) multiple-input multiple-output (MIMO) wireless communication systems that combine space- and frequency-domain spreadings, followed by a space-frequency multiplexing. Spreading across space (transmit antennas) and frequency (subcarriers) adds resilience against deep channel fades and provides space and frequency diversities, while orthogonal space-frequency multiplexing enables multi-stream transmission. We adopt a tensor-based formulation for the proposed SFSM MIMO system that incorporates space, frequency, time, and code dimensions by means of the parallel factor model. The developed SFSM tensor model unifies the tensorial formulation of some existing multiple-access/multicarrier MIMO signaling schemes as special cases, while revealing interesting tradeoffs due to combined space, frequency, and time diversities which are of practical relevance for joint symbol-channel-code estimation. The performance of the proposed SFSM MIMO system using either a zero forcing receiver or a semi-blind tensor-based receiver is illustrated by means of computer simulation results under realistic channel and system parameters.

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

Full-Wave Tomographic and Moment Tensor Inversion Based on 3D Multigrid Strain Green’s Tensor Databases

DTIC Science & Technology

2014-04-30

grade metamorphic rocks on the southern slope of the Himalaya is imaged as a band of high velocity anomaly...velocity structures closely follow the geological features. As an indication of resolution, the ductile extrusion of high-grade metamorphic rocks on...MATERIEL COMMAND KIRTLAND AIR FORCE BASE, NM 87117-5776 DTIC COPY NOTICE AND SIGNATURE PAGE Using Government drawings, specifications, or other data

Monte Carlo Volcano Seismic Moment Tensors

NASA Astrophysics Data System (ADS)

Waite, G. P.; Brill, K. A.; Lanza, F.

2015-12-01

Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.

Theory of the Maxwell pressure tensor and the tension in a water bridge.

PubMed

Widom, A; Swain, J; Silverberg, J; Sivasubramanian, S; Srivastava, Y N

2009-07-01

A water bridge refers to an experimental "flexible cable" made up of pure de-ionized water, which can hang across two supports maintained with a sufficiently large voltage difference. The resulting electric fields within the de-ionized water flexible cable maintain a tension that sustains the water against the downward force of gravity. A detailed calculation of the water bridge tension will be provided in terms of the Maxwell pressure tensor in a dielectric fluid medium. General properties of the dielectric liquid pressure tensor are discussed along with unusual features of dielectric fluid Bernoulli flows in an electric field. The "frictionless" Bernoulli flow is closely analogous to that of a superfluid.

Friction on a granular-continuum interface: Effects of granular media

NASA Astrophysics Data System (ADS)

Ecke, Robert; Geller, Drew

We consider the frictional interactions of two soft plates with interposed granular material subject to normal and shear forces. The plates are soft photo-elastic material, have length 50 cm, and are separated by a gap of variable width from 0 to 20 granular particle diameters. The granular materials are two-dimensional rods that are bi-dispersed in size to prevent crystallization. Different rod materials with frictional coefficients between 0 . 04 < μ < 0 . 5 are used to explore the effects of inter-granular friction on the effective friction of a granular medium. The gap is varied to test the dependence of the friction coefficient on the thickness of the granular layer. Because the soft plates absorb most of the displacement associated with the compressional normal force, the granular packing fractions are close to a jamming threshold, probably a shear jamming criterion. The overall shear and normal forces are measured using force sensors and the local strain tensor over a central portion of the gap is obtained using relative displacements of fiducial markers on the soft elastic material. These measurements provide a good characterization of the global and local forces giving rise to an effective friction coefficient. Funded by US DOE LDRD Program.

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.

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.

Nonsymmetric gravity theories: Inconsistencies and a cure

NASA Astrophysics Data System (ADS)

Damour, T.; Deser, S.; McCarthy, J.

1993-02-01

Motivated by the apparent dependence of string σ models on the sum of spacetime metric and antisymmetric tensor fields, we reconsider gravity theories constructed from a nonsymmetric metric. We first show, by expanding in powers of the antisymmetric field, that all such ``geometrical'' theories homogeneous in second derivatives violate standard physical requirements: ghost freedom, absence of algebraic inconsistencies, or continuity of degree-of-freedom content. This no-go result applies in particular to the old unified theory of Einstein and its recent avatars. However, we find that the addition of nonderivative, ``cosmological'' terms formally restores consistency by giving a mass to the antisymmetric tensor field, thereby transmuting it into a fifth-force-like massive vector but with novel possible matter couplings. The resulting macroscopic models also exhibit ``van der Waals''-type gravitational effects, and may provide useful phenomenological foils to general relativity.

A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part II: General formulation

NASA Astrophysics Data System (ADS)

Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.; Tang, Qi

2017-08-01

A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This added-mass partitioned (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this second part of a two-part series, the general formulation of the AMP scheme is presented including the form of the AMP interface conditions and added-damping tensors for general geometries. A fully second-order accurate implementation of the AMP scheme is developed in two dimensions based on a fractional-step method for the incompressible Navier-Stokes equations using finite difference methods and overlapping grids to handle the moving geometry. The numerical scheme is verified on a number of difficult benchmark problems.

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.

New cellular automaton model for magnetohydrodynamics

NASA Technical Reports Server (NTRS)

Chen, Hudong; Matthaeus, William H.

1987-01-01

A new type of two-dimensional cellular automation method is introduced for computation of magnetohydrodynamic fluid systems. Particle population is described by a 36-component tensor referred to a hexagonal lattice. By appropriate choice of the coefficients that control the modified streaming algorithm and the definition of the macroscopic fields, it is possible to compute both Lorentz-force and magnetic-induction effects. The method is local in the microscopic space and therefore suited to massively parallel computations.

Small-scale anisotropy induced by spectral forcing and by rotation in non-helical and helical turbulence

NASA Astrophysics Data System (ADS)

Vallefuoco, Donato; Naso, Aurore; Godeferd, Fabien S.

2018-02-01

We study the effect of large-scale spectral forcing on the scale-dependent anisotropy of the velocity field in direct numerical simulations of homogeneous turbulence. ABC-type forcing and helical or non-helical Euler-type forcing are considered. We propose a scale-dependent characterisation of anisotropy based on a modal decomposition of the two-point velocity tensor spectrum. This produces direction-dependent spectra of energy, helicity and polarisation. We examine the conditions that allow anisotropy to develop in the small scales due to forcing and we show that the theoretically expected isotropy is not exactly obtained, even in the smallest scales, for ABC and helical Euler forcings. When adding rotation, the anisotropy level in ABC-forced simulations is similar to that of lower Rossby number Euler-forced runs. Moreover, even at low rotation rate, the natural anisotropy induced by the Coriolis force is visible at all scales, and two distinct wavenumber ranges appear from our fine-grained characterisation, not separated by the Zeman scale but by a scale where rotation and dissipation are balanced.

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…

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.

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

Casimir effect for parallel plates in a Friedmann-Robertson-Walker universe

NASA Astrophysics Data System (ADS)

Bezerra de Mello, E. R.; Saharian, A. A.; Setare, M. R.

2017-03-01

We evaluate the Hadamard function, the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor for a massive scalar field with a general curvature coupling parameter in the geometry of two parallel plates on a spatially flat Friedmann-Robertson-Walker background with a general scale factor. On the plates, the field operator obeys the Robin boundary conditions with the coefficients depending on the scale factor. In all the spatial regions, the VEVs are decomposed into the boundary-free and boundary-induced contributions. Unlike the problem with the Minkowski bulk, in the region between the plates, the normal stress is not homogeneous and does not vanish in the geometry of a single plate. Near the plates, it has different signs for accelerated and decelerated expansions of the Universe. The VEV of the energy-momentum tensor, in addition to the diagonal components, has a nonzero off-diagonal component describing an energy flux along the direction normal to the boundaries. Expressions are derived for the Casimir forces acting on the plates. Depending on the Robin coefficients and on the vacuum state, these forces can be either attractive or repulsive. An important difference from the corresponding result in the Minkowski bulk is that the forces on the separate plates, in general, are different if the corresponding Robin coefficients differ. We give the applications of general results for the class of α vacua in the de Sitter bulk. It is shown that, compared with the Bunch-Davies vacuum state, the Casimir forces for a given α vacuum may change the sign.

Spacetime geodesy and the LAGEOS-3 satellite experiment

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

Miller, W.A.; Chen, Kaiyou; Habib, S.

1996-04-01

This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). LAGEOS-1 is a dense spherical satellite whose tracking accuracy is such as to yield a medium-term inertial reference frame and that is used as an adjunct to more difficult and more data-intensive absolute frame measurements. LAGEOS-3, an identical satellite to be launched into an orbit complementary to that of LAGEOS-1, would experience an equal and opposite classical precession to that of LAGEOS- 1. Besides providing a more accurate real-time measurement of the earth`s length of day and polar wobble,more » this paired-satellite system would provide the first direct measurement of the general relativistic frame-dragging effect. Of the five dominant error sources in this experiment, the largest one involves surface forces on the satellite and their consequent impact on the orbital nodal precession. The surface forces are a function of the spin dynamics of the satellite. We have modeled the spin dynamics of a LAGEOS-type satellite and used this spin model to estimate the impact of the thermal rocketing effect on the LAGEOS-3 experiment. We have also performed an analytic tensor expansion of Synge`s world function to better reveal the nature of the predicted frame-dragging effect. We showed that this effect is not due to the Riemann curvature tensor, but rather is a ``potential effect`` arising from the acceleration of the world lines in the Kerr spacetime geometry.« less

Gas-induced friction and diffusion of rigid rotors

NASA Astrophysics Data System (ADS)

Martinetz, Lukas; Hornberger, Klaus; Stickler, Benjamin A.

2018-05-01

We derive the Boltzmann equation for the rotranslational dynamics of an arbitrary convex rigid body in a rarefied gas. It yields as a limiting case the Fokker-Planck equation accounting for friction, diffusion, and nonconservative drift forces and torques. We provide the rotranslational friction and diffusion tensors for specular and diffuse reflection off particles with spherical, cylindrical, and cuboidal shape, and show that the theory describes thermalization, photophoresis, and the inverse Magnus effect in the free molecular regime.

The drift force on an object in an inviscid weakly-varying rotational flow

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

Wallis, G.B.

The force on any stationary object in an inviscid incompressible extensive steady flow is derived in terms of the added mass tensor and gradient of velocity of the undisturbed fluid. Taylor`s theorem is extended to flows with weak vorticity. There are possible applications to constitutive equations for two-phase flow.

Laser pumping Cs atom magnetometer of theory research based on gradient tensor measuring

NASA Astrophysics Data System (ADS)

Yang, Zhang; Chong, Kang; Wang, Qingtao; Lei, Cheng; Zheng, Caiping

2011-02-01

At present, due to space exploration, military technology, geological exploration, magnetic navigation, medical diagnosis and biological magnetic fields study of the needs of research and development, the magnetometer is given strong driving force. In this paper, it will discuss the theoretical analysis and system design of laser pumping cesium magnetometer, cesium atomic energy level formed hyperfine structure with the I-J coupling, the hyperfine structure has been further split into Zeeman sublevels for the effects of magnetic field. To use laser pump and RF magnetic field make electrons transition in the hyperfine structure to produce the results of magneto-optical double resonance, and ultimately through the resonant frequency will be able to achieve accurate value of the external magnetic field. On this basis, we further have a discussion about magnetic gradient tensor measuring method. To a large extent, it increases the magnetic field measurement of information.

Ponderomotive dynamics of waves in quasiperiodically modulated media

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

Ruiz, D. E.; Dodin, I. Y.

Similarly to how charged particles experience time-averaged ponderomotive forces in high-frequency fields, linear waves also experience time-averaged refraction in modulated media. We propose a covariant variational theory of this ponderomotive effect on waves for a general nondissipative linear medium. Using the Weyl calculus, our formulation accommodates waves with temporal and spatial period comparable to that of the modulation (provided that parametric resonances are avoided). This theory also shows that any wave is, in fact, a polarizable object that contributes to the linear dielectric tensor of the ambient medium. Furthermore, the dynamics of quantum particles is subsumed as a special case.more » As an illustration, ponderomotive Hamiltonians of quantum particles and photons are calculated within a number of models. We also explain a fundamental connection between these results and the well-known electrostatic dielectric tensor of quantum plasmas.« less

Ponderomotive dynamics of waves in quasiperiodically modulated media

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2017-03-14

Similarly to how charged particles experience time-averaged ponderomotive forces in high-frequency fields, linear waves also experience time-averaged refraction in modulated media. We propose a covariant variational theory of this ponderomotive effect on waves for a general nondissipative linear medium. Using the Weyl calculus, our formulation accommodates waves with temporal and spatial period comparable to that of the modulation (provided that parametric resonances are avoided). This theory also shows that any wave is, in fact, a polarizable object that contributes to the linear dielectric tensor of the ambient medium. Furthermore, the dynamics of quantum particles is subsumed as a special case.more » As an illustration, ponderomotive Hamiltonians of quantum particles and photons are calculated within a number of models. We also explain a fundamental connection between these results and the well-known electrostatic dielectric tensor of quantum plasmas.« less

Fluid Registration of Diffusion Tensor Images Using Information Theory

PubMed Central

Chiang, Ming-Chang; Leow, Alex D.; Klunder, Andrea D.; Dutton, Rebecca A.; Barysheva, Marina; Rose, Stephen E.; McMahon, Katie L.; de Zubicaray, Greig I.; Toga, Arthur W.; Thompson, Paul M.

2008-01-01

We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or J-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the J-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data. PMID:18390342

One-dimensional reduction of viscous jets. I. Theory

NASA Astrophysics Data System (ADS)

Pitrou, Cyril

2018-04-01

We build a general formalism to describe thin viscous jets as one-dimensional objects with an internal structure. We present in full generality the steps needed to describe the viscous jets around their central line, and we argue that the Taylor expansion of all fields around that line is conveniently expressed in terms of symmetric trace-free tensors living in the two dimensions of the fiber sections. We recover the standard results of axisymmetric jets and we report the first and second corrections to the lowest order description, also allowing for a rotational component around the axis of symmetry. When applied to generally curved fibers, the lowest order description corresponds to a viscous string model whose sections are circular. However, when including the first corrections, we find that curved jets generically develop elliptic sections. Several subtle effects imply that the first corrections cannot be described by a rod model since it amounts to selectively discard some corrections. However, in a fast rotating frame, we find that the dominant effects induced by inertial and Coriolis forces should be correctly described by rod models. For completeness, we also recover the constitutive relations for forces and torques in rod models and exhibit a missing term in the lowest order expression of viscous torque. Given that our method is based on tensors, the complexity of all computations has been beaten down by using an appropriate tensor algebra package such as xAct, allowing us to obtain a one-dimensional description of curved viscous jets with all the first order corrections consistently included. Finally, we find a description for straight fibers with elliptic sections as a special case of these results, and recover that ellipticity is dynamically damped by surface tension. An application to toroidal viscous fibers is presented in the companion paper [Pitrou, Phys. Rev. E 97, 043116 (2018), 10.1103/PhysRevE.97.043116].

Transport coefficients for the shear dynamo problem at small Reynolds numbers.

PubMed

Singh, Nishant K; Sridhar, S

2011-05-01

We build on the formulation developed in S. Sridhar and N. K. Singh [J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients α(il) and η(il) are derived. We prove that when the velocity field is nonhelical, the transport coefficient α(il) vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X(3) and time τ; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Rädler, M. Rheinhardt, and P. J. Käpylä [Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor η(il)(τ). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter. © 2011 American Physical Society

Transport coefficients for the shear dynamo problem at small Reynolds numbers

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

Singh, Nishant K.; Joint Astronomy Programme, Indian Institute of Science, Bangalore 560 012; Sridhar, S.

2011-05-15

We build on the formulation developed in S. Sridhar and N. K. Singh [J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients {alpha}{sub il} and {eta}{sub iml} are derived. We prove that when the velocity field is nonhelical, the transport coefficient {alpha}{sub il} vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynoldsmore » number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X{sub 3} and time {tau}; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Raedler, M. Rheinhardt, and P. J. Kaepylae [Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor {eta}{sub ij}({tau}). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.« less

Chameleons with field-dependent couplings

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

Brax, Philippe; Bruck, Carsten van de; Mota, David F.

2010-10-15

Certain scalar-tensor theories exhibit the so-called chameleon mechanism, whereby observational signatures of scalar fields are hidden by a combination of self-interactions and interactions with ambient matter. Not all scalar-tensor theories exhibit such a chameleon mechanism, which has been originally found in models with inverse power runaway potentials and field-independent couplings to matter. In this paper we investigate field theories with field-dependent couplings and a power-law potential for the scalar field. We show that the theory indeed is a chameleon field theory. We find the thin-shell solution for a spherical body and investigate the consequences for Eoet-Wash experiments, fifth-force searches andmore » Casimir-force experiments. Requiring that the scalar field evades gravitational tests, we find that the coupling is sensitive to a mass scale which is of order of the Hubble scale today.« less

Nuclear-relaxed elastic and piezoelectric constants of materials: Computational aspects of two quantum-mechanical approaches.

PubMed

Erba, Alessandro; Caglioti, Dominique; Zicovich-Wilson, Claudio Marcelo; Dovesi, Roberto

2017-02-15

Two alternative approaches for the quantum-mechanical calculation of the nuclear-relaxation term of elastic and piezoelectric tensors of crystalline materials are illustrated and their computational aspects discussed: (i) a numerical approach based on the geometry optimization of atomic positions at strained lattice configurations and (ii) a quasi-analytical approach based on the evaluation of the force- and displacement-response internal-strain tensors as combined with the interatomic force-constant matrix. The two schemes are compared both as regards their computational accuracy and performance. The latter approach, not being affected by the many numerical parameters and procedures of a typical quasi-Newton geometry optimizer, constitutes a more reliable and robust mean to the evaluation of such properties, at a reduced computational cost for most crystalline systems. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Experimental Validation of a Time-Accurate Finite Element Model for Coupled Multibody Dynamics and Liquid Sloshing

DTIC Science & Technology

2007-04-16

velocity of the fluid mesh, P is the relative pressure, xr is the position vector, τ is the deviatoric stress tensor, D is the rate of deformation...corresponds to a slip factor of zero. The slip factor determines how much of the fluid and structure forces are mutually exchanged. Equations 22 and 23...updated from last to first. viii.Average the fluid pressure (This step eliminates the pressure checker-boarding effect and allows use of equal

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.

Emergent gravity of fractons: Mach's principle revisited

NASA Astrophysics Data System (ADS)

Pretko, Michael

2017-07-01

Recent work has established the existence of stable quantum phases of matter described by symmetric tensor gauge fields, which naturally couple to particles of restricted mobility, such as fractons. We focus on a minimal toy model of a rank 2 tensor gauge field, consisting of fractons coupled to an emergent graviton (massless spin-2 excitation). We show how to reconcile the immobility of fractons with the expected gravitational behavior of the model. First, we reformulate the fracton phenomenon in terms of an emergent center of mass quantum number, and we show how an effective attraction arises from the principles of locality and conservation of center of mass. This interaction between fractons is always attractive and can be recast in geometric language, with a geodesiclike formulation, thereby satisfying the expected properties of a gravitational force. This force will generically be short-ranged, but we discuss how the power-law behavior of Newtonian gravity can arise under certain conditions. We then show that, while an isolated fracton is immobile, fractons are endowed with finite inertia by the presence of a large-scale distribution of other fractons, in a concrete manifestation of Mach's principle. Our formalism provides suggestive hints that matter plays a fundamental role, not only in perturbing, but in creating the background space in which it propagates.

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.

Gravitational radiation from compact binary systems in screened modified gravity

NASA Astrophysics Data System (ADS)

Zhang, Xing; Liu, Tan; Zhao, Wen

2017-05-01

Screened modified gravity (SMG) is a kind of scalar-tensor theory with screening mechanisms, which can suppress the fifth force in dense regions and allow theories to evade the solar system and laboratory tests. In this paper, we investigate how the screening mechanisms in SMG affect the gravitational radiation damping effects, calculate in detail the rate of the energy loss due to the emission of tensor and scalar gravitational radiations, and derive their contributions to the change in the orbital period of the binary system. We find that the scalar radiation depends on the screened parameters and the propagation speed of scalar waves, and the scalar dipole radiation dominates the orbital decay of the binary system. For strongly self-gravitating bodies, all effects of scalar sector are strongly suppressed by the screening mechanisms in SMG. By comparing our results to observations of binary system PSR J 1738 +0333 , we place the stringent constraints on the screening mechanisms in SMG. As an application of these results, we focus on three specific models of SMG (chameleon, symmetron, and dilaton), and derive the constraints on the model parameters, respectively.

Proton-Proton Scattering at 105 Mev and 75 Mev

DOE R&D Accomplishments Database

Birge, R. W.; Kruse, U. E.; Ramsey, N. F.

1951-01-31

The scattering of protons by protons provides an important method for studying the nature of nuclear forces. Recent proton-proton scattering experiments at energies as high as thirty Mev{sup 1} have failed to show any appreciable contribution to the cross section from higher angular momentum states, but it is necessary to bring in tensor forces to explain the magnitude of the observed cross section.

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.

Waveform inversion of oscillatory signatures in long-period events beneath volcanoes

USGS Publications Warehouse

Kumagai, H.; Chouet, B.A.; Nakano, M.

2002-01-01

The source mechanism of long-period (LP) events is examined using synthetic waveforms generated by the acoustic resonance of a fluid-filled crack. We perform a series of numerical tests in which the oscillatory signatures of synthetic LP waveforms are used to determine the source time functions of the six moment tensor components from waveform inversions assuming a point source. The results indicate that the moment tensor representation is valid for the odd modes of crack resonance with wavelengths 2L/n, 2W/n, n = 3, 5, 7, ..., where L and W are the crack length and width, respectively. For the even modes with wavelengths 2L/n, 2W/n, n = 2, 4, 6,..., a generalized source representation using higher-order tensors is required, although the efficiency of seismic waves radiated by the even modes is expected to be small. We apply the moment tensor inversion to the oscillatory signatures of an LP event observed at Kusatsu-Shirane Volcano, central Japan. Our results point to the resonance of a subhorizontal crack located a few hundred meters beneath the summit crater lakes. The present approach may be useful to quantify the source location, geometry, and force system of LP events, and opens the way for moment tensor inversions of tremor.

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure.

PubMed

Muhlestein, Michael B; Haberman, Michael R

2016-08-01

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed.

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure

PubMed Central

Haberman, Michael R.

2016-01-01

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed. PMID:27616932

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure

NASA Astrophysics Data System (ADS)

Muhlestein, Michael B.; Haberman, Michael R.

2016-08-01

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed.

Theory and computation of general force balance in non-axisymmetric tokamak equilibria

NASA Astrophysics Data System (ADS)

Park, Jong-Kyu; Logan, Nikolas; Wang, Zhirui; Kim, Kimin; Boozer, Allen; Liu, Yueqiang; Menard, Jonathan

2014-10-01

Non-axisymmetric equilibria in tokamaks can be effectively described by linearized force balance. In addition to the conventional isotropic pressure force, there are three important components that can strongly contribute to the force balance; rotational, anisotropic tensor pressure, and externally given forces, i.e. ∇ --> p + ρv-> . ∇ --> v-> + ∇ --> . <-->Π + f-> = j-> × B-> , especially in, but not limited to, high β and rotating plasmas. Within the assumption of nested flux surfaces, Maxwell equations and energy minimization lead to the modified-generalized Newcomb equation for radial displacements with simple algebraic relations for perpendicular and parallel displacements, including an inhomogeneous term if any of the forces are not explicitly dependent on displacements. The general perturbed equilibrium code (GPEC) solves this force balance consistent with energy and torque given by external perturbations. Local and global behaviors of solutions will be discussed when ∇ --> . <-->Π is solved by the semi-analytic code PENT and will be compared with MARS-K. Any first-principle transport code calculating ∇ --> . <-->Π or f-> , e.g. POCA, can also be incorporated without demanding iterations. This work was supported by DOE Contract DE-AC02-09CH11466.

Minkowski momentum resulting from a vacuum-medium mapping procedure, and a brief review of Minkowski momentum experiments

NASA Astrophysics Data System (ADS)

Brevik, Iver

2017-02-01

A discussion is given on the interpretation and physical importance of the Minkowski momentum in macroscopic electrodynamics (essential for the Abraham-Minkowski problem). We focus on the following two facets: (1) Adopting a simple dielectric model where the refractive index n is constant, we demonstrate by means of a mapping procedure how the electromagnetic field in a medium can be mapped into a corresponding field in vacuum. This mapping was presented many years ago (Brevik and Lautrup, 1970), but is apparently not well known. A characteristic property of this procedure is that it shows how naturally the Minkowski energy-momentum tensor fits into the canonical formalism. Especially the spacelike character of the electromagnetic total four-momentum for a radiation field (implying negative electromagnetic energy in some inertial frames), so strikingly demonstrated in the Cherenkov effect, is worth attention. (2) Our second objective is to give a critical analysis of some recent experiments on electromagnetic momentum. Care must here be taken in the interpretations: it is easy to be misled and conclude that an experiment is important for the energy-momentum problem, while what is demonstrated experimentally is merely the action of the Abraham-Minkowski force acting in surface layers or inhomogeneous regions. The Abraham-Minkowski force is common for the two energy-momentum tensors and carries no information about field momentum. As a final item, we propose an experiment that might show the existence of the Abraham force at high frequencies. This would eventually be a welcome optical analogue to the classic low-frequency 1975 Lahoz-Walker experiment.

Approximate arbitrary κ-state solutions of Dirac equation with Schiöberg and Manning-Rosen potentials within the coulomb-like Yukawa-like and generalized tensor interactions

NASA Astrophysics Data System (ADS)

Ikot, Akpan N.; Hassanabadi, Hassan; Obong, Hillary Patrick; Mehraban, H.; Yazarloo, Bentol Hoda

2015-07-01

The effects of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT) and generalized tensor (GLT) interactions are investigated in the Dirac theory with Schiöberg and Manning-Rosen potentials within the framework of spin and pseudospin symmetries using the Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions have been approximately obtained in the case of spin and pseudospin symmetries. We have also reported some numerical results and figures to show the effects these tensor interactions.

Higgs mechanism and the added-mass effect.

PubMed

Krishnaswami, Govind S; Phatak, Sachin S

2015-04-08

In the Higgs mechanism, mediators of the weak force acquire masses by interacting with the Higgs condensate, leading to a vector boson mass matrix. On the other hand, a rigid body accelerated through an inviscid, incompressible and irrotational fluid feels an opposing force linearly related to its acceleration, via an added-mass tensor. We uncover a striking physical analogy between the two effects and propose a dictionary relating them. The correspondence turns the gauge Lie algebra into the space of directions in which the body can move, encodes the pattern of gauge symmetry breaking in the shape of an associated body and relates symmetries of the body to those of the scalar vacuum manifold. The new viewpoint is illustrated with numerous examples, and raises interesting questions, notably on the fluid analogues of the broken symmetry and Higgs particle, and the field-theoretic analogue of the added mass of a composite body.

Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.

PubMed

Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N

2017-05-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

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.

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.

Frequency shift, damping, and tunneling current coupling with quartz tuning forks in noncontact atomic force microscopy

NASA Astrophysics Data System (ADS)

Nony, Laurent; Bocquet, Franck; Para, Franck; Loppacher, Christian

2016-09-01

A combined experimental and theoretical approach to the coupling between frequency-shift (Δ f ) , damping, and tunneling current (It) in combined noncontact atomic force microscopy/scanning tunneling microscopy using quartz tuning forks (QTF)-based probes is reported. When brought into oscillating tunneling conditions, the tip located at the QTF prong's end radiates an electromagnetic field which couples to the QTF prong motion via its piezoelectric tensor and loads its electrodes by induction. Our approach explains how those It-related effects ultimately modify the Δ f and the damping measurements. This paradigm to the origin of the coupling between It and the nc-AFM regular signals relies on both the intrinsic piezoelectric nature of the quartz constituting the QTF and its electrodes design.

Tensor-based spatiotemporal saliency detection

NASA Astrophysics Data System (ADS)

Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen

2018-03-01

This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.

Characterisation of the turbulent electromotive force and its magnetically-mediated quenching in a global EULAG-MHD simulation of solar convection

NASA Astrophysics Data System (ADS)

Simard, Corinne; Charbonneau, Paul; Dubé, Caroline

2016-10-01

We perform a mean-field analysis of the EULAG-MHD millenium simulation of global magnetohydrodynamical convection presented in Passos and Charbonneau (2014). The turbulent electromotive force (emf) operating in the simulation is assumed to be linearly related to the cyclic axisymmetric mean magnetic field and its first spatial derivatives. At every grid point in the simulation's meridional plane, this assumed relationship involves 27 independent tensorial coefficients. Expanding on Racine et al. (2011), we extract these coefficients from the simulation data through a least-squares minimization procedure based on singular value decomposition. The reconstructed α -tensor shows good agreement with that obtained by Racine et al. (2011), who did not include derivatives of the mean-field in their fit, as well as with the α -tensor extracted by Augustson et al. (2015) from a distinct ASH MHD simulation. The isotropic part of the turbulent magnetic diffusivity tensor β is positive definite and reaches values of 5.0 ×107 m2 s-1 in the middle of the convecting fluid layers. The spatial variations of both αϕϕ and βϕϕ component are well reproduced by expressions obtained under the Second Order Correlation Approximation, with a good matching of amplitude requiring a turbulent correlation time about five times smaller than the estimated turnover time of the small-scale turbulent flow. By segmenting the simulation data into epochs of magnetic cycle minima and maxima, we also measure α - and β -quenching. We find the magnetic quenching of the α -effect to be driven primarily by a reduction of the small-scale flow's kinetic helicity, with variations of the current helicity playing a lesser role in most locations in the simulation domain. Our measurements of turbulent diffusivity quenching are restricted to the βϕϕ component, but indicate a weaker quenching, by a factor of ≃ 1.36, than of the α -effect, which in our simulation drops by a factor of three between the minimum and maximum phases of the magnetic cycle.

The TensorMol-0.1 model chemistry: a neural network augmented with long-range physics.

PubMed

Yao, Kun; Herr, John E; Toth, David W; Mckintyre, Ryker; Parkhill, John

2018-02-28

Traditional force fields cannot model chemical reactivity, and suffer from low generality without re-fitting. Neural network potentials promise to address these problems, offering energies and forces with near ab initio accuracy at low cost. However a data-driven approach is naturally inefficient for long-range interatomic forces that have simple physical formulas. In this manuscript we construct a hybrid model chemistry consisting of a nearsighted neural network potential with screened long-range electrostatic and van der Waals physics. This trained potential, simply dubbed "TensorMol-0.1", is offered in an open-source Python package capable of many of the simulation types commonly used to study chemistry: geometry optimizations, harmonic spectra, open or periodic molecular dynamics, Monte Carlo, and nudged elastic band calculations. We describe the robustness and speed of the package, demonstrating its millihartree accuracy and scalability to tens-of-thousands of atoms on ordinary laptops. We demonstrate the performance of the model by reproducing vibrational spectra, and simulating the molecular dynamics of a protein. Our comparisons with electronic structure theory and experimental data demonstrate that neural network molecular dynamics is poised to become an important tool for molecular simulation, lowering the resource barrier to simulating chemistry.

R2 dark energy in the laboratory

NASA Astrophysics Data System (ADS)

Brax, Philippe; Valageas, Patrick; Vanhove, Pierre

2018-05-01

We analyze the role, on large cosmological scales and laboratory experiments, of the leading curvature squared contributions to the low-energy effective action of gravity. We argue for a natural relationship c0λ2≃1 at low energy between the R2 coefficients c0 of the Ricci scalar squared term in this expansion and the dark energy scale Λ =(λ MPl)4 in four-dimensional Planck mass units. We show how the compatibility between the acceleration of the expansion rate of the Universe, local tests of gravity and the quantum stability of the model all converge to select such a relationship up to a coefficient which should be determined experimentally. When embedding this low-energy theory of gravity into candidates for its ultraviolet completion, we find that the proposed relationship is guaranteed in string-inspired supergravity models with modulus stabilization and supersymmetry breaking leading to de Sitter compactifications. In this case, the scalar degree of freedom of R2 gravity is associated to a volume modulus. Once written in terms of a scalar-tensor theory, the effective theory corresponds to a massive scalar field coupled with the universal strength β =1 /√{6 } to the matter stress-energy tensor. When the relationship c0λ2≃1 is realized, we find that on astrophysical scales and in cosmology the scalar field is ultralocal and therefore no effect arises on such large scales. On the other hand, the scalar field mass is tightly constrained by the nonobservation of fifth forces in torsion pendulum experiments such as Eöt-Wash. It turns out that the observation of the dark energy scale in cosmology implies that the scalar field could be detectable by fifth-force experiments in the near future.

Dispersive transport and symmetry of the dispersion tensor in porous media

NASA Astrophysics Data System (ADS)

Pride, Steven R.; Vasco, Donald W.; Flekkoy, Eirik G.; Holtzman, Ran

2017-04-01

The macroscopic laws controlling the advection and diffusion of solute at the scale of the porous continuum are derived in a general manner that does not place limitations on the geometry and time evolution of the pore space. Special focus is given to the definition and symmetry of the dispersion tensor that is controlling how a solute plume spreads out. We show that the dispersion tensor is not symmetric and that the asymmetry derives from the advective derivative in the pore-scale advection-diffusion equation. When flow is spatially variable across a voxel, such as in the presence of a permeability gradient, the amount of asymmetry can be large. As first shown by Auriault [J.-L. Auriault et al. Transp. Porous Med. 85, 771 (2010), 10.1007/s11242-010-9591-y] in the limit of low Péclet number, we show that at any Péclet number, the dispersion tensor Di j satisfies the flow-reversal symmetry Di j(+q ) =Dj i(-q ) where q is the mean flow in the voxel under analysis; however, Reynold's number must be sufficiently small that the flow is reversible when the force driving the flow changes sign. We also demonstrate these symmetries using lattice-Boltzmann simulations and discuss some subtle aspects of how to measure the dispersion tensor numerically. In particular, the numerical experiments demonstrate that the off-diagonal components of the dispersion tensor are antisymmetric which is consistent with the analytical dependence on the average flow gradients that we propose for these off-diagonal components.

Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows.

PubMed

Lin, Chuandong; Xu, Aiguo; Zhang, Guangcai; Luo, Kai Hong; Li, Yingjun

2017-11-01

A discrete Boltzmann model (DBM) is proposed to probe the Rayleigh-Taylor instability (RTI) in two-component compressible flows. Each species has a flexible specific-heat ratio and is described by one discrete Boltzmann equation (DBE). Independent discrete velocities are adopted for the two DBEs. The collision and force terms in the DBE account for the molecular collision and external force, respectively. Two types of force terms are exploited. In addition to recovering the modified Navier-Stokes equations in the hydrodynamic limit, the DBM has the capability of capturing detailed nonequilibrium effects. Furthermore, we use the DBM to investigate the dynamic process of the RTI. The invariants of tensors for nonequilibrium effects are presented and studied. For low Reynolds numbers, both global nonequilibrium manifestations and the growth rate of the entropy of mixing show three stages (i.e., the reducing, increasing, and then decreasing trends) in the evolution of the RTI. On the other hand, the early reducing tendency is suppressed and even eliminated for high Reynolds numbers. Relevant physical mechanisms are analyzed and discussed.

Electromotive force and large-scale magnetic dynamo in a turbulent flow with a mean shear.

PubMed

Rogachevskii, Igor; Kleeorin, Nathan

2003-09-01

An effect of sheared large-scale motions on a mean electromotive force in a nonrotating turbulent flow of a conducting fluid is studied. It is demonstrated that in a homogeneous divergence-free turbulent flow the alpha effect does not exist, however a mean magnetic field can be generated even in a nonrotating turbulence with an imposed mean velocity shear due to a "shear-current" effect. A mean velocity shear results in an anisotropy of turbulent magnetic diffusion. A contribution to the electromotive force related to the symmetric parts of the gradient tensor of the mean magnetic field (the kappa effect) is found in nonrotating turbulent flows with a mean shear. The kappa effect and turbulent magnetic diffusion reduce the growth rate of the mean magnetic field. It is shown that a mean magnetic field can be generated when the exponent of the energy spectrum of the background turbulence (without the mean velocity shear) is less than 2. The shear-current effect was studied using two different methods: the tau approximation (the Orszag third-order closure procedure) and the stochastic calculus (the path integral representation of the solution of the induction equation, Feynman-Kac formula, and Cameron-Martin-Girsanov theorem). Astrophysical applications of the obtained results are discussed.

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

DOE PAGES

Rai, Prashant; Sargsyan, Khachik; Najm, Habib; ...

2017-03-07

Here, 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 vibrationalmore » 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.« less

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

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

Rai, Prashant; Sargsyan, Khachik; Najm, Habib

Here, 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 vibrationalmore » 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.« less

Anharmonic effects in IR, Raman, and Raman optical activity spectra of alanine and proline zwitterions.

PubMed

Danecek, Petr; Kapitán, Josef; Baumruk, Vladimír; Bednárová, Lucie; Kopecký, Vladimír; Bour, Petr

2007-06-14

The difference spectroscopy of the Raman optical activity (ROA) provides extended information about molecular structure. However, interpretation of the spectra is based on complex and often inaccurate simulations. Previously, the authors attempted to make the calculations more robust by including the solvent and exploring the role of molecular flexibility for alanine and proline zwitterions. In the current study, they analyze the IR, Raman, and ROA spectra of these molecules with the emphasis on the force field modeling. Vibrational harmonic frequencies obtained with 25 ab initio methods are compared to experimental band positions. The role of anharmonic terms in the potential and intensity tensors is also systematically explored using the vibrational self-consistent field, vibrational configuration interaction (VCI), and degeneracy-corrected perturbation calculations. The harmonic approach appeared satisfactory for most of the lower-wavelength (200-1800 cm(-1)) vibrations. Modern generalized gradient approximation and hybrid density functionals, such as the common B3LYP method, provided a very good statistical agreement with the experiment. Although the inclusion of the anharmonic corrections still did not lead to complete agreement between the simulations and the experiment, occasional enhancements were achieved across the entire region of wave numbers. Not only the transitional frequencies of the C-H stretching modes were significantly improved but also Raman and ROA spectral profiles including N-H and C-H lower-frequency bending modes were more realistic after application of the VCI correction. A limited Boltzmann averaging for the lowest-frequency modes that could not be included directly in the anharmonic calculus provided a realistic inhomogeneous band broadening. The anharmonic parts of the intensity tensors (second dipole and polarizability derivatives) were found less important for the entire spectral profiles than the force field anharmonicities (third and fourth energy derivatives), except for a few weak combination bands which were dominated by the anharmonic tensor contributions.

Anharmonic effects in IR, Raman, and Raman optical activity spectra of alanine and proline zwitterions

NASA Astrophysics Data System (ADS)

Daněček, Petr; Kapitán, Josef; Baumruk, Vladimír; Bednárová, Lucie; Kopecký, Vladimír; Bouř, Petr

2007-06-01

The difference spectroscopy of the Raman optical activity (ROA) provides extended information about molecular structure. However, interpretation of the spectra is based on complex and often inaccurate simulations. Previously, the authors attempted to make the calculations more robust by including the solvent and exploring the role of molecular flexibility for alanine and proline zwitterions. In the current study, they analyze the IR, Raman, and ROA spectra of these molecules with the emphasis on the force field modeling. Vibrational harmonic frequencies obtained with 25 ab initio methods are compared to experimental band positions. The role of anharmonic terms in the potential and intensity tensors is also systematically explored using the vibrational self-consistent field, vibrational configuration interaction (VCI), and degeneracy-corrected perturbation calculations. The harmonic approach appeared satisfactory for most of the lower-wavelength (200-1800cm-1) vibrations. Modern generalized gradient approximation and hybrid density functionals, such as the common B3LYP method, provided a very good statistical agreement with the experiment. Although the inclusion of the anharmonic corrections still did not lead to complete agreement between the simulations and the experiment, occasional enhancements were achieved across the entire region of wave numbers. Not only the transitional frequencies of the C-H stretching modes were significantly improved but also Raman and ROA spectral profiles including N-H and C-H lower-frequency bending modes were more realistic after application of the VCI correction. A limited Boltzmann averaging for the lowest-frequency modes that could not be included directly in the anharmonic calculus provided a realistic inhomogeneous band broadening. The anharmonic parts of the intensity tensors (second dipole and polarizability derivatives) were found less important for the entire spectral profiles than the force field anharmonicities (third and fourth energy derivatives), except for a few weak combination bands which were dominated by the anharmonic tensor contributions.

Vainshtein screening in scalar-tensor theories before and after GW170817: Constraints on theories beyond Horndeski

NASA Astrophysics Data System (ADS)

Dima, Alexandru; Vernizzi, Filippo

2018-05-01

Screening mechanisms are essential features of dark energy models mediating a fifth force on large scales. We study the regime of strong scalar field nonlinearities, known as Vainshtein screening, in the most general scalar-tensor theories propagating a single scalar degree of freedom. We first develop an effective approach to parametrize cosmological perturbations beyond linear order for these theories. In the quasistatic limit, the fully nonlinear effective Lagrangian contains six independent terms, one of which starts at cubic order in perturbations. We compute the two gravitational potentials around a spherical body. Outside and near the body, screening reproduces standard gravity, with a modified gravitational coupling. Inside the body, the two potentials are different and depend on the density profile, signalling the breaking of the Vainshtein screening. We provide the most general expressions for these modifications, revising and extending previous results. We apply our findings to show that the combination of the GW170817 event, the Hulse-Taylor pulsar and stellar structure physics, constrain the parameters of these general theories at the level of 10-1, and of Gleyzes-Langlois-Piazza-Vernizzi theories at the level of 10-2.

Effect of hip and knee position on tensor fasciae latae elongation during stretching: An ultrasonic shear wave elastography study.

PubMed

Umehara, Jun; Ikezoe, Tome; Nishishita, Satoru; Nakamura, Masatoshi; Umegaki, Hiroki; Kobayashi, Takuya; Fujita, Kosuke; Ichihashi, Noriaki

2015-12-01

Decreased flexibility of the tensor fasciae latae is one factor that causes iliotibial band syndrome. Stretching has been used to improve flexibility or tightness of the muscle. However, no studies have investigated the effective stretching position for the tensor fasciae latae using an index to quantify muscle elongation in vivo. The aim of this study was to investigate the effects of hip rotation and knee angle on tensor fasciae latae elongation during stretching in vivo using ultrasonic shear wave elastography. Twenty healthy men participated in this study. The shear elastic modulus of the tensor fasciae latae was calculated using ultrasonic shear wave elastography. Stretching was performed at maximal hip adduction and maximal hip extension in 12 different positions with three hip rotation conditions (neutral, internal, and external rotations) and four knee angles (0°, 45°, 90°, and 135°). Two-way analysis of variance showed a significant main effect for knee angle, but not for hip rotation. The post-hoc test for knee angle indicated that the shear elastic modulus at 90° and 135° were significantly greater than those at 0° and 45°. Our results suggest that adding hip rotation to the stretching position with hip adduction and extension may have less effect on tensor fasciae latae elongation, and that stretching at >90° of knee flexion may effectively elongate the tensor fasciae latae. Copyright © 2015 Elsevier Ltd. All rights reserved.

Hybrid immersed interface-immersed boundary methods for AC dielectrophoresis

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

Hossan, Mohammad Robiul; Department of Engineering and Physics, University of Central Oklahoma, Edmond, OK 73034-5209; Dillon, Robert

2014-08-01

Dielectrophoresis, a nonlinear electrokinetic transport mechanism, has become popular in many engineering applications including manipulation, characterization and actuation of biomaterials, particles and biological cells. In this paper, we present a hybrid immersed interface–immersed boundary method to study AC dielectrophoresis where an algorithm is developed to solve the complex Poisson equation using a real variable formulation. An immersed interface method is employed to obtain the AC electric field in a fluid media with suspended particles and an immersed boundary method is used for the fluid equations and particle transport. The convergence of the proposed algorithm as well as validation of themore » hybrid scheme with experimental results is presented. In this paper, the Maxwell stress tensor is used to calculate the dielectrophoretic force acting on particles by considering the physical effect of particles in the computational domain. Thus, this study eliminates the approximations used in point dipole methods for calculating dielectrophoretic force. A comparative study between Maxwell stress tensor and point dipole methods for computing dielectrophoretic forces are presented. The hybrid method is used to investigate the physics of dielectrophoresis in microfluidic devices using an AC electric field. The numerical results show that with proper design and appropriate selection of applied potential and frequency, global electric field minima can be obtained to facilitate multiple particle trapping by exploiting the mechanism of negative dielectrophoresis. Our numerical results also show that electrically neutral particles form a chain parallel to the applied electric field irrespective of their initial orientation when an AC electric field is applied. This proposed hybrid numerical scheme will help to better understand dielectrophoresis and to design and optimize microfluidic devices.« less

Spin and Pseudospin Symmetries of Hellmann Potential with Three Tensor Interactions Using Nikiforov-Uvarov Method

NASA Astrophysics Data System (ADS)

Akpan, N. Ikot; Hassan, Hassanabadi; Tamunoimi, M. Abbey

2015-12-01

The Dirac equation with Hellmann potential is presented in the presence of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT), and Hulthen-type tensor (HLT) interactions by using Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions are obtained approximately within the framework of spin and pseudospin symmetries limit. We have also reported some numerical results and figures to show the effects of the tensor interactions. Special cases of the potential are also discussed.

Long period seismic signals observed before the Caldera formation during the 2000 Miyake- jima volcanic activity

NASA Astrophysics Data System (ADS)

Ohminato, T.; Kobayashi, T.; Ida, Y.; Fujita, E.

2006-12-01

During the 2000 Miyake-jima volcanic activity started on 26 June 2000, an intense earthquake swarm occurred initially beneath the southwest flank near the summit and gradually migrated west of the island. A volcanic earthquake activity in the island was reactivated beneath the summit, leading to a summit eruption with a significant summit subsidence on 8 July. We detected small but numerous number of long period (LP) seismic signals during these activities. Most of them include both 0.2 and 0.4 Hz components suggesting an existence of a harmonic oscillator. Some of them have dominant frequency peak at 0.2Hz (LP1), while others have one at 0.4 Hz (LP2). At the beginning of each waveform of both LP1 and LP2, an impulsive signal with a pulse-width of about 2 s is clearly identified. The major axis of the particle motion for the initial impulsive signal is almost horizontal suggesting a shallow source beneath the summit, while the inclined particle motion for the latter phase suggests deeper source beneath the island. For both LP1 and LP2, we can identify a clear positive correlation between the amplitude of the initial pulse and that of the latter phase. We conducted waveform inversions for the LP events assuming a point source and determined the locations and mechanisms simultaneously. We assumed three types of source mechanisms; three single forces, six moment tensor components, and a combination of moment tensor and single forces. We used AIC to decide the optimal solutions. Firstly, we applied the method to the entire waveform including both the initial pulse and the latter phase. The source type with a combination of moment tensor and single force components yields the minimum values of the AIC for both LP events. However, the spatial distribution of the residual errors tends to have two local minima. Considering the error distribution and the characteristic particle motions, it is likely that the source of the LP event consists of two different parts. We thus divided the LP events into two parts; the initial and the latter phases, and applied the same waveform inversion procedure separately for each part of the waveform. The inversion results show that the initial impulsive phase and the latter oscillatory phase are well explained by a nearly horizontal single force and a moment solution, respectively. The single force solutions of the initial pulse are positioned at the depth of about 2 km beneath the summit. The single force initially oriented to the north, and then to the south. On the other hand, the sources of the moment solutions are significantly deeper than the single force solutions. The hypocenter of the later phase of LP1 is located at the depth of 5.5 km in the southern region of the island, while that for the LP2 event is at 5.1 km beneath the summit. The horizontal oscillations are relatively dominant for both the LP1 and LP2 events. Although the two sources are separated each other by several kilometers, the positive correlation between the amplitudes of the initial pulse and the latter phase strongly suggests that the shallow sources trigger the deeper sources. The source time histories of the 6 moment tensor components of the latter portion of the LP1 and LP2 are not in phase. This makes it difficult to extract information on source geometry using the amplitude ratio among moment tensor components in a traditional manner. It may suggest that the source is composed of two independent sources whose oscillations are out of phase.

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

NASA Astrophysics Data System (ADS)

Abdoli-Arani, A.; Ramezani-Arani, R.

2012-11-01

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.

A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue.

PubMed

Pajevic, Sinisa; Aldroubi, Akram; Basser, Peter J

2002-01-01

The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.

Investigation of the Three-Nucleon System Dynamics in the Deuteron-Proton Breakup Reaction

NASA Astrophysics Data System (ADS)

Ciepał, I.; Kłos, B.; Kistryn, St.; Stephan, E.; Biegun, A.; Bodek, K.; Deltuva, A.; Epelbaum, E.; Eslami-Kalantari, M.; Fonseca, A. C.; Golak, J.; Jha, V.; Kalantar-Nayestanaki, N.; Kamada, H.; Khatri, G.; Kirillov, Da.; Kirillov, Di.; Kliczewski, St.; Kozela, A.; Kravcikova, M.; Machner, H.; Magiera, A.; Martinska, G.; Messchendorp, J.; Nogga, A.; Parol, W.; Ramazani-Moghaddam-Arani, A.; Roy, B. J.; Sakai, H.; Sekiguchi, K.; Sitnik, I.; Siudak, R.; Skibiński, R.; Sworst, R.; Urban, J.; Witała, H.; Zejma, J.

2014-08-01

Precise and large sets of cross section, vector A x , A y and tensor A xx , A xy , A yy analyzing power data for the 1 H( d, pp) n breakup reactions were measured at 100 and 130 MeV deuteron beam energies with the SALAD and BINA detectors at KVI and the Germanium Wall setup at FZ-Jülich. Results are compared with various theoretical approaches which model the three-nucleon system dynamics. The cross section data reveal a sizable three-nucleon force (3NF) and Coulomb force influence. In case of the analyzing powers very low sensitivity to these effects was found and the data are well describe by 2N models only. For A xy at 130 MeV, serious disagreements were observed when 3NF models are included in the calculations.

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.

Lectures on gravitation

NASA Astrophysics Data System (ADS)

Das, Ashok

1. Basics of geometry and relativity. 1.1. Two dimensional geometry. 1.2. Inertial and gravitational masses. 1.3. Relativity -- 2. Relativistic dynamics. 2.1. Relativistic point particle. 2.2. Current and charge densities. 2.3. Maxwell's equations in the presence of sources. 2.4. Motion of a charged particle in EM field. 2.5. Energy-momentum tensor. 2.6. Angular momentum -- 3. Principle of general covariance. 3.1. Principle of equivalence. 3.2. Principle of general covariance. 3.3. Tensor densities -- 4. Affine connection and covariant derivative. 4.1. Parallel transport of a vector. 4.2. Christoffel symbol. 4.3. Covariant derivative of contravariant tensors. 4.4. Metric compatibility. 4.5. Covariant derivative of covariant and mixed tensors. 4.6. Electromagnetic analogy. 4.7. Gradient, divergence and curl -- 5. Geodesic equation. 5.1. Covariant differentiation along a curve. 5.2. Curvature from derivatives. 5.3. Parallel transport along a closed curve. 5.4. Geodesic equation. 5.5. Derivation of geodesic equation from a Lagrangian -- 6. Applications of the geodesic equation. 6.1. Geodesic as representing gravitational effect. 6.2. Rotating coordinate system and the Coriolis force. 6.3. Gravitational red shift. 6.4. Twin paradox and general covariance. 6.5. Other equations in the presence of gravitation -- 7. Curvature tensor and Einstein's equation. 7.1. Curvilinear coordinates versus gravitational field. 7.2. Definition of an inertial coordinate frame. 7.3. Geodesic deviation. 7.4. Properties of the curvature tensor. 7.5. Einstein's equation. 7.6. Cosmological constant. 7.7. Initial value problem. 7.8. Einstein's equation from an action -- 8. Schwarzschild solution. 8.1. Line element. 8.2. Connection. 8.3. Solution of the Einstein equation. 8.4. Properties of the Schwarzschild solution. 8.5. Isotropic coordinates -- 9. Tests of general relativity. 9.1. Radar echo experiment. 9.2. Motion of a particle in a Schwarzschild background. 9.3. Motion of light rays in a Schwarzschild background. 9.4. Perihelion advance of Mercury -- 10. Black holes. 10.1. Singularities of the metric. 10.2. Singularities of the Schwarzschild metric. 10.3. Black holes -- 11. Cosmological models and the big bang theory. 11.1. Homogeneity and isotropy. 11.2. Different models of the universe. 11.3. Hubble's law. 11.4. Evolution equation. 11.5. Big bang theory and blackbody radiation.

Obtaining orthotropic elasticity tensor using entries zeroing method.

NASA Astrophysics Data System (ADS)

Gierlach, Bartosz; Danek, Tomasz

2017-04-01

A generally anisotropic elasticity tensor obtained from measurements can be represented by a tensor belonging to one of eight material symmetry classes. Knowledge of symmetry class and orientation is helpful for describing physical properties of a medium. For each non-trivial symmetry class except isotropic this problem is nonlinear. A common method of obtaining effective tensor is a choosing its non-trivial symmetry class and minimizing Frobenius norm between measured and effective tensor in the same coordinate system. Global optimization algorithm has to be used to determine the best rotation of a tensor. In this contribution, we propose a new approach to obtain optimal tensor, with the assumption that it is orthotropic (or at least has a similar shape to the orthotropic one). In orthotropic form tensor 24 out of 36 entries are zeros. The idea is to minimize the sum of squared entries which are supposed to be equal to zero through rotation calculated with optimization algorithm - in this case Particle Swarm Optimization (PSO) algorithm. Quaternions were used to parametrize rotations in 3D space to improve computational efficiency. In order to avoid a choice of local minima we apply PSO several times and only if we obtain similar results for the third time we consider it as a correct value and finish computations. To analyze obtained results Monte-Carlo method was used. After thousands of single runs of PSO optimization, we obtained values of quaternion parts and plot them. Points concentrate in several points of the graph following the regular pattern. It suggests the existence of more complex symmetry in the analyzed tensor. Then thousands of realizations of generally anisotropic tensor were generated - each tensor entry was replaced with a random value drawn from normal distribution having a mean equal to measured tensor entry and standard deviation of the measurement. Each of these tensors was subject of PSO based optimization delivering quaternion for optimal rotation. Computations were parallelized with OpenMP to decrease computational time what enables different tensors to be processed by different threads. As a result the distributions of rotated tensor entries values were obtained. For the entries which were to be zeroed we can observe almost normal distributions having mean equal to zero or sum of two normal distributions having inverse means. Non-zero entries represent different distributions with two or three maxima. Analysis of obtained results shows that described method produces consistent values of quaternions used to rotate tensors. Despite of less complex target function in a process of optimization in comparison to common approach, entries zeroing method provides results which can be applied to obtain an orthotropic tensor with good reliability. Modification of the method can produce also a tool for obtaining effective tensors belonging to another symmetry classes. This research was supported by the Polish National Science Center under contract No. DEC-2013/11/B/ST10/0472.

Millimeter and Submillimeter Spectroscopy of Chlorine Nitrate: The C1 Quadropole Tensor and the Harmonic Force Field

NASA Technical Reports Server (NTRS)

Muller, Holger S. P.; Helminger, Paul; Young, Sidney H.

1996-01-01

The rotational spectra of (sup 35)ClONO(sub 2) and (sup 37)ClONO(sub 2) in their ground and first excited torsional states (v(sub 9)=1) have been reinvestigated in selected regions between 84 and 441 GHz.

A Generalization of the Einstein-Maxwell Equations

NASA Astrophysics Data System (ADS)

Cotton, Fredrick

2016-03-01

The proposed modifications of the Einstein-Maxwell equations include: (1) the addition of a scalar term to the electromagnetic side of the equation rather than to the gravitational side, (2) the introduction of a 4-dimensional, nonlinear electromagnetic constitutive tensor and (3) the addition of curvature terms arising from the non-metric components of a general symmetric connection. The scalar term is defined by the condition that a spherically symmetric particle be force-free and mathematically well-behaved everywhere. The constitutive tensor introduces two auxiliary fields which describe the particle structure. The additional curvature terms couple both to particle solutions and to electromagnetic and gravitational wave solutions. http://sites.google.com/site/fwcotton/em-30.pdf

Generalized isobaric multiplet mass equation and its application to the Nolen-Schiffer anomaly

NASA Astrophysics Data System (ADS)

Dong, J. M.; Zhang, Y. H.; Zuo, W.; Gu, J. Z.; Wang, L. J.; Sun, Y.

2018-02-01

The Wigner isobaric multiplet mass equation (IMME) is the most fundamental prediction in nuclear physics with the concept of isospin. However, it was deduced based on the Wigner-Eckart theorem with the assumption that all charge-violating interactions can be written as tensors of rank two. In the present work, the charge-symmetry breaking (CSB) and charge-independent breaking (CIB) components of the nucleon-nucleon force, which contribute to the effective interaction in nuclear medium, are established in the framework of Brueckner theory with AV18 and AV14 bare interactions. Because such charge-violating components can no longer be expressed as an irreducible tensor due to density dependence, its matrix element cannot be analytically reduced by the Wigner-Eckart theorem. With an alternative approach, we derive a generalized IMME (GIMME) that modifies the coefficients of the original IMME. As the first application of GIMME, we study the long-standing question of the origin of the Nolen-Schiffer anomaly (NSA) found in the Coulomb displacement energy of mirror nuclei. We find that the naturally emerged CSB term in GIMME is largely responsible for explaining the NSA.

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).

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.

Investigations of Few-Nucleon System Dynamics in Medium Energy Domain

NASA Astrophysics Data System (ADS)

Ciepał, I.; Kłos, B.; Kistryn, St.; Stephan, E.; Biegun, A.; Bodek, K.; Deltuva, A.; Epelbaum, E.; Eslami-Kalantari, M.; Fonseca, A. C.; Golak, J.; Jha, V.; Kalantar-Nayestanaki, N.; Kamada, H.; Khatri, G.; Kirillov, Da.; Kirillov, Di.; Kliczewski, St.; Kozela, A.; Kravcikova, M.; Machner, H.; Magiera, A.; Martinska, G.; Messchendorp, J.; Nogga, A.; Parol, W.; Ramazani-Moghaddam-Arani, A.; Roy, B. J.; Sakai, H.; Sekiguchi, K.; Sitnik, I.; Siudak, R.; Skibiński, R.; Sworst, R.; Urban, J.; Witała, H.; Wrońska, A.; Zejma, J.

2013-08-01

Precise and large set of cross sections, vector A x , A y and tensor A xx , A xy , A yy analyzing powers for the 1 H( d, pp) n breakup reactions were measured at 100 and 130 MeV deuteron beam energies with the use of the SALAD and BINA detectors at KVI and Germanium Wall setup at FZ-Jülich. Results are compared with various theoretical approaches which model the three-nucleon (3N) system dynamics. The calculations are based on different two-nucleon (2N) potentials which can be combined with models of the three-nucleon force (3NF) and other pieces of the dynamics can also be included like the Coulomb interaction and relativistic effects. The cross sections data reveal seizable 3NF and Coulomb force influence. In case of analyzing powers very low sensitivity to the effects was found and the data are well describe by 2N models only. At 130 MeV for A xy serious disagreements appear when 3NF models are included into calculations.

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

Breit interaction effects in relativistic theory of the nuclear spin-rotation tensor.

PubMed

Aucar, I Agustín; Gómez, Sergio S; Giribet, Claudia G; Ruiz de Azúa, Martín C

2013-09-07

In this work, relativistic effects on the nuclear spin-rotation (SR) tensor originated in the electron-nucleus and electron-electron Breit interactions are analysed. To this end, four-component numerical calculations were carried out in model systems HX (X=H,F,Cl,Br,I). The electron-nucleus Breit interaction couples the electrons and nuclei dynamics giving rise to a purely relativistic contribution to the SR tensor. Its leading order in 1/c is of the same value as that of relativistic corrections on the usual second order expression of the SR tensor considered in previous work [I. A. Aucar, S. S. Gómez, J. I. Melo, C. G. Giribet, and M. C. Ruiz de Azúa, J. Chem. Phys. 138, 134107 (2013)], and therefore it is absolutely necessary to establish its relative importance. For the sake of completeness, the corresponding effect originating in the electron-electron Breit interaction is also considered. It is verified that in all cases these Breit interactions yield only very small corrections to the SR tensors of both the X and H nuclei in the present series of compounds. Results of the present work strongly suggest that in order to achieve experimental accuracy in the theoretical study of the SR tensor both electron-nucleus and electron-electron Breit effects can be safely neglected.

Extracting the potential-well of a near-field optical trap using the Helmholtz-Hodge decomposition

NASA Astrophysics Data System (ADS)

Zaman, Mohammad Asif; Padhy, Punnag; Hansen, Paul C.; Hesselink, Lambertus

2018-02-01

The non-conservative nature of the force field generated by a near-field optical trap is analyzed. A plasmonic C-shaped engraving on a gold film is considered as the trap. The force field is calculated using the Maxwell stress tensor method. The Helmholtz-Hodge decomposition is used to extract the conservative and the non-conservative component of the force. Due to the non-negligible non-conservative component, it is found that the conventional approach of extracting the potential by direct integration of the force is not accurate. Despite the non-conservative nature of the force field, it is found that the statistical properties of a trapped nanoparticle can be estimated from the conservative component of the force field alone. Experimental and numerical results are presented to support the claims.

Soft tissue balance changes depending on joint distraction force in total knee arthroplasty.

PubMed

Nagai, Kanto; Muratsu, Hirotsugu; Matsumoto, Tomoyuki; Miya, Hidetoshi; Kuroda, Ryosuke; Kurosaka, Masahiro

2014-03-01

The influence of joint distraction force on intraoperative soft tissue balance was evaluated using Offset Repo-Tensor® for 78 knees that underwent primary posterior-stabilized total knee arthroplasty. The joint center gap and varus ligament balance were measured between osteotomized surfaces using 20, 40 and 60 lbs of joint distraction force. These values were significantly increased at extension and flexion as the distraction force increased. Furthermore, lateral compartment stiffness was significantly lower than medial compartment stiffness. Thus, larger joint distraction forces led to larger varus ligament balance and joint center gap, because of the difference in soft tissue stiffness between lateral and medial compartments. These findings indicate the importance of the strength of joint distraction force in the assessment of soft tissue balance, especially when using gap-balancing technique. © 2014.

Structure of Aristotelian electrodynamics

NASA Astrophysics Data System (ADS)

Jacobson, Ted

2015-07-01

Aristotelian electrodynamics (AE) describes the regime of a plasma with a very strong electric field that is not shorted out, with the charge current determined completely by pair production and the balance of the Lorentz 4-force against the curvature radiation reaction. Here it is shown how the principal null directions and associated eigenvalues of the field tensor govern AE, and how force-free electrodynamics arises smoothly from AE when the eigenvalues (and therefore the electric field in some frame) vanish. A criterion for validity of AE and force-free electrodynamics is proposed in terms of a pair of "field curvature scalars" formed from the first derivative of the principal null directions.

Tensor-based dynamic reconstruction method for electrical capacitance tomography

NASA Astrophysics Data System (ADS)

Lei, J.; Mu, H. P.; Liu, Q. B.; Li, Z. H.; Liu, S.; Wang, X. Y.

2017-03-01

Electrical capacitance tomography (ECT) is an attractive visualization measurement method, in which the acquisition of high-quality images is beneficial for the understanding of the underlying physical or chemical mechanisms of the dynamic behaviors of the measurement objects. In real-world measurement environments, imaging objects are often in a dynamic process, and the exploitation of the spatial-temporal correlations related to the dynamic nature will contribute to improving the imaging quality. Different from existing imaging methods that are often used in ECT measurements, in this paper a dynamic image sequence is stacked into a third-order tensor that consists of a low rank tensor and a sparse tensor within the framework of the multiple measurement vectors model and the multi-way data analysis method. The low rank tensor models the similar spatial distribution information among frames, which is slowly changing over time, and the sparse tensor captures the perturbations or differences introduced in each frame, which is rapidly changing over time. With the assistance of the Tikhonov regularization theory and the tensor-based multi-way data analysis method, a new cost function, with the considerations of the multi-frames measurement data, the dynamic evolution information of a time-varying imaging object and the characteristics of the low rank tensor and the sparse tensor, is proposed to convert the imaging task in the ECT measurement into a reconstruction problem of a third-order image tensor. An effective algorithm is developed to search for the optimal solution of the proposed cost function, and the images are reconstructed via a batching pattern. The feasibility and effectiveness of the developed reconstruction method are numerically validated.

The Einstein equations on the 3-brane world

NASA Astrophysics Data System (ADS)

Shiromizu, Tetsuya; Maeda, Kei-Ichi; Sasaki, Misao

2000-07-01

We carefully investigate the gravitational equations of the brane world, in which all the matter forces except gravity are confined on the 3-brane in a 5-dimensional spacetime with Z2 symmetry. We derive the effective gravitational equations on the brane, which reduce to the conventional Einstein equations in the low energy limit. From our general argument we conclude that the first Randall-Sundrum-type theory predicts that the brane with a negative tension is an antigravity world and hence should be excluded from the physical point of view. Their second-type theory where the brane has a positive tension provides the correct signature of gravity. In this latter case, if the bulk spacetime is exactly anti-de Sitter spacetime, generically the matter on the brane is required to be spatially homogeneous because of the Bianchi identities. By allowing deviations from anti-de Sitter spacetime in the bulk, the situation will be relaxed and the Bianchi identities give just the relation between the Weyl tensor and the energy momentum tensor. In the present brane world scenario, the effective Einstein equations cease to be valid during an era when the cosmological constant on the brane is not well defined, such as in the case of the matter dominated by the potential energy of the scalar field.

Towards Lattice QCD Baryon Forces at the Physical Point: First Results

NASA Astrophysics Data System (ADS)

Doi, Takumi; Aoki, Sinya; Gongyo, Shinya; Hatsuda, Tetsuo; Ikeda, Yoichi; Inoue, Takashi; Iritani, Takumi; Ishii, Noriyoshi; Miyamoto, Takaya; Murano, Keiko; Nemura, Hidekatsu; Sasaki, Kenji

Lattice QCD calculations of baryon forces are performed for the first time with (almost) physical quark masses. Nf = 2 + 1 dynamical clover fermion gauge configurations are generated at the lattice spacing of a ≃ 0.085 fm on a (96a)4 ≃ (8.2 fm)4 lattice with quark masses corresponding to (mπ,mK) ≃ (146,525) MeV. Baryon forces are calculated using the time-dependent HAL QCD method. In this report, we study ΞΞ and NN systems both in 1S0 and 3S1-3D1 channels, and the results for the central and tensor forces as well as phase shifts in the ΞΞ (1S0) channel are presented.

Manifestations of the rotation and gravity of the Earth in high-energy physics experiments

NASA Astrophysics Data System (ADS)

Obukhov, Yuri N.; Silenko, Alexander J.; Teryaev, Oleg V.

2016-08-01

The inertial (due to rotation) and gravitational fields of the Earth affect the motion of an elementary particle and its spin dynamics. This influence is not negligible and should be taken into account in high-energy physics experiments. Earth's influence is manifest in perturbations in the particle motion, in an additional precession of the spin, and in a change of the constitutive tensor of the Maxwell electrodynamics. Bigger corrections are oscillatory, and their contributions average to zero. Other corrections due to the inhomogeneity of the inertial field are not oscillatory but they are very small and may be important only for the storage ring electric dipole moment experiments. Earth's gravity causes the Newton-like force, the reaction force provided by a focusing system, and additional torques acting on the spin. However, there are no observable indications of the electromagnetic effects due to Earth's gravity.

Enhancement of local piezoelectric properties of a perforated ferroelectric thin film visualized via piezoresponse force microscopy

NASA Astrophysics Data System (ADS)

Ivanov, M. S.; Sherstyuk, N. E.; Mishina, E. D.; Khomchenko, V. A.; Tselev, A.; Mukhortov, V. M.; Paixão, J. A.; Kholkin, A. L.

2017-10-01

The local piezoresponse in a Ba0.8Sr0.2TiO3 epitaxial ferroelectric film perforated by cylindrical channels has been investigated experimentally by means of piezoresponse force microscopy (PFM). A large enhancement of the effective values for both lateral and vertical components of piezoelectric tensor was experimentally detected in the perforated film as compared to non-perforated structure—by a factor of 8 for the lateral and by a factor 2 for the vertical piezoresponse. This result is consistent with the previously reported enhancement of the optical second harmonic generation over perforated films observed in macroscopic experiments. We assume that a possible mechanism for the increased PFM response is due to reduction of stress and clamping in the film imposed by the substrate. The obtained insight is critical for understanding nanoscale piezo- and ferroelectric responses in photonic crystals fabricated by focused ion beam milling.

MRI diffusion tensor reconstruction with PROPELLER data acquisition.

PubMed

Cheryauka, Arvidas B; Lee, James N; Samsonov, Alexei A; Defrise, Michel; Gullberg, Grant T

2004-02-01

MRI diffusion imaging is effective in measuring the diffusion tensor in brain, cardiac, liver, and spinal tissue. Diffusion tensor tomography MRI (DTT MRI) method is based on reconstructing the diffusion tensor field from measurements of projections of the tensor field. Projections are obtained by appropriate application of rotated diffusion gradients. In the present paper, the potential of a novel data acquisition scheme, PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction), is examined in combination with DTT MRI for its capability and sufficiency for diffusion imaging. An iterative reconstruction algorithm is used to reconstruct the diffusion tensor field from rotated diffusion weighted blades by appropriate rotated diffusion gradients. DTT MRI with PROPELLER data acquisition shows significant potential to reduce the number of weighted measurements, avoid ambiguity in reconstructing diffusion tensor parameters, increase signal-to-noise ratio, and decrease the influence of signal distortion.

Introduction to Vector Field Visualization

NASA Technical Reports Server (NTRS)

Kao, David; Shen, Han-Wei

2010-01-01

Vector field visualization techniques are essential to help us understand the complex dynamics of flow fields. These can be found in a wide range of applications such as study of flows around an aircraft, the blood flow in our heart chambers, ocean circulation models, and severe weather predictions. The vector fields from these various applications can be visually depicted using a number of techniques such as particle traces and advecting textures. In this tutorial, we present several fundamental algorithms in flow visualization including particle integration, particle tracking in time-dependent flows, and seeding strategies. For flows near surfaces, a wide variety of synthetic texture-based algorithms have been developed to depict near-body flow features. The most common approach is based on the Line Integral Convolution (LIC) algorithm. There also exist extensions of LIC to support more flexible texture generations for 3D flow data. This tutorial reviews these algorithms. Tensor fields are found in several real-world applications and also require the aid of visualization to help users understand their data sets. Examples where one can find tensor fields include mechanics to see how material respond to external forces, civil engineering and geomechanics of roads and bridges, and the study of neural pathway via diffusion tensor imaging. This tutorial will provide an overview of the different tensor field visualization techniques, discuss basic tensor decompositions, and go into detail on glyph based methods, deformation based methods, and streamline based methods. Practical examples will be used when presenting the methods; and applications from some case studies will be used as part of the motivation.

Energy Dissipation of Rayleigh Waves due to Absorption Along the Path by the Use of Finite Element Method

DTIC Science & Technology

1979-07-31

3 x 3 t Strain vector a ij,j Space derivative of the stress tensor Fi Force vector per unit volume o Density x CHAPTER III F Total force K Stiffness...matrix 6Vector displacements M Mass matrix B Space operating matrix DO Matrix moduli 2 x 3 DZ Operating matrix in Z direction N Matrix of shape...dissipating medium the deformation of a solid is a function of time, temperature and space . Creep phenomenon is a deformation process in which there is

The Twist Tensor Nuclear Norm for Video Completion.

PubMed

Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui

2017-12-01

In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.

Dynamic coupling between coordinates in a model for biomolecular isomerization

NASA Astrophysics Data System (ADS)

Ma, Ao; Nag, Ambarish; Dinner, Aaron R.

2006-04-01

To understand a complex reaction, it is necessary to project the dynamics of the system onto a low-dimensional subspace of physically meaningful coordinates. We recently introduced an automatic method for identifying coordinates that relate closely to stable-state commitment probabilities and successfully applied it to a model for biomolecular isomerization, the C7eq→αR transition of the alanine dipeptide [A. Ma and A. R. Dinner, J. Phys. Chem. B 109, 6769 (2005)]. Here, we explore approximate means for estimating diffusion tensors for systems subject to restraints in one and two dimensions and then use the results together with an extension of Kramers theory for unimolecular reaction rates [A. Berezhkovskii and A. Szabo, J. Chem. Phys. 122, 014503 (2005)] to show explicitly that both the potential of mean force and the diffusion tensor are essential for describing the dynamics of the alanine dipeptide quantitatively. In particular, the signficance of off-diagonal elements of the diffusion tensor suggests that the coordinates of interest are coupled by the hydrodynamic-like response of the bath of remaining degrees of freedom.

Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector

NASA Technical Reports Server (NTRS)

Wu, Jie-Zhi; Zhou, Ye; Wu, Jian-Ming

1996-01-01

We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and computation may be achieved. For turbulent flows, this strategy immediately implies that a given Reynolds stress model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds stress tensor can be reduced to that of the mean turbulent Lamb vector alone, which is much simpler. As a first step of this alternative modeling development, we derive the governing equations for the Lamb vector and its square. These equations form a basis of new second-order closure schemes and, we believe, should be favorably compared to that of traditional Reynolds stress transport equation.

Stochastic analysis of transverse dispersion in density‐coupled transport in aquifers

USGS Publications Warehouse

Welty, Claire; Kane, Allen C.; Kauffman, Leon J.

2003-01-01

Spectral perturbation techniques have been used previously to derive integral expressions for dispersive mixing in concentration‐dependent transport in three‐dimensional, heterogeneous porous media, where fluid density and viscosity are functions of solute concentration. Whereas earlier work focused on evaluating longitudinal dispersivity in isotropic media and incorporating the result in a mean one‐dimensional transport model, the emphasis of this paper is on evaluation of the complete dispersion tensor, including the more general case of anisotropic media. Approximate analytic expressions for all components of the macroscopic dispersivity tensor are derived, and the tensor is shown to be asymmetric. The tensor is separated into its symmetric and antisymmetric parts, where the symmetric part is used to calculate the principal components and principal directions of dispersivity, and the antisymmetric part of the tensor is shown to modify the velocity of the solute body compared to that of the background fluid. An example set of numerical simulations incorporating the tensor illustrates the effect of density‐coupled dispersivity on a sinking plume in an aquifer. The simulations show that the effective transverse vertical spreading in a sinking plume to be significantly greater than would be predicted by a standard density‐coupled transport model that does not incorporate the coupling in the dispersivity tensor.

A Tensor-Based Subspace Approach for Bistatic MIMO Radar in Spatial Colored Noise

PubMed Central

Wang, Xianpeng; Wang, Wei; Li, Xin; Wang, Junxiang

2014-01-01

In this paper, a new tensor-based subspace approach is proposed to estimate the direction of departure (DOD) and the direction of arrival (DOA) for bistatic multiple-input multiple-output (MIMO) radar in the presence of spatial colored noise. Firstly, the received signals can be packed into a third-order measurement tensor by exploiting the inherent structure of the matched filter. Then, the measurement tensor can be divided into two sub-tensors, and a cross-covariance tensor is formulated to eliminate the spatial colored noise. Finally, the signal subspace is constructed by utilizing the higher-order singular value decomposition (HOSVD) of the cross-covariance tensor, and the DOD and DOA can be obtained through the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, which are paired automatically. Since the multidimensional inherent structure and the cross-covariance tensor technique are used, the proposed method provides better angle estimation performance than Chen's method, the ESPRIT algorithm and the multi-SVD method. Simulation results confirm the effectiveness and the advantage of the proposed method. PMID:24573313

A tensor-based subspace approach for bistatic MIMO radar in spatial colored noise.

PubMed

Wang, Xianpeng; Wang, Wei; Li, Xin; Wang, Junxiang

2014-02-25

In this paper, a new tensor-based subspace approach is proposed to estimate the direction of departure (DOD) and the direction of arrival (DOA) for bistatic multiple-input multiple-output (MIMO) radar in the presence of spatial colored noise. Firstly, the received signals can be packed into a third-order measurement tensor by exploiting the inherent structure of the matched filter. Then, the measurement tensor can be divided into two sub-tensors, and a cross-covariance tensor is formulated to eliminate the spatial colored noise. Finally, the signal subspace is constructed by utilizing the higher-order singular value decomposition (HOSVD) of the cross-covariance tensor, and the DOD and DOA can be obtained through the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, which are paired automatically. Since the multidimensional inherent structure and the cross-covariance tensor technique are used, the proposed method provides better angle estimation performance than Chen's method, the ESPRIT algorithm and the multi-SVD method. Simulation results confirm the effectiveness and the advantage of the proposed method.

Tensor-based Dictionary Learning for Spectral CT Reconstruction

PubMed Central

Zhang, Yanbo; Wang, Ge

2016-01-01

Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods. PMID:27541628

Rethinking moment tensor inversion methods to retrieve the source mechanisms of low-frequency seismic events

NASA Astrophysics Data System (ADS)

Karl, S.; Neuberg, J.

2011-12-01

Volcanoes exhibit a variety of seismic signals. One specific type, the so-called long-period (LP) or low-frequency event, has proven to be crucial for understanding the internal dynamics of the volcanic system. These long period (LP) seismic events have been observed at many volcanoes around the world, and are thought to be associated with resonating fluid-filled conduits or fluid movements (Chouet, 1996; Neuberg et al., 2006). While the seismic wavefield is well established, the actual trigger mechanism of these events is still poorly understood. Neuberg et al. (2006) proposed a conceptual model for the trigger of LP events at Montserrat involving the brittle failure of magma in the glass transition in response to the upwards movement of magma. In an attempt to gain a better quantitative understanding of the driving forces of LPs, inversions for the physical source mechanisms have become increasingly common. Previous studies have assumed a point source for waveform inversion. Knowing that applying a point source model to synthetic seismograms representing an extended source process does not yield the real source mechanism, it can, however, still lead to apparent moment tensor elements which then can be compared to previous results in the literature. Therefore, this study follows the proposed concepts of Neuberg et al. (2006), modelling the extended LP source as an octagonal arrangement of double couples approximating a circular ringfault bounding the circumference of the volcanic conduit. Synthetic seismograms were inverted for the physical source mechanisms of LPs using the moment tensor inversion code TDMTISO_INVC by Dreger (2003). Here, we will present the effects of changing the source parameters on the apparent moment tensor elements. First results show that, due to negative interference, the amplitude of the seismic signals of a ringfault structure is greatly reduced when compared to a single double couple source. Furthermore, best inversion results yield a solution comprised of positive isotropic and compensated linear vector dipole components. Thus, the physical source mechanisms of volcano seismic signals may be misinterpreted as opening shear or tensile cracks when wrongly assuming a point source. In order to approach the real physical sources with our models, inversions based on higher-order tensors might have to be considered in the future. An inversion technique where the point source is replaced by a so-called moment tensor density would allow inversions of volcano seismic signals for sources that can then be temporally and spatially extended.

Studies of the Three-Nucleon System Dynamics in the Deuteron-Proton Breakup Reaction

NASA Astrophysics Data System (ADS)

Ciepał, I.; Kłos, B.; Stephan, E.; Kistryn, St.; Biegun, A.; Bodek, K.; Deltuva, A.; Epelbaum, E.; Eslami-Kalantari, M.; Fonseca, A. C.; Golak, J.; Jha, V.; Kalantar-Nayestanaki, N.; Kamada, H.; Khatri, G.; Kirillov, Da.; Kirillov, Di.; Kliczewski, St.; Kozela, A.; Kravcikova, M.; Machner, H.; Magiera, A.; Martinska, G.; Messchendorp, J.; Nogga, A.; Parol, W.; Ramazani-Moghaddam-Arani, A.; Roy, B. J.; Sakai, H.; Sekiguchi, K.; Sitnik, I.; Siudak, R.; Skibiński, R.; Sworst, R.; Urban, J.; Witała, H.; Zejma, J.

2014-03-01

One of the most important goals of modern nuclear physics is to contruct nuclear force model which properly describes the experimental data. To develop and test predictions of current models the breakup 1H(overrightarrow d, pp)n reaction was investigated experimentally at 100 and 130 MeV deuteron beam energies. Rich set of data for cross section, vector and tensor analyzing powers was obtained with the use of the SALAD and BINA detectors at KVI and Germanium Wall setup at FZ-Jülich. Results are compared with various theoretical approaches which describe the three-nucleon (3N) system dynamics. For correct description of the cross section data both, three-nucleon force (3NF) and Coulomb force, have to be included into calculations and influence of those ingredients is seizable at specific parts of the phase space. In case of the vector analyzing powers very low sensitivity to any effects beyond nucleon-nucleon interaction was found. At 130 MeV, the Axy data are not correctly described when 3NF models are included into calculations.

Force measurements in stiff, 3D, opaque granular materials

NASA Astrophysics Data System (ADS)

Hurley, Ryan C.; Hall, Stephen A.; Andrade, José E.; Wright, Jonathan

2017-06-01

We present results from two experiments that provide the first quantification of inter-particle force networks in stiff, 3D, opaque granular materials. Force vectors between all grains were determined using a mathematical optimization technique that seeks to satisfy grain equilibrium and strain measurements. Quantities needed in the optimization - the spatial location of the inter-particle contact network and tensor grain strains - were found using 3D X-ray diffraction and X-ray computed tomography. The statistics of the force networks are consistent with those found in past simulations and 2D experiments. In particular, we observe an exponential decay of normal forces above the mean and a partition of forces into strong and weak networks. In the first experiment, involving 77 single-crystal quartz grains, we also report on the temporal correlation of the force network across two sequential load cycles. In the second experiment, involving 1099 single-crystal ruby grains, we characterize force network statistics at low levels of compression.

Optical trapping forces of a focused azimuthally polarized Bessel-Gaussian beam on a double-layered sphere

NASA Astrophysics Data System (ADS)

Wu, F. P.; Zhang, B.; Liu, Z. L.; Tang, Y.; Zhang, N.

2017-12-01

We calculate the trapping forces exerted by a highly focused Bessel-Gaussian beam on a double-layered sphere by means of vector diffraction integral, T-matrix method and Maxwell stress tensor integral. The Bessel-Gaussian beam is azimuthally polarized. Numerical results predicate that the double-layered sphere with air core can be stably trapped in three-dimensions. The trapping forces and efficiencies are dependent on the refraction index and size of the inner core. The trapping efficiency can be optimized by choosing the refraction indices of the inner core and outer layer. Our computational method can be easily modified for other laser beams and particles with arbitrary geometries and multilayers.

Inference of segmented color and texture description by tensor voting.

PubMed

Jia, Jiaya; Tang, Chi-Keung

2004-06-01

A robust synthesis method is proposed to automatically infer missing color and texture information from a damaged 2D image by (N)D tensor voting (N > 3). The same approach is generalized to range and 3D data in the presence of occlusion, missing data and noise. Our method translates texture information into an adaptive (N)D tensor, followed by a voting process that infers noniteratively the optimal color values in the (N)D texture space. A two-step method is proposed. First, we perform segmentation based on insufficient geometry, color, and texture information in the input, and extrapolate partitioning boundaries by either 2D or 3D tensor voting to generate a complete segmentation for the input. Missing colors are synthesized using (N)D tensor voting in each segment. Different feature scales in the input are automatically adapted by our tensor scale analysis. Results on a variety of difficult inputs demonstrate the effectiveness of our tensor voting approach.

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

NASA Astrophysics Data System (ADS)

Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian

The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.

Force-chain evolution in a two-dimensional granular packing compacted by vertical tappings

NASA Astrophysics Data System (ADS)

Iikawa, Naoki; Bandi, M. M.; Katsuragi, Hiroaki

2018-03-01

We experimentally study the statistics of force-chain evolution in a vertically-tapped two-dimensional granular packing by using photoelastic disks. In this experiment, the tapped granular packing is gradually compacted. During the compaction, the isotropy of grain configurations is quantified by measuring the deviator anisotropy derived from fabric tensor, and then the evolution of force-chain structure is quantified by measuring the interparticle forces and force-chain orientational order parameter. As packing fraction increases, the interparticle force increases and finally saturates to an asymptotic value. Moreover, the grain configurations and force-chain structures become isotropically random as the tapping-induced compaction proceeds. In contrast, the total length of force chains remains unchanged. From the correlations of those parameters, we find two relations: (i) a positive correlation between the isotropy of grain configurations and the disordering of force-chain orientations, and (ii) a negative correlation between the increasing of interparticle forces and the disordering of force-chain orientations. These relations are universally held regardless of the mode of particle motions with or without convection.

Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.

PubMed

Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben

2017-08-02

It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.

Neurocognitive Effects of Radiotherapy

DTIC Science & Technology

2013-11-05

tensor imaging ( DTI ), perfusion and diffusion. The majority of patients have completed baseline and at least two additional time-points in regards...completed a 1 hour standard MRI as well as additional testing including diffuse tensor imaging ( DTI ), perfusion and diffusion. The majority of...including diffuse tensor imaging ( DTI ), perfusion and diffusion. The majority of patients have completed baseline and at least two additional time

Black holes with surrounding matter in scalar-tensor theories.

PubMed

Cardoso, Vitor; Carucci, Isabella P; Pani, Paolo; Sotiriou, Thomas P

2013-09-13

We uncover two mechanisms that can render Kerr black holes unstable in scalar-tensor gravity, both associated with the presence of matter in the vicinity of the black hole and the fact that this introduces an effective mass for the scalar. Our results highlight the importance of understanding the structure of spacetime in realistic, astrophysical black holes in scalar-tensor theories.

Efficient calculation of nuclear spin-rotation constants from auxiliary density functional theory.

PubMed

Zuniga-Gutierrez, Bernardo; Camacho-Gonzalez, Monica; Bendana-Castillo, Alfonso; Simon-Bastida, Patricia; Calaminici, Patrizia; Köster, Andreas M

2015-09-14

The computation of the spin-rotation tensor within the framework of auxiliary density functional theory (ADFT) in combination with the gauge including atomic orbital (GIAO) scheme, to treat the gauge origin problem, is presented. For the spin-rotation tensor, the calculation of the magnetic shielding tensor represents the most demanding computational task. Employing the ADFT-GIAO methodology, the central processing unit time for the magnetic shielding tensor calculation can be dramatically reduced. In this work, the quality of spin-rotation constants obtained with the ADFT-GIAO methodology is compared with available experimental data as well as with other theoretical results at the Hartree-Fock and coupled-cluster level of theory. It is found that the agreement between the ADFT-GIAO results and the experiment is good and very similar to the ones obtained by the coupled-cluster single-doubles-perturbative triples-GIAO methodology. With the improved computational performance achieved, the computation of the spin-rotation tensors of large systems or along Born-Oppenheimer molecular dynamics trajectories becomes feasible in reasonable times. Three models of carbon fullerenes containing hundreds of atoms and thousands of basis functions are used for benchmarking the performance. Furthermore, a theoretical study of temperature effects on the structure and spin-rotation tensor of the H(12)C-(12)CH-DF complex is presented. Here, the temperature dependency of the spin-rotation tensor of the fluorine nucleus can be used to identify experimentally the so far unknown bent isomer of this complex. To the best of our knowledge this is the first time that temperature effects on the spin-rotation tensor are investigated.

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

Zuniga-Gutierrez, Bernardo, E-mail: bzuniga.51@gmail.com; Camacho-Gonzalez, Monica; Bendana-Castillo, Alfonso

The computation of the spin-rotation tensor within the framework of auxiliary density functional theory (ADFT) in combination with the gauge including atomic orbital (GIAO) scheme, to treat the gauge origin problem, is presented. For the spin-rotation tensor, the calculation of the magnetic shielding tensor represents the most demanding computational task. Employing the ADFT-GIAO methodology, the central processing unit time for the magnetic shielding tensor calculation can be dramatically reduced. In this work, the quality of spin-rotation constants obtained with the ADFT-GIAO methodology is compared with available experimental data as well as with other theoretical results at the Hartree-Fock and coupled-clustermore » level of theory. It is found that the agreement between the ADFT-GIAO results and the experiment is good and very similar to the ones obtained by the coupled-cluster single-doubles-perturbative triples-GIAO methodology. With the improved computational performance achieved, the computation of the spin-rotation tensors of large systems or along Born-Oppenheimer molecular dynamics trajectories becomes feasible in reasonable times. Three models of carbon fullerenes containing hundreds of atoms and thousands of basis functions are used for benchmarking the performance. Furthermore, a theoretical study of temperature effects on the structure and spin-rotation tensor of the H{sup 12}C–{sup 12}CH–DF complex is presented. Here, the temperature dependency of the spin-rotation tensor of the fluorine nucleus can be used to identify experimentally the so far unknown bent isomer of this complex. To the best of our knowledge this is the first time that temperature effects on the spin-rotation tensor are investigated.« less

Tensor Rank Preserving Discriminant Analysis for Facial Recognition.

PubMed

Tao, Dapeng; Guo, Yanan; Li, Yaotang; Gao, Xinbo

2017-10-12

Facial recognition, one of the basic topics in computer vision and pattern recognition, has received substantial attention in recent years. However, for those traditional facial recognition algorithms, the facial images are reshaped to a long vector, thereby losing part of the original spatial constraints of each pixel. In this paper, a new tensor-based feature extraction algorithm termed tensor rank preserving discriminant analysis (TRPDA) for facial image recognition is proposed; the proposed method involves two stages: in the first stage, the low-dimensional tensor subspace of the original input tensor samples was obtained; in the second stage, discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition. On the one hand, the proposed TRPDA algorithm fully utilizes the natural structure of the input samples, and it applies an optimization criterion that can directly handle the tensor spectral analysis problem, thereby decreasing the computation cost compared those traditional tensor-based feature selection algorithms. On the other hand, the proposed TRPDA algorithm extracts feature by finding a tensor subspace that preserves most of the rank order information of the intra-class input samples. Experiments on the three facial databases are performed here to determine the effectiveness of the proposed TRPDA algorithm.

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.

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.

Reconstruction of the arcuate fasciculus for surgical planning in the setting of peritumoral edema using two-tensor unscented Kalman filter tractography.

PubMed

Chen, Zhenrui; Tie, Yanmei; Olubiyi, Olutayo; Rigolo, Laura; Mehrtash, Alireza; Norton, Isaiah; Pasternak, Ofer; Rathi, Yogesh; Golby, Alexandra J; O'Donnell, Lauren J

2015-01-01

Diffusion imaging tractography is increasingly used to trace critical fiber tracts in brain tumor patients to reduce the risk of post-operative neurological deficit. However, the effects of peritumoral edema pose a challenge to conventional tractography using the standard diffusion tensor model. The aim of this study was to present a novel technique using a two-tensor unscented Kalman filter (UKF) algorithm to track the arcuate fasciculus (AF) in brain tumor patients with peritumoral edema. Ten right-handed patients with left-sided brain tumors in the vicinity of language-related cortex and evidence of significant peritumoral edema were retrospectively selected for the study. All patients underwent 3-Tesla magnetic resonance imaging (MRI) including a diffusion-weighted dataset with 31 directions. Fiber tractography was performed using both single-tensor streamline and two-tensor UKF tractography. A two-regions-of-interest approach was applied to perform the delineation of the AF. Results from the two different tractography algorithms were compared visually and quantitatively. Using single-tensor streamline tractography, the AF appeared disrupted in four patients and contained few fibers in the remaining six patients. Two-tensor UKF tractography delineated an AF that traversed edematous brain areas in all patients. The volume of the AF was significantly larger on two-tensor UKF than on single-tensor streamline tractography (p < 0.01). Two-tensor UKF tractography provides the ability to trace a larger volume AF than single-tensor streamline tractography in the setting of peritumoral edema in brain tumor patients.

Research on third-order susceptibility tensor of silicon at telecom wavelength

NASA Astrophysics Data System (ADS)

Zhang, Yu-Hong; Liu, Hang; Chen, Zhan-Guo; Jia, Gang; Ren, Ce

2010-10-01

In this paper, the electro-induced birefringence based on Kerr effect and Franz-Keldysh effect in bulk silicon crystal at 1.3μm wavelengths has been measured. By using Kerr effect, the third-order susceptibility tensor of bulk crystalline silicon has been calculated.The two independent tensor of silicon X (3) susceptibility can be obtained by calculation (3) 6.22 (1 2.2%) 10 -20 m2 V2 and Xxyxy(3) = and xxxx(3) 9.13 (1 +/-2.2%) 10-20 m2 V 2 = m2/V2. The research can drive the silicon utility in the photo-electricity field.

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.

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.

Theory of electron g-tensor in bulk and quantum-well semiconductors

NASA Astrophysics Data System (ADS)

Lau, Wayne H.; Flatte', Michael E.

2004-03-01

We present quantitative calculations for the electron g-tensors in bulk and quantum-well semiconductors based on a generalized P.p envelope function theory solved in a fourteen-band restricted basis set. The dependences of g-tensor on structure, magnetic field, carrier density, temperature, and spin polarization have been explored and will be described. It is found that at temperatures of a few Kelvin and fields of a few Tesla, the g-tensors for bulk semiconductors develop quasi-steplike dependences on carrier density or magnetic field due to magnetic quantization, and this effect is even more pronounced in quantum-well semiconductors due to the additional electric quantization along the growth direction. The influence of quantum confinement on the electron g-tensors in QWs is studied by examining the dependence of electron g-tensors on well width. Excellent agreement between these calculated electron g-tensors and measurements [1-2] is found for GaAs/AlGaAs QWs. This work was supported by DARPA/ARO. [1] A. Malinowski and R. T. Harley, Phys. Rev. B 62, 2051 (2000);[2] Le Jeune et al., Semicond. Sci. Technol. 12, 380 (1997).

Effects of motion and b-matrix correction for high resolution DTI with short-axis PROPELLER-EPI

PubMed Central

Aksoy, Murat; Skare, Stefan; Holdsworth, Samantha; Bammer, Roland

2010-01-01

Short-axis PROPELLER-EPI (SAP-EPI) has been proven to be very effective in providing high-resolution diffusion-weighted and diffusion tensor data. The self-navigation capabilities of SAP-EPI allow one to correct for motion, phase errors, and geometric distortion. However, in the presence of patient motion, the change in the effective diffusion-encoding direction (i.e. the b-matrix) between successive PROPELLER ‘blades’ can decrease the accuracy of the estimated diffusion tensors, which might result in erroneous reconstruction of white matter tracts in the brain. In this study, we investigate the effects of alterations in the b-matrix as a result of patient motion on the example of SAP-EPI DTI and eliminate these effects by incorporating our novel single-step non-linear diffusion tensor estimation scheme into the SAP-EPI post-processing procedure. Our simulations and in-vivo studies showed that, in the presence of patient motion, correcting the b-matrix is necessary in order to get more accurate diffusion tensor and white matter pathway reconstructions. PMID:20222149

Cut and join operator ring in tensor models

NASA Astrophysics Data System (ADS)

Itoyama, H.; Mironov, A.; Morozov, A.

2018-07-01

Recent advancement of rainbow tensor models based on their superintegrability (manifesting itself as the existence of an explicit expression for a generic Gaussian correlator) has allowed us to bypass the long-standing problem seen as the lack of eigenvalue/determinant representation needed to establish the KP/Toda integrability. As the mandatory next step, we discuss in this paper how to provide an adequate designation to each of the connected gauge-invariant operators that form a double coset, which is required to cleverly formulate a tree-algebra generalization of the Virasoro constraints. This problem goes beyond the enumeration problem per se tied to the permutation group, forcing us to introduce a few gauge fixing procedures to the coset. We point out that the permutation-based labeling, which has proven to be relevant for the Gaussian averages is, via interesting complexity, related to the one based on the keystone trees, whose algebra will provide the tensor counterpart of the Virasoro algebra for matrix models. Moreover, our simple analysis reveals the existence of nontrivial kernels and co-kernels for the cut operation and for the join operation respectively that prevent a straightforward construction of the non-perturbative RG-complete partition function and the identification of truly independent time variables. We demonstrate these problems by the simplest non-trivial Aristotelian RGB model with one complex rank-3 tensor, studying its ring of gauge-invariant operators, generated by the keystone triple with the help of four operations: addition, multiplication, cut and join.

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.

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.).

Calcium-43 chemical shift tensors as probes of calcium binding environments. Insight into the structure of the vaterite CaCO3 polymorph by 43Ca solid-state NMR spectroscopy.

PubMed

Bryce, David L; Bultz, Elijah B; Aebi, Dominic

2008-07-23

Natural-abundance (43)Ca solid-state NMR spectroscopy at 21.1 T and gauge-including projector-augmented-wave (GIPAW) DFT calculations are developed as tools to provide insight into calcium binding environments, with special emphasis on the calcium chemical shift (CS) tensor. The first complete analysis of a (43)Ca solid-state NMR spectrum, including the relative orientation of the CS and electric field gradient (EFG) tensors, is reported for calcite. GIPAW calculations of the (43)Ca CS and EFG tensors for a series of small molecules are shown to reproduce experimental trends; for example, the trend in available solid-state chemical shifts is reproduced with a correlation coefficient of 0.983. The results strongly suggest the utility of the calcium CS tensor as a novel probe of calcium binding environments in a range of calcium-containing materials. For example, for three polymorphs of CaCO3 the CS tensor span ranges from 8 to 70 ppm and the symmetry around calcium is manifested differently in the CS tensor as compared with the EFG tensor. The advantages of characterizing the CS tensor are particularly evident in very high magnetic fields where the effect of calcium CS anisotropy is augmented in hertz while the effect of second-order quadrupolar broadening is often obscured for (43)Ca because of its small quadrupole moment. Finally, as an application of the combined experimental-theoretical approach, the solid-state structure of the vaterite polymorph of calcium carbonate is probed and we conclude that the hexagonal P6(3)/mmc space group provides a better representation of the structure than does the orthorhombic Pbnm space group, thereby demonstrating the utility of (43)Ca solid-state NMR as a complementary tool to X-ray crystallographic methods.

Higher symmetries of the Schrödinger operator in Newton-Cartan geometry

NASA Astrophysics Data System (ADS)

Gundry, James

2017-03-01

We establish several relationships between the non-relativistic conformal symmetries of Newton-Cartan geometry and the Schrödinger equation. In particular we discuss the algebra sch(d) of vector fields conformally-preserving a flat Newton-Cartan spacetime, and we prove that its curved generalisation generates the symmetry group of the covariant Schrödinger equation coupled to a Newtonian potential and generalised Coriolis force. We provide intrinsic Newton-Cartan definitions of Killing tensors and conformal Schrödinger-Killing tensors, and we discuss their respective links to conserved quantities and to the higher symmetries of the Schrödinger equation. Finally we consider the role of conformal symmetries in Newtonian twistor theory, where the infinite-dimensional algebra of holomorphic vector fields on twistor space corresponds to the symmetry algebra cnc(3) on the Newton-Cartan spacetime.

Tensor non-Gaussianity from axion-gauge-fields dynamics: parameter search

NASA Astrophysics Data System (ADS)

Agrawal, Aniket; Fujita, Tomohiro; Komatsu, Eiichiro

2018-06-01

We calculate the bispectrum of scale-invariant tensor modes sourced by spectator SU(2) gauge fields during inflation in a model containing a scalar inflaton, a pseudoscalar axion and SU(2) gauge fields. A large bispectrum is generated in this model at tree-level as the gauge fields contain a tensor degree of freedom, and its production is dominated by self-coupling of the gauge fields. This is a unique feature of non-Abelian gauge theory. The shape of the tensor bispectrum is approximately an equilateral shape for 3lesssim mQlesssim 4, where mQ is an effective dimensionless mass of the SU(2) field normalised by the Hubble expansion rate during inflation. The amplitude of non-Gaussianity of the tensor modes, characterised by the ratio Bh/P2h, is inversely proportional to the energy density fraction of the gauge field. This ratio can be much greater than unity, whereas the ratio from the vacuum fluctuation of the metric is of order unity. The bispectrum is effective at constraining large mQ regions of the parameter space, whereas the power spectrum constrains small mQ regions.

A priori study of subgrid-scale flux of a passive scalar in isotropic homogeneous turbulence.

PubMed

Chumakov, Sergei G

2008-09-01

We perform a direct numerical simulation (DNS) of forced homogeneous isotropic turbulence with a passive scalar that is forced by mean gradient. The DNS data are used to study the properties of subgrid-scale flux of a passive scalar in the framework of large eddy simulation (LES), such as alignment trends between the flux, resolved, and subgrid-scale flow structures. It is shown that the direction of the flux is strongly coupled with the subgrid-scale stress axes rather than the resolved flow quantities such as strain, vorticity, or scalar gradient. We derive an approximate transport equation for the subgrid-scale flux of a scalar and look at the relative importance of the terms in the transport equation. A particular form of LES tensor-viscosity model for the scalar flux is investigated, which includes the subgrid-scale stress. Effect of different models for the subgrid-scale stress on the model for the subgrid-scale flux is studied.

Self-force as a probe of global structure

NASA Astrophysics Data System (ADS)

Davidson, Karl; Poisson, Eric

2018-05-01

We calculate the self-force on an electric charge and electric dipole held at rest in a closed universe that results from joining two copies of Minkowski spacetime at a common boundary. Spacetime is strictly flat on each side of the boundary, but there is curvature at the surface layer required to join the two Minkowski spacetimes. We find that the self-force on the charge is always directed away from the surface layer. This is analogous to the case of an electric charge held at rest inside a spherical shell of matter, for which the self-force is also directed away from the shell. For the dipole, the direction of the self-force is a function of the dipole's position and orientation. Both self-forces become infinite when the charge or dipole is made to approach the surface layer. This study reveals that a self-force can arise even when the Riemann tensor vanishes at the position of the charge or dipole; in such cases the self-force is a manifestation of the global curvature of spacetime.

A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis

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

Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.

A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This added-mass partitioned (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forcesmore » on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this second part of a two-part series, the general formulation of the AMP scheme is presented including the form of the AMP interface conditions and added-damping tensors for general geometries. A fully second-order accurate implementation of the AMP scheme is developed in two dimensions based on a fractional-step method for the incompressible Navier-Stokes equations using finite difference methods and overlapping grids to handle the moving geometry. Here, the numerical scheme is verified on a number of difficult benchmark problems.« less

A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis

DOE PAGES

Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.; ...

2017-01-20

A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This added-mass partitioned (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forcesmore » on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this second part of a two-part series, the general formulation of the AMP scheme is presented including the form of the AMP interface conditions and added-damping tensors for general geometries. A fully second-order accurate implementation of the AMP scheme is developed in two dimensions based on a fractional-step method for the incompressible Navier-Stokes equations using finite difference methods and overlapping grids to handle the moving geometry. Here, the numerical scheme is verified on a number of difficult benchmark problems.« less

Conservation Laws and Ponderomotive Force for Non-WKB, MHD Waves in the Solar Wind

NASA Astrophysics Data System (ADS)

McKenzie, J. F.; Webb, G. M.; Zank, G. P.; Kaghashvili, E. K.; Ratkiewicz, R. E.

2004-12-01

The interaction of non-WKB Alfvén waves in the Solar Wind was investigated by Heinemann and Olbert (1980), MacGregor and Charbonneau (1994) and others. MacGregor and Charbonneau (1994) investigated non-WKB Alfvén wave driven winds. We discuss both the canonical and physical wave stress energy tensors for non-WKB, MHD waves and the ponderomotive force exerted by the waves on the wind for the case where both compressible (magneto-acoustic type waves) and incompressible waves (Alfvén waves) are present. The equations for the waves include the effects of wave mixing (i.e. the interaction of the waves with each other via gradients in the background flow). Wave mixing is known to be an important element of turbulence theory in the Solar Wind. However, only the wave mixing of Alfvénic type disturbances have been accounted for in present models of Solar Wind turbulence (e.g. Zhou and Matthaeus, 1990), which use Elssässer variables to describe the perturbations. The relationship between the present analysis and nearly incompressible MHD (reduced MHD) is at present unclear. Also unclear is the relationship between the present analysis and theories using wave-mean field interactions (e.g. Grimshaw (1984), Holm (1999)). The analysis is based on a theory for wave and background stress-energy tensors developed by Webb et al. (2004a,b) using a Lagrangian formulation of the total system of waves and background plasma (see e.g. Dewar (1970) for the WKB case). Conservation laws for the total system of waves and background plasma result from application of Noether's theorems relating Lie symmetries of the action to conservation laws.

A simulation technique for 3D MR-guided acoustic radiation force imaging

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

Payne, Allison, E-mail: apayne@ucair.med.utah.edu; Bever, Josh de; Farrer, Alexis

2015-02-15

Purpose: In magnetic resonance-guided focused ultrasound (MRgFUS) therapies, the in situ characterization of the focal spot location and quality is critical. MR acoustic radiation force imaging (MR-ARFI) is a technique that measures the tissue displacement caused by the radiation force exerted by the ultrasound beam. This work presents a new technique to model the displacements caused by the radiation force of an ultrasound beam in a homogeneous tissue model. Methods: When a steady-state point-source force acts internally in an infinite homogeneous medium, the displacement of the material in all directions is given by the Somigliana elastostatic tensor. The radiation forcemore » field, which is caused by absorption and reflection of the incident ultrasound intensity pattern, will be spatially distributed, and the tensor formulation takes the form of a convolution of a 3D Green’s function with the force field. The dynamic accumulation of MR phase during the ultrasound pulse can be theoretically accounted for through a time-of-arrival weighting of the Green’s function. This theoretical model was evaluated experimentally in gelatin phantoms of varied stiffness (125-, 175-, and 250-bloom). The acoustic and mechanical properties of the phantoms used as parameters of the model were measured using independent techniques. Displacements at focal depths of 30- and 45-mm in the phantoms were measured by a 3D spin echo MR-ARFI segmented-EPI sequence. Results: The simulated displacements agreed with the MR-ARFI measured displacements for all bloom values and focal depths with a normalized RMS difference of 0.055 (range 0.028–0.12). The displacement magnitude decreased and the displacement pattern broadened with increased bloom value for both focal depths, as predicted by the theory. Conclusions: A new technique that models the displacements caused by the radiation force of an ultrasound beam in a homogeneous tissue model theory has been rigorously validated through comparison with experimentally obtained 3D displacement data in homogeneous gelatin phantoms using a 3D MR-ARFI sequence. The agreement of the experimentally measured and simulated results demonstrates the potential to use MR-ARFI displacement data in MRgFUS therapies.« less

Advanced Magnetic Resonance Imaging techniques to probe muscle structure and function

NASA Astrophysics Data System (ADS)

Malis, Vadim

Structural and functional Magnetic Resonance Imaging (MRI) studies of skeletal muscle allow the elucidation of muscle physiology under normal and pathological conditions. Continuing on the efforts of the Muscle Imaging and Modeling laboratory, the focus of the thesis is to (i) extend and refine two challenging imaging modalities: structural imaging using Diffusion Tensor Imaging (DTI) and functional imaging based on Velocity Encoded Phase Contrast Imaging (VE-PC) and (ii) apply these methods to explore age related structure and functional differences of the gastrocnemius muscle. Diffusion Tensor Imaging allows the study of tissue microstructure as well as muscle fiber architecture. The images, based on an ultrafast single shot Echo Planar Imaging (EPI) sequence, suffer from geometric distortions and low signal to noise ratio. A processing pipeline was developed to correct for distortions and to improve image Signal to Noise Ratio (SNR). DTI acquired on a senior and young cohort of subjects were processed through the pipeline and differences in DTI derived indices and fiber architecture between the two cohorts were explored. The DTI indices indicated that at the microstructural level, fiber atrophy was accompanied with a reduction in fiber volume fraction. At the fiber architecture level, fiber length and pennation angles decreased with age that potentially contribute to the loss of muscle force with age. Velocity Encoded Phase Contrast imaging provides tissue (e.g. muscle) velocity at each voxel which allows the study of strain and Strain Rate (SR) under dynamic conditions. The focus of the thesis was to extract 2D strain rate tensor maps from the velocity images and apply the method to study age related differences. The tensor mapping can potentially provide unique information on the extracellular matrix and lateral transmission the role of these two elements has recently emerged as important determinants of force loss with age. In the cross sectional study on aging, strain rate during isometric contraction was significantly reduced in the seniors; presumably from decrease in muscle slack and increase in stiffness with age. Other parameters of interest from this study that allow inferences on the ECM and lateral transmission are the asymmetry of deformation in the fiber cross section as well as the angle between the SR and muscle fiber. The last part of thesis, which is a 'work-in-progress', is the extension to 3D SR tensor mapping using a 3D spatial, 3D velocity encoded imaging sequence. This is combined with Diffusion Tensor Imaging to obtain the lead eigenvector (muscle fiber direction) at each voxel. The 3D SR is then rotated to the basis of the DTI to obtain a 'Fiber Aligned Strain rate: FASR'. The off diagonal elements of FASR are shear strain terms. Detailed analysis of the shear strain will provide a unique non-invasive method to probe lateral transmission.

Unsupervised Tensor Mining for Big Data Practitioners.

PubMed

Papalexakis, Evangelos E; Faloutsos, Christos

2016-09-01

Multiaspect data are ubiquitous in modern Big Data applications. For instance, different aspects of a social network are the different types of communication between people, the time stamp of each interaction, and the location associated to each individual. How can we jointly model all those aspects and leverage the additional information that they introduce to our analysis? Tensors, which are multidimensional extensions of matrices, are a principled and mathematically sound way of modeling such multiaspect data. In this article, our goal is to popularize tensors and tensor decompositions to Big Data practitioners by demonstrating their effectiveness, outlining challenges that pertain to their application in Big Data scenarios, and presenting our recent work that tackles those challenges. We view this work as a step toward a fully automated, unsupervised tensor mining tool that can be easily and broadly adopted by practitioners in academia and industry.

Reducing tensor magnetic gradiometer data for unexploded ordnance detection

USGS Publications Warehouse

Bracken, Robert E.; Brown, Philip J.

2005-01-01

We performed a survey to demonstrate the effectiveness of a prototype tensor magnetic gradiometer system (TMGS) for detection of buried unexploded ordnance (UXO). In order to achieve a useful result, we designed a data-reduction procedure that resulted in a realistic magnetic gradient tensor and devised a simple way of viewing complicated tensor data, not only to assess the validity of the final resulting tensor, but also to preview the data at interim stages of processing. The final processed map of the surveyed area clearly shows a sharp anomaly that peaks almost directly over the target UXO. This map agrees well with a modeled map derived from dipolar sources near the known target locations. From this agreement, it can be deduced that the reduction process is valid, making the prototype TMGS a foundation for development of future systems and processes.

EEG Classification for Hybrid Brain-Computer Interface Using a Tensor Based Multiclass Multimodal Analysis Scheme

PubMed Central

Ji, Hongfei; Li, Jie; Lu, Rongrong; Gu, Rong; Cao, Lei; Gong, Xiaoliang

2016-01-01

Electroencephalogram- (EEG-) based brain-computer interface (BCI) systems usually utilize one type of changes in the dynamics of brain oscillations for control, such as event-related desynchronization/synchronization (ERD/ERS), steady state visual evoked potential (SSVEP), and P300 evoked potentials. There is a recent trend to detect more than one of these signals in one system to create a hybrid BCI. However, in this case, EEG data were always divided into groups and analyzed by the separate processing procedures. As a result, the interactive effects were ignored when different types of BCI tasks were executed simultaneously. In this work, we propose an improved tensor based multiclass multimodal scheme especially for hybrid BCI, in which EEG signals are denoted as multiway tensors, a nonredundant rank-one tensor decomposition model is proposed to obtain nonredundant tensor components, a weighted fisher criterion is designed to select multimodal discriminative patterns without ignoring the interactive effects, and support vector machine (SVM) is extended to multiclass classification. Experiment results suggest that the proposed scheme can not only identify the different changes in the dynamics of brain oscillations induced by different types of tasks but also capture the interactive effects of simultaneous tasks properly. Therefore, it has great potential use for hybrid BCI. PMID:26880873

EEG Classification for Hybrid Brain-Computer Interface Using a Tensor Based Multiclass Multimodal Analysis Scheme.

PubMed

Ji, Hongfei; Li, Jie; Lu, Rongrong; Gu, Rong; Cao, Lei; Gong, Xiaoliang

2016-01-01

Electroencephalogram- (EEG-) based brain-computer interface (BCI) systems usually utilize one type of changes in the dynamics of brain oscillations for control, such as event-related desynchronization/synchronization (ERD/ERS), steady state visual evoked potential (SSVEP), and P300 evoked potentials. There is a recent trend to detect more than one of these signals in one system to create a hybrid BCI. However, in this case, EEG data were always divided into groups and analyzed by the separate processing procedures. As a result, the interactive effects were ignored when different types of BCI tasks were executed simultaneously. In this work, we propose an improved tensor based multiclass multimodal scheme especially for hybrid BCI, in which EEG signals are denoted as multiway tensors, a nonredundant rank-one tensor decomposition model is proposed to obtain nonredundant tensor components, a weighted fisher criterion is designed to select multimodal discriminative patterns without ignoring the interactive effects, and support vector machine (SVM) is extended to multiclass classification. Experiment results suggest that the proposed scheme can not only identify the different changes in the dynamics of brain oscillations induced by different types of tasks but also capture the interactive effects of simultaneous tasks properly. Therefore, it has great potential use for hybrid BCI.

Semi-Supervised Tensor-Based Graph Embedding Learning and Its Application to Visual Discriminant Tracking.

PubMed

Hu, Weiming; Gao, Jin; Xing, Junliang; Zhang, Chao; Maybank, Stephen

2017-01-01

An appearance model adaptable to changes in object appearance is critical in visual object tracking. In this paper, we treat an image patch as a two-order tensor which preserves the original image structure. We design two graphs for characterizing the intrinsic local geometrical structure of the tensor samples of the object and the background. Graph embedding is used to reduce the dimensions of the tensors while preserving the structure of the graphs. Then, a discriminant embedding space is constructed. We prove two propositions for finding the transformation matrices which are used to map the original tensor samples to the tensor-based graph embedding space. In order to encode more discriminant information in the embedding space, we propose a transfer-learning- based semi-supervised strategy to iteratively adjust the embedding space into which discriminative information obtained from earlier times is transferred. We apply the proposed semi-supervised tensor-based graph embedding learning algorithm to visual tracking. The new tracking algorithm captures an object's appearance characteristics during tracking and uses a particle filter to estimate the optimal object state. Experimental results on the CVPR 2013 benchmark dataset demonstrate the effectiveness of the proposed tracking algorithm.

13C and (15)N chemical shift tensors in adenosine, guanosine dihydrate, 2'-deoxythymidine, and cytidine.

PubMed

Stueber, Dirk; Grant, David M

2002-09-04

The (13)C and (15)N chemical shift tensor principal values for adenosine, guanosine dihydrate, 2'-deoxythymidine, and cytidine are measured on natural abundance samples. Additionally, the (13)C and (15)N chemical shielding tensor principal values in these four nucleosides are calculated utilizing various theoretical approaches. Embedded ion method (EIM) calculations improve significantly the precision with which the experimental principal values are reproduced over calculations on the corresponding isolated molecules with proton-optimized geometries. The (13)C and (15)N chemical shift tensor orientations are reliably assigned in the molecular frames of the nucleosides based upon chemical shielding tensor calculations employing the EIM. The differences between principal values obtained in EIM calculations and in calculations on isolated molecules with proton positions optimized inside a point charge array are used to estimate the contributions to chemical shielding arising from intermolecular interactions. Moreover, the (13)C and (15)N chemical shift tensor orientations and principal values correlate with the molecular structure and the crystallographic environment for the nucleosides and agree with data obtained previously for related compounds. The effects of variations in certain EIM parameters on the accuracy of the shielding tensor calculations are investigated.

Shining light on modifications of gravity

NASA Astrophysics Data System (ADS)

Brax, Philippe; Burrage, Clare; Davis, Anne-Christine

2012-10-01

Many modifications of gravity introduce new scalar degrees of freedom, and in such theories matter fields typically couple to an effective metric that depends on both the true metric of spacetime and on the scalar field and its derivatives. Scalar field contributions to the effective metric can be classified as conformal and disformal. Disformal terms introduce gradient couplings between scalar fields and the energy momentum tensor of other matter fields, and cannot be constrained by fifth force experiments because the effects of these terms are trivial around static non-relativistic sources. The use of high-precision, low-energy photon experiments to search for conformally coupled scalar fields, called axion-like particles, is well known. In this article we show that these experiments are also constraining for disformal scalar field theories, and are particularly important because of the difficulty of constraining these couplings with other laboratory experiments.

Chemical shift and electric field gradient tensors for the amide and carboxyl hydrogens in the model peptide N-acetyl-D,L-valine. Single-crystal deuterium NMR study.

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

Gerald, R. E., II; Bernhard, T.; Haeberlen, U.

1993-01-01

Solid-state NMR spectroscopy is well established as a method for describing molecular structure with resolution on the atomic scale. Many of the NMR observables result from anisotropic interactions between the nuclear spin and its environment. These observables can be described by second-rank tensors. For example, the eigenvalues of the traceless symmetric part of the hydrogen chemical shift (CS) tensor provide information about the strength of inter- or intramolecular hydrogen bonding. On the other hand, the eigenvectors of the deuterium electric field gradient (EFG) tensor give deuteron/proton bond directions with an accuracy rivalled only by neutron diffraction. In this paper themore » authors report structural information of this type for the amide and carboxyl hydrogen sites in a single crystal of the model peptide N-acetyl-D,L-valine (NAV). They use deuterium NMR to infer both the EFG and CS tensors at the amide and carboxyl hydrogen sites in NAV. Advantages of this technique over multiple-pulse proton NMR are that it works in the presence of {sup 14}N spins which are very hard to decouple from protons and that additional information in form of the EFG tensors can be derived. The change in the CS and EFG tensors upon exchange of a deuteron for a proton (the isotope effect) is anticipated to be very small; the effect on the CS tensors is certainly smaller than the experimental errors. NAV has served as a model peptide before in a variety of NMR studies, including those concerned with developing solid-state NMR spectroscopy as a method for determining the structure of proteins. NMR experiments on peptide or protein samples which are oriented in at least one dimension can provide important information about the three-dimensional structure of the peptide or the protein. In order to interpret the NMR data in terms of the structure of the polypeptide, the relationship of the CS and EFG tensors to the local symmetry elements of an amino acide, e.g., the peptide plane, is essential. The main purpose of this work is to investigate this relationship for the amide hydrogen CS tensor. The amide hydrogen CS tensor will also provide orientational information for peptide bonds in proteins complementary to that from the nitrogen CS and EFG tensors and the nitrogen-hydrogen heteronuclear dipole-dipole coupling which have been used previously to determine protein structures by solid-state NMR spectroscopy. This information will be particularly valuable because the amide hydrogen CS tensor is not axially symmetric. In addition, the use of the amide hydrogen CS interaction in high-field solid-state NMR experiments will increase the available resolution among peptide sites.« less

A general theory of linear cosmological perturbations: stability conditions, the quasistatic limit and dynamics

NASA Astrophysics Data System (ADS)

Lagos, Macarena; Bellini, Emilio; Noller, Johannes; Ferreira, Pedro G.; Baker, Tessa

2018-03-01

We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of all these theories. Based on this structure, we explore the viable space of parameters for each family of models by imposing the absence of ghosts and gradient instabilities. We then focus on the quasistatic regime and confirm that all these theories can be approximated by the phenomenological two-parameter model described by an effective Newton's constant and the gravitational slip. Within the quasistatic regime we pinpoint signatures which can distinguish between the broad classes of models (scalar-tensor, vector-tensor or bimetric). Finally, we present the equations of motion for our unified approach in such a way that they can be implemented in Einstein-Boltzmann solvers.

Influence of the Proton Pressure Tensor on the Turbulent Velocity Spectrum at Ion Kinetic Scales

NASA Astrophysics Data System (ADS)

Vasquez, B. J.; Markovskii, S.

2011-12-01

Numerical hybrid simulations with particle protons and fluid electrons are presented for turbulent fluctuations with spatial variations in a plane perpendicular to the background magnetic field. The steepened portion of the proton bulk velocity spectrum is found at smaller wavenumbers for larger background proton temperature. The velocity spectrum is determined, in part, by the proton pressure tensor. The proton pressure tensor is shown to possess non-gyrotropic and finite off-diagonal components in the places where the turbulent fluctuations have developed strong gradients. Proton demagnetization at these places is a factor in the departure from a Maxwellian velocity distribution function. How demagnetization could connect with both reversible and effectively irreversible aspects of the pressure tensor is considered. The effectively irreversible aspect corresponds to the net heating of the protons and to the dissipation of the turbulent energy cascade.

An ab initio MO study of heavy atom effects on the zero-field splitting tensors of high-spin nitrenes: how the spin-orbit contributions are affected.

PubMed

Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Kitagawa, Masahiro; Takui, Takeji

2014-05-21

The CASSCF and the hybrid CASSCF-MRMP2 methods are applied to the calculations of spin-spin and spin-orbit contributions to the zero-field splitting tensors (D tensors) of the halogen-substituted spin-septet 2,4,6-trinitrenopyridines, focusing on the heavy atom effects on the spin-orbit term of the D tensors (D(SO) tensors). The calculations reproduced experimentally determined |D| values within an error of 15%. Halogen substitutions at the 3,5-positions are less influential in the spin-spin dipolar (D(SS)) term of 2,4,6-trinitrenopyridines, although the D(SO) terms are strongly affected by the introduction of heavier halogens. The absolute sign of the D(SO) value (D = D(ZZ) - (D(XX) + D(YY))/2) of 3,5-dibromo derivative 3 is predicted to be negative, which contradicts the Pederson-Khanna (PK) DFT result previously reported. The large negative contributions to the D(SO) value of 3 arise from the excited spin-septet states ascribed mainly to the excitations of in-plane lone pair of bromine atoms → SOMO of π nature. The importance of the excited states involving electron transitions from the lone pair orbital of the halogen atom is also confirmed in the D(SO) tensors of halogen-substituted para-phenylnitrenes. A new scheme based on the orbital region partitioning is proposed for the analysis of the D(SO) tensors as calculated by means of the PK-DFT approach.

Short-range components of nuclear forces: Experiment versus mythology

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

Kukulin, V. I.; Platonova, M. N., E-mail: platonova@nucl-th.sinp.msu.ru

2013-12-15

The present-day situation around the description of various (central, spin-orbit, and tensor) components of short-range nuclear forces is discussed. A traditional picture of these interactions based on the idea of one-meson exchange is contrasted against numerous results of recent experiments. As is shown in the present study, these results often deviate strongly from the predictions of traditional models. One can therefore state that such models are inapplicable to describing short-range nuclear forces and that it is necessary to go over from a traditional description to some alternative QCD-based (or QCD-motivated) picture. This means that, despite the widespread popularity of traditionalmore » concepts of short-range nuclear forces and their applicability in many particular cases, these concepts are not more than scientific myths that show their inconsistency when analyzed from the viewpoint of the modern experiment.« less

Point force singularities outside a drop covered with an incompressible surfactant: Image systems and their applications

NASA Astrophysics Data System (ADS)

Shaik, Vaseem A.; Ardekani, Arezoo M.

2017-11-01

In this work we derive the image flow fields for point force singularities placed outside a stationary drop covered with an insoluble, nondiffusing, and incompressible surfactant. We assume the interface to be Newtonian and use the Boussinesq-Scriven constitutive law for the interfacial stress tensor. We use this analytical solution to investigate two different problems. First, we derive the mobility matrix for two drops of arbitrary sizes covered with an incompressible surfactant. In the second example, we calculate the velocity of a swimming microorganism (modeled as a Stokes dipole) outside a drop covered with an incompressible surfactant.

Contribution of cardiac-induced brain pulsation to the noise of the diffusion tensor in Turboprop diffusion tensor imaging (DTI).

PubMed

Gui, Minzhi; Tamhane, Ashish A; Arfanakis, Konstantinos

2008-05-01

To assess the effects of cardiac-induced brain pulsation on the noise of the diffusion tensor in Turboprop (a form of periodically rotated overlapping parallel lines with enhanced reconstruction [PROPELLER] imaging) diffusion tensor imaging (DTI). A total of six healthy human subjects were imaged with cardiac-gated as well as nongated Turboprop DTI. Gated and nongated Turboprop DTI datasets were also simulated using actual data acquired exclusively during the diastolic or systolic period of the cardiac cycle. The total variance of the diffusion tensor (TVDT) was measured and compared between acquisitions. The TVDT near the ventricles was significantly reduced in cardiac-gated compared to nongated Turboprop DTI acquisitions. Furthermore, the effects of brain pulsation were reduced, but not eliminated, when increasing the amount of data collected. Finally, data corrupted by cardiac-induced pulsation were not consistently detected by the step of the conventional Turboprop reconstruction algorithm that evaluates the quality of data in different blades. Thus, the inherent quality weighting of the conventional Turboprop reconstruction algorithm was unable to compensate for the increased noise in the diffusion tensor due to brain pulsation. Cardiac-induced brain pulsation increases the TVDT in Turboprop DTI. Use of cardiac gating to limit data acquisition to the diastolic period of the cardiac cycle reduces the TVDT at the expense of imaging time. (c) 2008 Wiley-Liss, Inc.

Dissipation consistent fabric tensor definition from DEM to continuum for granular media

NASA Astrophysics Data System (ADS)

Li, X. S.; Dafalias, Y. F.

2015-05-01

In elastoplastic soil models aimed at capturing the impact of fabric anisotropy, a necessary ingredient is a measure of anisotropic fabric in the form of an evolving tensor. While it is possible to formulate such a fabric tensor based on indirect phenomenological observations at the continuum level, it is more effective and insightful to have the tensor defined first based on direct particle level microstructural observations and subsequently deduce a corresponding continuum definition. A practical means able to provide such observations, at least in the context of fabric evolution mechanisms, is the discrete element method (DEM). Some DEM defined fabric tensors such as the one based on the statistics of interparticle contact normals have already gained widespread acceptance as a quantitative measure of fabric anisotropy among researchers of granular material behavior. On the other hand, a fabric tensor in continuum elastoplastic modeling has been treated as a tensor-valued internal variable whose evolution must be properly linked to physical dissipation. Accordingly, the adaptation of a DEM fabric tensor definition to a continuum constitutive modeling theory must be thermodynamically consistent in regards to dissipation mechanisms. The present paper addresses this issue in detail, brings up possible pitfalls if such consistency is violated and proposes remedies and guidelines for such adaptation within a recently developed Anisotropic Critical State Theory (ACST) for granular materials.

Analytical effective tensor for flow-through composites

DOEpatents

Sviercoski, Rosangela De Fatima [Los Alamos, NM

2012-06-19

A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an analytical calculation of an effective tensor K.sup.a suitable for use with a variety of media. The analytical calculation corresponds to an approximation to the tensor K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.

2PI effective action for the SYK model and tensor field theories

NASA Astrophysics Data System (ADS)

Benedetti, Dario; Gurau, Razvan

2018-05-01

We discuss the two-particle irreducible (2PI) effective action for the SYK model and for tensor field theories. For the SYK model the 2PI effective action reproduces the bilocal reformulation of the model without using replicas. In general tensor field theories the 2PI formalism is the only way to obtain a bilocal reformulation of the theory, and as such is a precious instrument for the identification of soft modes and for possible holographic interpretations. We compute the 2PI action for several models, and push it up to fourth order in the 1 /N expansion for the model proposed by Witten in [1], uncovering a one-loop structure in terms of an auxiliary bilocal action.

Relativistic Brueckner-Hartree-Fock theory for neutron drops

NASA Astrophysics Data System (ADS)

Shen, Shihang; Liang, Haozhao; Meng, Jie; Ring, Peter; Zhang, Shuangquan

2018-05-01

Neutron drops confined in an external field are studied in the framework of relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. The ground-state energies and radii of neutron drops with even numbers from N =4 to N =50 are calculated and compared with results obtained from other nonrelativistic ab initio calculations and from relativistic density functional theory. Special attention has been paid to the magic numbers and to the subshell closures. The single-particle energies are investigated and the monopole effect of the tensor force on the evolutions of the spin-orbit and the pseudospin-orbit splittings is discussed. The results provide interesting insights into neutron-rich systems and can form an important guide for future density functionals.

Adaptive momentum management for large space structures

NASA Technical Reports Server (NTRS)

Hahn, E.

1987-01-01

Momentum management is discussed for a Large Space Structure (LSS) with the structure selected configuration being the Initial Orbital Configuration (IOC) of the dual keel space station. The external forces considered were gravity gradient and aerodynamic torques. The goal of the momentum management scheme developed is to remove the bias components of the external torques and center the cyclic components of the stored angular momentum. The scheme investigated is adaptive to uncertainties of the inertia tensor and requires only approximate knowledge of principle moments of inertia. Computational requirements are minimal and should present no implementation problem in a flight type computer and the method proposed is shown to be effective in the presence of attitude control bandwidths as low as .01 radian/sec.

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.

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.

Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization.

PubMed

Sun, Yanfeng; Gao, Junbin; Hong, Xia; Mishra, Bamdev; Yin, Baocai

2016-03-01

Tensor clustering is an important tool that exploits intrinsically rich structures in real-world multiarray or Tensor datasets. Often in dealing with those datasets, standard practice is to use subspace clustering that is based on vectorizing multiarray data. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model taking into account cluster membership information. We propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the multinomial manifold for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization.

Progressive Stereo Locking (PSL): A Residual Dipolar Coupling Based Force Field Method for Determining the Relative Configuration of Natural Products and Other Small Molecules.

PubMed

Cornilescu, Gabriel; Ramos Alvarenga, René F; Wyche, Thomas P; Bugni, Tim S; Gil, Roberto R; Cornilescu, Claudia C; Westler, William M; Markley, John L; Schwieters, Charles D

2017-08-18

Establishing the relative configuration of a bioactive natural product represents the most challenging part in determining its structure. Residual dipolar couplings (RDCs) are sensitive probes of the relative spatial orientation of internuclear vectors. We adapted a force field structure calculation methodology to allow free sampling of both R and S configurations of the stereocenters of interest. The algorithm uses a floating alignment tensor in a simulated annealing protocol to identify the conformations and configurations that best fit experimental RDC and distance restraints (from NOE and J-coupling data). A unique configuration (for rigid molecules) or a very small number of configurations (for less rigid molecules) of the structural models having the lowest chiral angle energies and reasonable magnitudes of the alignment tensor are provided as the best predictions of the unknown configuration. For highly flexible molecules, the progressive locking of their stereocenters into their statistically dominant R or S state dramatically reduces the number of possible relative configurations. The result is verified by checking that the same configuration is obtained by initiating the locking from different regions of the molecule. For all molecules tested having known configurations (with conformations ranging from mostly rigid to highly flexible), the method accurately determined the correct configuration.

Influence of N-H...O and C-H...O hydrogen bonds on the 17O NMR tensors in crystalline uracil: computational study.

PubMed

Ida, Ramsey; De Clerk, Maurice; Wu, Gang

2006-01-26

We report a computational study for the 17O NMR tensors (electric field gradient and chemical shielding tensors) in crystalline uracil. We found that N-H...O and C-H...O hydrogen bonds around the uracil molecule in the crystal lattice have quite different influences on the 17O NMR tensors for the two C=O groups. The computed 17O NMR tensors on O4, which is involved in two strong N-H...O hydrogen bonds, show remarkable sensitivity toward the choice of cluster model, whereas the 17O NMR tensors on O2, which is involved in two weak C-H...O hydrogen bonds, show much smaller improvement when the cluster model includes the C-H...O hydrogen bonds. Our results demonstrate that it is important to have accurate hydrogen atom positions in the molecular models used for 17O NMR tensor calculations. In the absence of low-temperature neutron diffraction data, an effective way to generate reliable hydrogen atom positions in the molecular cluster model is to employ partial geometry optimization for hydrogen atom positions using a cluster model that includes all neighboring hydrogen-bonded molecules. Using an optimized seven-molecule model (a total of 84 atoms), we were able to reproduce the experimental 17O NMR tensors to a reasonably good degree of accuracy. However, we also found that the accuracy for the calculated 17O NMR tensors at O2 is not as good as that found for the corresponding tensors at O4. In particular, at the B3LYP/6-311++G(d,p) level of theory, the individual 17O chemical shielding tensor components differ by less than 10 and 30 ppm from the experimental values for O4 and O2, respectively. For the 17O quadrupole coupling constant, the calculated values differ by 0.30 and 0.87 MHz from the experimental values for O4 and O2, respectively.

Energy-momentum tensors in linearized Einstein's theory and massive gravity: The question of uniqueness

NASA Astrophysics Data System (ADS)

Bičák, Jiří; Schmidt, Josef

2016-01-01

The question of the uniqueness of energy-momentum tensors in the linearized general relativity and in the linear massive gravity is analyzed without using variational techniques. We start from a natural ansatz for the form of the tensor (for example, that it is a linear combination of the terms quadratic in the first derivatives), and require it to be conserved as a consequence of field equations. In the case of the linear gravity in a general gauge we find a four-parametric system of conserved second-rank tensors which contains a unique symmetric tensor. This turns out to be the linearized Landau-Lifshitz pseudotensor employed often in full general relativity. We elucidate the relation of the four-parametric system to the expression proposed recently by Butcher et al. "on physical grounds" in harmonic gauge, and we show that the results coincide in the case of high-frequency waves in vacuum after a suitable averaging. In the massive gravity we show how one can arrive at the expression which coincides with the "generalized linear symmetric Landau-Lifshitz" tensor. However, there exists another uniquely given simpler symmetric tensor which can be obtained by adding the divergence of a suitable superpotential to the canonical energy-momentum tensor following from the Fierz-Pauli action. In contrast to the symmetric tensor derived by the Belinfante procedure which involves the second derivatives of the field variables, this expression contains only the field and its first derivatives. It is simpler than the generalized Landau-Lifshitz tensor but both yield the same total quantities since they differ by the divergence of a superpotential. We also discuss the role of the gauge conditions in the proofs of the uniqueness. In the Appendix, the symbolic tensor manipulation software cadabra is briefly described. It is very effective in obtaining various results which would otherwise require lengthy calculations.

Nuclear spin relaxation due to chemical shift anisotropy of gas-phase 129Xe.

PubMed

Hanni, Matti; Lantto, Perttu; Vaara, Juha

2011-08-14

Nuclear spin relaxation provides detailed dynamical information on molecular systems and materials. Here, first-principles modeling of the chemical shift anisotropy (CSA) relaxation time for the prototypic monoatomic (129)Xe gas is carried out, both complementing and predicting the results of NMR measurements. Our approach is based on molecular dynamics simulations combined with pre-parametrized ab initio binary nuclear shielding tensors, an "NMR force field". By using the Redfield relaxation formalism, the simulated CSA time correlation functions lead to spectral density functions that, for the first time, quantitatively determine the experimental spin-lattice relaxation times T(1). The quality requirements on both the Xe-Xe interaction potential and binary shielding tensor are investigated in the context of CSA T(1). Persistent dimers Xe(2) are found to be responsible for the CSA relaxation mechanism in the low-density limit of the gas, completely in line with the earlier experimental findings.

Pressure gradients fail to predict diffusio-osmosis

NASA Astrophysics Data System (ADS)

Liu, Yawei; Ganti, Raman; Frenkel, Daan

2018-05-01

We present numerical simulations of diffusio-osmotic flow, i.e. the fluid flow generated by a concentration gradient along a solid-fluid interface. In our study, we compare a number of distinct approaches that have been proposed for computing such flows and compare them with a reference calculation based on direct, non-equilibrium molecular dynamics simulations. As alternatives, we consider schemes that compute diffusio-osmotic flow from the gradient of the chemical potentials of the constituent species and from the gradient of the component of the pressure tensor parallel to the interface. We find that the approach based on treating chemical potential gradients as external forces acting on various species agrees with the direct simulations, thereby supporting the approach of Marbach et al (2017 J. Chem. Phys. 146 194701). In contrast, an approach based on computing the gradients of the microscopic pressure tensor does not reproduce the direct non-equilibrium results.

Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology

NASA Astrophysics Data System (ADS)

Wang, Xin; Szalay, Alex

2016-03-01

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.

STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY

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

Wang, Xin; Szalay, Alex, E-mail: xwang@cita.utoronto.ca

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differentialmore » equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.« less

Simulations of Magnetic Reconnection - Kinetic Mechanisms Underlying the Fluid Description of Ions

NASA Technical Reports Server (NTRS)

Aunai, icolas; Belmont, Gerard; Smets, Roch

2012-01-01

Because of its ability to transfer the energy stored in magnetic field together with the breaking of the flux freezing constraint, magnetic reconnection is considered as one of the most important phenomena in plasma physics. When it happens in a collision less environment such as the terrestrial magnetosphere, it should a priori be modelled with in the framework of kinetic physics. The evidence of kinetic features has incidentally for a long time, been shown by researchers with the help of both numerical simulations and satellite observations. However, most of our understanding of the process comes from the more intuitive fluid interpretation with simple closure hypothesis which do not include kinetic effects. To what extent are these two separate descriptions of the same phenomenon related? What is the role of kinetic effects in the averaged/fluid dynamics of reconnection? This thesis addresses these questions for the proton population in the particular case of anti parallel merging with the help of 2D Hybrid simulations. We show that one can not assume, as is usually done, that the acceleration of the proton flow is only due to the Laplace force. Our results show, for symmetric and asymmetric connection, the importance of the pressure force, opposed to the electric one on the separatrices, in the decoupling region. In the symmetric case, we emphasize the kinetic origin of this force by analyzing the proton distribution functions and explain their structure by studying the underlying particle dynamics. Protons, as individual particles, are shown to bounce in the electric potential well created by the Hall effect. The spatial divergence of this well results in a mixing in phase space responsible for the observed structure of the pressure tensor. A detailed energy budget analysis confirms the role of the pressure force for the acceleration; but, contrary to what is sometimes assumed, it also reveals that the major part of the incoming Poynting flux is transferred to the thermal energy flux rather than to the convective kinetic energy flux, although the latter is generally supposed dominant. In the symmetric case, we propose the pressure tensor to be an additional proxy of the ion decoupling region in satellite data and verify this suggestion by studying a reconnection event encountered by the Cluster spacecrafts. Finally, the last part of this thesis is devoted to the study of the kinetic structure of asymmetric tangential current sheets where connection can develop. This theoretical part consists in finding a steady state solution to the Vlasov-Maxwell system for the protons in such a configuration. We present the theory and its first confrontation to numerical tests.

Approximate bound-state solutions of the Dirac equation for the generalized yukawa potential plus the generalized tensor interaction

NASA Astrophysics Data System (ADS)

Ikot, Akpan N.; Maghsoodi, Elham; Hassanabadi, Hassan; Obu, Joseph A.

2014-05-01

In this paper, we obtain the approximate analytical bound-state solutions of the Dirac particle with the generalized Yukawa potential within the framework of spin and pseudospin symmetries for the arbitrary к state with a generalized tensor interaction. The generalized parametric Nikiforov-Uvarov method is used to obtain the energy eigenvalues and the corresponding wave functions in closed form. We also report some numerical results and present figures to show the effect of the tensor interaction.

Tensor scale-based fuzzy connectedness image segmentation

NASA Astrophysics Data System (ADS)

Saha, Punam K.; Udupa, Jayaram K.

2003-05-01

Tangible solutions to image segmentation are vital in many medical imaging applications. Toward this goal, a framework based on fuzzy connectedness was developed in our laboratory. A fundamental notion called "affinity" - a local fuzzy hanging togetherness relation on voxels - determines the effectiveness of this segmentation framework in real applications. In this paper, we introduce the notion of "tensor scale" - a recently developed local morphometric parameter - in affinity definition and study its effectiveness. Although, our previous notion of "local scale" using the spherical model successfully incorporated local structure size into affinity and resulted in measureable improvements in segmentation results, a major limitation of the previous approach was that it ignored local structural orientation and anisotropy. The current approach of using tensor scale in affinity computation allows an effective utilization of local size, orientation, and ansiotropy in a unified manner. Tensor scale is used for computing both the homogeneity- and object-feature-based components of affinity. Preliminary results of the proposed method on several medical images and computer generated phantoms of realistic shapes are presented. Further extensions of this work are discussed.

Anisotropic mesoscale eddy transport in ocean general circulation models

NASA Astrophysics Data System (ADS)

Reckinger, Scott; Fox-Kemper, Baylor; Bachman, Scott; Bryan, Frank; Dennis, John; Danabasoglu, Gokhan

2014-11-01

In modern climate models, the effects of oceanic mesoscale eddies are introduced by relating subgrid eddy fluxes to the resolved gradients of buoyancy or other tracers, where the proportionality is, in general, governed by an eddy transport tensor. The symmetric part of the tensor, which represents the diffusive effects of mesoscale eddies, is universally treated isotropically. However, the diffusive processes that the parameterization approximates, such as shear dispersion and potential vorticity barriers, typically have strongly anisotropic characteristics. Generalizing the eddy diffusivity tensor for anisotropy extends the number of parameters from one to three: major diffusivity, minor diffusivity, and alignment. The Community Earth System Model (CESM) with the anisotropic eddy parameterization is used to test various choices for the parameters, which are motivated by observations and the eddy transport tensor diagnosed from high resolution simulations. Simply setting the ratio of major to minor diffusivities to a value of five globally, while aligning the major axis along the flow direction, improves biogeochemical tracer ventilation and reduces temperature and salinity biases. These effects can be improved by parameterizing the oceanic anisotropic transport mechanisms.

Short-range correlation in high-momentum antisymmetrized molecular dynamics

NASA Astrophysics Data System (ADS)

Myo, Takayuki

2018-03-01

We propose a new variational method for treating short-range repulsion of bare nuclear force for nuclei in antisymmetrized molecular dynamics (AMD). In AMD, the short-range correlation is described in terms of large imaginary centroids of Gaussian wave packets of nucleon pairs in opposite signs, causing high-momentum components in the nucleon pairs. We superpose these AMD basis states and call this method "high-momentum AMD" (HM-AMD), which is capable of describing the strong tensor correlation [T. Myo et al., Prog. Theor. Exp. Phys., 2017, 111D01 (2017)]. In this letter, we extend HM-AMD by including up to two kinds of nucleon pairs in each AMD basis state utilizing the cluster expansion, which produces many-body correlations involving high-momentum components. We investigate how well HM-AMD describes the short-range correlation by showing the results for ^3H using the Argonne V4^' central potential. It is found that HM-AMD reproduces the results of few-body calculations and also the tensor-optimized AMD. This means that HM-AMD is a powerful approach to describe the short-range correlation in nuclei. In HM-AMD, the momentum directions of nucleon pairs isotropically contribute to the short-range correlation, which is different from the tensor correlation.

Spatial Mapping of Translational Diffusion Coefficients Using Diffusion Tensor Imaging: A Mathematical Description

PubMed Central

SHETTY, ANIL N.; CHIANG, SHARON; MALETIC-SAVATIC, MIRJANA; KASPRIAN, GREGOR; VANNUCCI, MARINA; LEE, WESLEY

2016-01-01

In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain. PMID:27441031

A new formulation of the dispersion tensor in homogeneous porous media

NASA Astrophysics Data System (ADS)

Valdés-Parada, Francisco J.; Lasseux, Didier; Bellet, Fabien

2016-04-01

Dispersion is the result of two mass transport processes, namely molecular diffusion, which is a pure mixing effect and hydrodynamic dispersion, which combines mixing and spreading. The identification of each contribution is crucial and is often misinterpreted. Traditionally, under a volume averaging framework, a single closure problem is solved and the resulting fields are substituted into diffusive and dispersive filters. However the diffusive filter (that leads to the effective diffusivity) allows passing information from convection, which leads to an incorrect definition of the effective medium coefficients composing the total dispersion tensor. In this work, we revisit the definitions of the effective diffusivity and hydrodynamic dispersion tensors using the method of volume averaging. Our analysis shows that, in the context of laminar flow with or without inertial effects, two closure problems need to be computed in order to correctly define the corresponding effective medium coefficients. The first closure problem is associated to momentum transport and needs to be solved for a prescribed Reynolds number and flow orientation. The second closure problem is related to mass transport and it is solved first with a zero Péclet number and second with the required Péclet number and flow orientation. All the closure problems are written using closure variables only as required by the upscaling method. The total dispersion tensor is shown to depend on the microstructure, macroscopic flow angles, the cell (or pore) Péclet number and the cell (or pore) Reynolds number. It is non-symmetric in the general case. The condition for quasi-symmetry is highlighted. The functionality of the longitudinal and transverse components of this tensor with the flow angle is investigated for a 2D model porous structure obtaining consistent results with previous studies.

Scalar-tensor extension of the ΛCDM model

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

Algoner, W.C.; Velten, H.E.S.; Zimdahl, W., E-mail: w.algoner@cosmo-ufes.org, E-mail: velten@pq.cnpq.br, E-mail: winfried.zimdahl@pq.cnpq.br

2016-11-01

We construct a cosmological scalar-tensor-theory model in which the Brans-Dicke type scalar Φ enters the effective (Jordan-frame) Hubble rate as a simple modification of the Hubble rate of the ΛCDM model. This allows us to quantify differences between the background dynamics of scalar-tensor theories and general relativity (GR) in a transparent and observationally testable manner in terms of one single parameter. Problems of the mapping of the scalar-field degrees of freedom on an effective fluid description in a GR context are discused. Data from supernovae, the differential age of old galaxies and baryon acoustic oscillations are shown to strongly limitmore » potential deviations from the standard model.« less

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.

Effective field theory of statistical anisotropies for primordial bispectrum and gravitational waves

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

Rostami, Tahereh; Karami, Asieh; Firouzjahi, Hassan, E-mail: t.rostami@ipm.ir, E-mail: karami@ipm.ir, E-mail: firouz@ipm.ir

2017-06-01

We present the effective field theory studies of primordial statistical anisotropies in models of anisotropic inflation. The general action in unitary gauge is presented to calculate the leading interactions between the gauge field fluctuations, the curvature perturbations and the tensor perturbations. The anisotropies in scalar power spectrum and bispectrum are calculated and the dependence of these anisotropies to EFT couplings are presented. In addition, we calculate the statistical anisotropy in tensor power spectrum and the scalar-tensor cross correlation. Our EFT approach incorporates anisotropies generated in models with non-trivial speed for the gauge field fluctuations and sound speed for scalar perturbationsmore » such as in DBI inflation.« less

A propulsion-mass tensor coupling in relativistic rocket motion

NASA Astrophysics Data System (ADS)

Brito, Hector Hugo

1998-01-01

Following earlier speculations about antigravity machines and works on the relativistic dynamics of constant and variable rest mass point particles, a mass tensor is found in connection with the closed system consisting of the rocket driven spaceship and its propellant mass, provided a ``solidification'' point other than the system center of mass is considered. Therefore, the mass tensor form depends on whether the system is open or closed, and upon where the ``solidification'' point is located. An alternative propulsion principle is subsequently derived from the tensor mass approach. The new principle, the covariant equivalent of Newton's Third Law for the physical interpretation of the relativistic rocket motion, reads: A spaceship undergoes a propulsion effect when the whole system mass 4-ellipsoid warps.

Tensor form factor for the D → π(K) transitions with Twisted Mass fermions.

NASA Astrophysics Data System (ADS)

Lubicz, Vittorio; Riggio, Lorenzo; Salerno, Giorgio; Simula, Silvano; Tarantino, Cecilia

2018-03-01

We present a preliminary lattice calculation of the D → π and D → K tensor form factors fT (q2) as a function of the squared 4-momentum transfer q2. ETMC recently computed the vector and scalar form factors f+(q2) and f0(q2) describing D → π(K)lv semileptonic decays analyzing the vector current and the scalar density. The study of the weak tensor current, which is directly related to the tensor form factor, completes the set of hadronic matrix element regulating the transition between these two pseudoscalar mesons within and beyond the Standard Model where a non-zero tensor coupling is possible. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 flavors of dynamical quarks. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV and with the valence heavy quark in the mass range from ≃ 0.7 mc to ≃ 1.2mc. The matrix element of the tensor current are determined for a plethora of kinematical conditions in which parent and child mesons are either moving or at rest. As for the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data. We will present preliminary results on the removal of such hypercubic lattice effects.

Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density

NASA Astrophysics Data System (ADS)

Jiang, Li; Liu, Jie; Zhang, Jianzhong; Feng, Zhibing

2017-12-01

Variable-density sources have been paid more attention in gravity modeling. We conduct the computation of gravity gradient tensor of given mass sources with variable density in this paper. 3D rectangular prisms, as simple building blocks, can be used to approximate well 3D irregular-shaped sources. A polynomial function of depth can represent flexibly the complicated density variations in each prism. Hence, we derive the analytic expressions in closed form for computing all components of the gravity gradient tensor due to a 3D right rectangular prism with an arbitrary-order polynomial density function of depth. The singularity of the expressions is analyzed. The singular points distribute at the corners of the prism or on some of the lines through the edges of the prism in the lower semi-space containing the prism. The expressions are validated, and their numerical stability is also evaluated through numerical tests. The numerical examples with variable-density prism and basin models show that the expressions within their range of numerical stability are superior in computational accuracy and efficiency to the common solution that sums up the effects of a collection of uniform subprisms, and provide an effective method for computing gravity gradient tensor of 3D irregular-shaped sources with complicated density variation. In addition, the tensor computed with variable density is different in magnitude from that with constant density. It demonstrates the importance of the gravity gradient tensor modeling with variable density.

Optimizing the Four-Index Integral Transform Using Data Movement Lower Bounds Analysis

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

Rajbhandari, Samyam; Rastello, Fabrice; Kowalski, Karol

The four-index integral transform is a fundamental and computationally demanding calculation used in many computational chemistry suites such as NWChem. It transforms a four-dimensional tensor from an atomic basis to a molecular basis. This transformation is most efficiently implemented as a sequence of four tensor contractions that each contract a four-dimensional tensor with a two-dimensional transformation matrix. Differing degrees of permutation symmetry in the intermediate and final tensors in the sequence of contractions cause intermediate tensors to be much larger than the final tensor and limit the number of electronic states in the modeled systems. Loop fusion, in conjunction withmore » tiling, can be very effective in reducing the total space requirement, as well as data movement. However, the large number of possible choices for loop fusion and tiling, and data/computation distribution across a parallel system, make it challenging to develop an optimized parallel implementation for the four-index integral transform. We develop a novel approach to address this problem, using lower bounds modeling of data movement complexity. We establish relationships between available aggregate physical memory in a parallel computer system and ineffective fusion configurations, enabling their pruning and consequent identification of effective choices and a characterization of optimality criteria. This work has resulted in the development of a significantly improved implementation of the four-index transform that enables higher performance and the ability to model larger electronic systems than the current implementation in the NWChem quantum chemistry software suite.« less

The free energy of a reaction coordinate at multiple constraints: a concise formulation

NASA Astrophysics Data System (ADS)

Schlitter, Jürgen; Klähn, Marco

The free energy as a function of the reaction coordinate (rc) is the key quantity for the computation of equilibrium and kinetic quantities. When it is considered as the potential of mean force, the problem is the calculation of the mean force for given values of the rc. We reinvestigate the PMCF (potential of mean constraint force) method which applies a constraint to the rc to compute the mean force as the mean negative constraint force and a metric tensor correction. The latter allows for the constraint imposed to the rc and possible artefacts due to multiple constraints of other variables which for practical reasons are often used in numerical simulations. Two main results are obtained that are of theoretical and practical interest. First, the correction term is given a very concise and simple shape which facilitates its interpretation and evaluation. Secondly, a theorem describes various rcs and possible combinations with constraints that can be used without introducing any correction to the constraint force. The results facilitate the computation of free energy by molecular dynamics simulations.

An analysis of the high-latitude thermospheric wind pattern calculated by a thermospheric general circulation model. I - Momentum forcing

NASA Technical Reports Server (NTRS)

Killeen, T. L.; Roble, R. G.

1984-01-01

A diagnostic processor (DP) was developed for analysis of hydrodynamic and thermodynamic processes predicted by the NCAR thermospheric general circulation model (TGCM). The TGCM contains a history file on the projected wind, temperature and composition fields at each grid point for each hour of universal time. The DP assimilates the history file plus ion drag tensors and drift velocities, specific heats, coefficients of viscosity, and thermal conductivity and calculates the individual forcing terms for the momentum and energy equations for a given altitude. Sample momentum forcings were calculated for high latitudes in the presence of forcing by solar radiation and magnetospheric convection with a 60 kV cross-tail potential, i.e., conditions on Oct. 21, 1981. It was found that ion drag and pressure forces balance out at F region heights where ion drift velocities are small. The magnetic polar cap/auroral zone boundary featured the largest residual force or net acceleration. Diurnal oscillations were detected in the thermospheric convection, and geostrophic balance was dominant in the E layer.

Negative radiation forces on spheres illuminated by acoustic Bessel beams.

NASA Astrophysics Data System (ADS)

Marston, Philip L.; Thiessen, David B.

2007-11-01

An analytical solution for the scattering of an acoustic Bessel beam by a sphere centered on the beam has made it possible to explore the way the acoustic radiation force on elastic and fluid spheres depends on beam and material parameters. Situations have been previously noted where, even in the absence of absorption, the radiation force of the beam on the sphere is opposite the direction of beam propagation [1]. In extensions of that work, conditions have been identified for such a force reversal on solid spheres and elastic shells. Negative radiation forces may be useful for manipulation of objects in reduced gravity and of biological cells (with single beam acoustic tweezers). The finite element method (FEM) has been used to evaluate the total acoustic field in the region near the sphere. This makes it possible to evaluate the radiation force from numerical integration of an appropriate projection of the Brillouin radiation stress tensor. FEM and analytical results agree for plane wave and Bessel beam illumination. 1. P. L. Marston, J. Acoust. Soc. Am. 120, 3518-3524 (2006).

Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings

NASA Astrophysics Data System (ADS)

Bordin, Lorenzo; Cabass, Giovanni; Creminelli, Paolo; Vernizzi, Filippo

2017-09-01

We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the coefficients of the operators in the action: some couplings are effectively redundant. At leading order in derivatives and up to cubic order in perturbations, one has 6 free functions that can be used to set to zero 6 of the 17 operators at this order. This is used to show that the tensor three-point function cannot be modified at leading order in derivatives, while the scalar-tensor-tensor correlator can only be modified by changing the scalar dynamics. At higher order in derivatives there are transformations that do not affect the Einstein-Hilbert action: one can find 6 additional transformations that can be used to simplify the inflaton action, at least when the dynamics is dominated by the lowest derivative terms. We also identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum.

Quantitative Tractography and Volumetric MRI in Blast and Blunt Force TBI: Predictors of Neurocognitive and Behavioral Outcome

DTIC Science & Technology

2016-10-01

are related to mechanism of injury as well as white matter integrity using diffusion tensor imaging (DTI). We are also collecting and analyzing...APOE ε4] and brain-derived neurotrophic factor [BDNF]) to brain integrity , neuropsychological functioning, and neurobehavioral outcome. 15. SUBJECT...contribution of genetic factors (Apolipoprotein-E ε-4 [APOE ε4] and brain-derived neurotrophic factor [BDNF]) to brain integrity , neuropsychological

Effect of Tensor Range in Nuclear Two-Body Problems

DOE R&D Accomplishments Database

Feshbach, H.; Schwinger, J.; Harr, J. A.

1949-11-01

The interaction between neutron and proton in the triplet state is investigated, a wide variation in the values of both central and tensor ranges are included; the per cent D state in the deuteron and the effective triplet range have been computed; the results are applied tot he discussion of the magnetic moment of the deuteron, the photoelectric disintegration of the deuteron, and neutron-proton scattering.

Soft-tissue tension total knee arthroplasty.

PubMed

Asano, Hiroshi; Hoshino, Akiho; Wilton, Tim J

2004-08-01

It is far from clear how best to define the proper strength of soft-tissue tensioning in total knee arthroplasty (TKA). We attached a torque driver to the Monogram balancer/tensor device and measured soft-tissue tension in full extension and 90 degrees flexion during TKA. In our surgical procedure, when we felt proper soft-tissue tension was being applied, the mean distraction force was noted to be 126N in extension and 121N in flexion. There was no significant correlation between soft-tissue tension and the postoperative flexion angle finally achieved. To the best of our knowledge, this is the first study to assess the actual distraction forces in relation to soft-tissue tension in TKA. Further study may reveal the most appropriate forces to achieve proper soft-tissue tension in the wide variety of circumstances presenting at knee arthroplasty.

Nanoscale swimmers: hydrodynamic interactions and propulsion of molecular machines

NASA Astrophysics Data System (ADS)

Sakaue, T.; Kapral, R.; Mikhailov, A. S.

2010-06-01

Molecular machines execute nearly regular cyclic conformational changes as a result of ligand binding and product release. This cyclic conformational dynamics is generally non-reciprocal so that under time reversal a different sequence of machine conformations is visited. Since such changes occur in a solvent, coupling to solvent hydrodynamic modes will generally result in self-propulsion of the molecular machine. These effects are investigated for a class of coarse grained models of protein machines consisting of a set of beads interacting through pair-wise additive potentials. Hydrodynamic effects are incorporated through a configuration-dependent mobility tensor, and expressions for the propulsion linear and angular velocities, as well as the stall force, are obtained. In the limit where conformational changes are small so that linear response theory is applicable, it is shown that propulsion is exponentially small; thus, propulsion is nonlinear phenomenon. The results are illustrated by computations on a simple model molecular machine.

Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients

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

Ringholm, Magnus; Ruud, Kenneth; Bast, Radovan

We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields,more » reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.« less

Effects of a primordial magnetic field with log-normal distribution on the cosmic microwave background

NASA Astrophysics Data System (ADS)

Yamazaki, Dai G.; Ichiki, Kiyotomo; Takahashi, Keitaro

2011-12-01

We study the effect of primordial magnetic fields (PMFs) on the anisotropies of the cosmic microwave background (CMB). We assume the spectrum of PMFs is described by log-normal distribution which has a characteristic scale, rather than power-law spectrum. This scale is expected to reflect the generation mechanisms and our analysis is complementary to previous studies with power-law spectrum. We calculate power spectra of energy density and Lorentz force of the log-normal PMFs, and then calculate CMB temperature and polarization angular power spectra from scalar, vector, and tensor modes of perturbations generated from such PMFs. By comparing these spectra with WMAP7, QUaD, CBI, Boomerang, and ACBAR data sets, we find that the current CMB data set places the strongest constraint at k≃10-2.5Mpc-1 with the upper limit B≲3nG.

Elementary Development of the Gravitational Self-Force

NASA Astrophysics Data System (ADS)

Detweiler, Steven

The gravitational field of a particle of small mass m moving through curved spacetime, with metric g ab , is naturally and easily decomposed into two parts each of which satisfies the perturbed Einstein equations through O(m). One part is an inhomogeneous field h ab S which, near the particle, looks like the Coulomb m / r field with tidal distortion from the local Riemann tensor. This singular field is defined in a neighborhood of the small particle and does not depend upon boundary conditions or upon the behavior of the source in either the past or the future. The other part is a homogeneous field h ab R. In a perturbative analysis, the motion of the particle is then best described as being a geodesic in the metric g ab + h ab R. This geodesic motion includes all of the effects which might be called radiation reaction and conservative effects as well.

The effective boundary conditions and their lifespan of the logistic diffusion equation on a coated body

NASA Astrophysics Data System (ADS)

Li, Huicong; Wang, Xuefeng; Wu, Yanxia

2014-11-01

We consider the logistic diffusion equation on a bounded domain, which has two components with a thin coating surrounding a body. The diffusion tensor is isotropic on the body, and anisotropic on the coating. The size of the diffusion tensor on these components may be very different; within the coating, the diffusion rates in the normal and tangent directions may be in different scales. We find effective boundary conditions (EBCs) that are approximately satisfied by the solution of the diffusion equation on the boundary of the body. We also prove that the lifespan of each EBC, which measures how long the EBC remains effective, is infinite. The EBCs enable us to see clearly the effect of the coating and ease the difficult task of solving the PDE in a thin region with a small diffusion tensor. The motivation of the mathematics includes a nature reserve surrounded by a buffer zone.

Palatal botulinum toxin as a novel therapy for objective tinnitus in forced eyelid closure syndrome.

PubMed

Kaffenberger, Thomas M; Mandal, Rajarsi; Schaitkin, Barry M; Hirsch, Barry E

2017-05-01

Objective tinnitus associated with eyelid closure is a rare clinical entity with only a few reported cases. This association previously was identified as forced eyelid closure syndrome (FECS) and involves an aberrant neural reflex between cranial nerve VII (activating the orbicularis oculi muscle) and cranial nerve V (activating the tensor tympani muscle). We present a 52-year-old Caucasian female with a 2-month history of FECS who was successfully treated with intrapalatal botulinum toxin, with full resolution of her objective tinnitus symptoms. This is the first reported use of botulinum toxin in FECS. Laryngoscope, 127:1199-1201, 2017. © 2016 The American Laryngological, Rhinological and Otological Society, Inc.

Tensor Analyzing Powers for Quasi-Elastic Electron Scattering from Deuterium

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

Z.-L. Zhou; M. Bouwhuis; M. Ferro-Luzzi

1999-01-01

We report on a first measurement of tensor analyzing powers in quasi-elastic electron-deuteron scattering at an average three-momentum transfer of 1.7 fm{sup -1}. Data sensitive to the spin-dependent nucleon density in the deuteron were obtained for missing momenta up to 150 MeV/c with a tensor polarized {sup 2}H target internal to an electron storage ring. The data are well described by a calculation that includes the effects of final-state interaction, meson-exchange and isobar currents, and leading-order relativistic contributions.

Effective metrics and a fully covariant description of constitutive tensors in electrodynamics

NASA Astrophysics Data System (ADS)

Schuster, Sebastian; Visser, Matt

2017-12-01

Using electromagnetism to study analogue space-times is tantamount to considering consistency conditions for when a given (meta-) material would provide an analogue space-time model or—vice versa—characterizing which given metric could be modeled with a (meta-) material. While the consistency conditions themselves are by now well known and studied, the form the metric takes once they are satisfied is not. This question is mostly easily answered by keeping the formalisms of the two research fields here in contact as close to each other as possible. While fully covariant formulations of the electrodynamics of media have been around for a long while, they are usually abandoned for (3 +1 )- or six-dimensional formalisms. Here we use the fully unified and fully covariant approach. This enables us even to generalize the consistency conditions for the existence of an effective metric to arbitrary background metrics beyond flat space-time electrodynamics. We also show how the familiar matrices for permittivity ɛ , permeability μ-1, and magnetoelectric effects ζ can be seen as the three independent pieces of the Bel decomposition for the constitutive tensor Za b c d, i.e., the components of an orthogonal decomposition with respect to a given observer with four-velocity Va. Finally, we use the Moore-Penrose pseudoinverse and the closely related pseudodeterminant to then gain the desired reconstruction of the effective metric in terms of the permittivity tensor ɛa b, the permeability tensor [μ-1]a b, and the magnetoelectric tensor ζa b, as an explicit function geff(ɛ ,μ-1,ζ ).

Decentralized Dimensionality Reduction for Distributed Tensor Data Across Sensor Networks.

PubMed

Liang, Junli; Yu, Guoyang; Chen, Badong; Zhao, Minghua

2016-11-01

This paper develops a novel decentralized dimensionality reduction algorithm for the distributed tensor data across sensor networks. The main contributions of this paper are as follows. First, conventional centralized methods, which utilize entire data to simultaneously determine all the vectors of the projection matrix along each tensor mode, are not suitable for the network environment. Here, we relax the simultaneous processing manner into the one-vector-by-one-vector (OVBOV) manner, i.e., determining the projection vectors (PVs) related to each tensor mode one by one. Second, we prove that in the OVBOV manner each PV can be determined without modifying any tensor data, which simplifies corresponding computations. Third, we cast the decentralized PV determination problem as a set of subproblems with consensus constraints, so that it can be solved in the network environment only by local computations and information communications among neighboring nodes. Fourth, we introduce the null space and transform the PV determination problem with complex orthogonality constraints into an equivalent hidden convex one without any orthogonality constraint, which can be solved by the Lagrange multiplier method. Finally, experimental results are given to show that the proposed algorithm is an effective dimensionality reduction scheme for the distributed tensor data across the sensor networks.

Tractography from HARDI using an Intrinsic Unscented Kalman Filter

PubMed Central

Cheng, Guang; Salehian, Hesamoddin; Forder, John R.; Vemuri, Baba C.

2014-01-01

A novel adaptation of the unscented Kalman filter (UKF) was recently introduced in literature for simultaneous multi-tensor estimation and fiber tractography from diffusion MRI. This technique has the advantage over other tractography methods in terms of computational efficiency, due to the fact that the UKF simultaneously estimates the diffusion tensors and propagates the most consistent direction to track along. This UKF and its variants reported later in literature however are not intrinsic to the space of diffusion tensors. Lack of this key property can possibly lead to inaccuracies in the multi-tensor estimation as well as in the tractography. In this paper, we propose a novel intrinsic unscented Kalman filter (IUKF) in the space of diffusion tensors which are symmetric positive definite matrices, that can be used for simultaneous recursive estimation of multi-tensors and propagation of directional information for use in fiber tractography from diffusion weighted MR data. In addition to being more accurate, IUKF retains all the advantages of UKF mentioned above. We demonstrate the accuracy and effectiveness of the proposed method via experiments publicly available phantom data from the fiber cup-challenge (MICCAI 2009) and diffusion weighted MR scans acquired from human brains and rat spinal cords. PMID:25203986

Variational optical flow estimation based on stick tensor voting.

PubMed

Rashwan, Hatem A; Garcia, Miguel A; Puig, Domenec

2013-07-01

Variational optical flow techniques allow the estimation of flow fields from spatio-temporal derivatives. They are based on minimizing a functional that contains a data term and a regularization term. Recently, numerous approaches have been presented for improving the accuracy of the estimated flow fields. Among them, tensor voting has been shown to be particularly effective in the preservation of flow discontinuities. This paper presents an adaptation of the data term by using anisotropic stick tensor voting in order to gain robustness against noise and outliers with significantly lower computational cost than (full) tensor voting. In addition, an anisotropic complementary smoothness term depending on directional information estimated through stick tensor voting is utilized in order to preserve discontinuity capabilities of the estimated flow fields. Finally, a weighted non-local term that depends on both the estimated directional information and the occlusion state of pixels is integrated during the optimization process in order to denoise the final flow field. The proposed approach yields state-of-the-art results on the Middlebury benchmark.

Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

PubMed

Zhao, Qibin; Zhang, Liqing; Cichocki, Andrzej

2015-09-01

CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.

Spin dynamics of paramagnetic centers with anisotropic g tensor and spin of ½

PubMed Central

Maryasov, Alexander G.

2012-01-01

The influence of g tensor anisotropy on spin dynamics of paramagnetic centers having real or effective spin of 1/2 is studied. The g anisotropy affects both the excitation and the detection of EPR signals, producing noticeable differences between conventional continuous-wave (cw) EPR and pulsed EPR spectra. The magnitudes and directions of the spin and magnetic moment vectors are generally not proportional to each other, but are related to each other through the g tensor. The equilibrium magnetic moment direction is generally parallel to neither the magnetic field nor the spin quantization axis due to the g anisotropy. After excitation with short microwave pulses, the spin vector precesses around its quantization axis, in a plane that is generally not perpendicular to the applied magnetic field. Paradoxically, the magnetic moment vector precesses around its equilibrium direction in a plane exactly perpendicular to the external magnetic field. In the general case, the oscillating part of the magnetic moment is elliptically polarized and the direction of precession is determined by the sign of the g tensor determinant (g tensor signature). Conventional pulsed and cw EPR spectrometers do not allow determination of the g tensor signature or the ellipticity of the magnetic moment trajectory. It is generally impossible to set a uniform spin turning angle for simple pulses in an unoriented or ‘powder’ sample when g tensor anisotropy is significant. PMID:22743542

Spin dynamics of paramagnetic centers with anisotropic g tensor and spin of 1/2

NASA Astrophysics Data System (ADS)

Maryasov, Alexander G.; Bowman, Michael K.

2012-08-01

The influence of g tensor anisotropy on spin dynamics of paramagnetic centers having real or effective spin of 1/2 is studied. The g anisotropy affects both the excitation and the detection of EPR signals, producing noticeable differences between conventional continuous-wave (cw) EPR and pulsed EPR spectra. The magnitudes and directions of the spin and magnetic moment vectors are generally not proportional to each other, but are related to each other through the g tensor. The equilibrium magnetic moment direction is generally parallel to neither the magnetic field nor the spin quantization axis due to the g anisotropy. After excitation with short microwave pulses, the spin vector precesses around its quantization axis, in a plane that is generally not perpendicular to the applied magnetic field. Paradoxically, the magnetic moment vector precesses around its equilibrium direction in a plane exactly perpendicular to the external magnetic field. In the general case, the oscillating part of the magnetic moment is elliptically polarized and the direction of precession is determined by the sign of the g tensor determinant (g tensor signature). Conventional pulsed and cw EPR spectrometers do not allow determination of the g tensor signature or the ellipticity of the magnetic moment trajectory. It is generally impossible to set a uniform spin turning angle for simple pulses in an unoriented or 'powder' sample when g tensor anisotropy is significant.

TensorCalculator: exploring the evolution of mechanical stress in the CCMV capsid

NASA Astrophysics Data System (ADS)

Kononova, Olga; Maksudov, Farkhad; Marx, Kenneth A.; Barsegov, Valeri

2018-01-01

A new computational methodology for the accurate numerical calculation of the Cauchy stress tensor, stress invariants, principal stress components, von Mises and Tresca tensors is developed. The methodology is based on the atomic stress approach which permits the calculation of stress tensors, widely used in continuum mechanics modeling of materials properties, using the output from the MD simulations of discrete atomic and C_α -based coarse-grained structural models of biological particles. The methodology mapped into the software package TensorCalculator was successfully applied to the empty cowpea chlorotic mottle virus (CCMV) shell to explore the evolution of mechanical stress in this mechanically-tested specific example of a soft virus capsid. We found an inhomogeneous stress distribution in various portions of the CCMV structure and stress transfer from one portion of the virus structure to another, which also points to the importance of entropic effects, often ignored in finite element analysis and elastic network modeling. We formulate a criterion for elastic deformation using the first principal stress components. Furthermore, we show that von Mises and Tresca stress tensors can be used to predict the onset of a viral capsid’s mechanical failure, which leads to total structural collapse. TensorCalculator can be used to study stress evolution and dynamics of defects in viral capsids and other large-size protein assemblies.

Solution of Eshelby's inclusion problem with a bounded domain and Eshelby's tensor for a spherical inclusion in a finite spherical matrix based on a simplified strain gradient elasticity theory

NASA Astrophysics Data System (ADS)

Gao, X.-L.; Ma, H. M.

2010-05-01

A solution for Eshelby's inclusion problem of a finite homogeneous isotropic elastic body containing an inclusion prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient elasticity theory (SSGET). An extended Betti's reciprocal theorem and an extended Somigliana's identity based on the SSGET are proposed and utilized to solve the finite-domain inclusion problem. The solution for the disturbed displacement field is expressed in terms of the Green's function for an infinite three-dimensional elastic body in the SSGET. It contains a volume integral term and a surface integral term. The former is the same as that for the infinite-domain inclusion problem based on the SSGET, while the latter represents the boundary effect. The solution reduces to that of the infinite-domain inclusion problem when the boundary effect is not considered. The problem of a spherical inclusion embedded concentrically in a finite spherical elastic body is analytically solved by applying the general solution, with the Eshelby tensor and its volume average obtained in closed forms. This Eshelby tensor depends on the position, inclusion size, matrix size, and material length scale parameter, and, as a result, can capture the inclusion size and boundary effects, unlike existing Eshelby tensors. It reduces to the classical Eshelby tensor for the spherical inclusion in an infinite matrix if both the strain gradient and boundary effects are suppressed. Numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is very small and that the boundary effect can dominate when the inclusion volume fraction is very high. However, the inclusion size effect is diminishing as the inclusion becomes large enough, and the boundary effect is vanishing as the inclusion volume fraction gets sufficiently low.

Detection, localization and classification of multiple dipole-like magnetic sources using magnetic gradient tensor data

NASA Astrophysics Data System (ADS)

Gang, Yin; Yingtang, Zhang; Hongbo, Fan; Zhining, Li; Guoquan, Ren

2016-05-01

We have developed a method for automatic detection, localization and classification (DLC) of multiple dipole sources using magnetic gradient tensor data. First, we define modified tilt angles to estimate the approximate horizontal locations of the multiple dipole-like magnetic sources simultaneously and detect the number of magnetic sources using a fixed threshold. Secondly, based on the isotropy of the normalized source strength (NSS) response of a dipole, we obtain accurate horizontal locations of the dipoles. Then the vertical locations are calculated using magnitude magnetic transforms of magnetic gradient tensor data. Finally, we invert for the magnetic moments of the sources using the measured magnetic gradient tensor data and forward model. Synthetic and field data sets demonstrate effectiveness and practicality of the proposed method.

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)

Brownian motion of massive skyrmions in magnetic thin films

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

Troncoso, Roberto E., E-mail: r.troncoso.c@gmail.com; Núñez, Álvaro S., E-mail: alnunez@dfi.uchile.cl

2014-12-15

We report on the thermal effects on the motion of current-driven massive magnetic skyrmions. The reduced equation for the motion of skyrmion has the form of a stochastic generalized Thiele’s equation. We propose an ansatz for the magnetization texture of a non-rigid single skyrmion that depends linearly with the velocity. By using this ansatz it is found that the skyrmion mass tensor is closely related to intrinsic skyrmion parameters, such as Gilbert damping, skyrmion-charge and dissipative force. We have found an exact expression for the average drift velocity as well as the mean-square velocity of the skyrmion. The longitudinal andmore » transverse mobility of skyrmions for small spin-velocity of electrons is also determined and found to be independent of the skyrmion mass.« less

Optical forces near micro-fabricated devices

NASA Astrophysics Data System (ADS)

Mejia Prada, Camilo Andres

In this dissertation, I study optical forces near micro-fabricated devices for multi- particle manipulation. I consider particles of different sizes and compositions. In particular, I focus my study on both dielectric and gold particles as well as Giant Unilamellar Vesicles. First, I consider optical forces near a PhC and establish the feasibility of a technique which we term Light-Assisted Templated Self-assembly (LATS). In contrast to previous work on Fabry-Perot enhancement of trapping forces above a flat substrate, I exploit the guided resonance modes of a PhC to provide resonant enhancement of optical forces. Then, I explore optical forces near a Dual Beam Optical Trap (DBOT). I present a method to extract the bending modulus of the membrane from the area strain data. This method incorporates three-dimensional ray-tracing to calculate the applied stress in the DBOT within the ray optics approximation. I compare the optical force calculated using the ray optics approximation and Maxwell Stress Tensor method to ensure the approximation's accuracy. Next, we apply this method to 3 populations of GUVs to extract the bending modulus of membranes comprised of saturated and monounsaturated lipids in both gel and liquid phases.

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.

Structure of force networks in tapped particulate systems of disks and pentagons. II. Persistence analysis.

PubMed

Kondic, L; Kramár, M; Pugnaloni, Luis A; Carlevaro, C Manuel; Mischaikow, K

2016-06-01

In the companion paper [Pugnaloni et al., Phys. Rev. E 93, 062902 (2016)10.1103/PhysRevE.93.062902], we use classical measures based on force probability density functions (PDFs), as well as Betti numbers (quantifying the number of components, related to force chains, and loops), to describe the force networks in tapped systems of disks and pentagons. In the present work, we focus on the use of persistence analysis, which allows us to describe these networks in much more detail. This approach allows us not only to describe but also to quantify the differences between the force networks in different realizations of a system, in different parts of the considered domain, or in different systems. We show that persistence analysis clearly distinguishes the systems that are very difficult or impossible to differentiate using other means. One important finding is that the differences in force networks between disks and pentagons are most apparent when loops are considered: the quantities describing properties of the loops may differ significantly even if other measures (properties of components, Betti numbers, force PDFs, or the stress tensor) do not distinguish clearly or at all the investigated systems.

STELLAR STRUCTURE AND TESTS OF MODIFIED GRAVITY

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

Chang, Philip; Hui, Lam, E-mail: pchang@cita.utoronto.ca, E-mail: lhui@astro.columbia.edu

2011-05-01

Theories that attempt to explain cosmic acceleration by modifying gravity typically introduces a long-range scalar force that needs to be screened on small scales. One common screening mechanism is the chameleon, where the scalar force is screened in environments with a sufficiently deep gravitational potential, but acts unimpeded in regions with a shallow gravitational potential. This leads to a variation in the overall gravitational G with environment. We show that such a variation can occur within a star itself, significantly affecting its evolution and structure, provided that the host galaxy is unscreened. The effect is most pronounced for red giants,more » which would be smaller by a factor of tens of percent and thus hotter by hundreds of Kelvin, depending on the parameters of the underlying scalar-tensor theory. Careful measurements of these stars in suitable environments (nearby dwarf galaxies not associated with groups or clusters) would provide constraints on the chameleon mechanism that are four orders of magnitude better than current large-scale structure limits and two orders of magnitude better than present solar system tests.« less

Free energy from molecular dynamics with multiple constraints

NASA Astrophysics Data System (ADS)

den Otter, W. K.; Briels, W. J.

In molecular dynamics simulations of reacting systems, the key step to determining the equilibrium constant and the reaction rate is the calculation of the free energy as a function of the reaction coordinate. Intuitively the derivative of the free energy is equal to the average force needed to constrain the reaction coordinate to a constant value, but the metric tensor effect of the constraint on the sampled phase space distribution complicates this relation. The appropriately corrected expression for the potential of mean constraint force method (PMCF) for systems in which only the reaction coordinate is constrained was published recently. Here we will consider the general case of a system with multiple constraints. This situation arises when both the reaction coordinate and the 'hard' coordinates are constrained, and also in systems with several reaction coordinates. The obvious advantage of this method over the established thermodynamic integration and free energy perturbation methods is that it avoids the cumbersome introduction of a full set of generalized coordinates complementing the constrained coordinates. Simulations of n -butane and n -pentane in vacuum illustrate the method.

Large-eddy simulations of a forced homogeneous isotropic turbulence with polymer additives

NASA Astrophysics Data System (ADS)

Wang, Lu; Cai, Wei-Hua; Li, Feng-Chen

2014-03-01

Large-eddy simulations (LES) based on the temporal approximate deconvolution model were performed for a forced homogeneous isotropic turbulence (FHIT) with polymer additives at moderate Taylor Reynolds number. Finitely extensible nonlinear elastic in the Peterlin approximation model was adopted as the constitutive equation for the filtered conformation tensor of the polymer molecules. The LES results were verified through comparisons with the direct numerical simulation results. Using the LES database of the FHIT in the Newtonian fluid and the polymer solution flows, the polymer effects on some important parameters such as strain, vorticity, drag reduction, and so forth were studied. By extracting the vortex structures and exploring the flatness factor through a high-order correlation function of velocity derivative and wavelet analysis, it can be found that the small-scale vortex structures and small-scale intermittency in the FHIT are all inhibited due to the existence of the polymers. The extended self-similarity scaling law in the polymer solution flow shows no apparent difference from that in the Newtonian fluid flow at the currently simulated ranges of Reynolds and Weissenberg numbers.

Fast Fourier transform discrete dislocation dynamics

NASA Astrophysics Data System (ADS)

Graham, J. T.; Rollett, A. D.; LeSar, R.

2016-12-01

Discrete dislocation dynamics simulations have been generally limited to modeling systems described by isotropic elasticity. Effects of anisotropy on dislocation interactions, which can be quite large, have generally been ignored because of the computational expense involved when including anisotropic elasticity. We present a different formalism of dislocation dynamics in which the dislocations are represented by the deformation tensor, which is a direct measure of the slip in the lattice caused by the dislocations and can be considered as an eigenstrain. The stresses arising from the dislocations are calculated with a fast Fourier transform (FFT) method, from which the forces are determined and the equations of motion are solved. Use of the FFTs means that the stress field is only available at the grid points, which requires some adjustments/regularizations to be made to the representation of the dislocations and the calculation of the force on individual segments, as is discussed hereinafter. A notable advantage of this approach is that there is no computational penalty for including anisotropic elasticity. We review the method and apply it in a simple dislocation dynamics calculation.

The Effects of Racket Inertia Tensor on Elbow Loadings and Racket Behavior for Central and Eccentric Impacts

PubMed Central

Nesbit, Steven M.; Elzinga, Michael; Herchenroder, Catherine; Serrano, Monika

2006-01-01

This paper discusses the inertia tensors of tennis rackets and their influence on the elbow swing torques in a forehand motion, the loadings transmitted to the elbow from central and eccentric impacts, and the racket acceleration responses from central and eccentric impacts. Inertia tensors of various rackets with similar mass and mass center location were determined by an inertia pendulum and were found to vary considerably in all three orthogonal directions. Tennis swing mechanics and impact analyses were performed using a computer model comprised of a full-body model of a human, a parametric model of the racket, and an impact function. The swing mechanics analysis of a forehand motion determined that inertia values had a moderate linear effect on the pronation-supination elbow torques required to twist the racket, and a minor effect on the flexion-extension and valgus-varus torques. The impact analysis found that mass center inertia values had a considerable effect on the transmitted torques for both longitudinal and latitudinal eccentric impacts and significantly affected all elbow torque components. Racket acceleration responses to central and eccentric impacts were measured experimentally and found to be notably sensitive to impact location and mass center inertia values. Key Points Tennis biomechanics. Racket inertia tensor. Impact analysis. Full-body computer model. PMID:24260004

Numerical Study of Rotating Turbulence with External Forcing

NASA Technical Reports Server (NTRS)

Yeung, P. K.; Zhou, Ye

1998-01-01

Direct numerical simulation at 256(exp 3) resolution have been carried out to study the response of isotropic turbulence to the concurrent effects of solid-body rotation and numerical forcing at the large scales. Because energy transfer to the smaller scales is weakened by rotation, energy input from forcing gradually builds up at the large scales, causing the overall kinetic energy to increase. At intermediate wavenumbers the energy spectrum undergoes a transition from a limited k(exp -5/3) inertial range to k(exp -2) scaling recently predicted in the literature. Although the Reynolds stress tensor remains approximately isotropic and three-components, evidence for anisotropy and quasi- two-dimensionality in length scales and spectra in different velocity components and directions is strong. The small scales are found to deviate from local isotropy, primarily as a result of anisotropic transfer to the high wavenumbers. To understand the spectral dynamics of this flow we study the detailed behavior of nonlinear triadic interactions in wavenumber space. Spectral transfer in the velocity component parallel to the axis of rotation is qualitatively similar to that in non-rotating turbulence; however the perpendicular component is characterized by a greatly suppressed energy cascade at high wavenumber and a local reverse transfer at the largest scales. The broader implications of this work are briefly addressed.

Using tensor-based morphometry to detect structural brain abnormalities in rats with adolescent intermittent alcohol exposure

NASA Astrophysics Data System (ADS)

Paniagua, Beatriz; Ehlers, Cindy; Crews, Fulton; Budin, Francois; Larson, Garrett; Styner, Martin; Oguz, Ipek

2011-03-01

Understanding the effects of adolescent binge drinking that persist into adulthood is a crucial public health issue. Adolescent intermittent ethanol exposure (AIE) is an animal model that can be used to investigate these effects in rodents. In this work, we investigate the application of a particular image analysis technique, tensor-based morphometry, for detecting anatomical differences between AIE and control rats using Diffusion Tensor Imaging (DTI). Deformation field analysis is a popular method for detecting volumetric changes analyzing Jacobian determinants calculated on deformation fields. Recent studies showed that computing deformation field metrics on the full deformation tensor, often referred to as tensor-based morphometry (TBM), increases the sensitivity to anatomical differences. In this paper we conduct a comprehensive TBM study for precisely locating differences between control and AIE rats. Using a DTI RARE sequence designed for minimal geometric distortion, 12-directional images were acquired postmortem for control and AIE rats (n=9). After preprocessing, average images for the two groups were constructed using an unbiased atlas building approach. We non-rigidly register the two atlases using Large Deformation Diffeomorphic Metric Mapping, and analyze the resulting deformation field using TBM. In particular, we evaluate the tensor determinant, geodesic anisotropy, and deformation direction vector (DDV) on the deformation field to detect structural differences. This yields data on the local amount of growth, shrinkage and the directionality of deformation between the groups. We show that TBM can thus be used to measure group morphological differences between rat populations, demonstrating the potential of the proposed framework.

Integrability conditions for Killing-Yano tensors and conformal Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Batista, Carlos

2015-01-01

The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is shown that in certain Einstein spaces one can use a conformal Killing-Yano tensor of order p to generate a Killing-Yano tensor of order (p -1 ) . Finally, it is proved that in maximally symmetric spaces the covariant derivative of a Killing-Yano tensor is a closed conformal Killing-Yano tensor and that every conformal Killing-Yano tensor is uniquely decomposed as the sum of a Killing-Yano tensor and a closed conformal Killing-Yano tensor.

Flocking particles in a non-Newtonian shear thickening fluid

NASA Astrophysics Data System (ADS)

Mucha, Piotr B.; Peszek, Jan; Pokorný, Milan

2018-06-01

We prove the existence of strong solutions to the Cucker–Smale flocking model coupled with an incompressible viscous non-Newtonian fluid with the stress tensor of a power–law structure for . The fluid part of the system admits strong solutions while the solutions to the CS part are weak. The coupling is performed through a drag force on a periodic spatial domain . Additionally, we construct a Lyapunov functional determining the large time behavior of solutions to the system.

Covariant density functional theory: predictive power and first attempts of a microscopic derivation

NASA Astrophysics Data System (ADS)

Ring, Peter

2018-05-01

We discuss systematic global investigations with modern covariant density functionals. The number of their phenomenological parameters can be reduced considerable by using microscopic input from ab-initio calculations in nuclear matter. The size of the tensor force is still an open problem. Therefore we use the first full relativistic Brueckner-Hartree-Fock calculations in finite nuclear systems in order to study properties of such functionals, which cannot be obtained from nuclear matter calculations.

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

Motion of small bodies in classical field theory

NASA Astrophysics Data System (ADS)

Gralla, Samuel E.

2010-04-01

I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body’s composition (and, e.g., black holes are allowed). The worldline “left behind” by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the “Bianchi identity” for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the “monopoles” of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of “chameleon” bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.

Skeletal effects in Angle Class II/1 patients treated with the functional regulator type II : Cephalometric and tensor analysis.

PubMed

Schulz, Simone; Koos, Bernd; Duske, Kathrin; Stahl, Franka

2016-11-01

The purpose of this work was to employ both cephalometric and tensor analysis in characterizing the skeletal changes experienced by patients with Angle Class II/1 malocclusion during functional orthodontic treatment with the functional regulator type II. A total of 23 patients with Class II/1 malocclusion based on lateral cephalograms obtained before and after treatment with the functional regulator type II were analyzed. Another 23 patients with Angle Class II/1 malocclusion who had not undergone treatment were included as controls. Our cephalometric data attest to significant therapeutic effects of the functional regulator type II on the skeletal mandibular system, including significant advancement of the mandible, increases in effective mandibular length with enhancement of the chin profile, and reduction of growth-related bite deepening. No treatment-related effects were observed at the cranial-base and midface levels. In addition, tensor analysis revealed significant stimulation of mandibular growth in sagittal directions, without indications of growth effects on the maxilla. Its growth-pattern findings differed from those of cephalometric analysis by indicating that the appliance did promote horizontal development, which supports the functional orthodontic treatment effect in Angle Class II/1 cases. Tensor analysis yielded additional insights into sagittal and vertical growth changes not identifiable by strictly cephalometric means. The functional regulator type II was an effective treatment modality for Angle Class II/1 malocclusion and influenced the skeletal development of these patients in favorable ways.

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.

Extended effective field theory of inflation

NASA Astrophysics Data System (ADS)

Ashoorioon, Amjad; Casadio, Roberto; Cicoli, Michele; Geshnizjani, Ghazal; Kim, Hyung J.

2018-02-01

We present a general framework where the effective field theory of single field inflation is extended by the inclusion of operators with mass dimension 3 and 4 in the unitary gauge. These higher dimensional operators introduce quartic and sextic corrections to the dispersion relation. We study the regime of validity of this extended effective field theory of inflation and the effect of these higher dimensional operators on CMB observables associated with scalar perturbations, such as the speed of sound, the amplitude of the power spectrum and the tensor-to-scalar ratio. Tensor perturbations remain instead, unaltered.

The GOCE end-to-end system simulator

NASA Astrophysics Data System (ADS)

Catastini, G.; Cesare, S.; de Sanctis, S.; Detoma, E.; Dumontel, M.; Floberghagen, R.; Parisch, M.; Sechi, G.; Anselmi, A.

2003-04-01

The idea of an end-to-end simulator was conceived in the early stages of the GOCE programme, as an essential tool for assessing the satellite system performance, that cannot be fully tested on the ground. The simulator in its present form is under development at Alenia Spazio for ESA since the beginning of Phase B and is being used for checking the consistency of the spacecraft and of the payload specifications with the overall system requirements, supporting trade-off, sensitivity and worst-case analyses, and preparing and testing the on-ground and in-flight calibration concepts. The software simulates the GOCE flight along an orbit resulting from the application of Earth's gravity field, non-conservative environmental disturbances (atmospheric drag, coupling with Earth's magnetic field, etc.) and control forces/torques. The drag free control forces as well as the attitude control torques are generated by the current design of the dedicated algorithms. Realistic sensor models (star tracker, GPS receiver and gravity gradiometer) feed the control algorithms and the commanded forces are applied through realistic thruster models. The output of this stage of the simulator is a time series of Level-0 data, namely the gradiometer raw measurements and spacecraft ancillary data. The next stage of the simulator transforms Level-0 data into Level-1b (gravity gradient tensor) data, by implementing the following steps: - transformation of raw measurements of each pair of accelerometers into common and differential accelerations - calibration of the common and differential accelerations - application of the post-facto algorithm to rectify the phase of the accelerations and to estimate the GOCE angular velocity and attitude - computation of the Level-1b gravity gradient tensor from calibrated accelerations and estimated angular velocity in different reference frames (orbital, inertial, earth-fixed); computation of the spectral density of the error of the tensor diagonal components (measured gravity gradient minus input gravity gradient) in order to verify the requirement on the error of gravity gradient of 4 mE/sqrt(Hz) within the gradiometer measurement bandwidth (5 to 100 mHz); computation of the spectral density of the tensor trace in order to verify the requirement of 4 sqrt(3) mE/sqrt(Hz) within the measurement bandwidth - processing of GPS observations for orbit reconstruction within the required 10m accuracy and for gradiometer measurement geolocation. The current version of the end-to-end simulator, essentially focusing on the gradiometer payload, is undergoing detailed testing based on a time span of 10 days of simulated flight. This testing phase, ending in January 2003, will verify the current implementation and conclude the assessment of numerical stability and precision. Following that, the exercise will be repeated on a longer-duration simulated flight and the lesson learnt so far will be exploited to further improve the simulator's fidelity. The paper will describe the simulator's current status and will illustrate its capabilities for supporting the assessment of the quality of the scientific products resulting from the current spacecraft and payload design.

Quantum equivalence of f (R) gravity and scalar-tensor theories in the Jordan and Einstein frames

NASA Astrophysics Data System (ADS)

Ohta, Nobuyoshi

2018-03-01

The f(R) gravity and scalar-tensor theory are known to be equivalent at the classical level. We study if this equivalence is valid at the quantum level. There are two descriptions of the scalar-tensor theory in the Jordan and Einstein frames. It is shown that these three formulations of the theories give the same determinant or effective action on shell, and thus they are equivalent at the quantum one-loop level on shell in arbitrary dimensions. We also compute the one-loop divergence in f(R) gravity on an Einstein space.

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.

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.

Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings

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

Bordin, Lorenzo; Cabass, Giovanni; Creminelli, Paolo

We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the coefficients of the operators in the action: some couplings are effectively redundant. At leading order in derivatives and up to cubic order in perturbations, one has 6 free functions that can be used to set to zero 6 of the 17 operators at this order. This is used to show that the tensor three-point function cannot be modified at leading order in derivatives, while the scalar-tensor-tensor correlatormore » can only be modified by changing the scalar dynamics. At higher order in derivatives there are transformations that do not affect the Einstein-Hilbert action: one can find 6 additional transformations that can be used to simplify the inflaton action, at least when the dynamics is dominated by the lowest derivative terms. We also identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum.« less

The Electron Diffusion Region: Forces and Currents

NASA Technical Reports Server (NTRS)

Hesse, Michael

2008-01-01

The dissipation mechanism of magnetic reconnection remains a subject of intense scientific interest. On one hand, one set of recent studies have shown that particle inertia-based processes, which include thermal and bulk inertial effects, provide the reconnection electric field in the diffusion region. On the other hand, a second set of studies emphasizes the role of wave-particle interactions in providing anomalous resistivity in the diffusion region. In this presentation, we present analytical theory results, as well as PIC simulations of guide-field magnetic reconnection. We will show that the thermal electron inertia-based dissipation mechanism, expressed through nongyrotropic electron pressure tensors, remains viable in three dimensions. We will demonstrate the thermal inertia effect through studies of electron distribution functions. Furthermore, we will show that the reconnection electric field provides a transient acceleration on particles traversing the inner reconnection region. This inertia1 effect can be described as a diffusion-like term of the current density, which matches key features of electron distribution functions.

The Electron Diffusion Region: Forces and Currents

NASA Technical Reports Server (NTRS)

Hesse, Michael

2009-01-01

The dissipation mechanism of magnetic reconnection remains a subject of intense scientific interest. On one hand, one set of recent studies have shown that particle inertia-based processes, which include thermal and bulk inertial effects, provide the reconnection electric field in the diffusion region. On the other hand, a second set of studies emphasizes the role of wave-particle interactions in providing anomalous resistivity in the diffusion region. In this presentation, we present analytical theory results, as well as PIC simulations of guide-field magnetic reconnection. We will show that the thermal electron inertia-based dissipation mechanism, expressed through nongyrotropic electron pressure tensors, remains viable in three dimensions. We will demonstrate the thermal inertia effect through studies of electron distribution functions. Furthermore, we will show that the reconnection electric field provides a transient acceleration on particles traversing the inner reconnection region. This inertial effect can be described as a diffusion-like term of the current density, which matches key features of electron distribution functions.

Density functional theory calculations of 95Mo NMR parameters in solid-state compounds.

PubMed

Cuny, Jérôme; Furet, Eric; Gautier, Régis; Le Pollès, Laurent; Pickard, Chris J; d'Espinose de Lacaillerie, Jean-Baptiste

2009-12-21

The application of periodic density functional theory-based methods to the calculation of (95)Mo electric field gradient (EFG) and chemical shift (CS) tensors in solid-state molybdenum compounds is presented. Calculations of EFG tensors are performed using the projector augmented-wave (PAW) method. Comparison of the results with those obtained using the augmented plane wave + local orbitals (APW+lo) method and with available experimental values shows the reliability of the approach for (95)Mo EFG tensor calculation. CS tensors are calculated using the recently developed gauge-including projector augmented-wave (GIPAW) method. This work is the first application of the GIPAW method to a 4d transition-metal nucleus. The effects of ultra-soft pseudo-potential parameters, exchange-correlation functionals and structural parameters are precisely examined. Comparison with experimental results allows the validation of this computational formalism.

A new validation technique for estimations of body segment inertia tensors: Principal axes of inertia do matter.

PubMed

Rossi, Marcel M; Alderson, Jacqueline; El-Sallam, Amar; Dowling, James; Reinbolt, Jeffrey; Donnelly, Cyril J

2016-12-08

The aims of this study were to: (i) establish a new criterion method to validate inertia tensor estimates by setting the experimental angular velocity data of an airborne objects as ground truth against simulations run with the estimated tensors, and (ii) test the sensitivity of the simulations to changes in the inertia tensor components. A rigid steel cylinder was covered with reflective kinematic markers and projected through a calibrated motion capture volume. Simulations of the airborne motion were run with two models, using inertia tensor estimated with geometric formula or the compound pendulum technique. The deviation angles between experimental (ground truth) and simulated angular velocity vectors and the root mean squared deviation angle were computed for every simulation. Monte Carlo analyses were performed to assess the sensitivity of simulations to changes in magnitude of principal moments of inertia within ±10% and to changes in orientation of principal axes of inertia within ±10° (of the geometric-based inertia tensor). Root mean squared deviation angles ranged between 2.9° and 4.3° for the inertia tensor estimated geometrically, and between 11.7° and 15.2° for the compound pendulum values. Errors up to 10% in magnitude of principal moments of inertia yielded root mean squared deviation angles ranging between 3.2° and 6.6°, and between 5.5° and 7.9° when lumped with errors of 10° in principal axes of inertia orientation. The proposed technique can effectively validate inertia tensors from novel estimation methods of body segment inertial parameter. Principal axes of inertia orientation should not be neglected when modelling human/animal mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.

Flow properties and hydrodynamic interactions of rigid spherical microswimmers

NASA Astrophysics Data System (ADS)

Adhyapak, Tapan Chandra; Jabbari-Farouji, Sara

2017-11-01

We analyze a minimal model for a rigid spherical microswimmer and explore the consequences of its extended surface on the interplay between its self-propulsion and flow properties. The model is the first order representation of microswimmers, such as bacteria and algae, with rigid bodies and flexible propelling appendages. The flow field of such a microswimmer at finite distances significantly differs from that of a point-force (Stokeslet) dipole. For a suspension of microswimmers, we derive the grand mobility matrix that connects the motion of an individual swimmer to the active and passive forces and torques acting on all the swimmers. Our investigation of the mobility tensors reveals that hydrodynamic interactions among rigid-bodied microswimmers differ considerably from those among the corresponding point-force dipoles. Our results are relevant for the study of collective behavior of hydrodynamically interacting microswimmers by means of Stokesian dynamics simulations at moderate concentrations.

Theory of interacting dislocations on cylinders.

PubMed

Amir, Ariel; Paulose, Jayson; Nelson, David R

2013-04-01

We study the mechanics and statistical physics of dislocations interacting on cylinders, motivated by the elongation of rod-shaped bacterial cell walls and cylindrical assemblies of colloidal particles subject to external stresses. The interaction energy and forces between dislocations are solved analytically, and analyzed asymptotically. The results of continuum elastic theory agree well with numerical simulations on finite lattices even for relatively small systems. Isolated dislocations on a cylinder act like grain boundaries. With colloidal crystals in mind, we show that saddle points are created by a Peach-Koehler force on the dislocations in the circumferential direction, causing dislocation pairs to unbind. The thermal nucleation rate of dislocation unbinding is calculated, for an arbitrary mobility tensor and external stress, including the case of a twist-induced Peach-Koehler force along the cylinder axis. Surprisingly rich phenomena arise for dislocations on cylinders, despite their vanishing Gaussian curvature.

Gravitational body forces focus North American intraplate earthquakes

USGS Publications Warehouse

Levandowski, William Brower; Zellman, Mark; Briggs, Richard

2017-01-01

Earthquakes far from tectonic plate boundaries generally exploit ancient faults, but not all intraplate faults are equally active. The North American Great Plains exemplify such intraplate earthquake localization, with both natural and induced seismicity generally clustered in discrete zones. Here we use seismic velocity, gravity and topography to generate a 3D lithospheric density model of the region; subsequent finite-element modelling shows that seismicity focuses in regions of high-gravity-derived deviatoric stress. Furthermore, predicted principal stress directions generally align with those observed independently in earthquake moment tensors and borehole breakouts. Body forces therefore appear to control the state of stress and thus the location and style of intraplate earthquakes in the central United States with no influence from mantle convection or crustal weakness necessary. These results show that mapping where gravitational body forces encourage seismicity is crucial to understanding and appraising intraplate seismic hazard.

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.

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.

Gravitational body forces focus North American intraplate earthquakes

PubMed Central

Levandowski, Will; Zellman, Mark; Briggs, Rich

2017-01-01

Earthquakes far from tectonic plate boundaries generally exploit ancient faults, but not all intraplate faults are equally active. The North American Great Plains exemplify such intraplate earthquake localization, with both natural and induced seismicity generally clustered in discrete zones. Here we use seismic velocity, gravity and topography to generate a 3D lithospheric density model of the region; subsequent finite-element modelling shows that seismicity focuses in regions of high-gravity-derived deviatoric stress. Furthermore, predicted principal stress directions generally align with those observed independently in earthquake moment tensors and borehole breakouts. Body forces therefore appear to control the state of stress and thus the location and style of intraplate earthquakes in the central United States with no influence from mantle convection or crustal weakness necessary. These results show that mapping where gravitational body forces encourage seismicity is crucial to understanding and appraising intraplate seismic hazard. PMID:28211459

Evolution of Lamb Vector as a Vortex Breaking into Turbulence.

NASA Astrophysics Data System (ADS)

Wu, J. Z.; Lu, X. Y.

1996-11-01

In an incompressible flow, either laminar or turbulent, the Lamb vector is solely responsible to nonlinear interactions. While its longitudinal part is balanced by stagnation enthalpy, its transverse part is the unique source (as an external forcing in spectral space) that causes the flow to evolve. Moreover, in Reynolds-averaged flows the turbulent force can be derived exclusively from the Lamb vector instead of the full Reynolds stress tensor. Therefore, studying the evolution of the Lamb vector itself (both longitudinal and transverse parts) is of great interest. We have numerically examined this problem, taking the nonlinear distabilization of a viscous vortex as an example. In the later stage of this evolution we introduced a forcing to keep a statistically steady state, and observed the Lamb vector behavior in the resulting fine turbulence. The result is presented in both physical and spectral spaces.

Simultaneous Tensor Decomposition and Completion Using Factor Priors.

PubMed

Chen, Yi-Lei; Hsu, Chiou-Ting Candy; Liao, Hong-Yuan Mark

2013-08-27

Tensor completion, which is a high-order extension of matrix completion, has generated a great deal of research interest in recent years. Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors. In this paper, we introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure. To this end, we propose a method called Simultaneous Tensor Decomposition and Completion (STDC) that combines a rank minimization technique with Tucker model decomposition. Moreover, as the model structure is implicitly included in the Tucker model, we use factor priors, which are usually known a priori in real-world tensor objects, to characterize the underlying joint-manifold drawn from the model factors. We conducted experiments to empirically verify the convergence of our algorithm on synthetic data, and evaluate its effectiveness on various kinds of real-world data. The results demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications. It also outperforms state-of-the-art methods on multilinear model analysis and visual data completion tasks.

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.

A new Weyl-like tensor of geometric origin

NASA Astrophysics Data System (ADS)

Vishwakarma, Ram Gopal

2018-04-01

A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.

An anisotropic universe due to dimension-changing vacuum decay

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

Scargill, James H.C., E-mail: james.scargill@physics.ox.ac.uk

In this paper we consider the question of observational signatures of a false vacuum decay event in the early universe followed by a period of inflation; in particular, motivated by the string landscape, we consider decays in which the parent vacuum has a smaller number of large dimensions than the current vacuum, which leads to an anisotropic universe. We go beyond previous studies, and examine the effects on the CMB temperature and polarisation power spectra, due to both scalar and tensor modes, and consider not only late-time effects but also the full cosmological perturbation theory at early times. We findmore » that whilst the scalar mode behaves as one would expect, and the effects of anisotropy at early times are sub-dominant to the late-time effects already studied, for the tensor modes in fact the the early-time effects grow with multipole and can become much larger than one would expect, even dominating over the late-time effects. Thus these effects should be included if one is looking for such a signal in the tensor modes.« less

Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems.

PubMed

Guérin, T; Dean, D S

2015-12-01

We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems.

Development of the Tensoral Computer Language

NASA Technical Reports Server (NTRS)

Ferziger, Joel; Dresselhaus, Eliot

1996-01-01

The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.

A tensor analysis to evaluate the effect of high-pull headgear on Class II malocclusions.

PubMed

Ngan, P; Scheick, J; Florman, M

1993-03-01

The inaccuracies inherent in cephalometric analysis of treatment effects are well known. The objective of this article is to present a more reliable research tool in the analysis of cephalometric data. Bookstein introduced a dilation function by means of a homogeneous deformation tensor as a method of describing changes in cephalometric data. His article gave an analytic description of the deformation tensor that permits the rapid and highly accurate calculation of it on a desktop computer. The first part of this article describes the underlying ideas and mathematics. The second part uses the tensor analysis to analyze the cephalometric results of a group of patients treated with high-pull activator (HPA) to demonstrate the application of this research tool. Eight patients with Class II skeletal open bite malocclusions in the mixed dentition were treated with HPA. A control sample consisting of eight untreated children with Class II who were obtained from The Ohio State University Growth Study was used as a comparison group. Lateral cephalograms taken before and at the completion of treatment were traced, digitized, and analyzed with the conventional method and tensor analysis. The results showed that HPA had little or no effect on maxillary skeletal structures. However, reduction in growth rate was found with the skeletal triangle S-N-A, indicating a posterior tipping and torquing of the maxillary incisors. The treatment also induced additional deformation on the mandible in a downward and slightly forward direction. Together with the results from the conventional cephalometric analysis, HPA seemed to provide the vertical and rotational control of the maxilla during orthopedic Class II treatment by inhibiting the downward and forward eruptive path of the upper posterior teeth. The newly designed computer software permits rapid analysis of cephalometric data with the tensor analysis on a desktop computer. This tool may be useful in analyzing growth changes for research data.

Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit

NASA Astrophysics Data System (ADS)

Izvekov, Sergei

2017-01-01

We derive alternative Markov approximations for the projected (stochastic) force and memory function in the coarse-grained (CG) generalized Langevin equation, which describes the time evolution of the center-of-mass coordinates of clusters of particles in the microscopic ensemble. This is done with the aid of the Mori-Zwanzig projection operator method based on the recently introduced projection operator [S. Izvekov, J. Chem. Phys. 138, 134106 (2013), 10.1063/1.4795091]. The derivation exploits the "generalized additive fluctuating force" representation to which the projected force reduces in the adopted projection operator formalism. For the projected force, we present a first-order time expansion which correctly extends the static fluctuating force ansatz with the terms necessary to maintain the required orthogonality of the projected dynamics in the Markov limit to the space of CG phase variables. The approximant of the memory function correctly accounts for the momentum dependence in the lowest (second) order and indicates that such a dependence may be important in the CG dynamics approaching the Markov limit. In the case of CG dynamics with a weak dependence of the memory effects on the particle momenta, the expression for the memory function presented in this work is applicable to non-Markov systems. The approximations are formulated in a propagator-free form allowing their efficient evaluation from the microscopic data sampled by standard molecular dynamics simulations. A numerical application is presented for a molecular liquid (nitromethane). With our formalism we do not observe the "plateau-value problem" if the friction tensors for dissipative particle dynamics (DPD) are computed using the Green-Kubo relation. Our formalism provides a consistent bottom-up route for hierarchical parametrization of DPD models from atomistic simulations.

Ab initio and DFT studies of the spin-orbit and spin-spin contributions to the zero-field splitting tensors of triplet nitrenes with aryl scaffolds.

PubMed

Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Kitagawa, Masahiro; Takui, Takeji

2011-04-21

Spin-orbit and spin-spin contributions to the zero-field splitting (ZFS) tensors (D tensors) of spin-triplet phenyl-, naphthyl-, and anthryl-nitrenes in their ground state are investigated by quantum chemical calculations, focusing on the effects of the ring size and substituted position of nitrene on the D tensor. A hybrid CASSCF/MRMP2 approach to the spin-orbit term of the D tensor (D(SO) tensor), which was recently proposed by us, has shown that the spin-orbit contribution to the entire D value, termed the ZFS parameter or fine-structure constant, is about 10% in all the arylnitrenes under study and less depends on the size and connectivity of the aryl groups. Order of the absolute values for D(SO) can be explained by the perturbation on the energy level and spatial distributions of π-SOMO through the orbital interaction between SOMO of the nitrene moiety and frontier orbitals of the aryl scaffolds. Spin-spin contribution to the D tensor (D(SS) tensor) has been calculated in terms of the McWeeny-Mizuno equation with the DFT/EPR-II spin densities. The D(SS) value calculated with the RO-B3LYP spin density agrees well with the D(Exptl) -D(SO) reference value in phenylnitrene, but agreement with the reference value gradually becomes worse as the D value decreases. Exchange-correlation functional dependence on the D(SS) tensor has been explored with standard 23 exchange-correlation functionals in both RO- and U-DFT methodologies, and the RO-HCTH/407 method gives the best agreement with the D(Exptl) -D(SO) reference value. Significant exchange-correlation functional dependence is observed in spin-delocalized systems such as 9-anthrylnitrene (6). By employing the hybrid CASSCF/MRMP2 approach and the McWeeny-Mizuno equation combined with the RO-HCTH/407/EPR-II//U-HCTH/407/6-31G* spin densities for D(SO) and D(SS), respectively, a quantitative agreement with the experiment is achieved with errors less than 10% in all the arylnitrenes under study. Guidelines to the putative approaches to D(SS) tensor calculations are given.

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.

Effects of Resection of Posterior Condyles of Femur on Extension Gap of Knee Joint in Total Knee Arthroplasty.

PubMed

Seo, Seung-Suk; Kim, Chang-Wan; Seo, Jin-Hyuk; Kim, Do-Hun; Kim, Ok-Gul; Lee, Chang-Rack

2017-06-01

When evaluating the effects of the preparation of the flexion gap on the extension gap in total knee arthroplasty (TKA), the effects of posterior condylar resection and osteophyte removal on the extension gap should be differentiated. Although the amount of osteophytes differs between patients, posterior condylar resection is a procedure that is routinely implemented in TKA. The aim of this study was to assess the effects of the resection of the posterior condyle of the femur on the extension gap in posterior-stabilized (PS) TKA. We enrolled 40 knees that underwent PS TKA between July 2010 and February 2011 with no or minimal osteophytes in the posterior compartment and a varus deformity of <15°. We measured the extension gap before and after the resection of the posterior condyle of the femur using a tensor under 20 and 40 lb of distraction force. Under 20 lb of distraction force, the average extension gap was 13.3 mm (standard deviation [SD], 1.6) before and 13.8 mm (SD, 1.6) after posterior condylar resection. Under 40 lb of distraction force, the average extension gap was 15.1 mm (SD, 1.5) before and 16.1 mm (SD, 1.7) after posterior condylar resection. The resection of the posterior condyle of the femur in PS TKA increased the extension gap. However, this increase was only by approximately 1 mm. In conclusion, posterior condylar resection does increase the extension gap by approximately 1 mm. However, in most case, this change in unlikely to be clinically important. Copyright © 2017 Elsevier Inc. All rights reserved.

Recursive computation of mutual potential between two polyhedra

NASA Astrophysics Data System (ADS)

Hirabayashi, Masatoshi; Scheeres, Daniel J.

2013-11-01

Recursive computation of mutual potential, force, and torque between two polyhedra is studied. Based on formulations by Werner and Scheeres (Celest Mech Dyn Astron 91:337-349, 2005) and Fahnestock and Scheeres (Celest Mech Dyn Astron 96:317-339, 2006) who applied the Legendre polynomial expansion to gravity interactions and expressed each order term by a shape-dependent part and a shape-independent part, this paper generalizes the computation of each order term, giving recursive relations of the shape-dependent part. To consider the potential, force, and torque, we introduce three tensors. This method is applicable to any multi-body systems. Finally, we implement this recursive computation to simulate the dynamics of a two rigid-body system that consists of two equal-sized parallelepipeds.

Databases post-processing in Tensoral

NASA Technical Reports Server (NTRS)

Dresselhaus, Eliot

1994-01-01

The Center for Turbulent Research (CTR) post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, introduced in this document and currently existing in prototype form, is the foundation of this effort. Tensoral provides a convenient and powerful protocol to connect users who wish to analyze fluids databases with the authors who generate them. In this document we introduce Tensoral and its prototype implementation in the form of a user's guide. This guide focuses on use of Tensoral for post-processing turbulence databases. The corresponding document - the Tensoral 'author's guide' - which focuses on how authors can make databases available to users via the Tensoral system - is currently unwritten. Section 1 of this user's guide defines Tensoral's basic notions: we explain the class of problems at hand and how Tensoral abstracts them. Section 2 defines Tensoral syntax for mathematical expressions. Section 3 shows how these expressions make up Tensoral statements. Section 4 shows how Tensoral statements and expressions are embedded into other computer languages (such as C or Vectoral) to make Tensoral programs. We conclude with a complete example program.

The 1/ N Expansion of Tensor Models with Two Symmetric Tensors

NASA Astrophysics Data System (ADS)

Gurau, Razvan

2018-06-01

It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.

Differentiating G-inflation from string gas cosmology using the effective field theory approach

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

He, Minxi; Liu, Junyu; Lu, Shiyun

A characteristic signature of String Gas Cosmology is primordial power spectra for scalar and tensor modes which are almost scale-invariant but with a red tilt for scalar modes but a blue tilt for tensor modes. This feature, however, can also be realized in the so-called G-inflation model, in which Horndeski operators are introduced which leads to a blue tensor tilt by softly breaking the Null Energy Condition. In this article we search for potential observational differences between these two cosmologies by performing detailed perturbation analyses based on the Effective Field Theory approach. Our results show that, although both two modelsmore » produce blue tilted tensor perturbations, they behave differently in three aspects. Firstly, String Gas Cosmology predicts a specific consistency relation between the index of the scalar modes n {sub s} and that of tensor ones n {sub t} , which is hard to be reproduced by G-inflation. Secondly, String Gas Cosmology typically predicts non-Gaussianities which are highly suppressed on observable scales, while G-inflation gives rise to observationally large non-Gaussianities because the kinetic terms in the action become important during inflation. However, after finely tuning the model parameters of G-inflation it is possible to obtain a blue tensor spectrum and negligible non-Gaussianities with a degeneracy between the two models. This degeneracy can be broken by a third observable, namely the scale dependence of the nonlinearity parameter, which vanishes for G-inflation but has a blue tilt in the case of String Gas Cosmology. Therefore, we conclude that String Gas Cosmology is in principle observationally distinguishable from the single field inflationary cosmology, even allowing for modifications such as G-inflation.« less

The Weyl curvature tensor, Cotton-York tensor and gravitational waves: A covariant consideration

NASA Astrophysics Data System (ADS)

Osano, Bob

1 + 3 covariant approach to cosmological perturbation theory often employs the electric part (Eab), the magnetic part (Hab) of the Weyl tensor or the shear tensor (σab) in a phenomenological description of gravitational waves. The Cotton-York tensor is rarely mentioned in connection with gravitational waves in this approach. This tensor acts as a source for the magnetic part of the Weyl tensor which should not be neglected in studies of gravitational waves in the 1 + 3 formalism. The tensor is only mentioned in connection with studies of “silent model” but even there the connection with gravitational waves is not exhaustively explored. In this study, we demonstrate that the Cotton-York tensor encodes contributions from both electric and magnetic parts of the Weyl tensor and in directly from the shear tensor. In our opinion, this makes the Cotton-York tensor arguably the natural choice for linear gravitational waves in the 1 + 3 covariant formalism. The tensor is cumbersome to work with but that should negate its usefulness. It is conceivable that the tensor would equally be useful in the metric approach, although we have not demonstrated this in this study. We contend that the use of only one of the Weyl tensor or the shear tensor, although phenomenologically correct, leads to loss of information. Such information is vital particularly when examining the contribution of gravitational waves to the anisotropy of an almost-Friedmann-Lamitre-Robertson-Walker (FLRW) universe. The recourse to this loss is the use Cotton-York tensor.

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.

Geometric decomposition of the conformation tensor in viscoelastic turbulence

NASA Astrophysics Data System (ADS)

Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.

2018-05-01

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

Domain Processes in Ferroelectric Ceramics

DTIC Science & Technology

1994-04-14

elastic strain tensor and eikl is the Levi - Civita density. Eqs (11) and (12) has three nontrivial solutions: Xr3 = 0 (13) Xr"= -1 { [ 2sj2Q 12 -Sl I...ABSTRACT (aA~iMUM 200 wardt) This report Outlines the progres achieved during a two year effort sponsored by the AFOSR on the theoretical study of domain...INTRODUCTION This is the final progress report for this two year program sponsored by the Air Force Office of Scientific Research on "Domain Processes in

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

Substrate strain induced interaction of adatoms on W (110)

NASA Astrophysics Data System (ADS)

Kappus, W.

1980-09-01

The interaction of adatoms due to elastic strains created in an elastically isotropic substrate is investigated. For cases where the adatoms occupy sites with low symmetry, an angular dependent interaction results which falls off as s-3 at large distances. An exact expression is given for the long range interaction in terms of an anisotropy parameter of the force dipole tensor. The short range interaction is calculated by introducing a smooth cutoff. Interactions of adatoms on near neighbour sites on W (110) are given.

Quantitative Tractography and Volumetric MRI in Blast and Blunt Force TBI: Predictors of Neurocognitive and Behavioral Outcome

DTIC Science & Technology

2012-10-01

consciousness predict 9 neuropsychological decrements after concussion? Clin J Sport Med. 1999;9:193-198. 10 38. Belanger HG, Proctor-Weber Z , Kretzmer T...on diffusion tensor imaging in an 3 ICBM template. Neuroimage. 2008;40:570-582. 4 58. Wozniak JR, Krach L, Ward E, et al. Neurocognitive and...consciousness predict 9 neuropsychological decrements after concussion? Clin J Sport Med. 1999;9:193-198. 10 38. Belanger HG, Proctor-Weber Z , Kretzmer T, Kim

United States Air Force Summer Faculty Research Program. Management Report. Volume 3

DTIC Science & Technology

1988-12-01

xyz values are basically correct, we plotted the perspective view of a target using the xyz values with MATLAB (a matrix-based mathematics softwaie...initially included all the pixels of the image in calculating votes for each accumulator. Two target types, the M-60 tank and the fuel truck, were used...J.F., Gouin, H. and Gaviglio, J., "Evolution of the Reynolds Stress Tensor in a Shock Wave-Turbulence Interaction," Indian Journal of Technology, Vol

White Dwarf Critical Tests for Modified Gravity.

PubMed

Jain, Rajeev Kumar; Kouvaris, Chris; Nielsen, Niklas Grønlund

2016-04-15

Scalar-tensor theories of gravity can lead to modifications of the gravitational force inside astrophysical objects. We exhibit that compact stars such as white dwarfs provide a unique setup to test beyond Horndeski theories of G^{3} type. We obtain stringent and independent constraints on the parameter ϒ characterizing the deviations from Newtonian gravity using the mass-radius relation, the Chandrasekhar mass limit, and the maximal rotational frequency of white dwarfs. We find that white dwarfs impose stronger constraints on ϒ than red and brown dwarfs.

The Role of Standardized and Study-specific Human Brain Diffusion Tensor Templates in Inter-subject Spatial Normalization

PubMed Central

Zhang, Shengwei; Arfanakis, Konstantinos

2012-01-01

Purpose To investigate the effect of standardized and study-specific human brain diffusion tensor templates on the accuracy of spatial normalization, without ignoring the important roles of data quality and registration algorithm effectiveness. Materials and Methods Two groups of diffusion tensor imaging (DTI) datasets, with and without visible artifacts, were normalized to two standardized diffusion tensor templates (IIT2, ICBM81) as well as study-specific templates, using three registration approaches. The accuracy of inter-subject spatial normalization was compared across templates, using the most effective registration technique for each template and group of data. Results It was demonstrated that, for DTI data with visible artifacts, the study-specific template resulted in significantly higher spatial normalization accuracy than standardized templates. However, for data without visible artifacts, the study-specific template and the standardized template of higher quality (IIT2) resulted in similar normalization accuracy. Conclusion For DTI data with visible artifacts, a carefully constructed study-specific template may achieve higher normalization accuracy than that of standardized templates. However, as DTI data quality improves, a high-quality standardized template may be more advantageous than a study-specific template, since in addition to high normalization accuracy, it provides a standard reference across studies, as well as automated localization/segmentation when accompanied by anatomical labels. PMID:23034880

Tensor Algebra Library for NVidia Graphics Processing Units

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

Liakh, Dmitry

This is a general purpose math library implementing basic tensor algebra operations on NVidia GPU accelerators. This software is a tensor algebra library that can perform basic tensor algebra operations, including tensor contractions, tensor products, tensor additions, etc., on NVidia GPU accelerators, asynchronously with respect to the CPU host. It supports a simultaneous use of multiple NVidia GPUs. Each asynchronous API function returns a handle which can later be used for querying the completion of the corresponding tensor algebra operation on a specific GPU. The tensors participating in a particular tensor operation are assumed to be stored in local RAMmore » of a node or GPU RAM. The main research area where this library can be utilized is the quantum many-body theory (e.g., in electronic structure theory).« less

Retrospective Correction of Physiological Noise in DTI Using an Extended Tensor Model and Peripheral Measurements

PubMed Central

Mohammadi, Siawoosh; Hutton, Chloe; Nagy, Zoltan; Josephs, Oliver; Weiskopf, Nikolaus

2013-01-01

Diffusion tensor imaging is widely used in research and clinical applications, but this modality is highly sensitive to artefacts. We developed an easy-to-implement extension of the original diffusion tensor model to account for physiological noise in diffusion tensor imaging using measures of peripheral physiology (pulse and respiration), the so-called extended tensor model. Within the framework of the extended tensor model two types of regressors, which respectively modeled small (linear) and strong (nonlinear) variations in the diffusion signal, were derived from peripheral measures. We tested the performance of four extended tensor models with different physiological noise regressors on nongated and gated diffusion tensor imaging data, and compared it to an established data-driven robust fitting method. In the brainstem and cerebellum the extended tensor models reduced the noise in the tensor-fit by up to 23% in accordance with previous studies on physiological noise. The extended tensor model addresses both large-amplitude outliers and small-amplitude signal-changes. The framework of the extended tensor model also facilitates further investigation into physiological noise in diffusion tensor imaging. The proposed extended tensor model can be readily combined with other artefact correction methods such as robust fitting and eddy current correction. PMID:22936599

Federated Tensor Factorization for Computational Phenotyping

PubMed Central

Kim, Yejin; Sun, Jimeng; Yu, Hwanjo; Jiang, Xiaoqian

2017-01-01

Tensor factorization models offer an effective approach to convert massive electronic health records into meaningful clinical concepts (phenotypes) for data analysis. These models need a large amount of diverse samples to avoid population bias. An open challenge is how to derive phenotypes jointly across multiple hospitals, in which direct patient-level data sharing is not possible (e.g., due to institutional policies). In this paper, we developed a novel solution to enable federated tensor factorization for computational phenotyping without sharing patient-level data. We developed secure data harmonization and federated computation procedures based on alternating direction method of multipliers (ADMM). Using this method, the multiple hospitals iteratively update tensors and transfer secure summarized information to a central server, and the server aggregates the information to generate phenotypes. We demonstrated with real medical datasets that our method resembles the centralized training model (based on combined datasets) in terms of accuracy and phenotypes discovery while respecting privacy. PMID:29071165

Diffusion in shear flow

NASA Astrophysics Data System (ADS)

Dufty, J. W.

1984-09-01

Diffusion of a tagged particle in a fluid with uniform shear flow is described. The continuity equation for the probability density describing the position of the tagged particle is considered. The diffusion tensor is identified by expanding the irreversible part of the probability current to first order in the gradient of the probability density, but with no restriction on the shear rate. The tensor is expressed as the time integral of a nonequilibrium autocorrelation function for the velocity of the tagged particle in its local fluid rest frame, generalizing the Green-Kubo expression to the nonequilibrium state. The tensor is evaluated from results obtained previously for the velocity autocorrelation function that are exact for Maxwell molecules in the Boltzmann limit. The effects of viscous heating are included and the dependence on frequency and shear rate is displayed explicitly. The mode-coupling contributions to the frequency and shear-rate dependent diffusion tensor are calculated.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

NASA Astrophysics Data System (ADS)

Gyrya, V.; Lipnikov, K.

2017-11-01

We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE PAGES

Gyrya, V.; Lipnikov, K.

2017-07-18

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

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.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

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

Gyrya, V.; Lipnikov, K.

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

Mild hypothermia for treatment of diffuse axonal injury: a quantitative analysis of diffusion tensor imaging

PubMed Central

Jing, Guojie; Yao, Xiaoteng; Li, Yiyi; Xie, Yituan; Li, Wang#x2019;an; Liu, Kejun; Jing, Yingchao; Li, Baisheng; Lv, Yifan; Ma, Baoxin

2014-01-01

Fractional anisotropy values in diffusion tensor imaging can quantitatively reflect the consistency of nerve fibers after brain damage, where higher values generally indicate less damage to nerve fibers. Therefore, we hypothesized that diffusion tensor imaging could be used to evaluate the effect of mild hypothermia on diffuse axonal injury. A total of 102 patients with diffuse axonal injury were randomly divided into two groups: normothermic and mild hypothermic treatment groups. Patient's modified Rankin scale scores 2 months after mild hypothermia were significantly lower than those for the normothermia group. The difference in average fractional anisotropy value for each region of interest before and after mild hypothermia was 1.32-1.36 times higher than the value in the normothermia group. Quantitative assessment of diffusion tensor imaging indicates that mild hypothermia therapy may be beneficial for patients with diffuse axonal injury. PMID:25206800

Stix Award: The ponderomotive effect beyond the ponderomotive force

NASA Astrophysics Data System (ADS)

Dodin, I. Y.

2014-10-01

The classical ponderomotive effect (PE) is typically understood as the nonlinear time-average force produced by a rapidly oscillating electromagnetic field on a nonresonant particle. It is instructive to contrast this understanding with the common quantum interpretation of the PE as the ac Stark shift, i.e., phase modulation, or a Kerr effect experienced by the wave function. Then the PE is naturally extended from particles to waves and can be calculated efficiently in general settings, including for strongly nonlinear interactions and resonant dynamics. In particular, photons (plasmons, etc.) are hence seen to have polarizability and contribute to the linear dielectric tensor exactly like ``true'' particles such as electrons and ions. The talk will briefly review the underlying variational theory and some nonintuitive PE-based techniques of wave and particle manipulation that the theory predicts. It will also be shown that the PE can be understood as the cause for the basic properties of both linear and nonlinear waves in plasma, including their dispersion, energy-momentum transport, and various modulational instabilities. Linear collisionless dissipation (both on particles and classical waves, treated on the same footing) also appears merely as a special case of the modulational dynamics. The work was supported by NNSA grant DE274-FG52-08NA28553, DOE contract DE-AC02-09CH11466, and DTRA grant HDTRA1-11-1-0037.

[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].

PubMed

Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

2016-04-01

Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.

C%2B%2B tensor toolbox user manual.

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

Plantenga, Todd D.; Kolda, Tamara Gibson

2012-04-01

The C++ Tensor Toolbox is a software package for computing tensor decompositions. It is based on the Matlab Tensor Toolbox, and is particularly optimized for sparse data sets. This user manual briefly overviews tensor decomposition mathematics, software capabilities, and installation of the package. Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors in C++. The Toolbox compiles into libraries and is intended for use with custom applications written by users.

Tensor Factorization for Low-Rank Tensor Completion.

PubMed

Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao

2018-03-01

Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.

Similar Tensor Arrays - A Framework for Storage of Tensor Array Data

NASA Astrophysics Data System (ADS)

Brun, Anders; Martin-Fernandez, Marcos; Acar, Burak; Munoz-Moreno, Emma; Cammoun, Leila; Sigfridsson, Andreas; Sosa-Cabrera, Dario; Svensson, Björn; Herberthson, Magnus; Knutsson, Hans

This chapter describes a framework for storage of tensor array data, useful to describe regularly sampled tensor fields. The main component of the framework, called Similar Tensor Array Core (STAC), is the result of a collaboration between research groups within the SIMILAR network of excellence. It aims to capture the essence of regularly sampled tensor fields using a minimal set of attributes and can therefore be used as a “greatest common divisor” and interface between tensor array processing algorithms. This is potentially useful in applied fields like medical image analysis, in particular in Diffusion Tensor MRI, where misinterpretation of tensor array data is a common source of errors. By promoting a strictly geometric perspective on tensor arrays, with a close resemblance to the terminology used in differential geometry, (STAC) removes ambiguities and guides the user to define all necessary information. In contrast to existing tensor array file formats, it is minimalistic and based on an intrinsic and geometric interpretation of the array itself, without references to other coordinate systems.

Tensor Factorization for Precision Medicine in Heart Failure with Preserved Ejection Fraction

PubMed Central

Luo, Yuan; Ahmad, Faraz S.; Shah, Sanjiv J.

2017-01-01

Heart failure with preserved ejection fraction (HFpEF) is a heterogeneous clinical syndrome that may benefit from improved subtyping in order to better characterize its pathophysiology and to develop novel targeted therapies. The United States Precision Medicine Initiative comes amid the rapid growth in quantity and modality of clinical data for HFpEF patients ranging from deep phenotypic to trans-omic data. Tensor factorization, a form of machine learning, allows for the integration of multiple data modalities to derive clinically relevant HFpEF subtypes that may have significant differences in underlying pathophysiology and differential response to therapies. Tensor factorization also allows for better interpretability by supporting dimensionality reduction and identifying latent groups of data for meaningful summarization of both features and disease outcomes. In this narrative review, we analyze the modest literature on the application of tensor factorization to related biomedical fields including genotyping and phenotyping. Based on the cited work including work of our own, we suggest multiple tensor factorization formulations capable of integrating the deep phenotypic and trans-omic modalities of data for HFpEF, or accounting for interactions between genetic variants at different -omic hierarchies. We encourage extensive experimental studies to tackle challenges in applying tensor factorization for precision medicine in HFpEF, including effectively incorporating existing medical knowledge, properly accounting for uncertainty, and efficiently enforcing sparsity for better interpretability. PMID:28116551

Constraining the break of spatial diffeomorphism invariance with Planck data

NASA Astrophysics Data System (ADS)

Graef, L. L.; Benetti, M.; Alcaniz, J. S.

2017-07-01

The current most accepted paradigm for the early universe cosmology, the inflationary scenario, shows a good agreement with the recent Cosmic Microwave Background (CMB) and polarization data. However, when the inflation consistency relation is relaxed, these observational data exclude a larger range of red tensor tilt values, prevailing the blue ones which are not predicted by the minimal inflationary models. Recently, it has been shown that the assumption of spatial diffeomorphism invariance breaking (SDB) in the context of an effective field theory of inflation leads to interesting observational consequences. Among them, the possibility of generating a blue tensor spectrum, which can recover the specific consistency relation of the String Gas Cosmology, for a certain choice of parameters. We use the most recent CMB data to constrain the SDB model and test its observational viability through a Bayesian analysis assuming as reference an extended ΛCDM+tensor perturbation model, which considers a power-law tensor spectrum parametrized in terms of the tensor-to-scalar ratio, r, and the tensor spectral index, nt. If the inflation consistency relation is imposed, r=-8 nt, we obtain a strong evidence in favor of the reference model whereas if such relation is relaxed, a weak evidence in favor of the model with diffeomorphism breaking is found. We also use the same CMB data set to make an observational comparison between the SDB model, standard inflation and String Gas Cosmology.

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

Tensor Toolbox for MATLAB v. 3.0

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

Kola, Tamara; Bader, Brett W.; Acar Ataman, Evrim NMN

Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors using MATLAB's object-oriented features. It also provides algorithms for tensor decomposition and factorization, algorithms for computing tensor eigenvalues, and methods for visualization of results.

Low temperature EPR investigation of Co2+ ion doped into rutile TiO2 single crystal: Experiments and simulations

NASA Astrophysics Data System (ADS)

Zerentürk, A.; Açıkgöz, M.; Kazan, S.; Yıldız, F.; Aktaş, B.

2017-02-01

In this paper, we present the results of X-band EPR spectra of Co2+ ion doped rutile (TiO2) which is one of the most promising memristor material. We obtained the angular variation of spectra in three mutually perpendicular planes at liquid helium (7-13 K) temperatures. Since the impurity ions have ½ effective spin and 7/2 nuclear spin, a relatively simple spin Hamiltonian containing only electronic Zeeman and hyperfine terms was utilized. Two different methods were used in theoretical analysis. Firstly, a linear regression analysis of spectra based on perturbation theory was studied. However, this approach is not sufficient for analyzing Co+2 spectra and leads to complex eigenvectors for G and A tensors due to large anisotropy of eigenvalues. Therefore, all spectra were analyzed again with exact diagonalization of spin Hamiltonian and the high accuracy eigenvalues and eigenvectors of G and A tensors were obtained by taking into account the effect of small sample misalignment from the exact crystallographic planes due to experimental conditions. Our results show that eigen-axes of g and A tensors are parallel to crystallographic directions. Hence, our EPR experiments proves that Co2+ ions substitute for Ti4+ ions in lattice. The obtained principal values of g tensor are gx=2.110(6), gy=5.890(2), gz=3.725(7) and principal values of hyperfine tensor are Ax=42.4, Ay=152.7, Az=26 (in 10-4/cm).

Diffusion Tensor Image Registration Using Hybrid Connectivity and Tensor Features

PubMed Central

Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang

2014-01-01

Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. PMID:24293159

Spherical Tensor Calculus for Local Adaptive Filtering

NASA Astrophysics Data System (ADS)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

Modeling the effects of structure on seismic anisotropy in the Chester gneiss dome, southeast Vermont

NASA Astrophysics Data System (ADS)

Saif, S.; Brownlee, S. J.

2017-12-01

Compositional and structural heterogeneity in the continental crust are factors that contribute to the complex expression of crustal seismic anisotropy. Understanding deformation and flow in the crust using seismic anisotropy has thus proven difficult. Seismic anisotropy is affected by rock microstructure and mineralogy, and a number of studies have begun to characterize the full elastic tensors of crustal rocks in an attempt to increase our understanding of these intrinsic factors. However, there is still a large gap in length-scale between laboratory characterization on the scale of centimeters and seismic wavelengths on the order of kilometers. To address this length-scale gap we are developing a 3D crustal model that will help us determine the effects of rotating laboratory-scale elastic tensors into field-scale structures. The Chester gneiss dome in southeast Vermont is our primary focus. The model combines over 2000 structural data points from field measurements and published USGS structural data with elastic tensors of Chester dome rocks derived from electron backscatter diffraction data. We created a uniformly spaced grid by averaging structural measurements together in equally spaced grid boxes. The surface measurements are then projected into the third dimension using existing subsurface interpretations. A measured elastic tensor for the specific rock type is rotated according to its unique structural input at each point in the model. The goal is to use this model to generate artificial seismograms using existing numerical wave propagation codes. Once completed, the model input can be varied to examine the effects of different subsurface structure interpretations, as well as heterogeneity in rock composition and elastic tensors. Our goal is to be able to make predictions for how specific structures will appear in seismic data, and how that appearance changes with variations in rock composition.

Calculation of binary magnetic properties and potential energy curve in xenon dimer: second virial coefficient of (129)Xe nuclear shielding.

PubMed

Hanni, Matti; Lantto, Perttu; Runeberg, Nino; Jokisaari, Jukka; Vaara, Juha

2004-09-22

Quantum chemical calculations of the nuclear shielding tensor, the nuclear quadrupole coupling tensor, and the spin-rotation tensor are reported for the Xe dimer using ab initio quantum chemical methods. The binary chemical shift delta, the anisotropy of the shielding tensor Delta sigma, the nuclear quadrupole coupling tensor component along the internuclear axis chi( parallel ), and the spin-rotation constant C( perpendicular ) are presented as a function of internuclear distance. The basis set superposition error is approximately corrected for by using the counterpoise correction (CP) method. Electron correlation effects are systematically studied via the Hartree-Fock, complete active space self-consistent field, second-order Møller-Plesset many-body perturbation, and coupled-cluster singles and doubles (CCSD) theories, the last one without and with noniterative triples, at the nonrelativistic all-electron level. We also report a high-quality theoretical interatomic potential for the Xe dimer, gained using the relativistic effective potential/core polarization potential scheme. These calculations used valence basis set of cc-pVQZ quality supplemented with a set of midbond functions. The second virial coefficient of Xe nuclear shielding, which is probably the experimentally best-characterized intermolecular interaction effect in nuclear magnetic resonance spectroscopy, is computed as a function of temperature, and compared to experiment and earlier theoretical results. The best results for the second virial coefficient, obtained using the CCSD(CP) binary chemical shift curve and either our best theoretical potential or the empirical potentials from the literature, are in good agreement with experiment. Zero-point vibrational corrections of delta, Delta sigma, chi (parallel), and C (perpendicular) in the nu=0, J=0 rovibrational ground state of the xenon dimer are also reported.

Evading the non-continuity equation in the f( R, T) cosmology

NASA Astrophysics Data System (ADS)

Moraes, P. H. R. S.; Correa, R. A. C.; Ribeiro, G.

2018-03-01

We present a new approach for the f( R, T) gravity formalism, by thoroughly exploring the extra terms of its effective energy-momentum tensor T_{μ ν }^eff, which we name \\tilde{T}_{μ ν }, so that T_{μ ν }^eff=T_{μ ν }+\\tilde{T}_{μ ν }, with T_{μ ν } being the usual energy-momentum tensor of matter. Purely from the Bianchi identities, we obtain the conservation of both parts of the effective energy-momentum tensor, rather than the non-conservation of T_{μ ν }, originally occurring in the f( R, T) theories. In this way, the intriguing scenario of matter creation, which still lacks observational evidence, is evaded. One is left, then, with two sets of cosmological equations to be solved: the Friedmann-like equations along with the conservation of T_{μ ν } and along with the conservation of \\tilde{T}_{μ ν }. We present a physical interpretation for the conservation of \\tilde{T}_{μ ν }, which can be related to the presence of stiff matter in the universe. The cosmological consequences of this approach are presented and discussed as well as the benefits of evading the matter energy-momentum tensor non-conservation.

Electromagnetic Radiation Reaction in General Relativity.

NASA Astrophysics Data System (ADS)

O'Donnell, Nuala

Available from UMI in association with The British Library. This thesis examines the electromagnetic radiation reaction felt by a charged body falling freely in an external gravitational field in general relativity. The original objective was to find a new derivation of the radiation reaction force F^{i} of DeWitt and DeWitt^1 which was calculated for the special case of a point charge falling in slow motion in a weak, static gravitational field: F ^{i} = {2over 3}e^2R^{i}_{0j0 }v^{j}. This may be thought of as a local expression since it involves the particle's velocity v^{j } and the local Riemann curvature tensor R ^{i}_{0j0}. Its derivation involves integrals over the whole history of the particle, covering distances of approximately the length scale on which R^{i}_{0j0 } changes. This is different from calculations of the Abraham-Lorentz force of flat space-time involving integrals over distances only a few times the size of the charge. This work was motivated by the wish to find a "local" derivation of the local reaction force. Using Schutz's^2 local initial value method to solve the problem of a charged, rigid, spherically symmetric body moving in an external gravitational field of arbitrary metric. Calculations are done in a Riemann normal coordinate system ^3 and are only valid in a normal neighbourhood of the origin, where geodesics have not begun to cross one another. We solve Maxwell's equations for the self -force by making a slow-motion approximation and keeping terms to first order only in the Riemann tensor and velocity. It is surprising that we find no local radiation reaction. Consider two particles in a static spacetime with the same initial conditions at t = 0. Particle A is that of DeWitt and DeWitt; it feels a reaction force F^{i} = {2over 3}e^2R^{i }_{0j0}v^{j}. Particle B is accelerated from rest to the same small velocity; it feels no reaction force. The two particles therefore follow different trajectories. We conclude that there is a certain amount of history dependence in curved spacetime which is absent in flat spacetime where the Abraham-Lorentz reaction force acts equally on both particles. ftn ^1C. M. DeWitt and B. S. Brehme, Falling Charges, Phys., 1, 3 (1964). ^2B. F. Schutz, Statistical Formulation of Gravitational Radiation Reaction, Phys. Rev. D., 22, 249 (1980). ^3See for example A. Z. Petrov, Einstein Spaces, p.33, Pergamon Press (1969).

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.

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.

Trifocal Tensor-Based Adaptive Visual Trajectory Tracking Control of Mobile Robots.

PubMed

Chen, Jian; Jia, Bingxi; Zhang, Kaixiang

2017-11-01

In this paper, a trifocal tensor-based approach is proposed for the visual trajectory tracking task of a nonholonomic mobile robot equipped with a roughly installed monocular camera. The desired trajectory is expressed by a set of prerecorded images, and the robot is regulated to track the desired trajectory using visual feedback. Trifocal tensor is exploited to obtain the orientation and scaled position information used in the control system, and it works for general scenes owing to the generality of trifocal tensor. In the previous works, the start, current, and final images are required to share enough visual information to estimate the trifocal tensor. However, this requirement can be easily violated for perspective cameras with limited field of view. In this paper, key frame strategy is proposed to loosen this requirement, extending the workspace of the visual servo system. Considering the unknown depth and extrinsic parameters (installing position of the camera), an adaptive controller is developed based on Lyapunov methods. The proposed control strategy works for almost all practical circumstances, including both trajectory tracking and pose regulation tasks. Simulations are made based on the virtual experimentation platform (V-REP) to evaluate the effectiveness of the proposed approach.

Ostrogradsky in theories with multiple fields

NASA Astrophysics Data System (ADS)

de Rham, Claudia; Matas, Andrew

2016-06-01

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.

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).

Two-body problem in scalar-tensor theories as a deformation of general relativity: An effective-one-body approach

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis; Deruelle, Nathalie

2017-06-01

In this paper we address the two-body problem in massless scalar-tensor (ST) theories within an effective-one-body (EOB) framework. We focus on the first building block of the EOB approach, that is, mapping the conservative part of the two-body dynamics onto the geodesic motion of a test particle in an effective external metric. To this end, we first deduce the second post-Keplerian (2PK) Hamiltonian of the two-body problem from the known 2PK Lagrangian. We then build, by means of a canonical transformation, a ST deformation of the general relativistic EOB Hamiltonian that allows us to incorporate the scalar-tensor (2PK) corrections to the currently best available general relativity EOB results. This EOB-ST Hamiltonian defines a resummation of the dynamics that may provide information on the strong-field regime, in particular, the ISCO location and associated orbital frequency, and can be compared to, other, e.g., tidal, corrections.

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.

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Sain, M. K.

1983-01-01

Tensor model order reduction, recursive tensor model identification, input design for tensor model identification, software development for nonlinear feedback control laws based upon tensors, and development of the CATNAP software package for tensor modeling, identification and simulation were studied. The last of these are discussed.

Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.

PubMed

Kindlmann, Gordon; Estépar, Raúl San José; Niethammer, Marc; Haker, Steven; Westin, Carl-Fredrik

2007-01-01

In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.

Nongyrotropic Electrons in Guide Field Reconnection

NASA Technical Reports Server (NTRS)

Wendel, D. E.; Hesse, M.; Bessho, N.; Adrian, M. L.; Kuznetsova, M.

2016-01-01

We apply a scalar measure of nongyrotropy to the electron pressure tensor in a 2D particle-in-cell simulation of guide field reconnection and assess the corresponding electron distributions and the forces that account for the nongyrotropy. The scalar measure reveals that the nongyrotropy lies in bands that straddle the electron diffusion region and the separatrices, in the same regions where there are parallel electric fields. Analysis of electron distributions and fields shows that the nongyrotropy along the inflow and outflow separatrices emerges as a result of multiple populations of electrons influenced differently by large and small-scale parallel electric fields and by gradients in the electric field. The relevant parallel electric fields include large-scale potential ramps emanating from the x-line and sub-ion inertial scale bipolar electron holes. Gradients in the perpendicular electric field modify electrons differently depending on their phase, thus producing nongyrotropy. Magnetic flux violation occurs along portions of the separatrices that coincide with the parallel electric fields. An inductive electric field in the electron EB drift frame thus develops, which has the effect of enhancing nongyrotropies already produced by other mechanisms and under certain conditions producing their own nongyrotropy. Particle tracing of electrons from nongyrotropic populations along the inflows and outflows shows that the striated structure of nongyrotropy corresponds to electrons arriving from different source regions. We also show that the relevant parallel electric fields receive important contributions not only from the nongyrotropic portion of the electron pressure tensor but from electron spatial and temporal inertial terms as well.

Turbulent transport coefficients in spherical wedge dynamo simulations of solar-like stars

NASA Astrophysics Data System (ADS)

Warnecke, J.; Rheinhardt, M.; Tuomisto, S.; Käpylä, P. J.; Käpylä, M. J.; Brandenburg, A.

2018-01-01

Aims: We investigate dynamo action in global compressible solar-like convective dynamos in the framework of mean-field theory. Methods: We simulate a solar-type star in a wedge-shaped spherical shell, where the interplay between convection and rotation self-consistently drives a large-scale dynamo. To analyze the dynamo mechanism we apply the test-field method for azimuthally (φ) averaged fields to determine the 27 turbulent transport coefficients of the electromotive force, of which six are related to the α tensor. This method has previously been used either in simulations in Cartesian coordinates or in the geodynamo context and is applied here for the first time to fully compressible simulations of solar-like dynamos. Results: We find that the φφ-component of the α tensor does not follow the profile expected from that of kinetic helicity. The turbulent pumping velocities significantly alter the effective mean flows acting on the magnetic field and therefore challenge the flux transport dynamo concept. All coefficients are significantly affected by dynamically important magnetic fields. Quenching as well as enhancement are being observed. This leads to a modulation of the coefficients with the activity cycle. The temporal variations are found to be comparable to the time-averaged values and seem to be responsible for a nonlinear feedback on the magnetic field generation. Furthermore, we quantify the validity of the Parker-Yoshimura rule for the equatorward propagation of the mean magnetic field in the present case.

Evaluation of a vortex-based subgrid stress model using DNS databases

NASA Technical Reports Server (NTRS)

Misra, Ashish; Lund, Thomas S.

1996-01-01

The performance of a SubGrid Stress (SGS) model for Large-Eddy Simulation (LES) developed by Misra k Pullin (1996) is studied for forced and decaying isotropic turbulence on a 32(exp 3) grid. The physical viability of the model assumptions are tested using DNS databases. The results from LES of forced turbulence at Taylor Reynolds number R(sub (lambda)) approximately equals 90 are compared with filtered DNS fields. Probability density functions (pdfs) of the subgrid energy transfer, total dissipation, and the stretch of the subgrid vorticity by the resolved velocity-gradient tensor show reasonable agreement with the DNS data. The model is also tested in LES of decaying isotropic turbulence where it correctly predicts the decay rate and energy spectra measured by Comte-Bellot & Corrsin (1971).

Diffusive sensitivity to muscle architecture: a magnetic resonance diffusion tensor imaging study of the human calf.

PubMed

Galbán, Craig J; Maderwald, Stefan; Uffmann, Kai; de Greiff, Armin; Ladd, Mark E

2004-12-01

The aim of this study was to examine the diffusive properties of adjacent muscles at rest, and to determine the relationship between diffusive and architectural properties, which are task-specific to muscles. The principle, second, and third eigenvalues, trace of the diffusion tensor, and two anisotropic parameters, ellipsoid eccentricity (e) and fractional anisotropy (FA), of various muscles in the human calf were calculated by diffusion tensor imaging (DTI). Linear correlations of the calculated parameters to the muscle physiological cross-sectional area (PCSA), which is proportional to maximum muscle force, were performed to ascertain any linear relation between muscle architecture and diffusivity. Images of the left calf were acquired from six healthy male volunteers. Seven muscles were investigated in this study. These comprised the soleus, lateral gastrocnemius, medial gastrocnemius, posterior tibialis, anterior tibialis, extensor digitorum longus, and peroneus longus. All data were presented as the mean and standard error of the mean (SEM). In general, differences in diffusive parameter values occurred primarily between functionally different muscles. A strong correlation was also found between PCSA and the third eigenvalue, e, and FA. A mathematical derivation revealed a linear relationship between PCSA and the third eigenvalue as a result of their dependence on the average radius of all fibers within a single muscle. These findings demonstrated the ability of DTI to differentiate between functionally different muscles in the same region of the body on the basis of their diffusive properties.

Test-particle motion in the nonsymmetric gravitation theory

NASA Astrophysics Data System (ADS)

Moffat, J. W.

1987-06-01

A derivation of the motion of test particles in the nonsymmetric gravitational theory (NGT) is given using the field equations in the presence of matter. The motion of the particle is governed by the Christoffel symbols, which are formed from the symmetric part of the fundamental tensor gμν, as well as by a tensorial piece determined by the skew part of the contracted curvature tensor Rμν. Given the energy-momentum tensor for a perfect fluid and the definition of a test particle in the NGT, the equations of motion follow from the conservation laws. The tensorial piece in the equations of motion describes a new force in nature that acts on the conserved charge in a body. Particles that carry this new charge do not follow geodesic world lines in the NGT, whereas photons do satisfy geodesic equations of motion and the equivalence principle of general relativity. Astronomical predictions, based on the exact static, spherically symmetric solution of the field equations in a vacuum and the test-particle equations of motion, are derived in detail. The maximally extended coordinates that remove the event-horizon singularities in the static, spherically symmetric solution are presented. It is shown how an inward radially falling test particle can be prevented from forming an event horizon for a value greater than a specified critical value of the source charge. If a test particle does fall through an event horizon, then it must continue to fall until it reaches the singularity at r=0.

Dark matter relics and the expansion rate in scalar-tensor theories

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

Dutta, Bhaskar; Jimenez, Esteban; Zavala, Ivonne, E-mail: dutta@physics.tamu.edu, E-mail: este1985@physics.tamu.edu, E-mail: e.i.zavalacarrasco@swansea.ac.uk

We study the impact of a modified expansion rate on the dark matter relic abundance in a class of scalar-tensor theories. The scalar-tensor theories we consider are motivated from string theory constructions, which have conformal as well as disformally coupled matter to the scalar. We investigate the effects of such a conformal coupling to the dark matter relic abundance for a wide range of initial conditions, masses and cross-sections. We find that exploiting all possible initial conditions, the annihilation cross-section required to satisfy the dark matter content can differ from the thermal average cross-section in the standard case. We alsomore » study the expansion rate in the disformal case and find that physically relevant solutions require a nontrivial relation between the conformal and disformal functions. We study the effects of the disformal coupling in an explicit example where the disformal function is quadratic.« less

Quantum-metric contribution to the pair mass in spin-orbit-coupled Fermi superfluids

NASA Astrophysics Data System (ADS)

Iskin, M.

2018-03-01

As a measure of the quantum distance between Bloch states in the Hilbert space, the quantum metric was introduced to solid-state physics through the real part of the so-called geometric Fubini-Study tensor, the imaginary part of which corresponds to the Berry curvature measuring the emergent gauge field in momentum space. Here, we first derive the Ginzburg-Landau theory near the critical superfluid transition temperature and then identify and analyze the geometric effects on the effective mass tensor of the Cooper pairs. By showing that the quantum-metric contribution accounts for a sizable fraction of the pair mass in a surprisingly large parameter regime throughout the BCS-Bose-Einstein condensate crossover, we not only reveal the physical origin of its governing role in the superfluid density tensor but also hint at its plausible roles in many other observables.

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Radiation force of an arbitrary acoustic beam on an elastic sphere in a fluid

PubMed Central

Sapozhnikov, Oleg A.; Bailey, Michael R.

2013-01-01

A theoretical approach is developed to calculate the radiation force of an arbitrary acoustic beam on an elastic sphere in a liquid or gas medium. First, the incident beam is described as a sum of plane waves by employing conventional angular spectrum decomposition. Then, the classical solution for the scattering of a plane wave from an elastic sphere is applied for each plane-wave component of the incident field. The net scattered field is expressed as a superposition of the scattered fields from all angular spectrum components of the incident beam. With this formulation, the incident and scattered waves are superposed in the far field to derive expressions for components of the radiation stress tensor. These expressions are then integrated over a spherical surface to analytically describe the radiation force on an elastic sphere. Limiting cases for particular types of incident beams are presented and are shown to agree with known results. Finally, the analytical expressions are used to calculate radiation forces associated with two specific focusing transducers. PMID:23363086

Development of a pneumatic tensioning device for gap measurement during total knee arthroplasty.

PubMed

Kwak, Dai-Soon; Kong, Chae-Gwan; Han, Seung-Ho; Kim, Dong-Hyun; In, Yong

2012-09-01

Despite the importance of soft tissue balancing during total knee arthroplasty (TKA), all estimating techniques are dependent on a surgeon's manual distraction force or subjective feeling based on experience. We developed a new device for dynamic gap balancing, which can offer constant load to the gap between the femur and tibia, using pneumatic pressure during range of motion. To determine the amount of distraction force for the new device, 3 experienced surgeons' manual distraction force was measured using a conventional spreader. A new device called the consistent load pneumatic tensor was developed on the basis of the biomechanical tests. Reliability testing for the new device was performed using 5 cadaveric knees by the same surgeons. Intraclass correlation coefficients (ICCs) were calculated. The distraction force applied to the new pneumatic tensioning device was determined to be 150 N. The interobserver reliability was very good for the newly tested spreader device with ICCs between 0.828 and 0.881. The new pneumatic tensioning device can enable us to properly evaluate the soft tissue balance throughout the range of motion during TKA with acceptable reproducibility.

Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical electromagnetism techniques

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

Rodriguez, Alejandro; Ibanescu, Mihai; Joannopoulos, J. D.

2007-09-15

We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustratemore » our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a pistonlike geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising nonmonotonic ''lateral'' force from the walls.« less

Quantum properties of affine-metric gravity with the cosmological term

NASA Astrophysics Data System (ADS)

Baurov, A. Yu; Pronin, P. I.; Stepanyantz, K. V.

2018-04-01

The paper contains analysis of the one-loop effective action for affine-metric gravity of the Hilbert–Einstein type with the cosmological term. We discuss different approaches to the calculation of the effective action, which depends on two independent variables, namely, the metric tensor and the affine connection. In the one-loop approximation we explain how the effective action can be obtained, if, at the first step of the calculation, the metric tensor is integrated out. It is demonstrated that the result is the same as in the case when one starts by integrating out the connection.

On the dynamics of a human body model.

NASA Technical Reports Server (NTRS)

Huston, R. L.; Passerello, C. E.

1971-01-01

Equations of motion for a model of the human body are developed. Basically, the model consists of an elliptical cylinder representing the torso, together with a system of frustrums of elliptical cones representing the limbs. They are connected to the main body and each other by hinges and ball and socket joints. Vector, tensor, and matrix methods provide a systematic organization of the geometry. The equations of motion are developed from the principles of classical mechanics. The solution of these equations then provide the displacement and rotation of the main body when the external forces and relative limb motions are specified. Three simple example motions are studied to illustrate the method. The first is an analysis and comparison of simple lifting on the earth and the moon. The second is an elementary approach to underwater swimming, including both viscous and inertia effects. The third is an analysis of kicking motion and its effect upon a vertically suspended man such as a parachutist.

Aspects of the Antisymmetric Tensor Field

NASA Astrophysics Data System (ADS)

Lahiri, Amitabha

1991-02-01

With the possible exception of gravitation, fundamental interactions are generally described by theories of point particles interacting via massless gauge fields. Since the advent of string theories the picture of physical interaction has changed to accommodate one in which extended objects interact with each other. The generalization of the gauge theories to extended objects leads to theories of antisymmetric tensor fields. At scales corresponding to present-day laboratory experiments one expects to see only point particles, their interactions modified by the presence of antisymmetric tensor fields in the theory. Therefore, in order to establish the validity of any theory with antisymmetric tensor fields one needs to look for manifestations of these fields at low energies. The principal problem of gauge theories is the failure to provide a suitable explanation for the generation of masses for the fields in the theory. While there is a known mechanism (spontaneous symmetry breaking) for generating masses for both the matter fields and the gauge fields, the lack of experimental evidence in support of an elementary scalar field suggests that one look for alternative ways of generating masses for the fields. The interaction of gauge fields with an antisymmetric tensor field seems to be an attractive way of doing so, especially since all indications point to the possibility that there will be no remnant degrees of freedom. On the other hand the interaction of such a field with black holes suggest an independent way of verifying the existence of such fields. In this dissertation the origins of the antisymmetric tensor field are discussed in terms of string theory. The interaction of black holes with such a field is discussed next. The last chapter discusses the effects of an antisymmetric tensor field on quantum electrodynamics when the fields are minimally coupled.

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.

Gravitational wave memory in an expanding universe

NASA Astrophysics Data System (ADS)

Tolish, Alexander; Wald, Robert

2016-03-01

We investigate the gravitational wave memory effect in an expanding FLRW spacetime. We find that if the gravitational field is decomposed into gauge-invariant scalar, vector, and tensor modes after the fashion of Bardeen, only the tensor mode gives rise to memory, and this memory can be calculated using the retarded Green's function associated with the tensor wave equation. If locally similar radiation source events occur on flat and FLRW backgrounds, we find that the resulting memories will differ only by a redshift factor, and we explore whether or not this factor depends on the expansion history of the FLRW universe. We compare our results to related work by Bieri, Garfinkle, and Yau.

Radiation forces and the Abraham-Minkowski problem

NASA Astrophysics Data System (ADS)

Brevik, Iver

2018-04-01

Recent years have witnessed a number of beautiful experiments in radiation optics. Our purpose with this paper is to highlight some developments of radiation pressure physics in general, and thereafter to focus on the importance of the mentioned experiments in regard to the classic Abraham-Minkowski problem. That means, what is the “correct” expression for electromagnetic momentum density in continuous matter. In our opinion, one often sees that authors over-interpret the importance of their experimental findings with respect to the momentum problem. Most of these experiments are actually unable to discriminate between these energy-momentum tensors at all, since they can be easily described in terms of force expressions that are common for Abraham and Minkowski. Moreover, we emphasize the inherent ambiguity in applying the formal conservation principles to the radiation field in a dielectric, the reason being that the electromagnetic field in matter is only a subsystem which has to be supplemented by the mechanical subsystem to be closed. Finally, we make some suggestions regarding the connection between macroscopic electrodynamics and the Casimir effect, suggesting that there is a limit for the magnitudes of the cutoff parameters in QFT related to surface tension in ordinary hydromechanics.

Scalar Contribution to the Graviton Self-Energy During Inflation

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

Park, Sohyun

2012-01-01

We use dimensional regularization to evaluate the one loop contribution to the graviton self-energy from a massless, minimally coupled scalar on a locally de Sitter background. For noncoincident points our result agrees with the stress tensor correlators obtained recently by Perez-Nadal, Roura and Verdaguer. We absorb the ultraviolet divergences using the R 2 and C 2 counterterms first derived by ’t Hooft and Veltman, and we take the D = 4 limit of the finite remainder. The renormalized result is expressed as the sum of two transverse, 4th order differential operators acting on nonlocal, de Sitter invariant structure functions. Inmore » this form it can be used to quantum-correct the linearized Einstein equations so that one can study how the inflationary production of infrared scalars affects the propagation of dynamical gravitons and the force of gravity. We have seen that they have no effect on the propagation of dynamical gravitons. Our computation motivates a conjecture for the first correction to the vacuum state wave functional of gravitons. We comment as well on performing the same analysis for the more interesting contribution from inflationary gravitons, and on inferring one loop corrections to the force of gravity.« less

Bridging meso- and microscopic anisotropic unilateral damage formulations for microcracked solids

NASA Astrophysics Data System (ADS)

Zhu, Qi-Zhi; Yuan, Shuang-Shuang; Shao, Jian-fu

2017-04-01

A mathematically consistent and unified description of induced anisotropy and unilateral effects constitutes one of the central tasks in the continuum damage theories developed so far. This paper aims at bridging constitutive damage formulations on meso- and micro-scales with an emphasis on a complete mesoscopic determination of material effective properties for microcracked solids. The key is to introduce a new set of invariants in terms of strain tensor and fabric tensor by making use of the Walpole's tensorial base. This invariant set proves to be equivalent to the classical one, while the new one provides great conveniences to high-order orientation-dependent tensor manipulations. When limited to the case of parallel microcracks, potential relations between ten combination coefficients are established by applying continuity conditions. It is found that the dilute approximation with penny-shaped microcracks is a particular case of the present one. By originally introducing effective strain effect, interactions between microcracks are taken into account with comparison to the Mori-Tanaka method as well as the Ponte-Castaneda and Willis scheme. For completeness, discussions are also addressed on macroscopic formulations with high-order damage variables.

Visualizing second order tensor fields with hyperstreamlines

NASA Technical Reports Server (NTRS)

Delmarcelle, Thierry; Hesselink, Lambertus

1993-01-01

Hyperstreamlines are a generalization to second order tensor fields of the conventional streamlines used in vector field visualization. As opposed to point icons commonly used in visualizing tensor fields, hyperstreamlines form a continuous representation of the complete tensor information along a three-dimensional path. This technique is useful in visulaizing both symmetric and unsymmetric three-dimensional tensor data. Several examples of tensor field visualization in solid materials and fluid flows are provided.

A Local Fast Marching-Based Diffusion Tensor Image Registration Algorithm by Simultaneously Considering Spatial Deformation and Tensor Orientation

PubMed Central

Xue, Zhong; Li, Hai; Guo, Lei; Wong, Stephen T.C.

2010-01-01

It is a key step to spatially align diffusion tensor images (DTI) to quantitatively compare neural images obtained from different subjects or the same subject at different timepoints. Different from traditional scalar or multi-channel image registration methods, tensor orientation should be considered in DTI registration. Recently, several DTI registration methods have been proposed in the literature, but deformation fields are purely dependent on the tensor features not the whole tensor information. Other methods, such as the piece-wise affine transformation and the diffeomorphic non-linear registration algorithms, use analytical gradients of the registration objective functions by simultaneously considering the reorientation and deformation of tensors during the registration. However, only relatively local tensor information such as voxel-wise tensor-similarity, is utilized. This paper proposes a new DTI image registration algorithm, called local fast marching (FM)-based simultaneous registration. The algorithm not only considers the orientation of tensors during registration but also utilizes the neighborhood tensor information of each voxel to drive the deformation, and such neighborhood tensor information is extracted from a local fast marching algorithm around the voxels of interest. These local fast marching-based tensor features efficiently reflect the diffusion patterns around each voxel within a spherical neighborhood and can capture relatively distinctive features of the anatomical structures. Using simulated and real DTI human brain data the experimental results show that the proposed algorithm is more accurate compared with the FA-based registration and is more efficient than its counterpart, the neighborhood tensor similarity-based registration. PMID:20382233

Yield Scaling of Frequency Domain Moment Tensors from Contained Chemical Explosions Detonated in Granite

NASA Astrophysics Data System (ADS)

MacPhail, M. D.; Stump, B. W.; Zhou, R.

2017-12-01

The Source Phenomenology Experiment (SPE - Arizona) was a series of nine, contained and partially contained chemical explosions within the porphyry granite at the Morenci Copper mine in Arizona. Its purpose was to detonate, record and analyze seismic waveforms from these single-fired explosions. Ground motion data from the SPE is analyzed in this study to assess the uniqueness of the time domain moment tensor source representation and its ability to quantify containment and yield scaling. Green's functions were computed for each of the explosions based on a 1D velocity model developed for the SPE. The Green's functions for the sixteen, near-source stations focused on observations from 37 to 680 m. This study analyzes the three deepest, fully contained explosions with a depth of burial of 30 m and yields of 0.77e-3, 3.08e-3 and 6.17e-3 kt. Inversions are conducted within the frequency domain and moment tensors are decomposed into deviatoric and isotropic components to evaluate the effects of containment and yield on the resulting source representation. Isotropic moments are compared to those for other contained explosions as reported by Denny and Johnson, 1991, and are in good agreement with their scaling results. The explosions in this study have isotropic moments of 1.2e12, 3.1e12 and 6.1e13 n*m. Isotropic and Mzz moment tensor spectra are compared to Mueller-Murphy, Denny-Johnson and revised Heard-Ackerman (HA) models and suggest that the larger explosions fit the HA model better. Secondary source effects resulting from free surface interactions including the effects of spallation contribute to the resulting moment tensors which include a CLVD component. Hudson diagrams, using frequency domain moment tensor data, are computed as a tool to assess how these containment scenarios affect the source representation. Our analysis suggests that, within our band of interest (2-20 Hz), as the frequency increases, the source representation becomes more explosion like, peaking at around 20 Hz. These results guide additional analysis of the observational data and the practical resolution of physical phenomenology accompanying underground explosions.

Antisymmetric tensor generalizations of affine vector fields.

PubMed

Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro

2016-02-01

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.

Diffusion tensor analysis with invariant gradients and rotation tangents.

PubMed

Kindlmann, Gordon; Ennis, Daniel B; Whitaker, Ross T; Westin, Carl-Fredrik

2007-11-01

Guided by empirically established connections between clinically important tissue properties and diffusion tensor parameters, we introduce a framework for decomposing variations in diffusion tensors into changes in shape and orientation. Tensor shape and orientation both have three degrees-of-freedom, spanned by invariant gradients and rotation tangents, respectively. As an initial demonstration of the framework, we create a tunable measure of tensor difference that can selectively respond to shape and orientation. Second, to analyze the spatial gradient in a tensor volume (a third-order tensor), our framework generates edge strength measures that can discriminate between different neuroanatomical boundaries, as well as creating a novel detector of white matter tracts that are adjacent yet distinctly oriented. Finally, we apply the framework to decompose the fourth-order diffusion covariance tensor into individual and aggregate measures of shape and orientation covariance, including a direct approximation for the variance of tensor invariants such as fractional anisotropy.

Real-time object recognition in multidimensional images based on joined extended structural tensor and higher-order tensor decomposition methods

NASA Astrophysics Data System (ADS)

Cyganek, Boguslaw; Smolka, Bogdan

2015-02-01

In this paper a system for real-time recognition of objects in multidimensional video signals is proposed. Object recognition is done by pattern projection into the tensor subspaces obtained from the factorization of the signal tensors representing the input signal. However, instead of taking only the intensity signal the novelty of this paper is first to build the Extended Structural Tensor representation from the intensity signal that conveys information on signal intensities, as well as on higher-order statistics of the input signals. This way the higher-order input pattern tensors are built from the training samples. Then, the tensor subspaces are built based on the Higher-Order Singular Value Decomposition of the prototype pattern tensors. Finally, recognition relies on measurements of the distance of a test pattern projected into the tensor subspaces obtained from the training tensors. Due to high-dimensionality of the input data, tensor based methods require high memory and computational resources. However, recent achievements in the technology of the multi-core microprocessors and graphic cards allows real-time operation of the multidimensional methods as is shown and analyzed in this paper based on real examples of object detection in digital images.

Simultaneous tensor decomposition and completion using factor priors.

PubMed

Chen, Yi-Lei; Hsu, Chiou-Ting; Liao, Hong-Yuan Mark

2014-03-01

The success of research on matrix completion is evident in a variety of real-world applications. Tensor completion, which is a high-order extension of matrix completion, has also generated a great deal of research interest in recent years. Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors. In this paper, we introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure. To this end, we propose a method called simultaneous tensor decomposition and completion (STDC) that combines a rank minimization technique with Tucker model decomposition. Moreover, as the model structure is implicitly included in the Tucker model, we use factor priors, which are usually known a priori in real-world tensor objects, to characterize the underlying joint-manifold drawn from the model factors. By exploiting this auxiliary information, our method leverages two classic schemes and accurately estimates the model factors and missing entries. We conducted experiments to empirically verify the convergence of our algorithm on synthetic data and evaluate its effectiveness on various kinds of real-world data. The results demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications. It also outperforms state-of-the-art methods on multilinear model analysis and visual data completion tasks.

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.

Constraining the break of spatial diffeomorphism invariance with Planck data

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

Graef, L.L.; Benetti, M.; Alcaniz, J.S., E-mail: leilagraef@on.br, E-mail: micolbenetti@on.br, E-mail: alcaniz@on.br

The current most accepted paradigm for the early universe cosmology, the inflationary scenario, shows a good agreement with the recent Cosmic Microwave Background (CMB) and polarization data. However, when the inflation consistency relation is relaxed, these observational data exclude a larger range of red tensor tilt values, prevailing the blue ones which are not predicted by the minimal inflationary models. Recently, it has been shown that the assumption of spatial diffeomorphism invariance breaking (SDB) in the context of an effective field theory of inflation leads to interesting observational consequences. Among them, the possibility of generating a blue tensor spectrum, whichmore » can recover the specific consistency relation of the String Gas Cosmology, for a certain choice of parameters. We use the most recent CMB data to constrain the SDB model and test its observational viability through a Bayesian analysis assuming as reference an extended ΛCDM+tensor perturbation model, which considers a power-law tensor spectrum parametrized in terms of the tensor-to-scalar ratio, r , and the tensor spectral index, n {sub t} . If the inflation consistency relation is imposed, r =−8 n {sub t} , we obtain a strong evidence in favor of the reference model whereas if such relation is relaxed, a weak evidence in favor of the model with diffeomorphism breaking is found. We also use the same CMB data set to make an observational comparison between the SDB model, standard inflation and String Gas Cosmology.« less

New perspectives in the PAW/GIPAW approach: J(P-O-Si) coupling constants, antisymmetric parts of shift tensors and NQR predictions.

PubMed

Bonhomme, Christian; Gervais, Christel; Coelho, Cristina; Pourpoint, Frédérique; Azaïs, Thierry; Bonhomme-Coury, Laure; Babonneau, Florence; Jacob, Guy; Ferrari, Maude; Canet, Daniel; Yates, Jonathan R; Pickard, Chris J; Joyce, Siân A; Mauri, Francesco; Massiot, Dominique

2010-12-01

In 2001, Pickard and Mauri implemented the gauge including projected augmented wave (GIPAW) protocol for first-principles calculations of NMR parameters using periodic boundary conditions (chemical shift anisotropy and electric field gradient tensors). In this paper, three potentially interesting perspectives in connection with PAW/GIPAW in solid-state NMR and pure nuclear quadrupole resonance (NQR) are presented: (i) the calculation of J coupling tensors in inorganic solids; (ii) the calculation of the antisymmetric part of chemical shift tensors and (iii) the prediction of (14)N and (35)Cl pure NQR resonances including dynamics. We believe that these topics should open new insights in the combination of GIPAW, NMR/NQR crystallography, temperature effects and dynamics. Points (i), (ii) and (iii) will be illustrated by selected examples: (i) chemical shift tensors and heteronuclear (2)J(P-O-Si) coupling constants in the case of silicophosphates and calcium phosphates [Si(5)O(PO(4))(6), SiP(2)O(7) polymorphs and α-Ca(PO(3))(2)]; (ii) antisymmetric chemical shift tensors in cyclopropene derivatives, C(3)X(4) (X = H, Cl, F) and (iii) (14)N and (35)Cl NQR predictions in the case of RDX (C(3)H(6)N(6)O(6)), β-HMX (C(4)H(8)N(8)O(8)), α-NTO (C(2)H(2)N(4)O(3)) and AlOPCl(6). RDX, β-HMX and α-NTO are explosive compounds. Copyright © 2010 John Wiley & Sons, Ltd.

Strain Variation along Cimandiri Fault, West Java Based on Continuous and Campaign GPS Observation From 2006-2016

NASA Astrophysics Data System (ADS)

Safitri, A. A.; Meilano, I.; Gunawan, E.; Abidin, H. Z.; Efendi, J.; Kriswati, E.

2018-03-01

The Cimandiri fault which is running in the direction from Pelabuhan Ratu to Padalarang is the longest fault in West Java with several previous shallow earthquakes in the last 20 years. By using continues and campaign GPS observation from 2006-2016, we obtain the deformation pattern along the fault through the variation of strain tensor. We use the velocity vector of GPS station which is fixed in stable International Terrestrial Reference Frame 2008 to calculate horizontal strain tensor. Least Square Collocation is applied to produce widely dense distributed velocity vector and optimum scale factor for the Least Square Weighting matrix. We find that the strain tensor tend to change from dominantly contraction in the west to dominantly extension to the east of fault. Both the maximum shear strain and dilatation show positive value along the fault and increasing from the west to the east. The findings of strain tensor variation along Cimandiri Fault indicate the post seismic effect of the 2006 Java Earthquake.

Combined analysis of magnetic and gravity anomalies using normalized source strength (NSS)

NASA Astrophysics Data System (ADS)

Li, L.; Wu, Y.

2017-12-01

Gravity field and magnetic field belong to potential fields which lead inherent multi-solution. Combined analysis of magnetic and gravity anomalies based on Poisson's relation is used to determinate homology gravity and magnetic anomalies and decrease the ambiguity. The traditional combined analysis uses the linear regression of the reduction to pole (RTP) magnetic anomaly to the first order vertical derivative of the gravity anomaly, and provides the quantitative or semi-quantitative interpretation by calculating the correlation coefficient, slope and intercept. In the calculation process, due to the effect of remanent magnetization, the RTP anomaly still contains the effect of oblique magnetization. In this case the homology gravity and magnetic anomalies display irrelevant results in the linear regression calculation. The normalized source strength (NSS) can be transformed from the magnetic tensor matrix, which is insensitive to the remanence. Here we present a new combined analysis using NSS. Based on the Poisson's relation, the gravity tensor matrix can be transformed into the pseudomagnetic tensor matrix of the direction of geomagnetic field magnetization under the homologous condition. The NSS of pseudomagnetic tensor matrix and original magnetic tensor matrix are calculated and linear regression analysis is carried out. The calculated correlation coefficient, slope and intercept indicate the homology level, Poisson's ratio and the distribution of remanent respectively. We test the approach using synthetic model under complex magnetization, the results show that it can still distinguish the same source under the condition of strong remanence, and establish the Poisson's ratio. Finally, this approach is applied in China. The results demonstrated that our approach is feasible.

Homogenized moment tensor and the effect of near-field heterogeneities on nonisotropic radiation in nuclear explosion

NASA Astrophysics Data System (ADS)

Burgos, Gaël.; Capdeville, Yann; Guillot, Laurent

2016-06-01

We investigate the effect of small-scale heterogeneities close to a seismic explosive source, at intermediate periods (20-50 s), with an emphasis on the resulting nonisotropic far-field radiation. First, using a direct numerical approach, we show that small-scale elastic heterogeneities located in the near-field of an explosive source, generate unexpected phases (i.e., long period S waves). We then demonstrate that the nonperiodic homogenization theory applied to 2-D and 3-D elastic models, with various pattern of small-scale heterogeneities near the source, leads to accurate waveforms at a reduced computational cost compared to direct modeling. Further, it gives an interpretation of how nearby small-scale features interact with the source at low frequencies, through an explicit correction to the seismic moment tensor. In 2-D simulations, we find a deviatoric contribution to the moment tensor, as high as 21% for near-source heterogeneities showing a 25% contrast of elastic values (relative to a homogeneous background medium). In 3-D this nonisotropic contribution reaches 27%. Second, we analyze intermediate-periods regional seismic waveforms associated with some underground nuclear explosions conducted at the Nevada National Security Site and invert for the full moment tensor, in order to quantify the relative contribution of the isotropic and deviatoric components of the tensor. The average value of the deviatoric part is about 35%. We conclude that the interactions between an explosive source and small-scale local heterogeneities of moderate amplitude may lead to a deviatoric contribution to the seismic moment, close to what is observed using regional data from nuclear test explosions.

Tensoral for post-processing users and simulation authors

NASA Technical Reports Server (NTRS)

Dresselhaus, Eliot

1993-01-01

The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral's generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.

Is nuclear matter a quantum crystal?

NASA Technical Reports Server (NTRS)

Canuto, V.; Chitre, S. M.

1973-01-01

A possible alternative to the ordinary gas-like computation for nuclear matter is investigated under the assumption that the nucleons are arranged in a lattice. BCC, FCC and HCP structures are investigated. Only HCP shows a minimum in the energy vs. density curve with a modest binding energy of -1.5 MeV. The very low density limit is investigated and sensible results are obtained only if the tensor force decreases with the density. A study of the elastic properties indicates that the previous structures are mechanically unstable against shearing stresses.

Anatomy of the Eustachian Tube.

PubMed

Leuwer, Rudolf

2016-10-01

The eustachian tube consists of 2 compartments: the Rüdinger's safety canal and the auxiliary gap. It is surrounded by a cartilaginous wall on the craniomedial side and a membranous wall on the inferolateral side. The eustachian tube cartilage is firmly attached to the skull base by the lateral and the medial suspensory ligaments, which are separated by the medial Ostmann fat pad. The function of the isometric tensor veli palatini muscle is modulated by hypomochlia, which have an influence on the muscular force vectors. Copyright © 2016 Elsevier Inc. All rights reserved.

FDTD simulation of trapping nanowires with linearly polarized and radially polarized optical tweezers.

PubMed

Li, Jing; Wu, Xiaoping

2011-10-10

In this paper a model of the trapping force on nanowires is built by three dimensional finite-difference time-domain (FDTD) and Maxwell stress tensor methods, and the tightly focused laser beam is expressed by spherical vector wave functions (VSWFs). The trapping capacities on nanoscale-diameter nanowires are discussed in terms of a strongly focused linearly polarized beam and radially polarized beam. Simulation results demonstrate that the radially polarized beam has higher trapping efficiency on nanowires with higher refractive indices than linearly polarized beam.

FDTD simulation of trapping nanowires with linearly polarized and radially polarized optical tweezers

PubMed Central

Li, Jing; Wu, Xiaoping

2011-01-01

In this paper a model of the trapping force on nanowires is built by three dimensional finite-difference time-domain (FDTD) and Maxwell stress tensor methods, and the tightly focused laser beam is expressed by spherical vector wave functions (VSWFs). The trapping capacities on nanoscale-diameter nanowires are discussed in terms of a strongly focused linearly polarized beam and radially polarized beam. Simulation results demonstrate that the radially polarized beam has higher trapping efficiency on nanowires with higher refractive indices than linearly polarized beam. PMID:21997083

Fluid moments of the nonlinear Landau collision operator

DOE PAGES

Hirvijoki, E.; Lingam, M.; Pfefferle, D.; ...

2016-08-09

An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. In conclusion, the proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to arbitrary collisionality and flow.

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

Testing the seismology-based landquake monitoring system

NASA Astrophysics Data System (ADS)

Chao, Wei-An

2016-04-01

I have developed a real-time landquake monitoring system (RLMs), which monitor large-scale landquake activities in the Taiwan using real-time seismic network of Broadband Array in Taiwan for Seismology (BATS). The RLM system applies a grid-based general source inversion (GSI) technique to obtain the preliminary source location and force mechanism. A 2-D virtual source-grid on the Taiwan Island is created with an interval of 0.2° in both latitude and longitude. The depth of each grid point is fixed on the free surface topography. A database is stored on the hard disk for the synthetics, which are obtained using Green's functions computed by the propagator matrix approach for 1-D average velocity model, at all stations from each virtual source-grid due to nine elementary source components: six elementary moment tensors and three orthogonal (north, east and vertical) single-forces. Offline RLM system was carried out for events detected in previous studies. An important aspect of the RLM system is the implementation of GSI approach for different source types (e.g., full moment tensor, double couple faulting, and explosion source) by the grid search through the 2-D virtual source to automatically identify landquake event based on the improvement in waveform fitness and evaluate the best-fit solution in the monitoring area. With this approach, not only the force mechanisms but also the event occurrence time and location can be obtained simultaneously about 6-8 min after an occurrence of an event. To improve the insufficient accuracy of GSI-determined lotion, I further conduct a landquake epicenter determination (LED) method that maximizes the coherency of the high-frequency (1-3 Hz) horizontal envelope functions to determine the final source location. With good knowledge about the source location, I perform landquake force history (LFH) inversion to investigate the source dynamics (e.g., trajectory) for the relatively large-sized landquake event. With providing aforementioned source information in real-time, the government and emergency response agencies have sufficient reaction time for rapid assessment and response to landquake hazards. Since 2016, the RLM system has operated online.

Monopole-driven shell evolution below the doubly magic nucleus 132Sn explored with the long-lived isomer in 126Pd.

PubMed

Watanabe, H; Lorusso, G; Nishimura, S; Otsuka, T; Ogawa, K; Xu, Z Y; Sumikama, T; Söderström, P-A; Doornenbal, P; Li, Z; Browne, F; Gey, G; Jung, H S; Taprogge, J; Vajta, Zs; Wu, J; Yagi, A; Baba, H; Benzoni, G; Chae, K Y; Crespi, F C L; Fukuda, N; Gernhäuser, R; Inabe, N; Isobe, T; Jungclaus, A; Kameda, D; Kim, G D; Kim, Y K; Kojouharov, I; Kondev, F G; Kubo, T; Kurz, N; Kwon, Y K; Lane, G J; Moon, C-B; Montaner-Pizá, A; Moschner, K; Naqvi, F; Niikura, M; Nishibata, H; Nishimura, D; Odahara, A; Orlandi, R; Patel, Z; Podolyák, Zs; Sakurai, H; Schaffner, H; Simpson, G S; Steiger, K; Suzuki, H; Takeda, H; Wendt, A; Yoshinaga, K

2014-07-25

A new isomer with a half-life of 23.0(8) ms has been identified at 2406 keV in (126)Pd and is proposed to have a spin and parity of 10(+) with a maximally aligned configuration comprising two neutron holes in the 1h(11/2) orbit. In addition to an internal-decay branch through a hindered electric octupole transition, β decay from the long-lived isomer was observed to populate excited states at high spins in (126)Ag. The smaller energy difference between the 10(+) and 7(-) isomers in (126)Pd than in the heavier N=80 isotones can be interpreted as being ascribed to the monopole shift of the 1h(11/2) neutron orbit. The effects of the monopole interaction on the evolution of single-neutron energies below (132)Sn are discussed in terms of the central and tensor forces.

Neutrino-nucleus reactions based on recent structure studies

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

Suzuki, Toshio; National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588

2015-05-15

Neutrino-nucleus reactions are studied with the use of new shell model Hamiltonians, which have proper tensor components in the interactions and prove to be successful in the description of Gamow-Teller (GT) strengths in nuclei. The new Hamiltonians are applied to obtain new neutrino-nucleus reaction cross sections in {sup 12}C, {sup 13}C, {sup 56}Fe and {sup 56}Ni induced by solar and supernova neutrinos. The element synthesis by neutrino processes in supernova explosions is discussed with the new cross sections. The enhancement of the production yields of {sup 7}Li, {sup 11}B and {sup 55}Mn is obtained while fragmented GT strength in {supmore » 56}Ni with two-peak structure is found to result in smaller e-capture rates at stellar environments. The monopole-based universal interaction with tensor force of π+ρ meson exchanges is used to evaluate GT strength in {sup 40}Ar and ν-induced reactions on {sup 40}Ar. It is found to reproduce well the experimental GT strength in {sup 40}Ar.« less

Vainshtein mechanism after GW170817

NASA Astrophysics Data System (ADS)

Crisostomi, Marco; Koyama, Kazuya

2018-01-01

The almost simultaneous detection of gravitational waves and a short gamma-ray burst from a neutron star merger has put a tight constraint on the difference between the speed of gravity and light. In the four-dimensional scalar-tensor theory with second-order equations of motion, the Horndeski theory, this translates into a significant reduction of the viable parameter space of the theory. Recently, extensions of Horndeski theory, which are free from Ostrogradsky ghosts despite the presence of higher-order derivatives in the equations of motion, have been identified and classified exploiting the degeneracy criterium. In these new theories, the fifth force mediated by the scalar field must be suppressed in order to evade the stringent Solar System constraints. We study the Vainshtein mechanism in the most general degenerate higher-order scalar-tensor theory in which light and gravity propagate at the same speed. We find that the Vainshtein mechanism generally works outside a matter source but it is broken inside matter, similarly to beyond Horndeski theories. This leaves interesting possibilities to test these theories that are compatible with gravitational wave observations using astrophysical objects.

f( R, L m ) gravity

NASA Astrophysics Data System (ADS)

Harko, Tiberiu; Lobo, Francisco S. N.

2010-11-01

We generalize the f( R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert-Einstein Lagrange density are also derived.

Nonlinear resistivity for magnetohydrodynamical models

DOE PAGES

Lingam, M.; Hirvijoki, E.; Pfefferlé, D.; ...

2017-04-20

A new formulation of the plasma resistivity that stems from the collisional momentum-transfer rate between electrons and ions is presented. The resistivity computed herein is shown to depend not only on the temperature and density but also on all other polynomial velocity-space moments of the distribution function, such as the pressure tensor and heat flux vector. The full expression for the collisional momentum-transfer rate is determined and is used to formulate the nonlinear anisotropic resistivity. The new formalism recovers the Spitzer resistivity, as well as the concept of thermal force if the heat flux is assumed to be proportional tomore » a temperature gradient. Furthermore, if the pressure tensor is related to viscous stress, the latter enters the expression for the resistivity. The relative importance of the nonlinear term(s) with respect to the well-established electron inertia and Hall terms is also examined. Lastly, the subtle implications of the nonlinear resistivity, and its dependence on the fluid variables, are discussed in the context of magnetized plasma environments and phenomena such as magnetic reconnection.« less

Automatic deformable diffusion tensor registration for fiber population analysis.

PubMed

Irfanoglu, M O; Machiraju, R; Sammet, S; Pierpaoli, C; Knopp, M V

2008-01-01

In this work, we propose a novel method for deformable tensor-to-tensor registration of Diffusion Tensor Images. Our registration method models the distances in between the tensors with Geode-sic-Loxodromes and employs a version of Multi-Dimensional Scaling (MDS) algorithm to unfold the manifold described with this metric. Defining the same shape properties as tensors, the vector images obtained through MDS are fed into a multi-step vector-image registration scheme and the resulting deformation fields are used to reorient the tensor fields. Results on brain DTI indicate that the proposed method is very suitable for deformable fiber-to-fiber correspondence and DTI-atlas construction.

FAST TRACK COMMUNICATION Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor

NASA Astrophysics Data System (ADS)

Senovilla, José M. M.

2010-11-01

The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved.

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

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

NASA Technical Reports Server (NTRS)

Hanson, R. J.; Krogh, Fred T.

1992-01-01

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

Scalar and tensor perturbations in loop quantum cosmology: high-order corrections

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

Zhu, Tao; Wang, Anzhong; Wu, Qiang

2015-10-01

Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using the third-order uniform asymptotic approximations, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratiomore » is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are ∼< 0.15%, these results represent the most accurate results obtained so far in the literature. It is also shown that with the inverse-volume corrections, both scalar and tensor spectra exhibit a deviation from the usual shape at large scales. Then, using the Planck, BAO and SN data we obtain new constraints on quantum gravitational effects from LQC corrections, and find that such effects could be within the detection of the forthcoming experiments.« less

A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis

NASA Astrophysics Data System (ADS)

Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.; Tang, Qi

2017-08-01

A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This added-mass partitioned (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added-mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this first part of a two-part series, the properties of the AMP scheme are motivated and evaluated through the development and analysis of some model problems. The analysis shows when and why the traditional partitioned scheme becomes unstable due to either added-mass or added-damping effects. The analysis also identifies the proper form of the added-damping which depends on the discrete time-step and the grid-spacing normal to the rigid body. The results of the analysis are confirmed with numerical simulations that also demonstrate a second-order accurate implementation of the AMP scheme.

Sparse alignment for robust tensor learning.

PubMed

Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming

2014-10-01

Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Stochastic interactions of two Brownian hard spheres in the presence of depletants

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

Karzar-Jeddi, Mehdi; Fan, Tai-Hsi, E-mail: thfan@engr.uconn.edu; Tuinier, Remco

2014-06-07

A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamicsmore » as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions.« less

Ostrogradsky in theories with multiple fields

DOE PAGES

de Rham, Claudia; Matas, Andrew

2016-06-23

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamicalmore » or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.« less

Concepts and procedures required for successful reduction of tensor magnetic gradiometer data obtained from an unexploded ordnance detection demonstration at Yuma Proving Grounds, Arizona

USGS Publications Warehouse

Bracken, Robert E.; Brown, Philip J.

2006-01-01

On March 12, 2003, data were gathered at Yuma Proving Grounds, in Arizona, using a Tensor Magnetic Gradiometer System (TMGS). This report shows how these data were processed and explains concepts required for successful TMGS data reduction. Important concepts discussed include extreme attitudinal sensitivity of vector measurements, low attitudinal sensitivity of gradient measurements, leakage of the common-mode field into gradient measurements, consequences of thermal drift, and effects of field curvature. Spatial-data collection procedures and a spin-calibration method are addressed. Discussions of data-reduction procedures include tracking of axial data by mathematically matching transfer functions among the axes, derivation and application of calibration coefficients, calculation of sensor-pair gradients, thermal-drift corrections, and gradient collocation. For presentation, the magnetic tensor at each data station is converted to a scalar quantity, the I2 tensor invariant, which is easily found by calculating the determinant of the tensor. At important processing junctures, the determinants for all stations in the mapped area are shown in shaded relief map-view. Final processed results are compared to a mathematical model to show the validity of the assumptions made during processing and the reasonableness of the ultimate answer obtained.

A metamodel for the apparent permeability tensor of three-dimensional porous media in the inertial regime

NASA Astrophysics Data System (ADS)

Luminari, Nicola; Airiau, Christophe; Bottaro, Alessandro

2017-11-01

In the description of the homogenized flow through a porous medium saturated by a fluid, the apparent permeability tensor is one of the most important parameters to evaluate. In this work we compute numerically the apparent permeability tensor for a 3D porous medium constituted by rigid cylinder using the VANS (Volume-Averaged Navier-Stokes) theory. Such a tensor varies with the Reynolds number, the mean pressure gradient orientation and the porosity. A database is created exploring the space of the above parameters. Including the two Euler angles that define the mean pressure gradient is extremely important to capture well possible 3D effects. Based on the database, a kriging interpolation metamodel is used to obtain an estimate of all the tensor components for any input parameters. Preliminary results of the flow in a porous channel based on the metamodel and the VANS closure are shown; the use of such a reduced order model together with a numerical code based on the equations at the macroscopic scale permit to maintain the computational times to within reasonable levels. The authors acknowledge the IDEX Foundation of the University of Toulouse 570 for the financial support Granted to the last author under the project Attractivity Chairs.

Ostrogradsky in theories with multiple fields

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

de Rham, Claudia; Matas, Andrew

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamicalmore » or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.« less

Waveform inversion of very long period impulsive signals associated with magmatic injection beneath Kilauea Volcano, Hawaii

USGS Publications Warehouse

Ohminato, T.; Chouet, B.A.; Dawson, P.; Kedar, S.

1998-01-01

We use data from broadband seismometers deployed around the summit of Kilauea Volcano to quantify the mechanism associated with a transient in the flow of magma feeding the east rift eruption of the volcano. The transient is marked by rapid inflation of the Kilauea summit peaking at 22 ??rad 4.5 hours after the event onset, followed by slow deflation over a period of 3 days. Superimposed on the summit inflation is a series of sawtooth displacement pulses, each characterized by a sudden drop in amplitude lasting 5-10 s followed by an exponential recovery lasting 1-3 min. The sawtooth waveforms display almost identical shapes, suggesting a process involving the repeated activation of a fixed source. The particle motion associated with each sawtooth is almost linear, and its major swing shows compressional motion at all stations. Analyses of semblance and particle motion are consistent with a point source located 1 km beneath the northeast edge of the Halemaumau pit crater. To estimate the source mechanism, we apply a moment tensor inversion to the waveform data, assuming a point source embedded in a homogeneous half-space with compressional and shear wave velocities representative of the average medium properties at shallow depth under Kilauea. Synthetic waveforms are constructed by a superposition of impulse responses for six moment tensor components and three single force components. The origin times of individual impulses are distributed along the time axis at appropriately small, equal intervals, and their amplitudes are determined by least squares. In this inversion, the source time functions of the six tensor and three force components are determined simultaneously. We confirm the accuracy of the inversion method through a series of numerical tests. The results from the inversion show that the waveform data are well explained by a pulsating transport mechanism operating on a subhorizontal crack linking the summit reservoir to the east rift of Kilauea. The crack acts like a buffer in which a batch of fluid (magma and/or gas) accumulates over a period of 1-3 min before being rapidly injected into a larger reservoir (possibly the east rift) over a timescale of 5-10 s. The seismic moment and volume change associated with a typical batch of fluid are approximately 1014 N m and 3000 m3, respectively. Our results also point to the existence of a single force component with amplitude of 109 N, which may be explained as the drag force generated by the flow of viscous magma through a narrow constriction in the flow path. The total volume of magma associated with the 4.5-hour-long activation of the pulsating source is roughly 500,000 m3 in good agreement with the integrated volume flow rate of magma estimated near the eruptive site.

Extended scalar-tensor theories of gravity

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

Crisostomi, Marco; Koyama, Kazuya; Tasinato, Gianmassimo

2016-04-21

We study new consistent scalar-tensor theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-tensor theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and disformal transformations. Finally, we point out that these theories can be associated with new operators inmore » the effective field theory of dark energy, which might open up new possibilities to test dark energy models in future surveys.« less

Natural chemical shielding analysis of nuclear magnetic resonance shielding tensors from gauge-including atomic orbital calculations

NASA Astrophysics Data System (ADS)

Bohmann, Jonathan A.; Weinhold, Frank; Farrar, Thomas C.

1997-07-01

Nuclear magnetic shielding tensors computed by the gauge including atomic orbital (GIAO) method in the Hartree-Fock self-consistent-field (HF-SCF) framework are partitioned into magnetic contributions from chemical bonds and lone pairs by means of natural chemical shielding (NCS) analysis, an extension of natural bond orbital (NBO) analysis. NCS analysis complements the description provided by alternative localized orbital methods by directly calculating chemical shieldings due to delocalized features in the electronic structure, such as bond conjugation and hyperconjugation. Examples of NCS tensor decomposition are reported for CH4, CO, and H2CO, for which a graphical mnemonic due to Cornwell is used to illustrate the effect of hyperconjugative delocalization on the carbon shielding.

Studying the Polarization Switching in Polycrystalline BiFeO3 Films by 2D Piezoresponse Force Microscopy

NASA Astrophysics Data System (ADS)

Jin, Yaming; Lu, Xiaomei; Zhang, Junting; Kan, Yi; Bo, Huifeng; Huang, Fengzhen; Xu, Tingting; Du, Yingchao; Xiao, Shuyu; Zhu, Jinsong

2015-07-01

For rhombohedral multiferroelectrics, non-180° ferroelectric domain switching may induce ferroelastic and/or (anti-)ferromagnetic effect. So the determination and control of ferroelectric domain switching angles is crucial for nonvolatile information storage and exchange-coupled magnetoelectric devices. We try to study the intrinsic characters of polarization switching in BiFeO3 by introducing a special data processing method to determine the switching angle from 2D PFM (Piezoresponse Force Microscopy) images of randomly oriented samples. The response surface of BiFeO3 is first plotted using the piezoelectric tensor got from first principles calculations. Then from the normalized 2D PFM signals before and after switching, the switching angles of randomly oriented BiFeO3 grains can be determined through numerical calculations. In the polycrystalline BiFeO3 films, up to 34% of all switched area is that with original out-of-plane (OP) polarization parallel to the poling field. 71° polarization switching is more favorable, with the area percentages of 71°, 109° and 180° domain switching being about 42%, 29% and 29%, respectively. Our analysis further reveals that IP stress and charge migration have comparable effect on switching, and they are sensitive to the geometric arrangements. This work helps exploring a route to control polarization switching in BiFeO3, so as to realize desirable magnetoelectric coupling.

Canonical Descriptions of High Intensity Laser-Plasma Interaction

NASA Astrophysics Data System (ADS)

Le Cornu, B. J.

The problem of laser-plasma interaction has been studied extensively in the context of inertial confinement fusion (ICF). These studies have focussed on effects like the nonlinear force, self-focusing, Rayleigh- Taylor instabilities, stimulated Brillouin scattering and stimulated Raman scattering observed in ICF schemes. However, there remains a large discrepancy between theory and experiment in the context of nuclear fusion schemes. Several authors have attempted to gain greater understanding of the physics involved by the application of standard or 'canonical' methods used in Lagrangian and Hamiltonian mechanics to the problem of plasma physics. This thesis presents a new canonical description of laser-plasma interaction based on the Podolsky Lagrangian. Finite self-energy of charged particles, incroporation of high-frequency effects and an ability to quantise are the main advantages of this new model. The nature of the Podolsky constant is also analysed in the context of plasma physics, specifically in terms of the plasma dispersion relation. A new gauge invariant expression of the energy-momentum tensor for any gauge invariant Lagrangian dependent on second order derivatives is derived for the first time. Finally, the transient and nontransient expressions of the nonlinear ponderomotive force in laser-plasma interaction are discussed and shown to be closely approximated by a canonical derivation of the electromagnetic Lagrangian, a fact that seems to have been missed in the literature.

Turbulent fluid motion 2: Scalars, vectors, and tensors

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1991-01-01

The author shows that the sum or difference of two vectors is a vector. Similarly the sum of any two tensors of the same order is a tensor of that order. No meaning is attached to the sum of tensors of different orders, say u(sub i) + u(sub ij); that is not a tensor. In general, an equation containing tensors has meaning only if all the terms in the equation are tensors of the same order, and if the same unrepeated subscripts appear in all the terms. These facts will be used in obtaining appropriate equations for fluid turbulence. With the foregoing background, the derivation of appropriate continuum equations for turbulence should be straightforward.

Generalized Higher Order Orthogonal Iteration for Tensor Learning and Decomposition.

PubMed

Liu, Yuanyuan; Shang, Fanhua; Fan, Wei; Cheng, James; Cheng, Hong

2016-12-01

Low-rank tensor completion (LRTC) has successfully been applied to a wide range of real-world problems. Despite the broad, successful applications, existing LRTC methods may become very slow or even not applicable for large-scale problems. To address this issue, a novel core tensor trace-norm minimization (CTNM) method is proposed for simultaneous tensor learning and decomposition, and has a much lower computational complexity. In our solution, first, the equivalence relation of trace norm of a low-rank tensor and its core tensor is induced. Second, the trace norm of the core tensor is used to replace that of the whole tensor, which leads to two much smaller scale matrix TNM problems. Finally, an efficient alternating direction augmented Lagrangian method is developed to solve our problems. Our CTNM formulation needs only O((R N +NRI)log(√{I N })) observations to reliably recover an N th-order I×I×…×I tensor of n -rank (r,r,…,r) , compared with O(rI N-1 ) observations required by those tensor TNM methods ( I > R ≥ r ). Extensive experimental results show that CTNM is usually more accurate than them, and is orders of magnitude faster.

Tensor gauge condition and tensor field decomposition

NASA Astrophysics Data System (ADS)

Zhu, Ben-Chao; Chen, Xiang-Song

2015-10-01

We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

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.

Anisotropic Mesoscale Eddy Transport in Ocean General Circulation Models

NASA Astrophysics Data System (ADS)

Reckinger, S. J.; Fox-Kemper, B.; Bachman, S.; Bryan, F.; Dennis, J.; Danabasoglu, G.

2014-12-01

Modern climate models are limited to coarse-resolution representations of large-scale ocean circulation that rely on parameterizations for mesoscale eddies. The effects of eddies are typically introduced by relating subgrid eddy fluxes to the resolved gradients of buoyancy or other tracers, where the proportionality is, in general, governed by an eddy transport tensor. The symmetric part of the tensor, which represents the diffusive effects of mesoscale eddies, is universally treated isotropically in general circulation models. Thus, only a single parameter, namely the eddy diffusivity, is used at each spatial and temporal location to impart the influence of mesoscale eddies on the resolved flow. However, the diffusive processes that the parameterization approximates, such as shear dispersion, potential vorticity barriers, oceanic turbulence, and instabilities, typically have strongly anisotropic characteristics. Generalizing the eddy diffusivity tensor for anisotropy extends the number of parameters to three: a major diffusivity, a minor diffusivity, and the principal axis of alignment. The Community Earth System Model (CESM) with the anisotropic eddy parameterization is used to test various choices for the newly introduced parameters, which are motivated by observations and the eddy transport tensor diagnosed from high resolution simulations. Simply setting the ratio of major to minor diffusivities to a value of five globally, while aligning the major axis along the flow direction, improves biogeochemical tracer ventilation and reduces global temperature and salinity biases. These effects can be improved even further by parameterizing the anisotropic transport mechanisms in the ocean.

Cosmology of non-minimal derivative coupling to gravity in Palatini formalism and its chaotic inflation

NASA Astrophysics Data System (ADS)

Kaewkhao, Narakorn; Gumjudpai, Burin

2018-06-01

We consider, in Palatini formalism, a modified gravity of which the scalar field derivative couples to Einstein tensor. In this scenario, Ricci scalar, Ricci tensor and Einstein tensor are functions of connection field. As a result, the connection field gives rise to relation, hμν = fgμν between effective metric, hμν and the usual metric gμν where f = 1 - κϕ,αϕ,α / 2. In FLRW universe, NMDC coupling constant is limited in a range of - 2 /ϕ˙2 < κ ≤ ∞ preserving Lorentz signature of the effective metric. Slowly-rolling regime provides κ < 0 forbidding graviton from traveling at superluminal speed. Effective gravitational coupling and entropy of blackhole's apparent horizon are derived. In case of negative coupling, acceleration could happen even with weff > - 1 / 3. Power-law potentials of chaotic inflation are considered. For V ∝ϕ2 and V ∝ϕ4, it is possible to obtain tensor-to-scalar ratio lower than that of GR so that it satisfies r < 0 . 12 as constrained by Planck 2015 (Ade et al., 2016). The V ∝ϕ2 case yields acceptable range of spectrum index and r values. The quartic potential's spectrum index is disfavored by the Planck results. Viable range of κ for V ∝ϕ2 case lies in positive region, resulting in less blackhole's entropy, superluminal metric, more amount of inflation, avoidance of super-Planckian field initial value and stronger gravitational constant.

Gauge and Non-Gauge Tensor Multiplets in 5D Conformal Supergravity

NASA Astrophysics Data System (ADS)

Kugo, T.; Ohashi, K.

2002-12-01

An off-shell formulation of two distinct tensor multiplets, a massive tensor multiplet and a tensor gauge multiplet, is presented in superconformal tensor calculus in five-dimensional space-time. Both contain a rank 2 antisymmetric tensor field, but there is no gauge symmetry in the former, while it is a gauge field in the latter. Both multiplets have 4 bosonic and 4 fermionic on-shell modes, but the former consists of 16 (boson)+16 (fermion) component fields, while the latter consists of 8 (boson)+8 (fermion) component fields.

The energy-momentum tensor(s) in classical gauge theories

DOE PAGES

Blaschke, Daniel N.; Gieres, François; Reboud, Méril; ...

2016-07-12

We give an introduction to, and review of, the energy-momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy-momentum tensor. In conclusion, the relationship with the Einstein-Hilbert tensor following from the coupling to a gravitational field is also discussed.

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.

Effective description of higher-order scalar-tensor theories

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

Langlois, David; Mancarella, Michele; Vernizzi, Filippo

Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initialmore » Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called 'beyond Horndeski' theories. We also discuss Lorentz-breaking models inspired by Horava gravity.« less

Using Perturbation Theory to Reduce Noise in Diffusion Tensor Fields

PubMed Central

Bansal, Ravi; Staib, Lawrence H.; Xu, Dongrong; Laine, Andrew F.; Liu, Jun; Peterson, Bradley S.

2009-01-01

We propose the use of Perturbation theory to reduce noise in Diffusion Tensor (DT) fields. Diffusion Tensor Imaging (DTI) encodes the diffusion of water molecules along different spatial directions in a positive-definite, 3 × 3 symmetric tensor. Eigenvectors and eigenvalues of DTs allow the in vivo visualization and quantitative analysis of white matter fiber bundles across the brain. The validity and reliability of these analyses are limited, however, by the low spatial resolution and low Signal-to-Noise Ratio (SNR) in DTI datasets. Our procedures can be applied to improve the validity and reliability of these quantitative analyses by reducing noise in the tensor fields. We model a tensor field as a three-dimensional Markov Random Field and then compute the likelihood and the prior terms of this model using Perturbation theory. The prior term constrains the tensor field to be smooth, whereas the likelihood term constrains the smoothed tensor field to be similar to the original field. Thus, the proposed method generates a smoothed field that is close in structure to the original tensor field. We evaluate the performance of our method both visually and quantitatively using synthetic and real-world datasets. We quantitatively assess the performance of our method by computing the SNR for eigenvalues and the coherence measures for eigenvectors of DTs across tensor fields. In addition, we quantitatively compare the performance of our procedures with the performance of one method that uses a Riemannian distance to compute the similarity between two tensors, and with another method that reduces noise in tensor fields by anisotropically filtering the diffusion weighted images that are used to estimate diffusion tensors. These experiments demonstrate that our method significantly increases the coherence of the eigenvectors and the SNR of the eigenvalues, while simultaneously preserving the fine structure and boundaries between homogeneous regions, in the smoothed tensor field. PMID:19540791

Baryon interactions from lattice QCD with physical quark masses - Nuclear forces and ΞΞ forces -

NASA Astrophysics Data System (ADS)

Doi, Takumi; Iritani, Takumi; Aoki, Sinya; Gongyo, Shinya; Hatsuda, Tetsuo; Ikeda, Yoichi; Inoue, Takashi; Ishii, Noriyoshi; Miyamoto, Takaya; Nemura, Hidekatsu; Sasaki, Kenji

2018-03-01

We present the latest lattice QCD results for baryon interactions obtained at nearly physical quark masses. Nf = 2 + 1 nonperturbatively O(a)-improved Wilson quark action with stout smearing and Iwasaki gauge action are employed on the lattice of (96a)4 ≃(8.1fm)4 with a-1 ≃2.3 GeV, where mπ ≃146 MeV and mK ≃525 MeV. In this report, we study the two-nucleon systems and two-Ξ systems in 1S0 channel and 3S1-3D1 coupled channel, and extract central and tensor interactions by the HAL QCD method. We also present the results for the NΩ interaction in 5S2 channel which is relevant to the NΩ pair-momentum correlation in heavy-ion collision experiments.

Hidden discriminative features extraction for supervised high-order time series modeling.

PubMed

Nguyen, Ngoc Anh Thi; Yang, Hyung-Jeong; Kim, Sunhee

2016-11-01

In this paper, an orthogonal Tucker-decomposition-based extraction of high-order discriminative subspaces from a tensor-based time series data structure is presented, named as Tensor Discriminative Feature Extraction (TDFE). TDFE relies on the employment of category information for the maximization of the between-class scatter and the minimization of the within-class scatter to extract optimal hidden discriminative feature subspaces that are simultaneously spanned by every modality for supervised tensor modeling. In this context, the proposed tensor-decomposition method provides the following benefits: i) reduces dimensionality while robustly mining the underlying discriminative features, ii) results in effective interpretable features that lead to an improved classification and visualization, and iii) reduces the processing time during the training stage and the filtering of the projection by solving the generalized eigenvalue issue at each alternation step. Two real third-order tensor-structures of time series datasets (an epilepsy electroencephalogram (EEG) that is modeled as channel×frequency bin×time frame and a microarray data that is modeled as gene×sample×time) were used for the evaluation of the TDFE. The experiment results corroborate the advantages of the proposed method with averages of 98.26% and 89.63% for the classification accuracies of the epilepsy dataset and the microarray dataset, respectively. These performance averages represent an improvement on those of the matrix-based algorithms and recent tensor-based, discriminant-decomposition approaches; this is especially the case considering the small number of samples that are used in practice. Copyright © 2016 Elsevier Ltd. All rights reserved.

Killing(-Yano) tensors in string theory

NASA Astrophysics Data System (ADS)

Chervonyi, Yuri; Lunin, Oleg

2015-09-01

We construct the Killing(-Yano) tensors for a large class of charged black holes in higher dimensions and study general properties of such tensors, in particular, their behavior under string dualities. Killing(-Yano) tensors encode the symmetries beyond isometries, which lead to insights into dynamics of particles and fields on a given geometry by providing a set of conserved quantities. By analyzing the eigenvalues of the Killing tensor, we provide a prescription for constructing several conserved quantities starting from a single object, and we demonstrate that Killing tensors in higher dimensions are always associated with ellipsoidal coordinates. We also determine the transformations of the Killing(-Yano) tensors under string dualities, and find the unique modification of the Killing-Yano equation consistent with these symmetries. These results are used to construct the explicit form of the Killing(-Yano) tensors for the Myers-Perry black hole in arbitrary number of dimensions and for its charged version.

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.

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.

Plasmon-mediated binding forces on gold or silver homodimer and heterodimer

NASA Astrophysics Data System (ADS)

Liaw, Jiunn-Woei; Kuo, Ting-Yu; Kuo, Mao-Kuen

2016-02-01

This study theoretically investigates plasmon-mediated optical binding forces, which are exerted on metal homo or heterodimers, induced by the normal illumination of a linearly polarized plane wave or Gaussian beam. Using the multiple multipole method, we analyzed the optical force in terms of Maxwell's stress tensor for various interparticle distance at some specific wavelengths. Numerical results show that for a given wavelength there are several stable equilibrium distances between two nanoparticles (NPs) of a homodimer, which are slightly shorter than some integer multiples of the wavelength in medium, such that metal dimer acts as bonded together. At these specific interparticle distances, the optical force between dimer is null and serves a restoring force, which is repulsive and attractive, respectively, as the two NPs are moving closer to and away from each other. The spring constant of the restoring force at the first stable equilibrium is always the largest, indicating that the first stable equilibrium distance is the most stable one. Moreover, the central line (orientation) of a dimer tends to be perpendicular to the polarization of light. For the cases of heterodimers, the phenomenon of stable equilibrium interparticle distance still exists, except there is an extra net photophoretic force drifting the heterodimer as one. Moreover, gradient force provided by a Gaussian beam may reduce the stability of these equilibriums, so larger NPs are preferred to stabilize a dimer under illumination of Gaussian beam. The finding may pave the way for using optical manipulation on the gold or silver colloidal self-assembly.

The source mechanisms of low frequency events in volcanoes - a comparison of synthetic and real seismic data on Soufriere Hills Volcano, Montserrat

NASA Astrophysics Data System (ADS)

Karl, S.; Neuberg, J. W.

2012-04-01

Low frequency seismic signals are one class of volcano seismic earthquakes that have been observed at many volcanoes around the world, and are thought to be associated with resonating fluid-filled conduits or fluid movements. Amongst others, Neuberg et al. (2006) proposed a conceptual model for the trigger of low frequency events at Montserrat involving the brittle failure of magma in the glass transition in response to high shear stresses during the upwards movement of magma in the volcanic edifice. For this study, synthetic seismograms were generated following the proposed concept of Neuberg et al. (2006) by using an extended source modelled as an octagonal arrangement of double couples approximating a circular ringfault. For comparison, synthetic seismograms were generated using single forces only. For both scenarios, synthetic seismograms were generated using a seismic station distribution as encountered on Soufriere Hills Volcano, Montserrat. To gain a better quantitative understanding of the driving forces of low frequency events, inversions for the physical source mechanisms have become increasingly common. Therefore, we perform moment tensor inversions (Dreger, 2003) using the synthetic data as well as a chosen set of seismograms recorded on Soufriere Hills Volcano. The inversions are carried out under the (wrong) assumption to have an underlying point source rather than an extended source as the trigger mechanism of the low frequency seismic events. We will discuss differences between inversion results, and how to interpret the moment tensor components (double couple, isotropic, or CLVD), which were based on a point source, in terms of an extended source.

A Communication-Optimal Framework for Contracting Distributed Tensors

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

Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei

Tensor contractions are extremely compute intensive generalized matrix multiplication operations encountered in many computational science fields, such as quantum chemistry and nuclear physics. Unlike distributed matrix multiplication, which has been extensively studied, limited work has been done in understanding distributed tensor contractions. In this paper, we characterize distributed tensor contraction algorithms on torus networks. We develop a framework with three fundamental communication operators to generate communication-efficient contraction algorithms for arbitrary tensor contractions. We show that for a given amount of memory per processor, our framework is communication optimal for all tensor contractions. We demonstrate performance and scalability of our frameworkmore » on up to 262,144 cores of BG/Q supercomputer using five tensor contraction examples.« less

On the Tensorial Nature of Fluxes in Continuous Media.

ERIC Educational Resources Information Center

Stokes, Vijay Kumar; Ramkrishna, Doraiswami

1982-01-01

Argues that mass and energy fluxes in a fluid are vectors. Topics include the stress tensor, theorem for tensor fields, mass flux as a vector, stress as a second order tensor, and energy flux as a tensor. (SK)

Dark neutrino interactions make gravitational waves blue

NASA Astrophysics Data System (ADS)

Ghosh, Subhajit; Khatri, Rishi; Roy, Tuhin S.

2018-03-01

New interactions of neutrinos can stop them from free-streaming in the early Universe even after the weak decoupling epoch. This results in the enhancement of the primordial gravitational wave amplitude on small scales compared to the standard Λ CDM prediction. In this paper, we calculate the effect of dark matter neutrino interactions in CMB tensor B -modes spectrum. We show that the effect of new neutrino interactions generates a scale- or ℓ-dependent imprint in the CMB B -modes power spectrum at ℓ≳100 . In the event that primordial B -modes are detected by future experiments, a departure from scale invariance, with a blue spectrum, may not necessarily mean failure of simple inflationary models but instead may be a sign of nonstandard interactions of relativistic particles. New interactions of neutrinos also induce a phase shift in the CMB B -mode power spectrum which cannot be mimicked by simple modifications of the primordial tensor power spectrum. There is rich information hidden in the CMB B -modes spectrum beyond just the tensor-to-scalar ratio.

Reducing the two-body problem in scalar-tensor theories to the motion of a test particle: A scalar-tensor effective-one-body approach

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis

2018-01-01

Starting from the second post-Keplerian (2PK) Hamiltonian describing the conservative part of the two-body dynamics in massless scalar-tensor (ST) theories, we build an effective-one-body (EOB) Hamiltonian which is a ν deformation (where ν =0 is the test mass limit) of the analytically known ST Hamiltonian of a test particle. This ST-EOB Hamiltonian leads to a simple (yet canonically equivalent) formulation of the conservative 2PK two-body problem, but also defines a resummation of the dynamics which is well-suited to ST regimes that depart strongly from general relativity (GR) and which may provide information on the strong field dynamics; in particular, the ST innermost stable circular orbit location and associated orbital frequency. Results will be compared and contrasted with those deduced from the ST-deformation of the (5PN) GR-EOB Hamiltonian previously obtained in [Phys. Rev. D 95, 124054 (2017), 10.1103/PhysRevD.95.124054].

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

Green-Kubo relations for the viscosity of biaxial nematic liquid crystals

NASA Astrophysics Data System (ADS)

Sarman, Sten

1996-09-01

We derive Green-Kubo relations for the viscosities of a biaxial nematic liquid crystal. In this system there are seven shear viscosities, three twist viscosities, and three cross coupling coefficients between the antisymmetric strain rate and the symmetric traceless pressure tensor. According to the Onsager reciprocity relations these couplings are equal to the cross couplings between the symmetric traceless strain rate and the antisymmetric pressure. Our method is based on a comparison of the microscopic linear response generated by the SLLOD equations of motion for planar Couette flow (so named because of their close connection to the Doll's tensor Hamiltonian) and the macroscopic linear phenomenological relations between the pressure tensor and the strain rate. In order to obtain simple Green-Kubo relations we employ an equilibrium ensemble where the angular velocities of the directors are identically zero. This is achieved by adding constraint torques to the equations for the molecular angular accelerations. One finds that all the viscosity coefficients can be expressed as linear combinations of time correlation function integrals (TCFIs). This is much simpler compared to the expressions in the conventional canonical ensemble, where the viscosities are complicated rational functions of the TCFIs. The reason for this is, that in the constrained angular velocity ensemble, the thermodynamic forces are given external parameters whereas the thermodynamic fluxes are ensemble averages of phase functions. This is not the case in the canonical ensemble. The simplest way of obtaining numerical estimates of viscosity coefficients of a particular molecular model system is to evaluate these fluctuation relations by equilibrium molecular dynamics simulations.

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.

Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

NASA Technical Reports Server (NTRS)

Reifler, Frank; Morris, Randall

1994-01-01

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.

Simultaneous inversion of seismic velocity and moment tensor using elastic-waveform inversion of microseismic data: Application to the Aneth CO2-EOR field

NASA Astrophysics Data System (ADS)

Chen, Y.; Huang, L.

2017-12-01

Moment tensors are key parameters for characterizing CO2-injection-induced microseismic events. Elastic-waveform inversion has the potential to providing accurate results of moment tensors. Microseismic waveforms contains information of source moment tensors and the wave propagation velocity along the wavepaths. We develop an elastic-waveform inversion method to jointly invert the seismic velocity model and moment tensor. We first use our adaptive moment-tensor joint inversion method to estimate moment tensors of microseismic events. Our adaptive moment-tensor inversion method jointly inverts multiple microseismic events with similar waveforms within a cluster to reduce inversion uncertainty for microseismic data recorded using a single borehole geophone array. We use this inversion result as the initial model for our elastic-waveform inversion to minimize the cross-correlated-based data misfit between observed data and synthetic data. We verify our method using synthetic microseismic data and obtain improved results of both moment tensors and seismic velocity model. We apply our new inversion method to microseismic data acquired at a CO2-enhanced oil recovery field in Aneth, Utah, using a single borehole geophone array. The results demonstrate that our new inversion method significantly reduces the data misfit compared to the conventional ray-theory-based moment-tensor inversion.

Ferrotoroidial propertiesof Non-Crystallographic Pointgroups

NASA Astrophysics Data System (ADS)

Sireesha, G.; Devi, S. Uma; Yamini Sankar, CH.

2017-08-01

Primary ferroic crystals are the crystals with domain states that are distinguished by properties like spontaneous magnetization, strain, or polarisation. Secondary ferroic crystals are the crystals with domain states that are distinguished by piezoelectric tensor and they are named as Ferromagnetotoroidic (eV2), Ferromagnetoelastic (aeV [V2]) crystals respectively. Here “e” denotes zero rank tensor that changes under spatial inversion, “a” denotes zero rank tensor that changes under time inversion, and “V” denotes a polar vector. Recent observations (Van Aken et al., 2007) identified the fourth type of primary ferroic crystals, a ferrotoroidic crystal with domains distinguished by a toroidial moment. The number of independent constants of quasi crystals is theoretically derived by Wenge Yang et al., (1995). He also formulated the number of independent components of any physical property tensor of quasi crystals using group representation theory. This paper accounts the effect of symmetry on some ferrotoroidial properties of quasi Crystals with 5-fold, 8-fold, 10-fold and 12-fold symmetries using group theoretical methods. Also the number of independent constants is calculated and tabulated that helps in describing the ferrotoroidial properties.

Influence of tensor interactions on masses and decay widths of dibaryons

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

Pang Hourong; Ping Jialun; Chen Lingzhi

The influence of gluon and Goldstone boson induced tensor interactions on the dibaryon masses and D-wave decay widths has been studied in the quark delocalization, color screening model. The effective S-D wave transition interactions induced by gluon and Goldstone boson exchanges decrease rapidly with increasing strangeness of the channel. The tensor contribution of K and {eta} mesons is negligible in this model. There is no six-quark state in the light flavor world studied so far that can become bound by means of these tensor interactions besides the deuteron. The partial D-wave decay widths of the IJ{sup p}=(1/2)2{sup +}N{omega} state tomore » spin 0 and 1 {lambda}{xi} final states are 12.0 and 21.9 keV, respectively. This is a very narrow dibaryon resonance that might be detectable in those production reactions with rich high strangeness particles through the reconstruction of the vertex mass of the decay product {lambda}{xi} by existing detectors at RHIC and COMPASS at CERN or at JHF in Japan and FAIR in Germany in the future.« less

Fine-scale features in the far-field of a turbulent jet

NASA Astrophysics Data System (ADS)

Buxton, Oliver; Ganapathisubramani, Bharathram

2008-11-01

The structure of a fully turbulent axisymmetric jet, at Reynolds number based on jet exit conditions of 5000, is investigated with cinematographic (1 kHz) stereoscopic PIV in a plane normal to the jet axis. Taylor's hypothesis is employed to calculate all three velocity gradients in the axial direction. The technique's resolution allows all terms of the velocity gradient tensor, hence strain rate tensor and kinetic energy dissipation, to be computed at each point within the plane. The data reveals that the vorticity field is dominated by high enstrophy tube-like structures. Conversely, the dissipation field appears to consist of sheet-like structures. Several criteria for isolating these strongly swirling vortical structures from the background turbulence were employed. One such technique involves isolating points in which the velocity gradient tensor has a real and a pair of complex conjugate eigenvectors. Once identified, the alignment of the various structures with relation to the vorticity vector and the real velocity gradient tensor eigenvector is investigated. The effect of the strain field on the geometry of the structures is also examined.

Elucidating the DEP phenomena using a volumetric polarization approach with consideration of the electric double layer

PubMed Central

Brcka, Jozef; Faguet, Jacques; Zhang, Guigen

2017-01-01

Dielectrophoretic (DEP) phenomena have been explored to great success for various applications like particle sorting and separation. To elucidate the underlying mechanism and quantify the DEP force experienced by particles, the point-dipole and Maxwell Stress Tensor (MST) methods are commonly used. However, both methods exhibit their own limitations. For example, the point-dipole method is unable to fully capture the essence of particle-particle interactions and the MST method is not suitable for particles of non-homogeneous property. Moreover, both methods fare poorly when it comes to explaining DEP phenomena such as the dependence of crossover frequency on medium conductivity. To address these limitations, the authors have developed a new method, termed volumetric-integration method, with the aid of computational implementation, to reexamine the DEP phenomena, elucidate the governing mechanism, and quantify the DEP force. The effect of an electric double layer (EDL) on particles' crossover behavior is dealt with through consideration of the EDL structure along with surface ionic/molecular adsorption, unlike in other methods, where the EDL is accounted for through simply assigning a surface conductance value to the particles. For validation, by comparing with literature experimental data, the authors show that the new method can quantify the DEP force on not only homogeneous particles but also non-homogeneous ones, and predict particle-particle interactions fairly accurately. Moreover, the authors also show that the predicted dependence of crossover frequency on medium conductivity and particle size agrees very well with experimental measurements. PMID:28396710

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

Video denoising using low rank tensor decomposition

NASA Astrophysics Data System (ADS)

Gui, Lihua; Cui, Gaochao; Zhao, Qibin; Wang, Dongsheng; Cichocki, Andrzej; Cao, Jianting

2017-03-01

Reducing noise in a video sequence is of vital important in many real-world applications. One popular method is block matching collaborative filtering. However, the main drawback of this method is that noise standard deviation for the whole video sequence is known in advance. In this paper, we present a tensor based denoising framework that considers 3D patches instead of 2D patches. By collecting the similar 3D patches non-locally, we employ the low-rank tensor decomposition for collaborative filtering. Since we specify the non-informative prior over the noise precision parameter, the noise variance can be inferred automatically from observed video data. Therefore, our method is more practical, which does not require knowing the noise variance. The experimental on video denoising demonstrates the effectiveness of our proposed method.

FLRW Cosmology from Yang-Mills Gravity

NASA Astrophysics Data System (ADS)

Katz, Daniel

2013-04-01

We extend to basic cosmology the subject of Yang-Mills gravity - a theory of gravity based on local translational gauge invariance in flat spacetime. It has been shown that this particular gauge invariance leads to tensor factors in the macroscopic limit of the equations of motion of particles which plays the same role as the metric tensor of General Relativity. The assumption that this ``effective metric" tensor takes on the standard FLRW form is our starting point. Equations analogous to the Friedman equations are derived and then solved in closed form for the three special cases of a universe dominated by 1) matter, 2) radiation, and 3) dark energy. We find that the solutions for the scale factor are similar to, but distinct from, those found in the corresponding GR based treatment.

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

A framework for developing a mimetic tensor artificial viscosity for Lagrangian hydrocodes on arbitrary polygonal and polyhedral meshes (u)

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

Lipnikov, Konstantin; Shashkov, Mikhail

2011-01-11

We construct a new mimetic tensor artificial viscosity on general polygonal and polyhedral meshes. The tensor artificial viscosity is based on a mimetic discretization of coordinate invariant operators, divergence of a tensor and gradient of a vector. The focus of this paper is on the symmetric form, div ({mu},{var_epsilon}(u)), of the tensor artificial viscosity where {var_epsilon}(u) is the symmetrized gradient of u and {mu}, is a tensor. The mimetic discretizations of this operator is derived for the case of a full tensor coefficient {mu}, that may reflect a shock direction. We demonstrate performance of the new viscosity for the Nohmore » implosion, Sedov explosion and Saltzman piston problems in both Cartesian and axisymmetric coordinate systems.« less

Rigorous derivation of electromagnetic self-force

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

Gralla, Samuel E.; Harte, Abraham I.; Wald, Robert M.

2009-07-15

During the past century, there has been considerable discussion and analysis of the motion of a point charge in an external electromagnetic field in special relativity, taking into account 'self-force' effects due to the particle's own electromagnetic field. We analyze the issue of 'particle motion' in classical electromagnetism in a rigorous and systematic way by considering a one-parameter family of solutions to the coupled Maxwell and matter equations corresponding to having a body whose charge-current density J{sup a}({lambda}) and stress-energy tensor T{sub ab}({lambda}) scale to zero size in an asymptotically self-similar manner about a worldline {gamma} as {lambda}{yields}0. In thismore » limit, the charge, q, and total mass, m, of the body go to zero, and q/m goes to a well-defined limit. The Maxwell field F{sub ab}({lambda}) is assumed to be the retarded solution associated with J{sup a}({lambda}) plus a homogeneous solution (the 'external field') that varies smoothly with {lambda}. We prove that the worldline {gamma} must be a solution to the Lorentz force equations of motion in the external field F{sub ab}({lambda}=0). We then obtain self-force, dipole forces, and spin force as first-order perturbative corrections to the center-of-mass motion of the body. We believe that this is the first rigorous derivation of the complete first-order correction to Lorentz force motion. We also address the issue of obtaining a self-consistent perturbative equation of motion associated with our perturbative result, and argue that the self-force equations of motion that have previously been written down in conjunction with the 'reduction of order' procedure should provide accurate equations of motion for a sufficiently small charged body with negligible dipole moments and spin. (There is no corresponding justification for the non-reduced-order equations.) We restrict consideration in this paper to classical electrodynamics in flat spacetime, but there should be no difficulty in extending our results to the motion of a charged body in an arbitrary globally hyperbolic curved spacetime.« less

Computer simulation of thermal conductivity in vulcanized polyisoprene at variable strain and temperature

NASA Astrophysics Data System (ADS)

Engelmann, Sven; Meyer, Jan; Hentschke, Reinhard

2017-08-01

We study the thermal conductivity tensor in an atomistic model of vulcanized cis-1,4-polyisoprene (PI) rubber via molecular dynamics simulations. Our polymer force field is based on V. A. Harmandaris et al. [J. Chem. Phys. 116, 436 (2002), 10.1063/1.1416872], whereas the polymerization algorithm follows the description in J. Hager et al. [Macromolecules 48, 9039 (2015), 10.1021/acs.macromol.5b01864]. The polymer chains are chemically cross linked via sulfur bridges of adjustable cross-link density. A volume-conserving uniaxial strain of up to 200% is applied to the systems. The widely used GROMACS simulation package is adapted to allow using the Green-Kubo approach to calculate the thermal conductivity tensor components. Our analysis of the heat flux autocorrelation functions leads to the conclusion that the thermal conductivity in PI is governed by short-lived phonon modes at low wave numbers due to deformation of the monomers along the polymer backbone. Applying uniaxial strain causes increased orientation of monomers along the strain direction, which enhances the attendant thermal conductivity component. We find an exponential increase of the conductivity in stretch direction in terms of an attendant orientation order parameter. This is accompanied by a simultaneous decline of thermal conductivity in the orthogonal directions. Increase of the cross-link density only has a weak effect on thermal conductivity in the unstrained system, even at high cross-link density. In the strained system we do observed a rising thermal conductivity in the limit of high stress. This increase is attributed to enhanced coupling between chains rather than to their orientation.

Multipolar Ewald methods, 1: theory, accuracy, and performance.

PubMed

Giese, Timothy J; Panteva, Maria T; Chen, Haoyuan; York, Darrin M

2015-02-10

The Ewald, Particle Mesh Ewald (PME), and Fast Fourier–Poisson (FFP) methods are developed for systems composed of spherical multipole moment expansions. A unified set of equations is derived that takes advantage of a spherical tensor gradient operator formalism in both real space and reciprocal space to allow extension to arbitrary multipole order. The implementation of these methods into a novel linear-scaling modified “divide-and-conquer” (mDC) quantum mechanical force field is discussed. The evaluation times and relative force errors are compared between the three methods, as a function of multipole expansion order. Timings and errors are also compared within the context of the quantum mechanical force field, which encounters primary errors related to the quality of reproducing electrostatic forces for a given density matrix and secondary errors resulting from the propagation of the approximate electrostatics into the self-consistent field procedure, which yields a converged, variational, but nonetheless approximate density matrix. Condensed-phase simulations of an mDC water model are performed with the multipolar PME method and compared to an electrostatic cutoff method, which is shown to artificially increase the density of water and heat of vaporization relative to full electrostatic treatment.

Characterizing granular networks using topological metrics

NASA Astrophysics Data System (ADS)

Dijksman, Joshua A.; Kovalcinova, Lenka; Ren, Jie; Behringer, Robert P.; Kramar, Miroslav; Mischaikow, Konstantin; Kondic, Lou

2018-04-01

We carry out a direct comparison of experimental and numerical realizations of the exact same granular system as it undergoes shear jamming. We adjust the numerical methods used to optimally represent the experimental settings and outcomes up to microscopic contact force dynamics. Measures presented here range from microscopic through mesoscopic to systemwide characteristics of the system. Topological properties of the mesoscopic force networks provide a key link between microscales and macroscales. We report two main findings: (1) The number of particles in the packing that have at least two contacts is a good predictor for the mechanical state of the system, regardless of strain history and packing density. All measures explored in both experiments and numerics, including stress-tensor-derived measures and contact numbers depend in a universal manner on the fraction of nonrattler particles, fNR. (2) The force network topology also tends to show this universality, yet the shape of the master curve depends much more on the details of the numerical simulations. In particular we show that adding force noise to the numerical data set can significantly alter the topological features in the data. We conclude that both fNR and topological metrics are useful measures to consider when quantifying the state of a granular system.

On the construction of a ground truth framework for evaluating voxel-based diffusion tensor MRI analysis methods.

PubMed

Van Hecke, Wim; Sijbers, Jan; De Backer, Steve; Poot, Dirk; Parizel, Paul M; Leemans, Alexander

2009-07-01

Although many studies are starting to use voxel-based analysis (VBA) methods to compare diffusion tensor images between healthy and diseased subjects, it has been demonstrated that VBA results depend heavily on parameter settings and implementation strategies, such as the applied coregistration technique, smoothing kernel width, statistical analysis, etc. In order to investigate the effect of different parameter settings and implementations on the accuracy and precision of the VBA results quantitatively, ground truth knowledge regarding the underlying microstructural alterations is required. To address the lack of such a gold standard, simulated diffusion tensor data sets are developed, which can model an array of anomalies in the diffusion properties of a predefined location. These data sets can be employed to evaluate the numerous parameters that characterize the pipeline of a VBA algorithm and to compare the accuracy, precision, and reproducibility of different post-processing approaches quantitatively. We are convinced that the use of these simulated data sets can improve the understanding of how different diffusion tensor image post-processing techniques affect the outcome of VBA. In turn, this may possibly lead to a more standardized and reliable evaluation of diffusion tensor data sets of large study groups with a wide range of white matter altering pathologies. The simulated DTI data sets will be made available online (http://www.dti.ua.ac.be).

Tensor network method for reversible classical computation

NASA Astrophysics Data System (ADS)

Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.

2018-03-01

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.

Inflation in anisotropic scalar-tensor theories

NASA Technical Reports Server (NTRS)

Pimentel, Luis O.; Stein-Schabes, Jaime

1988-01-01

The existence of an inflationary phase in anisotropic Scalar-Tensor Theories is investigated by means of a conformal transformation that allows us to rewrite these theories as gravity minimally coupled to a scalar field with a nontrivial potential. The explicit form of the potential is then used and the No Hair Theorem concludes that there is an inflationary phase in all open or flat anisotropic spacetimes in these theories. Several examples are constructed where the effect becomes manifest.

Improvement of Accuracy for Background Noise Estimation Method Based on TPE-AE

NASA Astrophysics Data System (ADS)

Itai, Akitoshi; Yasukawa, Hiroshi

This paper proposes a method of a background noise estimation based on the tensor product expansion with a median and a Monte carlo simulation. We have shown that a tensor product expansion with absolute error method is effective to estimate a background noise, however, a background noise might not be estimated by using conventional method properly. In this paper, it is shown that the estimate accuracy can be improved by using proposed methods.

Critical Analysis of Cluster Models and Exchange-Correlation Functionals for Calculating Magnetic Shielding in Molecular Solids.

PubMed

Holmes, Sean T; Iuliucci, Robbie J; Mueller, Karl T; Dybowski, Cecil

2015-11-10

Calculations of the principal components of magnetic-shielding tensors in crystalline solids require the inclusion of the effects of lattice structure on the local electronic environment to obtain significant agreement with experimental NMR measurements. We assess periodic (GIPAW) and GIAO/symmetry-adapted cluster (SAC) models for computing magnetic-shielding tensors by calculations on a test set containing 72 insulating molecular solids, with a total of 393 principal components of chemical-shift tensors from 13C, 15N, 19F, and 31P sites. When clusters are carefully designed to represent the local solid-state environment and when periodic calculations include sufficient variability, both methods predict magnetic-shielding tensors that agree well with experimental chemical-shift values, demonstrating the correspondence of the two computational techniques. At the basis-set limit, we find that the small differences in the computed values have no statistical significance for three of the four nuclides considered. Subsequently, we explore the effects of additional DFT methods available only with the GIAO/cluster approach, particularly the use of hybrid-GGA functionals, meta-GGA functionals, and hybrid meta-GGA functionals that demonstrate improved agreement in calculations on symmetry-adapted clusters. We demonstrate that meta-GGA functionals improve computed NMR parameters over those obtained by GGA functionals in all cases, and that hybrid functionals improve computed results over the respective pure DFT functional for all nuclides except 15N.

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.

The relationship between functional magnetic resonance imaging activation, diffusion tensor imaging, and training effects.

PubMed

Farrar, Danielle; Budson, Andrew E

2017-04-01

While the relationship between diffusion tensor imaging (DTI) measurements and training effects is explored by Voelker et al. (this issue), a cursory discussion of functional magnetic resonance imaging (fMRI) measurements categorizes increased activation with findings of greater white matter integrity. Evidence of the relationship between fMRI activation and white matter integrity is conflicting, as is the relationship between fMRI activation and training effects. An examination of the changes in fMRI activation in response to training is helpful, but the relationship between DTI and fMRI activation, particularly in the context of white matter changes, must be examined further before general conclusions can be drawn.

Higher-derivative operators and effective field theory for general scalar-tensor theories

NASA Astrophysics Data System (ADS)

Solomon, Adam R.; Trodden, Mark

2018-02-01

We discuss the extent to which it is necessary to include higher-derivative operators in the effective field theory of general scalar-tensor theories. We explore the circumstances under which it is correct to restrict to second-order operators only, and demonstrate this using several different techniques, such as reduction of order and explicit field redefinitions. These methods are applied, in particular, to the much-studied Horndeski theories. The goal is to clarify the application of effective field theory techniques in the context of popular cosmological models, and to explicitly demonstrate how and when higher-derivative operators can be cast into lower-derivative forms suitable for numerical solution techniques.

Genten: Software for Generalized Tensor Decompositions v. 1.0.0

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

Phipps, Eric T.; Kolda, Tamara G.; Dunlavy, Daniel

Tensors, or multidimensional arrays, are a powerful mathematical means of describing multiway data. This software provides computational means for decomposing or approximating a given tensor in terms of smaller tensors of lower dimension, focusing on decomposition of large, sparse tensors. These techniques have applications in many scientific areas, including signal processing, linear algebra, computer vision, numerical analysis, data mining, graph analysis, neuroscience and more. The software is designed to take advantage of parallelism present emerging computer architectures such has multi-core CPUs, many-core accelerators such as the Intel Xeon Phi, and computation-oriented GPUs to enable efficient processing of large tensors.

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).

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE

PubMed Central

Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S.

2017-01-01

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order-k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k}. We derive general inequalities between the lp-norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm (p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations. PMID:28286347

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.

PubMed

Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S

2017-05-01

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order- k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k }. We derive general inequalities between the l p -norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm ( p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations.

Solid-state (185/187)Re NMR and GIPAW DFT study of perrhenates and Re2(CO)10: chemical shift anisotropy, NMR crystallography, and a metal-metal bond.

PubMed

Widdifield, Cory M; Perras, Frédéric A; Bryce, David L

2015-04-21

Advances in solid-state nuclear magnetic resonance (SSNMR) methods, such as dynamic nuclear polarization (DNP), intricate pulse sequences, and increased applied magnetic fields, allow for the study of systems which even very recently would be impractical. However, SSNMR methods using certain quadrupolar probe nuclei (i.e., I > 1/2), such as (185/187)Re remain far from fully developed due to the exceedingly strong interaction between the quadrupole moment of these nuclei and local electric field gradients (EFGs). We present a detailed high-field (B0 = 21.1 T) experimental SSNMR study on several perrhenates (KReO4, AgReO4, Ca(ReO4)2·2H2O), as well as ReO3 and Re2(CO)10. We propose solid ReO3 as a new rhenium SSNMR chemical shift standard due to its reproducible and sharp (185/187)Re NMR resonances. We show that for KReO4, previously poorly understood high-order quadrupole-induced effects (HOQIE) on the satellite transitions can be used to measure the EFG tensor asymmetry (i.e., ηQ) to nearly an order-of-magnitude greater precision than competing SSNMR and nuclear quadrupole resonance (NQR) approaches. Samples of AgReO4 and Ca(ReO4)2·2H2O enable us to comment on the effects of counter-ions and hydration upon Re(vii) chemical shifts. Calcium-43 and (185/187)Re NMR tensor parameters allow us to conclude that two proposed crystal structures for Ca(ReO4)2·2H2O, which would be considered as distinct, are in fact the same structure. Study of Re2(CO)10 provides insights into the effects of Re-Re bonding on the rhenium NMR tensor parameters and rhenium oxidation state on the Re chemical shift value. As overtone NQR experiments allowed us to precisely measure the (185/187)Re EFG tensor of Re2(CO)10, we were able to measure rhenium chemical shift anisotropy (CSA) for the first time in a powdered sample. Experimental observations are supported by gauge-including projector augmented-wave (GIPAW) density functional theory (DFT) calculations, with NMR tensor calculations also provided for NH4ReO4, NaReO4 and RbReO4. These calculations are able to reproduce many of the experimental trends in rhenium δiso values and EFG tensor magnitudes. Using KReO4 as a prototypical perrhenate-containing system, we establish a correlation between the tetrahedral shear strain parameter (|ψ|) and the nuclear electric quadrupolar coupling constant (CQ), which enables the refinement of the structure of ND4ReO4. Shortcomings in traditional DFT approaches, even when including relativistic effects via the zeroth-order regular approximation (ZORA), for calculating rhenium NMR tensor parameters are identified for Re2(CO)10.

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements.

PubMed

Daszkiewicz, Karol; Maquer, Ghislain; Zysset, Philippe K

2017-06-01

Boundary conditions (BCs) and sample size affect the measured elastic properties of cancellous bone. Samples too small to be representative appear stiffer under kinematic uniform BCs (KUBCs) than under periodicity-compatible mixed uniform BCs (PMUBCs). To avoid those effects, we propose to determine the effective properties of trabecular bone using an embedded configuration. Cubic samples of various sizes (2.63, 5.29, 7.96, 10.58 and 15.87 mm) were cropped from [Formula: see text] scans of femoral heads and vertebral bodies. They were converted into [Formula: see text] models and their stiffness tensor was established via six uniaxial and shear load cases. PMUBCs- and KUBCs-based tensors were determined for each sample. "In situ" stiffness tensors were also evaluated for the embedded configuration, i.e. when the loads were transmitted to the samples via a layer of trabecular bone. The Zysset-Curnier model accounting for bone volume fraction and fabric anisotropy was fitted to those stiffness tensors, and model parameters [Formula: see text] (Poisson's ratio) [Formula: see text] and [Formula: see text] (elastic and shear moduli) were compared between sizes. BCs and sample size had little impact on [Formula: see text]. However, KUBCs- and PMUBCs-based [Formula: see text] and [Formula: see text], respectively, decreased and increased with growing size, though convergence was not reached even for our largest samples. Both BCs produced upper and lower bounds for the in situ values that were almost constant across samples dimensions, thus appearing as an approximation of the effective properties. PMUBCs seem also appropriate for mimicking the trabecular core, but they still underestimate its elastic properties (especially in shear) even for nearly orthotropic samples.

Inflationary tensor perturbations after BICEP2.

PubMed

Caligiuri, Jerod; Kosowsky, Arthur

2014-05-16

The measurement of B-mode polarization of the cosmic microwave background at large angular scales by the BICEP experiment suggests a stochastic gravitational wave background from early-Universe inflation with a surprisingly large amplitude. The power spectrum of these tensor perturbations can be probed both with further measurements of the microwave background polarization at smaller scales and also directly via interferometry in space. We show that sufficiently sensitive high-resolution B-mode measurements will ultimately have the ability to test the inflationary consistency relation between the amplitude and spectrum of the tensor perturbations, confirming their inflationary origin. Additionally, a precise B-mode measurement of the tensor spectrum will predict the tensor amplitude on solar system scales to 20% accuracy for an exact power-law tensor spectrum, so a direct detection will then measure the running of the tensor spectral index to high precision.

Decorated tensor network renormalization for lattice gauge theories and spin foam models

NASA Astrophysics Data System (ADS)

Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian

2016-05-01

Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.

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.

Measurement of the β-asymmetry parameter of Cu67 in search for tensor-type currents in the weak interaction

NASA Astrophysics Data System (ADS)

Soti, G.; Wauters, F.; Breitenfeldt, M.; Finlay, P.; Herzog, P.; Knecht, A.; Köster, U.; Kraev, I. S.; Porobic, T.; Prashanth, P. N.; Towner, I. S.; Tramm, C.; Zákoucký, D.; Severijns, N.

2014-09-01

Background: Precision measurements at low energy search for physics beyond the standard model in a way complementary to searches for new particles at colliders. In the weak sector the most general β-decay Hamiltonian contains, besides vector and axial-vector terms, also scalar, tensor, and pseudoscalar terms. Current limits on the scalar and tensor coupling constants from neutron and nuclear β decay are on the level of several percent. Purpose: Extracting new information on tensor coupling constants by measuring the β-asymmetry parameter in the pure Gamow-Teller decay of Cu67, thereby testing the V-A structure of the weak interaction. Method: An iron sample foil into which the radioactive nuclei were implanted was cooled down to mK temperatures in a 3He-4He dilution refrigerator. An external magnetic field of 0.1 T, in combination with the internal hyperfine magnetic field, oriented the nuclei. The anisotropic β radiation was observed with planar high-purity germanium detectors operating at a temperature of about 10 K. An on-line measurement of the β asymmetry of Cu68 was performed as well for normalization purposes. Systematic effects were investigated using geant4 simulations. Results: The experimental value, Ã=0.587(14), is in agreement with the standard model value of 0.5991(2) and is interpreted in terms of physics beyond the standard model. The limits obtained on possible tensor-type charged currents in the weak interaction Hamiltonian are -0.045<(CT+CT')/CA<0.159 (90% C.L.). Conclusions: The obtained limits are comparable to limits from other correlation measurements in nuclear β decay and contribute to further constraining tensor coupling constants.

Uncertainty estimations for moment tensor inversions: the issue of the 2012 May 20 Emilia earthquake

NASA Astrophysics Data System (ADS)

Scognamiglio, Laura; Magnoni, Federica; Tinti, Elisa; Casarotti, Emanuele

2016-08-01

Seismic moment tensor is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Geoscientists ordinarily use moment tensor catalogues, however, few attempts have been done to assess possible impacts of moment magnitude uncertainties upon their analysis. The 2012 May 20 Emilia main shock is a representative event since it is defined in literature with a moment magnitude value (Mw) spanning between 5.63 and 6.12. A variability of ˜0.5 units in magnitude leads to a controversial knowledge of the real size of the event and reveals how the solutions could be poorly constrained. In this work, we investigate the stability of the moment tensor solution for this earthquake, studying the effect of five different 1-D velocity models, the number and the distribution of the stations used in the inversion procedure. We also introduce a 3-D velocity model to account for structural heterogeneity. We finally estimate the uncertainties associated to the computed focal planes and the obtained Mw. We conclude that our reliable source solutions provide a moment magnitude that ranges from 5.87, 1-D model, to 5.96, 3-D model, reducing the variability of the literature to ˜0.1. We endorse that the estimate of seismic moment from moment tensor solutions, as well as the estimate of the other kinematic source parameters, requires coming out with disclosed assumptions and explicit processing workflows. Finally and, probably more important, when moment tensor solution is used for secondary analyses it has to be combined with the same main boundary conditions (e.g. wave-velocity propagation model) to avoid conflicting results.

Tensor scale: An analytic approach with efficient computation and applications☆

PubMed Central

Xu, Ziyue; Saha, Punam K.; Dasgupta, Soura

2015-01-01

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods. PMID:26236148

Software Toolbox for Low-Frequency Conductivity and Current Density Imaging Using MRI.

PubMed

Sajib, Saurav Z K; Katoch, Nitish; Kim, Hyung Joong; Kwon, Oh In; Woo, Eung Je

2017-11-01

Low-frequency conductivity and current density imaging using MRI includes magnetic resonance electrical impedance tomography (MREIT), diffusion tensor MREIT (DT-MREIT), conductivity tensor imaging (CTI), and magnetic resonance current density imaging (MRCDI). MRCDI and MREIT provide current density and isotropic conductivity images, respectively, using current-injection phase MRI techniques. DT-MREIT produces anisotropic conductivity tensor images by incorporating diffusion weighted MRI into MREIT. These current-injection techniques are finding clinical applications in diagnostic imaging and also in transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and electroporation where treatment currents can function as imaging currents. To avoid adverse effects of nerve and muscle stimulations due to injected currents, conductivity tensor imaging (CTI) utilizes B1 mapping and multi-b diffusion weighted MRI to produce low-frequency anisotropic conductivity tensor images without injecting current. This paper describes numerical implementations of several key mathematical functions for conductivity and current density image reconstructions in MRCDI, MREIT, DT-MREIT, and CTI. To facilitate experimental studies of clinical applications, we developed a software toolbox for these low-frequency conductivity and current density imaging methods. This MR-based conductivity imaging (MRCI) toolbox includes 11 toolbox functions which can be used in the MATLAB environment. The MRCI toolbox is available at http://iirc.khu.ac.kr/software.html . Its functions were tested by using several experimental datasets, which are provided together with the toolbox. Users of the toolbox can focus on experimental designs and interpretations of reconstructed images instead of developing their own image reconstruction softwares. We expect more toolbox functions to be added from future research outcomes. Low-frequency conductivity and current density imaging using MRI includes magnetic resonance electrical impedance tomography (MREIT), diffusion tensor MREIT (DT-MREIT), conductivity tensor imaging (CTI), and magnetic resonance current density imaging (MRCDI). MRCDI and MREIT provide current density and isotropic conductivity images, respectively, using current-injection phase MRI techniques. DT-MREIT produces anisotropic conductivity tensor images by incorporating diffusion weighted MRI into MREIT. These current-injection techniques are finding clinical applications in diagnostic imaging and also in transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and electroporation where treatment currents can function as imaging currents. To avoid adverse effects of nerve and muscle stimulations due to injected currents, conductivity tensor imaging (CTI) utilizes B1 mapping and multi-b diffusion weighted MRI to produce low-frequency anisotropic conductivity tensor images without injecting current. This paper describes numerical implementations of several key mathematical functions for conductivity and current density image reconstructions in MRCDI, MREIT, DT-MREIT, and CTI. To facilitate experimental studies of clinical applications, we developed a software toolbox for these low-frequency conductivity and current density imaging methods. This MR-based conductivity imaging (MRCI) toolbox includes 11 toolbox functions which can be used in the MATLAB environment. The MRCI toolbox is available at http://iirc.khu.ac.kr/software.html . Its functions were tested by using several experimental datasets, which are provided together with the toolbox. Users of the toolbox can focus on experimental designs and interpretations of reconstructed images instead of developing their own image reconstruction softwares. We expect more toolbox functions to be added from future research outcomes.

Spaceborne gravity gradiometry characterizing the data type

NASA Technical Reports Server (NTRS)

Sonnabend, D.

1987-01-01

Satellite gravity gradiometers, particularly the two stage drag free carrier vehicle are discussed. An inner stage, carrying the tracking antenna(s), measures the relative position of the internal free proof mass, and feeds this to a set of magnetic forcers, acting against the outer or main vehicle. As the external forces on the inner stage are low, and as the position relative to the proof mass is tightly controlled, carrier phase disturbances are greatly reduced. The arrangement lowers instantaneous accelerations. It is stressed that gravity gradiometers do not measure gradients, they measure components of an intrinsic tensor.

Spacetimes dressed with stealth electromagnetic fields

NASA Astrophysics Data System (ADS)

Smolić, Ivica

2018-04-01

Stealth field configurations by definition have a vanishing energy-momentum tensor, and thus do not contribute to the gravitational field equations. While only trivial fields can be stealth in Maxwell's electrodynamics, nontrivial stealth fields appear in some nonlinear models of electromagnetism. We find the necessary and sufficient conditions for the electromagnetic fields to be stealth and analyze which models admit such configurations. Furthermore, we present some concrete exact solutions, featuring a class of black holes dressed with the stealth electromagnetic hair, closely related to force-free solutions. Stealth hair does not alter the generalized Smarr formula, but may contribute to the Komar charges.

Precise calculation of the local pressure tensor in Cartesian and spherical coordinates in LAMMPS

NASA Astrophysics Data System (ADS)

Nakamura, Takenobu; Kawamoto, Shuhei; Shinoda, Wataru

2015-05-01

An accurate and efficient algorithm for calculating the 3D pressure field has been developed and implemented in the open-source molecular dynamics package, LAMMPS. Additionally, an algorithm to compute the pressure profile along the radial direction in spherical coordinates has also been implemented. The latter is particularly useful for systems showing a spherical symmetry such as micelles and vesicles. These methods yield precise pressure fields based on the Irving-Kirkwood contour integration and are particularly useful for biomolecular force fields. The present methods are applied to several systems including a buckled membrane and a vesicle.

Long-time dynamics of Rouse-Zimm polymers in dilute solutions with hydrodynamic memory.

PubMed

Lisy, V; Tothova, J; Zatovsky, A V

2004-12-01

The dynamics of flexible polymers in dilute solutions is studied taking into account the hydrodynamic memory, as a consequence of fluid inertia. As distinct from the Rouse-Zimm (RZ) theory, the Boussinesq friction force acts on the monomers (beads) instead of the Stokes force, and the motion of the solvent is governed by the nonstationary Navier-Stokes equations. The obtained generalized RZ equation is solved approximately using the preaveraging of the Oseen tensor. It is shown that the time correlation functions describing the polymer motion essentially differ from those in the RZ model. The mean-square displacement (MSD) of the polymer coil is at short times approximately t(2) (instead of approximately t). At long times the MSD contains additional (to the Einstein term) contributions, the leading of which is approximately t. The relaxation of the internal normal modes of the polymer differs from the traditional exponential decay. It is displayed in the long-time tails of their correlation functions, the longest lived being approximately t(-3/2) in the Rouse limit and t(-5/2) in the Zimm case, when the hydrodynamic interaction is strong. It is discussed that the found peculiarities, in particular, an effectively slower diffusion of the polymer coil, should be observable in dynamic scattering experiments. (c) 2004 American Institute of Physics

Computer simulations of polymer chain structure and dynamics on a hypersphere in four-space

NASA Astrophysics Data System (ADS)

Râsmark, Per Johan; Ekholm, Tobias; Elvingson, Christer

2005-05-01

There is a rapidly growing interest in performing computer simulations in a closed space, avoiding periodic boundary conditions. To extend the range of potential systems to include also macromolecules, we describe an algorithm for computer simulations of polymer chain molecules on S3, a hypersphere in four dimensions. In particular, we show how to generate initial conformations with a bond angle distribution given by the persistence length of the chain and how to calculate the bending forces for a molecule moving on S3. Furthermore, we discuss how to describe the shape of a macromolecule on S3, by deriving the radius of gyration tensor in this non-Euclidean space. The results from both Monte Carlo and Brownian dynamics simulations in the infinite dilution limit show that the results on S3 and in R3 coincide, both with respect to the size and shape as well as for the diffusion coefficient. All data on S3 can also be described by master curves by suitable scaling by the corresponding values in R3. We thus show how to extend the use of spherical boundary conditions, which are most effective for calculating electrostatic forces, to polymer chain molecules, making it possible to perform simulations on S3 also for polyelectrolyte systems.

Notes on super Killing tensors

NASA Astrophysics Data System (ADS)

Howe, P. S.; Lindström, U.

2016-03-01

The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.

Tensor Train Neighborhood Preserving Embedding

NASA Astrophysics Data System (ADS)

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2018-05-01

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.

Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence

DOE PAGES

Rubinstein, Robert; Kurien, Susan; Cambon, Claude

2015-06-22

The representation theory of the rotation group is applied to construct a series expansion of the correlation tensor in homogeneous anisotropic turbulence. The resolution of angular dependence is the main analytical difficulty posed by anisotropic turbulence; representation theory parametrises this dependence by a tensor analogue of the standard spherical harmonics expansion of a scalar. As a result, the series expansion is formulated in terms of explicitly constructed tensor bases with scalar coefficients determined by angular moments of the correlation tensor.

Geometry of Lax pairs: Particle motion and Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Cariglia, Marco; Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2013-01-01

A geometric formulation of the Lax pair equation on a curved manifold is studied using the phase-space formalism. The corresponding (covariantly conserved) Lax tensor is defined and the method of generation of constants of motion from it is discussed. It is shown that when the Hamilton equations of motion are used, the conservation of the Lax tensor translates directly to the well-known Lax pair equation, with one matrix identified with components of the Lax tensor and the other matrix constructed from the (metric) connection. A generalization to Clifford objects is also discussed. Nontrivial examples of Lax tensors for geodesic and charged particle motion are found in spacetimes admitting a hidden symmetry of Killing-Yano tensors.

On Lovelock analogs of the Riemann tensor

NASA Astrophysics Data System (ADS)

Camanho, Xián O.; Dadhich, Naresh

2016-03-01

It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.

Mapping forces in a 3D elastic assembly of grains

NASA Astrophysics Data System (ADS)

Saadatfar, Mohammad; Sheppard, Adrian P.; Senden, Tim J.; Kabla, Alexandre J.

2012-01-01

Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterise their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positions, shapes and contact areas; this is used to investigate the material's microstructure and its evolution upon strain. In addition to morphological measurements, we develop a technique to quantify contact forces and estimate the internal stress tensor. As will be illustrated in this paper, this opens the door to a broad array of static and dynamical measurements in 3D disordered systems.

Shear failure of granular materials

NASA Astrophysics Data System (ADS)

Degiuli, Eric; Balmforth, Neil; McElwaine, Jim; Schoof, Christian; Hewitt, Ian

2012-02-01

Connecting the macroscopic behavior of granular materials with the microstructure remains a great challenge. Recent work connects these scales with a discrete calculus [1]. In this work we generalize this formalism from monodisperse packings of disks to 2D assemblies of arbitrarily shaped grains. In particular, we derive Airy's expression for a symmetric, divergence-free stress tensor. Using these tools, we derive, from first-principles and in a mean-field approximation, the entropy of frictional force configurations in the Force Network Ensemble. As a macroscopic consequence of the Coulomb friction condition at contacts, we predict shear failure at a critical shear stress, in accordance with the Mohr-Coulomb failure condition well known in engineering. Results are compared with numerical simulations, and the dependence on the microscopic geometric configuration is discussed. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310

Anisotropic tensor power spectrum at interferometer scales induced by tensor squeezed non-Gaussianity

NASA Astrophysics Data System (ADS)

Ricciardone, Angelo; Tasinato, Gianmassimo

2018-02-01

We develop a scenario of inflation with spontaneously broken time and space diffeomorphisms, with distinctive features for the primordial tensor modes. Inflationary tensor fluctuations are not conserved outside the horizon, and can acquire a mass during the inflationary epoch. They can evade the Higuchi bound around de Sitter space, thanks to interactions with the fields driving expansion. Correspondingly, the primordial stochastic gravitational wave background (SGWB) is characterised by a tuneable scale dependence, and can be detectable at interferometer scales. In this set-up, tensor non-Gaussianity can be parametrically enhanced in the squeezed limit. This induces a coupling between long and short tensor modes, leading to a specific quadrupolar anisotropy in the primordial SGWB spectrum, which can be used to build estimators for tensor non-Gaussianity. We analyse how our inflationary system can be tested with interferometers, also discussing how an interferometer can be sensitive to a primordial anisotropic SGWB.

Current density tensors

NASA Astrophysics Data System (ADS)

Lazzeretti, Paolo

2018-04-01

It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.

Entanglement branching operator

NASA Astrophysics Data System (ADS)

Harada, Kenji

2018-01-01

We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.

Spacetime encodings. IV. The relationship between Weyl curvature and Killing tensors in stationary axisymmetric vacuum spacetimes

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

Brink, Jeandrew

The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst potential is considered. The coupling between the nonlocal curvature content of the spacetime as encoded in the Weyl tensor, and the existence of a Killing tensor is explored and a constructive, algebraic test for a fourth-order Killing tensor suggested. The approach used exploits the variables defined for the Baecklund transformations to clarify the relationship between Weyl curvature, constants of geodesic motion, expressed as Killing tensors, and the solution-generation techniques. A new symmetricmore » noncovariant formulation of the Killing equations is given. This formulation transforms the problem of looking for fourth-order Killing tensors in 4D into one of looking for four interlocking two-manifolds admitting fourth-order Killing tensors in 2D.« less

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.

Generalized lattice Boltzmann equation with forcing term for computation of wall-bounded turbulent flows.

PubMed

Premnath, Kannan N; Pattison, Martin J; Banerjee, Sanjoy

2009-02-01

In this paper, we present a framework based on the generalized lattice Boltzmann equation (GLBE) using multiple relaxation times with forcing term for eddy capturing simulation of wall-bounded turbulent flows. Due to its flexibility in using disparate relaxation times, the GLBE is well suited to maintaining numerical stability on coarser grids and in obtaining improved solution fidelity of near-wall turbulent fluctuations. The subgrid scale (SGS) turbulence effects are represented by the standard Smagorinsky eddy viscosity model, which is modified by using the van Driest wall-damping function to account for reduction of turbulent length scales near walls. In order to be able to simulate a wider class of problems, we introduce forcing terms, which can represent the effects of general nonuniform forms of forces, in the natural moment space of the GLBE. Expressions for the strain rate tensor used in the SGS model are derived in terms of the nonequilibrium moments of the GLBE to include such forcing terms, which comprise a generalization of those presented in a recent work [Yu, Comput. Fluids 35, 957 (2006)]. Variable resolutions are introduced into this extended GLBE framework through a conservative multiblock approach. The approach, whose optimized implementation is also discussed, is assessed for two canonical flow problems bounded by walls, viz., fully developed turbulent channel flow at a shear or friction Reynolds number (Re) of 183.6 based on the channel half-width and three-dimensional (3D) shear-driven flows in a cubical cavity at a Re of 12 000 based on the side length of the cavity. Comparisons of detailed computed near-wall turbulent flow structure, given in terms of various turbulence statistics, with available data, including those from direct numerical simulations (DNS) and experiments showed good agreement. The GLBE approach also exhibited markedly better stability characteristics and avoided spurious near-wall turbulent fluctuations on coarser grids when compared with the single-relaxation-time (SRT)-based approach. Moreover, its implementation showed excellent parallel scalability on a large parallel cluster with over a thousand processors.

Tensor Based Representation and Analysis of Diffusion-Weighted Magnetic Resonance Images

ERIC Educational Resources Information Center

Barmpoutis, Angelos

2009-01-01

Cartesian tensor bases have been widely used to model spherical functions. In medical imaging, tensors of various orders can approximate the diffusivity function at each voxel of a diffusion-weighted MRI data set. This approximation produces tensor-valued datasets that contain information about the underlying local structure of the scanned tissue.…

Monograph On Tensor Notations

NASA Technical Reports Server (NTRS)

Sirlin, Samuel W.

1993-01-01

Eight-page report describes systems of notation used most commonly to represent tensors of various ranks, with emphasis on tensors in Cartesian coordinate systems. Serves as introductory or refresher text for scientists, engineers, and others familiar with basic concepts of coordinate systems, vectors, and partial derivatives. Indicial tensor, vector, dyadic, and matrix notations, and relationships among them described.

ac-driven vortices and the Hall effect in a superconductor with a tilted washboard pinning potential

NASA Astrophysics Data System (ADS)

Shklovskij, Valerij A.; Dobrovolskiy, Oleksandr V.

2008-09-01

The Langevin equation for a two-dimensional (2D) nonlinear guided vortex motion in a tilted cosine pinning potential in the presence of an ac is exactly solved in terms of a matrix continued fraction at arbitrary value of the Hall effect. The influence of an ac of arbitrary amplitude and frequency on the dc and ac magnetoresistivity tensors is analyzed. The ac density and frequency dependence of the overall shape and the number and position of the Shapiro steps on the anisotropic current-voltage characteristics are considered. The influence of a subcritical or overcritical dc on the time-dependent stationary ac longitudinal and transverse resistive vortex responses (on the frequency of an ac drive Ω ) in terms of the nonlinear impedance tensor Ẑ and the nonlinear ac response at Ω harmonics are studied. Analytical formulas for 2D temperature-dependent linear impedance tensor ẐL in the presence of a dc which depend on the angle α between the current-density vector and the guiding direction of the washboard planar pinning potential are derived and analyzed. Influence of α anisotropy and the Hall effect on the nonlinear power absorption by vortices is discussed.

Frame-dependence of higher-order inflationary observables in scalar-tensor theories

NASA Astrophysics Data System (ADS)

Karam, Alexandros; Pappas, Thomas; Tamvakis, Kyriakos

2017-09-01

In the context of scalar-tensor theories of gravity we compute the third-order corrected spectral indices in the slow-roll approximation. The calculation is carried out by employing the Green's function method for scalar and tensor perturbations in both the Einstein and Jordan frames. Then, using the interrelations between the Hubble slow-roll parameters in the two frames we find that the frames are equivalent up to third order. Since the Hubble slow-roll parameters are related to the potential slow-roll parameters, we express the observables in terms of the latter which are manifestly invariant. Nevertheless, the same inflaton excursion leads to different predictions in the two frames since the definition of the number of e -folds differs. To illustrate this effect we consider a nonminimal inflationary model and find that the difference in the predictions grows with the nonminimal coupling, and it can actually be larger than the difference between the first and third order results for the observables. Finally, we demonstrate the effect of various end-of-inflation conditions on the observables. These effects will become important for the analyses of inflationary models in view of the improved sensitivity of future experiments.

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.