Numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity

NASA Astrophysics Data System (ADS)

Korepanov, V. V.; Matveenko, V. P.; Fedorov, A. Yu.; Shardakov, I. N.

2013-07-01

An algorithm for the numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity is considered. The algorithm is based on separation of a power-law dependence from the finite-element solution in a neighborhood of singular points in the domain under study, where singular solutions are possible. The obtained power-law dependencies allow one to conclude whether the stresses have singularities and what the character of these singularities is. The algorithm was tested for problems of classical elasticity by comparing the stress singularity exponents obtained by the proposed method and from known analytic solutions. Problems with various cases of singular points, namely, body surface points at which either the smoothness of the surface is violated, or the type of boundary conditions is changed, or distinct materials are in contact, are considered as applications. The stress singularity exponents obtained by using the models of classical and asymmetric elasticity are compared. It is shown that, in the case of cracks, the stress singularity exponents are the same for the elasticity models under study, but for other cases of singular points, the stress singularity exponents obtained on the basis of asymmetric elasticity have insignificant quantitative distinctions from the solutions of the classical elasticity.

Finite element techniques applied to cracks interacting with selected singularities

NASA Technical Reports Server (NTRS)

Conway, J. C.

1975-01-01

The finite-element method for computing the extensional stress-intensity factor for cracks approaching selected singularities of varied geometry is described. Stress-intensity factors are generated using both displacement and J-integral techniques, and numerical results are compared to those obtained experimentally in a photoelastic investigation. The selected singularities considered are a colinear crack, a circular penetration, and a notched circular penetration. Results indicate that singularities greatly influence the crack-tip stress-intensity factor as the crack approaches the singularity. In addition, the degree of influence can be regulated by varying the overall geometry of the singularity. Local changes in singularity geometry have little effect on the stress-intensity factor for the cases investigated.

Stress singularities at the vertex of a cylindrically anisotropic wedge

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.; Boduroglu, H.

1980-01-01

The plane elasticity problem for a cylindrically anisotropic solid is formulated. The form of the solution for an infinite wedge shaped domain with various homogeneous boundary conditions is derived and the nature of the stress singularity at the vertex of the wedge is studied. The characteristic equations giving the stress singularity and the angular distribution of the stresses around the vertex of the wedge are obtained for three standard homogeneous boundary conditions. The numerical examples show that the singular behavior of the stresses around the vertex of an anisotropic wedge may be significantly different from that of the isotropic material. Some of the results which may be of practical importance are that for a half plane the stress state at r = 0 may be singular and for a crack the power of stress singularity may be greater or less than 1/2.

Boundary-layer effects in composite laminates: Free-edge stress singularities, part 6

NASA Technical Reports Server (NTRS)

Wanag, S. S.; Choi, I.

1981-01-01

A rigorous mathematical model was obtained for the boundary-layer free-edge stress singularity in angleplied and crossplied fiber composite laminates. The solution was obtained using a method consisting of complex-variable stress function potentials and eigenfunction expansions. The required order of the boundary-layer stress singularity is determined by solving the transcendental characteristic equation obtained from the homogeneous solution of the partial differential equations. Numerical results obtained show that the boundary-layer stress singularity depends only upon material elastic constants and fiber orientation of the adjacent plies. For angleplied and crossplied laminates the order of the singularity is weak in general.

Torsion analysis of cracked circular bars actuated by a piezoelectric coating

NASA Astrophysics Data System (ADS)

Hassani, A. R.; Faal, R. T.

2016-12-01

This study presents a formulation for a bar with circular cross-section, coated by a piezoelectric layer and subjected to Saint-Venant torsion loading. The bar is weakened by a Volterra-type screw dislocation. First, with aid of the finite Fourier transform, the stress fields in the circular bar and the piezoelectric layer are obtained. The problem is then reduced to a set of singular integral equations with a Cauchy-type singularity. Unknown dislocation density is achieved by numerical solution of these integral equations. Numerical results are discussed, to reveal the effect of the piezoelectric layer on the reduction of the mechanical stress intensity factor in the bar.

Absolute and convective instabilities of a film flow down a vertical fiber subjected to a radial electric field

NASA Astrophysics Data System (ADS)

Liu, Rong; Chen, Xue; Ding, Zijing

2018-01-01

We consider the motion of a gravity-driven flow down a vertical fiber subjected to a radial electric field. This flow exhibits rich dynamics including the formation of droplets, or beads, driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the Maxwell stress at the interface. A spatiotemporal stability analysis is performed to investigate the effect of electric field on the absolute-convective instability (AI-CI) characteristics. We performed a numerical simulation on the nonlinear evolution of the film to examine the transition from CI to AI regime. The numerical results are in excellent agreement with the spatiotemporal stability analysis. The blowup behavior of nonlinear simulation predicts the formation of touchdown singularity of the interface due to the effect of electric field. We try to connect the blowup behavior with the AI-CI characteristics. It is found that the singularities mainly occur in the AI regime. The results indicate that the film may have a tendency to form very sharp tips due to the enhancement of the absolute instability induced by the electric field. We perform a theoretical analysis to study the behaviors of the singularities. The results show that there exists a self-similarity between the temporal and spatial distances from the singularities.

Interlaminar stress singularities at a straight free edge in composite laminates

NASA Technical Reports Server (NTRS)

Raju, I. S.; Crews, J. H., Jr.

1980-01-01

A quasi three dimensional finite element analysis was used to analyze the edge stress problem in four-ply, composite laminates. Convergence studies were made to explore the existence of stress singularities near the free edge. The existence of stress singularities at the intersection of the interface and the free edge is confirmed.

On the problem of stress singularities in bonded orthotropic materials

NASA Technical Reports Server (NTRS)

Erdogan, F.; Delale, F.

1976-01-01

The problem of stress singularities at the leading edge of a crack lying in the neighborhood of a bimaterial interface in bonded orthotropic materials is considered. The main objective is to study the effect of material orthotropy on the singular behavior of the stress state when the crack touches or intersects the interface. The results indicate that, due to the large number of material constants involved, in orthotropic materials, the power of stress singularity as well as the stress intensity factor can be considerably different than that found in the isotropic materials with the same stiffness ratio perpendicular to the crack.

Interlaminar stress singularities at a straight free edge in composite laminates

NASA Technical Reports Server (NTRS)

Raju, I. S.; Crews, J. H., Jr.

1981-01-01

A quasi-three-dimensional finite-element analysis was used to analyze the edge-stress problem in four-ply, composite laminates. The seven laminates that were considered belong to the laminate family where the outer ply angle is between 0 and 90 deg. Systematic convergence studies were made to explore the existence of stress singularities near the free edge. The present analysis appears to confirm the existence of stress singularities at the intersection of the interface and the free edge. The power of the stress singularity was the same for all seven laminates considered.

Singularity in structural optimization

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Guptill, J. D.; Berke, L.

1993-01-01

The conditions under which global and local singularities may arise in structural optimization are examined. Examples of these singularities are presented, and a framework is given within which the singularities can be recognized. It is shown, in particular, that singularities can be identified through the analysis of stress-displacement relations together with compatibility conditions or the displacement-stress relations derived by the integrated force method of structural analysis. Methods of eliminating the effects of singularities are suggested and illustrated numerically.

Boundary layer thermal stresses in angle-ply composite laminates, part 1. [graphite-epoxy composites

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1981-01-01

Thermal boundary-layer stresses (near free edges) and displacements were determined by a an eigenfunction expansion technique and the establishment of an appropriate particular solution. Current solutions in the region away from the singular domain (free edge) are found to be excellent agreement with existing approximate numerical results. As the edge is approached, the singular term controls the near field behavior of the boundary layer. Results are presented for cases of various angle-ply graphite/epoxy laminates with (theta/-theta/theta/theta) configurations. These results show high interlaminar (through-the-thickness) stresses. Thermal boundary-layer thicknesses of different composite systems are determined by examining the strain energy density distribution in composites. It is shown that the boundary-layer thickness depends on the degree of anisotropy of each individual lamina, thermomechanical properties of each ply, and the relative thickness of adjacent layers. The interlaminar thermal stresses are compressive with increasing temperature. The corresponding residual stresses are tensile and may enhance interply delaminations.

Analysis of delamination in unidirectional and crossplied fiber composites containing surface cracks

NASA Technical Reports Server (NTRS)

Wang, S. S.; Mandell, J. F.

1977-01-01

A two-dimensional hybrid stress finite element analysis is described which was used to study the local stress field around delamination cracks in composite materials. The analysis employs a crack tip singularity element which is embedded in a matrix interlayer between plies of the laminate. Results are given for a unidirectional graphite/epoxy laminate containing a delamination emanating from a surface crack through the outside ply. The results illustrate several aspects of delamination cracks: (1) the localization of the singular stress domain within the interlayer; (2) the local concentration of stress in the ply adjacent to the crack; (3) the nature of the transverse normal and interlaminar shear stress distributions; and (4) the relative magnitudes of K sub 1 and K sub 2 associated with the delamination. A simple example of the use of the analysis in predicting delamination crack growth is demonstrated for a glass/epoxy laminate. The comparisons with experimental data show good agreement.

On the stress singularities generated by anisotropic eigenstrains and the hydrostatic stress due to annular inhomogeneities

NASA Astrophysics Data System (ADS)

Yavari, Arash; Goriely, Alain

2015-03-01

The problems of singularity formation and hydrostatic stress created by an inhomogeneity with eigenstrain in an incompressible isotropic hyperelastic material are considered. For both a spherical ball and a cylindrical bar with a radially symmetric distribution of finite possibly anisotropic eigenstrains, we show that the anisotropy of these eigenstrains at the center (the center of the sphere or the axis of the cylinder) controls the stress singularity. If they are equal at the center no stress singularity develops but if they are not equal then stress always develops a logarithmic singularity. In both cases, the energy density and strains are everywhere finite. As a related problem, we consider annular inclusions for which the eigenstrains vanish in a core around the center. We show that even for an anisotropic distribution of eigenstrains, the stress inside the core is always hydrostatic. We show how these general results are connected to recent claims on similar problems in the limit of small eigenstrains.

Convergence rates for finite element problems with singularities. Part 1: Antiplane shear. [crack

NASA Technical Reports Server (NTRS)

Plunkett, R.

1980-01-01

The problem of a finite crack in an infinite medium under antiplane shear load is considered. It is shown that the nodal forces at the tip of the crack accurately gives the order of singularity, that n energy release methods can give the strength to better than 1 percent with element size 1/10 the crack length, and that nodal forces give a much better estimate of the stress field than do the elements themselves. The finite element formulation and the factoring of tridiagonal matrices are discussed.

Cauchy horizon stability in a collapsing spherical dust cloud: II. Energy bounds for test fields and odd-parity gravitational perturbations

NASA Astrophysics Data System (ADS)

Ortiz, Néstor; Sarbach, Olivier

2018-01-01

We analyze the stability of the Cauchy horizon associated with a globally naked, shell-focussing singularity arising from the complete gravitational collapse of a spherical dust cloud. In a previous work, we have studied the dynamics of spherical test scalar fields on such a background. In particular, we proved that such fields cannot develop any divergences which propagate along the Cauchy horizon. In the present work, we extend our analysis to the more general case of test fields without symmetries and to linearized gravitational perturbations with odd parity. To this purpose, we first consider test fields possessing a divergence-free stress-energy tensor satisfying the dominant energy condition, and we prove that a suitable energy norm is uniformly bounded in the domain of dependence of the initial slice. In particular, this result implies that free-falling observers co-moving with the dust particles measure a finite energy of the field, even as they cross the Cauchy horizon at points lying arbitrarily close to the central singularity. Next, for the case of Klein–Gordon fields, we derive point-wise bounds from our energy estimates which imply that the scalar field cannot diverge at the Cauchy horizon, except possibly at the central singular point. Finally, we analyze the behaviour of odd-parity, linear gravitational and dust perturbations of the collapsing spacetime. Similarly to the scalar field case, we prove that the relevant gauge-invariant combinations of the metric perturbations stay bounded away from the central singularity, implying that no divergences can propagate in the vacuum region. Our results are in accordance with previous numerical studies and analytic work in the self-similar case.

Constraints on Stress Components at the Internal Singular Point of an Elastic Compound Structure

NASA Astrophysics Data System (ADS)

Pestrenin, V. M.; Pestrenina, I. V.

2017-03-01

The classical analytical and numerical methods for investigating the stress-strain state (SSS) in the vicinity of a singular point consider the point as a mathematical one (having no linear dimensions). The reliability of the solution obtained by such methods is valid only outside a small vicinity of the singular point, because the macroscopic equations become incorrect and microscopic ones have to be used to describe the SSS in this vicinity. Also, it is impossible to set constraint or to formulate solutions in stress-strain terms for a mathematical point. These problems do not arise if the singular point is identified with the representative volume of material of the structure studied. In authors' opinion, this approach is consistent with the postulates of continuum mechanics. In this case, the formulation of constraints at a singular point and their investigation becomes an independent problem of mechanics for bodies with singularities. This method was used to explore constraints at an internal singular point (representative volume) of a compound wedge and a compound rib. It is shown that, in addition to the constraints given in the classical approach, there are also constraints depending on the macroscopic parameters of constituent materials. These constraints turn the problems of deformable bodies with an internal singular point into nonclassical ones. Combinations of material parameters determine the number of additional constraints and the critical stress state at the singular point. Results of this research can be used in the mechanics of composite materials and fracture mechanics and in studying stress concentrations in composite structural elements.

Comninou contact zones for a crack parallel to an interface

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

Joseph, P.F.; Gadi, K.S.; Erdogen, F.

One of the interesting features in studying the state of stress in elastic solids near singular points, is the so called complex singularity that gives rise to an apparent local oscillatory behavior in the stress and displacement fields. The region in which this occurs is very small, much smaller than any plastic zone would be, and therefore the oscillations can be ignored in practical applications. Nevertheless, it is a matter of interesting theoretical investigation. The Comninou model of a small contact zone near the crack tip appears to correct for this anomaly within the framework of the linear theory. Thismore » model seems to make sense out of a {open_quotes}solution{close_quotes} that violates the boundary conditions. Erdogan and Joseph, showed (to themselves anyway) that the Comninou model actually has a physical basis. They considered a crack parallel to an interface where the order of the singularity is always real. With great care in solving the singular integral equations, it was shown that as the crack approaches the interface, a pinching effect is observed at the crack tip. This pinching effect proves that in the limit as the crack approaches the interface, the correct way to handle the problem is to consider crack surface contact. In this way, the issue of {open_quotes}oscillations{close_quotes} is never encountered for the interface crack problem. In the present study, the value of h/a that corresponds to crack closure (zero value of the stress intensity factor) will be determined for a given material pair for tensile loading. An asymptotic numerical method for the solution of singular integral equations making use of is used to obtain this result. Results for the crack opening displacement near the tip of the crack and the behavior of the stress intensity factor for cracks very close to the interface are presented. Among other interesting issues to be discussed, this solution shows that the semi-infinite crack parallel to an interface is closed.« less

Singularities in Optimal Structural Design

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Guptill, J. D.; Berke, L.

1992-01-01

Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis.

Singularities in optimal structural design

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Guptill, J. D.; Berke, L.

1992-01-01

Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis.

The problem of a finite strip compressed between two rough rigid stamps

NASA Technical Reports Server (NTRS)

Gupta, G. D.

1975-01-01

A finite strip compressed between two rough rigid stamps is considered. The elastostatic problem is formulated in terms of a singular integral equation from which the proper stress singularities at the corners are determined. The singular integral equation is solved numerically to determine the stresses along the fixed ends of the strip. The effect of material properties and strip geometry on the stress-intensity factor is presented graphically.

Three-dimensional analysis of surface crack-Hertzian stress field interaction

NASA Technical Reports Server (NTRS)

Ballarini, R.; Hsu, Y.

1989-01-01

The results are presented of a stress intensity factor analysis of semicircular surface cracks in the inner raceway of an engine bearing. The loading consists of a moving spherical Hertzian contact load and an axial stress due to rotation and shrink fit. A 3-D linear elastic Boundary Element Method code was developed to perform the stress analysis. The element library includes linear and quadratic isoparametric surface elements. Singular quarter point elements were employed to capture the square root displacement variation and the inverse square root stress singularity along the crack front. The program also possesses the capability to separate the whole domain into two subregions. This procedure enables one to solve nonsymmetric fracture mechanics problems without having to separate the crack surfaces a priori. A wide range of configuration parameters was investigated. The ratio of crack depth to bearing thickness was varied from one-sixtieth to one-fifth for several different locations of the Hertzian load. The stress intensity factors for several crack inclinations were also investigated. The results demonstrate the efficiency and accuracy of the Boundary Element Method. Moreover, the results can provide the basis for crack growth calculations and fatigue life prediction.

The crack problem in bonded nonhomogeneous materials

NASA Technical Reports Server (NTRS)

Erdogan, Fazil; Kaya, A. C.; Joseph, P. F.

1988-01-01

The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors.

The crack problem in bonded nonhomogeneous materials

NASA Technical Reports Server (NTRS)

Erdogan, F.; Joseph, P. F.; Kaya, A. C.

1991-01-01

The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip termination at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors.

Contact Line Dynamics

NASA Astrophysics Data System (ADS)

Kreiss, Gunilla; Holmgren, Hanna; Kronbichler, Martin; Ge, Anthony; Brant, Luca

2017-11-01

The conventional no-slip boundary condition leads to a non-integrable stress singularity at a moving contact line. This makes numerical simulations of two-phase flow challenging, especially when capillarity of the contact point is essential for the dynamics of the flow. We will describe a modeling methodology, which is suitable for numerical simulations, and present results from numerical computations. The methodology is based on combining a relation between the apparent contact angle and the contact line velocity, with the similarity solution for Stokes flow at a planar interface. The relation between angle and velocity can be determined by theoretical arguments, or from simulations using a more detailed model. In our approach we have used results from phase field simulations in a small domain, but using a molecular dynamics model should also be possible. In both cases more physics is included and the stress singularity is removed.

Field singularities at lossless metal-dielectric arbitrary-angle edges and their ramifications to the numerical modeling of gratings.

PubMed

Li, Lifeng

2012-04-01

I extend a previous work [J. Opt. Soc. Am. A, 738 (2011)] on field singularities at lossless metal-dielectric right-angle edges and their ramifications to the numerical modeling of gratings to the case of arbitrary metallic wedge angles. Simple criteria are given that allow one knowing the lossless permittivities and the arbitrary wedge angles to determine if the electric field at the edges is nonsingular, can be regularly singular, or can be irregularly singular without calculating the singularity exponent. Furthermore, the knowledge of the singularity type enables one to predict immediately if a numerical method that uses Fourier expansions of the transverse electric field components at the edges will converge or not without making any numerical tests. All conclusions of the previous work about the general relationships between field singularities, Fourier representation of singular fields, and convergence of numerical methods for modeling lossless metal-dielectric gratings have been reconfirmed.

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.

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle

PubMed Central

Brzezicki, Samuel J.

2017-01-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function. PMID:28690412

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle.

PubMed

Crowdy, Darren G; Brzezicki, Samuel J

2017-06-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function.

Analysis of singular interface stresses in dissimilar material joints for plasma facing components

NASA Astrophysics Data System (ADS)

You, J. H.; Bolt, H.

2001-10-01

Duplex joint structures are typical material combinations for the actively cooled plasma facing components of fusion devices. The structural integrity under the incident heat loads from the plasma is one of the most crucial issues in the technology of these components. The most critical domain in a duplex joint component is the free surface edge of the bond interface between heterogeneous materials. This is due to the fact that the thermal stress usually shows a singular intensification in this region. If the plasma facing armour tile consists of a brittle material, the existence of the stress singularity can be a direct cause of failure. The present work introduces a comprehensive analytical tool to estimate the impact of the stress singularity for duplex PFC design and quantifies the relative stress intensification in various materials joints by use of a model formulated by Munz and Yang. Several candidate material combinations of plasma facing armour and metallic heat sink are analysed and the results are compared with each other.

Strain intensity factor approach for predicting the strength of continuously reinforced metal matrix composites

NASA Technical Reports Server (NTRS)

Poe, Clarence C., Jr.

1989-01-01

A method was previously developed to predict the fracture toughness (stress intensity factor at failure) of composites in terms of the elastic constants and the tensile failing strain of the fibers. The method was applied to boron/aluminum composites made with various proportions of 0 deg and +/- 45 deg plies. Predicted values of fracture toughness were in gross error because widespread yielding of the aluminum matrix made the compliance very nonlinear. An alternate method was develolped to predict the strain intensity factor at failure rather than the stress intensity factor because the singular strain field was not affected by yielding as much as the stress field. Far-field strains at failure were calculated from the strain intensity factor, and then strengths were calculated from the far-field strains using uniaxial stress-strain curves. The predicted strengths were in good agreement with experimental values, even for the very nonlinear laminates that contained only +/- 45 deg plies. This approach should be valid for other metal matrix composites that have continuous fibers.

Mixed-mode singularity and temperature effects on dislocation nucleation in strained interconnects

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

Lee, Jinhaeng; Gao, Yanfei

2011-01-01

Dislocations can be nucleated from sharp geometric features in strained interconnects due to thermal expansion coefficient mismatch, lattice mismatch, or stresses that arise during material processing. The asymptotic stress fields near the edge root can be described by mixed-mode singularities, which depend on the dihedral angle and material properties, and a transverse T-stress, which depends on how residual stress is realized in the interconnects. The critical condition for stress nucleation can be determined when an appropriate measure of the stress intensity factors (SIFs) reaches a critical value. Such a method, however, does not offer an explicit picture of the dislocationmore » nucleation process so that it has difficulties in studying complicated structures, mode mixity effects, and more importantly the temperature effects. Based on the Peierls concept, a dislocation can be described by a continuous slip field, and the dislocation nucleation condition corresponds when the total potential energy reaches a stationary state. Through implementing this ad hoc interface model into a finite element framework, it is found that dislocation nucleation becomes more difficult with the increase of mode mixity and T-stress, or the decrease of the width-to-height ratio of the surface pad, while the shape of the surface pad, being a square or a long line, plays a less important role. The Peierls dislocation model also allows us to determine the activation energy, which is the energy needed for the thermal activation of a dislocation when the applied load is lower than the athermal critical value. The calculated saddle point configuration compares favorably the molecular simulations in literature. Suggestions on making immortal strained interconnects are provided.« less

Elastic interactions between two-dimensional geometric defects

NASA Astrophysics Data System (ADS)

Moshe, Michael; Sharon, Eran; Kupferman, Raz

2015-12-01

In this paper, we introduce a methodology applicable to a wide range of localized two-dimensional sources of stress. This methodology is based on a geometric formulation of elasticity. Localized sources of stress are viewed as singular defects—point charges of the curvature associated with a reference metric. The stress field in the presence of defects can be solved using a scalar stress function that generalizes the classical Airy stress function to the case of materials with nontrivial geometry. This approach allows the calculation of interaction energies between various types of defects. We apply our methodology to two physical systems: shear-induced failure of amorphous materials and the mechanical interaction between contracting cells.

Singularities in loop quantum cosmology.

PubMed

Cailleteau, Thomas; Cardoso, Antonio; Vandersloot, Kevin; Wands, David

2008-12-19

We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of loop quantum cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficient to avoid the occurrence of curvature singularities.

On a 3-D singularity element for computation of combined mode stress intensities

NASA Technical Reports Server (NTRS)

Atluri, S. N.; Kathiresan, K.

1976-01-01

A special three-dimensional singularity element is developed for the computation of combined modes 1, 2, and 3 stress intensity factors, which vary along an arbitrarily curved crack front in three dimensional linear elastic fracture problems. The finite element method is based on a displacement-hybrid finite element model, based on a modified variational principle of potential energy, with arbitrary element interior displacements, interelement boundary displacements, and element boundary tractions as variables. The special crack-front element used in this analysis contains the square root singularity in strains and stresses, where the stress-intensity factors K(1), K(2), and K(3) are quadratically variable along the crack front and are solved directly along with the unknown nodal displacements.

Managing focal fields of vector beams with multiple polarization singularities.

PubMed

Han, Lei; Liu, Sheng; Li, Peng; Zhang, Yi; Cheng, Huachao; Gan, Xuetao; Zhao, Jianlin

2016-11-10

We explore the tight focusing behavior of vector beams with multiple polarization singularities, and analyze the influences of the number, position, and topological charge of the singularities on the focal fields. It is found that the ellipticity of the local polarization states at the focal plane could be determined by the spatial distribution of the polarization singularities of the vector beam. When the spatial location and topological charge of singularities have even-fold rotation symmetry, the transverse fields at the focal plane are locally linearly polarized. Otherwise, the polarization state becomes a locally hybrid one. By appropriately arranging the distribution of the polarization singularities in the vector beam, the polarization distributions of the focal fields could be altered while the intensity maintains unchanged.

Collective Surfing of Chemically Active Particles

NASA Astrophysics Data System (ADS)

Masoud, Hassan; Shelley, Michael J.

2014-03-01

We study theoretically the collective dynamics of immotile particles bound to a 2D surface atop a 3D fluid layer. These particles are chemically active and produce a chemical concentration field that creates surface-tension gradients along the surface. The resultant Marangoni stresses create flows that carry the particles, possibly concentrating them. For a 3D diffusion-dominated concentration field and Stokesian fluid we show that the surface dynamics of active particle density can be determined using nonlocal 2D surface operators. Remarkably, we also show that for both deep or shallow fluid layers this surface dynamics reduces to the 2D Keller-Segel model for the collective chemotactic aggregation of slime mold colonies. Mathematical analysis has established that the Keller-Segel model can yield finite-time, finite-mass concentration singularities. We show that such singular behavior occurs in our finite-depth system, and study the associated 3D flow structures.

Stress and strain field singularities, micro-cracks, and their role in failure initiation at the composite laminate free-edge

NASA Astrophysics Data System (ADS)

Dustin, Joshua S.

A state-of-the-art multi-scale analysis was performed to predict failure initiation at the free-edge of an angle-ply laminate using the Strain Invariant Failure Theory (SIFT), and multiple improvements to this analysis methodology were proposed and implemented. Application of this analysis and theory led to the conclusion that point-wise failure criteria which ignore the singular stress and strain fields from a homogenized analysis and the presence of free-edge damage in the form of micro-cracking, may do so at the expense of failure prediction capability. The main contributions of this work then are made in the study of the laminate free-edge singularity and in the effects of micro-cracking at the composite laminate free-edge. Study of both classical elasticity and finite element solutions of the laminate free-edge stress field based upon the assumption of homogenized lamina properties reveal that the order of the free-edge singularity is sufficiently small such that the domain of dominance of this term away from the laminate free-edge is much smaller than the relevant dimensions of the microstructure. In comparison to a crack-tip field, these free-edge singularities generate stress and strain fields which are half as intense as those at the crack-tip, leading to the conclusion that existing flaws at the free-edge in the form of micro-cracks would be more prone to the initiation of free-edge failure than the existence of a singularity in the free-edge elasticity solutions. A methodical experiment was performed on a family of [±25°/90°] s laminates made of IM7/8552 carbon/epoxy composite, to both characterize micro-cracks present at the laminate free-edge and to study their behavior under the application of a uniform extensional load. The majority of these micro-cracks were of length on the order of a few fiber diameters, though larger micro-cracks as long as 100 fiber diameters were observed in thicker laminates. A strong correlation between the application of vacuum during cure and the presence of micro-cracks was observed. The majority of micro-cracks were located along ply interfaces, even along the interfaces of plies with identical orientation, further implicating processing methods and conditions in the formation of these micro-cracks and suggesting that a region of interphase is present between composite plies. No micro-cracks of length smaller than approximately 36 fiber diameters (180 µm) grew or interacted with the free-edge delamination or damage at ultimate laminate failure, and the median length of micro-cracks which did grow was approximately 50 fiber diameters (250 µm). While the internal depth of these free-edge cracks was unknown, the results of these experiments then suggests a critical free-edge crack-length in the [±25°/90°]s family of laminates of approximately 50 fiber diameters (250 µm, or 1.5 lamina thicknesses). A multi-scale analysis of free-edge micro-cracks using traditional displacement based finite element submodeling and XFEM was used to explain the experimental observation that micro-cracks did not grow unless they were of sufficient length. Analysis of the stress-intensity factors along the micro-crack front revealed that penny shaped micro-cracks in the 90° plies of the [±25°/90°] s family of laminates of length two fiber diameters or longer are under mode I dominated loading conditions when oriented parallel or perpendicular to the laminate loading direction. The maximum observed KI along the crack-front of these modeled micro-cracks was no larger than 26% of the ultimate KIC of the matrix material, under the application of a uniform temperature change (ΔT=-150°C) and uniform extension equal to the experimentally measured ultimate failure strain of the laminate. This indicates that insufficient energy is supplied to these small micro-cracks to facilitate crack growth, confirming what was experimentally observed. A method for estimating a critical micro-crack length based upon the results of the fracture mechanics analysis was developed, and predictions for this critical crack length were between 26 and 255 fiber diameters with a nominal prediction of approximately 73 fiber diameters, which agreed quite well with the experimentally observed critical micro-crack length of approximately 50 fiber diameters. The overall conclusion of this work is that the composite laminate does not appear to be as sensitive to free-edge singular stress-fields or free-edge micro-cracking and damage as the research community has portrayed in the literature. In laminates designed to delaminate, material flaws on the order of the relevant dimensions of the micro-structure appear to have little to no effect on the static strength of a composite laminate.

Flux-pinning-induced interfacial shearing and transverse normal stress in a superconducting coated conductor long strip

NASA Astrophysics Data System (ADS)

Jing, Ze; Yong, Huadong; Zhou, Youhe

2012-08-01

In this paper, a theoretical model is proposed to analyze the transverse normal stress and interfacial shearing stress induced by the electromagnetic force in the superconducting coated conductor. The plane strain approach is used and a singular integral equation is derived. By assuming that the critical current density is magnetic field independent and the superconducting film is infinitely thin, the interfacial shearing stress and normal stress in the film are evaluated for the coated conductor during the increasing and decreasing in the transport current, respectively. The calculation results are discussed and compared for the conductor with different substrate and geometry. The results indicate that the coated conductor with stiffer substrate and larger width experiences larger interfacial shearing stress and less normal stress in the film.

Specialty functions singularity mechanics problems

NASA Technical Reports Server (NTRS)

Sarigul, Nesrin

1989-01-01

The focus is in the development of more accurate and efficient advanced methods for solution of singular problems encountered in mechanics. At present, finite element methods in conjunction with special functions, boolean sum and blending interpolations are being considered. In dealing with systems which contain a singularity, special finite elements are being formulated to be used in singular regions. Further, special transition elements are being formulated to couple the special element to the mesh that models the rest of the system, and to be used in conjunction with 1-D, 2-D and 3-D elements within the same mesh. Computational simulation with a least squares fit is being utilized to construct special elements, if there is an unknown singularity in the system. A novel approach is taken in formulation of the elements in that: (1) the material properties are modified to include time, temperature, coordinate and stress dependant behavior within the element; (2) material properties vary at nodal points of the elements; (3) a hidden-symbolic computation scheme is developed and utilized in formulating the elements; and (4) special functions and boolean sum are utilized in order to interpolate the field variables and their derivatives along the boundary of the elements. It may be noted that the proposed methods are also applicable to fluids and coupled problems.

Nonlinear elastic inclusions in isotropic solids.

PubMed

Yavari, Arash; Goriely, Alain

2013-12-08

We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construction. The problem of residual stress calculation is then reduced to finding a mapping from the Riemannian material manifold to the ambient Euclidean space. Using this construction, we find the residual stress fields of three model systems with spherical and cylindrical symmetries in both incompressible and compressible isotropic elastic solids. In particular, we consider a finite spherical ball with a spherical inclusion with uniform pure dilatational eigenstrain and we show that the stress in the inclusion is uniform and hydrostatic. We also show how singularities in the stress distribution emerge as a consequence of a mismatch between radial and circumferential eigenstrains at the centre of a sphere or the axis of a cylinder.

Nonlinear elastic inclusions in isotropic solids

PubMed Central

Yavari, Arash; Goriely, Alain

2013-01-01

We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construction. The problem of residual stress calculation is then reduced to finding a mapping from the Riemannian material manifold to the ambient Euclidean space. Using this construction, we find the residual stress fields of three model systems with spherical and cylindrical symmetries in both incompressible and compressible isotropic elastic solids. In particular, we consider a finite spherical ball with a spherical inclusion with uniform pure dilatational eigenstrain and we show that the stress in the inclusion is uniform and hydrostatic. We also show how singularities in the stress distribution emerge as a consequence of a mismatch between radial and circumferential eigenstrains at the centre of a sphere or the axis of a cylinder. PMID:24353470

Classical and quantum Big Brake cosmology for scalar field and tachyonic models

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

Kamenshchik, A. Yu.; Manti, S.

We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bangmore » and Big Crunch singularities are not traversable.« less

Study on the Strength of GFRP/Stainless Steel Adhesive Joints Reinforced with Glass Mat

NASA Astrophysics Data System (ADS)

Iwasa, Masaaki

The adhesive strengths of glass fiber reinforced plastics/metal adhesive joints reinforced with glass mat under tensile shear loads and tensile loads were investigated analytically and experimentally. First, the stress singularity parameters of the bonding edges were analyzed by FEM for various types of adhesive joints reinforced with glass mat. The shear stress and normal stress distributions near the bonding edge can be expressed by two stress singularity parameters. Second, tensile shear tests were performed on taper lap joint and taper lap joint reinforced with glass mat and tensile tests were performed on T-type adhesive joint and T-type adhesive joint reinforced with glass mat. The relationships between the loads and the crosshead displacements were measured. We concluded that reinforcing adhesive joints has a greater effect on strength under tensile load than under tensile shear load. The adhesive joints strength reinforced with glass mat can be evaluated by using stress singularity parameters.

Tangled nonlinear driven chain reactions of all optical singularities

NASA Astrophysics Data System (ADS)

Vasil'ev, V. I.; Soskin, M. S.

2012-03-01

Dynamics of polarization optical singularities chain reactions in generic elliptically polarized speckle fields created in photorefractive crystal LiNbO3 was investigated in details Induced speckle field develops in the tens of minutes scale due to photorefractive 'optical damage effect' induced by incident beam of He-Ne laser. It was shown that polarization singularities develop through topological chain reactions of developing speckle fields driven by photorefractive nonlinearities induced by incident laser beam. All optical singularities (C points, optical vortices, optical diabolos,) are defined by instantaneous topological structure of the output wavefront and are tangled by singular optics lows. Therefore, they have develop in tangled way by six topological chain reactions driven by nonlinear processes in used nonlinear medium (photorefractive LiNbO3:Fe in our case): C-points and optical diabolos for right (left) polarized components domains with orthogonally left (right) polarized optical vortices underlying them. All elements of chain reactions consist from loop and chain links when nucleated singularities annihilated directly or with alien singularities in 1:9 ratio. The topological reason of statistics was established by low probability of far enough separation of born singularities pair from existing neighbor singularities during loop trajectories. Topology of developing speckle field was measured and analyzed by dynamic stokes polarimetry with few seconds' resolution. The hierarchy of singularities govern scenario of tangled chain reactions was defined. The useful space-time data about peculiarities of optical damage evolution were obtained from existence and parameters of 'islands of stability' in developing speckle fields.

Singularity-free solutions for anisotropic charged fluids with Chaplygin equation of state

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

Rahaman, Farook; Ray, Saibal; Jafry, Abdul Kayum

2010-11-15

We extend the Krori-Barua analysis of the static, spherically symmetric, Einstein-Maxwell field equations and consider charged fluid sources with anisotropic stresses. The inclusion of a new variable (tangential pressure) allows the use of a nonlinear, Chaplygin-type equation of state with coefficients fixed by the matching conditions at the boundary of the source. Some physical features are briefly discussed.

Correlation between topological structure and its properties in dynamic singular vector fields.

PubMed

Vasilev, Vasyl; Soskin, Marat

2016-04-20

A new technique for establishment of topology measurements for static and dynamic singular vector fields is elaborated. It is based on precise measurement of the 3D landscape of ellipticity distribution for a checked singular optical field with C points on the tops of ellipticity hills. Vector fields possess three-component topology: areas with right-hand (RH) and left-hand (LH) ellipses, and delimiting those L lines as the singularities of handedness. The azimuth map of polarization ellipses is common for both RH and LH ellipses of vector fields and do not feel L lines. The strict rules were confirmed experimentally, which define the connection between the sign of underlying optical vortices and morphological parameters of upper-lying C points. Percolation phenomena explain their realization in-between singular vector fields and long duration of their chains of 10³  s order.

Spatial Distribution of Phase Singularities in Optical Random Vector Waves.

PubMed

De Angelis, L; Alpeggiani, F; Di Falco, A; Kuipers, L

2016-08-26

Phase singularities are dislocations widely studied in optical fields as well as in other areas of physics. With experiment and theory we show that the vectorial nature of light affects the spatial distribution of phase singularities in random light fields. While in scalar random waves phase singularities exhibit spatial distributions reminiscent of particles in isotropic liquids, in vector fields their distribution for the different vector components becomes anisotropic due to the direct relation between propagation and field direction. By incorporating this relation in the theory for scalar fields by Berry and Dennis [Proc. R. Soc. A 456, 2059 (2000)], we quantitatively describe our experiments.

On important precursor of singular optics (tutorial)

NASA Astrophysics Data System (ADS)

Polyanskii, Peter V.; Felde, Christina V.; Bogatyryova, Halina V.; Konovchuk, Alexey V.

2018-01-01

The rise of singular optics is usually associated with the seminal paper by J. F. Nye and M. V. Berry [Proc. R. Soc. Lond. A, 336, 165-189 (1974)]. Intense development of this area of modern photonics has started since the early eighties of the XX century due to invention of the interfrence technique for detection and diagnostics of phase singularities, such as optical vortices in complex speckle-structured light fields. The next powerful incentive for formation of singular optics into separate area of the science on light was connectected with discovering of very practical technique for creation of singular optical beams of various kinds on the base of computer-generated holograms. In the eghties and ninetieth of the XX century, singular optics evolved, almost entirely, under the approximation of complete coherency of light field. Only at the threshold of the XXI century, it has been comprehended that the singular-optics approaches can be fruitfully expanded onto partially spatially coherent, partially polarized and polychromatic light fields supporting singularities of new kinds, that has been resulted in establishing of correlation singular optics. Here we show that correlation singular optics has much deeper roots, ascending to "pre-singular" and even pre-laser epoch and associated with the concept of partial coherence and polarization. It is remarcable that correlation singular optics in its present interpretation has forestalled the standard coherent singular optics. This paper is timed to the sixtieth anniversary of the most profound precursor of modern correlation singular optics [J. Opt. Soc. Am., 47, 895-902 (1957)].

Singular trajectories: space-time domain topology of developing speckle fields

NASA Astrophysics Data System (ADS)

Vasil'ev, Vasiliy; Soskin, Marat S.

2010-02-01

It is shown the space-time dynamics of optical singularities is fully described by singularities trajectories in space-time domain, or evolution of transverse coordinates(x, y) in some fixed plane z0. The dynamics of generic developing speckle fields was realized experimentally by laser induced scattering in LiNbO3:Fe photorefractive crystal. The space-time trajectories of singularities can be divided topologically on two classes with essentially different scenario and duration. Some of them (direct topological reactions) consist from nucleation of singularities pair at some (x, y, z0, t) point, their movement and annihilation. They possess form of closed loops with relatively short time of existence. Another much more probable class of trajectories are chain topological reactions. Each of them consists from sequence of links, i.e. of singularities nucleation in various points (xi yi, ti) and following annihilation of both singularities in other space-time points with alien singularities of opposite topological indices. Their topology and properties are established. Chain topological reactions can stop on the borders of a developing speckle field or go to infinity. Examples of measured both types of topological reactions for optical vortices (polarization C points) in scalar (elliptically polarized) natural developing speckle fields are presented.

Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows

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

Berzi, Diego; Vescovi, Dalila

2015-01-15

We use previous results from discrete element simulations of simple shear flows of rigid, identical spheres in the collisional regime to show that the volume fraction-dependence of the stresses is singular at the shear rigidity. Here, we identify the shear rigidity, which is a decreasing function of the interparticle friction, as the maximum volume fraction beyond which a random collisional assembly of grains cannot be sheared without developing force chains that span the entire domain. In the framework of extended kinetic theory, i.e., kinetic theory that accounts for the decreasing in the collisional dissipation due to the breaking of molecularmore » chaos at volume fractions larger than 0.49, we also show that the volume fraction-dependence of the correlation length (measure of the velocity correlation) is singular at random close packing, independent of the interparticle friction. The difference in the singularities ensures that the ratio of the shear stress to the pressure at shear rigidity is different from zero even in the case of frictionless spheres: we identify that with the yield stress ratio of granular materials, and we show that the theoretical predictions, once the different singularities are inserted into the functions of extended kinetic theory, are in excellent agreement with the results of numerical simulations.« less

Spontaneous generation of singularities in paraxial optical fields.

PubMed

Aiello, Andrea

2016-04-01

In nonrelativistic quantum mechanics, the spontaneous generation of singularities in smooth and finite wave functions is a well understood phenomenon also occurring for free particles. We use the familiar analogy between the two-dimensional Schrödinger equation and the optical paraxial wave equation to define a new class of square-integrable paraxial optical fields that develop a spatial singularity in the focal point of a weakly focusing thin lens. These fields are characterized by a single real parameter whose value determines the nature of the singularity. This novel field enhancement mechanism may stimulate fruitful research for diverse technological and scientific applications.

Evaluation of advanced materials through experimental mechanics and modelling

NASA Technical Reports Server (NTRS)

Yang, Yii-Ching

1993-01-01

Composite materials have been frequently used in aerospace vehicles. Very often defects are inherited during the manufacture and damages are inherited during the construction and services. It becomes critical to understand the mechanical behavior of such composite structure before it can be further used. One good example of these composite structures is the cylindrical bottle of solid rocket motor case with accidental impact damages. Since the replacement of this cylindrical bottle is expensive, it is valuable to know how the damages affects the material, and how it can be repaired. To reach this goal, the damage must be characterized and the stress/strain field must be carefully analyzed. First the damage area, due to impact, is surveyed and identified with a shearography technique which uses the principle of speckle shearing interferometry to measure displacement gradient. Within the damage area of a composite laminate, such as the bottle of solid rocket motor case, all layers are considered to be degraded. Once a lamina being degraded the stiffness as well as strength will be drastically decreased. It becomes a critical area of failure to the whole bottle. And hence the stress/strain field within and around a damage should be accurately evaluated for failure prediction. To investigate the stress/strain field around damages a Hybrid-Numerical method which combines experimental measurement and finite element analysis is used. It is known the stress or strain at the singular point can not be accurately measured by an experimental technique. Nevertheless, if the location is far away from the singular spot, the displacement can be found accurately. Since it reflects the true displacement field locally regardless of the boundary conditions, it is an excellent input data for a finite element analysis to replace the usually assumed boundary conditions. Therefore, the Hybrid-Numerical method is chosen to avoid the difficulty and to take advantage of both experimental technique and finite element analysis. Experimentally, the digital image correlation technique is employed to measure the displacement field. It is done by comparing two digitized images, before and after loading. Numerically, the finite element program, ABAQUS (version 5.2), is used to analyze the stress and strain field. It takes advantage of the high speed and huge memory size of modern supercomputer, CRAY Y-MP, at NASA Marshall Space Flight Center.

Interaction between a circular inclusion and an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Gupta, G. D.; Ratwani, M.

1975-01-01

The plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.

Stress singularities in a model of a wood disk under sinusoidal pressure

Treesearch

Jay A. Johnson; John C. Hermanson; Steven M. Cramer; Charles Amundson

2005-01-01

A thin, solid, circular wood disk, cut from the transverse plane of a tree stem, can be modeled as a cylindrically orthotropic elastic material. It is known that a stress singularity can occur at the center of a cylindrically orthotropic disk subjected to uniform pressure. If a solid cylindrically orthotropic disk is subjected to sinusoidal pressure distributions, then...

The geometry of singularities and the black hole information paradox

NASA Astrophysics Data System (ADS)

Stoica, O. C.

2015-07-01

The information loss occurs in an evaporating black hole only if the time evolution ends at the singularity. But as we shall see, the black hole solutions admit analytical extensions beyond the singularities, to globally hyperbolic solutions. The method used is similar to that for the apparent singularity at the event horizon, but at the singularity, the resulting metric is degenerate. When the metric is degenerate, the covariant derivative, the curvature, and the Einstein equation become singular. However, recent advances in the geometry of spacetimes with singular metric show that there are ways to extend analytically the Einstein equation and other field equations beyond such singularities. This means that the information can get out of the singularity. In the case of charged black holes, the obtained solutions have nonsingular electromagnetic field. As a bonus, if particles are such black holes, spacetime undergoes dimensional reduction effects like those required by some approaches to perturbative Quantum Gravity.

Electric and magnetic polarization singularities of first-order Laguerre-Gaussian beams diffracted at a half-plane screen.

PubMed

Luo, Yamei; Gao, Zenghui; Tang, Bihua; Lü, Baida

2013-08-01

Based on the vector Fresnel diffraction integrals, analytical expressions for the electric and magnetic components of first-order Laguerre-Gaussian beams diffracted at a half-plane screen are derived and used to study the electric and magnetic polarization singularities in the diffraction field for both two- and three-dimensional (2D and 3D) cases. It is shown that there exist 2D and 3D electric and magnetic polarization singularities in the diffraction field, which do not coincide each other in general. By suitably varying the waist width ratio, off-axis displacement parameter, amplitude ratio, or propagation distance, the motion, pair-creation, and annihilation of circular polarization singularities, and the motion of linear polarization singularities take place in 2D and 3D electric and magnetic fields. The V point, at which two circular polarization singularities with the same topological charge but opposite handedness collide, appears in the 2D electric field under certain conditions in the diffraction field and free-space propagation. A comparison with the free-space propagation is also made.

Singularity Crossing, Transformation of Matter Properties and the Problem of Parametrization in Field Theories

NASA Astrophysics Data System (ADS)

Kamenshchik, A. Yu.

2018-03-01

We investigate particular cosmological models, based either on tachyon fields or on perfect fluids, for which soft future singularities arise in a natural way. Our main result is the description of a smooth crossing of the soft singularity in models with an anti-Chaplygin gas or with a particular tachyon field in the presence of dust. Such a crossing is made possible by certain transformations of matter properties. We discuss and compare also different approaches to the problem of crossing of the Big Bang-Big Crunch singularities.

Tachyon field in loop quantum cosmology: An example of traversable singularity

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

Li Lifang; Zhu Jianyang

2009-06-15

Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universe through a bounce in the high energy region. But LQC has an ambiguity about the quantization scheme. Recently, the authors in [Phys. Rev. D 77, 124008 (2008)] proposed a new quantization scheme. Similar to others, this new quantization scheme also replaces the big bang singularity with the quantum bounce. More interestingly, it introduces a quantum singularity, which is traversable. We investigate this novel dynamics quantitatively with a tachyon scalar field, which gives us a concrete example. Our result shows that our universe can evolve through the quantum singularity regularly,more » which is different from the classical big bang singularity. So this singularity is only a weak singularity.« less

The mode 3 crack problem in bonded materials with a nonhomogeneous interfacial zone

NASA Technical Reports Server (NTRS)

Erdogan, Fazil; Kaya, A. C.; Joseph, P. F.

1988-01-01

The mode 3 crack problem for two bonded homogeneous half planes was considered. The interfacial zone was modelled by a nonhomogeneous strip in such a way that the shear modulus is a continuous function throughout the composite medium and has discontinuous derivatives along the boundaries of the interfacial zone. The problem was formulated for cracks perpendicular to the nominal interface and was solved for various crack locations in and around the interfacial region. The asymptotic stress field near the tip of a crack terminating at an interface was examined and it was shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case the stresses have the standard square root singularity and their angular variation was identical to that of a crack in a homogeneous medium. With application to the subcritical crack growth process in mind, the results given include mostly the stress intensity factors for some typical crack geometries and various material combinations.

The mode III crack problem in bonded materials with a nonhomogeneous interfacial zone

NASA Technical Reports Server (NTRS)

Erdogan, F.; Joseph, P. F.; Kaya, A. C.

1991-01-01

The mode 3 crack problem for two bonded homogeneous half planes was considered. The interfacial zone was modelled by a nonhomogeneous strip in such a way that the shear modulus is a continuous function throughout the composite medium and has discontinuous derivatives along the boundaries of the interfacial zone. The problem was formulated for cracks perpendicular to the nominal interface and was solved for various crack locations in and around the interfacial region. The asymptotic stress field near the tip of a crack terminating at an interface was examined and it was shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case the stresses have the standard square root singularity and their angular variation was identical to that of a crack in a homogeneous medium. With application to the subcritical crack growth process in mind, the results given include mostly the stress intensity factors for some typical crack geometries and various material combinations.

Strain intensity factor approach for predicting the strength of continuously reinforced metal matrix composites

NASA Technical Reports Server (NTRS)

Poe, C. C., Jr.

1988-01-01

A method was previously developed to predict the fracture toughness (stress intensity factor at failure) of composites in terms of the elastic constants and the tensile failing strain of the fibers. The method was applied to boron/aluminum composites made with various proportions of 0 to + or - 45 deg plies. Predicted values of fracture toughness were in gross error because widespread yielding of the aluminum matrix made the compliance very nonlinear. An alternate method was developed to predict the strain intensity factor at failure rather than the stress intensity factor because the singular strain field was not affected by yielding as much as the stress field. Strengths of specimens containing crack-like slits were calculated from predicted failing strains using uniaxial stress-strain curves. Predicted strengths were in good agreement with experimental values, even for the very nonlinear laminates that contained only + or - 45 deg plies. This approach should be valid for other metal matrix composites that have continuous fibers.

Stress Singularities in Swelling Soft Solids.

PubMed

Goriely, Alain; Weickenmeier, Johannes; Kuhl, Ellen

2016-09-23

When a swelling soft solid is rigidly constrained on all sides except for a circular opening, it will bulge out to expand as observed during decompressive craniectomy, a surgical procedure used to reduce stresses in swollen brains. While the elastic energy of the solid decreases throughout this process, large stresses develop close to the opening. At the point of contact, the stresses exhibit a singularity similar to the ones found in the classic punch indentation problem. Here, we study the stresses generated by swelling and the evolution of the bulging shape associated with this process. We also consider the possibility of damage triggered by zones of either high shear stresses or high fiber stretches.

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

NASA Astrophysics Data System (ADS)

Fang, M.; Hager, B. H.

2014-12-01

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

Argand-plane vorticity singularities in complex scalar optical fields: an experimental study using optical speckle.

PubMed

Rothschild, Freda; Bishop, Alexis I; Kitchen, Marcus J; Paganin, David M

2014-03-24

The Cornu spiral is, in essence, the image resulting from an Argand-plane map associated with monochromatic complex scalar plane waves diffracting from an infinite edge. Argand-plane maps can be useful in the analysis of more general optical fields. We experimentally study particular features of Argand-plane mappings known as "vorticity singularities" that are associated with mapping continuous single-valued complex scalar speckle fields to the Argand plane. Vorticity singularities possess a hierarchy of Argand-plane catastrophes including the fold, cusp and elliptic umbilic. We also confirm their connection to vortices in two-dimensional complex scalar waves. The study of vorticity singularities may also have implications for higher-dimensional fields such as coherence functions and multi-component fields such as vector and spinor fields.

Quantum singularities in (2+1) dimensional matter coupled black hole spacetimes

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

Unver, O.; Gurtug, O.

2010-10-15

Quantum singularities considered in the 3D Banados-Teitelboim-Zanelli (BTZ) spacetime by Pitelli and Letelier [Phys. Rev. D 77, 124030 (2008)] is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurrence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and nonlinear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analyzed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields, the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence,more » the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying the Klein-Gordon equation but nonsingular for fermions obeying the Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes does not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.« less

Edge delamination in angle-ply composite laminates, part 5

NASA Technical Reports Server (NTRS)

Wang, S. S.

1981-01-01

A theoretical method was developed for describing the edge delamination stress intensity characteristics in angle-ply composite laminates. The method is based on the theory of anisotropic elasticity. The edge delamination problem is formulated using Lekhnitskii's complex-variable stress potentials and an especially developed eigenfunction expansion method. The method predicts exact orders of the three-dimensional stress singularity in a delamination crack tip region. With the aid of boundary collocation, the method predicts the complete stress and displacement fields in a finite-dimensional, delaminated composite. Fracture mechanics parameters such as the mixed-mode stress intensity factors and associated energy release rates for edge delamination can be calculated explicity. Solutions are obtained for edge delaminated (theta/-theta theta/-theta) angle-ply composites under uniform axial extension. Effects of delamination lengths, fiber orientations, lamination and geometric variables are studied.

A critical assessment of viscous models of trench topography and corner flow

NASA Technical Reports Server (NTRS)

Zhang, J.; Hager, B. H.; Raefsky, A.

1984-01-01

Stresses for Newtonian viscous flow in a simple geometry (e.g., corner flow, bending flow) are obtained in order to study the effect of imposed velocity boundary conditions. Stress for a delta function velocity boundary condition decays as 1/R(2); for a step function velocity, stress goes as 1/R; for a discontinuity in curvature, the stress singularity is logarithmic. For corner flow, which has a discontinuity of velocity at a certain point, the corresponding stress has a 1/R singularity. However, for a more realistic circular-slab model, the stress singularity becomes logarithmic. Thus the stress distribution is very sensitive to the boundary conditions, and in evaluating the applicability of viscous models of trench topography it is essential to use realistic geometries. Topography and seismicity data from northern Hoshu, Japan, were used to construct a finite element model, with flow assumed tangent to the top of the grid, for both Newtonian and non-Newtonian flow (power law 3 rheology). Normal stresses at the top of the grid are compared to the observed trench topography and gravity anomalies. There is poor agreement. Purely viscous models of subducting slables with specified velocity boundary conditions do not predict normal stress patterns compatible with observed topography and gravity. Elasticity and plasticity appear to be important for the subduction process.

Persistence and Lifelong Fidelity of Phase Singularities in Optical Random Waves.

PubMed

De Angelis, L; Alpeggiani, F; Di Falco, A; Kuipers, L

2017-11-17

Phase singularities are locations where light is twisted like a corkscrew, with positive or negative topological charge depending on the twisting direction. Among the multitude of singularities arising in random wave fields, some can be found at the same location, but only when they exhibit opposite topological charge, which results in their mutual annihilation. New pairs can be created as well. With near-field experiments supported by theory and numerical simulations, we study the persistence and pairing statistics of phase singularities in random optical fields as a function of the excitation wavelength. We demonstrate how such entities can encrypt fundamental properties of the random fields in which they arise.

Persistence and Lifelong Fidelity of Phase Singularities in Optical Random Waves

NASA Astrophysics Data System (ADS)

De Angelis, L.; Alpeggiani, F.; Di Falco, A.; Kuipers, L.

2017-11-01

Phase singularities are locations where light is twisted like a corkscrew, with positive or negative topological charge depending on the twisting direction. Among the multitude of singularities arising in random wave fields, some can be found at the same location, but only when they exhibit opposite topological charge, which results in their mutual annihilation. New pairs can be created as well. With near-field experiments supported by theory and numerical simulations, we study the persistence and pairing statistics of phase singularities in random optical fields as a function of the excitation wavelength. We demonstrate how such entities can encrypt fundamental properties of the random fields in which they arise.

The effect of contact stresses in four-point bend testing of graphite/epoxy and graphite/PMR-15 composite beams

NASA Technical Reports Server (NTRS)

Binienda, Wieslaw K.; Roberts, Gary D.; Papadopoulos, Demetrios S.

1992-01-01

The results of in-plane four-point bend experiments on unidirectionally reinforced composite beams are presented for graphite/epoxy (T300/934) and graphite/polyimide (G30-500/PMR-15) composites. The maximum load and the location of cracks formed during failure were measured for testpieces with fibers oriented at various angles to the beam axis. Since most of the beams failed near one or more of the load points, the strength of the beams was evaluated in terms of a proposed model, for the local stress distribution. In this model, an exact solution to the problem of a localized contact force acting on a unidirectionally reinforced half plane is used to describe the local stress field. The stress singularity at the load points is treated in a manner similar to the stress singularity at a crack tip in fracture mechanisms problems. Using this approach, the effect of fiber angle and elastic material properties on the strength of the beam is described in terms of a load intensity factor. For fiber angles less than 45 deg from the beam axis, a single crack is initiated near one of the load points at a critical value of the load intensity factor. The critical load intensity factor decreases with the increasing fiber angle. For larger fiber angles, multiple cracks occur at locations both near and away from the load points, and the load intensity factor at failure increases sharply with increasing fiber angle.

Effect of contact stresses in four-point bend testing of graphite/epoxy and graphite/PMR-15 composite beams

NASA Technical Reports Server (NTRS)

Binienda, W. K.; Roberts, G. D.; Papadopoulos, D. S.

1992-01-01

The results of in-plane four-point bend experiments on unidirectionally reinforced composite beams are presented for graphite/epoxy (T300/934) and graphite/polyimide (G30-500/PMR-15) composites. The maximum load and the location of cracks formed during failure were measured for testpieces with fibers oriented at various angles to the beam axis. Since most of the beams failed near one or more of the load points, the strength of the beams was evaluated in terms of a proposed model for the local stress distribution. In this model, an exact solution to the problem of a localized contact force acting on a unidirectionally reinforced half plane is used to describe the local stress field. The stress singularity at the load points is treated in a manner similar to the stress singularity at a crack tip in fracture mechanisms problems. Using this approach, the effect of fiber angle and elastic material properties on the strength of the beam is described in terms of a load intensity factor. For fiber angles less than 45 deg from the beam axis, a single crack is initiated near one of the load points at a critical value of the load intensity factor. The critical load intensity factor decreases with increasing fiber angle. For larger fiber angles, multiple cracks occur at locations both near and away from the load points, and the load intensity factor at failure increases sharply with increasing fiber angle.

An extended 3D discrete-continuous model and its application on single- and bi-crystal micropillars

NASA Astrophysics Data System (ADS)

Huang, Minsheng; Liang, Shuang; Li, Zhenhuan

2017-04-01

A 3D discrete-continuous model (3D DCM), which couples the 3D discrete dislocation dynamics (3D DDD) and finite element method (FEM), is extended in this study. New schemes for two key information transfers between DDD and FEM, i.e. plastic-strain distribution from DDD to FEM and stress transfer from FEM to DDD, are suggested. The plastic strain induced by moving dislocation segments is distributed to an elementary spheroid (ellipsoid or sphere) via a specific new distribution function. The influence of various interfaces (such as free surfaces and grain boundaries (GBs)) on the plastic-strain distribution is specially considered. By these treatments, the deformation fields can be solved accurately even for dislocations on slip planes severely inclined to the FE mesh, with no spurious stress concentration points produced. In addition, a stress correction by singular and non-singular theoretical solutions within a cut-off sphere is introduced to calculate the stress on the dislocations accurately. By these schemes, the present DCM becomes less sensitive to the FE mesh and more numerically efficient, which can also consider the interaction between neighboring dislocations appropriately even though they reside in the same FE mesh. Furthermore, the present DCM has been employed to model the compression of single-crystal and bi-crystal micropillars with rigid and dislocation-absorbed GBs. The influence of internal GB on the jerky stress-strain response and deformation mode is studied in detail to shed more light on these important micro-plastic problems.

Polarized vortices in optical speckle field: observation of rare polarization singularities.

PubMed

Dupont, Jan; Orlik, Xavier

2015-03-09

Using a recent method able to characterize the polarimetry of a random field with high polarimetric and spatial accuracy even near places of destructive interference, we study polarized optical vortices at a scale below the transverse correlation width of a speckle field. We perform high accuracy polarimetric measurements of known singularities described with an half-integer topological index and we study rare integer index singularities which have, to our knowledge, never been observed in a speckle field.

Topological dynamics of optical singularities in speckle-fields induced by photorefractive scattering in a LiNbO{sub 3} : Fe crystal

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

Vasil'ev, Vasilii I; Soskin, M S

2013-02-28

A natural singular dynamics of elliptically polarised speckle-fields induced by the 'optical damage' effect in a photorefractive crystal of lithium niobate by a passing beam of a helium - neon laser is studied by the developed methods of singular optics. For the polarisation singularities (C points), a new class of chain reactions, namely, singular chain reactions are discovered and studied. It is shown that they obey the topological charge and sum Poincare index conservation laws. In addition, they exist for all the time of crystal irradiation. They consist of a series of interlocking chains, where singularity pairs arising in amore » chain annihilate with singularities from neighbouring independently created chains. Less often singular 'loop' reactions are observed where arising pairs of singularities annihilate after reversible transformations in within the boundaries of a single speckle. The type of a singular reaction is determined by a topology and dynamics of the speckles, in which the reactions are developing. (laser optics 2012)« less

Geometric charges in theories of elasticity and plasticity

NASA Astrophysics Data System (ADS)

Moshe, Michael

The mechanics of many natural systems is governed by localized sources of stresses. Examples include ''plastic events'' that occur in amorphous solids under external stress, defects formation in crystalline material, and force-dipoles applied by cells adhered to an elastic substrate. Recent developments in a geometric formulation of elasticity theory paved the way for a unifying mathematical description of such singular sources of stress, as ''elastic charges''. In this talk I will review basic results in this emerging field, focusing on the geometry and mechanics of elastic charges in two-dimensional solid bodies. I will demonstrate the applicability of this new approach in three different problems: failure of an amorphous solid under load, mechanics of Kirigami, and wrinkle patterns in geometrically-incompatible elastic sheets.

Singular orientations and faceted motion of dislocations in body-centered cubic crystals.

PubMed

Kang, Keonwook; Bulatov, Vasily V; Cai, Wei

2012-09-18

Dislocation mobility is a fundamental material property that controls strength and ductility of crystals. An important measure of dislocation mobility is its Peierls stress, i.e., the minimal stress required to move a dislocation at zero temperature. Here we report that, in the body-centered cubic metal tantalum, the Peierls stress as a function of dislocation orientation exhibits fine structure with several singular orientations of high Peierls stress-stress spikes-surrounded by vicinal plateau regions. While the classical Peierls-Nabarro model captures the high Peierls stress of singular orientations, an extension that allows dislocations to bend is necessary to account for the plateau regions. Our results clarify the notion of dislocation kinks as meaningful only for orientations within the plateau regions vicinal to the Peierls stress spikes. These observations lead us to propose a Read-Shockley type classification of dislocation orientations into three distinct classes-special, vicinal, and general-with respect to their Peierls stress and motion mechanisms. We predict that dislocation loops expanding under stress at sufficiently low temperatures, should develop well defined facets corresponding to two special orientations of highest Peierls stress, the screw and the M111 orientations, both moving by kink mechanism. We propose that both the screw and the M111 dislocations are jointly responsible for the yield behavior of BCC metals at low temperatures.

Directional stability of crack propagation

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

Streit, R.D.; Finnie, I.

Despite many alternative models, the original Erdogan and Sih (1963) hypothesis that a crack will grow in the direction perpendicular to the maximum circumferential stress sigma/sub theta/ is seen to be adequate for predicting the angle of crack growth under the condition of mixed mode loading. Their predictions, which were based on the singularity terms in the series expansion for the Mode I and Mode II stress fields, can be improved if the second term in the series is also included. Although conceptually simple, their predictions of the crack growth direction fit very closely to the data obtained from manymore » sources.« less

Incoherent averaging of phase singularities in speckle-shearing interferometry.

PubMed

Mantel, Klaus; Nercissian, Vanusch; Lindlein, Norbert

2014-08-01

Interferometric speckle techniques are plagued by the omnipresence of phase singularities, impairing the phase unwrapping process. To reduce the number of phase singularities by physical means, an incoherent averaging of multiple speckle fields may be applied. It turns out, however, that the results may strongly deviate from the expected √N behavior. Using speckle-shearing interferometry as an example, we investigate the mechanism behind the reduction of phase singularities, both by calculations and by computer simulations. Key to an understanding of the reduction mechanism during incoherent averaging is the representation of the physical averaging process in terms of certain vector fields associated with each speckle field.

Initial singularity and pure geometric field theories

NASA Astrophysics Data System (ADS)

Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.

2018-01-01

In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.

Bonded orthotropic strips with cracks

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1979-01-01

The elastostatic problem for a nonhomogeneous plane which consists of two sets of periodically arranged dissimilar orthotropic strips is considered. It is assumed that the plane contains a series of collinear cracks perpendicular to the interfaces and is loaded in tension away from and perpendicular to the cracks. The problem of cracks fully imbedded into the homogeneous strips is considered. The singular behavior of the stresses for two special crack geometries is studied. The first is the case of a broken laminate in which the crack tips touch the interfaces. The second is the case of cracks crossing the interfaces. An interesting result found from the analysis of the latter is that for certain orthotropic material combinations the stress state at the point of intersection of a crack and an interface may be bounded whereas in isotropic materials at this point stresses are always singular. A number of numerical examples are worked out to separate the primary material parameters influencing the stress intensity factors and the powers of stress singularity, and to determine the trends regarding the influence of the secondary parameters. Some numerical results are given for the stress intensity factors in certain basic crack geometries and for typical material combinations.

Elasto-plastic flow in cracked bodies using a new finite element model. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Karabin, M. E., Jr.

1977-01-01

Cracked geometries were studied by finite element techniques with the aid of a new special element embedded at the crack tip. This model seeked to accurately represent the singular stresses and strains associated with the elasto-plastic flow process. The present model was not restricted to a material type and did not predetermine a singularity. Rather the singularity was treated as an unknown. For each step of the incremental process the nodal degrees of freedom and the unknown singularity were found through minimization of an energy-like functional. The singularity and nodal degrees of freedom were determined by means of an iterative process.

Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon

NASA Astrophysics Data System (ADS)

Kay, Bernard S.; Radzikowski, Marek J.; Wald, Robert M.

1997-02-01

We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, (M,g_{ab}), with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain base points of the Cauchy horizon, which are defined as 'past terminal accumulation points' of the horizon generators. Thus, the theorems may be interpreted as giving support to Hawking's 'Chronology Protection Conjecture', according to which the laws of physics prevent one from manufacturing a 'time machine'. Specifically, we prove: Theorem 1. There is no extension to (M,g_{ab}) of the usual field algebra on the initial globally hyperbolic region which satisfies the condition of F-locality at any base point. In other words, any extension of the field algebra must, in any globally hyperbolic neighbourhood of any base point, differ from the algebra one would define on that neighbourhood according to the rules for globally hyperbolic spacetimes. Theorem 2. The two-point distribution for any Hadamard state defined on the initial globally hyperbolic region must (when extended to a distributional bisolution of the covariant Klein-Gordon equation on the full spacetime) be singular at every base point x in the sense that the difference between this two point distribution and a local Hadamard distribution cannot be given by a bounded function in any neighbourhood (in M 2 M) of (x,x). In consequence of Theorem 2, quantities such as the renormalized expectation value of J2 or of the stress-energy tensor are necessarily ill-defined or singular at any base point. The proof of these theorems relies on the 'Propagation of Singularities' theorems of Duistermaat and Hörmander.

Cluster self-organization of nanotubes in a nematic phase: The percolation behavior and appearance of optical singularities

NASA Astrophysics Data System (ADS)

Ponevchinsky, V. V.; Goncharuk, A. I.; Vasil'Ev, V. I.; Lebovka, N. I.; Soskin, M. S.

2010-03-01

The structural features, as well as the optical and electrophysical properties of a 5CB nematic liquid crystal with additions of multilayer carbon nanotubes, have been investigated in the concentration range C = 0.0025-0.1 wt %. The self-aggregation of nanotubes into clusters with a fractal structure occurs in the liquid crystal. At 0.025 wt %, the clusters are merged, initiating the percolation transition of the composite to a state with a high electric conductivity. The strong interaction of 5CB molecules with the surface of nanotube clusters is responsible for the formation of micron surface liquid crystal layers with an irregular field of elastic stresses and a complex structure of birefringence. They are easily observed in a polarization microscope and visualize directly invisible submicron nanotube aggregates. Their transverse size increases when an electric field is applied to the liquid crystal cell. Two mechanisms of the generation of optical singularities in the passing laser beam have been revealed. Optical vortices appear in the speckle fields of laser radiation scattered at the indented boundaries of the nanotube clusters, whereas the birefringence of the beam in surface liquid-crystal layers is accompanied by the appearance of polarization C points.

Inflation and acceleration of the universe by nonlinear magnetic monopole fields

NASA Astrophysics Data System (ADS)

Övgün, A.

2017-02-01

Despite impressive phenomenological success, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. In the context of Friedmann-Robertson-Walker (FRW) spacetime, we show that singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory for strong fields. A new mathematical model is proposed for which the analytical nonsingular extension of FRW solutions is obtained by using the nonlinear magnetic monopole fields.

Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate.

PubMed

Kotlyar, Victor V; Almazov, Anton A; Khonina, Svetlana N; Soifer, Victor A; Elfstrom, Henna; Turunen, Jari

2005-05-01

We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularity's integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to rho2n, where p is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with nth-order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity (n = 2) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.

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

Alani, Ivo; Santillán, Osvaldo P., E-mail: firenzecita@hotmail.com, E-mail: osantil@dm.uba.ar

In the present work some generalizations of the Hawking singularity theorems in the context of f ( R ) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition ( T {sub ij} −( g {sub ij} /2) T ) k {sup i} k {sup j} ≥ 0 for any generic unit time like field k {sup i} ; the scalaron takes bounded positive values during its evolution and the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper-surface Σ for which the expansion parameter θ of the geodesic congruencemore » emanating orthogonally from Σ satisfies some specific bounds, then the resulting space time is geodesically incomplete. Some mathematical results of reference [92] are very important for proving this. The generalized theorems presented here apply directly for some specific models such as the Hu-Sawicki or Starobinsky ones [27,38]. For other scenarios, some extra assumptions should be implemented in order to have a geodesically incomplete space time. The hypothesis considered in this text are sufficient, but not necessary. In other words, their negation does not imply that a singularity is absent.« less

Evolution of singularities in a partially coherent vortex beam.

PubMed

van Dijk, Thomas; Visser, Taco D

2009-04-01

We study the evolution of phase singularities and coherence singularities in a Laguerre-Gauss beam that is rendered partially coherent by letting it pass through a spatial light modulator. The original beam has an on-axis minumum of intensity--a phase singularity--that transforms into a maximum of the far-field intensity. In contrast, although the original beam has no coherence singularities, such singularities are found to develop as the beam propagates. This disappearance of one kind of singularity and the gradual appearance of another is illustrated with numerical examples.

Tailored vectorial light fields: flower, spider web and hybrid structures

NASA Astrophysics Data System (ADS)

Otte, Eileen; Alpmann, Christina; Denz, Cornelia

2017-04-01

We present the realization and analysis of tailored vector fields including polarization singularities. The fields are generated by a holographic method based on an advanced system including a spatial light modulator. We demonstrate our systems capabilities realizing specifically customized vector fields including stationary points of defined polarization in its transverse plane. Subsequently, vectorial flowers and spider webs as well as unique hybrid structures of these are introduced, and embedded singular points are characterized. These sophisticated light fields reveal attractive properties that pave the way to advanced application in e.g. optical micromanipulation. Beyond particle manipulation, they contribute essentially to actual questions in singular optics.

On the Plasticity of Amorphous Solids

NASA Astrophysics Data System (ADS)

Lin, Jie

Mechanical behaviors of amorphous materials under external stress are central to various phenomena including earthquakes and landslides. Most amorphous materials possess a well defined yield stress when thermal fluctuations are negligible. Only when the shear stress is above the yield stress, the material can flow as a fluid, otherwise it deforms as a solid. There are accumulating evidences that the yielding transition between the flowing and solid phase is a critical phenomenon, and one evidence is the long ranged correlations of plastic strain during adiabatic shear. In spite of this, we still have not fully understood the associated critical exponents and their scaling relations. In the last decade, it has been widely accepted that the elementary rearrangements in amorphous solids are not well-defined topological defects as crystals, instead they are local irreversible rearrangements of a few particles, denoted as shear transformations. Because a single shear transformation changes the local arrangement of particles, it therefore generates an elastic stress field propagating over the whole system. The resulting changes in the local stresses in other regions of the system may in turn trigger more shear transformations. A central feature that complicates the yielding transition is the long range and anisotropic stress field generated by shear transformations. This peculiar interaction between shear transformations leads to two important characteristics: 1.the mechanical noises generated by plastic deformation are broadly distributed 2.those regions that are undergoing plastic deformation has equal probability to make other parts of the material to be more stable or more unstable, depending on the direction between them. In this thesis, we show that these two important factors leads to a singular density of shear transformations, P( x) xtheta at small x, where x is a local measure of stability, namely, the extra stress one needs to add locally to reach the elastic instabilities. We denote such a singular distribution as a pseudo gap, and the theta exponent as the pseudo gap exponent. The fact that the plastic avalanche rates, i.e., number of avalanches per unit strain, during quasi-static shear is not proportional to system size implies the existence of a finite pseudo gap exponent. Arguments based on stability against local perturbations lead to a lower bound of the pseudo gap exponents. In the flowing phase, we construct the scaling description of the yielding transition of soft amorphous solids at zero temperature. The yielding transition shares similarities with another well studied dynamic phase transition, the depinning transition where an elastic interface is driven in a disordered medium, however, there are also striking differences between them. Avalanches are fractal in the yielding transition, characterized by a fractal dimension smaller than the spatial dimension, while avalanches are compact with a fractal dimension, not smaller than the spatial dimension in the depinning transition. We make connections between the Herschel-Bulkley exponent characterizing the singularity of the flow curve near the yield stress, the extension and duration of the avalanches of plasticity, and the pseudo gap exponent. On the other hand, in the solid phase, the pseudo gap also plays a significant role as one increases the shear stress adiabatically. We point out the connection between the local slope of stress-strain curve in the transient state and mean avalanche sizes as the system approaches failure. We argue that the entire solid phase below the yield stress is critical as long as there is finite amount of plastic strain, and plasticity always involves system-spanning events because of the finite pseudo gap exponent. We use the elasto-plastic model, a mesoscopic approach, to verify our theoretical predictions and obtain satisfying results. Finally, a mean field description of plastic flow in amorphous solids are proposed and solved analytically. The mean field models captures the broad distribution of mechanical noise generated by plasticity, leading to a biased Levy flight behavior of local stresses, with the elastic instabilities as the absorbing boundary. The mean field model implies an upper critical dimension as dc = 4.

The Poincaré-Hopf Theorem for line fields revisited

NASA Astrophysics Data System (ADS)

Crowley, Diarmuid; Grant, Mark

2017-07-01

A Poincaré-Hopf Theorem for line fields with point singularities on orientable surfaces can be found in Hopf's 1956 Lecture Notes on Differential Geometry. In 1955 Markus presented such a theorem in all dimensions, but Markus' statement only holds in even dimensions 2 k ≥ 4. In 1984 Jänich presented a Poincaré-Hopf theorem for line fields with more complicated singularities and focussed on the complexities arising in the generalized setting. In this expository note we review the Poincaré-Hopf Theorem for line fields with point singularities, presenting a careful proof which is valid in all dimensions.

Singular cosmological evolution using canonical and ghost scalar fields

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

Nojiri, Shin'ichi; Odintsov, S.D.; Oikonomou, V.K.

2015-09-01

We demonstrate that finite time singularities of Type IV can be consistently incorporated in the Universe's cosmological evolution, either appearing in the inflationary era, or in the late-time regime. While using only one scalar field instabilities can in principle occur at the time of the phantom-divide crossing, when two fields are involved we are able to avoid such instabilities. Additionally, the two-field scalar-tensor theories prove to be able to offer a plethora of possible viable cosmological scenarios, at which various types of cosmological singularities can be realized. Amongst others, it is possible to describe inflation with the appearance of amore » Type IV singularity, and phantom late-time acceleration which ends in a Big Rip. Finally, for completeness, we also present the Type IV realization in the context of suitably reconstructed F(R) gravity.« less

On the Convergence of Stresses in Fretting Fatigue

PubMed Central

Pereira, Kyvia; Bordas, Stephane; Tomar, Satyendra; Trobec, Roman; Depolli, Matjaz; Kosec, Gregor; Abdel Wahab, Magd

2016-01-01

Fretting is a phenomenon that occurs at the contacts of surfaces that are subjected to oscillatory relative movement of small amplitudes. Depending on service conditions, fretting may significantly reduce the service life of a component due to fretting fatigue. In this regard, the analysis of stresses at contact is of great importance for predicting the lifetime of components. However, due to the complexity of the fretting phenomenon, analytical solutions are available for very selective situations and finite element (FE) analysis has become an attractive tool to evaluate stresses and to study fretting problems. Recent laboratory studies in fretting fatigue suggested the presence of stress singularities in the stick-slip zone. In this paper, we constructed finite element models, with different element sizes, in order to verify the existence of stress singularity under fretting conditions. Based on our results, we did not find any singularity for the considered loading conditions and coefficients of friction. Since no singularity was found, the present paper also provides some comments regarding the convergence rate. Our analyses showed that the convergence rate in stress components depends on coefficient of friction, implying that this rate also depends on the loading condition. It was also observed that errors can be relatively high for cases with a high coefficient of friction, suggesting the importance of mesh refinement in these situations. Although the accuracy of the FE analysis is very important for satisfactory predictions, most of the studies in the literature rarely provide information regarding the level of error in simulations. Thus, some recommendations of mesh sizes for those who wish to perform FE analysis of fretting problems are provided for different levels of accuracy. PMID:28773760

Appearance of singularities of optical fields under torsion of crystals containing threefold symmetry axes.

PubMed

Skab, Ihor; Vasylkiv, Yurij; Zapeka, Bohdan; Savaryn, Viktoriya; Vlokh, Rostyslav

2011-07-01

We present an analysis of the effect of torsion stresses on the spatial distribution of optical birefringence in crystals of different point symmetry groups. The symmetry requirements needed so that the optical beam carries dislocations of the phase front are evaluated for the case when the crystals are twisted and the beam closely corresponds to a plane wave. It is shown that the torsion stresses can produce screw-edge, pure screw, or pure edge dislocations of the phase front in the crystals belonging to cubic and trigonal systems. The conditions for appearance of canonical and noncanonical vortices in the conditions of crystal torsion are analyzed. © 2011 Optical Society of America

Workshop on Condition Based Maintenance Held in Atlantic Beach, North Carolina on November 15 - 17, 1993

DTIC Science & Technology

1993-11-17

pounds of Torque Over Three Minutes Continuous Operation IYMCO1A 14 DMAE Corporation C-130 Engine Gearbox January 19925 Stress Wave Analysis - I in’. I...FaUi.O The CBM needs associated with surface initiated failure mechanisms can be divided into I singular defects and low (h/a) operation. Singular defec-t...These include nicks, scratches, corrosion pits and dents caused by third’ body particles (hard or soft). These defects cause local stress risers

{lambda} elements for singular problems in CFD: Viscoelastic fluids

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

Wong, K.K.; Surana, K.S.

1996-10-01

This paper presents two dimensional {lambda} element formulation for viscoelastic fluid flow containing point singularities in the flow field. The flow of viscoelastic fluid even without singularities are a difficult class of problems for increasing Deborah number or Weissenburg number due to increased dominance of convective terms and thus increased hyperbolicity. In the present work the equations of fluid motion and the constitutive laws are recast in the form of a first order system of coupled equations with the use of auxiliary variables. The velocity, pressure and stresses are interpolated using equal order C{sup 0} {lambda} element approximations. The Leastmore » Squares Finite Element Method (LSFEM) is used to construct the integral form (error functional I) corresponding to these equations. The error functional is constructed by taking the integrated sum of the squares of the errors or residuals (over the whole discretization) resulting when the element approximation is substituted into these equations. The conditions resulting from the minimization of the error functional are satisfied by using Newton`s method with line search. LSFEM has much superior performance when dealing with non-linear and convection dominated problems.« less

Tests of conformal field theory at the Yang-Lee singularity

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

Wydro, Tomasz; McCabe, John F.

2009-12-14

This paper studies the Yang-Lee edge singularity of 2-dimensional (2D) Ising model based on a quantum spin chain and transfer matrix measurements on the cylinder. Based on finite-size scaling, the low-lying excitation spectrum is found at the Yang-Lee edge singularity. Based on transfer matrix techniques, the single structure constant is evaluated at the Yang-Lee edge singularity. The results of both types of measurements are found to be fully consistent with the predictions for the (A{sub 4}, A{sub 1}) minimal conformal field theory, which was previously identified with this critical point.

Quantum probe of Hořava-Lifshitz gravity

NASA Astrophysics Data System (ADS)

Gurtug, O.; Mangut, M.

2018-04-01

Particle probe analysis of the Kehagias-Sfetsos black hole spacetime of Hořava-Lifshitz gravity is extended to wave probe analysis within the framework of quantum mechanics. The time-like naked singularity that develops when ωM2 < 1/2 is probed with quantum fields obeying Klein-Gordon and Chandrasekhar-Dirac equations. The quantum field probe of the naked singularity has revealed that both the spatial part of the wave and the Hamiltonian operators of Klein-Gordon and Chandrasekhar-Dirac equations are essentially self-adjoint, and thus, the naked singularity in the Kehagias-Sfetsos spacetime becomes quantum mechanically non-singular.

Numerical methods for coupled fracture problems

NASA Astrophysics Data System (ADS)

Viesca, Robert C.; Garagash, Dmitry I.

2018-04-01

We consider numerical solutions in which the linear elastic response to an opening- or sliding-mode fracture couples with one or more processes. Classic examples of such problems include traction-free cracks leading to stress singularities or cracks with cohesive-zone strength requirements leading to non-singular stress distributions. These classical problems have characteristic square-root asymptotic behavior for stress, relative displacement, or their derivatives. Prior work has shown that such asymptotics lead to a natural quadrature of the singular integrals at roots of Chebyhsev polynomials of the first, second, third, or fourth kind. We show that such quadratures lead to convenient techniques for interpolation, differentiation, and integration, with the potential for spectral accuracy. We further show that these techniques, with slight amendment, may continue to be used for non-classical problems which lack the classical asymptotic behavior. We consider solutions to example problems of both the classical and non-classical variety (e.g., fluid-driven opening-mode fracture and fault shear rupture driven by thermal weakening), with comparisons to analytical solutions or asymptotes, where available.

Implementation of equivalent domain integral method in the two-dimensional analysis of mixed mode problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Shivakumar, K. N.

1989-01-01

An equivalent domain integral (EDI) method for calculating J-intergrals for two-dimensional cracked elastic bodies is presented. The details of the method and its implementation are presented for isoparametric elements. The total and product integrals consist of the sum of an area of domain integral and line integrals on the crack faces. The line integrals vanish only when the crack faces are traction free and the loading is either pure mode 1 or pure mode 2 or a combination of both with only the square-root singular term in the stress field. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented. The procedure that uses the symmetric and antisymmetric components of the stress and displacement fields to calculate the individual modes gave accurate values of the integrals for all problems analyzed. The EDI method when applied to a problem of an interface crack in two different materials showed that the mode 1 and mode 2 components are domain dependent while the total integral is not. This behavior is caused by the presence of the oscillatory part of the singularity in bimaterial crack problems. The EDI method, thus, shows behavior similar to the virtual crack closure method for bimaterial problems.

Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field

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

Ryabov, Pavel E; Kharlamov, Mikhail P

2012-02-28

The problem of motion of the Kovalevskaya top in a double force field is investigated (the integrable case of A.G. Reyman and M.A. Semenov-Tian-Shansky without a gyrostatic momentum). It is a completely integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems with two degrees of freedom. The critical set of the integral map is studied. The critical subsystems and bifurcation diagrams are described. The classification of all nondegenerate critical points is given. The set of these points consists of equilibria (nondegenerate singularities of rank 0), of singular periodic motions (nondegenerate singularities of rank 1),more » and also of critical two-frequency motions (nondegenerate singularities of rank 2). Bibliography: 32 titles.« less

Singular reduction of resonant Hamiltonians

NASA Astrophysics Data System (ADS)

Meyer, Kenneth R.; Palacián, Jesús F.; Yanguas, Patricia

2018-06-01

We investigate the dynamics of resonant Hamiltonians with n degrees of freedom to which we attach a small perturbation. Our study is based on the geometric interpretation of singular reduction theory. The flow of the Hamiltonian vector field is reconstructed from the cross sections corresponding to an approximation of this vector field in an energy surface. This approximate system is also built using normal forms and applying reduction theory obtaining the reduced Hamiltonian that is defined on the orbit space. Generically, the reduction is of singular character and we classify the singularities in the orbit space, getting three different types of singular points. A critical point of the reduced Hamiltonian corresponds to a family of periodic solutions in the full system whose characteristic multipliers are approximated accordingly to the nature of the critical point.

Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d-dimensional hypercubic lattices: A series expansion study.

PubMed

Singh, R R P; Young, A P

2017-08-01

We study the ±J transverse-field Ising spin-glass model at zero temperature on d-dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d=6, which is below the upper critical dimension of d=8. In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d -dimensional hypercubic lattices: A series expansion study

NASA Astrophysics Data System (ADS)

Singh, R. R. P.; Young, A. P.

2017-08-01

We study the ±J transverse-field Ising spin-glass model at zero temperature on d -dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d =6 , which is below the upper critical dimension of d =8 . In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

Stress intensity factors for bonded orthotropic strips with cracks

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1978-01-01

The elastostatic problem for a nonhomogeneous plane which consists of two sets of periodically arranged dissimilar orthotropic strips is considered. It is assumed that the plane contains a series of collinear cracks perpendicular to the interfaces and is loaded in tension away from and perpendicular to the cracks. Cracks fully imbedded into the homogenous strips were analyzed as well as the singular behavior of the stresses for two special crack geometries. The analysis of cracks crossing interfaces indicates that, for certain orthotropic material combinations, the stress state at the point of intersection of a crack and an interface may be bounded. A number of numerical examples are worked out in order to separate the primary material parameters influencing the stress intensity factors and the powers of stress singularity, and to determine the trends regarding the influence of the secondary parameters.

Calculating corner singularities by boundary integral equations.

PubMed

Shi, Hualiang; Lu, Ya Yan; Du, Qiang

2017-06-01

Accurate numerical solutions for electromagnetic fields near sharp corners and edges are important for nanophotonics applications that rely on strong near fields to enhance light-matter interactions. For cylindrical structures, the singularity exponents of electromagnetic fields near sharp edges can be solved analytically, but in general the actual fields can only be calculated numerically. In this paper, we use a boundary integral equation method to compute electromagnetic fields near sharp edges, and construct the leading terms in asymptotic expansions based on numerical solutions. Our integral equations are formulated for rescaled unknown functions to avoid unbounded field components, and are discretized with a graded mesh and properly chosen quadrature schemes. The numerically found singularity exponents agree well with the exact values in all the test cases presented here, indicating that the numerical solutions are accurate.

Interface with weakly singular points always scatter

NASA Astrophysics Data System (ADS)

Li, Long; Hu, Guanghui; Yang, Jiansheng

2018-07-01

Assume that a bounded scatterer is embedded into an infinite homogeneous isotropic background medium in two dimensions. The refractive index function is supposed to be piecewise constant. If the scattering interface contains a weakly singular point, we prove that the scattered field cannot vanish identically. This implies the absence of non-scattering energies for piecewise analytic interfaces with one singular point. Local uniqueness is obtained for shape identification problems in inverse medium scattering with a single far-field pattern.

The Friedmann-Lemaître-Robertson-Walker Big Bang Singularities are Well Behaved

NASA Astrophysics Data System (ADS)

Stoica, Ovidiu Cristinel

2016-01-01

We show that the Big Bang singularity of the Friedmann-Lemaître-Robertson-Walker model does not raise major problems to General Relativity. We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang. The physical interpretation of the fields used is discussed. These results follow from our research on singular semi-Riemannian geometry and singular General Relativity.

Finite element simulation and analysis of local stress concentration in polymers with a nonlinear viscoelastic constitutive model

NASA Astrophysics Data System (ADS)

Chea, Limdara O.

Given a nonlinear viscoelastic (NLVE) constitutive model for a polymer, this numerical study aims at simulating local stress concentrations in a boundary value problem with a corner stress singularity. A rectangular sample of Polyvinyl Acetate (PVAc)-like cross-linked polymer clamped by two metallic rigid grips and subjected to a compression and tension load is numerically simulated. A modified version of the finite element code FEAP, that incorporated a NLVE model based on the free volume theory, was used. First, the program was validated by comparing numerical and analytical results. Two simple mechanical tests (a uniaxial and a simple shear test) were performed on a Standard Linear Solid material model, using a linear viscoelastic (LVE) constitutive model. The LVE model was obtained by setting the proportionality coefficient [...] to zero in the free volume theory equations. Second, the LVE model was used on the corner singularity boundary value problem for three material models with different bulk relaxation functions K(t). The time-dependent stress field distribution was investigated using two sets of plots: the stress distribution contour plots and the stress time curves. Third, using the NLVE constitutive model, compression and tension cases were compared using the stress results (normal stress [...] and shear stress [...]). These two cases assessed the effect of the creep retardation-creep acceleration phenomena. The shift between the beginning of the relaxation moduli was shown to play an important role. This parameter affects strongly the fluctuation pattern of the stress curves. For two different shift values, in one case, the stress response presents a 'double peak' and 'stress inversion' characteristic whereas, in the other case, it presents a 'single peak' and no 'inversion'. Another important factor was the material's compressibility. In the case of a nearly-incompressible material, the LVE and NLVE models yielded identical results; thus, the simpler LVE model is preferable. However, in the case of sufficient volume dilatation (or contraction), the NLVE model predicted correct characteristic responses, whereas LVE results were erroneous. This proves the necessity of using the NLVE model over the LVE model.

Bonded orthotropic strips with cracks

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1978-01-01

The elastostatic problem for a nonhomogeneous plane which consists of two sets of periodically arranged dissimilar orthotropic strips is considered. First, the problem of cracks fully imbedded into the homogeneous strips is considered. Then, the singular behavior of the stresses for two special crack geometries is studied in some detail. The first is the case of a broken laminate in which the crack tips touch the interfaces. The second is the case of cracks crossing the interfaces. A number of numerical examples are worked out in order to separate the primary material parameters influencing the stress intensity factors and the powers of stress singularity, and to determine the trends regarding the influence of the secondary parameters. Finally, some numerical results are given for the stress intensity factors in certain basic crack geometries and for typical material combinations.

Steady sliding frictional contact problem for a 2d elastic half-space with a discontinuous friction coefficient and related stress singularities

NASA Astrophysics Data System (ADS)

Ballard, Patrick

2016-12-01

The steady sliding frictional contact problem between a moving rigid indentor of arbitrary shape and an isotropic homogeneous elastic half-space in plane strain is extensively analysed. The case where the friction coefficient is a step function (with respect to the space variable), that is, where there are jumps in the friction coefficient, is considered. The problem is put under the form of a variational inequality which is proved to always have a solution which, in addition, is unique in some cases. The solutions exhibit different kinds of universal singularities that are explicitly given. In particular, it is shown that the nature of the universal stress singularity at a jump of the friction coefficient is different depending on the sign of the jump.

Can accretion disk properties observationally distinguish black holes from naked singularities?

NASA Astrophysics Data System (ADS)

Kovács, Z.; Harko, T.

2010-12-01

Naked singularities are hypothetical astrophysical objects, characterized by a gravitational singularity without an event horizon. Penrose has proposed a conjecture, according to which there exists a cosmic censor who forbids the occurrence of naked singularities. Distinguishing between astrophysical black holes and naked singularities is a major challenge for present day observational astronomy. In the context of stationary and axially symmetrical geometries, a possibility of differentiating naked singularities from black holes is through the comparative study of thin accretion disks properties around rotating naked singularities and Kerr-type black holes, respectively. In the present paper, we consider accretion disks around axially-symmetric rotating naked singularities, obtained as solutions of the field equations in the Einstein-massless scalar field theory. A first major difference between rotating naked singularities and Kerr black holes is in the frame dragging effect, the angular velocity of a rotating naked singularity being inversely proportional to its spin parameter. Because of the differences in the exterior geometry, the thermodynamic and electromagnetic properties of the disks (energy flux, temperature distribution and equilibrium radiation spectrum) are different for these two classes of compact objects, consequently giving clear observational signatures that could discriminate between black holes and naked singularities. For specific values of the spin parameter and of the scalar charge, the energy flux from the disk around a rotating naked singularity can exceed by several orders of magnitude the flux from the disk of a Kerr black hole. In addition to this, it is also shown that the conversion efficiency of the accreting mass into radiation by rotating naked singularities is always higher than the conversion efficiency for black holes, i.e., naked singularities provide a much more efficient mechanism for converting mass into radiation than black holes. Thus, these observational signatures may provide the necessary tools from clearly distinguishing rotating naked singularities from Kerr-type black holes.

Singular Behaviour of the Electrodynamic Fields of an Oscillating Dipole

ERIC Educational Resources Information Center

Leung, P. T.

2008-01-01

The singularity of the exact electromagnetic fields is derived to include the "source terms" for harmonically oscillating electric (and magnetic) dipoles, so that the fields will be consistent with the full Maxwell equations with a source. It is shown explicitly, as somewhat expected, that the same [delta]-function terms for the case of static…

EDITORIAL: The plurality of optical singularities

NASA Astrophysics Data System (ADS)

Berry, Michael; Dennis, Mark; Soskin, Marat

2004-05-01

This collection of papers arose from an Advanced Research Workshop on Singular Optics, held at the Bogolyubov Institute in Kiev, Ukraine, during 24-28 June 2003. The workshop was generously financed by NATO, with welcome additional support from Institute of Physics Publishing and the National Academy of Sciences of Ukraine. There had been two previous international meetings devoted to singular optics, in Crimea in 1997 and 2000, reflecting the strong involvement of former Soviet Union countries in this research. Awareness of singular optics is growing within the wider optics community, indicated by symposia on the subject at several general optics meetings. As the papers demonstrate, the field of singular optics has reached maturity. Although the subject originated in an observation on ultrasound, it has been largely theory-driven until recently. Now, however, there is close contact between theory and experiment, and we speculate that this is one reason for its accelerated development. To single out particular papers for mention here would be invidious, and since the papers speak for themselves it is not necessary to describe them all. Instead, we will confine ourselves to a brief description of the main areas included in singular optics, to illustrate the broad scope of the subject. Optical vortices are lines of phase singularity: nodal lines where the intensity of the light, represented by a complex scalar field, vanishes. The subject has emerged from flatland, where the vortices are points characterized by topological charges, into the much richer world of vortex lines in three dimensions. By combining Laguerre-Gauss or Bessel beams, or reflecting light from plates with spiral steps, intricate arrangements can be generated, with vortices that are curved, looped, knotted, linked or braided. With light whose state of polarization varies with position, different singularities occur, associated with the vector nature of light. These are also lines, on which the electric (or magnetic) polarization ellipse is purely circular (C lines) or purely linear (L lines). The patterns of ellipse-fields are different for purely paraxial and fully three-dimensional fields. White-light diffraction generates richly coloured vortices—the colours of dark light. The description of these chromatic effects, and also those associated with polarization singularities, leads to new applications of coherence theory. For non-monochromatic light, it is natural to seek singularities of the full electromagnetic field, rather than of the electric or magnetic field separately. Such electromagnetic singularities are the Riemann-Silberstein vortices; these are relativistically covariant nodal lines of a complex scalar field constructed from the electromagnetic field. Optical fields have dynamical aspects, particularly those associated with angular momentum. Although angular momentum is not inevitably associated with optical singularities, in practice the two phenomena can occur together. Orbital angular momentum is associated with the spatial structure of light, and in beams with optical vortices it can be used to rotate particles in the field. Spin angular momentum is associated with the polarization structure of the light. There are tricky questions associated with the angular momentum of light in a refracting medium, echoing the Abraham-Minkowski controversy about linear momentum. In optically nonlinear materials (leading to second-harmonic generation, for example), new classes of phenomena can occur, such as, for example, dynamical interaction between vortex lines, whose stability needs to be considered. At a more fundamental level, it is important to investigate quantum effects associated with optical singularities, and a start has been made. The dark centre of an optical vortex can be regarded as a window onto the vacuum fluctuations of quantum optics, with the quantum core emerging as a distinct entity when the classical light is intense. And for light in a rapidly and inhomogeneously flowing material, horizons can develop, analogous to those surrounding black holes in general relativity, and these new optical singularities can be regarded as wave catastrophes, and new associated quantum effects anticipated. Three decades after wave dislocations were introduced as ‘a new concept in ... wave theory’, these phase singularities have been extensively explored and are now familiar. New ideas—in addition to those described in this special issue—continue to emerge. For example, x-ray vortices were observed recently; there is a proposal to create lenses to form atomic beams containing vortices; and astrophysical applications have been suggested for both photon orbital angular momentum and optical vortices. We can safely assume that the science of wave singularities will develop further, and diffuse into new areas of physics.

Towards timelike singularity via AdS dual

NASA Astrophysics Data System (ADS)

Bhowmick, Samrat; Chatterjee, Soumyabrata

2017-07-01

It is well known that Kasner geometry with spacelike singularity can be extended to bulk AdS-like geometry, furthermore, one can study field theory on this Kasner space via its gravity dual. In this paper, we show that there exists a Kasner-like geometry with timelike singularity for which one can construct a dual gravity description. We then study various extremal surfaces including spacelike geodesics in the dual gravity description. Finally, we compute correlators of highly massive operators in the boundary field theory with a geodesic approximation.

Phase singularities, correlation singularities, and conditions for complete destructive interference.

PubMed

Rosenbury, Christopher; Gu, Yalong; Gbur, Greg

2012-04-01

A previously derived condition for the complete destructive interference of partially coherent light emerging from a trio of pinholes in an opaque screen is generalized to the case when the coherence properties of the field are asymmetric. It is shown by example that the interference condition is necessary, but not sufficient, and that the existence of complete destructive interference also depends on the intensity of light emerging from the pinholes and the system geometry; more general conditions for such interference are derived. The phase of the wave field exhibits both phase singularities and correlation singularities, and a number of nonintuitive situations in which complete destructive interference occurs are described and explained.

Black hole solutions in mimetic Born-Infeld gravity

NASA Astrophysics Data System (ADS)

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

2018-01-01

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularity is found to be infinite.

Black hole solutions in mimetic Born-Infeld gravity.

PubMed

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

2018-01-01

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularity is found to be infinite.

Criticality and big brake singularities in the tachyonic evolutions of closed Friedmann universes with cold dark matter

NASA Astrophysics Data System (ADS)

Horváth, Zsolt; Keresztes, Zoltán; Kamenshchik, Alexander Yu.; Gergely, László Á.

2015-05-01

The evolution of a closed Friedmann universe filled by a tachyon scalar field with a trigonometric potential and cold dark matter (CDM) is investigated. A subset of the evolutions consistent to 1 σ confidence level with the Union 2.1 supernova data set is identified. The evolutions of the tachyon field are classified. Some of them evolve into a de Sitter attractor, while others proceed through a pseudotachyonic regime into a sudden future singularity. Critical evolutions leading to big brake singularities in the presence of CDM are found and a new type of cosmological evolution characterized by singularity avoidance in the pseudotachyon regime is presented.

Collapse of a self-similar cylindrical scalar field with non-minimal coupling II: strong cosmic censorship

NASA Astrophysics Data System (ADS)

Condron, Eoin; Nolan, Brien C.

2014-08-01

We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is shown that the scalar field is dependent on a single unknown function of the same variable and that the scalar field potential has exponential form. The Einstein equations then take the form of a set of ODEs. Self-similarity also gives rise to a singularity at the scaling origin. We extend the work of Condron and Nolan (2014 Class. Quantum Grav. 31 015015), which determined the global structure of all solutions with a regular axis in the causal past of the singularity. We identified a class of solutions that evolves through the past null cone of the singularity. We give the global structure of these solutions and show that the singularity is censored in all cases.

Magnetic charge and photon mass: Physical string singularities, Dirac condition, and magnetic confinement

NASA Astrophysics Data System (ADS)

Evans, Timothy J.; Singleton, Douglas

2018-04-01

We find exact, simple solutions to the Proca version of Maxwell’s equations with magnetic sources. Several properties of these solutions differ from the usual case of magnetic charge with a massless photon: (i) the string singularities of the usual 3-vector potentials become real singularities in the magnetic fields; (ii) the different 3-vector potentials become gauge inequivalent and physically distinct solutions; (iii) the magnetic field depends on r and 𝜃 and thus is no longer rotationally symmetric; (iv) a combined system of electric and magnetic charge carries a field angular momentum even when the electric and magnetic charges are located at the same place (i.e. for dyons); (v) for these dyons, one recovers the standard Dirac condition despite the photon being massive. We discuss the reason for this. We conclude by proposing that the string singularity in the magnetic field of an isolated magnetic charge suggests a confinement mechanism for magnetic charge, similar to the flux tube confinement of quarks in QCD.

Investigation of the stress distribution around a mode 1 crack with a novel strain gradient theory

NASA Astrophysics Data System (ADS)

Lederer, M.; Khatibi, G.

2017-01-01

Stress concentrations at the tip of a sharp crack have extensively been investigated in the past century. According to the calculations of Inglis, the stress ahead of a mode 1 crack shows the characteristics of a singularity. This solution is exact in the framework of linear elastic fracture mechanics (LEFM). From the viewpoint of multiscale modelling, however, it is evident that the stress at the tip of a stable crack cannot be infinite, because the strengths of atomic bonds are finite. In order to prevent the problem of this singularity, a new version of strain gradient elasticity is employed here. This theory is implemented in the commercial FEM code ABAQUS through user subroutine UEL. Convergence of the model is proved through consecutive mesh refinement. In consequence, the stresses ahead of a mode 1 crack become finite. Furthermore, the model predicts a size effect in the sense “smaller is stronger”.

Generation of fractional acoustic vortex with a discrete Archimedean spiral structure plate

NASA Astrophysics Data System (ADS)

Jia, Yu-Rou; Wei, Qi; Wu, Da-Jian; Xu, Zheng; Liu, Xiao-Jun

2018-04-01

Artificial structure plates engraved with discrete Archimedean spiral slits have been well designed to achieve fractional acoustic vortices (FAVs). The phase and pressure field distributions of FAVs are investigated theoretically and demonstrated numerically. It is found that the phase singularities relating to the integer and fractional parts of the topological charge (TC) result in dark spots in the upper half of the pressure field profile and a low-intensity stripe in the lower half of the pressure field profile, respectively. The dynamic progress of the FAV is also discussed in detail as TC increases from 1 to 2. With increasing TC from 1 to 1.5, the splitting of the phase singularity leads to the deviation of the phase of the FAV from the integer case and hence a new phase singularity occurs. As TC m increases from 1.5 to 2, two phase singularities of the FAV approach together and finally merge as a new central phase singularity. We further perform an experiment based on the Schlieren method to demonstrate the generation of the FAV.

New method for detecting singularities in experimental incompressible flows

NASA Astrophysics Data System (ADS)

Kuzzay, Denis; Saw, Ewe-Wei; Martins, Fabio J. W. A.; Faranda, Davide; Foucaut, Jean-Marc; Daviaud, François; Dubrulle, Bérengère

2017-06-01

We introduce two new criteria based on the work of Duchon and Robert (2000 Nonlinearity 13 249) and Eyink (2006 Phys. Rev. E 74 066302), which allow for the local detection of Navier-Stokes singularities in experimental flows. We discuss the difference between non-dissipative or dissipative Euler quasi-singularities and genuine Navier-Stokes dissipative singularites, and classify them with respect to their Hölder exponent h. We show that our criteria allow us to detect areas in a flow where the velocity field is no more regular than Hölder continuous with some Hölder exponent h ≤slant 1/2 . We illustrate our discussion using classical tomographic particle image velocimetry (TPIV) measurements obtained inside a high Reynolds number flow generated in the boundary layer of a wind tunnel. Our study shows that, in order to detect singularities or quasi-singularities, one does not need to have access to the whole velocity field inside a volume, but can instead look for them from stereoscopic PIV data on a plane. We also provide a discussion about the link between areas detected by our criteria and areas corresponding to large vorticity. We argue that this link might provide either a clue about the genesis of these quasi-singularities or a way to discriminate dissipative Euler quasi-singularities and genuine Navier-Stokes singularities.

Influence of vorticity distribution on singularities in linearized supersonic flow

NASA Astrophysics Data System (ADS)

Gopal, Vijay; Maddalena, Luca

2018-05-01

The linearized steady three-dimensional supersonic flow can be analyzed using a vector potential approach which transforms the governing equation to a standard form of two-dimensional wave equation. Of particular interest are the canonical horseshoe line-vortex distribution and the resulting induced velocity field in supersonic flow. In this case, the singularities are present at the vortex line itself and also at the surface of the cone of influence originating from the vertices of the horseshoe structure. This is a characteristic of the hyperbolic nature of the flow which renders the study of supersonic vortex dynamics a challenging task. It is conjectured in this work that the presence of the singularity at the cone of influence is associated with the step-function nature of the vorticity distribution specified in the canonical case. At the phenomenological level, if one considers the three-dimensional steady supersonic flow, then a sudden appearance of a line-vortex will generate a ripple of singularities in the induced velocity field which convect downstream and laterally spread, at the most, to the surface of the cone of influence. Based on these findings, this work includes an exploration of potential candidates for vorticity distributions that eliminate the singularities at the cone of influence. The analysis of the resulting induced velocity field is then compared with the canonical case, and it is observed that the singularities were successfully eliminated. The manuscript includes an application of the proposed method to study the induced velocity field in a confined supersonic flow.

2 + 1 dimensional de Sitter universe emerging from the gauge structure of a nonlinear quantum system.

PubMed

Kam, Chon-Fai; Liu, Ren-Bao

2017-08-29

Berry phases and gauge structures are fundamental quantum phenomena. In linear quantum mechanics the gauge field in parameter space presents monopole singularities where the energy levels become degenerate. In nonlinear quantum mechanics, which is an effective theory of interacting quantum systems, there can be phase transitions and hence critical surfaces in the parameter space. We find that these critical surfaces result in a new type of gauge field singularity, namely, a conic singularity that resembles the big bang of a 2 + 1 dimensional de Sitter universe, with the fundamental frequency of Bogoliubov excitations acting as the cosmic scale, and mode softening at the critical surface, where the fundamental frequency vanishes, causing a causal singularity. Such conic singularity may be observed in various systems such as Bose-Einstein condensates and molecular magnets. This finding offers a new approach to quantum simulation of fundamental physics.

Naked singularities are not singular in distorted gravity

NASA Astrophysics Data System (ADS)

Garattini, Remo; Majumder, Barun

2014-07-01

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheele-DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.

New singularities in unexpected places

NASA Astrophysics Data System (ADS)

Barrow, John D.; Graham, Alexander A. H.

2015-09-01

Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature invariants. So far, these singularities have appeared to require rather exotic and unphysical matter for their occurrence. Here, we show that a large class of singularities of this form can be found in a simple Friedmann cosmology containing only a scalar-field with a power-law self-interaction potential. Their existence challenges several preconceived ideas about the nature of spacetime singularities and has an impact upon the end of inflation in the early universe.

Dynamic fields near a crack tip growing in an elastic-perfectly-plastic solid

NASA Technical Reports Server (NTRS)

Nemat-Nasser, S.; Gao, Y. C.

1983-01-01

A full asymptotic solution is presented for the fields in the neighborhood of the tip of a steadily advancing crack in an incompressible elastic-perfectly-plastic solid. There are four findings for mode I crack growth in the plane strain condition. The first is that the entire crack tip in steady crack growth is surrounded by a plastic region and that no elastic unloading is predicted by the complete dynamic asymptotic solution. The second is that, in contrast to the quasi-static solution, the dynamic solution yields strain fields with a logarithmic singularity everywhere near the crack tip. The third is that whereas the stress field varies throughout the entire crack tip neighborhood, it does not exhibit behavior that can be approximated by a constant field followed by an essentially centered-fan field and then by another constant field, especially for small crack growth speeds. The fourth finding is that there are two shock fronts emanating from the crack tip across which certain stress and strain components undergo jump discontinuities. After reviewing the mode III steady-state crack growth, it is concluded that ductile fracture criteria for nonstationary cracks must be based on solutions that include the inertia effects and that for this purpose quasi-static solutions may be inadequate.

A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods.

PubMed

Li, Xiaofan; Nie, Qing

2009-07-01

Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green's functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated.

A cylindrical shell with a stress-free end which contains an axial part-through or through crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Yahsi, O. S.

1985-01-01

The interaction problem of a through or a part through crack with a stress free boundary in a semi-infinite cylindrical shell is considered. It is assumed that the crack lies in a meridional plane which is a plane of symmetry with respect to the external loads as well as the geometry. The circular boundary of the semi-infinite cylinder is assumed to be stress free. By using a transverse shear theory the problem is formulated in terms of a system of singular integral equations. The line spring model is used to treat the part through crack problem. In the case of a through crack the interaction between the perturbed stress fields due to the crack and the free boundary is quite strong and there is a considerable increase in the stress intensity factors caused by the interaction. On the other hand in the problem of a surface crack the interaction appears to be much weaker and consequently the magnification in the stress intensity factors is much less significant.

A cylindrical shell with a stress-free end which contains an axial part-through or through crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Yahsi, O. S.

1983-01-01

The interaction problem of a through or a part through crack with a stress free boundary in a semi-infinite cylindrical shell is considered. It is assumed that the crack lies in a meridional plane which is a plane of symmetry with respect to the external loads as well as the geometry. The circular boundary of the semi-infinite cylinder is assumed to be stress free. By using a transverse shear theory the problem is formulated in terms of a system of singular integral equations. The line spring model is used to treat the part through crack problem. In the case of a through crack the interaction between the perturbed stress fields due to the crack and the free boundary is quite strong and there is a considerable increase in the stress intensity factors caused by the interaction. On the other hand in the problem of a surface crack the interaction appears to be much weaker and consequently the magnification in the stress intensity factors is much less significant.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1974-01-01

The plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle is discussed. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Contact and crack problems for an elastic wedge. [stress concentration in elastic half spaces

NASA Technical Reports Server (NTRS)

Erdogan, F.; Gupta, G. D.

1974-01-01

The contact and the crack problems for an elastic wedge of arbitrary angle are considered. The problem is reduced to a singular integral equation which, in the general case, may have a generalized Cauchy kernel. The singularities under the stamp as well as at the wedge apex were studied, and the relevant stress intensity factors are defined. The problem was solved for various wedge geometries and loading conditions. The results may be applicable to certain foundation problems and to crack problems in symmetrically loaded wedges in which cracks initiate from the apex.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1976-01-01

The paper deals with the plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Considerations on the moving contact-line singularity, with application to frictional drag on a slender drop

NASA Technical Reports Server (NTRS)

Durbin, P. A.

1988-01-01

It has previously been shown that the no-slip boundary conditions leads to a singularity at a moving contact line and that this presumes some form of slip. Present considerations on the energetics of slip due to shear stress lead to a yield stress boundary condition. A model for the distortion of the liquid state near solid boundaries gives a physical basis for this boundary condition. The yield stress condition is illustrated by an analysis of a slender drop rolling down an incline. That analysis provides a formula for the frictional drag resisting the drop movement. With the present boundary condition, the length of the slip region becomes a property of the fluid flow.

Singularity computations. [finite element methods for elastoplastic flow

NASA Technical Reports Server (NTRS)

Swedlow, J. L.

1978-01-01

Direct descriptions of the structure of a singularity would describe the radial and angular distributions of the field quantities as explicitly as practicable along with some measure of the intensity of the singularity. This paper discusses such an approach based on recent development of numerical methods for elastoplastic flow. Attention is restricted to problems where one variable or set of variables is finite at the origin of the singularity but a second set is not.

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2014-12-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees and orders, are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the higher-order partial derivatives of the magnetic field in local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (version 0.0) and the main magnetic field model of IGRF11. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the potential field.

Energy levels of a scalar particle in a static gravitational field close to the black hole limit

NASA Astrophysics Data System (ADS)

Gossel, G. H.; Berengut, J. C.; Flambaum, V. V.

2011-10-01

The bound-state energy levels of a scalar particle in the gravitational field of finite-sized objects with interiors described by the Florides and Schwarzschild metrics are found. For these metrics, bound states with zero energy (where the binding energy is equal to the rest mass of the scalar particle) only exist when a singularity occurs in the metric. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides metric the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the center. Moreover, the energy spectrum is shown to become quasi-continuous as the metric becomes singular.

Singular Stokes-polarimetry as new technique for metrology and inspection of polarized speckle fields

NASA Astrophysics Data System (ADS)

Soskin, Marat S.; Denisenko, Vladimir G.; Egorov, Roman I.

2004-08-01

Polarimetry is effective technique for polarized light fields characterization. It was shown recently that most full "finger-print" of light fields with arbitrary complexity is network of polarization singularities: C points with circular polarization and L lines with variable azimuth. The new singular Stokes-polarimetry was elaborated for such measurements. It allows define azimuth, eccentricity and handedness of elliptical vibrations in each pixel of receiving CCD camera in the range of mega-pixels. It is based on precise measurement of full set of Stokes parameters by the help of high quality analyzers and quarter-wave plates with λ/500 preciseness and 4" adjustment. The matrices of obtained data are processed in PC by special programs to find positions of polarization singularities and other needed topological features. The developed SSP technique was proved successfully by measurements of topology of polarized speckle-fields produced by multimode "photonic-crystal" fibers, double side rubbed polymer films, biomedical samples. Each singularity is localized with preciseness up to +/- 1 pixel in comparison with 500 pixels dimensions of typical speckle. It was confirmed that network of topological features appeared in polarized light field after its interaction with specimen under inspection is exact individual "passport" for its characterization. Therefore, SSP can be used for smart materials characterization. The presented data show that SSP technique is promising for local analysis of properties and defects of thin films, liquid crystal cells, optical elements, biological samples, etc. It is able discover heterogeneities and defects, which define essentially merits of specimens under inspection and can"t be checked by usual polarimetry methods. The detected extra high sensitivity of polarization singularities position and network to any changes of samples position and deformation opens quite new possibilities for sensing of deformations and displacement of checked elements in the sub-micron range.

Singular-Arc Time-Optimal Trajectory of Aircraft in Two-Dimensional Wind Field

NASA Technical Reports Server (NTRS)

Nguyen, Nhan

2006-01-01

This paper presents a study of a minimum time-to-climb trajectory analysis for aircraft flying in a two-dimensional altitude dependent wind field. The time optimal control problem possesses a singular control structure when the lift coefficient is taken as a control variable. A singular arc analysis is performed to obtain an optimal control solution on the singular arc. Using a time-scale separation with the flight path angle treated as a fast state, the dimensionality of the optimal control solution is reduced by eliminating the lift coefficient control. A further singular arc analysis is used to decompose the original optimal control solution into the flight path angle solution and a trajectory solution as a function of the airspeed and altitude. The optimal control solutions for the initial and final climb segments are computed using a shooting method with known starting values on the singular arc The numerical results of the shooting method show that the optimal flight path angle on the initial and final climb segments are constant. The analytical approach provides a rapid means for analyzing a time optimal trajectory for aircraft performance.

Geometry of Optimal Paths around Focal Singular Surfaces in Differential Games

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

Melikyan, Arik; Bernhard, Pierre

2005-06-15

We investigate a special type of singularity in non-smooth solutions of first-order partial differential equations, with emphasis on Isaacs' equation. This type, called focal manifold, is characterized by the incoming trajectory fields on the two sides and a discontinuous gradient. We provide a complete set of constructive equations under various hypotheses on the singularity, culminating with the case where no a priori hypothesis on its geometry is known, and where the extremal trajectory fields need not be collinear. We show two examples of differential games exhibiting non-collinear fields of extremal trajectories on the focal manifold, one with a transversal approachmore » and one with a tangential approach.« less

Observer-dependent sign inversions of polarization singularities.

PubMed

Freund, Isaac

2014-10-15

We describe observer-dependent sign inversions of the topological charges of vector field polarization singularities: C points (points of circular polarization), L points (points of linear polarization), and two virtually unknown singularities we call γ(C) and α(L) points. In all cases, the sign of the charge seen by an observer can change as she changes the direction from which she views the singularity. Analytic formulas are given for all C and all L point sign inversions.

Propagation of the Lissajous singularity dipole emergent from non-paraxial polychromatic beams

NASA Astrophysics Data System (ADS)

Haitao, Chen; Gao, Zenghui; Wang, Wanqing

2017-06-01

The propagation of the Lissajous singularity dipole (LSD) emergent from the non-paraxial polychromatic beams is studied. It is found that the handedness reversal of Lissajous singularities, the change in the shape of Lissajous figures, as well as the creation and annihilation of the LSD may take place by varying the propagation distance, off-axis parameter, wavelength, or amplitude factor. Comparing with the LSD emergent from paraxial polychromatic beams, the output field of non-paraxial polychromatic beams is more complicated, which results in some richer dynamic behaviors of Lissajous singularities, such as more Lissajous singularities and no vanishing of a single Lissajous singularity at the plane z>0.

A circumferential crack in a cylindrical shell under tension.

NASA Technical Reports Server (NTRS)

Duncan-Fama, M. E.; Sanders, J. L., Jr.

1972-01-01

A closed cylindrical shell under uniform internal pressure has a slit around a portion of its circumference. Linear shallow shell theory predicts inverse square-root-type singularities in certain of the stresses at the crack tips. This paper reports the computed strength of these singularities for different values of a dimensionless parameter based on crack length, shell radius and shell thickness.

Diffraction of V-point singularities through triangular apertures.

PubMed

Ram, B S Bhargava; Sharma, Anurag; Senthilkumaran, P

2017-05-01

In this paper we present experimental studies on diffraction of V-point singularities through equilateral and isosceles right triangular apertures. When V-point index, also called Poincare-Hopf index (η), of the optical field is +1, the diffraction disintegrates it into two monstars/lemons. When V-point index η is -1, diffraction produces two stars. The diffraction pattern, unlike phase singularity, is insensitive to polarity of the polarization singularity and the intensity pattern remains invariant. Higher order V-point singularities are generated using Sagnac interferometer and it is observed that the diffraction disintegrates them into lower order C-points.

Van Hove singularities in the paramagnetic phase of the Hubbard model: DMFT study

NASA Astrophysics Data System (ADS)

Žitko, Rok; Bonča, Janez; Pruschke, Thomas

2009-12-01

Using the dynamical mean-field theory (DMFT) with the numerical renormalization-group impurity solver we study the paramagnetic phase of the Hubbard model with the density of states (DOS) corresponding to the three-dimensional (3D) cubic lattice and the two-dimensional (2D) square lattice, as well as a DOS with inverse square-root singularity. We show that the electron correlations rapidly smooth out the square-root van Hove singularities (kinks) in the spectral function for the 3D lattice and that the Mott metal-insulator transition (MIT) as well as the magnetic-field-induced MIT differ only little from the well-known results for the Bethe lattice. The consequences of the logarithmic singularity in the DOS for the 2D lattice are more dramatic. At half filling, the divergence pinned at the Fermi level is not washed out, only its integrated weight decreases as the interaction is increased. While the Mott transition is still of the usual kind, the magnetic-field-induced MIT falls into a different universality class as there is no field-induced localization of quasiparticles. In the case of a power-law singularity in the DOS at the Fermi level, the power-law singularity persists in the presence of interaction, albeit with a different exponent, and the effective impurity model in the DMFT turns out to be a pseudogap Anderson impurity model with a hybridization function which vanishes at the Fermi level. The system is then a generalized Fermi liquid. At finite doping, regular Fermi-liquid behavior is recovered.

Scalar field as an intrinsic time measure in coupled dynamical matter-geometry systems. II. Electrically charged gravitational collapse

NASA Astrophysics Data System (ADS)

Nakonieczna, Anna; Yeom, Dong-han

2016-05-01

Investigating the dynamics of gravitational systems, especially in the regime of quantum gravity, poses a problem of measuring time during the evolution. One of the approaches to this issue is using one of the internal degrees of freedom as a time variable. The objective of our research was to check whether a scalar field or any other dynamical quantity being a part of a coupled multi-component matter-geometry system can be treated as a `clock' during its evolution. We investigated a collapse of a self-gravitating electrically charged scalar field in the Einstein and Brans-Dicke theories using the 2+2 formalism. Our findings concentrated on the spacetime region of high curvature existing in the vicinity of the emerging singularity, which is essential for the quantum gravity applications. We investigated several values of the Brans-Dicke coupling constant and the coupling between the Brans-Dicke and the electrically charged scalar fields. It turned out that both evolving scalar fields and a function which measures the amount of electric charge within a sphere of a given radius can be used to quantify time nearby the singularity in the dynamical spacetime part, in which the apparent horizon surrounding the singularity is spacelike. Using them in this respect in the asymptotic spacetime region is possible only when both fields are present in the system and, moreover, they are coupled to each other. The only nonzero component of the Maxwell field four-potential cannot be used to quantify time during the considered process in the neighborhood of the whole central singularity. None of the investigated dynamical quantities is a good candidate for measuring time nearby the Cauchy horizon, which is also singular due to the mass inflation phenomenon.

Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities

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

Zhou, Yao

Coronal heating has been a long-standing conundrum in solar physics. Parker's conjecture that spontaneous current singularities lead to nanoflares that heat the corona has been controversial. In ideal magnetohydrodynamics (MHD), can genuine current singularities emerge from a smooth 3D line-tied magnetic field? To numerically resolve this issue, the schemes employed must preserve magnetic topology exactly to avoid artificial reconnection in the presence of (nearly) singular current densities. Structure-preserving numerical methods are favorable for mitigating numerical dissipation, and variational integration is a powerful machinery for deriving them. However, successful applications of variational integration to ideal MHD have been scarce. In thismore » thesis, we develop variational integrators for ideal MHD in Lagrangian labeling by discretizing Newcomb's Lagrangian on a moving mesh using discretized exterior calculus. With the built-in frozen-in equation, the schemes are free of artificial reconnection, hence optimal for studying current singularity formation. Using this method, we first study a fundamental prototype problem in 2D, the Hahm-Kulsrud-Taylor (HKT) problem. It considers the effect of boundary perturbations on a 2D plasma magnetized by a sheared field, and its linear solution is singular. We find that with increasing resolution, the nonlinear solution converges to one with a current singularity. The same signature of current singularity is also identified in other 2D cases with more complex magnetic topologies, such as the coalescence instability of magnetic islands. We then extend the HKT problem to 3D line-tied geometry, which models the solar corona by anchoring the field lines in the boundaries. The effect of such geometry is crucial in the controversy over Parker's conjecture. The linear solution, which is singular in 2D, is found to be smooth. However, with finite amplitude, it can become pathological above a critical system length. The nonlinear solution turns out smooth for short systems. Nonetheless, the scaling of peak current density vs. system length suggests that the nonlinear solution may become singular at a finite length. With the results in hand, we cannot confirm or rule out this possibility conclusively, since we cannot obtain solutions with system lengths near the extrapolated critical value.« less

Metric dimensional reduction at singularities with implications to Quantum Gravity

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

Stoica, Ovidiu Cristinel, E-mail: holotronix@gmail.com

2014-08-15

A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being justmore » non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity. - Highlights: • The singularities we introduce are described by finite geometric/physical objects. • Our singularities are accompanied by dimensional reduction effects. • They affect the metric, the measure, the topology, the gravitational DOF (Weyl = 0). • Effects proposed in other approaches to Quantum Gravity are obtained naturally. • The geometric dimensional reduction obtained opens new ways for Quantum Gravity.« less

Use of adjoint methods in the probabilistic finite element approach to fracture mechanics

NASA Technical Reports Server (NTRS)

Liu, Wing Kam; Besterfield, Glen; Lawrence, Mark; Belytschko, Ted

1988-01-01

The adjoint method approach to probabilistic finite element methods (PFEM) is presented. When the number of objective functions is small compared to the number of random variables, the adjoint method is far superior to the direct method in evaluating the objective function derivatives with respect to the random variables. The PFEM is extended to probabilistic fracture mechanics (PFM) using an element which has the near crack-tip singular strain field embedded. Since only two objective functions (i.e., mode I and II stress intensity factors) are needed for PFM, the adjoint method is well suited.

Simulation of generation and dynamics of polarization singularities with circular Airy beams.

PubMed

Ye, Dong; Peng, Xinyu; Zhou, Muchun; Xin, Yu; Song, Minmin

2017-11-01

The generation and dynamics of polarization singularities have been underresearched for years, while the focusing property of the topological configuration has not been explored much. In this paper, we simulated the generation of low-order polarization singularities with a circular Airy beam and explored the focusing property of the synthetic light field during propagation due to the autofocusing of the component. Our work researched the focusing properties of the polarization singularity configuration, which may help to develop its application prospect.

Bardeen regular black hole with an electric source

NASA Astrophysics Data System (ADS)

Rodrigues, Manuel E.; Silva, Marcos V. de S.

2018-06-01

If some energy conditions on the stress-energy tensor are violated, is possible construct regular black holes in General Relativity and in alternative theories of gravity. This type of solution has horizons but does not present singularities. The first regular black hole was presented by Bardeen and can be obtained from Einstein equations in the presence of an electromagnetic field. E. Ayon-Beato and A. Garcia reinterpreted the Bardeen metric as a magnetic solution of General Relativity coupled to a nonlinear electrodynamics. In this work, we show that the Bardeen model may also be interpreted as a solution of Einstein equations in the presence of an electric source, whose electric field does not behave as a Coulomb field. We analyzed the asymptotic forms of the Lagrangian for the electric case and also analyzed the energy conditions.

Singularity-sensitive gauge-based radar rainfall adjustment methods for urban hydrological applications

NASA Astrophysics Data System (ADS)

Wang, L.-P.; Ochoa-Rodríguez, S.; Onof, C.; Willems, P.

2015-09-01

Gauge-based radar rainfall adjustment techniques have been widely used to improve the applicability of radar rainfall estimates to large-scale hydrological modelling. However, their use for urban hydrological applications is limited as they were mostly developed based upon Gaussian approximations and therefore tend to smooth off so-called "singularities" (features of a non-Gaussian field) that can be observed in the fine-scale rainfall structure. Overlooking the singularities could be critical, given that their distribution is highly consistent with that of local extreme magnitudes. This deficiency may cause large errors in the subsequent urban hydrological modelling. To address this limitation and improve the applicability of adjustment techniques at urban scales, a method is proposed herein which incorporates a local singularity analysis into existing adjustment techniques and allows the preservation of the singularity structures throughout the adjustment process. In this paper the proposed singularity analysis is incorporated into the Bayesian merging technique and the performance of the resulting singularity-sensitive method is compared with that of the original Bayesian (non singularity-sensitive) technique and the commonly used mean field bias adjustment. This test is conducted using as case study four storm events observed in the Portobello catchment (53 km2) (Edinburgh, UK) during 2011 and for which radar estimates, dense rain gauge and sewer flow records, as well as a recently calibrated urban drainage model were available. The results suggest that, in general, the proposed singularity-sensitive method can effectively preserve the non-normality in local rainfall structure, while retaining the ability of the original adjustment techniques to generate nearly unbiased estimates. Moreover, the ability of the singularity-sensitive technique to preserve the non-normality in rainfall estimates often leads to better reproduction of the urban drainage system's dynamics, particularly of peak runoff flows.

A submerged singularity method for calculating potential flow velocities at arbitrary near-field points

NASA Technical Reports Server (NTRS)

Maskew, B.

1976-01-01

A discrete singularity method has been developed for calculating the potential flow around two-dimensional airfoils. The objective was to calculate velocities at any arbitrary point in the flow field, including points that approach the airfoil surface. That objective was achieved and is demonstrated here on a Joukowski airfoil. The method used combined vortices and sources ''submerged'' a small distance below the airfoil surface and incorporated a near-field subvortex technique developed earlier. When a velocity calculation point approached the airfoil surface, the number of discrete singularities effectively increased (but only locally) to keep the point just outside the error region of the submerged singularity discretization. The method could be extended to three dimensions, and should improve nonlinear methods, which calculate interference effects between multiple wings, and which include the effects of force-free trailing vortex sheets. The capability demonstrated here would extend the scope of such calculations to allow the close approach of wings and vortex sheets (or vortices).

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

NASA Astrophysics Data System (ADS)

Ishibashi, Akihiro; Maeda, Kengo; Mefford, Eric

2017-07-01

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

On spinodal points and Lee-Yang edge singularities

NASA Astrophysics Data System (ADS)

An, X.; Mesterházy, D.; Stephanov, M. A.

2018-03-01

We address a number of outstanding questions associated with the analytic properties of the universal equation of state of the φ4 theory, which describes the critical behavior of the Ising model and ubiquitous critical points of the liquid–gas type. We focus on the relation between spinodal points that limit the domain of metastability for temperatures below the critical temperature, i.e. T < Tc , and Lee-Yang edge singularities that restrict the domain of analyticity around the point of zero magnetic field H for T > Tc . The extended analyticity conjecture (due to Fonseca and Zamolodchikov) posits that, for T < Tc , the Lee-Yang edge singularities are the closest singularities to the real H axis. This has interesting implications, in particular, that the spinodal singularities must lie off the real H axis for d < 4 , in contrast to the commonly known result of the mean-field approximation. We find that the parametric representation of the Ising equation of state obtained in the \\renewcommandε{\\varepsilon} \

Laser singular Theta-pinch

NASA Astrophysics Data System (ADS)

Okulov, A. Yu.

2010-10-01

The interaction of the two counter-propagating ultrashort laser pulses with singular wavefronts in the thin slice of the underdense plasma is considered. It is shown that ion-acoustic wave is excited via Brillouin three-wave resonance by corkscrew interference pattern of paraxial singular laser beams. The orbital angular momentum carried by light is transferred to plasma ion-acoustic vortex. The rotation of the density perturbations of electron fluid is the cause of helical current which produces the kilogauss axial quasi-static magnetic field. The exact analytical configurations are presented for an ion-acoustic current field and magnetic induction. The range of experimentally accessible parameters is evaluated.

Coherent backscattering of singular beams

NASA Astrophysics Data System (ADS)

Schwartz, Chaim; Dogariu, Aristide

2006-02-01

The phenomenon of coherent backscattering depends on both the statistical characteristics of a random scattering medium and the correlation features of the incident field. Imposing a wavefront singularity on the incident field offers a unique and very attractive way to modify the field correlations in a deterministic manner. The field correlations are found to act as a path-length filter which modifies the distribution of different contributions to the enhancement cone. This effect is thoroughly discussed and demonstrated experimentally for the case of single scale scattering systems.

Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

NASA Technical Reports Server (NTRS)

Atluri, S. N.; Nakagaki, M.; Kathiresan, K.

1980-01-01

In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.

Fracture and fatigue analysis of functionally graded and homogeneous materials using singular integral equation approach

NASA Astrophysics Data System (ADS)

Zhao, Huaqing

There are two major objectives of this thesis work. One is to study theoretically the fracture and fatigue behavior of both homogeneous and functionally graded materials, with or without crack bridging. The other is to further develop the singular integral equation approach in solving mixed boundary value problems. The newly developed functionally graded materials (FGMs) have attracted considerable research interests as candidate materials for structural applications ranging from aerospace to automobile to manufacturing. From the mechanics viewpoint, the unique feature of FGMs is that their resistance to deformation, fracture and damage varies spatially. In order to guide the microstructure selection and the design and performance assessment of components made of functionally graded materials, in this thesis work, a series of theoretical studies has been carried out on the mode I stress intensity factors and crack opening displacements for FGMs with different combinations of geometry and material under various loading conditions, including: (1) a functionally graded layer under uniform strain, far field pure bending and far field axial loading, (2) a functionally graded coating on an infinite substrate under uniform strain, and (3) a functionally graded coating on a finite substrate under uniform strain, far field pure bending and far field axial loading. In solving crack problems in homogeneous and non-homogeneous materials, a very powerful singular integral equation (SEE) method has been developed since 1960s by Erdogan and associates to solve mixed boundary value problems. However, some of the kernel functions developed earlier are incomplete and possibly erroneous. In this thesis work, mode I fracture problems in a homogeneous strip are reformulated and accurate singular Cauchy type kernels are derived. Very good convergence rates and consistency with standard data are achieved. Other kernel functions are subsequently developed for mode I fracture in functionally graded materials. This work provides a solid foundation for further applications of the singular integral equation approach to fracture and fatigue problems in advanced composites. The concept of crack bridging is a unifying theory for fracture at various length scales, from atomic cleavage to rupture of concrete structures. However, most of the previous studies are limited to small scale bridging analyses although large scale bridging conditions prevail in engineering materials. In this work, a large scale bridging analysis is included within the framework of singular integral equation approach. This allows us to study fracture, fatigue and toughening mechanisms in advanced materials with crack bridging. As an example, the fatigue crack growth of grain bridging ceramics is studied. With the advent of composite materials technology, more complex material microstructures are being introduced, and more mechanics issues such as inhomogeneity and nonlinearity come into play. Improved mathematical and numerical tools need to be developed to allow theoretical modeling of these materials. This thesis work is an attempt to meet these challenges by making contributions to both micromechanics modeling and applied mathematics. It sets the stage for further investigations of a wide range of problems in the deformation and fracture of advanced engineering materials.

Probing the degenerate states of V-point singularities.

PubMed

Ram, B S Bhargava; Sharma, Anurag; Senthilkumaran, Paramasivam

2017-09-15

V-points are polarization singularities in spatially varying linearly polarized optical fields and are characterized by the Poincare-Hopf index η. Each V-point singularity is a superposition of two oppositely signed orbital angular momentum states in two orthogonal spin angular momentum states. Hence, a V-point singularity has zero net angular momentum. V-points with given |η| have the same (amplitude) intensity distribution but have four degenerate polarization distributions. Each of these four degenerate states also produce identical diffraction patterns. Hence to distinguish these degenerate states experimentally, we present in this Letter a method involving a combination of polarization transformation and diffraction. This method also shows the possibility of using polarization singularities in place of phase singularities in optical communication and quantum information processing.

Phase singularities of the transverse field component of high numerical aperture dark-hollow Gaussian beams in the focal region

NASA Astrophysics Data System (ADS)

Liu, Pusheng; Lü, Baida

2007-04-01

By using the vectorial Debye diffraction theory, phase singularities of high numerical aperture (NA) dark-hollow Gaussian beams in the focal region are studied. The dependence of phase singularities on the truncation parameter δ and semi-aperture angle α (or equally, NA) is illustrated numerically. A comparison of phase singularities of high NA dark-hollow Gaussian beams with those of scalar paraxial Gaussian beams and high NA Gaussian beams is made. For high NA dark-hollow Gaussian beams the beam order n additionally affects the spatial distribution of phase singularities, and there exist phase singularities outside the focal plane, which may be created or annihilated by variation of the semi-aperture angle in a certain region.

Finite energy quantization on a topology changing spacetime

NASA Astrophysics Data System (ADS)

Krasnikov, S.

2016-08-01

The "trousers" spacetime is a pair of flat two-dimensional cylinders ("legs") merging into a single one ("trunk"). In spite of its simplicity this spacetime has a few features (including, in particular, a naked singularity in the "crotch") each of which is presumably unphysical, but for none of which a mechanism is known able to prevent its occurrence. Therefore, it is interesting and important to study the behavior of the quantum fields in such a space. Anderson and DeWitt were the first to consider the free scalar field in the trousers spacetime. They argued that the crotch singularity produces an infinitely bright flash, which was interpreted as evidence that the topology of space is dynamically preserved. Similar divergencies were later discovered by Manogue, Copeland, and Dray who used a more exotic quantization scheme. Later yet the same result obtained within a somewhat different approach led Sorkin to the conclusion that the topological transition in question is suppressed in quantum gravity. In this paper I show that the Anderson-DeWitt divergence is an artifact of their choice of the Fock space. By choosing a different one-particle Hilbert space one gets a quantum state in which the components of the stress-energy tensor (SET) are bounded in the frame of a free-falling observer.

Singularity computations

NASA Technical Reports Server (NTRS)

Swedlow, J. L.

1976-01-01

An approach is described for singularity computations based on a numerical method for elastoplastic flow to delineate radial and angular distribution of field quantities and measure the intensity of the singularity. The method is applicable to problems in solid mechanics and lends itself to certain types of heat flow and fluid motion studies. Its use is not limited to linear, elastic, small strain, or two-dimensional situations.

The Singular Set of Solutions to Non-Differentiable Elliptic Systems

NASA Astrophysics Data System (ADS)

Mingione, Giuseppe

We estimate the Hausdorff dimension of the singular set of solutions to elliptic systems of the type If the vector fields a and b are Hölder continuous with respect to the variable x with exponent α, then the Hausdorff dimension of the singular set of any weak solution is at most n-2α.

Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities

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

Virbhadra, K. S.; Keeton, C. R.; Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854

We model the massive dark object at the center of the Galaxy as a Schwarzschild black hole as well as Janis-Newman-Winicour naked singularities, characterized by the mass and scalar charge parameters, and study gravitational lensing (particularly time delay, magnification centroid, and total magnification) by them. We find that the lensing features are qualitatively similar (though quantitatively different) for Schwarzschild black holes, weakly naked, and marginally strongly naked singularities. However, the lensing characteristics of strongly naked singularities are qualitatively very different from those due to Schwarzschild black holes. The images produced by Schwarzschild black hole lenses and weakly naked and marginallymore » strongly naked singularity lenses always have positive time delays. On the other hand, strongly naked singularity lenses can give rise to images with positive, zero, or negative time delays. In particular, for a large angular source position the direct image (the outermost image on the same side as the source) due to strongly naked singularity lensing always has a negative time delay. We also found that the scalar field decreases the time delay and increases the total magnification of images; this result could have important implications for cosmology. As the Janis-Newman-Winicour metric also describes the exterior gravitational field of a scalar star, naked singularities as well as scalar star lenses, if these exist in nature, will serve as more efficient cosmic telescopes than regular gravitational lenses.« less

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2015-07-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees/orders are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the third-order partial derivatives of the magnetic potential field in the local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields and also the third-order partial derivatives of the magnetic potential field at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (GFZ Reference Internal Magnetic Model, version 0.0) with spherical harmonic degrees 16-90. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the magnetic potential field.

Numerical Study of the Effect of Presence of Geometric Singularities on the Mechanical Behavior of Laminated Plates

NASA Astrophysics Data System (ADS)

Khechai, Abdelhak; Tati, Abdelouahab; Guettala, Abdelhamid

2017-05-01

In this paper, an effort is made to understand the effects of geometric singularities on the load bearing capacity and stress distribution in thin laminated plates. Composite plates with variously shaped cutouts are frequently used in both modern and classical aerospace, mechanical and civil engineering structures. Finite element investigation is undertaken to show the effect of geometric singularities on stress distribution. In this study, the stress concentration factors (SCFs) in cross-and-angle-ply laminated as well as in isotropic plates subjected to uniaxial loading are studied using a quadrilateral finite element of four nodes with thirty-two degrees-of-freedom per element. The varying parameters such as the cutout shape and hole sizes (a/b) are considered. The numerical results obtained by the present element are compared favorably with those obtained using the finite element software Freefem++ and the analytic findings published in literature, which demonstrates the accuracy of the present element. Freefem++ is open source software based on the finite element method, which could be helpful to study and improving the analyses of the stress distribution in composite plates with cutouts. The Freefem++ and the quadrilateral finite element formulations will be given in the beginning of this paper. Finally, to show the effect of the fiber orientation angle and anisotropic modulus ratio on the (SCF), number of figures are given for various ratio (a/b).

Creep crack-growth: A new path-independent integral (T sub c), and computational studies. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Stonesifer, R. B.; Atluri, S. N.

1982-01-01

The development of valid creep fracture criteria is considered. Two path-independent integral parameters which show some degree of promise are the C* and (Delta T)sub c integrals. The mathematical aspects of these parameters are reviewed by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects, and large deformations. Two principal conclusions are that (Delta T)sub c has an energy rate interpretation whereas C* does not. The development and application of fracture criteria often involves the solution of boundary/initial value problems associated with deformation and stresses. The finite element method is used for this purpose. An efficient, small displacement, infinitesimal strain, displacement based finite element model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations. A mesh shifting/remeshing procedure is used for simulating crack growth. The model is implemented with the quartz-point node technique and also with specially developed, conforming, crack-tip singularity elements which provide for the r to the n-(1+n) power strain singularity associated with the HRR crack-tip field. Comparisons are made with a variety of analytical solutions and alternate numerical solutions for a number of problems.

Formation of curvature singularities on the interface between dielectric liquids in a strong vertical electric field.

PubMed

Kochurin, Evgeny A; Zubarev, Nikolay M; Zubareva, Olga V

2013-08-01

The nonlinear dynamics of the interface between two deep dielectric fluids in the presence of a vertical electric field is studied. We consider the limit of a strong external electric field where electrostatic forces dominate over gravitational and capillary forces. The nonlinear integrodifferential equations for the interface motion are derived under the assumption of small interfacial slopes. It is shown in the framework of these equations that, in the generic case, the instability development leads to the formation of root singularities at the interface in a finite time. The interfacial curvature becomes infinite at singular points, while the slope angles remain relatively small. The curvature is negative in the vicinity of singularities if the ratio of the permittivities of the fluids exceeds the inverse ratio of their densities, and it is positive in the opposite case (we consider that the lower fluid is heavier than the upper one). In the intermediate case, the interface evolution equations describe the formation and sharpening of dimples at the interface. The results obtained are applicable for the description of the instability of the interface between two magnetic fluids in a vertical magnetic field.

Inflection point caustic problems and solutions for high-gain dual-shaped reflectors

NASA Technical Reports Server (NTRS)

Galindo-Israel, Victor; Veruttipong, Thavath; Imbriale, William; Rengarajan, Sembiam

1990-01-01

The singular nature of the uniform geometrical theory of diffraction (UTD) subreflector scattered field at the vicinity of the main reflector edge (for a high-gain antenna design) is investigated. It is shown that the singularity in the UTD edge-diffracted and slope-diffracted fields is due to the reflection distance parameter approaching infinity in the transition functions. While the geometrical optics (GO) and UTD edge-diffracted fields exhibit singularities of the same order, the edge slope-diffracted field singularity is more significant and is substantial for greater subreflector edge tapers. The diffraction analysis of such a subreflector in the vicinity of the main reflector edge has been carried out efficiently and accurately by a stationary phase evaluation of the phi-integral, whereas the theta-integral is carried out numerically. Computational results from UTD and physical optics (PO) analysis of a 34-m ground station dual-shaped reflector confirm the analytical formulations for both circularly symmetric and offset asymmetric subreflectors. It is concluded that the proposed PO(theta)GO(phi) technique can be used to study the spillover or noise temperature characteristics of a high-gain reflector antenna efficiently and accurately.

On SYM theory and all order bulk singularity structures of BPS strings in type II theory

NASA Astrophysics Data System (ADS)

Hatefi, Ehsan

2018-06-01

The complete forms of the S-matrix elements of a transverse scalar field, two world volume gauge fields, and a Potential Cn-1 Ramond-Ramond (RR) form field are investigated. In order to find an infinite number of t , s , (t + s + u)-channel bulk singularity structures of this particular mixed open-closed amplitude, we employ all the conformal field theory techniques to , exploring all the entire correlation functions and all order α‧ contact interactions to these supersymmetric Yang-Mills (SYM) couplings. Singularity and contact term comparisons with the other symmetric analysis, and are also carried out in detail. Various couplings from pull-Back of branes, Myers terms and several generalized Bianchi identities should be taken into account to be able to reconstruct all order α‧ bulk singularities of type IIB (IIA) superstring theory. Finally, we make a comment on how to derive without any ambiguity all order α‧ contact terms of this S-matrix which carry momentum of RR in transverse directions.

Loop quantum cosmology and singularities.

PubMed

Struyve, Ward

2017-08-15

Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.

Statics of wrinkling films

NASA Technical Reports Server (NTRS)

Zak, M.

1982-01-01

An analytical investigation of the equilibrium of wrinkling films is conducted. Zak (1979) has shown that wrinkling occurs in connection with the instability of a smooth film having no resistance to bending in the case of compression. The governing equation for the equilibrium of a film with possible regions of wrinkling is considered. The introduction of fictitious stress reduces the governing equation to a form which formally coincides with the governing equation for a string. Equilibrium conditions in the case of an absence of external forces are explored, taking into account the stretching of a semispherical film, the torsion of a convex film of revolution, and stress singularities. A study is conducted of the equilibrium under conditions in which external forces normal to the surface of a film are present. Attention is also given to the equilibrium in a potential field.

Inversion of residual stress profiles from ultrasonic Rayleigh wave dispersion data

NASA Astrophysics Data System (ADS)

Mora, P.; Spies, M.

2018-05-01

We investigate theoretically and with synthetic data the performance of several inversion methods to infer a residual stress state from ultrasonic surface wave dispersion data. We show that this particular problem may reveal in relevant materials undesired behaviors for some methods that could be reliably applied to infer other properties. We focus on two methods, one based on a Taylor-expansion, and another one based on a piecewise linear expansion regularized by a singular value decomposition. We explain the instabilities of the Taylor-based method by highlighting singularities in the series of coefficients. At the same time, we show that the other method can successfully provide performances which only weakly depend on the material.

On Resolutions of Cosmological Singularities in Higher-Spin Gravity

NASA Astrophysics Data System (ADS)

Burrington, Benjamin; Pando Zayas, Leopoldo; Rombes, Nicholas

2014-03-01

Gravity in three dimensions is simpler than in four, due to the lack of gravitational waves, and can be recast as a Chern-Simons theory. In this context, it is straightforward to generalize Einstein's gravity, with or without cosmological constant, by changing the gauge group. Using this, we study the resolution of certain cosmological singularities, and extend the singularity resolution scheme proposed by Krishnan and Roy. We discuss the resolution of a big-bang singularity in the case of gravity coupled to a spin-4 field realized as Chern-Simons theory with gauge group SL (4 , C) . We show the existence of gauge transformations that do not change the holonomy of the Chern-Simons gauge potential and lead to metrics without the initial singularity. We argue that such transformations always exist in the context of gravity coupled to a spin-N field when described by Chern-Simons with gauge group SL (N , C) . This work was supported by the DOE under grant DE-FG02-95ER40899, a research grant from Troy University, and the Honors Summer Fellowship at the University of Michigan.

Bound states of spin-half particles in a static gravitational field close to the black hole field

NASA Astrophysics Data System (ADS)

Spencer-Smith, A. F.; Gossel, G. H.; Berengut, J. C.; Flambaum, V. V.

2013-03-01

We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.

Curved singular beams for three-dimensional particle manipulation.

PubMed

Zhao, Juanying; Chremmos, Ioannis D; Song, Daohong; Christodoulides, Demetrios N; Efremidis, Nikolaos K; Chen, Zhigang

2015-07-13

For decades, singular beams carrying angular momentum have been a topic of considerable interest. Their intriguing applications are ubiquitous in a variety of fields, ranging from optical manipulation to photon entanglement, and from microscopy and coronagraphy to free-space communications, detection of rotating black holes, and even relativistic electrons and strong-field physics. In most applications, however, singular beams travel naturally along a straight line, expanding during linear propagation or breaking up in nonlinear media. Here, we design and demonstrate diffraction-resisting singular beams that travel along arbitrary trajectories in space. These curved beams not only maintain an invariant dark "hole" in the center but also preserve their angular momentum, exhibiting combined features of optical vortex, Bessel, and Airy beams. Furthermore, we observe three-dimensional spiraling of microparticles driven by such fine-shaped dynamical beams. Our findings may open up new avenues for shaped light in various applications.

Equilibrium stellar systems with spindle singularities

NASA Technical Reports Server (NTRS)

Shapiro, Stuart L.; Teukolsky, Saul A.

1992-01-01

Equilibrium sequences of axisymmetric Newtonian clusters that tend toward singular states are constructed. The distribution functions are chosen to be of the form f = f(E, Jz). The numerical method then determines the density and gravitational potential self-consistently to satisfy Poisson's equation. For the prolate models, spindle singularities arise from the depletion of angular momentum near the symmetry axis. While the resulting density enhancement is confined to the region near the axis, the influence of the spindle extends much further out through its tidal gravitational field. Centrally condensed prolate clusters may contain strong-field regions even though the spindle mass is small and the mean cluster eccentricity is not extreme. While the calculations performed here are entirely Newtonian, the issue of singularities is an important topic in general relativity. Equilibrium solutions for relativistic star clusters can provide a testing ground for exploring this issue. The methods used in this paper for building nonspherical clusters can be extended to relativistic systems.

Phase retrieval of singular scalar light fields using a two-dimensional directional wavelet transform and a spatial carrier.

PubMed

Federico, Alejandro; Kaufmann, Guillermo H

2008-10-01

We evaluate a method based on the two-dimensional directional wavelet transform and the introduction of a spatial carrier to retrieve optical phase distributions in singular scalar light fields. The performance of the proposed phase-retrieval method is compared with an approach based on Fourier transform. The advantages and limitations of the proposed method are discussed.

Non-singular spacetimes with a negative cosmological constant: IV. Stationary black hole solutions with matter fields

NASA Astrophysics Data System (ADS)

Chruściel, Piotr T.; Delay, Erwann; Klinger, Paul

2018-02-01

We use an elliptic system of equations with complex coefficients for a set of complex-valued tensor fields as a tool to construct infinite-dimensional families of non-singular stationary black holes, real-valued Lorentzian solutions of the Einstein–Maxwell-dilaton-scalar fields-Yang–Mills–Higgs–Chern–Simons-f(R) equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.

The stress intensity factor for the double cantilever beam

NASA Technical Reports Server (NTRS)

Fichter, W. B.

1983-01-01

Fourier transforms and the Wiener-Hopf technique are used in conjunction with plane elastostatics to examine the singular crack tip stress field in the double cantilever beam (DCB) specimen. In place of the Dirac delta function, a family of functions which duplicates the important features of the concentrated forces without introducing unmanageable mathematical complexities is used as a loading function. With terms of order h-squared/a-squared retained in the series expansion, the dimensionless stress intensity factor is found to be K (h to the 1/2)/P = 12 to the 1/2 (a/h + 0.6728 + 0.0377 h-squared/a-squared), in which P is the magnitude of the concentrated forces per unit thickness, a is the distance from the crack tip to the points of load application, and h is the height of each cantilever beam. The result is similar to that obtained by Gross and Srawley by fitting a line to discrete results from their boundary collocation analysis.

Polarization singularity indices in Gaussian laser beams

NASA Astrophysics Data System (ADS)

Freund, Isaac

2002-01-01

Two types of point singularities in the polarization of a paraxial Gaussian laser beam are discussed in detail. V-points, which are vector point singularities where the direction of the electric vector of a linearly polarized field becomes undefined, and C-points, which are elliptic point singularities where the ellipse orientations of elliptically polarized fields become undefined. Conventionally, V-points are characterized by the conserved integer valued Poincaré-Hopf index η, with generic value η=±1, while C-points are characterized by the conserved half-integer singularity index IC, with generic value IC=±1/2. Simple algorithms are given for generating V-points with arbitrary positive or negative integer indices, including zero, at arbitrary locations, and C-points with arbitrary positive or negative half-integer or integer indices, including zero, at arbitrary locations. Algorithms are also given for generating continuous lines of these singularities in the plane, V-lines and C-lines. V-points and C-points may be transformed one into another. A topological index based on directly measurable Stokes parameters is used to discuss this transformation. The evolution under propagation of V-points and C-points initially embedded in the beam waist is studied, as is the evolution of V-dipoles and C-dipoles.

String loops in the field of braneworld spherically symmetric black holes and naked singularities

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

Stuchlík, Z.; Kološ, M., E-mail: zdenek.stuchlik@fpf.slu.cz, E-mail: martin.kolos@fpf.slu.cz

We study motion of current-carrying string loops in the field of braneworld spherically symmetric black holes and naked singularities. The spacetime is described by the Reissner-Nordström geometry with tidal charge b reflecting the non-local tidal effects coming from the external dimension; both positive and negative values of the spacetime parameter b are considered. We restrict attention to the axisymmetric motion of string loops when the motion can be fully governed by an appropriately defined effective potential related to the energy and angular momentum of the string loops. In dependence on these two constants of the motion, the string loops canmore » be captured, trapped, or can escape to infinity. In close vicinity of stable equilibrium points at the centre of trapped states the motion is regular. We describe how it is transformed to chaotic motion with growing energy of the string loop. In the field of naked singularities the trapped states located off the equatorial plane of the system exist and trajectories unable to cross the equatorial plane occur, contrary to the trajectories in the field of black holes where crossing the equatorial plane is always admitted. We concentrate our attention to the so called transmutation effect when the string loops are accelerated in the deep gravitational field near the black hole or naked singularity by transforming the oscillatory energy to the energy of the transitional motion. We demonstrate that the influence of the tidal charge can be substantial especially in the naked singularity spacetimes with b > 1 where the acceleration to ultrarelativistic velocities with Lorentz factor γ ∼ 100 can be reached, being more than one order higher in comparison with those obtained in the black hole spacetimes.« less

Fracture analysis of a transversely isotropic high temperature superconductor strip based on real fundamental solutions

NASA Astrophysics Data System (ADS)

Gao, Zhiwen; Zhou, Youhe

2015-04-01

Real fundamental solution for fracture problem of transversely isotropic high temperature superconductor (HTS) strip is obtained. The superconductor E-J constitutive law is characterized by the Bean model where the critical current density is independent of the flux density. Fracture analysis is performed by the methods of singular integral equations which are solved numerically by Gauss-Lobatto-Chybeshev (GSL) collocation method. To guarantee a satisfactory accuracy, the convergence behavior of the kernel function is investigated. Numerical results of fracture parameters are obtained and the effects of the geometric characteristics, applied magnetic field and critical current density on the stress intensity factors (SIF) are discussed.

Treatment of nonconvergence of Fourier modal method arising from irregular field singularities at lossless metal-dielectric right-angle edges.

PubMed

Mei, Yanpeng; Liu, Haitao; Zhong, Ying

2014-04-01

In a recent work [J. Opt. Soc. Am. A28, 738 (2011)], Lifeng Li and Gerard Granet investigate nonconvergence cases of the Fourier modal method (FMM). They demonstrate that the nonconvergence is due to the irregular field singularities at lossless metal-dielectric right-angle edges. Here we make further investigations on the problem and find that the FMM surprisingly converges for deep sub-wavelength gratings (grating period being much smaller than the illumination wavelength). To overcome the nonconvergence for gratings that are not deep sub-wavelength, we approximately replace the lossless metal-dielectric right-angle edges by a medium with a gradually varied refraction index, so as to remove the irregular field singularities. With such treatment, convergence is observed as the region of the approximate medium approaches vanishing.

Quantum Hall states and conformal field theory on a singular surface

NASA Astrophysics Data System (ADS)

Can, T.; Wiegmann, P.

2017-12-01

In Can et al (2016 Phys. Rev. Lett. 117), quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic adiabatic states, which we define in the paper. We highlight the connection between the universal features of geometric transport of quantum Hall states and holomorphic dimension of primary fields in conformal field theory. In parallel we compute the universal finite-size corrections to the free energy of a critical system on a hyperbolic sphere with conical and cusp singularities, thus extending the result of Cardy and Peschel for critical systems on a flat cone (Cardy and Peschel 1988 Nucl. Phys. B 300 377-92), and the known results for critical systems on polyhedra and flat branched Riemann surfaces.

Black hole solutions in mimetic Born-Infeld gravity

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

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. Here, we find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularitymore » is found to be infinite.« less

Black hole solutions in mimetic Born-Infeld gravity

DOE PAGES

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

2018-01-23

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. Here, we find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularitymore » is found to be infinite.« less

Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities

NASA Astrophysics Data System (ADS)

Kamenshchik, Alexander Yu.; Pozdeeva, Ekaterina O.; Vernov, Sergey Yu.; Tronconi, Alessandro; Venturi, Giovanni

2016-09-01

We study the relation between the Jordan-Einstein frame transition and the possible description of the crossing of singularities in flat Friedmann universes, using the fact that the regular evolution in one frame can correspond to crossing singularities in the other frame. We show that some interesting effects arise in simple models such as one with a massless scalar field or another wherein the potential is constant in the Einstein frame. The dynamics in these models and in their conformally coupled counterparts are described in detail, and a method for the continuation of such cosmological evolutions beyond the singularity is developed. We compare our approach with some other, recently developed, approaches to the problem of the crossing of singularities.

Tension fracture of laminates for transport fuselage. Part 2: Large notches

NASA Technical Reports Server (NTRS)

Walker, Tom H.; Ilcewicz, Larry B.; Polland, D. R.; Poe, C. C., Jr.

1993-01-01

Tests were conducted on over 200 center-crack specimens to evaluate: (a) the tension-fracture performance of candidate materials and laminates for commercial fuselage applications; and (b) the accuracy of several failure criteria in predicting response. Crack lengths of up to 12 inches were considered. Other variables included fiber/matrix combination, layup, lamination manufacturing process, and intraply hybridization. Laminates fabricated using the automated tow-placement process provided significantly higher tension-fracture strengths than nominally identical tape laminates. This confirmed earlier findings for other layups, and possibly relates to a reduced stress concentration resulting from a larger scale of repeatable material inhomogeneity in the tow-placed laminates. Changes in material and layup result in a trade-off between small-notch and large-notch strengths. Toughened resins and 0 deg-dominate layups result in higher small-notch strengths but lower large-notch strengths than brittle resins, 90 deg and 45 deg dominated layups, and intraply S2-glass hybrid material forms. Test results indicate that strength-prediction methods that allow for a reduced order singularity of the crack-tip stress field are more successful at predicting failure over a range of notch sizes than those relying on the classical square-root singularity. The order of singularity required to accurately predict large-notch strength from small-notch data was affected by both material and layup. Measured crack-tip strain distributions were generally higher than those predicted using classical methods. Traditional methods of correcting for finite specimen width were found to be lacking, confirming earlier findings with other specimen geometries. Fracture tests of two stiffened panels, identical except for differing materials, with severed central stiffeners resulted in nearly identical damage progression and failure sequences. Strain-softening laws implemented within finite element models appear attractive to account for load redistribution in configured structure due to damage-induced crack tip softening

Structure of polarization singularities of a light beam at triple frequency generated in isotropic medium by singularly polarized beam.

PubMed

Grigoriev, K S; Ryzhikov, P S; Cherepetskaya, E B; Makarov, V A

2017-10-16

The components of electric field of the third harmonic beam, generated in isotropic medium with cubic nonlinearity by a monochromatic light beam carrying polarization singularity of an arbitrary type, are found analytically. The relation between C-points characteristics in the fundamental and signal beams are determined, as well as the impact of the phase mismatch on the shape of the C-lines.

Kinematics, influence functions and field quantities for disturbance propagation from moving disturbance sources

NASA Technical Reports Server (NTRS)

Das, A.

1984-01-01

A unified method is presented for deriving the influence functions of moving singularities which determine the field quantities in aerodynamics and aeroacoustics. The moving singularities comprise volume and surface distributions having arbitrary orientations in space and to the trajectory. Hence one generally valid formula for the influence functions which reveal some universal relationships and remarkable properties in the disturbance fields. The derivations used are completely consistent with the physical processes in the propagation field, such that treatment renders new descriptions for some standard concepts. The treatment is uniformly valid for subsonic and supersonic Mach numbers.

Scattering of classical and quantum particles by impulsive fields

NASA Astrophysics Data System (ADS)

Balasin, Herbert; Aichelburg, Peter C.

2018-05-01

We investigate the scattering of classical and quantum particles in impulsive backgrounds fields. These fields model short outbursts of radiation propagating with the speed of light. The singular nature of the problem will be accounted for by the use of Colombeau’s generalized function which however give rise to ambiguities. It is the aim of the paper to show that these ambiguities can be overcome by implementing additional physical conditions, which in the non-singular case would be satisfied automatically. As example we discuss the scattering of classical, Klein–Gordon and Dirac particles in impulsive electromagnetic fields.

Scalar field collapse in Gauss-Bonnet gravity

NASA Astrophysics Data System (ADS)

Banerjee, Narayan; Paul, Tanmoy

2018-02-01

We consider a "scalar-Einstein-Gauss-Bonnet" theory in four dimension, where the scalar field couples non-minimally with the Gauss-Bonnet (GB) term. This coupling with the scalar field ensures the non-topological character of the GB term. In this scenario, we examine the possibility for collapsing of the scalar field. Our result reveals that such a collapse is possible in the presence of Gauss-Bonnet gravity for suitable choices of parametric regions. The singularity formed as a result of the collapse is found to be a curvature singularity which is hidden from the exterior by an apparent horizon.

Analysis of the Fisher solution

NASA Astrophysics Data System (ADS)

Abdolrahimi, Shohreh; Shoom, Andrey A.

2010-01-01

We study the d-dimensional Fisher solution which represents a static, spherically symmetric, asymptotically flat spacetime with a massless scalar field. The solution has two parameters, the mass M and the “scalar charge” Σ. The Fisher solution has a naked curvature singularity which divides the spacetime manifold into two disconnected parts. The part which is asymptotically flat we call the Fisher spacetime, and another part we call the Fisher universe. The d-dimensional Schwarzschild-Tangherlini solution and the Fisher solution belong to the same theory and are dual to each other. The duality transformation acting in the parameter space (M,Σ) maps the exterior region of the Schwarzschild-Tangherlini black hole into the Fisher spacetime which has a naked timelike singularity, and interior region of the black hole into the Fisher universe, which is an anisotropic expanding-contracting universe and which has two spacelike singularities representing its “big bang” and “big crunch.” The big bang singularity and the singularity of the Fisher spacetime are radially weak in the sense that a 1-dimensional object moving along a timelike radial geodesic can arrive to the singularities intact. At the vicinity of the singularity the Fisher spacetime of nonzero mass has a region where its Misner-Sharp energy is negative. The Fisher universe has a marginally trapped surface corresponding to the state of its maximal expansion in the angular directions. These results and derived relations between geometric quantities of the Fisher spacetime, the Fisher universe, and the Schwarzschild-Tangherlini black hole may suggest that the massless scalar field transforms the black hole event horizon into the naked radially weak disjoint singularities of the Fisher spacetime and the Fisher universe which are “dual to the horizon.”

Analysis of the Fisher solution

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

Abdolrahimi, Shohreh; Shoom, Andrey A.

2010-01-15

We study the d-dimensional Fisher solution which represents a static, spherically symmetric, asymptotically flat spacetime with a massless scalar field. The solution has two parameters, the mass M and the 'scalar charge' {Sigma}. The Fisher solution has a naked curvature singularity which divides the spacetime manifold into two disconnected parts. The part which is asymptotically flat we call the Fisher spacetime, and another part we call the Fisher universe. The d-dimensional Schwarzschild-Tangherlini solution and the Fisher solution belong to the same theory and are dual to each other. The duality transformation acting in the parameter space (M,{Sigma}) maps the exteriormore » region of the Schwarzschild-Tangherlini black hole into the Fisher spacetime which has a naked timelike singularity, and interior region of the black hole into the Fisher universe, which is an anisotropic expanding-contracting universe and which has two spacelike singularities representing its 'big bang' and 'big crunch'. The big bang singularity and the singularity of the Fisher spacetime are radially weak in the sense that a 1-dimensional object moving along a timelike radial geodesic can arrive to the singularities intact. At the vicinity of the singularity the Fisher spacetime of nonzero mass has a region where its Misner-Sharp energy is negative. The Fisher universe has a marginally trapped surface corresponding to the state of its maximal expansion in the angular directions. These results and derived relations between geometric quantities of the Fisher spacetime, the Fisher universe, and the Schwarzschild-Tangherlini black hole may suggest that the massless scalar field transforms the black hole event horizon into the naked radially weak disjoint singularities of the Fisher spacetime and the Fisher universe which are 'dual to the horizon'.« less

Problems of interaction longitudinal shear waves with V-shape tunnels defect

NASA Astrophysics Data System (ADS)

Popov, V. G.

2018-04-01

The problem of determining the two-dimensional dynamic stress state near a tunnel defect of V-shaped cross-section is solved. The defect is located in an infinite elastic medium, where harmonic longitudinal shear waves are propagating. The initial problem is reduced to a system of two singular integral or integro-differential equations with fixed singularities. A numerical method for solving these systems with regard to the true asymptotics of the unknown functions is developed.

Interior sound field control using generalized singular value decomposition in the frequency domain.

PubMed

Pasco, Yann; Gauthier, Philippe-Aubert; Berry, Alain; Moreau, Stéphane

2017-01-01

The problem of controlling a sound field inside a region surrounded by acoustic control sources is considered. Inspired by the Kirchhoff-Helmholtz integral, the use of double-layer source arrays allows such a control and avoids the modification of the external sound field by the control sources by the approximation of the sources as monopole and radial dipole transducers. However, the practical implementation of the Kirchhoff-Helmholtz integral in physical space leads to large numbers of control sources and error sensors along with excessive controller complexity in three dimensions. The present study investigates the potential of the Generalized Singular Value Decomposition (GSVD) to reduce the controller complexity and separate the effect of control sources on the interior and exterior sound fields, respectively. A proper truncation of the singular basis provided by the GSVD factorization is shown to lead to effective cancellation of the interior sound field at frequencies below the spatial Nyquist frequency of the control sources array while leaving the exterior sound field almost unchanged. Proofs of concept are provided through simulations achieved for interior problems by simulations in a free field scenario with circular arrays and in a reflective environment with square arrays.

Stress intensity factors for long, deep surface flaws in plates under extensional fields

NASA Technical Reports Server (NTRS)

Harms, A. E.; Smith, C. W.

1973-01-01

Using a singular solution for a part circular crack, a Taylor Series Correction Method (TSCM) was verified for extracting stress intensity factors from photoelastic data. Photoelastic experiments were then conducted on plates with part circular and flat bottomed cracks for flaw depth to thickness ratios of 0.25, 0.50 and 0.75 and for equivalent flaw depth to equivalent ellipse length values ranging from 0.066 to 0.319. Experimental results agreed well with the Smith theory but indicated that the use of the ''equivalent'' semi-elliptical flaw results was not valid for a/2c less than 0.20. Best overall agreement for the moderate (a/t approximately 0.5) to deep flaws (a/t approximatelly 0.75) and a/2c greater than 0.15 was found with a semi-empirical theory, when compared on the basis of equivalent flaw depth and area.

Structure and propagation of supersonic singularities from helicoidal sources

NASA Technical Reports Server (NTRS)

Myers, M. K.; Farassat, F.

1987-01-01

An asymptotic analysis of the acoustic field radiated by a supersonic helicoidal line source distribution is given. The asymptotic results are valid in the vicinity of the Mach surfaces associated with the moving sources. Particular attention is paid to the singular nature of the field on the Mach surfaces, which the analysis describes exactly. In addition, it is found that the asymptotic approximation predicts numerical values of the pressure with considerable accuracy. Some details on the field of a single source are derived as a special case.

String modular phases in Calabi-Yau families

NASA Astrophysics Data System (ADS)

Kadir, Shabnam; Lynker, Monika; Schimmrigk, Rolf

2011-12-01

We investigate the structure of singular Calabi-Yau varieties in moduli spaces that contain a Brieskorn-Pham point. Our main tool is a construction of families of deformed motives over the parameter space. We analyze these motives for general fibers and explicitly compute the L-series for singular fibers for several families. We find that the resulting motivic L-functions agree with the L-series of modular forms whose weight depends both on the rank of the motive and the degree of the degeneration of the variety. Surprisingly, these motivic L-functions are identical in several cases to L-series derived from weighted Fermat hypersurfaces. This shows that singular Calabi-Yau spaces of non-conifold type can admit a string worldsheet interpretation, much like rational theories, and that the corresponding irrational conformal field theories inherit information from the Gepner conformal field theory of the weighted Fermat fiber of the family. These results suggest that phase transitions via non-conifold configurations are physically plausible. In the case of severe degenerations we find a dimensional transmutation of the motives. This suggests further that singular configurations with non-conifold singularities may facilitate transitions between Calabi-Yau varieties of different dimensions.

Gravitational lensing by rotating naked singularities

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

Gyulchev, Galin N.; Yazadjiev, Stoytcho S.; Institut fuer Theoretische Physik, Universitaet Goettingen, Friedrich-Hund-Platz 1, D-37077 Goettingen

We model massive compact objects in galactic nuclei as stationary, axially symmetric naked singularities in the Einstein-massless scalar field theory and study the resulting gravitational lensing. In the weak deflection limit we study analytically the position of the two weak field images, the corresponding signed and absolute magnifications as well as the centroid up to post-Newtonian order. We show that there are static post-Newtonian corrections to the signed magnification and their sum as well as to the critical curves, which are functions of the scalar charge. The shift of the critical curves as a function of the lens angular momentummore » is found, and it is shown that they decrease slightly for the weakly naked and vastly for the strongly naked singularities with the increase of the scalar charge. The pointlike caustics drift away from the optical axis and do not depend on the scalar charge. In the strong deflection limit approximation, we compute numerically the position of the relativistic images and their separability for weakly naked singularities. All of the lensing quantities are compared to particular cases as Schwarzschild and Kerr black holes as well as Janis-Newman-Winicour naked singularities.« less

Singular instantons in Eddington-inspired-Born-Infeld gravity

DOE PAGES

Arroja, Frederico; Chen, Che -Yu; Chen, Pisin; ...

2017-03-23

In this study, we investigate O(4)-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI) . We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, but theremore » is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.« less

Holographic curvature perturbations in a cosmology with a space-like singularity

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

Ferreira, Elisa G.M.; Brandenberger, Robert; Institute for Theoretical Studies, ETH Zürich,Clausiusstr. 47, Zürich, CH-8092

2016-07-19

We study the evolution of cosmological perturbations in an anti-de-Sitter (AdS) bulk through a cosmological singularity by mapping the dynamics onto the boundary conformal fields theory by means of the AdS/CFT correspondence. We consider a deformed AdS space-time obtained by considering a time-dependent dilaton which induces a curvature singularity in the bulk at a time which we call t=0, and which asymptotically approaches AdS both for large positive and negative times. The boundary field theory becomes free when the bulk curvature goes to infinity. Hence, the evolution of the fluctuations is under better controle on the boundary than in themore » bulk. To avoid unbounded particle production across the bounce it is necessary to smooth out the curvature singularity at very high curvatures. We show how the bulk cosmological perturbations can be mapped onto boundary gauge field fluctuations. We evolve the latter and compare the spectrum of fluctuations on the infrared scales relevant for cosmological observations before and after the bounce point. We find that the index of the power spectrum of fluctuations is the same before and after the bounce.« less

Modeling of Graphene Planar Grating in the THz Range by the Method of Singular Integral Equations

NASA Astrophysics Data System (ADS)

Kaliberda, Mstislav E.; Lytvynenko, Leonid M.; Pogarsky, Sergey A.

2018-04-01

Diffraction of the H-polarized electromagnetic wave by the planar graphene grating in the THz range is considered. The scattering and absorption characteristics are studied. The scattered field is represented in the spectral domain via unknown spectral function. The mathematical model is based on the graphene surface impedance and the method of singular integral equations. The numerical solution is obtained by the Nystrom-type method of discrete singularities.

Evolution of coherence singularities of Schell-model beams.

PubMed

Rodrigo, José A; Alieva, Tatiana

2015-08-01

We show that the propagation of the widely used Schell-model partially coherent light can be easily understood using the ambiguity function. This approach is especially beneficial for the analysis of the mutual intensity of Schell-model beams (SMBs), which are associated with stable coherent beams such as Laguerre-, Hermite-, and Ince-Gaussian. We study the evolution of the coherence singularities during the SMB propagation. It is demonstrated that the distance of singularity formation depends on the coherence degree of the input beam. Moreover, it is proved that the shape, position, and number of singularity curves in far field are defined by the associated coherent beam.

Polymer-Fourier quantization of the scalar field revisited

NASA Astrophysics Data System (ADS)

Garcia-Chung, Angel; Vergara, J. David

2016-10-01

The polymer quantization of the Fourier modes of the real scalar field is studied within algebraic scheme. We replace the positive linear functional of the standard Poincaré invariant quantization by a singular one. This singular positive linear functional is constructed as mimicking the singular limit of the complex structure of the Poincaré invariant Fock quantization. The resulting symmetry group of such polymer quantization is the subgroup SDiff(ℝ4) which is a subgroup of Diff(ℝ4) formed by spatial volume preserving diffeomorphisms. In consequence, this yields an entirely different irreducible representation of the canonical commutation relations, nonunitary equivalent to the standard Fock representation. We also compared the Poincaré invariant Fock vacuum with the polymer Fourier vacuum.

On the high Mach number shock structure singularity caused by overreach of Maxwellian molecules

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

Myong, R. S., E-mail: myong@gnu.ac.kr

2014-05-15

The high Mach number shock structure singularity arising in moment equations of the Boltzmann equation was investigated. The source of the singularity is shown to be the unbalanced treatment between two high order kinematic and dissipation terms caused by the overreach of Maxwellian molecule assumption. In compressive gaseous flow, the high order stress-strain coupling term of quadratic nature will grow far faster than the strain term, resulting in an imbalance with the linear dissipation term and eventually a blow-up singularity in high thermal nonequilibrium. On the other hand, the singularity arising from unbalanced treatment does not occur in the casemore » of velocity shear and expansion flows, since the high order effects are cancelled under the constraint of the free-molecular asymptotic behavior. As an alternative method to achieve the balanced treatment, Eu's generalized hydrodynamics, consistent with the second law of thermodynamics, was revisited. After introducing the canonical distribution function in exponential form and applying the cumulant expansion to the explicit calculation of the dissipation term, a natural platform suitable for the balanced treatment was derived. The resulting constitutive equation with the nonlinear factor was then shown to be well-posed for all regimes, effectively removing the high Mach number shock structure singularity.« less

Performance and limitations of p-version finite element method for problems containing singularities

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

Wong, K.K.; Surana, K.S.

1996-10-01

In this paper, the authors investigate the performance of p-version Least Squares Finite Element Formulation (LSFEF) for a hyperbolic system of equations describing a one-dimensional radial flow of an upper-convected Maxwell fluid. This problem has r{sup 2} singularity in stress and r{sup {minus}1} singularity in velocity at r = 0. By carefully controlling the inner radius r{sub j}, Deborah number DE and Reynolds number Re, this problem can be used to simulate the following four classes of problems: (a) smooth linear problems, (b) smooth non-linear problems, (c) singular linear problems and (d) singular non-linear problems. They demonstrate that in casesmore » (a) and (b) the p-version method, in particular p-version LSFEF is meritorious. However, for cases (c) and (d) p-version LSFEF, even with extreme mesh refinement and very high p-levels, either produces wrong solutions, or results in the failure of the iterative solution procedure. Even though in the numerical studies they have considered p-version LSFEF for the radial flow of the upper-convected Maxwell fluid, the findings and conclusions are equally valid for other smooth and singular problems as well, regardless of the formulation strategy chosen and element approximation functions employed.« less

A regional seismic stress field in Taiwan inferred from damped inversion of earthquake focal mechanisms

NASA Astrophysics Data System (ADS)

Huang, P. H.; Liang, W. T.; Huang, Y. L.; Li, W. H.; Jian, P. R.; Tseng, T. L.

2016-12-01

We have inverted 3014 source mechanisms by applying a newly developed multiple solution method (AutoBATS) to the Broadband Array in Taiwan for Seismology (BATS) for earthquakes occurred in the Taiwan region between 1996 and 2016. To evaluate the solution reliability, we have compared our solutions with the GlobalCMT (GCMT) ones that are in common. The result shows that 83% of the Kagan angles are smaller than 35°, which is much higher than the regular BATS CMT solution and therefore indicates a good agreement among these two catalogs. In average, the Mw derived from our method is about 0.1 smaller than that obtained by the GCMT. According to the classification by Frohlich (1992), 43% of our solutions show thrusting, which is the dominant faulting type occurred mainly along the subduction zone, the eastern collision zone and the western foothill zone. A regional seismic stress field has been pursued by using a damped stress inversion algorithm over a grid whose node spacing is 0.1°. The s1 orientation is parallel to the plate motion direction of the Philippine Sea plate with respect to the Eurasian plate in the eastern offshore area. A fan-shape s1 orientation is clearly found in the western Taiwan. Across the southern Taiwan, we observed an S-shape trajectory of the s1 orientation, which may reflect the rheology contrast between the Central Range and the Pingtung Plain. In addition, we noticed that there is a singularity point of the s1 orientation at 24.3°N along the eastern coast, which may mark the transition from the effective collision to the lateral bending in the upper seismogenic layer of the crust. The inter-seismic surface GPS deformation also presents this singularity. In the north-east of this location, the s1 orientation is subparallel to the strike of the Okinawa Trough, which is almost perpendicular to the relative plate motion direction. This newly obtained CMT catalog may help decipher more sophisticated seismotectonic features in the Taiwan region.

International Education Research and the Sociology of Knowledge

ERIC Educational Resources Information Center

Cambridge, James

2012-01-01

The ontology of the field of international education is described and analysed in terms of singular, regional and generic modes of pedagogized knowledge. In contrast to singular and regional modes of knowledge which synthesize introjection (orientation onto themselves) and projection (orientation towards external contingencies), generic modes…

Revisiting the analogue of the Jebsen-Birkhoff theorem in Brans-Dicke gravity

NASA Astrophysics Data System (ADS)

Faraoni, Valerio; Hammad, Fayçal; Cardini, Adriana M.; Gobeil, Thomas

2018-04-01

We report the explicit form of the general static, spherically symmetric, and asymptotically flat solution of vacuum Brans-Dicke gravity in the Jordan frame, assuming that the Brans-Dicke scalar field has no singularities or zeros (except possibly for a central singularity). This general solution is conformal to the Fisher-Wyman geometry of Einstein theory and its nature depends on a scalar charge parameter. Apart from the Schwarzschild black hole, only wormhole throats and central naked singularities are possible.

Development of the triplet singularity for the analysis of wings and bodies in supersonic flow

NASA Technical Reports Server (NTRS)

Woodward, F. A.

1981-01-01

A supersonic triplet singularity was developed which eliminates internal waves generated by panels having supersonic edges. The triplet is a linear combination of source and vortex distributions which gives directional properties to the perturbation flow field surrounding the panel. The theoretical development of the triplet singularity is described together with its application to the calculation of surface pressures on wings and bodies. Examples are presented comparing the results of the new method with other supersonic methods and with experimental data.

Singular vectors for the WN algebras

NASA Astrophysics Data System (ADS)

Ridout, David; Siu, Steve; Wood, Simon

2018-03-01

In this paper, we use free field realisations of the A-type principal, or Casimir, WN algebras to derive explicit formulae for singular vectors in Fock modules. These singular vectors are constructed by applying screening operators to Fock module highest weight vectors. The action of the screening operators is then explicitly evaluated in terms of Jack symmetric functions and their skew analogues. The resulting formulae depend on sequences of pairs of integers that completely determine the Fock module as well as the Jack symmetric functions.

Why do naked singularities form in gravitational collapse? II

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

Joshi, Pankaj S.; Goswami, Rituparno; Dadhich, Naresh

We examine physical features that could lead to formation of a naked singularity rather than black hole, as end state of spherical collapse. Generalizing earlier results on dust collapse to general type I matter fields, it is shown that collapse always creates black hole if shear vanishes or density is homogeneous. It follows that nonzero shear is a necessary condition for singularity to be visible to external observers, when trapped surface formation is delayed by shearing forces or inhomogeneity within the collapsing cloud.

k-essence in the DGP brane-world cosmology

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

Bouhmadi-Lopez, Mariam; Chimento, Luis P.

We analyze a Dvali-Gabadadze-Porrati (DGP) brane filled with a k-essence field and assume the k field evolving linearly with the cosmic time of the brane. We then solve analytically the Friedmann equation and deduce the different behavior of the brane at the low- and the high-energy regimes. The asymptotic behavior can be quite different involving accelerating branes, big bangs, big crunches, big rips, or quiescent singularities. The latter correspond to a type of sudden singularity.

Shot-noise at a Fermi-edge singularity: Non-Markovian dynamics

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

Ubbelohde, N.; Maire, N.; Haug, R. J.

2013-12-04

For an InAs quantum dot we study the current shot noise at a Fermi-edge singularity in low temperature cross-correlation measurements. In the regime of the interaction effect the strong suppression of noise observed at zero magnetic field and the sequence of enhancement and suppression in magnetic field go beyond a Markovian master equation model. Qualitative and quantitative agreement can however be achieved by a generalized master equation model taking non-Markovian dynamics into account.

Multiphase model for transformation induced plasticity. Extended Leblond's model

NASA Astrophysics Data System (ADS)

Weisz-Patrault, Daniel

2017-09-01

Transformation induced plasticity (TRIP) classically refers to plastic strains observed during phase transitions that occur under mechanical loads (that can be lower than the yield stress). A theoretical approach based on homogenization is proposed to deal with multiphase changes and to extend the validity of the well known and widely used model proposed by Leblond (1989). The approach is similar, but several product phases are considered instead of one and several assumptions have been released. Thus, besides the generalization for several phases, one can mention three main improvements in the calculation of the local equivalent plastic strain: the deviatoric part of the phase transformation is taken into account, both parent and product phases are elastic-plastic with linear isotropic hardening and the applied stress is considered. Results show that classical issues of singularities arising in the Leblond's model (corrected by ad hoc numerical functions or thresholding) are solved in this contribution excepted when the applied equivalent stress reaches the yield stress. Indeed, in this situation the parent phase is entirely plastic as soon as the phase transformation begins and the same singularity as in the Leblond's model arises. A physical explanation of the cutoff function is introduced in order to regularize the singularity. Furthermore, experiments extracted from the literature dealing with multiphase transitions and multiaxial loads are compared with the original Leblond's model and the proposed extended version. For the extended version, very good agreement is observed without any fitting procedures (i.e., material parameters are extracted from other dedicated experiments) and for the original version results are more qualitative.

Probabilistic finite elements for fracture and fatigue analysis

NASA Technical Reports Server (NTRS)

Liu, W. K.; Belytschko, T.; Lawrence, M.; Besterfield, G. H.

1989-01-01

The fusion of the probabilistic finite element method (PFEM) and reliability analysis for probabilistic fracture mechanics (PFM) is presented. A comprehensive method for determining the probability of fatigue failure for curved crack growth was developed. The criterion for failure or performance function is stated as: the fatigue life of a component must exceed the service life of the component; otherwise failure will occur. An enriched element that has the near-crack-tip singular strain field embedded in the element is used to formulate the equilibrium equation and solve for the stress intensity factors at the crack-tip. Performance and accuracy of the method is demonstrated on a classical mode 1 fatigue problem.

Electromagnetic fields and potentials generated by massless charged particles

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

Azzurli, Francesco, E-mail: francesco.azzurli@gmail.com; Lechner, Kurt, E-mail: lechner@pd.infn.it; INFN, Sezione di Padova, Via F. Marzolo, 8, 35131 Padova

2014-10-15

We provide for the first time the exact solution of Maxwell’s equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the electromagnetic field, which were both previously unknown, finding that they entail different physical features for bounded and unbounded trajectories. With respect to the standard Liénard–Wiechert field the electromagnetic field acquires singular δ-like contributions whose support and dimensionality depend crucially on whether the motion is (a) linear, (b) accelerated unbounded, (c) accelerated bounded. In the first two cases the particle generates amore » planar shock-wave-like electromagnetic field traveling along a straight line. In the second and third cases the field acquires, in addition, a δ-like contribution supported on a physical singularity-string attached to the particle. For generic accelerated motions a genuine radiation field is also present, represented by a regular principal-part type distribution diverging on the same singularity-string. - Highlights: • First exact solution of Maxwell’s equations for massless charges in arbitrary motion. • Explicit expressions of electromagnetic fields and potentials. • Derivations are rigorous and based on distribution theory. • The form of the field depends heavily on whether the motion is bounded or unbounded. • The electromagnetic field contains unexpected Dirac-delta-function contributions.« less

Introducing time-dependent molecular fields: a new derivation of the wave equations

NASA Astrophysics Data System (ADS)

Baer, Michael

2018-02-01

This article is part of a series of articles trying to establish the concept molecular field. The theory that induced us to introduce this novel concept is based on the Born-Huang expansion as applied to the Schroedinger equation that describes the interaction of a molecular system with an external electric field. Assuming the molecular system is made up of two coupled adiabatic states the theory leads from a single spatial curl equation, two space-time curl equations and one single space-time divergent equation to a pair of decoupled wave equations usually encountered within the theory of fields. In the present study, just like in the previous study [see Baer et al., Mol. Phys. 114, 227 (2016)] the wave equations are derived for an electric field having two features: (a) its intensity is high enough; (b) its duration is short enough. Although not all the findings are new the derivation, in the present case, is new, straightforward, fluent and much friendlier as compared to the previous one and therefore should be presented again. For this situation the study reveals that the just described interaction creates two fields that coexist within a molecule: one is a novel vectorial field formed via the interaction of the electric field with the Born-Huang non-adiabatic coupling terms (NACTs) and the other is an ordinary, scalar, electric field essentially identical to the original electric field. Section 4 devoted to the visualization of the outcomes via two intersecting Jahn-Teller cones which contain NACTs that become singular at the intersection point of these cones. Finally, the fact that eventually we are facing a kind of a cosmic situation may bring us to speculate that singular NACTs are a result of cosmic phenomena. Thus, if indeed this singularity is somehow connected to reality then, like other singularities in physics, it is formed at (or immediately after) the Big Bang and consequently, guarantees the formation of molecules.

Singularly Perturbed Lie Bracket Approximation

DOE PAGES

Durr, Hans-Bernd; Krstic, Miroslav; Scheinker, Alexander; ...

2015-03-27

Here, we consider the interconnection of two dynamical systems where one has an input-affine vector field. We show that by employing a singular perturbation analysis and the Lie bracket approximation technique, the stability of the overall system can be analyzed by regarding the stability properties of two reduced, uncoupled systems.

Nonnormal operators in physics, a singular-vectors approach: illustration in polarization optics.

PubMed

Tudor, Tiberiu

2016-04-20

The singular-vectors analysis of a general nonnormal operator defined on a finite-dimensional complex vector space is given in the frame of a pure operatorial ("nonmatrix," "coordinate-free") approach, performed in a Dirac language. The general results are applied in the field of polarization optics, where the nonnormal operators are widespread as operators of various polarization devices. Two nonnormal polarization devices representative for the class of nonnormal and even pathological operators-the standard two-layer elliptical ideal polarizer (singular operator) and the three-layer ambidextrous ideal polarizer (singular and defective operator)-are analyzed in detail. It is pointed out that the unitary polar component of the operator exists and preserves, in such pathological case too, its role of converting the input singular basis of the operator in its output singular basis. It is shown that for any nonnormal ideal polarizer a complementary one exists, so that the tandem of their operators uniquely determines their (common) unitary polar component.

Generalized teleparallel cosmology and initial singularity crossing

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

Awad, Adel; Nashed, Gamal, E-mail: Adel.Awad@bue.edu.eg, E-mail: gglnashed@sci.asu.edu.eg

We present a class of cosmological solutions for a generalized teleparallel gravity with f ( T )= T +α̃ (− T ) {sup n} , where α̃ is some parameter and n is an integer or half-integer. Choosing α̃ ∼ G {sup n} {sup −1}, where G is the gravitational constant, and working with an equation of state p = w ρ, one obtains a cosmological solution with multiple branches. The dynamics of the solution describes standard cosmology at late times, but the higher-torsion correction changes the nature of the initial singularity from big bang to a sudden singularity. Themore » milder behavior of the sudden singularity enables us to extend timelike or lightlike curves, through joining two disconnected branches of solution at the singularity, leaving the singularity traversable. We show that this extension is consistent with the field equations through checking the known junction conditions for generalized teleparallel gravity. This suggests that these solutions describe a contracting phase a prior to the expanding phase of the universe.« less

Formation of current singularity in a topologically constrained plasma

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

Zhou, Yao; Huang, Yi-Min; Qin, Hong

2016-02-01

Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranovmore » solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.« less

Rotating charged black holes accelerated by an electric field

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

Bicak, Jiri; Kofron, David; Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Muehlenberg 1, D-14476 Golm

The Ernst method of removing nodal singularities from the charged C-metric representing a uniformly accelerated black hole with mass m, charge q and acceleration A by 'adding' an electric field E is generalized. Utilizing the new form of the C-metric found recently, Ernst's simple 'equilibrium condition' mA=qE valid for small accelerations is generalized for arbitrary A. The nodal singularity is removed also in the case of accelerating and rotating charged black holes, and the corresponding equilibrium condition is determined.

Singular temperature dependence of the equation of state of superconductors with spin–orbit interaction in the low-temperature region

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

Ovchinnikov, Yu. N., E-mail: ovc@itp.ac.ru

The equation of state is investigated for a thin superconducting film in a longitudinal magnetic field and with strong spin-orbit interaction at the critical point. As a first step, the state with the maximal value of the magnetic field for a given value of spin–orbit interaction at T = 0 is chosen. This state is investigated in the low-temperature region. The temperature contribution to the equation of state is weakly singular.

The surface crack problem for a functionally graded coating bonded to a homogeneous layer

NASA Astrophysics Data System (ADS)

Kasmalkar, Maheendra B.

In the continuing search for materials which can withstand the grueling requirements of modern day applications, Functionally Graded Materials (FGMs) seem to be a promising alternative to conventional materials. These nonhomogeneous materials offer better interfacial properties by improving bond strength and reducing thermal mismatch. Before putting these materials into application, an important step in the design of FGMs is the stress analysis and fracture characterization. The fracture performance of FGM coatings on homogeneous substrates is the focus of this study. In this study, various internal and surface crack configurations in the coating and the substrate are subjected to mechanical and thermal loads. The analysis is linear elastic. The thermo-mechanical properties of the FGM coating are assumed to vary exponentially with the spatial coordinate. The equilibrium equations are solved using integral transforms. The resulting singular integral equations are solved using numerical integration. The results of interest for this mode I formulation are the stress intensity factors and the crack opening displacements. The effects of the nonhomogeneity parameter and various dimensionless length parameters are studied. One of the most important outcomes of this study is the theoretical proof that "kink" in material property at the interface does not introduce any singularity. In the numerical results it is observed that generally the stress intensity factors tend to increase with material nonhomogeneity. Also, it is observed that the substrate thickness tends to suppress cracking in the coating. In pure thermal loading, the surface cracks may either be arrested or there might be crack closure. The stress intensity factors from different loadings can be added up to obtain the resultant stress intensity factor for multiple loading. Results in this study have wide-ranging applications. They can be applied to thermal barrier coatings on turbine components, combustion chambers, parts of the airframe for the "Space Plane", soil mechanics, bone fractures and many more applications where the material is macroscopically nonhomogeneous. Thus this study solves a basic problem common to a variety of applications in diverse fields.

Non-singular bounce transitions in the multiverse

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

Garriga, Jaume; Vilenkin, Alexander; Zhang, Jun, E-mail: jaume.garriga@ub.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: jun.zhang@tufts.edu

2013-11-01

According to classical GR, negative-energy (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by non-singular bounces. Here we explore possible dynamics of such bounces using a simple modification of the Friedmann equation, which ensures that the scale factor bounces when the matter density reaches some critical value ρ{sub c}. This is combined with a simple scalar field 'landscape', where the energy barriers between different vacua are small compared to ρ{sub c}. We find that the bounce typically results in a transition tomore » another vacuum, with a scalar field displacement Δφ ∼ 1 in Planck units. If the new vacuum is AdS, we have another bounce, and so on, until the field finally transits to a positive-energy (de Sitter) vacuum. We also consider perturbations about the homogeneous solution and discuss some of their amplification mechanisms (e.g., tachyonic instability and parametric resonance). For a generic potential, these mechanisms are much less efficient than in models of slow-roll inflation. But the amplification may still be strong enough to cause the bubble to fragment into a mosaic of different vacua.« less

Orbiting naked singularities in large-ω Brans-Dicke gravity

NASA Astrophysics Data System (ADS)

Chauvineau, Bertrand

2017-11-01

Brans-Dicke gravity admits spherical solutions describing naked singularities rather than black holes. Depending on some parameters entering such a solution, stable circular orbits exist for all radii. One shows that, despite the fact a naked singularity is an infinite redshift location, the far observed orbital motion frequency is unbounded for an adiabatically decreasing radius. We then argue that this feature remains true in a wide set of scalar(s)-tensor theories if gravity. This is a salient difference with general relativity, and the repercussion on the gravitational radiation by EMRI systems is stressed. Since this behaviour survives the ω \\longrightarrow ∞ limit, the possibility of such solutions is of utmost interest in the new gravitational wave astronomy context, despite the current constraints on scalar-tensor gravity.

The approximation of anomalous magnetic field by array of magnetized rods

NASA Astrophysics Data System (ADS)

Denis, Byzov; Lev, Muravyev; Natalia, Fedorova

2017-07-01

The method for calculation the vertical component of an anomalous magnetic field from its absolute value is presented. Conversion is based on the approximation of magnetic induction module anomalies by the set of singular sources and the subsequent calculation for the vertical component of the field with the chosen distribution. The rods that are uniformly magnetized along their axis were used as a set of singular sources. Applicability analysis of different methods of nonlinear optimization for solving the given task was carried out. The algorithm is implemented using the parallel computing technology on the NVidia GPU. The approximation and calculation of vertical component is demonstrated for regional magnetic field of North Eurasia territories.

Crack Turning and Arrest Mechanisms for Integral Structure

NASA Technical Reports Server (NTRS)

Pettit, Richard; Ingraffea, Anthony

1999-01-01

In the course of several years of research efforts to predict crack turning and flapping in aircraft fuselage structures and other problems related to crack turning, the 2nd order maximum tangential stress theory has been identified as the theory most capable of predicting the observed test results. This theory requires knowledge of a material specific characteristic length, and also a computation of the stress intensity factors and the T-stress, or second order term in the asymptotic stress field in the vicinity of the crack tip. A characteristic length, r(sub c), is proposed for ductile materials pertaining to the onset of plastic instability, as opposed to the void spacing theories espoused by previous investigators. For the plane stress case, an approximate estimate of r(sub c), is obtained from the asymptotic field for strain hardening materials given by Hutchinson, Rice and Rosengren (HRR). A previous study using of high order finite element methods to calculate T-stresses by contour integrals resulted in extremely high accuracy values obtained for selected test specimen geometries, and a theoretical error estimation parameter was defined. In the present study, it is shown that a large portion of the error in finite element computations of both K and T are systematic, and can be corrected after the initial solution if the finite element implementation utilizes a similar crack tip discretization scheme for all problems. This scheme is applied for two-dimensional problems to a both a p-version finite element code, showing that sufficiently accurate values of both K(sub I) and T can be obtained with fairly low order elements if correction is used. T-stress correction coefficients are also developed for the singular crack tip rosette utilized in the adaptive mesh finite element code FRANC2D, and shown to reduce the error in the computed T-stress significantly. Stress intensity factor correction was not attempted for FRANC2D because it employs a highly accurate quarter-point scheme to obtain stress intensity factors.

On the possibility of singularities in the acoustic field of supersonic sources when BEM is applied to a wave equation

NASA Technical Reports Server (NTRS)

De Bernardis, E.; Farassat, F.

1989-01-01

Using a time domain method based on the Ffowcs Williams-Hawkings equation, a reliable explanation is provided for the origin of singularities observed in the numerical prediction of supersonic propeller noise. In the last few years Tam and, more recently, Amiet have analyzed the phenomenon from different points of view. The method proposed here offers a clear interpretation of the singularities based on a new description of sources, relating to the behavior of lines where the propeller blade surface exhibit slope discontinuity.

Singular perturbations with boundary conditions and the Casimir effect in the half space

NASA Astrophysics Data System (ADS)

Albeverio, S.; Cognola, G.; Spreafico, M.; Zerbini, S.

2010-06-01

We study the self-adjoint extensions of a class of nonmaximal multiplication operators with boundary conditions. We show that these extensions correspond to singular rank 1 perturbations (in the sense of Albeverio and Kurasov [Singular Perturbations of Differential Operaters (Cambridge University Press, Cambridge, 2000)]) of the Laplace operator, namely, the formal Laplacian with a singular delta potential, on the half space. This construction is the appropriate setting to describe the Casimir effect related to a massless scalar field in the flat space-time with an infinite conducting plate and in the presence of a pointlike "impurity." We use the relative zeta determinant (as defined in the works of Müller ["Relative zeta functions, relative determinants and scattering theory," Commun. Math. Phys. 192, 309 (1998)] and Spreafico and Zerbini ["Finite temperature quantum field theory on noncompact domains and application to delta interactions," Rep. Math. Phys. 63, 163 (2009)]) in order to regularize the partition function of this model. We study the analytic extension of the associated relative zeta function, and we present explicit results for the partition function and for the Casimir force.

Observational constraints on cosmological future singularities

NASA Astrophysics Data System (ADS)

Beltrán Jiménez, Jose; Lazkoz, Ruth; Sáez-Gómez, Diego; Salzano, Vincenzo

2016-11-01

In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H( z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means {˜ }2.8 Gyrs from the present time.

The fields of a naked singularity and a black hole in mutual equilibrium

NASA Astrophysics Data System (ADS)

Paolino, Armando; Pizzi, Marco

2008-01-01

Recently Alekseev and Belinski have presented a new exact solution of the Einstein-Maxwell equation which describes two Reissner-Nordstrom (RN) sources in reciprocal equilibrium (no struts nor strings) one source is a naked singularity, the other is a black hole. In this paper we use the Alekseev-Belinki solution in the special case in which the charge of the black hole is zero-therefore we have a naked singularity near a neutral black hole. We give the plots of the electric force lines in both the cases in which the naked singularity has a mass comparable with the black hole and in which it is much smaller. The analysis of this latter case confirm the goodness of the Hanni-Ruffini approximation.

RAS one-equation turbulence model with non-singular eddy-viscosity coefficient

NASA Astrophysics Data System (ADS)

Rahman, M. M.; Agarwal, R. K.; Siikonen, T.

2016-02-01

A simplified consistency formulation for Pk/ε (production to dissipation ratio) is devised to obtain a non-singular Cμ (coefficient of eddy-viscosity) in the explicit algebraic Reynolds stress model of Gatski and Speziale. The coefficient Cμ depends non-linearly on both rotational/irrotational strains and is used in the framework of an improved RAS (Rahman-Agarwal-Siikonen) one-equation turbulence model to calculate a few well-documented turbulent flows, yielding predictions in good agreement with the direct numerical simulation and experimental data. The strain-dependent Cμ assists the RAS model in constructing the coefficients and functions such as to benefit complex flows with non-equilibrium turbulence. Comparisons with the Spalart-Allmaras one-equation model and the shear stress transport k-ω model demonstrate that Cμ improves the response of RAS model to non-equilibrium effects.

The presence of a phantom field in a Randall–Sundrum scenario

NASA Astrophysics Data System (ADS)

Acuña-Cárdenas, Rubén O.; Astorga-Moreno, J. A.; García-Aspeitia, Miguel A.; López-Domínguez, J. C.

2018-02-01

The presence of phantom dark energy in brane world cosmology generates important new effects, causing a premature big rip singularity when we increase the presence of extra dimensions and considerably competing with the other components of our Universe. This article first considers only a field with the characteristic equation ω<-1 and then the explicit form of the scalar field with a potential with a maximum (with the aim of avoiding a big rip singularity). In both cases we study the dynamics robustly through dynamical analysis theory, considering in detail parameters such as the deceleration q and the vector field associated to the dynamical system. Results are discussed with the purpose of treating the cosmology with a phantom field as dark energy in a Randall–Sundrum scenario.

On D-brane -anti D-brane effective actions and their all order bulk singularity structures

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

Hatefi, Ehsan; Institute for Theoretical Physics, TU Wien,Wiedner Hauptstrasse 8-10/136, A-1040 Vienna

All four point functions of brane anti brane system including their correct all order α{sup ′} corrections have been addressed. All five point functions of one closed string Ramond-Ramond (RR), two real tachyons and either one gauge field or the scalar field in both symmetric and asymmetric pictures have also been explored. The entire analysis of is carried out. Not only does it fix the vertex operator of RR in asymmetric picture and in higher point functions of string theory amplitudes but also it confirms the fact that there is no issue of picture dependence of the mixed closed RR,more » gauge fields, tachyons and fermion fields in all symmetric or anti symmetric ones. We compute S-matrix in the presence of a transverse scalar field, two real tachyons and that reveals two different kinds of bulk singularity structures, involving an infinite number of u-channel gauge field and (u+s{sup ′}+t{sup ′})-channel scalar bulk poles. In order to produce all those bulk singularity structures, we define various couplings at the level of the effective field theory that involve the mixing term of Chern-Simons coupling (with C-potential field) and a covariant derivative of the scalar field that comes from the pull-back of brane. Eventually we explore their all order α{sup ′} corrections in the presence of brane anti brane system where various remarks will be also pointed out.« less

The solid angle hidden in polyhedron gravitation formulations

NASA Astrophysics Data System (ADS)

Werner, Robert A.

2017-03-01

Formulas of a homogeneous polyhedron's gravitational potential typically include two arctangent terms for every edge of every face and a special term to eliminate a possible facial singularity. However, the arctangent and singularity terms are equivalent to the face's solid angle viewed from the field point. A face's solid angle can be evaluated with a single arctangent, saving computation.

A clamped rectangular plate containing a crack

NASA Technical Reports Server (NTRS)

Tang, R.; Erdogan, F.

1985-01-01

The general problem of a rectangular plate clamped along two parallel sides and containing a crack parallel to the clamps is considered. The problem is formulated in terms of a system of singular integral equations and the asymptotic behavior of the stress state near the corners is investigated. Numerical examples are considered for a clamped plate without a crack and with a centrally located crack, and the stress intensity factors and the stresses along the clamps are calculated.

Bianchi type string cosmological models in f(R,T) gravity

NASA Astrophysics Data System (ADS)

Sahoo, P. K.; Mishra, B.; Sahoo, Parbati; Pacif, S. K. J.

2016-09-01

In this work we have studied Bianchi-III and - VI 0 cosmological models with string fluid source in f( R, T) gravity (T. Harko et al., Phys. Rev. D 84, 024020 (2011)), where R is the Ricci scalar and T the trace of the stress energy-momentum tensor in the context of late time accelerating expansion of the universe as suggested by the present observations. The exact solutions of the field equations are obtained by using a time-varying deceleration parameter. The universe is anisotropic and free from initial singularity. Our model initially shows acceleration for a certain period of time and then decelerates consequently. Several dynamical and physical behaviors of the model are also discussed in detail.

Smart built-in test

NASA Technical Reports Server (NTRS)

Richards, Dale W.

1990-01-01

The work which built-in test (BIT) is asked to perform in today's electronic systems increases with every insertion of new technology or introduction of tighter performance criteria. Yet the basic purpose remains unchanged -- to determine with high confidence the operational capability of that equipment. Achievement of this level of BIT performance requires the management and assimilation of a large amount of data, both realtime and historical. Smart BIT has taken advantage of advanced techniques from the field of artificial intelligence (AI) in order to meet these demands. The Smart BIT approach enhances traditional functional BIT by utilizing AI techniques to incorporate environmental stress data, temporal BIT information and maintenance data, and realtime BIT reports into an integrated test methodology for increased BIT effectiveness and confidence levels. Future research in this area will incorporate onboard fault-logging of BIT output, stress data and Smart BIT decision criteria in support of a singular, integrated and complete test and maintenance capability. The state of this research is described along with a discussion of directions for future development.

Smart built-in test

NASA Astrophysics Data System (ADS)

Richards, Dale W.

1990-03-01

The work which built-in test (BIT) is asked to perform in today's electronic systems increases with every insertion of new technology or introduction of tighter performance criteria. Yet the basic purpose remains unchanged -- to determine with high confidence the operational capability of that equipment. Achievement of this level of BIT performance requires the management and assimilation of a large amount of data, both realtime and historical. Smart BIT has taken advantage of advanced techniques from the field of artificial intelligence (AI) in order to meet these demands. The Smart BIT approach enhances traditional functional BIT by utilizing AI techniques to incorporate environmental stress data, temporal BIT information and maintenance data, and realtime BIT reports into an integrated test methodology for increased BIT effectiveness and confidence levels. Future research in this area will incorporate onboard fault-logging of BIT output, stress data and Smart BIT decision criteria in support of a singular, integrated and complete test and maintenance capability. The state of this research is described along with a discussion of directions for future development.

A limiting analysis for edge effects in angle-ply laminates

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1976-01-01

A zeroth order solution for edge effects in angle ply composite laminates using perturbation techniques and a limiting free body approach was developed. The general method of solution for laminates is developed and then applied to the special case of a graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness to width ratio h/b and compared to existing numerical results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress for two laminates, and provides mathematical evidence for singular interlaminar shear stresses.

Quantum Griffiths singularity of superconductor-metal transition in Ga thin films.

PubMed

Xing, Ying; Zhang, Hui-Min; Fu, Hai-Long; Liu, Haiwen; Sun, Yi; Peng, Jun-Ping; Wang, Fa; Lin, Xi; Ma, Xu-Cun; Xue, Qi-Kun; Wang, Jian; Xie, X C

2015-10-30

The Griffiths singularity in a phase transition, caused by disorder effects, was predicted more than 40 years ago. Its signature, the divergence of the dynamical critical exponent, is challenging to observe experimentally. We report the experimental observation of the quantum Griffiths singularity in a two-dimensional superconducting system. We measured the transport properties of atomically thin gallium films and found that the films undergo superconductor-metal transitions with increasing magnetic field. Approaching the zero-temperature quantum critical point, we observed divergence of the dynamical critical exponent, which is consistent with the Griffiths singularity behavior. We interpret the observed superconductor-metal quantum phase transition as the infinite-randomness critical point, where the properties of the system are controlled by rare large superconducting regions. Copyright © 2015, American Association for the Advancement of Science.

Removing singular refractive indices with sculpted surfaces

PubMed Central

Horsley, S. A. R.; Hooper, I. R.; Mitchell–Thomas, R. C.; Quevedo–Teruel, O.

2014-01-01

The advent of Transformation Optics established the link between geometry and material properties, and has resulted in a degree of control over electromagnetic fields that was previously impossible. For waves confined to a surface it is known that there is a simpler, but related, geometrical equivalence between the surface shape and the refractive index, and here we demonstrate that conventional devices possessing a singularity — that is, the requirement of an infinite refractive index — can be realised for waves confined to an appropriately sculpted surface. In particular, we redesign three singular omnidirectional devices: the Eaton lens, the generalized Maxwell Fish–Eye, and the invisible sphere. Our designs perfectly reproduce the behaviour of these singular devices, and can be achieved with simple isotropic media of low refractive index contrast. PMID:24786649

Stress-free end problem in layered materials

NASA Technical Reports Server (NTRS)

Erdogan, F.; Bakioglu, M.

1977-01-01

In this paper the plane elastostatic problem for a medium which consists of periodically arranged two sets of bonded dissimilar layers or strips is considered. First it is assumed that one set of strips contains a crack which crosses the bimaterial interfaces. Then, by letting the collinear cracks join, the stress-free end problem is formulated. The singular behavior of the solutions at the point on intersection of the stress-free boundary and the interfaces is examined and appropriate stress intensity factors are defined. The results of some numerical examples are then presented which include the cases of both plane stress and plane strain.

The singularity structure of scale-invariant rank-2 Coulomb branches

NASA Astrophysics Data System (ADS)

Argyres, Philip C.; Long, Cody; Martone, Mario

2018-05-01

We compute the spectrum of scaling dimensions of Coulomb branch operators in 4d rank-2 N=2 superconformal field theories. Only a finite rational set of scaling dimensions is allowed. It is determined by using information about the global topology of the locus of metric singularities on the Coulomb branch, the special Kähler geometry near those singularities, and electric-magnetic duality monodromies along orbits of the U(1) R symmetry. A set of novel topological and geometric results are developed which promise to be useful for the study and classification of Coulomb branch geometries at all ranks.

Caustic Singularities Of High-Gain, Dual-Shaped Reflectors

NASA Technical Reports Server (NTRS)

Galindo, Victor; Veruttipong, Thavath W.; Imbriale, William A.; Rengarajan, Sambiam

1991-01-01

Report presents study of some sources of error in analysis, by geometric theory of diffraction (GTD), of performance of high-gain, dual-shaped antenna reflector. Study probes into underlying analytic causes of singularity, with view toward devising and testing practical methods to avoid problems caused by singularity. Hybrid physical optics (PO) approach used to study near-field spillover or noise-temperature characteristics of high-gain relector antenna efficiently and accurately. Report illustrates this approach and underlying principles by presenting numerical results, for both offset and symmetrical reflector systems, computed by GTD, PO, and PO/GO methods.

Displacement Fields and Self-Energies of Circular and Polygonal Dislocation Loops in Homogeneous and Layered Anisotropic Solids

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

Gao, Yanfei; Larson, Ben C.

There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order -1, we have shown thatmore » the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental–theoretical investigations.« less

Displacement Fields and Self-Energies of Circular and Polygonal Dislocation Loops in Homogeneous and Layered Anisotropic Solids

DOE PAGES

Gao, Yanfei; Larson, Ben C.

2015-06-19

There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order -1, we have shown thatmore » the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental–theoretical investigations.« less

A spin-liquid with pinch-line singularities on the pyrochlore lattice.

PubMed

Benton, Owen; Jaubert, L D C; Yan, Han; Shannon, Nic

2016-05-26

The mathematics of gauge theories lies behind many of the most profound advances in physics in the past 200 years, from Maxwell's theory of electromagnetism to Einstein's theory of general relativity. More recently it has become clear that gauge theories also emerge in condensed matter, a prime example being the spin-ice materials which host an emergent electromagnetic gauge field. In spin-ice, the underlying gauge structure is revealed by the presence of pinch-point singularities in neutron-scattering measurements. Here we report the discovery of a spin-liquid where the low-temperature physics is naturally described by the fluctuations of a tensor field with a continuous gauge freedom. This gauge structure underpins an unusual form of spin correlations, giving rise to pinch-line singularities: line-like analogues of the pinch points observed in spin-ice. Remarkably, these features may already have been observed in the pyrochlore material Tb2Ti2O7.

A spin-liquid with pinch-line singularities on the pyrochlore lattice

PubMed Central

Benton, Owen; Jaubert, L.D.C.; Yan, Han; Shannon, Nic

2016-01-01

The mathematics of gauge theories lies behind many of the most profound advances in physics in the past 200 years, from Maxwell's theory of electromagnetism to Einstein's theory of general relativity. More recently it has become clear that gauge theories also emerge in condensed matter, a prime example being the spin-ice materials which host an emergent electromagnetic gauge field. In spin-ice, the underlying gauge structure is revealed by the presence of pinch-point singularities in neutron-scattering measurements. Here we report the discovery of a spin-liquid where the low-temperature physics is naturally described by the fluctuations of a tensor field with a continuous gauge freedom. This gauge structure underpins an unusual form of spin correlations, giving rise to pinch-line singularities: line-like analogues of the pinch points observed in spin-ice. Remarkably, these features may already have been observed in the pyrochlore material Tb2Ti2O7. PMID:27225400

On the evaluation of the gravity effects of polyhedral bodies and a consistent treatment of related singularities

NASA Astrophysics Data System (ADS)

D'Urso, M. G.

2013-03-01

We show that the singularities which can affect the computation of the gravity effects (potential, gravity and tensor gradient fields) can be systematically addressed by invoking distribution theory and suitable formulas of differential calculus. Thus, differently from previous contributions on the subject, the use of a-posteriori corrections of the formulas derived in absence of singularities can be ruled out. The general approach presented in the paper is further specialized to the case of polyhedral bodies and detailed for a rectangular prism having a constant mass density. With reference to this last case, we derive novel expressions for the related gravitational field, as well as for its first and second derivative, at an observation point coincident with a prism vertex and show that they turn out to be more compact than the ones reported in the specialized literature.

Quantum space and quantum completeness

NASA Astrophysics Data System (ADS)

Jurić, Tajron

2018-05-01

Motivated by the question whether quantum gravity can "smear out" the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one observes the effect of "smearing out" the singularity.

Opening of an interface flaw in a layered elastic half-plane under compressive loading

NASA Technical Reports Server (NTRS)

Kennedy, J. M.; Fichter, W. B.; Goree, J. G.

1984-01-01

A static analysis is given of the problem of an elastic layer perfectly bonded, except for a frictionless interface crack, to a dissimilar elastic half-plane. The free surface of the layer is loaded by a finite pressure distribution directly over the crack. The problem is formulated using the two dimensional linear elasticity equations. Using Fourier transforms, the governing equations are converted to a pair of coupled singular integral equations. The integral equations are reduced to a set of simultaneous algebraic equations by expanding the unknown functions in a series of Jacobi polynomials and then evaluating the singular Cauchy-type integrals. The resulting equations are found to be ill-conditioned and, consequently, are solved in the least-squares sense. Results from the analysis show that, under a normal pressure distribution on the free surface of the layer and depending on the combination of geometric and material parameters, the ends of the crack can open. The resulting stresses at the crack-tips are singular, implying that crack growth is possible. The extent of the opening and the crack-top stress intensity factors depend on the width of the pressure distribution zone, the layer thickness, and the relative material properties of the layer and half-plane.

Light focusing through a multiple scattering medium: ab initio computer simulation

NASA Astrophysics Data System (ADS)

Danko, Oleksandr; Danko, Volodymyr; Kovalenko, Andrey

2018-01-01

The present study considers ab initio computer simulation of the light focusing through a complex scattering medium. The focusing is performed by shaping the incident light beam in order to obtain a small focused spot on the opposite side of the scattering layer. MSTM software (Auburn University) is used to simulate the propagation of an arbitrary monochromatic Gaussian beam and obtain 2D distribution of the optical field in the selected plane of the investigated volume. Based on the set of incident and scattered fields, the pair of right and left eigen bases and corresponding singular values were calculated. The pair of right and left eigen modes together with the corresponding singular value constitute the transmittance eigen channel of the disordered media. Thus, the scattering process is described in three steps: 1) initial field decomposition in the right eigen basis; 2) scaling of decomposition coefficients for the corresponding singular values; 3) assembling of the scattered field as the composition of the weighted left eigen modes. Basis fields are represented as a linear combination of the original Gaussian beams and scattered fields. It was demonstrated that 60 independent control channels provide focusing the light into a spot with the minimal radius of approximately 0.4 μm at half maximum. The intensity enhancement in the focal plane was equal to 68 that coincided with theoretical prediction.

Normal forms of Hopf-zero singularity

NASA Astrophysics Data System (ADS)

Gazor, Majid; Mokhtari, Fahimeh

2015-01-01

The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative-nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov-Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov-Takens singularities. Despite this, the normal form computations of Bogdanov-Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative-nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto-Sivashinsky equations to demonstrate the applicability of our results.

The mechanics of delamination in fiber-reinforced composite materials. Part 2: Delamination behavior and fracture mechanics parameters

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1983-01-01

Based on theories of laminate anisotropic elasticity and interlaminar fracture, the complete solution structure associated with a composite delamination is determined. Fracture mechanics parameters characterizing the interlaminar crack behavior are defined from asymptotic stress solutions for delaminations with different crack-tip deformation configurations. A numerical method employing singular finite elements is developed to study delaminations in fiber composites with any arbitrary combinations of lamination, material, geometric, and crack variables. The special finite elements include the exact delamination stress singularity in its formulation. The method is shown to be computationally accurate and efficient, and operationally simple. To illustrate the basic nature of composite delamination, solutions are shown for edge-delaminated (0/-0/-0/0) and (+ or - 0/+ or - 0/90/90 deg) graphite-epoxy systems under uniform axial extenstion. Three-dimensional crack-tip stress intensity factors, associated energy release rates, and delamination crack-closure are determined for each individual case. The basic mechanics and mechanisms of composite delamination are studied, and fundamental characteristics unique to recently proposed tests for interlaminar fracture toughness of fiber composite laminates are examined.

A note on singularities of the 3-D Euler equation

NASA Technical Reports Server (NTRS)

Tanveer, S.

1994-01-01

In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.

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

Arroja, Frederico; Chen, Che-Yu; Chen, Pisin

In this work, we investigate O (4)-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI) . We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, butmore » there is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.« less

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

Arroja, Frederico; Chen, Che -Yu; Chen, Pisin

In this study, we investigate O(4)-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI) . We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, but theremore » is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.« less

Current singularities at quasi-separatrix layers and three-dimensional magnetic nulls

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

Craig, I. J. D.; Effenberger, Frederic, E-mail: feffen@waikato.ac.nz

2014-11-10

The open problem of how singular current structures form in line-tied, three-dimensional magnetic fields is addressed. A Lagrangian magneto-frictional relaxation method is employed to model the field evolution toward the final near-singular state. Our starting point is an exact force-free solution of the governing magnetohydrodynamic equations that is sufficiently general to allow for topological features like magnetic nulls to be inside or outside the computational domain, depending on a simple set of parameters. Quasi-separatrix layers (QSLs) are present in these structures and, together with the magnetic nulls, they significantly influence the accumulation of current. It is shown that perturbations affectingmore » the lateral boundaries of the configuration lead not only to collapse around the magnetic null but also to significant QSL currents. Our results show that once a magnetic null is present, the developing currents are always attracted to that specific location and show a much stronger scaling with resolution than the currents that form along the QSL. In particular, the null-point scalings can be consistent with models of 'fast' reconnection. The QSL currents also appear to be unbounded but give rise to weaker singularities, independent of the perturbation amplitude.« less

Unsteady three-dimensional flow separation

NASA Technical Reports Server (NTRS)

Hui, W. H.

1988-01-01

A concise mathematical framework is constructed to study the topology of steady 3-D separated flows of an incompressible, or a compressible viscous fluid. Flow separation is defined by the existence of a stream surface which intersects with the body surface. The line of separation is itself a skin-friction line. Flow separation is classified as being either regular or singular, depending respectively on whether the line of separation contains only a finite number of singular points or is a singular line of the skin-friction field. The special cases of 2-D and axisymmetric flow separation are shown to be of singular type. In regular separation it is shown that a line of separation originates from a saddle point of separation of the skin-friction field and ends at nodal points of separation. Unsteady flow separation is defined relative to a coordinate system fixed to the body surface. It is shown that separation of an unsteady 3-D incompressible viscous flow at time t, when viewed from such a frame of reference, is topologically the same as that of the fictitious steady flow obtained by freezing the unsteady flow at the instant t. Examples are given showing effects of various forms of flow unsteadiness on flow separation.

Cosmological applications of singular hypersurfaces in general relativity

NASA Astrophysics Data System (ADS)

Laguna-Castillo, Pablo

Three applications to cosmology of surface layers, based on Israel's formalism of singular hypersurfaces and thin shells in general relativity, are presented. Einstein's field equations are analyzed in the presence of a bubble nucleated in vacuum phase transitions within the context of the old inflationary universe scenario. The evolution of a bubble with vanishing surface energy density is studied. It is found that such bubbles lead to a worm-hole matching. Next, the observable four-dimensional universe is considered as a singular hypersurface of discontinuity embedded in a five-dimensional Kaluza-Klein cosmology. It is possible to rewrite the projected five-dimensional Einstein equations on the surface layer in a similar way to the four-dimensional Robertson-Walker cosmology equations. Next, a model is described for an infinite-length, straight U(1) cosmic string as a cylindrical, singular shell enclosing a region of false vacuum. A set of equations is introduced which are required to develop a three-dimensional computer code whose purpose is to study the process of intercommuting cosmic strings with the inclusion of gravitational effects. The outcome is evolution and constraint equations for the gravitational, scalar and gauge field of two initially separated, perpendicular, cosmic strings.

Two-order parameters theory of the metal-insulator phase transition kinetics in the magnetic field

NASA Astrophysics Data System (ADS)

Dubovskii, L. B.

2018-05-01

The metal-insulator phase transition is considered within the framework of the Ginzburg-Landau approach for the phase transition described with two coupled order parameters. One of the order parameters is the mass density which variation is responsible for the origin of nonzero overlapping of the two different electron bands and the appearance of free electron carriers. This transition is assumed to be a first-order phase one. The free electron carriers are described with the vector-function representing the second-order parameter responsible for the continuous phase transition. This order parameter determines mostly the physical properties of the metal-insulator transition and leads to a singularity of the surface tension at the metal-insulator interface. The magnetic field is involved into the consideration of the system. The magnetic field leads to new singularities of the surface tension at the metal-insulator interface and results in a drastic variation of the phase transition kinetics. A strong singularity in the surface tension results from the Landau diamagnetism and determines anomalous features of the metal-insulator transition kinetics.

Stress intensity factor in a tapered specimen

NASA Technical Reports Server (NTRS)

Xue-Hui, L.; Erdogan, F.

1985-01-01

The general problem of a tapered specimen containing an edge crack is formulated in terms of a system of singular integral equations. The equations are solved and the stress intensity factor is calculated for a compact and for a slender tapered specimen, the latter simulating the double cantilever beam. The results are obtained primarily for a pair of concentrated forces and for crack surface wedge forces. The stress intensity factors are also obtained for a long strip under uniform tension which contains inclined edge cracks.

Computation at a coordinate singularity

NASA Astrophysics Data System (ADS)

Prusa, Joseph M.

2018-05-01

Coordinate singularities are sometimes encountered in computational problems. An important example involves global atmospheric models used for climate and weather prediction. Classical spherical coordinates can be used to parameterize the manifold - that is, generate a grid for the computational spherical shell domain. This particular parameterization offers significant benefits such as orthogonality and exact representation of curvature and connection (Christoffel) coefficients. But it also exhibits two polar singularities and at or near these points typical continuity/integral constraints on dependent fields and their derivatives are generally inadequate and lead to poor model performance and erroneous results. Other parameterizations have been developed that eliminate polar singularities, but problems of weaker singularities and enhanced grid noise compared to spherical coordinates (away from the poles) persist. In this study reparameterization invariance of geometric objects (scalars, vectors and the forms generated by their covariant derivatives) is utilized to generate asymptotic forms for dependent fields of interest valid in the neighborhood of a pole. The central concept is that such objects cannot be altered by the metric structure of a parameterization. The new boundary conditions enforce symmetries that are required for transformations of geometric objects. They are implemented in an implicit polar filter of a structured grid, nonhydrostatic global atmospheric model that is simulating idealized Held-Suarez flows. A series of test simulations using different configurations of the asymptotic boundary conditions are made, along with control simulations that use the default model numerics with no absorber, at three different grid sizes. Typically the test simulations are ∼ 20% faster in wall clock time than the control-resulting from a decrease in noise at the poles in all cases. In the control simulations adverse numerical effects from the polar singularity are observed to increase with grid resolution. In contrast, test simulations demonstrate robust polar behavior independent of grid resolution.

Determination of nuclear quadrupolar parameters using singularities in field-swept NMR patterns.

PubMed

Ichijo, Naoki; Takeda, Kazuyuki; Yamada, Kazuhiko; Takegoshi, K

2016-10-07

We propose a simple data-analysis scheme to determine the coupling constant and the asymmetry parameter of nuclear quadrupolar interactions in field-swept nuclear magnetic resonance (NMR) for static powder samples. This approach correlates the quadrupolar parameters to the positions of the singularities, which can readily be found out as sharp peaks in the field-swept pattern. Moreover, the parameters can be determined without quantitative acquisition and elaborate calculation of the overall profile of the pattern. Since both experimental and computational efforts are significantly reduced, the approach presented in this work will enhance the power of the field-swept NMR for yet unexplored quadrupolar nuclei. We demonstrate this approach in 33 S in α-S 8 and 35 Cl in chloranil. The accuracy of the obtained quadrupolar parameters is also discussed.

Singular values behaviour optimization in the diagnosis of feed misalignments in radioastronomical reflectors

NASA Astrophysics Data System (ADS)

Capozzoli, Amedeo; Curcio, Claudio; Liseno, Angelo; Savarese, Salvatore; Schipani, Pietro

2016-07-01

The communication presents an innovative method for the diagnosis of reflector antennas in radio astronomical applications. The approach is based on the optimization of the number and the distribution of the far field sampling points exploited to retrieve the antenna status in terms of feed misalignments, this to drastically reduce the time length of the measurement process and minimize the effects of variable environmental conditions and simplifying the tracking process of the source. The feed misplacement is modeled in terms of an aberration function of the aperture field. The relationship between the unknowns and the far field pattern samples is linearized thanks to a Principal Component Analysis. The number and the position of the field samples are then determined by optimizing the Singular Values behaviour of the relevant operator.

Non-free gas of dipoles of non-singular screw dislocations and the shear modulus near the melting

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

Malyshev, Cyril, E-mail: malyshev@pdmi.ras.ru

2014-12-15

The behavior of the shear modulus caused by proliferation of dipoles of non-singular screw dislocations with finite-sized core is considered. The representation of two-dimensional Coulomb gas with smoothed-out coupling is used, and the stress–stress correlation function is calculated. A convolution integral expressed in terms of the modified Bessel function K{sub 0} is derived in order to obtain the shear modulus in approximation of interacting dipoles. Implications are demonstrated for the shear modulus near the melting transition which are due to the singularityless character of the dislocations. - Highlights: • Thermodynamics of dipoles of non-singular screw dislocations is studied below themore » melting. • The renormalization of the shear modulus is obtained for interacting dipoles. • Dependence of the shear modulus on the system scales is presented near the melting.« less

Asymptotically (A)dS dilaton black holes with nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Hajkhalili, S.; Sheykhi, A.

It is well known that with an appropriate combination of three Liouville-type dilaton potentials, one can construct charged dilaton black holes in an (anti)-de Sitter [(A)dS] spaces in the presence of linear Maxwell field. However, asymptotically (A)dS dilaton black holes coupled to nonlinear gauge field have not been found. In this paper, we construct, for the first time, three new classes of dilaton black hole solutions in the presence of three types of nonlinear electrodynamics, namely Born-Infeld (BI), Logarithmic (LN) and Exponential nonlinear (EN) electrodynamics. All these solutions are asymptotically (A)dS and in the linear regime reduce to the Einstein-Maxwell-dilaton (EMd) black holes in (A)dS spaces. We investigate physical properties and the causal structure, as well as asymptotic behavior of the obtained solutions, and show that depending on the values of the metric parameters, the singularity can be covered by various horizons. We also calculate conserved and thermodynamic quantities of the obtained solutions. Interestingly enough, we find that the coupling of dilaton field and nonlinear gauge field in the background of (A)dS spaces leads to a strange behavior for the electric field. We observe that the electric field is zero at singularity and increases smoothly until reaches a maximum value, then it decreases smoothly until goes to zero as r →∞. The maximum value of the electric field increases with increasing the nonlinear parameter β or decreasing the dilaton coupling α and is shifted to the singularity in the absence of either dilaton field (α = 0) or nonlinear gauge field (β →∞).

Heating of the corona by magnetic singularities

NASA Technical Reports Server (NTRS)

Antiochos, Spiro K.

1990-01-01

Theoretical models of current-sheet formation and magnetic heating in the solar corona are examined analytically. The role of photospheric connectivity in determining the topology of the coronal magnetic field and its equilibrium properties is explored; nonequilibrium models of current-sheet formation (assuming an initially well connected field) are described; and particular attention is given to models with discontinuous connectivity, where magnetic singularities arise from smooth footpoint motions. It is shown that current sheets arise from connectivities in which the photospheric flux structure is complex, with three or more polarity regions and a magnetic null point within the corona.

Singular gauge transformation and the Erler-Maccaferri solution in bosonic open string field theory

NASA Astrophysics Data System (ADS)

Miwa, Akitsugu; Sugita, Kazuhiro

2017-09-01

We study candidate multiple-brane solutions of bosonic open string field theory. They are constructed by performing a singular gauge transformation n times for the Erler-Maccaferri solution. We check the equation of motion in the strong sense, and find that it is satisfied only when we perform the gauge transformation once. We calculate the energy for that case and obtain a support that the solution is a multiple-brane solution. We also check the tachyon profile for a specific solution that we interpret as describing a D24-brane placed on a D25-brane.

An improved cylindrical FDTD method and its application to field-tissue interaction study in MRI.

PubMed

Chi, Jieru; Liu, Feng; Xia, Ling; Shao, Tingting; Mason, David G; Crozier, Stuart

2010-01-01

This paper presents a three dimensional finite-difference time-domain (FDTD) scheme in cylindrical coordinates with an improved algorithm for accommodating the numerical singularity associated with the polar axis. The regularization of this singularity problem is entirely based on Ampere's law. The proposed algorithm has been detailed and verified against a problem with a known solution obtained from a commercial electromagnetic simulation package. The numerical scheme is also illustrated by modeling high-frequency RF field-human body interactions in MRI. The results demonstrate the accuracy and capability of the proposed algorithm.

Formation of Singularities at the Interface of Liquid Dielectrics in a Horizontal Electric Field in the Presence of Tangential Velocity Discontinuity

NASA Astrophysics Data System (ADS)

Zubarev, N. M.; Kochurin, E. A.

2018-03-01

Nonlinear dynamics of the interface of dielectric liquids under the conditions of suppression of the Kelvin-Helmholz instability by a tangential electric field has been investigated. Two broad classes of exact analytical solutions to the equations of motion describing the evolution of spatially localized and periodic interface perturbations have been found. Both classes of solutions tend to the formation of strong singularities: interface discontinuities with formally infinite amplitudes. The discontinuity sign is determined by the sign of liquid velocity jump at the interface.

Compacted dimensions and singular plasmonic surfaces

NASA Astrophysics Data System (ADS)

Pendry, J. B.; Huidobro, Paloma Arroyo; Luo, Yu; Galiffi, Emanuele

2017-11-01

In advanced field theories, there can be more than four dimensions to space, the excess dimensions described as compacted and unobservable on everyday length scales. We report a simple model, unconnected to field theory, for a compacted dimension realized in a metallic metasurface periodically structured in the form of a grating comprising a series of singularities. An extra dimension of the grating is hidden, and the surface plasmon excitations, though localized at the surface, are characterized by three wave vectors rather than the two of typical two-dimensional metal grating. We propose an experimental realization in a doped graphene layer.

Identification and modification of dominant noise sources in diesel engines

NASA Astrophysics Data System (ADS)

Hayward, Michael D.

Determination of dominant noise sources in diesel engines is an integral step in the creation of quiet engines, but is a process which can involve an extensive series of expensive, time-consuming fired and motored tests. The goal of this research is to determine dominant noise source characteristics of a diesel engine in the near and far-fields with data from fewer tests than is currently required. Pre-conditioning and use of numerically robust methods to solve a set of cross-spectral density equations results in accurate calculation of the transfer paths between the near- and far-field measurement points. Application of singular value decomposition to an input cross-spectral matrix determines the spectral characteristics of a set of independent virtual sources, that, when scaled and added, result in the input cross spectral matrix. Each virtual source power spectral density is a singular value resulting from the decomposition performed over a range of frequencies. The complex relationship between virtual and physical sources is estimated through determination of virtual source contributions to each input measurement power spectral density. The method is made more user-friendly through use of a percentage contribution color plotting technique, where different normalizations can be used to help determine the presence of sources and the strengths of their contributions. Convolution of input measurements with the estimated path impulse responses results in a set of far-field components, to which the same singular value contribution plotting technique can be applied, thus allowing dominant noise source characteristics in the far-field to also be examined. Application of the methods presented results in determination of the spectral characteristics of dominant noise sources both in the near- and far-fields from one fired test, which significantly reduces the need for extensive fired and motored testing. Finally, it is shown that the far-field noise time history of a physically altered engine can be simulated through modification of singular values and recalculation of transfer paths between input and output measurements of previously recorded data.

Unattainable extended spacetime regions in conformal gravity

NASA Astrophysics Data System (ADS)

Chakrabarty, Hrishikesh; Benavides-Gallego, Carlos A.; Bambi, Cosimo; Modesto, Leonardo

2018-03-01

The Janis-Newman-Winicour metric is a solution of Einstein's gravity minimally coupled to a real massless scalar field. The γ-metric is instead a vacuum solution of Einstein's gravity. Both spacetimes have no horizon and possess a naked singularity at a finite value of the radial coordinate, where curvature invariants diverge and the spacetimes are geodetically incomplete. In this paper, we reconsider these solutions in the framework of conformal gravity and we show that it is possible to solve the spacetime singularities with a suitable choice of the conformal factor. Now curvature invariants remain finite over the whole spacetime. Massive particles never reach the previous singular surface and massless particles can never do it with a finite value of their affine parameter. Our results support the conjecture according to which conformal gravity can fix the singularity problem that plagues Einstein's gravity.

Elementary exact calculations of degree growth and entropy for discrete equations.

PubMed

Halburd, R G

2017-05-01

Second-order discrete equations are studied over the field of rational functions [Formula: see text], where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations that arise in singularity confinement analysis, even when the singularities are not confined. This produces elementary yet rigorous entropy calculations.

Radiation-reaction force on a small charged body to second order

NASA Astrophysics Data System (ADS)

Moxon, Jordan; Flanagan, Éanna

2018-05-01

In classical electrodynamics, an accelerating charged body emits radiation and experiences a corresponding radiation-reaction force, or self-force. We extend to higher order in the total charge a previous rigorous derivation of the electromagnetic self-force in flat spacetime by Gralla, Harte, and Wald. The method introduced by Gralla, Harte, and Wald computes the self-force from the Maxwell field equations and conservation of stress-energy in a limit where the charge, size, and mass of the body go to zero, and it does not require regularization of a singular self-field. For our higher-order computation, an adjustment of the definition of the mass of the body is necessary to avoid including self-energy from the electromagnetic field sourced by the body in the distant past. We derive the evolution equations for the mass, spin, and center-of-mass position of the body through second order. We derive, for the first time, the second-order acceleration dependence of the evolution of the spin (self-torque), as well as a mixing between the extended body effects and the acceleration-dependent effects on the overall body motion.

Effective field theory models for nonviolent information transfer from black holes

NASA Astrophysics Data System (ADS)

Giddings, Steven B.; Shi, Yinbo

2014-06-01

Transfer of quantum information from the interior of a black hole to its atmosphere is described, in models based on effective field theory. This description illustrates that such transfer need not be violent to the semiclassical geometry or to infalling observers, and in particular can avoid producing a singular horizon or "firewall". One can specifically quantify the rate of information transfer and show that a rate necessary to unitarize black hole evaporation produces a relatively mild modification to the stress tensor near the horizon. In an exterior description of the transfer, the new interactions responsible for it are approximated by "effective sources" acting on fields in the black hole atmosphere. If the necessary interactions couple to general modes in the black hole atmosphere, one also finds a straightforward mechanism for information transfer rates to increase when a black hole is mined, avoiding paradoxical behavior. Correspondence limits are discussed, in the presence of such new interactions, for both small black holes and large ones; the near-horizon description of the latter is approximately that of Rindler space.

Interlaminar stresses in composite laminates: A perturbation analysis

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1976-01-01

A general method of solution for an elastic balanced symmetric composite laminate subject to a uniaxial extension was developed based upon a perturbation analysis of a limiting free body containing an interfacial plane. The solution satisfies more physical requirements and boundary conditions than previous investigations, and predicts smooth continuous interlaminar stresses with no instabilities. It determines the finite maximum intensity for the interlaminar normal stress in all laminates, provides mathematical evidences for the singular stresses in angle-ply laminates, suggests the need for the experimental determination of an important problem parameter, and introduces a viable means for solving related problems of practical interest.

Edge effects in angle-ply composite laminates

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1977-01-01

This paper presents the results of a zeroth-order solution for edge effects in angle-ply composite laminates obtained using perturbation techniques and a limiting free body approach. The general solution for edge effects in laminates of arbitrary angle ply is applied to the special case of a (+ or - 45)s graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness-to-width ratio and compared to finite difference results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress and provides mathematical evidence for singular interlaminar shear stresses in (+ or - 45) graphite/epoxy laminates.

Work stress and patient safety: observer-rated work stressors as predictors of characteristics of safety-related events reported by young nurses.

PubMed

Elfering, A; Semmer, N K; Grebner, S

This study investigates the link between workplace stress and the 'non-singularity' of patient safety-related incidents in the hospital setting. Over a period of 2 working weeks 23 young nurses from 19 hospitals in Switzerland documented 314 daily stressful events using a self-observation method (pocket diaries); 62 events were related to patient safety. Familiarity of safety-related events and probability of recurrence, as indicators of non-singularity, were the dependent variables in multilevel regression analyses. Predictor variables were both situational (self-reported situational control, safety compliance) and chronic variables (job stressors such as time pressure, or concentration demands and job control). Chronic work characteristics were rated by trained observers. The most frequent safety-related stressful events included incomplete or incorrect documentation (40.3%), medication errors (near misses 21%), delays in delivery of patient care (9.7%), and violent patients (9.7%). Familiarity of events and probability of recurrence were significantly predicted by chronic job stressors and low job control in multilevel regression analyses. Job stressors and low job control were shown to be risk factors for patient safety. The results suggest that job redesign to enhance job control and decrease job stressors may be an important intervention to increase patient safety.

Passive scalars chaotic dynamics induced by two vortices in a two-layer geophysical flow with shear and rotation

NASA Astrophysics Data System (ADS)

Ryzhov, Eugene

2015-11-01

Vortex motion in shear flows is of great interest from the point of view of nonlinear science, and also as an applied problem to predict the evolution of vortices in nature. Considering applications to the ocean and atmosphere, it is well-known that these media are significantly stratified. The simplest way to take stratification into account is to deal with a two-layer flow. In this case, vortices perturb the interface, and consequently, the perturbed interface transits the vortex influences from one layer to another. Our aim is to investigate the dynamics of two point vortices in an unbounded domain where a shear and rotation are imposed as the leading order influence from some generalized perturbation. The two vortices are arranged within the bottom layer, but an emphasis is on the upper-layer fluid particle motion. Point vortices induce singular velocity fields in the layer they belong to, however, in the other layers of a multi-layer flow, they induce regular velocity fields. The main feature is that singular velocity fields prohibit irregular dynamics in the vicinity of the singular points, but regular velocity fields, provided optimal conditions, permit irregular dynamics to extend almost in every point of the corresponding phase space.

Covariant electromagnetic field lines

NASA Astrophysics Data System (ADS)

Hadad, Y.; Cohen, E.; Kaminer, I.; Elitzur, A. C.

2017-08-01

Faraday introduced electric field lines as a powerful tool for understanding the electric force, and these field lines are still used today in classrooms and textbooks teaching the basics of electromagnetism within the electrostatic limit. However, despite attempts at generalizing this concept beyond the electrostatic limit, such a fully relativistic field line theory still appears to be missing. In this work, we propose such a theory and define covariant electromagnetic field lines that naturally extend electric field lines to relativistic systems and general electromagnetic fields. We derive a closed-form formula for the field lines curvature in the vicinity of a charge, and show that it is related to the world line of the charge. This demonstrates how the kinematics of a charge can be derived from the geometry of the electromagnetic field lines. Such a theory may also provide new tools in modeling and analyzing electromagnetic phenomena, and may entail new insights regarding long-standing problems such as radiation-reaction and self-force. In particular, the electromagnetic field lines curvature has the attractive property of being non-singular everywhere, thus eliminating all self-field singularities without using renormalization techniques.

Triangular dislocation: an analytical, artefact-free solution

NASA Astrophysics Data System (ADS)

Nikkhoo, Mehdi; Walter, Thomas R.

2015-05-01

Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space {R}3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

Microscopic processes controlling the Herschel-Bulkley exponent

NASA Astrophysics Data System (ADS)

Lin, Jie; Wyart, Matthieu

2018-01-01

The flow curve of various yield stress materials is singular as the strain rate vanishes and can be characterized by the so-called Herschel-Bulkley exponent n =1 /β . A mean-field approximation due to Hebraud and Lequeux (HL) assumes mechanical noise to be Gaussian and leads to β =2 in rather good agreement with observations. Here we prove that the improved mean-field model where the mechanical noise has fat tails instead leads to β =1 with logarithmic correction. This result supports that HL is not a suitable explanation for the value of β , which is instead significantly affected by finite-dimensional effects. From considerations on elastoplastic models and on the limitation of speed at which avalanches of plasticity can propagate, we argue that β =1 +1 /(d -df) , where df is the fractal dimension of avalanches and d the spatial dimension. Measurements of df then supports that β ≈2.1 and β ≈1.7 in two and three dimensions, respectively. We discuss theoretical arguments leading to approximations of β in finite dimensions.

Quantum Backreaction on Three-Dimensional Black Holes and Naked Singularities.

PubMed

Casals, Marc; Fabbri, Alessandro; Martínez, Cristián; Zanelli, Jorge

2017-03-31

We analytically investigate backreaction by a quantum scalar field on two rotating Bañados-Teitelboim-Zanelli (BTZ) geometries: that of a black hole and that of a naked singularity. In the former case, we explore the quantum effects on various regions of relevance for a rotating black hole space-time. We find that the quantum effects lead to a growth of both the event horizon and the radius of the ergosphere, and to a reduction of the angular velocity, compared to the unperturbed values. Furthermore, they give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the case of a naked singularity, we find that quantum effects lead to the formation of a horizon that shields it, thus supporting evidence for the rôle of quantum mechanics as a cosmic censor in nature.

On the electric field model for an open magnetosphere

NASA Technical Reports Server (NTRS)

Wang, Zhi; Ashour-Abdalla, Maha; Walker, Raymond J.

1993-01-01

We have developed a new canonical separator line type magnetospheric magnetic field and electric field model for use in magnetospheric calculations, we determine the magnetic and electric field by controlling the reconnection rate at the subsolar magnetopause. The model is applicable only for purely southward interplanetary magnetic field (IMF). We have obtained a more realistic magnetotail configuration by applying a stretch transformation to an axially symmetric field solution. We also discuss the Stern singularity in which there is an electric field singlarity in the canonical separate line models for B(sub y) not = to 0 by using a new technique that solves for the electric field along a field line directly instead of determining it by a potential mapping. The singularity not only causes an infinite electric field on the polar cap, but also causes the boundary conditions at plus infinity and minus infinity in the solar wind to contradict each other. This means that the canonical separator line models do not represent the open magnetosphere well, except for the case of purely southward IMF.

Chaotic attractors of relaxation oscillators

NASA Astrophysics Data System (ADS)

Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang

2006-03-01

We develop a general technique for proving the existence of chaotic attractors for three-dimensional vector fields with two time scales. Our results connect two important areas of dynamical systems: the theory of chaotic attractors for discrete two-dimensional Henon-like maps and geometric singular perturbation theory. Two-dimensional Henon-like maps are diffeomorphisms that limit on non-invertible one-dimensional maps. Wang and Young formulated hypotheses that suffice to prove the existence of chaotic attractors in these families. Three-dimensional singularly perturbed vector fields have return maps that are also two-dimensional diffeomorphisms limiting on one-dimensional maps. We describe a generic mechanism that produces folds in these return maps and demonstrate that the Wang-Young hypotheses are satisfied. Our analysis requires a careful study of the convergence of the return maps to their singular limits in the Ck topology for k >= 3. The theoretical results are illustrated with a numerical study of a variant of the forced van der Pol oscillator.

Topological features of vector vortex beams perturbed with uniformly polarized light

PubMed Central

D’Errico, Alessio; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; Cardano, Filippo; Marrucci, Lorenzo

2017-01-01

Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell’s equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian beam; by varying the amplitudes of the two fields, we control the formation of pairs of these singular points and their spatial separation. We complete this study by applying the same analysis to vector vortex beams with higher topological charges, and by investigating the features that arise when increasing the intensity of the Gaussian term. Our results can find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams. PMID:28079134

Topological features of vector vortex beams perturbed with uniformly polarized light

NASA Astrophysics Data System (ADS)

D'Errico, Alessio; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; Cardano, Filippo; Marrucci, Lorenzo

2017-01-01

Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell’s equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian beam; by varying the amplitudes of the two fields, we control the formation of pairs of these singular points and their spatial separation. We complete this study by applying the same analysis to vector vortex beams with higher topological charges, and by investigating the features that arise when increasing the intensity of the Gaussian term. Our results can find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams.

Topological features of vector vortex beams perturbed with uniformly polarized light.

PubMed

D'Errico, Alessio; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; Cardano, Filippo; Marrucci, Lorenzo

2017-01-12

Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell's equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian beam; by varying the amplitudes of the two fields, we control the formation of pairs of these singular points and their spatial separation. We complete this study by applying the same analysis to vector vortex beams with higher topological charges, and by investigating the features that arise when increasing the intensity of the Gaussian term. Our results can find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams.

Quantum critical singularities in two-dimensional metallic XY ferromagnets

NASA Astrophysics Data System (ADS)

Varma, Chandra M.; Gannon, W. J.; Aronson, M. C.; Rodriguez-Rivera, J. A.; Qiu, Y.

2018-02-01

An important problem in contemporary physics concerns quantum-critical fluctuations in metals. A scaling function for the momentum, frequency, temperature, and magnetic field dependence of the correlation function near a 2D-ferromagnetic quantum-critical point (QCP) is constructed, and its singularities are determined by comparing to the recent calculations of the correlation functions of the dissipative quantum XY model (DQXY). The calculations are motivated by the measured properties of the metallic compound YFe2Al10 , which is a realization of the DQXY model in 2D. The frequency, temperature, and magnetic field dependence of the scaling function as well as the singularities measured in the experiments are given by the theory without adjustable exponents. The same model is applicable to the superconductor-insulator transitions, classes of metallic AFM-QCPs, and as fluctuations of the loop-current ordered state in hole-doped cuprates. The results presented here lend credence to the solution found for the 2D-DQXY model and its applications in understanding quantum-critical properties of diverse systems.

Compacted dimensions and singular plasmonic surfaces.

PubMed

Pendry, J B; Huidobro, Paloma Arroyo; Luo, Yu; Galiffi, Emanuele

2017-11-17

In advanced field theories, there can be more than four dimensions to space, the excess dimensions described as compacted and unobservable on everyday length scales. We report a simple model, unconnected to field theory, for a compacted dimension realized in a metallic metasurface periodically structured in the form of a grating comprising a series of singularities. An extra dimension of the grating is hidden, and the surface plasmon excitations, though localized at the surface, are characterized by three wave vectors rather than the two of typical two-dimensional metal grating. We propose an experimental realization in a doped graphene layer. Copyright © 2017, American Association for the Advancement of Science.

Singularity-driven second- and third-harmonic generation at {epsilon}-near-zero crossing points

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

Vincenti, M. A.; Ceglia, D. de; Ciattoni, A.

We show an alternative path to efficient second- and third-harmonic generation in proximity of the zero crossing points of the dielectric permittivity in conjunction with low absorption. Under these circumstances, any material, either natural or artificial, will show similar degrees of field enhancement followed by strong harmonic generation, without resorting to any resonant mechanism. The results presented in this paper provide a general demonstration of the potential that the zero-crossing-point condition holds for nonlinear optical phenomena. We investigate a generic Lorentz medium and demonstrate that a singularity-driven enhancement of the electric field may be achieved even in extremely thin layersmore » of material. We also discuss the role of nonlinear surface sources in a realistic scenario where a 20-nm layer of CaF{sub 2} is excited at 21 {mu}m, where {epsilon}{approx} 0. Finally, we show similar behavior in an artificial composite material that includes absorbing dyes in the visible range, provide a general tool for the improvement of harmonic generation using the {epsilon}{approx} 0 condition, and illustrate that this singularity-driven enhancement of the field lowers the thresholds for a plethora of nonlinear optical phenomena.« less

Geometry of a naked singularity created by standing waves near a Schwarzschild horizon, and its application to the binary black hole problem

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

Mandel, Ilya

The most promising way to compute the gravitational waves emitted by binary black holes (BBHs) in their last dozen orbits, where post-Newtonian techniques fail, is a quasistationary approximation introduced by Detweiler and being pursued by Price and others. In this approximation the outgoing gravitational waves at infinity and downgoing gravitational waves at the holes' horizons are replaced by standing waves so as to guarantee that the spacetime has a helical Killing vector field. Because the horizon generators will not, in general, be tidally locked to the holes' orbital motion, the standing waves will destroy the horizons, converting the black holesmore » into naked singularities that resemble black holes down to near the horizon radius. This paper uses a spherically symmetric, scalar-field model problem to explore in detail the following BBH issues: (i) The destruction of a horizon by the standing waves. (ii) The accuracy with which the resulting naked singularity resembles a black hole. (iii) The conversion of the standing-wave spacetime (with a destroyed horizon) into a spacetime with downgoing waves by the addition of a 'radiation-reaction field'. (iv) The accuracy with which the resulting downgoing waves agree with the downgoing waves of a true black-hole spacetime (with horizon). The model problem used to study these issues consists of a Schwarzschild black hole endowed with spherical standing waves of a scalar field, whose wave frequency and near-horizon energy density are chosen to match those of the standing gravitational waves of the BBH quasistationary approximation. It is found that the spacetime metric of the singular, standing-wave spacetime, and its radiation-reaction-field-constructed downgoing waves are quite close to those for a Schwarzschild black hole with downgoing waves--sufficiently close to make the BBH quasistationary approximation look promising for non-tidally-locked black holes.« less

Quantum descriptions of singularities leading to pair creation. [of gravitons

NASA Technical Reports Server (NTRS)

Misner, C. W.

1974-01-01

A class of cosmological models is analyzed which provide a mathematically convenient (but idealized) description of a cosmological singularity that develops into a pair creation epoch and terminates in an adiabatic expansion with redshifting particle energies. This class of models was obtained by Gowdy (1971, 1974) as a set of exact solutions of the classical empty space Einstein equations describing inhomogeneous universes populated only by gravitational waves. It is shown that these models can be used to exhibit simplified models of quantized gravitational fields, and that a quantum description can be given arbitrarily near a cosmological singularity. Graviton pair creation occurs, and can be seen to convert anisotropic expansion rates into the energy of graviton pairs.

Einstein-Langevin and Einstein-Fokker-Planck equations for Oppenheimer-Snyder gravitational collapse in a spacetime with conformal vacuum fluctuations

NASA Astrophysics Data System (ADS)

Miller, Steven David

1999-10-01

A consistent extension of the Oppenheimer-Snyder gravitational collapse formalism is presented which incorporates stochastic, conformal, vacuum fluctuations of the metric tensor. This results in a tractable approach to studying the possible effects of vacuum fluctuations on collapse and singularity formation. The motivation here, is that it is known that coupling stochastic noise to a classical field theory can lead to workable methodologies that accommodate or reproduce many aspects of quantum theory, turbulence or structure formation. The effect of statistically averaging over the metric fluctuations gives the appearance of a deterministic Riemannian structure, with an induced non-vanishing cosmological constant arising from the nonlinearity. The Oppenheimer-Snyder collapse of a perfect fluid or dust star in the fluctuating or `turbulent' spacetime, is reformulated in terms of nonlinear Einstein-Langevin field equations, with an additional noise source in the energy-momentum tensor. The smooth deterministic worldlines of collapsing matter within the classical Oppenheimer-Snyder model, now become nonlinear Brownian motions due to the backreaction induced by vacuum fluctuations. As the star collapses, the matter worldlines become increasingly randomized since the backreaction coupling to the vacuum fluctuations is nonlinear; the input assumptions of the Hawking-Penrose singularity theorems should then be violated. Solving the nonlinear Einstein-Langevin field equation for collapse - via the Ito interpretation - gives a singularity-free solution, which is equivalent to the original Oppenheimer solution but with higher-order stochastic corrections; the original singular solution is recovered in the limit of zero vacuum fluctuations. The `geometro-hydrodynamics' of noisy gravitational collapse, were also translated into an equivalent mathematical formulation in terms of nonlinear Einstein-Fokker-Planck (EFP) continuity equations with respect to comoving coordinates: these describe the collapse as a conserved flow of probability. A solution was found in the dilute limit of weak fluctuations where the EFP equation is linearized. There is zero probability that the star collapses to a singular state in the presence of background vacuum fluctuations, but the singularity returns with unit probability when the fluctuations are reduced to zero. Finally, an EFP equation was considered with respect to standard exterior coordinates. Using the thermal Brownian motion paradigm, an exact stationary or equilibrium solution was found in the infinite standard time relaxation limit. The solution gives the conditions required for the final collapsed object (a black hole) to be in thermal equilibrium with the background vacuum fluctuations. From this solution, one recovers the Hawking temperature without using field theory. The stationary solution then seems to correspond to a black hole in thermal equilibrium with a fluctuating conformal scalar field; or the Hawking-Hartle state.

The mechanics of delamination in fiber-reinforced composite materials. II - The delamination behavior and fracture mechanics parameters

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1983-01-01

Based on theories of laminate anisotropic elasticity and interlaminar fracture, the complete solution structure associated with a composite delamination is determined. Fracture mechanics parameters characterizing the interlaminar crack behavior are defined from asymptotic stress solutions for delaminations with different crack-tip deformation configurations. A numerical method employing singular finite elements is developed to study delaminations in fiber composites with any arbitrary combinations of lamination, material, geometric, and crack variables. The special finite elements include the exact delamination stress singularity in its formulation. The method is shown to be computationally accurate and efficient, and operationally simple. To illustrate the basic nature of composite delamination, solutions are shown for edge-delaminated (0/-0/-0/0) and (+ or - 0/+ or - 0/90/90 deg) graphite-epoxy systems under uniform axial extension. Three-dimensional crack-tip stress intensity factors, associated energy release rates, and delamination crack-closure are determined for each individual case. The basic mechanics and mechanisms of composite delamination are studied, and fundamental characteristics unique to recently proposed tests for interlaminar fracture toughness of fiber composite laminates are examined. Previously announced in STAR as N84-13222

Production of confluent hypergeometric beam by computer-generated hologram

NASA Astrophysics Data System (ADS)

Chen, Jiannong; Wang, Gang; Xu, Qinfeng

2011-02-01

Because of their spiral wave front, phase singularity, zero-intensity center and orbital angular momentum, dark hollow vortex beams have been found many applications in the field of atom optics such as atom cooling, atom transport and atom guiding. In this paper, a method for generating confluent hypergeometric beam by computer-generated hologram displayed on the spatial light modulator is presented. The hologram is formed by interference between a single ring Laguerre-Gaussian beam and a plane wave. The far-field Fraunhofer diffraction of this optical field transmitted from the hologram is the confluent hypergeometric beam. This beam is a circular symmetric beam which has a phase singularity, spiral wave front, zero-intensity center, and intrinsic orbital angular momentum. It is a new dark hollow vortex beam.

Three-dimensional stress intensity factor analysis of a surface crack in a high-speed bearing

NASA Technical Reports Server (NTRS)

Ballarini, Roberto; Hsu, Yingchun

1990-01-01

The boundary element method is applied to calculate the stress intensity factors of a surface crack in the rotating inner raceway of a high-speed roller bearing. The three-dimensional model consists of an axially stressed surface cracked plate subjected to a moving Hertzian contact loading. A multidomain formulation and singular crack-tip elements were employed to calculate the stress intensity factors accurately and efficiently for a wide range of configuration parameters. The results can provide the basis for crack growth calculations and fatigue life predictions of high-performance rolling element bearings that are used in aircraft engines.

Scaling Properties of Particle Density Fields Formed in Simulated Turbulent Flows

NASA Technical Reports Server (NTRS)

Hogan, Robert C.; Cuzzi, Jeffrey N.; Dobrovolskis, Anthony R.; DeVincenzi, Donald (Technical Monitor)

1998-01-01

Direct numerical simulations (DNS) of particle concentrations in fully developed 3D turbulence were carried out in order to study the nonuniform structure of the particle density field. Three steady-state turbulent fluid fields with Taylor microscale Reynolds numbers (Re(sub lambda)) of 40, 80 and 140 were generated by solving the Navier-Stokes equations with pseudospectral methods. Large scale forcing was used to drive the turbulence and maintain temporal stationarity. The response of the particles to the fluid was parameterized by the particle Stokes number St, defined as the ratio of the particle's stopping time to the mean period of eddies on the Kolmogorov scale (eta). In this paper, we consider only passive particles optimally coupled to these eddies (St approx. = 1) because of their tendency to concentrate more than particles with lesser or greater St values. The trajectories of up to 70 million particles were tracked in the equilibrated turbulent flows until the particle concentration field reached a statistically stationary state. The nonuniform structure of the concentration fields was characterized by the multifractal singularity spectrum, f(alpha), derived from measures obtained after binning particles into cells ranging from 2(eta) to 15(eta) in size. We observed strong systematic variations of f(alpha) across this scale range in all three simulations and conclude that the particle concentration field is not statistically self similar across the scale range explored. However, spectra obtained at the 2(eta), 4(eta), and 8(eta) scales of each flow case were found to be qualitatively similar. This result suggests that the local structure of the particle concentration field may be flow-Independent. The singularity spectra found for 2n-sized cells were used to predict concentration distributions in good agreement with those obtained directly from the particle data. This Singularity spectrum has a shape similar to the analogous spectrum derived for the inertial-range energy dissipation fields of experimental turbulent flows at Re(sub lambda) = 110 and 1100. Based on this agreement, and the expectation that both dissipation and particle concentration are controlled by the same cascade process, we hypothesize that singularity spectra similar to the ones found in this work provide a good characterization of the spatially averaged statistical properties of preferentially concentrated particles in higher Re(sub lambda) turbulent flows.

An Exact Solution of Einstein-Maxwell Gravity Coupled to a Scalar Field

NASA Technical Reports Server (NTRS)

Turyshev, S. G.

1995-01-01

The general solution to low-energy string theory representing static spherically symmetric solution of the Einstein-Maxwell gravity with a massless scalar field has been found. Some of the partial cases appear to coincide with known solutions to black holes, naked singularities, and gravity and electromagnetic fields.

Coulomb branches with complex singularities

NASA Astrophysics Data System (ADS)

Argyres, Philip C.; Martone, Mario

2018-06-01

We construct 4d superconformal field theories (SCFTs) whose Coulomb branches have singular complex structures. This implies, in particular, that their Coulomb branch coordinate rings are not freely generated. Our construction also gives examples of distinct SCFTs which have identical moduli space (Coulomb, Higgs, and mixed branch) geometries. These SCFTs thus provide an interesting arena in which to test the relationship between moduli space geometries and conformal field theory data. We construct these SCFTs by gauging certain discrete global symmetries of N = 4 superYang-Mills (sYM) theories. In the simplest cases, these discrete symmetries are outer automorphisms of the sYM gauge group, and so these theories have lagrangian descriptions as N = 4 sYM theories with disconnected gauge groups.

A classification of the mechanisms producing pathological tissue changes.

PubMed

Grippo, John O; Oh, Daniel S

2013-05-01

The objectives are to present a classification of mechanisms which can produce pathological changes in body tissues and fluids, as well as to clarify and define the term biocorrosion, which has had a singular use in engineering. Considering the emerging field of biomedical engineering, it is essential to use precise definitions in the lexicons of engineering, bioengineering and related sciences such as medicine, dentistry and veterinary medicine. The mechanisms of stress, friction and biocorrosion and their pathological effects on tissues are described. Biocorrosion refers to the chemical, biochemical and electrochemical changes by degradation or induced growth of living body tissues and fluids. Various agents which can affect living tissues causing biocorrosion are enumerated which support the necessity and justify the use of this encompassing and more precise definition of biocorrosion. A distinction is made between the mechanisms of corrosion and biocorrosion.

Higher-dimensional gravitational collapse of perfect fluid spherically symmetric spacetime in f(R, T) gravity

NASA Astrophysics Data System (ADS)

Khan, Suhail; Khan, Muhammad Shoaib; Ali, Amjad

2018-04-01

In this paper, our aim is to study (n + 2)-dimensional collapse of perfect fluid spherically symmetric spacetime in the context of f(R, T) gravity. The matching conditions are acquired by considering a spherically symmetric non-static (n + 2)-dimensional metric in the inner region and Schwarzschild (n + 2)-dimensional metric in the outer region of the star. To solve the field equations for above settings in f(R, T) gravity, we choose the stress-energy tensor trace and the Ricci scalar as constants. It is observed that two physical horizons, namely, cosmological and black hole horizons appear as a consequence of this collapse. A singularity is also formed after the birth of both the horizons. It is also observed that the term f(R0, T0) slows down the collapsing process.

C-field cosmological models: revisited

NASA Astrophysics Data System (ADS)

Yadav, Anil Kumar; Tawfiq Ali, Ahmad; Ray, Saibal; Rahaman, Farook; Hossain Sardar, Iftikar

2016-12-01

We investigate plane symmetric spacetime filled with perfect fluid in the C-field cosmology of Hoyle and Narlikar. A new class of exact solutions has been obtained by considering the creation field C as a function of time only. To get the deterministic solution, it has been assumed that the rate of creation of matter-energy density is proportional to the strength of the existing C-field energy density. Several physical aspects and geometrical properties of the models are discussed in detail, especially showing that some of our solutions of C-field cosmology are free from singularity in contrast to the Big Bang cosmology. A comparative study has been carried out between two models, one singular and the other nonsingular, by contrasting the behaviour of the physical parameters. We note that the model in a unique way represents both the features of the accelerating as well as decelerating universe depending on the parameters and thus seems to provide glimpses of the oscillating or cyclic model of the universe without invoking any other agent or theory in allowing cyclicity.

Canonical field anticommutators in the extended gauged Rarita-Schwinger theory

NASA Astrophysics Data System (ADS)

Adler, Stephen L.; Henneaux, Marc; Pais, Pablo

2017-10-01

We reexamine canonical quantization of the gauged Rarita-Schwinger theory using the extended theory, incorporating a dimension 1/2 auxiliary spin-1/2 field Λ , in which there is an exact off-shell gauge invariance. In Λ =0 gauge, which reduces to the original unextended theory, our results agree with those found by Johnson and Sudarshan, and later verified by Velo and Zwanziger, which give a canonical Rarita-Schwinger field Dirac bracket that is singular for small gauge fields. In gauge covariant radiation gauge, the Dirac bracket of the Rarita-Schwinger fields is nonsingular, but does not correspond to a positive semidefinite anticommutator, and the Dirac bracket of the auxiliary fields has a singularity of the same form as found in the unextended theory. These results indicate that gauged Rarita-Schwinger theory is somewhat pathological, and cannot be canonically quantized within a conventional positive semidefinite metric Hilbert space. We leave open the questions of whether consistent quantizations can be achieved by using an indefinite metric Hilbert space, by path integral methods, or by appropriate couplings to conventional dimension 3/2 spin-1/2 fields.

Finite-surface method for the Maxwell equations with corner singularities

NASA Technical Reports Server (NTRS)

Vinokur, Marcel; Yarrow, Maurice

1994-01-01

The finite-surface method for the two-dimensional Maxwell equations in generalized coordinates is extended to treat perfect conductor boundaries with sharp corners. Known singular forms of the grid and the electromagnetic fields in the neighborhood of each corner are used to obtain accurate approximations to the surface and line integrals appearing in the method. Numerical results are presented for a harmonic plane wave incident on a finite flat plate. Comparisons with exact solutions show good agreement.

Singularities of Floquet scattering and tunneling

NASA Astrophysics Data System (ADS)

Landa, H.

2018-04-01

We study quasibound states and scattering with short-range potentials in three dimensions, subject to an axial periodic driving. We find that poles of the scattering S matrix can cross the real energy axis as a function of the drive amplitude, making the S matrix nonanalytic at a singular point. For the corresponding quasibound states that can tunnel out of (or get captured within) a potential well, this results in a discontinuous jump in both the angular momentum and energy of emitted (absorbed) waves. We also analyze elastic and inelastic scattering of slow particles in the time-dependent potential. For a drive amplitude at the singular point, there is a total absorption of incoming low-energy (s wave) particles and their conversion to high-energy outgoing (mostly p ) waves. We examine the relation of such Floquet singularities, lacking in an effective time-independent approximation, with well-known "spectral singularities" (or "exceptional points"). These results are based on an analytic approach for obtaining eigensolutions of time-dependent periodic Hamiltonians with mixed cylindrical and spherical symmetry, and apply broadly to particles interacting via power-law forces and subject to periodic fields, e.g., co-trapped ions and atoms.

Cosmological singularities in Bakry-Émery spacetimes

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.; Woolgar, Eric

2014-12-01

We consider spacetimes consisting of a manifold with Lorentzian metric and a weight function or scalar field. These spacetimes admit a Bakry-Émery-Ricci tensor which is a natural generalization of the Ricci tensor. We impose an energy condition on the Bakry-Émery-Ricci tensor and obtain singularity theorems of a cosmological type, both for zero and for positive cosmological constant. That is, we find conditions under which every timelike geodesic is incomplete. These conditions are given by 'open' inequalities, so we examine the borderline (equality) cases and show that certain singularities are avoided in these cases only if the geometry is rigid; i.e., if it splits as a Lorentzian product or, for a positive cosmological constant, a warped product, and the weight function is constant along the time direction. Then the product case is future timelike geodesically complete while, in the warped product case, worldlines of certain conformally static observers are complete. Our results answer a question posed by J Case. We then apply our results to the cosmology of scalar-tensor gravitation theories. We focus on the Brans-Dicke family of theories in 4 spacetime dimensions, where we obtain 'Jordan frame' singularity theorems for big bang singularities.

Interfacial tension and vapor-liquid equilibria in the critical region of mixtures

NASA Technical Reports Server (NTRS)

Moldover, Michael R.; Rainwater, James C.

1988-01-01

In the critical region, the concept of two-scale-factor universality can be used to accurately predict the surface tension between near-critical vapor and liquid phases from the singularity in the thermodynamic properties of the bulk fluid. In the present work, this idea is generalized to binary mixtures and is illustrated using the data of Hsu et al. (1985) for CO2 + n-butane. The pressure-temperature-composition-density data for coexisting, near-critical phases of the mixtures are fitted with a thermodynamic potential comprised of a sum of a singular term and nonsingular terms. The nonuniversal amplitudes characterizing the singular term for the mixtures are obtained from the amplitudes for the pure components by interpolation in a space of thermodynamic 'field' variables. The interfacial tensions predicted for the mixtures from the singular term are within 10 percent of the data on three isotherms in the pressure range (Pc - P)/Pc of less than 0.5. This difference is comparable to the combined experimental and model errors.

Normalization and Implementation of Three Gravitational Acceleration Models

NASA Technical Reports Server (NTRS)

Eckman, Randy A.; Brown, Aaron J.; Adamo, Daniel R.; Gottlieb, Robert G.

2016-01-01

Unlike the uniform density spherical shell approximations of Newton, the consequence of spaceflight in the real universe is that gravitational fields are sensitive to the asphericity of their generating central bodies. The gravitational potential of an aspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities that must be removed to generalize the method and solve for any possible orbit, including polar orbits. Samuel Pines, Bill Lear, and Robert Gottlieb developed three unique algorithms to eliminate these singularities. This paper documents the methodical normalization of two of the three known formulations for singularity-free gravitational acceleration (namely, the Lear and Gottlieb algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre polynomials and Associated Legendre Functions (ALFs) for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

How to Integrate Bilingual Education without Tracking.

ERIC Educational Resources Information Center

Glenn, Charles L.

1990-01-01

Integrated schools that stress learning among students in two languages are called two-way schools. They provide a singularly rich educational environment and avoid the negative effects of educational segregation by tracking. A Chelsea, Massachusetts, bilingual elementary school focused on team building to use existing resources more effectively.…

Topology and convection of a northward interplanetary magnetic field reconnection event

NASA Astrophysics Data System (ADS)

Wendel, Deirdre E.

>From observations and global MHD simulations, we deduce the local and global magnetic topology and current structure of a northward IMF reconnection event in the dayside magnetopause. The ESA four-satellite Cluster suite crossed the magnetopause at a location mapping along field lines to an ionospheric H-alpha emission observed by the IMAGE spacecraft. Therefore, we seek reconnection signatures in the Cluster data. From the four-point Cluster observations, we develop a superposed epoch method to find the instantaneous x-line, its associated current sheet, and the nature of the reconnecting particle flows. This method is unique in that it removes the motion of the hyperbolic structure and the magnetopause relative to the spacecraft. We detect singular field line reconnection--planar hyperbolic reconnecting fields superposed on an out-of- plane field. We also detect the non-ideal electric field that is required to certify reconnection at locations where the magnetic field does not vanish, and estimate a reconnection electric field of - 4 mV/m. The current sheet appears bifurcated, embedding a 30 km current sheet of opposite polarity within a broader current sheet about 130 km thick. Using a resistive MHD simulation and ionospheric satellite data, we examine the same event at global length scales. This gives a 3D picture of where reconnection occurs on the magnetopause for northward IMF with B x and B y components and a tilted dipole field. It also demonstrates that northward IMF 3D reconnection couples the reconnection electric field and field-aligned currents to the ionosphere, driving sunward convection in a manner that agrees with satellite measurements of sunward flows. We find singular field line reconnection of the IMF with both open and closed field lines near nulls in both hemispheres. The reconnection in turn produces both open and closed field lines. We discuss for the first time how line-tying in the ionosphere and draping of open and IMF field lines produce a torsion of the reconnecting singular magnetic field lines within the magnetopause. The simulation and data show that magnetopause reconnection topology is three-dimensional in a way that challenges accepted models of neutral lines and x-lines with guide fields.

Topologically nontrivial black holes in Lovelock-Born-Infeld gravity

NASA Astrophysics Data System (ADS)

Farhangkhah, N.

2018-04-01

We present the black hole solutions possessing horizon with nonconstant-curvature and additional scalar restrictions on the base manifold in Lovelock gravity coupled to Born-Infeld (BI) nonlinear electrodynamics. The asymptotic and near origin behavior of the metric is presented and we analyze different behaviors of the singularity. We find that, in contrast to the case of black hole solutions of BI-Lovelock gravity with constant curvature horizon and Maxwell-Lovelock gravity with non constant horizon which have only timelike singularities, spacelike, and timelike singularities may exist for BI-Lovelock black holes with nonconstant curvature horizon. By calculating the thermodynamic quantities, we study the effects of nonlinear electrodynamics via the Born-Infeld action. Stability analysis shows that black holes with positive sectional curvature, κ , possess an intermediate unstable phase and large and small black holes are stable. We see that while Ricci flat Lovelock-Born-Infeld black holes having exotic horizons are stable in the presence of Maxwell field or either Born Infeld field with large born Infeld parameter β , unstable phase appears for smaller values of β , and therefore nonlinearity brings in the instability.

High order Nyström method for elastodynamic scattering

NASA Astrophysics Data System (ADS)

Chen, Kun; Gurrala, Praveen; Song, Jiming; Roberts, Ron

2016-02-01

Elastic waves in solids find important applications in ultrasonic non-destructive evaluation. The scattering of elastic waves has been treated using many approaches like the finite element method, boundary element method and Kirchhoff approximation. In this work, we propose a novel accurate and efficient high order Nyström method to solve the boundary integral equations for elastodynamic scattering problems. This approach employs high order geometry description for the element, and high order interpolation for fields inside each element. Compared with the boundary element method, this approach makes the choice of the nodes for interpolation based on the Gaussian quadrature, which renders matrix elements for far field interaction free from integration, and also greatly simplifies the process for singularity and near singularity treatment. The proposed approach employs a novel efficient near singularity treatment that makes the solver able to handle extreme geometries like very thin penny-shaped crack. Numerical results are presented to validate the approach. By using the frequency domain response and performing the inverse Fourier transform, we also report the time domain response of flaw scattering.

Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice

NASA Astrophysics Data System (ADS)

Biswas, Sounak; Damle, Kedar

2018-02-01

A transverse magnetic field Γ is known to induce antiferromagnetic three-sublattice order of the Ising spins σz in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wave vector Q : <σz(R ⃗) σz(0 ) > ˜cos(Q .R ⃗) /|R⃗| η (T ) with the temperature-dependent power-law exponent η (T )∈(1 /9 ,1 /4 ) . Here, we use a quantum cluster algorithm to study the ferromagnetic easy-axis susceptibility χu(L ) of an L ×L sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular L dependence χu(L ) ˜L2 -9 η when η (T ) is in the range (1 /9 ,2 /9 ) . This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility χu(B ) to a uniform field B along the easy axis is singular at intermediate temperatures in the small B limit, χu(B ) ˜|B| -4/-18 η 4 -9 η for η (T )∈(1 /9 ,2 /9 ) , although there is no ferromagnetic long-range order in the low temperature state. Additionally we establish similar two-step melting behavior (via a study of the order parameter susceptibility χQ) in the case of the ferrimagnetic three-sublattice ordered phase which is stabilized by ferromagnetic next-neighbor couplings (J2) and confirm that the ferromagnetic susceptibility obeys the predicted singular form in the associated power-law ordered phase.

Sudden bending of a cracked laminate

NASA Technical Reports Server (NTRS)

Sih, G. C.; Chen, E. P.

1981-01-01

The intensification of stresses near a through crack in the laminate that suddenly undergoes bending is investigated. A dynamic plate theory is developed which includes the effects of material inhomogeneity in the thickness direction and realistic crack edge stress singularity and distribution. Numerical examples indicate that (1) the crack moment intensity tends to decrease as the crack length to laminate thickness is increased, and (2) the average load intensity transmitted to a through crack can be reduced by making the inner layers to be stiffer than the outer layers.

The elasticity problem for a thick-walled cylinder containing a circumferential crack

NASA Technical Reports Server (NTRS)

Nied, H. F.; Erdogan, F.

1983-01-01

The elasticity problem for a long hollow circular cylinder containing an axisymmetric circumferential crack subjected to general nonaxisymmetric external loads is considered. The problem is formulated in terms of a system of singular integral equations with the Fourier coefficients of the derivative of the crack surface displacement as density functions. The stress intensity factors and the crack opening displacement are calculated for a cylinder under uniform tension, bending by end couples, and self-equilibrating residual stresses.

The elasticity problem for a thick-walled cylinder containing a circumferential crack

NASA Technical Reports Server (NTRS)

Nied, H. F.; Erdogan, F.

1982-01-01

The elasticity problem for a long hollow circular cylinder containing an axisymmetric circumferential crack subjected to general nonaxisymmetric external loads is considered. The problem is formulated in terms of a system of singular integral equations with the Fourier coefficients of the derivative of the crack surface displacement as density functions. The stress intensity factors and the crack opening displacement are calculated for a cylinder under uniform tension, bending by end couples, and self-equilibrating residual stresses.

Fermi-Edge Singularity of Spin-Polarized Electrons

NASA Astrophysics Data System (ADS)

Plochocka-Polack, P.; Groshaus, J. G.; Rappaport, M.; Umansky, V.; Gallais, Y.; Pinczuk, A.; Bar-Joseph, I.

2007-05-01

We study the absorption spectrum of a two-dimensional electron gas (2DEG) in a magnetic field. We find that at low temperatures, when the 2DEG is spin polarized, the absorption spectra, which correspond to the creation of spin up or spin down electrons, differ in magnitude, linewidth, and filling factor dependence. We show that these differences can be explained as resulting from the creation of a Mahan exciton in one case, and of a power law Fermi-edge singularity in the other.

Singular growth shapes in turbulent field theories

NASA Astrophysics Data System (ADS)

Conrado, Claudine V.; Bohr, Tomas

1994-05-01

In this work we study deterministic, turbulent partial differential equations (the Kuramoto-Sivashinsky equation and generalizations) with initial conditions which are nonzero only in a small region. We demonstrate that the asymptotic state has a well-defined growth shape, which can be determined by the combination of nonlinear growth velocities, and front propagation governed by the linear instabilities. We show that the growth shapes are, in general, singular and that a new type of instability occurs when the growth shape becomes discontinuous.

The surface and through crack problems in layered orthotropic plates

NASA Technical Reports Server (NTRS)

Erdogan, Fazil; Wu, Binghua

1991-01-01

An analytical method is developed for a relatively accurate calculation of Stress Intensity Factors in a laminated orthotropic plate containing a through or part-through crack. The laminated plate is assumed to be under bending or membrane loading and the mode 1 problem is considered. First three transverse shear deformation plate theories (Mindlin's displacement based first-order theory, Reissner's stress-based first-order theory, and a simple-higher order theory due to Reddy) are reviewed and examined for homogeneous, laminated and heterogeneous orthotropic plates. Based on a general linear laminated plate theory, a method by which the stress intensity factors can be obtained in orthotropic laminated and heterogeneous plates with a through crack is developed. Examples are given for both symmetrically and unsymmetrically laminated plates and the effects of various material properties on the stress intensity factors are studied. In order to implement the line-spring model which is used later to study the surface crack problem, the corresponding plane elasticity problem of a two-bonded orthotropic plated containing a crack perpendicular to the interface is also considered. Three different crack profiles: an internal crack, an edge crack, and a crack terminating at the interface are considered. The effect of the different material combinations, geometries, and material orthotropy on the stress intensity factors and on the power of stress singularity for a crack terminating at the interface is fully examined. The Line Spring model of Rice and Levy is used for the part-through crack problem. The surface crack is assumed to lie in one of the two-layered laminated orthotropic plates due to the limitation of the available plane strain results. All problems considered are of the mixed boundary value type and are reduced to Cauchy type of singular integral equations which are then solved numerically.

Non-minimally coupled varying constants quantum cosmologies

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

Balcerzak, Adam, E-mail: abalcerz@wmf.univ.szczecin.pl

We consider gravity theory with varying speed of light and varying gravitational constant. Both constants are represented by non-minimally coupled scalar fields. We examine the cosmological evolution in the near curvature singularity regime. We find that at the curvature singularity the speed of light goes to infinity while the gravitational constant vanishes. This corresponds to the Newton's Mechanics limit represented by one of the vertex of the Bronshtein-Zelmanov-Okun cube [1,2]. The cosmological evolution includes both the pre-big-bang and post-big-bang phases separated by the curvature singularity. We also investigate the quantum counterpart of the considered theory and find the probability ofmore » transition of the universe from the collapsing pre-big-bang phase to the expanding post-big-bang phase.« less

Global structure of static spherically symmetric solutions surrounded by quintessence

NASA Astrophysics Data System (ADS)

Cruz, Miguel; Ganguly, Apratim; Gannouji, Radouane; Leon, Genly; Saridakis, Emmanuel N.

2017-06-01

We investigate all static spherically symmetric solutions in the context of general relativity surrounded by a minimally-coupled quintessence field, using dynamical system analysis. Applying the 1  +  1  +  2 formalism and introducing suitable normalized variables involving the Gaussian curvature, we were able to reformulate the field equations as first order differential equations. In the case of a massless canonical scalar field we recovered all known black hole results, such as the Fisher solution, and we found that apart from the Schwarzschild solution all other solutions are naked singularities. Additionally, we identified the symmetric phase space which corresponds to the white hole part of the solution and in the case of a phantom field, we were able to extract the conditions for the existence of wormholes and define all possible classes of solutions such as cold black holes, singular spacetimes and wormholes such as the Ellis wormhole, for example. For an exponential potential, we found that the black hole solution which is asymptotically flat is unique and it is the Schwarzschild spacetime, while all other solutions are naked singularities. Furthermore, we found solutions connecting to a white hole through a maximum radius, and not a minimum radius (throat) such as wormhole solutions, therefore violating the flare-out condition. Finally, we have found a necessary and sufficient condition on the form of the potential to have an asymptotically AdS spacetime along with a necessary condition for the existence of asymptotically flat black holes.

Symmetry breaking in smectics and surface models of their singularities

PubMed Central

Chen, Bryan Gin-ge; Alexander, Gareth P.; Kamien, Randall D.

2009-01-01

The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the interaction between translations and rotations. Dislocations are associated, as usual, with branch points in a phase field, whereas disclinations arise as critical points and singularities in the phase field. We introduce a three-dimensional model for two-dimensional smectics that clarifies the topology of disclinations and geometrically captures known results without the need to add compatibility conditions. Our work suggests natural generalizations of the two-dimensional smectic theory to higher dimensions and to crystals. PMID:19717435

Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity

DOE PAGES

Juan, Pierre -Alexandre; Dingreville, Remi

2016-10-31

Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive “interferences” aremore » directly affected by the interface structure and its elastic response. Furthermore, this general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.« less

Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity

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

Juan, Pierre -Alexandre; Dingreville, Remi

Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive “interferences” aremore » directly affected by the interface structure and its elastic response. Furthermore, this general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.« less

Micromechanics, Fracture Mechanics and Gas Permeability of Composite Laminates for Cryogenic Storage Systems

NASA Technical Reports Server (NTRS)

Choi, Sukjoo; Sankar, Bhavani; Ebaugh, Newton C.

2005-01-01

A micromechanics method is developed to investigate microcrack propagation in a liquid hydrogen composite tank at cryogenic temperature. The unit cell is modeled using square and hexagonal shapes depends on fiber and matrix layout from microscopic images of composite laminates. Periodic boundary conditions are applied to the unit cell. The temperature dependent properties are taken into account in the analysis. The laminate properties estimated by the micromechanics method are compared with empirical solutions using constituent properties. The micro stresses in the fiber and matrix phases based on boundary conditions in laminate level are calculated to predict the formation of microcracks in the matrix. The method is applied to an actual liquid hydrogen storage system. The analysis predicts micro stresses in the matrix phase are large enough to cause microcracks in the composite. Stress singularity of a transverse crack normal to a ply-interface is investigated to predict the fracture behavior at cryogenic conditions using analytical and finite element analysis. When a transverse crack touches a ply-interface of a composite layer with same fiber orientation, the stress singularity is equal to 1/2. When the transverse crack propagates to a stiffer layer normal to the ply-direction, the singularity becomes less than 1/2 and vice versa. Finite element analysis is performed to predict the fracture toughness of a laminated beam subjected to fracture loads measured by four-point bending tests at room and cryogenic temperatures. As results, the fracture load at cryogenic temperature is significantly lower than that at room temperature. However, when thermal stresses are taken into consideration, for both cases of room and cryogenic temperatures, the difference of the fracture toughness becomes insignificant. The result indicates fracture toughness is a characteristic property, which is independent to temperature changes. The experimental analysis is performed to investigate the effect of cryogenic cycling on permeability for various composite material systems. Textile composites have lower permeability than laminated composites even with increasing number of cryogenic cycle. Nano-particles dispersed in laminated composites do not show improvement on permeability. The optical inspection is performed to investigate the microcrack propagation and void content in laminated composites and compared the microscopic results before and after cryogenic cycling.

Financial Markets during Highly Anxious Time: Multifractal Fluctuations in Asset Returns

NASA Astrophysics Data System (ADS)

Siokis, Fotios M.

Building on the notion that systems and in particular complex systems such as stock exchange markets reveal their structure better when they are under stress, we analyze the multifractal character and nonlinear properties of four major stock market indices during financial meltdowns by means of the multifractal detrended fluctuation analysis (MF-DFA). The three distinct financial crises under investigation are the Black Monday, the Dot-Com and the Great Recession. Scaling and Hurst exponents are derived as well as the singularity spectra. The results show that all indices exhibit strong multifractal properties. The complexity of the markets is higher under the Black Monday event revealed by the width of the singularity spectrum and the higher α0 parameter.

Marangoni-driven chemotaxis, chemotactic collapse, and the Keller-Segel equation

NASA Astrophysics Data System (ADS)

Shelley, Michael; Masoud, Hassan

2013-11-01

Almost by definition, chemotaxis involves the biased motion of motile particles along gradients of a chemical concentration field. Perhaps the most famous model for collective chemotaxis in mathematical biology is the Keller-Segel model, conceived to describe collective aggregation of slime mold colonies in response to an intrinsically produced, and diffusing, chemo-attractant. Heavily studied, particularly in 2D where the system is ``super-critical'', it has been proved that the KS model can develop finite-time singularities - so-called chemotactic collapse - of delta-function type. Here, we study the collective dynamics of immotile particles bound to a 2D interface above a 3D fluid. These particles are chemically active and produce a diffusing field that creates surface-tension gradients along the surface. The resultant Marangoni stresses create flows that carry the particles, possibly concentrating them. Remarkably, we show that this system involving 3D diffusion and fluid dynamics, exactly yields the 2D Keller-Segel model for the surface-flow of active particles. We discuss the consequences of collapse on the 3D fluid dynamics, and generalizations of the fluid-dynamical model.

Recent Results on Singularity Strengths

NASA Astrophysics Data System (ADS)

Nolan, Brien

2002-12-01

In this contribution, we review some recent results on strengths of singularities. In a space-time (M,g), let γ[τ0, 0) → M be an incomplete, inextendible causal geodesic, affinely parametrised by τ, tangent ěc k. Let Jτ1 :=set of Jacobi fields along γ, orthogonal to γ and vanishing at time τ1 ≥ τ0 i.e. ěc ξ ∈ J{τ 1 } iff D2ξa = -Rbcdakbkdξc, gabξakb = 0, and ěc ξ (τ 1 ) = 0. Vτ1(τ) := volume element defined by full set of independent elements of Jτ1 (2-dim for null geodesies, 3-dim for time-like); Vτ1 := ∥Vτ1∥. Definition (Tipler 1977): γ terminates in a gravitationally strong singularity if for all 0 > τ1 ≥ τ0, lim infτ→0- Vτ1(τ) = 0. γ... gravitationally weak ... lim infτ→0- Vτ1(τ) > 0. The interpretation is that at a strong singularity, an extended body, e.g. a gravitational wave detector, is crushed to zero volume by the singularity. Tipler's definition does not take account of the possibility that (i) V → ∞ or (ii) V → finite, non-zero value, but with infinite stretching/crushing in orthogonal directions ('spaghettifying singularity'). Extended definition (Nolan 1999): strong if either V → 0,∞ or if for every τ1, there is an element ěc ξ of Jτ1 satisfying ||ěc ξ || -> 0. Otherwise weak. (Ori 2000): singularity is 'deformationally strong' if either (i) it is Tipler-strong or (ii) for every τ1, there is an element ěc ξ of Jτ1 satisfying ||ěc ξ || -> ∞ . Otherwise, deformationally weak...

Maximum Entropy Methods as the Bridge Between Microscopic and Macroscopic Theory

NASA Astrophysics Data System (ADS)

Taylor, Jamie M.

2016-09-01

This paper is concerned with an investigation into a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability distributions on a state space, defined so that it corresponds to the maximum possible entropy given known observed statistical averages, although non-classical entropy-like objective functions will also be considered. First the set of admissible moments must be established, and under the conditions presented in this work the set is open, bounded and convex allowing a description in terms of supporting hyperplanes, which provides estimates on the development of singularities for related probability distributions. Under appropriate conditions it is shown that the singular potential is strictly convex, as differentiable as the microscopic entropy, and blows up uniformly as the macroscopic variable tends to the boundary of the set of admissible moments. Applications of the singular potential are then discussed, and particular consideration will be given to certain free-energy functionals typical in mean-field theory, demonstrating an equivalence between certain microscopic and macroscopic free-energy functionals. This allows statements about L^1-local minimisers of Onsager's free energy to be obtained which cannot be given by two-sided variations, and overcomes the need to ensure local minimisers are bounded away from zero and +∞ before taking L^∞ variations. The analysis also permits the definition of a dual order parameter for which Onsager's free energy allows an explicit representation. Also, the difficulties in approximating the singular potential by everywhere defined functions, in particular by polynomial functions, are addressed, with examples demonstrating the failure of the Taylor approximation to preserve relevant shape properties of the singular potential.

Geometry and the onset of rigidity in a disordered network

NASA Astrophysics Data System (ADS)

Vermeulen, Mathijs F. J.; Bose, Anwesha; Storm, Cornelis; Ellenbroek, Wouter G.

2017-11-01

Disordered spring networks that are undercoordinated may abruptly rigidify when sufficient strain is applied. Since the deformation in response to applied strain does not change the generic quantifiers of network architecture, the number of nodes and the number of bonds between them, this rigidity transition must have a geometric origin. Naive, degree-of-freedom-based mechanical analyses such as the Maxwell-Calladine count or the pebble game algorithm overlook such geometric rigidity transitions and offer no means of predicting or characterizing them. We apply tools that were developed for the topological analysis of zero modes and states of self-stress on regular lattices to two-dimensional random spring networks and demonstrate that the onset of rigidity, at a finite simple shear strain γ★, coincides with the appearance of a single state of self-stress, accompanied by a single floppy mode. The process conserves the topologically invariant difference between the number of zero modes and the number of states of self-stress but imparts a finite shear modulus to the spring network. Beyond the critical shear, the network acquires a highly anisotropic elastic modulus, resisting further deformation most strongly in the direction of the rigidifying shear. We confirm previously reported critical scaling of the corresponding differential shear modulus. In the subcritical regime, a singular value decomposition of the network's compatibility matrix foreshadows the onset of rigidity by way of a continuously vanishing singular value corresponding to the nascent state of self-stress.

Stress-strain state of the lithosphere in the southern Baikal region and northern Mongolia from data on seismic moments of earthquakes

NASA Astrophysics Data System (ADS)

Klyuchevskii, A. V.; Dem'yanovich, V. M.

2006-05-01

Investigation and understanding of the present-day geodynamic situation are of key importance for the elucidation of the laws and evolution of the seismic process in a seismically active region. In this work, seismic moments of nearly 26000 earthquakes with K p ≥ 7 ( M LH ≥ 2) that occurred in the southern Baikal region and northern Mongolia (SBNM) (48° 54°N, 96° 108°E) from 1968 through 1994 are determined from amplitudes and periods of maximum displacements in transverse body waves. The resulting set of seismic moments is used for spatial-temporal analysis of the stress-strain state of the SBNM lithosphere. The stress fields of the Baikal rift and the India-Asia collision zone are supposed to interact in the region studied. Since the seismic moment of a tectonic earthquake depends on the type of motion in the source, seismic moments and focal mechanisms of earthquakes belonging to four long-term aftershock and swarm clusters of shocks in the Baikal region were used to “calibrate” average seismic moments in accordance with the source faulting type. The study showed that the stress-strain state of the SBNM lithosphere is spatially inhomogeneous and nonstationary. A space-time discrepancy is observed in the formation of faulting types in sources of weak ( K p = 7 and 8) and stronger ( K p ≥ 9) earthquakes. This discrepancy is interpreted in terms of rock fracture at various hierarchical levels of ruptures on differently oriented general, regional, and local faults. A gradual increase and an abrupt, nearly pulsed, decrease in the vertical component of the stress field S v is a characteristic feature of time variations. The zones where the stress S v prevails are localized at “singular points” of the lithosphere. Shocks of various energy classes in these zones are dominated by the normal-fault slip mechanism. For earthquakes with K p = 9, the source faulting changes with depth from the strike-slip type to the normal-strike-slip and normal types, suggesting an increase in S v . On the whole, the results of this study are well consistent with the synergism of open unstable dissipative systems and are usable for interpreting the main observable variations in the stress-strain state of the lithosphere in terms of spatiotemporal variations in the vertical component of the stress field S v . This suggests the influence of rifting on the present-day geodynamic processes in the SBNM lithosphere.

76 FR 60031 - Notice of Order: Revisions to Enterprise Public Use Database Incorporating High-Cost Single...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-09-28

... Database Incorporating High-Cost Single-Family Securitized Loan Data Fields and Technical Data Field... single-family matrix in FHFA's Public Use Database (PUDB) to include data fields for the high-cost single... of loan attributes in FHFA's databases that could be used, singularly or in some combination, to...

Experimental Evidence of Accelerated Seismic Release without Critical Failure in Acoustic Emissions of Compressed Nanoporous Materials

NASA Astrophysics Data System (ADS)

Baró, Jordi; Dahmen, Karin A.; Davidsen, Jörn; Planes, Antoni; Castillo, Pedro O.; Nataf, Guillaume F.; Salje, Ekhard K. H.; Vives, Eduard

2018-06-01

The total energy of acoustic emission (AE) events in externally stressed materials diverges when approaching macroscopic failure. Numerical and conceptual models explain this accelerated seismic release (ASR) as the approach to a critical point that coincides with ultimate failure. Here, we report ASR during soft uniaxial compression of three silica-based (SiO2 ) nanoporous materials. Instead of a singular critical point, the distribution of AE energies is stationary, and variations in the activity rate are sufficient to explain the presence of multiple periods of ASR leading to distinct brittle failure events. We propose that critical failure is suppressed in the AE statistics by mechanisms of transient hardening. Some of the critical exponents estimated from the experiments are compatible with mean field models, while others are still open to interpretation in terms of the solution of frictional and fracture avalanche models.

Leading singularities and off-shell conformal integrals

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

Drummond, James; Duhr, Claude; Eden, Burkhard

2013-08-29

The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In our paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol — with an appropriate ansatz for its structure — as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certainmore » limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. Furthermore, we develop techniques that can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.« less

Macroscopic theory of dark sector

NASA Astrophysics Data System (ADS)

Meierovich, Boris

A simple Lagrangian with squared covariant divergence of a vector field as a kinetic term turned out an adequate tool for macroscopic description of the dark sector. The zero-mass field acts as the dark energy. Its energy-momentum tensor is a simple additive to the cosmological constant [1]. Space-like and time-like massive vector fields describe two different forms of dark matter. The space-like massive vector field is attractive. It is responsible for the observed plateau in galaxy rotation curves [2]. The time-like massive field displays repulsive elasticity. In balance with dark energy and ordinary matter it provides a four parametric diversity of regular solutions of the Einstein equations describing different possible cosmological and oscillating non-singular scenarios of evolution of the universe [3]. In particular, the singular big bang turns into a regular inflation-like transition from contraction to expansion with the accelerate expansion at late times. The fine-tuned Friedman-Robertson-Walker singular solution corresponds to the particular limiting case at the boundary of existence of regular oscillating solutions in the absence of vector fields. The simplicity of the general covariant expression for the energy-momentum tensor allows to analyse the main properties of the dark sector analytically and avoid unnecessary model assumptions. It opens a possibility to trace how the additional attraction of the space-like dark matter, dominating in the galaxy scale, transforms into the elastic repulsion of the time-like dark matter, dominating in the scale of the Universe. 1. B. E. Meierovich. "Vector fields in multidimensional cosmology". Phys. Rev. D 84, 064037 (2011). 2. B. E. Meierovich. "Galaxy rotation curves driven by massive vector fields: Key to the theory of the dark sector". Phys. Rev. D 87, 103510, (2013). 3. B. E. Meierovich. "Towards the theory of the evolution of the Universe". Phys. Rev. D 85, 123544 (2012).

Calculation of periodic flows in a continuously stratified fluid

NASA Astrophysics Data System (ADS)

Vasiliev, A.

2012-04-01

Analytic theory of disturbances generated by an oscillating compact source in a viscous continuously stratified fluid was constructed. Exact solution of the internal waves generation problem was constructed taking into account diffusivity effects. This analysis is based on set of fundamental equations of incompressible flows. The linearized problem of periodic flows in a continuously stratified fluid, generated by an oscillating part of the inclined plane was solved by methods of singular perturbation theory. A rectangular or disc placed on a sloping plane and oscillating linearly in an arbitrary direction was selected as a source of disturbances. The solutions include regularly perturbed on dissipative component functions describing internal waves and a family of singularly perturbed functions. One of the functions from the singular components family has an analogue in a homogeneous fluid that is a periodic or Stokes' flow. Its thickness is defined by a universal micro scale depending on kinematics viscosity coefficient and a buoyancy frequency with a factor depending on the wave slope. Other singular perturbed functions are specific for stratified flows. Their thickness are defined the diffusion coefficient, kinematic viscosity and additional factor depending on geometry of the problem. Fields of fluid density, velocity, vorticity, pressure, energy density and flux as well as forces acting on the source are calculated for different types of the sources. It is shown that most effective source of waves is the bi-piston. Complete 3D problem is transformed in various limiting cases that are into 2D problem for source in stratified or homogeneous fluid and the Stokes problem for an oscillating infinite plane. The case of the "critical" angle that is equality of the emitting surface and the wave cone slope angles needs in separate investigations. In this case, the number of singular component is saved. Patterns of velocity and density fields were constructed and analyzed by methods of computational mathematics. Singular components of the solution affect the flow pattern of the inhomogeneous stratified fluid, not only near the source of the waves, but at a large distance. Analytical calculations of the structure of wave beams are matched with laboratory experiments. Some deviations at large distances from the source are formed due to the contribution of background wave field associated with seiches in the laboratory tank. In number of the experiments vortices with closed contours were observed on some distances from the disk. The work was supported by Ministry of Education and Science RF (Goscontract No. 16.518.11.7059), experiments were performed on set up USU "HPC IPMec RAS".

C-point and V-point singularity lattice formation and index sign conversion methods

NASA Astrophysics Data System (ADS)

Kumar Pal, Sushanta; Ruchi; Senthilkumaran, P.

2017-06-01

The generic singularities in an ellipse field are C-points namely stars, lemons and monstars in a polarization distribution with C-point indices (-1/2), (+1/2) and (+1/2) respectively. Similar to C-point singularities, there are V-point singularities that occur in a vector field and are characterized by Poincare-Hopf index of integer values. In this paper we show that the superposition of three homogenously polarized beams in different linear states leads to the formation of polarization singularity lattice. Three point sources at the focal plane of the lens are used to create three interfering plane waves. A radial/azimuthal polarization converter (S-wave plate) placed near the focal plane modulates the polarization states of the three beams. The interference pattern is found to host C-points and V-points in a hexagonal lattice. The C-points occur at intensity maxima and V-points occur at intensity minima. Modulating the state of polarization (SOP) of three plane waves from radial to azimuthal does not essentially change the nature of polarization singularity lattice as the Poincare-Hopf index for both radial and azimuthal polarization distributions is (+1). Hence a transformation from a star to a lemon is not trivial, as such a transformation requires not a single SOP change, but a change in whole spatial SOP distribution. Further there is no change in the lattice structure and the C- and V-points appear at locations where they were present earlier. Hence to convert an interlacing star and V-point lattice into an interlacing lemon and V-point lattice, the interferometer requires modification. We show for the first time a method to change the polarity of C-point and V-point indices. This means that lemons can be converted into stars and stars can be converted into lemons. Similarly the positive V-point can be converted to negative V-point and vice versa. The intensity distribution in all these lattices is invariant as the SOPs of the three beams are changed in an orderly fashion. It shows degeneracy as long as the SOPs of the three beams are drawn from polarization distributions that have Poincare-Hopf index of same magnitude. Various topological aspects of these lattices are presented with the help of Stokes field S12, which is constructed using generalized Stokes parameters of a fully polarized light. We envisage that such polarization lattice structure may lead to novel concept of structured polarization illumination methods in super resolution microscopy.

Stress-Constrained Structural Topology Optimization with Design-Dependent Loads

NASA Astrophysics Data System (ADS)

Lee, Edmund

Topology optimization is commonly used to distribute a given amount of material to obtain the stiffest structure, with predefined fixed loads. The present work investigates the result of applying stress constraints to topology optimization, for problems with design-depending loading, such as self-weight and pressure. In order to apply pressure loading, a material boundary identification scheme is proposed, iteratively connecting points of equal density. In previous research, design-dependent loading problems have been limited to compliance minimization. The present study employs a more practical approach by minimizing mass subject to failure constraints, and uses a stress relaxation technique to avoid stress constraint singularities. The results show that these design dependent loading problems may converge to a local minimum when stress constraints are enforced. Comparisons between compliance minimization solutions and stress-constrained solutions are also given. The resulting topologies of these two solutions are usually vastly different, demonstrating the need for stress-constrained topology optimization.

Normalization of Gravitational Acceleration Models

NASA Technical Reports Server (NTRS)

Eckman, Randy A.; Brown, Aaron J.; Adamo, Daniel R.

2011-01-01

Unlike the uniform density spherical shell approximations of Newton, the con- sequence of spaceflight in the real universe is that gravitational fields are sensitive to the nonsphericity of their generating central bodies. The gravitational potential of a nonspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities which must be removed in order to generalize the method and solve for any possible orbit, including polar orbits. Three unique algorithms have been developed to eliminate these singularities by Samuel Pines [1], Bill Lear [2], and Robert Gottlieb [3]. This paper documents the methodical normalization of two1 of the three known formulations for singularity-free gravitational acceleration (namely, the Lear [2] and Gottlieb [3] algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre Polynomials and ALFs for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

Cyclic multiverses

NASA Astrophysics Data System (ADS)

Marosek, Konrad; Dąbrowski, Mariusz P.; Balcerzak, Adam

2016-09-01

Using the idea of regularization of singularities due to the variability of the fundamental constants in cosmology we study the cyclic universe models. We find two models of oscillating and non-singular mass density and pressure (`non-singular' bounce) regularized by varying gravitational constant G despite the scale factor evolution is oscillating and having sharp turning points (`singular' bounce). Both violating (big-bang) and non-violating (phantom) null energy condition models appear. Then, we extend this idea on to the multiverse containing cyclic individual universes with either growing or decreasing entropy though leaving the net entropy constant. In order to get an insight into the key idea, we consider the doubleverse with the same geometrical evolution of the two `parallel' universes with their physical evolution [physical coupling constants c(t) and G(t)] being different. An interesting point is that there is a possibility to exchange the universes at the point of maximum expansion - the fact which was already noticed in quantum cosmology. Similar scenario is also possible within the framework of Brans-Dicke theory where varying G(t) is replaced by the dynamical Brans-Dicke field φ(t) though these theories are slightly different.

Automatic classification of singular elements for the electrostatic analysis of microelectromechanical systems

NASA Astrophysics Data System (ADS)

Su, Y.; Ong, E. T.; Lee, K. H.

2002-05-01

The past decade has seen an accelerated growth of technology in the field of microelectromechanical systems (MEMS). The development of MEMS products has generated the need for efficient analytical and simulation methods for minimizing the requirement for actual prototyping. The boundary element method is widely used in the electrostatic analysis for MEMS devices. However, singular elements are needed to accurately capture the behavior at singular regions, such as sharp corners and edges, where standard elements fail to give an accurate result. The manual classification of boundary elements based on their singularity conditions is an immensely laborious task, especially when the boundary element model is large. This process can be automated by querying the geometric model of the MEMS device for convex edges based on geometric information of the model. The associated nodes of the boundary elements on these edges can then be retrieved. The whole process is implemented in the MSC/PATRAN platform using the Patran Command Language (the source code is available as supplementary data in the electronic version of this journal issue).

Normal forms for Hopf-Zero singularities with nonconservative nonlinear part

NASA Astrophysics Data System (ADS)

Gazor, Majid; Mokhtari, Fahimeh; Sanders, Jan A.

In this paper we are concerned with the simplest normal form computation of the systems x˙=2xf(x,y2+z2), y˙=z+yf(x,y2+z2), z˙=-y+zf(x,y2+z2), where f is a formal function with real coefficients and without any constant term. These are the classical normal forms of a larger family of systems with Hopf-Zero singularity. Indeed, these are defined such that this family would be a Lie subalgebra for the space of all classical normal form vector fields with Hopf-Zero singularity. The simplest normal forms and simplest orbital normal forms of this family with nonzero quadratic part are computed. We also obtain the simplest parametric normal form of any non-degenerate perturbation of this family within the Lie subalgebra. The symmetry group of the simplest normal forms is also discussed. This is a part of our results in decomposing the normal forms of Hopf-Zero singular systems into systems with a first integral and nonconservative systems.

Holographic dark energy with linearly varying deceleration parameter and escaping big rip singularity of the Bianchi type-V universe

NASA Astrophysics Data System (ADS)

Sarkar, Sanjay

2014-08-01

The present work deals with the accretion of two minimally interacting fluids: dark matter and a hypothetical isotropic fluid as the holographic dark energy components onto black hole and wormhole in a spatially homogeneous and anisotropic Bianchi type-V universe. To obtain an exact solution of the Einstein's field equations, we use the assumption of linearly varying deceleration parameter. Solution describes effectively the actual acceleration and indicates a big rip type future singularity of the universe. We have studied the evolution of the mass of black hole and the wormhole embedded in this anisotropic universe in order to reproduce a stable universe protected against future-time singularity. It is observed that the accretion of these dark components leads to a gradual decrease and increase of black hole and wormhole mass respectively. Finally, we have found that contrary to our previous case (Sarkar in Astrophys. Space. Sci. 341:651, 2014a), the big rip singularity of the universe with a divergent Hubble parameter of this dark energy model may be avoided by a big trip.

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

Merkle, J.G.

In order to study effects of constraint on fracture toughness, it is important to select the right location within the crack-tip field for investigation. In 1950 Hill postulated that close to a circular notch tip the principal stress directions would be radial and circumferential, so that the plastic slip lines (maximum shear stress trajectories) would be logarithmic spirals. The resulting equation for stress normal to the notch symmetry plane, neglecting strain hardening, was identical to that for the circumferential stress near the bore of an ideally plastic thick-walled hollow cylinder under external radial tension, because the relevant geometries are identical.more » In 1969, Rice and Johnson developed a near crack-tip, plane strain, large-strain rigid-plastic analysis considering strain hardening and assuming an infinitely sharp initial crack tip. Shortly afterwards, Merkle, following Hill's suggestion, proposed an approximate analysis of the stresses and strains ahead of a blunted crack tip on the plane of symmetry, based on a circular blunted crack tip. The analysis amounted to a hollow cylinder analogy, including the effects of strain hardening. The original hollow cylinder analogy was based on small strain theory, and the calculated strain distributions did not agree well with the Rice and Johnson results very near the blunted crack tip. Therefore, the hollow cylinder analogy equations have been rederived, based on large strain theory, and the agreement with the Rice and Johnson results and other more recent numerical results is good. Calculations illustrate the effects of transverse strain on the principal stresses very close to a blunting crack tip and show that, theoretically, a singularity still exists at the tip of a blunting crack. 10 refs., 9 figs.« less

Extended hamiltonian formalism and Lorentz-violating lagrangians

NASA Astrophysics Data System (ADS)

Colladay, Don

2017-09-01

A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.

Horizon quantum fuzziness for non-singular black holes

NASA Astrophysics Data System (ADS)

Giugno, Andrea; Giusti, Andrea; Helou, Alexis

2018-03-01

We study the extent of quantum gravitational effects in the internal region of non-singular, Hayward-like solutions of Einstein's field equations according to the formalism known as horizon quantum mechanics. We grant a microscopic description to the horizon by considering a huge number of soft, off-shell gravitons, which superimpose in the same quantum state, as suggested by Dvali and Gomez. In addition to that, the constituents of such a configuration are understood as loosely confined in a binding harmonic potential. A simple analysis shows that the resolution of a central singularity through quantum physics does not tarnish the classical description, which is bestowed upon this extended self-gravitating system by General Relativity. Finally, we estimate the appearance of an internal horizon as being negligible, because of the suppression of the related probability caused by the large number of virtual gravitons.

Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse

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

Mitsuda, Eiji; Yoshino, Hirotaka; Tomimatsu, Akira

Dynamical evolution of test fields in background geometry with a naked singularity is an important problem relevant to the Cauchy horizon instability and the observational signatures different from black hole formation. In this paper we study electromagnetic perturbations generated by a given current distribution in collapsing matter under a spherically symmetric self-similar background. Using the Green's function method, we construct the formula to evaluate the outgoing energy flux observed at the future null infinity. The contributions from 'quasinormal' modes of the self-similar system as well as 'high-frequency' waves are clarified. We find a characteristic power-law time evolution of the outgoingmore » energy flux which appears just before naked singularity formation and give the criteria as to whether or not the outgoing energy flux diverges at the future Cauchy horizon.« less

The supersonic triplet - A new aerodynamic panel singularity with directional properties. [internal wave elimination

NASA Technical Reports Server (NTRS)

Woodward, F. A.; Landrum, E. J.

1979-01-01

A new supersonic triplet singularity has been developed which eliminates internal waves generated by panels having supersonic edges. The triplet is a linear combination of source and vortex distributions which provides the desired directional properties in the flow field surrounding the panel. The theoretical development of the triplet is described, together with its application to the calculation of surface pressure on arbitrary body shapes. Examples are presented comparing the results of the new method with other supersonic panel methods and with experimental data.

FREQ: A computational package for multivariable system loop-shaping procedures

NASA Technical Reports Server (NTRS)

Giesy, Daniel P.; Armstrong, Ernest S.

1989-01-01

Many approaches in the field of linear, multivariable time-invariant systems analysis and controller synthesis employ loop-sharing procedures wherein design parameters are chosen to shape frequency-response singular value plots of selected transfer matrices. A software package, FREQ, is documented for computing within on unified framework many of the most used multivariable transfer matrices for both continuous and discrete systems. The matrices are evaluated at user-selected frequency-response values, and singular values against frequency. Example computations are presented to demonstrate the use of the FREQ code.

Alien calculus and non perturbative effects in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Bellon, Marc P.

2016-12-01

In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.

Renormalized asymptotic enumeration of Feynman diagrams

NASA Astrophysics Data System (ADS)

Borinsky, Michael

2017-10-01

A method to obtain all-order asymptotic results for the coefficients of perturbative expansions in zero-dimensional quantum field is described. The focus is on the enumeration of the number of skeleton or primitive diagrams of a certain QFT and its asymptotics. The procedure heavily applies techniques from singularity analysis. To utilize singularity analysis, a representation of the zero-dimensional path integral as a generalized hyperelliptic curve is deduced. As applications the full asymptotic expansions of the number of disconnected, connected, 1PI and skeleton Feynman diagrams in various theories are given.

Singularity-free spinors in gravity with propagating torsion

NASA Astrophysics Data System (ADS)

Fabbri, Luca

2017-12-01

We consider the most general renormalizable theory of propagating torsion in Einstein gravity for the Dirac matter distribution and we demonstrate that in this case, torsion is a massive axial-vector field whose coupling to the spinor gives rise to conditions in terms of which gravitational singularities are not bound to form; we discuss how our results improve those that are presented in the existing literature, and that no further improvement can be achieved unless one is ready to re-evaluate some considerations on the renormalizability of the theory.

Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities

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

Zampeli, Adamantia; Pailas, Theodoros; Terzis, Petros A.

2016-05-01

In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow [1] and impose the operators related to the classical conditional symmetries onmore » the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.« less

Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field.

PubMed

Carmelo, J M P; Sacramento, P D; Machado, J D P; Campbell, D K

2015-10-14

We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the 'pseudofermion dynamical theory' (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents ζ(τ)(k) controlling the singularities for both the longitudinal (τ = l) and transverse (τ = t) dynamical structure factors for the whole momentum range k ∈ ]0,π[, in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.

Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field

NASA Astrophysics Data System (ADS)

Carmelo, J. M. P.; Sacramento, P. D.; Machado, J. D. P.; Campbell, D. K.

2015-10-01

We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the ‘pseudofermion dynamical theory’ (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents {{\\zeta}τ}(k) controlling the singularities for both the longitudinal ≤ft(τ =l\\right) and transverse ≤ft(τ =t\\right) dynamical structure factors for the whole momentum range k\\in ]0,π[ , in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.

Dynamics of magnetic shells and information loss problem

NASA Astrophysics Data System (ADS)

Lee, Bum-Hoon; Lee, Wonwoo; Yeom, Dong-han

2015-07-01

We investigate dynamics of magnetic thin-shells in three dimensional anti-de Sitter background. Because of the magnetic field, an oscillatory solution is possible. This oscillating shell can tunnel to a collapsing shell or a bouncing shell, where both tunnelings induce an event horizon and a singularity. In the entire path integral, via the oscillating solution, there is a nonzero probability to maintain a trivial causal structure without a singularity. Therefore, due to the path integral, the entire wave function can conserve information. Since an oscillating shell can tunnel after a number of oscillations, in the end, it will allow an infinite number of different branchings to classical histories. This system can be a good model of the effective loss of information, where information is conserved by a solution that is originated from gauge fields.

The scatter of obliquely incident plane waves from a corrugated conducting surface

NASA Technical Reports Server (NTRS)

Levine, D. N.

1975-01-01

A physical optics solution is presented for the scattering of plane waves from a perfectly conducting corrugated surface in the case of waves incident from an arbitrary direction and for an observer far from the surface. This solution was used to compute the radar cross section of the surface in the case of backscatter from irregular (i.e., stochastic) corrugations and to point out a correction to the literature on this problem. A feature of the solution is the occurrence of singularities in the scattered fields which appear to be a manifestation of focussing by the surface at its stationary points. Whether or not the singularities occur in the solution depends on the manner in which one restricts the analysis to the far field.

A penny shaped crack in a filament-reinforced matrix. 2: The crack problem

NASA Technical Reports Server (NTRS)

Pacella, A. H.; Erdogan, F.

1973-01-01

The elastostatic interaction problem between a penny-shaped crack and a slender inclusion or filament in an elastic matrix was formulated. For a single filament as well as multiple identical filaments located symmetrically around the crack the problem is shown to reduce to a singular integral equation. The solution of the problem is obtained for various geometries and filament-to-matrix stiffness ratios, and the results relating to the angular variation of the stress intensity factor and the maximum filament stress are presented.

Stress state of a piecewise uniform layered space with doubly periodic internal cracks

NASA Astrophysics Data System (ADS)

Hakobyan, V. N.; Dashtoyan, L. L.

2018-04-01

The present paper deals with the stress state of a piecewise homogeneous plane formed by alternation junction of two distinct strips of equal height manufactured of different materials. There is a doubly periodic system of cracks on the plane. The governing system of singular integral equations of the first kind for the density of the crack dislocation is derived. The solution of the problem in the case where only one of the repeated strips contains one doubly-periodic crack is obtained by the method of mechanical quadratures.

Optimization of Processing Variables Which Affect Adhesion of Organic Coatings to Anodized Aluminum Alloys

DTIC Science & Technology

1975-10-01

DC anodizing all adhesion values were lower but almost equal. 36 mnamnminmh TABU X SWOT OF EFFECT OF CURRaTT DEÄITT, TIME ABD SEAUK OF CHJOOC...Continuum Interpretation for Fracture and Adhesion", J. Appl . Polymer Science, 1^, 29 (I969) 3. Williams, M. L., "Stress Singularities, Adhesion, and

Cross-talk between topological defects in different fields revealed by nematic microfluidics

PubMed Central

Giomi, Luca; Kos, Žiga; Ravnik, Miha

2017-01-01

Topological defects are singularities in material fields that play a vital role across a range of systems: from cosmic microwave background polarization to superconductors and biological materials. Although topological defects and their mutual interactions have been extensively studied, little is known about the interplay between defects in different fields—especially when they coevolve—within the same physical system. Here, using nematic microfluidics, we study the cross-talk of topological defects in two different material fields—the velocity field and the molecular orientational field. Specifically, we generate hydrodynamic stagnation points of different topological charges at the center of star-shaped microfluidic junctions, which then interact with emergent topological defects in the orientational field of the nematic director. We combine experiments and analytical and numerical calculations to show that a hydrodynamic singularity of a given topological charge can nucleate a nematic defect of equal topological charge and corroborate this by creating −1, −2, and −3 topological defects in four-, six-, and eight-arm junctions. Our work is an attempt toward understanding materials that are governed by distinctly multifield topology, where disparate topology-carrying fields are coupled and concertedly determine the material properties and response. PMID:28674012

Concentration dependence of the wings of a dipole-broadened magnetic resonance line in magnetically diluted lattices

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

Zobov, V. E., E-mail: rsa@iph.krasn.ru; Kucherov, M. M.

2017-01-15

The singularities of the time autocorrelation functions (ACFs) of magnetically diluted spin systems with dipole–dipole interaction (DDI), which determine the high-frequency asymptotics of autocorrelation functions and the wings of a magnetic resonance line, are studied. Using the self-consistent fluctuating local field approximation, nonlinear equations are derived for autocorrelation functions averaged over the independent random arrangement of spins (magnetic atoms) in a diamagnetic lattice with different spin concentrations. The equations take into account the specificity of the dipole–dipole interaction. First, due to its axial symmetry in a strong static magnetic field, the autocorrelation functions of longitudinal and transverse spin components aremore » described by different equations. Second, the long-range type of the dipole–dipole interaction is taken into account by separating contributions into the local field from distant and near spins. The recurrent equations are obtained for the expansion coefficients of autocorrelation functions in power series in time. From them, the numerical value of the coordinate of the nearest singularity of the autocorrelation function is found on the imaginary time axis, which is equal to the radius of convergence of these expansions. It is shown that in the strong dilution case, the logarithmic concentration dependence of the coordinate of the singularity is observed, which is caused by the presence of a cluster of near spins whose fraction is small but contribution to the modulation frequency is large. As an example a silicon crystal with different {sup 29}Si concentrations in magnetic fields directed along three crystallographic axes is considered.« less

Influence of local meshing size on stress intensity factor of orthopedic lag screw

NASA Astrophysics Data System (ADS)

Husain, M. N.; Daud, R.; Basaruddin, K. S.; Mat, F.; Bajuri, M. Y.; Arifin, A. K.

2017-09-01

Linear elastic fracture mechanics (LEFM) concept is generally used to study the influence of crack on the performance of structures. In order to study the LEFM concept on damaged structure, the usage of finite element analysis software is implemented to do the simulation of the structure. Mesh generation is one of the most crucial procedures in finite element method. For the structure that crack or damaged, it is very important to determine the accurate local meshing size at the crack tip of the crack itself in order to get the accurate value of stress intensity factor, KI. Pre crack will be introduced to the lag screw based on the von mises' stress result that had been performed in previous research. This paper shows the influence of local mesh arrangement on numerical value of the stress intensity factor, KI obtained by the displacement method. This study aims to simulate the effect of local meshing which is the singularity region on stress intensity factor, KI to the critical point of failure in screw. Five different set of wedges meshing size are introduced during the simulation of finite element analysis. The number of wedges used to simulate this research is 8, 10, 14, 16 and 20. There are three set of numerical equations used to validate the results which are brown and srawley, gross and brown and Tada equation. The result obtained from the finite element software (ANSYS APDL) has a positive agreement with the numerical analysis which is Brown and Srawley compared to other numerical formula. Radius of first row size of 0.014 and singularity element with 14 numbers of wedges is proved to be the best local meshing for this study.

MIB Galerkin method for elliptic interface problems.

PubMed

Xia, Kelin; Zhan, Meng; Wei, Guo-Wei

2014-12-15

Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm the designed second order convergence of the MIB Galerkin method in the L ∞ and L 2 errors. Some of the best results are obtained in the present work when the interface is C 1 or Lipschitz continuous and the solution is C 2 continuous.

An exact solution to the Einstein-Maxwell equations representing a nonspherical, highly charged object

NASA Astrophysics Data System (ADS)

Menon, Govind K.

The Reissner-Nordstrom solution possesses a naked singularity when e2 > m2, where m is the mass and e is the net charge of the system. Also, the singularity at r = 0 is repulsive (i.e., no timelike geodesics (neutral particles) can reach the singularity). These unusual properties of the Reissner-Nordstrom geometry are considered as an accident resulting from the highly symmetric nature of the space-time. Here we wish to generalize the condition of spherical symmetry to axial symmetry and to probe into the issues of naked singularity and gravitational repulsion. To do this, we must construct a nonspherical solution to the Einstein-Maxwell set of equations in the event that e2 > m2. The Erez-Rosen extension of the vacuum Schwarzschild solution to the non-spherical case gave one of the first physically significant solutions of the Einstein field equations. Nonvacuum extensions of the Erez-Rosen solution representing a non-spherical mass containing a very high net charge (i.e., when e2 > m2) will be discussed. The special case of spherical symmetry, as would be expected, results in the Reissner-Nordstrom solution. The search for the physical singularities involves the calculation of a nontrivial scalar constructed from the Riemann curvature tensor. As it turns out, the resulting geometry does indeed possess a naked singularity. In addition, the space-time also entertains gravitational repulsion. However, unlike the Reissner-Nordstrom solution, it has been found that all timelike geodesics are not necessarily repelled from the origin.

Poisson traces, D-modules, and symplectic resolutions

NASA Astrophysics Data System (ADS)

Etingof, Pavel; Schedler, Travis

2018-03-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Perfect fluid tori orbiting Kehagias-Sfetsos naked singularities

NASA Astrophysics Data System (ADS)

Stuchlík, Z.; Pugliese, D.; Schee, J.; Kučáková, H.

2015-09-01

We construct perfect fluid tori in the field of the Kehagias-Sfetsos (K-S) naked singularities. These are spherically symmetric vacuum solutions of the modified Hořava quantum gravity, characterized by a dimensionless parameter ω M^2, combining the gravitational mass parameter M of the spacetime with the Hořava parameter ω reflecting the role of the quantum corrections. In dependence on the value of ω M^2, the K-S naked singularities demonstrate a variety of qualitatively different behavior of their circular geodesics that is fully reflected in the properties of the toroidal structures, demonstrating clear distinction to the properties of the torii in the Schwarzschild spacetimes. In all of the K-S naked singularity spacetimes the tori are located above an "antigravity" sphere where matter can stay in a stable equilibrium position, which is relevant for the stability of the orbiting fluid toroidal accretion structures. The signature of the K-S naked singularity is given by the properties of marginally stable tori orbiting with the uniform distribution of the specific angular momentum of the fluid, l= const. In the K-S naked singularity spacetimes with ω M^2 > 0.2811, doubled tori with the same l= const can exist; mass transfer between the outer torus and the inner one is possible under appropriate conditions, while only outflow to the outer space is allowed in complementary conditions. In the K-S spacetimes with ω M^2 < 0.2811, accretion from cusped perfect fluid tori is not possible due to the non-existence of unstable circular geodesics.

Poisson traces, D-modules, and symplectic resolutions.

PubMed

Etingof, Pavel; Schedler, Travis

2018-01-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Deformations of the Almheiri-Polchinski model

NASA Astrophysics Data System (ADS)

Kyono, Hideki; Okumura, Suguru; Yoshida, Kentaroh

2017-03-01

We study deformations of the Almheiri-Polchinski (AP) model by employing the Yang-Baxter deformation technique. The general deformed AdS2 metric becomes a solution of a deformed AP model. In particular, the dilaton potential is deformed from a simple quadratic form to a hyperbolic function-type potential similarly to integrable deformations. A specific solution is a deformed black hole solution. Because the deformation makes the spacetime structure around the boundary change drastically and a new naked singularity appears, the holographic interpretation is far from trivial. The Hawking temperature is the same as the undeformed case but the Bekenstein-Hawking entropy is modified due to the deformation. This entropy can also be reproduced by evaluating the renormalized stress tensor with an appropriate counter-term on the regularized screen close to the singularity.

Study of nonlinear MHD equations governing the wave propagation in twisted coronal loops

NASA Technical Reports Server (NTRS)

Parhi, S.; DeBruyne, P.; Goossens, M.; Zhelyazkov, I.

1995-01-01

The solar corona, modelled by a low beta, resistive plasma slab, sustains MHD wave propagations due to shearing footpoint motions in the photosphere. By using a numerical algorithm the excitation and nonlinear development of MHD waves in twisted coronal loops are studied. The plasma responds to the footpoint motion by sausage waves if there is no twist. The twist in the magnetic field of the loop destroys initially developed sausage-like wave modes and they become kinks. The transition from sausage to kink modes is analyzed. The twist brings about mode degradation producing high harmonics and this generates more complex fine structures. This can be attributed to several local extrema in the perturbed velocity profiles. The Alfven wave produces remnants of the ideal 1/x singularity both for zero and non-zero twist and this pseudo-singularity becomes less pronounced for larger twist. The effect of nonlinearity is clearly observed by changing the amplitude of the driver by one order of magnitude. The magnetosonic waves also exhibit smoothed remnants of ideal logarithmic singularities when the frequency of the driver is correctly chosen. This pseudo-singularity for fast waves is absent when the coronal loop does not undergo any twist but becomes pronounced when twist is included. On the contrary, it is observed for slow waves even if there is no twist. Increasing the twist leads to a higher heating rate of the loop. The larger twist shifts somewhat uniformly distributed heating to layers inside the slab corresponding to peaks in the magnetic field strength.

Singular boundary method for global gravity field modelling

NASA Astrophysics Data System (ADS)

Cunderlik, Robert

2014-05-01

The singular boundary method (SBM) and method of fundamental solutions (MFS) are meshless boundary collocation techniques that use the fundamental solution of a governing partial differential equation (e.g. the Laplace equation) as their basis functions. They have been developed to avoid singular numerical integration as well as mesh generation in the traditional boundary element method (BEM). SBM have been proposed to overcome a main drawback of MFS - its controversial fictitious boundary outside the domain. The key idea of SBM is to introduce a concept of the origin intensity factors that isolate singularities of the fundamental solution and its derivatives using some appropriate regularization techniques. Consequently, the source points can be placed directly on the real boundary and coincide with the collocation nodes. In this study we deal with SBM applied for high-resolution global gravity field modelling. The first numerical experiment presents a numerical solution to the fixed gravimetric boundary value problem. The achieved results are compared with the numerical solutions obtained by MFS or the direct BEM indicating efficiency of all methods. In the second numerical experiments, SBM is used to derive the geopotential and its first derivatives from the Tzz components of the gravity disturbing tensor observed by the GOCE satellite mission. A determination of the origin intensity factors allows to evaluate the disturbing potential and gravity disturbances directly on the Earth's surface where the source points are located. To achieve high-resolution numerical solutions, the large-scale parallel computations are performed on the cluster with 1TB of the distributed memory and an iterative elimination of far zones' contributions is applied.

Study of the 3D Euler equations using Clebsch potentials: dual mechanisms for geometric depletion

NASA Astrophysics Data System (ADS)

Ohkitani, Koji

2018-02-01

After surveying analyses of the 3D Euler equations using the Clebsch potentials scattered over the literature, we report some preliminary new results. 1. Assuming that flow fields are free from nulls of the impulse and the vorticity fields, we study how constraints imposed by the Clebsch potentials lead to a degenerate geometrical structure, typically in the form of depletion of nonlinearity. We consider a vorticity surface spanned by \\boldsymbol ω and another material vector \\boldsymbol {W} such that \\boldsymbol γ=\\boldsymbol ω× \\boldsymbol {W}, where \\boldsymbol γ is the impulse variable in geometric gauge. We identify dual mechanism for geometric depletion and show that at least of one them is acting if \\boldsymbol {W} does not develop a null. This suggests that formation of singularity in flows endowed with Clebsch potentials is less likely to happen than in more general flows. Some arguments are given towards exclusion of ‘type I’ blowup. A mathematical challenge remains to rule out singularity formation for flows which have Clebsch potentials everywhere. 2. We exploit classical differential geometry kinematically to write down the Gauss-Weingarten equations for the vorticity surface of the Clebsch potential in terms of fluid dynamical variables, as are the first, second and third fundamental forms. In particular, we derive a constraint on the size of the Gaussian curvature near the point of a possible singularity. On the other hand, an application of the Gauss-Bonnet theorem reveals that the tangential curvature of the surface becomes large in the neighborhood of near-singularity. 3. Using spatially-periodic flows with highly-symmetry, i.e. initial conditions of the Taylor-Green vortex and the Kida-Pelz flow, we present explicit formulas of the Clebsch potentials with exceptional singular surfaces where the Clebsch potentials are undefined. This is done by connecting the known expressions with the solenoidal impulse variable (i.e. the incompressible velocity) using suitable canonical transforms. By a simple argument we show that they keep forming material separatrices under the time evolution of the 3D Euler equations. We argue on this basis that a singularity, if developed, will be associated with these exceptional material surfaces. The difficulty of having Clebsch potentials globally on all of space have been with us for a long time. The proposal rather seeks to turn the difficulty into an advantage by using their absence to identify and locate possible singularities.

A robust indicator based on singular value decomposition for flaw feature detection from noisy ultrasonic signals

NASA Astrophysics Data System (ADS)

Cui, Ximing; Wang, Zhe; Kang, Yihua; Pu, Haiming; Deng, Zhiyang

2018-05-01

Singular value decomposition (SVD) has been proven to be an effective de-noising tool for flaw echo signal feature detection in ultrasonic non-destructive evaluation (NDE). However, the uncertainty in the arbitrary manner of the selection of an effective singular value weakens the robustness of this technique. Improper selection of effective singular values will lead to bad performance of SVD de-noising. What is more, the computational complexity of SVD is too large for it to be applied in real-time applications. In this paper, to eliminate the uncertainty in SVD de-noising, a novel flaw indicator, named the maximum singular value indicator (MSI), based on short-time SVD (STSVD), is proposed for flaw feature detection from a measured signal in ultrasonic NDE. In this technique, the measured signal is first truncated into overlapping short-time data segments to put feature information of a transient flaw echo signal in local field, and then the MSI can be obtained from the SVD of each short-time data segment. Research shows that this indicator can clearly indicate the location of ultrasonic flaw signals, and the computational complexity of this STSVD-based indicator is significantly reduced with the algorithm proposed in this paper. Both simulation and experiments show that this technique is very efficient for real-time application in flaw detection from noisy data.

An internal crack parallel to the boundary of a nonhomogeneous half plane under thermal loading

NASA Astrophysics Data System (ADS)

Jin, Zhi-He; Noda, Naotake

1993-05-01

This paper considers the crack problem for a semi-infinite nonhomogeneous thermoelastic solid subjected to steady heat flux over the boundary. The crack faces are assumed to be insulated. The research is aimed at understanding the effect of nonhomogeneities of materials on stress intensity factors. By using the Fourier transform, the problem is reduced to a system of singular integral equations which are solved numerically. Results are presented illustrating the influence of the nonhomogeneity of the material on the stress intensity factors. Zero Mode I stress intensity factors are found for some groups of the material constants, which may be interesting for the understanding of compositions of advanced Functionally Gradient Materials.

A new class of asymptotically non-chaotic vacuum singularities

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

Klinger, Paul, E-mail: paul.klinger@univie.ac.at

2015-12-15

The BKL conjecture, stated in the 1960s and early 1970s by Belinski, Khalatnikov and Lifschitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated chaotic behaviour in the generic case, but simpler non-chaotic one in cases with symmetry assumptions or certain kinds of matter fields. Here we construct a new class of four-dimensional vacuum spacetimes containing spacelike singularities which show non-chaotic behaviour. In contrast with previous constructions, no symmetry assumptions are made. Rather, the metric is decomposed in Iwasawa variables and conditions on the asymptotic evolution of some ofmore » them are imposed. The constructed solutions contain five free functions of all space coordinates, two of which are constrained by inequalities. We investigate continuous and discrete isometries and compare the solutions to previous constructions. Finally, we give the asymptotic behaviour of the metric components and curvature.« less

Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities

PubMed Central

Ackerman, Paul J.; Qi, Zhiyuan; Lin, Yiheng; Twombly, Christopher W.; Laviada, Mauricio J.; Lansac, Yves; Smalyukh, Ivan I.

2012-01-01

Topological defect lines are ubiquitous and important in a wide variety of fascinating phenomena and theories in many fields ranging from materials science to early-universe cosmology, and to engineering of laser beams. However, they are typically hard to control in a reliable manner. Here we describe facile erasable “optical drawing” of self-assembled defect clusters in liquid crystals. These quadrupolar defect clusters, stabilized by the medium's chirality and the tendency to form twisted configurations, are shaped into arbitrary two-dimensional patterns, including reconfigurable phase gratings capable of generating and controlling optical phase singularities in laser beams. Our findings bridge the studies of defects in condensed matter physics and optics and may enable applications in data storage, singular optics, displays, electro-optic devices, diffraction gratings, as well as in both optically- and electrically-addressed pixel-free spatial light modulators. PMID:22679553

Laser-Directed Hierarchical Assembly of Liquid Crystal Defects and Control of Optical Phase Singularities

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

Ackerman, P. J.; Qi, Z. Y.; Lin, Y. H.

2012-06-07

Topological defect lines are ubiquitous and important in a wide variety of fascinating phenomena and theories in many fields ranging from materials science to early-universe cosmology, and to engineering of laser beams. However, they are typically hard to control in a reliable manner. Here we describe facile erasable 'optical drawing' of self-assembled defect clusters in liquid crystals. These quadrupolar defect clusters, stabilized by the medium's chirality and the tendency to form twisted configurations, are shaped into arbitrary two-dimensional patterns, including reconfigurable phase gratings capable of generating and controlling optical phase singularities in laser beams. Our findings bridge the studies ofmore » defects in condensed matter physics and optics and may enable applications in data storage, singular optics, displays, electro-optic devices, diffraction gratings, as well as in both optically- and electrically-addressed pixel-free spatial light modulators.« less

Rural Literacies: Toward Social Cartography

ERIC Educational Resources Information Center

Corbett, Michael; Donehower, Kim

2017-01-01

In this article we analyze the emergence of the field of rural literacies. We attempt to map this field in a way that illustrates the foundational ideas of literacy and rurality as relational concepts, which are devoid of meaning as what we call "singularities." Our insistence on the importance of context and place reveals multiple rural…

Collapse of charged scalar field in dilaton gravity

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

Borkowska, Anna; Rogatko, Marek; Moderski, Rafal

2011-04-15

We elaborated the gravitational collapse of a self-gravitating complex charged scalar field in the context of the low-energy limit of the string theory, the so-called dilaton gravity. We begin with the regular spacetime and follow the evolution through the formation of an apparent horizon and the final central singularity.

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.

IIB duals of D = 3 {N} = 4 circular quivers

NASA Astrophysics Data System (ADS)

Assel, Benjamin; Bachas, Costas; Estes, John; Gomis, Jaume

2012-12-01

We construct the type-IIB AdS4 ⋉ K supergravity solutions which are dual to the three-dimensional {N} = 4 superconformal field theories that arise as infrared fixed points of circular-quiver gauge theories. These superconformal field theories are labeled by a triple ( {ρ, hat{ρ},L} ) subject to constraints, where ρ and hat{ρ} are two partitions of a number N, and L is a positive integer. We show that in the limit of large L the localized five- branes in our solutions are effectively smeared, and these type-IIB solutions are dual to the near-horizon geometry of M-theory M2-branes at a {{{{{{C}}^4}}} / {{( {{Z_k}× {Z_{widehat{k}}}} )}} .} orbifold singularity. Our IIB solutions resolve the singularity into localized five-brane throats, without breaking the conformal symmetry. The constraints satisfied by the triple ( {ρ, hat{ρ},L} ) , together with the enhanced non-abelian flavour symmetries of the superconformal field theories are precisely reproduced by the type-IIB supergravity solutions. As a bonus, we uncover a novel type of "orbifold equivalence" between different quantum field theories and provide quantitative evidence for this equivalence.

Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field

NASA Astrophysics Data System (ADS)

Karagiorgos, A.; Pailas, T.; Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.

2018-03-01

We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor Fμν the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor Tμν, suffice to reduce the general Fμν to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingly similar to the Reissner-Nordstr{öm one. This points to a connection between the black hole geometry and the cosmological solution here found, which is the analog of the known correlation between the Schwarzschild and the Kantowski-Sachs metrics. The configuration space is drastically modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave geometry. We map the emerging linear and quadratic classical integrals of motion, to quantum observables. Along with the Wheeler-DeWitt equation these observables provide unique, up to constants, wave functions. The employment of a Bohmian interpretation of these quantum states results in deterministic (semi-classical) geometries most of which are singularity free.

Static black hole solutions with a self-interacting conformally coupled scalar field

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

Dotti, Gustavo; Gleiser, Reinaldo J.; Martinez, Cristian

2008-05-15

We study static, spherically symmetric black hole solutions of the Einstein equations with a positive cosmological constant and a conformally coupled self-interacting scalar field. Exact solutions for this model found by Martinez, Troncoso, and Zanelli were subsequently shown to be unstable under linear gravitational perturbations, with modes that diverge arbitrarily fast. We find that the moduli space of static, spherically symmetric solutions that have a regular horizon--and satisfy the weak and dominant energy conditions outside the horizon--is a singular subset of a two-dimensional space parametrized by the horizon radius and the value of the scalar field at the horizon. Themore » singularity of this space of solutions provides an explanation for the instability of the Martinez, Troncoso, and Zanelli spacetimes and leads to the conclusion that, if we include stability as a criterion, there are no physically acceptable black hole solutions for this system that contain a cosmological horizon in the exterior of its event horizon.« less

Black Hole Magnetospheres

NASA Astrophysics Data System (ADS)

Nathanail, Antonios; Contopoulos, Ioannis

2014-06-01

We investigate the structure of the steady-state force-free magnetosphere around a Kerr black hole in various astrophysical settings. The solution Ψ(r, θ) depends on the distributions of the magnetic field line angular velocity ω(Ψ) and the poloidal electric current I(Ψ). These are obtained self-consistently as eigenfunctions that allow the solution to smoothly cross the two singular surfaces of the problem, the inner light surface inside the ergosphere, and the outer light surface, which is the generalization of the pulsar light cylinder. Magnetic field configurations that cross both singular surfaces (e.g., monopole, paraboloidal) are uniquely determined. Configurations that cross only one light surface (e.g., the artificial case of a rotating black hole embedded in a vertical magnetic field) are degenerate. We show that, similar to pulsars, black hole magnetospheres naturally develop an electric current sheet that potentially plays a very important role in the dissipation of black hole rotational energy and in the emission of high-energy radiation.

Stress intensity factors in a cracked infinite elastic wedge loaded by a rigid punch

NASA Technical Reports Server (NTRS)

Erdogan, F.; Civelek, M. B.

1978-01-01

A plane elastic wedge-shaped solid was split through the application of a rigid punch. It was assumed that the coefficient of friction on the the contact area was constant, and the problem had a plane of symmetry with respect to loading and geometry, with the crack in the plane of symmetry. The problem was formulated in terms of a system of integral equations with the contact stress and the derivative of the crack surface displacement as the unknown functions. The solution was obtained for an internal crack and for an edge crack. The results include primarily the stress intensity factors at the crack tips, and the measure of the stress singularity at the wedge apex, and at the end points of the contact area.

The axisymmetric elasticity problem for a laminated plate containing a circular hole

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

The elasticity problem for a laminated thick plate which consists of two bonded dissimilar layers and which contains a circular hole is considered. The problem is formulated for arbitrary axisymmetric tractions on the hole surface by using the Love strain function. Through the expansion of the boundary conditions into Fourier series the problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Of particular interest in the problem are the stresses along the interface as they relate to the question of delamination failure of the composite plate. These stresses are calculated and are observed to become unbounded at the hole boundary. An approximate treatment of the singular behavior of the stress state is presented and the stress intensity factors are calculated.

Nonpolynomial Lagrangian approach to regular black holes

NASA Astrophysics Data System (ADS)

Colléaux, Aimeric; Chinaglia, Stefano; Zerbini, Sergio

We present a review on Lagrangian models admitting spherically symmetric regular black holes (RBHs), and cosmological bounce solutions. Nonlinear electrodynamics, nonpolynomial gravity, and fluid approaches are explained in details. They consist respectively in a gauge invariant generalization of the Maxwell-Lagrangian, in modifications of the Einstein-Hilbert action via nonpolynomial curvature invariants, and finally in the reconstruction of density profiles able to cure the central singularity of black holes. The nonpolynomial gravity curvature invariants have the special property to be second-order and polynomial in the metric field, in spherically symmetric spacetimes. Along the way, other models and results are discussed, and some general properties that RBHs should satisfy are mentioned. A covariant Sakharov criterion for the absence of singularities in dynamical spherically symmetric spacetimes is also proposed and checked for some examples of such regular metric fields.

Green's functions for dislocations in bonded strips and related crack problems

NASA Technical Reports Server (NTRS)

Ballarini, R.; Luo, H. A.

1990-01-01

Green's functions are derived for the plane elastostatics problem of a dislocation in a bimaterial strip. Using these fundamental solutions as kernels, various problems involving cracks in a bimaterial strip are analyzed using singular integral equations. For each problem considered, stress intensity factors are calculated for several combinations of the parameters which describe loading, geometry and material mismatch.

Vorticity dipoles and a theoretical model of a finite force at the moving contact line singularity

NASA Astrophysics Data System (ADS)

Zhang, Peter; Devoria, Adam; Mohseni, Kamran

2017-11-01

In the well known works of Moffatt (1964) and Huh & Scriven (1971), an infinite force was reported at the moving contact line (MCL) and attributed to a non-integrable stress along the fluid-solid boundary. In our recent investigation of the boundary driven wedge, a model of the MCL, we find that the classical solution theoretically predicts a finite force at the contact line if the forces applied by the two boundaries that make up the corner are taken into consideration. Mathematically, this force can be obtained by the complex contour integral of the holomorphic vorticity-pressure function given by G = μω + ip . Alternatively, this force can also be found using a carefully defined real integral that incorporates the two boundaries. Motivated by this discovery, we have found that the rate of change in circulation, viscous energy dissipation, and viscous energy flux is also finite per unit contact line length. The analysis presented demonstrates that despite a singular stress and a relatively simple geometry, the no-slip semi-infinite wedge is capable of capturing some physical quantities of interest. Furthermore, this result provides a foundation for other challenging topics such as dynamic contact angle.

Application of a Reduced Order Kalman Filter to Initialize a Coupled Atmosphere-Ocean Model: Impact on the Prediction of El Nino

NASA Technical Reports Server (NTRS)

Ballabrera-Poy, J.; Busalacchi, A.; Murtugudde, R.

2000-01-01

A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model of Zebiak and Cane. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.

Application of a Reduced Order Kalman Filter to Initialize a Coupled Atmosphere-Ocean Model: Impact on the Prediction of El Nino

NASA Technical Reports Server (NTRS)

Ballabrera-Poy, Joaquim; Busalacchi, Antonio J.; Murtugudde, Ragu

2000-01-01

A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N. In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions I up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.

Generation and dynamics of optical beams with polarization singularities.

PubMed

Cardano, Filippo; Karimi, Ebrahim; Marrucci, Lorenzo; de Lisio, Corrado; Santamato, Enrico

2013-04-08

We present a convenient method to generate vector beams of light having polarization singularities on their axis, via partial spin-to-orbital angular momentum conversion in a suitably patterned liquid crystal cell. The resulting polarization patterns exhibit a C-point on the beam axis and an L-line loop around it, and may have different geometrical structures such as "lemon", "star", and "spiral". Our generation method allows us to control the radius of L-line loop around the central C-point. Moreover, we investigate the free-air propagation of these fields across a Rayleigh range.

Cosmological BCS mechanism and the big bang singularity

NASA Astrophysics Data System (ADS)

Alexander, Stephon; Biswas, Tirthabir

2009-07-01

We provide a novel mechanism that resolves the big bang singularity present in Friedman-Lemaitre-Robertson-Walker space-times without the need for ghost fields. Building on the fact that a four-fermion interaction arises in general relativity when fermions are covariantly coupled, we show that at early times the decrease in scale factor enhances the correlation between pairs of fermions. This enhancement leads to a BCS-like condensation of the fermions and opens a gap dynamically driving the Hubble parameter H to zero and results in a nonsingular bounce, at least in some special cases.

Quantum propagation across cosmological singularities

NASA Astrophysics Data System (ADS)

Gielen, Steffen; Turok, Neil

2017-05-01

The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.

Imaging a non-singular rotating black hole at the center of the Galaxy

NASA Astrophysics Data System (ADS)

Lamy, F.; Gourgoulhon, E.; Paumard, T.; Vincent, F. H.

2018-06-01

We show that the rotating generalization of Hayward’s non-singular black hole previously studied in the literature is geodesically incomplete, and that its straightforward extension leads to a singular spacetime. We present another extension, which is devoid of any curvature singularity. The obtained metric depends on three parameters and, depending on their values, yields an event horizon or not. These two regimes, named respectively regular rotating Hayward black hole and naked rotating wormhole, are studied both numerically and analytically. In preparation for the upcoming results of the Event Horizon Telescope, the images of an accretion torus around Sgr A*, the supermassive object at the center of the Galaxy, are computed. These images contain, even in the absence of a horizon, a central faint region which bears a resemblance to the shadow of Kerr black holes and emphasizes the difficulty of claiming the existence of an event horizon from the analysis of strong-field images. The frequencies of the co- and contra-rotating orbits at the innermost stable circular orbit (ISCO) in this geometry are also computed, in the hope that quasi-periodic oscillations may permit to compare this model with Kerr’s black hole on observational grounds.

``All that Matter ... in One Big Bang ...'', &Other Cosmological Singularities

NASA Astrophysics Data System (ADS)

Elizalde, Emilio

2018-02-01

The first part of this paper contains a brief description of the beginnings of modern cosmology, which, the author will argue, was most likely born in the Year 1912. Some of the pieces of evidence presented here have emerged from recent research in the history of science, and are not usually shared with the general audiences in popular science books. In special, the issue of the correct formulation of the original Big Bang concept, according to the precise words of Fred Hoyle, is discussed. Too often, this point is very deficiently explained (when not just misleadingly) in most of the available generalist literature. Other frequent uses of the same words, Big Bang, as to name the initial singularity of the cosmos, and also whole cosmological models, are then addressed, as evolutions of its original meaning. Quantum and inflationary additions to the celebrated singularity theorems by Penrose, Geroch, Hawking and others led to subsequent results by Borde, Guth and Vilenkin. And corresponding corrections to the Einstein field equations have originated, in particular, $R^2$, $f(R)$, and scalar-tensor gravities, giving rise to a plethora of new singularities. For completeness, an updated table with a classification of the same is given.

NEC violation in mimetic cosmology revisited

DOE PAGES

Ijjas, Anna; Ripley, Justin; Steinhardt, Paul J.

2016-06-28

In the context of Einstein gravity, if the null energy condition (NEC) is satisfied, the energy density in expanding space–times always decreases while in contracting space–times the energy density grows and the universe eventually collapses into a singularity. In particular, no non-singular bounce is possible. It is, though, an open question if this energy condition can be violated in a controlled way, i.e., without introducing pathologies, such as unstable negative-energy states or an imaginary speed of sound. In this letter, we will re-examine the claim that the recently proposed mimetic scenario can violate the NEC without pathologies. We show thatmore » mimetic cosmology is prone to gradient instabilities even in cases when the NEC is satisfied (except for trivial examples). Most interestingly, the source of the instability is always the Einstein–Hilbert term in the action. The matter stress-energy component does not contribute spatial gradient terms but instead makes the problematic curvature modes dynamical. Finally, we also show that mimetic cosmology can be understood as a singular limit of known, well-behaved theories involving higher-derivative kinetic terms and discuss ways of removing the instability.« less

NEC violation in mimetic cosmology revisited

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

Ijjas, Anna; Ripley, Justin; Steinhardt, Paul J.

In the context of Einstein gravity, if the null energy condition (NEC) is satisfied, the energy density in expanding space–times always decreases while in contracting space–times the energy density grows and the universe eventually collapses into a singularity. In particular, no non-singular bounce is possible. It is, though, an open question if this energy condition can be violated in a controlled way, i.e., without introducing pathologies, such as unstable negative-energy states or an imaginary speed of sound. In this letter, we will re-examine the claim that the recently proposed mimetic scenario can violate the NEC without pathologies. We show thatmore » mimetic cosmology is prone to gradient instabilities even in cases when the NEC is satisfied (except for trivial examples). Most interestingly, the source of the instability is always the Einstein–Hilbert term in the action. The matter stress-energy component does not contribute spatial gradient terms but instead makes the problematic curvature modes dynamical. Finally, we also show that mimetic cosmology can be understood as a singular limit of known, well-behaved theories involving higher-derivative kinetic terms and discuss ways of removing the instability.« less

Dipole and quadrupole synthesis of electric potential fields. M.S. Thesis

NASA Technical Reports Server (NTRS)

Tilley, D. G.

1979-01-01

A general technique for expanding an unknown potential field in terms of a linear summation of weighted dipole or quadrupole fields is described. Computational methods were developed for the iterative addition of dipole fields. Various solution potentials were compared inside the boundary with a more precise calculation of the potential to derive optimal schemes for locating the singularities of the dipole fields. Then, the problem of determining solutions to Laplace's equation on an unbounded domain as constrained by pertinent electron trajectory data was considered.

Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere

PubMed Central

Oh, Sangchul; Hu, Xuedong; Nori, Franco; Kais, Sabre

2016-01-01

Adiabatic perturbation is shown to be singular from the exact solution of a spin-1/2 particle in a uniformly rotating magnetic field. Due to a non-adiabatic effect, its quantum trajectory on a Bloch sphere is a cycloid traced by a circle rolling along an adiabatic path. As the magnetic field rotates more and more slowly, the time-energy uncertainty, proportional to the length of the quantum trajectory, calculated by the exact solution is entirely different from the one obtained by the adiabatic path traced by the instantaneous eigenstate. However, the non-adiabatic Aharonov- Anandan geometric phase, measured by the area enclosed by the exact path, approaches smoothly the adiabatic Berry phase, proportional to the area enclosed by the adiabatic path. The singular limit of the time-energy uncertainty and the regular limit of the geometric phase are associated with the arc length and arc area of the cycloid on a Bloch sphere, respectively. Prolate and curtate cycloids are also traced by different initial states outside and inside of the rolling circle, respectively. The axis trajectory of the rolling circle, parallel to the adiabatic path, is shown to be an example of transitionless driving. The non-adiabatic resonance is visualized by the number of cycloid arcs. PMID:26916031

Source of the Kerr-Newman solution as a gravitating bag model: 50 years of the problem of the source of the Kerr solution

NASA Astrophysics Data System (ADS)

Burinskii, Alexander

2016-01-01

It is known that gravitational and electromagnetic fields of an electron are described by the ultra-extreme Kerr-Newman (KN) black hole solution with extremely high spin/mass ratio. This solution is singular and has a topological defect, the Kerr singular ring, which may be regularized by introducing the solitonic source based on the Higgs mechanism of symmetry breaking. The source represents a domain wall bubble interpolating between the flat region inside the bubble and external KN solution. It was shown recently that the source represents a supersymmetric bag model, and its structure is unambiguously determined by Bogomolnyi equations. The Dirac equation is embedded inside the bag consistently with twistor structure of the Kerr geometry, and acquires the mass from the Yukawa coupling with Higgs field. The KN bag turns out to be flexible, and for parameters of an electron, it takes the form of very thin disk with a circular string placed along sharp boundary of the disk. Excitation of this string by a traveling wave creates a circulating singular pole, indicating that the bag-like source of KN solution unifies the dressed and point-like electron in a single bag-string-quark system.

The quantum realm of the ''Little Sibling'' of the Big Rip singularity

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

Albarran, Imanol; Bouhmadi-López, Mariam; Cabral, Francisco

We analyse the quantum behaviour of the ''Little Sibling'' of the Big Rip singularity (LSBR) [1]. The quantisation is carried within the geometrodynamical approach given by the Wheeler-DeWitt (WDW) equation. The classical model is based on a Friedmann-Lemaître-Robertson-Walker Universe filled by a perfect fluid that can be mapped to a scalar field with phantom character. We analyse the WDW equation in two setups. In the first step, we consider the scale factor as the single degree of freedom, which from a classical perspective parametrises both the geometry and the matter content given by the perfect fluid. We then solve themore » WDW equation within a WKB approximation, for two factor ordering choices. On the second approach, we consider the WDW equation with two degrees of freedom: the scale factor and a scalar field. We solve the WDW equation, with the Laplace-Beltrami factor-ordering, using a Born-Oppenheimer approximation. In both approaches, we impose the DeWitt (DW) condition as a potential criterion for singularity avoidance. We conclude that in all the cases analysed the DW condition can be verified, which might be an indication that the LSBR can be avoided or smoothed in the quantum approach.« less

Analysis of a Generally Oriented Crack in a Functionally Graded Strip Sandwiched Between Two Homogeneous Half Planes

NASA Technical Reports Server (NTRS)

Shbeeb, N.; Binienda, W. K.; Kreider, K.

1999-01-01

The driving forces for a generally oriented crack embedded in a Functionally Graded strip sandwiched between two half planes are analyzed using singular integral equations with Cauchy kernels, and integrated using Lobatto-Chebyshev collocation. Mixed-mode Stress Intensity Factors (SIF) and Strain Energy Release Rates (SERR) are calculated. The Stress Intensity Factors are compared for accuracy with previously published results. Parametric studies are conducted for various nonhomogeneity ratios, crack lengths. crack orientation and thickness of the strip. It is shown that the SERR is more complete and should be used for crack propagation analysis.

Analysis of an Interface Crack for a Functionally Graded Strip Sandwiched between Two Homogeneous Layers of Finite Thickness

NASA Technical Reports Server (NTRS)

Shbeeh, N. I.; Binienda, W. K.

1999-01-01

The interface crack problem for a composite layer that consists of a homogeneous substrate, coating and a non-homogeneous interface was formulated for singular integral equations with Cauchy kernels and integrated using the Lobatto-Chebyshev collocation technique. Mixed-mode Stress Intensity Factors and Strain Energy Release Rates were calculated. The Stress Intensity Factors were compared for accuracy with relevant results previously published. The parametric studies were conducted for the various thickness of each layer and for various non-homogeneity ratios. Particular application to the Zirconia thermal barrier on steel substrate is demonstrated.

Off-equatorial circular orbits in magnetic fields of compact objects

NASA Astrophysics Data System (ADS)

Stuchlík, Zdeněk; Kovář, Jiří; Karas, Vladimír

2009-04-01

We present results of investigation of the off-equatorial circular orbits existence in the vicinity of neutron stars, Schwarzschild black holes with plasma ring, and near Kerr-Newman black holes and naked singularities.

Quantum electromagnetic stress tensor in an inhomogeneous medium

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Portraying Real Science in Science Communication

ERIC Educational Resources Information Center

van Dijk, Esther M.

2011-01-01

In both formal and informal settings, not only science but also views on the nature of science are communicated. Although there probably is no singular nature shared by all fields of science, in the field of science education it is commonly assumed that on a certain level of generality there is a consensus on many features of science. In this…

Magneto-optical visualization of three spatial components of inhomogeneous stray fields

NASA Astrophysics Data System (ADS)

Ivanov, V. E.

2012-08-01

The article deals with the physical principles of magneto-optical visualization (MO) of three spatial components of inhomogeneous stray fields with the help of FeCo metal indicator films in the longitudinal Kerr effect geometry. The inhomogeneous field is created by permanent magnets. Both p- and s-polarization light is used for obtaining MO images with their subsequent summing, subtracting and digitizing. As a result, the MO images and corresponding intensity coordinate dependences reflecting the distributions of the horizontal and vertical magnetization components in pure form have been obtained. Modeling of both the magnetization distribution in the indicator film and the corresponding MO images shows that corresponding to polar sensitivity the intensity is proportional to the normal field component, which permits normal field component mapping. Corresponding to longitudinal sensitivity, the intensity of the MO images reflects the angular distribution of the planar field component. MO images have singular points in which the planar component is zero and their movement under an externally homogeneous planar field permits obtaining of additional information on the two planar components of the field under study. The intensity distribution character in the vicinity of sources and sinks (singular points) remains the same under different orientations of the light incidence plane. The change of incident plane orientation by π/2 alters the distribution pattern in the vicinity of the saddle points.

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

DOE PAGES

Argyres, Philip C.; Uensal, Mithat

2012-08-10

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are magnetic bions which carry net magnetic charge and induce a massmore » gap for gauge fluctuations. Another type are neutral bions which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics — which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription — to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion-anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Écalle’s resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.« less

Modeling electro-magneto-hydrodynamic thermo-fluidic transport of biofluids with new trend of fractional derivative without singular kernel

NASA Astrophysics Data System (ADS)

Abdulhameed, M.; Vieru, D.; Roslan, R.

2017-10-01

This paper investigates the electro-magneto-hydrodynamic flow of the non-Newtonian behavior of biofluids, with heat transfer, through a cylindrical microchannel. The fluid is acted by an arbitrary time-dependent pressure gradient, an external electric field and an external magnetic field. The governing equations are considered as fractional partial differential equations based on the Caputo-Fabrizio time-fractional derivatives without singular kernel. The usefulness of fractional calculus to study fluid flows or heat and mass transfer phenomena was proven. Several experimental measurements led to conclusion that, in such problems, the models described by fractional differential equations are more suitable. The most common time-fractional derivative used in Continuum Mechanics is Caputo derivative. However, two disadvantages appear when this derivative is used. First, the definition kernel is a singular function and, secondly, the analytical expressions of the problem solutions are expressed by generalized functions (Mittag-Leffler, Lorenzo-Hartley, Robotnov, etc.) which, generally, are not adequate to numerical calculations. The new time-fractional derivative Caputo-Fabrizio, without singular kernel, is more suitable to solve various theoretical and practical problems which involve fractional differential equations. Using the Caputo-Fabrizio derivative, calculations are simpler and, the obtained solutions are expressed by elementary functions. Analytical solutions of the biofluid velocity and thermal transport are obtained by means of the Laplace and finite Hankel transforms. The influence of the fractional parameter, Eckert number and Joule heating parameter on the biofluid velocity and thermal transport are numerically analyzed and graphic presented. This fact can be an important in Biochip technology, thus making it possible to use this analysis technique extremely effective to control bioliquid samples of nanovolumes in microfluidic devices used for biological analysis and medical diagnosis.

Characterizing omega-limit sets which are closed orbits

NASA Astrophysics Data System (ADS)

Bautista, S.; Morales, C.

Let X be a vector field in a compact n-manifold M, n⩾2. Given Σ⊂M we say that q∈M satisfies (P) Σ if the closure of the positive orbit of X through q does not intersect Σ, but, however, there is an open interval I with q as a boundary point such that every positive orbit through I intersects Σ. Among those q having saddle-type hyperbolic omega-limit set ω(q) the ones with ω(q) being a closed orbit satisfy (P) Σ for some closed subset Σ. The converse is true for n=2 but not for n⩾4. Here we prove the converse for n=3. Moreover, we prove for n=3 that if ω(q) is a singular-hyperbolic set [C. Morales, M. Pacifico, E. Pujals, On C robust singular transitive sets for three-dimensional flows, C. R. Acad. Sci. Paris Sér. I 26 (1998) 81-86], [C. Morales, M. Pacifico, E. Pujals, Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers, Ann. of Math. (2) 160 (2) (2004) 375-432], then ω(q) is a closed orbit if and only if q satisfies (P) Σ for some Σ closed. This result improves [S. Bautista, Sobre conjuntos hiperbólicos-singulares (On singular-hyperbolic sets), thesis Uiversidade Federal do Rio de Janeiro, 2005 (in Portuguese)] and [C. Morales, M. Pacifico, Mixing attractors for 3-flows, Nonlinearity 14 (2001) 359-378].

Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries.

PubMed

Brachet, M E; Bustamante, M D; Krstulovic, G; Mininni, P D; Pouquet, A; Rosenberg, D

2013-01-01

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the fourfold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a regridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of 6144(3) points and three different configurations on grids of 4096(3) points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between t=2.33 and t=2.70. More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.

An Application of Singularity Analysis to a Heavy Precipitation Event

DTIC Science & Technology

1993-01-01

difference in this plot. 61 NORMAN RADAR ELEVATION: 3.094 DATE 28 MAY 87 TIM 005342 GUT Cumin a 10 Tpam c CD low am am Io CID e0UC 100 "CC C d~Cc 100...element of fluid shaped like a sphere. Assuming the fluid is friction- less, no tangential stresses or forces are applied to its surface. The pressure

Modeling and Application of Piezoelectric Materials in Repair of Engineering Structures

NASA Astrophysics Data System (ADS)

Wu, Nan

The shear horizontal wave propagation and vibration of piezoelectric coupled structures under an open circuit electrical boundary condition are studied. Following the studies on the dynamic response of piezoelectric coupled structures, the repair of both crack/notch and delaminated structures using piezoelectric materials are conducted. The main contribution was the proposed the active structural repair design using piezoelectric materials for different structures. An accurate model for the piezoelectric effect on the shear wave propagation is first proposed to guide the application of piezoelectric materials as sensors and actuators in the repair of engineering structures. A vibration analysis of a circular steel substrate surface bonded by a piezoelectric layer with open circuit is presented. The mechanical models and solutions for the wave propagation and vibration analysis of piezoelectric coupled structures are established based on the Kirchhoff plate model and Maxwell equation. Following the studies of the dynamic response of piezoelectric coupled structures, a close-loop feedback control repair methodology is proposed for a vibrating delaminated beam structure by using piezoelectric patches. The electromechanical characteristic of the piezoelectric material is employed to induce a local shear force above the delamination area via an external actuation voltage, which is designed as a feedback of the deflection of a vibrating beam and a delaminated plate, to reduce the stress singularity around the delamination tips. Furthermore, an experimental realization of an effective repair of a notched cantilever beam structure subjected to a dynamic loading by use of piezoelectric patches is reported. A small piezoelectric patch used as a sensor is placed on the notch position to monitor the severity of the stress singularity around the notch area by measuring the charge output on the sensor, and a patch used as an actuator is located around the notch area to generate a required bending moment by employing an actuation voltage to reduce the stress singularity at the notch position. The actuation voltage on the actuator is designed from a feedback circuit process. Through the analytical model, FEM simulation and experimental studies, the active structural repair method using piezoelectric materials is realized and proved to be feasible and practical.

Singularity-free anisotropic strange quintessence star

NASA Astrophysics Data System (ADS)

Bhar, Piyali

2015-04-01

Present paper provides a new model of anisotropic strange star corresponding to the exterior Schwarzschild metric. The Einstein field equations have been solved by utilizing the Krori-Barua (KB) ansatz (Krori and Barua in J. Phys. A, Math. Gen. 8:508, 1975) in presence of quintessence field characterized by a parameter ω q with . The obtained solutions are free from central singularity. Our model is potentially stable. The numerical values of mass of the different strange stars SAXJ1808.4-3658(SS1) (radius=7.07 km), 4U1820-30 (radius=10 km), Vela X-12 (radius=9.99 km), PSR J 1614-2230 (radius=10.3 km) obtained from our model is very close to the observational data that confirms the validity of our proposed model. The interior solution is also matched to the exterior Schwarzschild spacetime in presence of thin shell where negative surface pressure is required to hold the thin shell against collapsing.

Global Symmetries of Six Dimensional Superconformal Field Theories

NASA Astrophysics Data System (ADS)

Merkx, Peter R.

In this work we investigate the global symmetries of six-dimensional superconformal field theories (6D SCFTs) via their description in F-theory. We provide computer algebra system routines determining global symmetry maxima for all known 6D SCFTs while tracking the singularity types of the associated elliptic fibrations. We tabulate these bounds for many CFTs including every 0-link based theory. The approach we take provides explicit tracking of geometric information which has remained implicit in the classifications of 6D SCFTs to date. We derive a variety of new geometric restrictions on collections of singularity collisions in elliptically fibered Calabi-Yau varieties and collect data from local model analyses of these collisions. The resulting restrictions are sufficient to match the known gauge enhancement structure constraints for all 6D SCFTs without appeal to anomaly cancellation and enable our global symmetry computations for F-theory SCFT models to proceed similarly.

Magnetic solutions in Einstein-massive gravity with linear and nonlinear fields

NASA Astrophysics Data System (ADS)

Hendi, Seyed Hossein; Panah, Behzad Eslam; Panahiyan, Shahram; Momennia, Mehrab

2018-06-01

The solutions of U(1) gauge-gravity coupling is one of the interesting models for analyzing the semi-classical nature of spacetime. In this regard, different well-known singular and nonsingular solutions have been taken into account. The paper at hand investigates the geometrical properties of the magnetic solutions by considering Maxwell and power Maxwell invariant (PMI) nonlinear electromagnetic fields in the context of massive gravity. These solutions are free of curvature singularity, but have a conic one which leads to presence of deficit/surplus angle. The emphasize is on modifications that these generalizations impose on deficit angle which determine the total geometrical structure of the solutions, hence, physical/gravitational properties. It will be shown that depending on the background spacetime [being anti de Sitter (AdS) or de Sitter (dS)], these generalizations present different effects and modify the total structure of the solutions differently.

Regularity results for the minimum time function with Hörmander vector fields

NASA Astrophysics Data System (ADS)

Albano, Paolo; Cannarsa, Piermarco; Scarinci, Teresa

2018-03-01

In a bounded domain of Rn with boundary given by a smooth (n - 1)-dimensional manifold, we consider the homogeneous Dirichlet problem for the eikonal equation associated with a family of smooth vector fields {X1 , … ,XN } subject to Hörmander's bracket generating condition. We investigate the regularity of the viscosity solution T of such problem. Due to the presence of characteristic boundary points, singular trajectories may occur. First, we characterize these trajectories as the closed set of all points at which the solution loses point-wise Lipschitz continuity. Then, we prove that the local Lipschitz continuity of T, the local semiconcavity of T, and the absence of singular trajectories are equivalent properties. Finally, we show that the last condition is satisfied whenever the characteristic set of {X1 , … ,XN } is a symplectic manifold. We apply our results to several examples.

Black holes in magnetic monopoles

NASA Technical Reports Server (NTRS)

Lee, Kimyeong; Nair, V. P.; Weinberg, Erick J.

1991-01-01

We study magnetically charged classical solutions of a spontaneously broken gauge theory interacting with gravity. We show that nonsingular monopole solutions exist only if the Higgs field vacuum expectation value v is less than or equal to a critical value v sub cr, which is of the order of the Planck mass. In the limiting case, the monopole becomes a black hole, with the region outside the horizon described by the critical Reissner-Nordstrom solution. For v less than v sub cr, we find additional solutions which are singular at f = 0, but which have this singularity hidden within a horizon. These have nontrivial matter fields outside the horizon, and may be interpreted as small black holes lying within a magnetic monopole. The nature of these solutions as a function of v and of the total mass M and their relation to the Reissner-Nordstrom solutions is discussed.

Three dimensional finite-element analysis of finite-thickness fracture specimens

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1977-01-01

The stress-intensity factors for most of the commonly used fracture specimens (center-crack tension, single and double edge-crack tension, and compact), those that have a through-the-thickness crack, were calculated using a three dimensional finite-element elastic stress analysis. Three-dimensional singularity elements were used around the crack front. The stress intensity factors along the crack front were evaluated by using a force method, developed herein, that requires no prior assumption of either plane stress or plane strain. The calculated stress-intensity factors from the present analysis were compared with those from the literature whenever possible and were generally found to be in good agreement. The stress-intensity factors at the midplane for all specimens analyzed were within 3 percent of the two dimensional plane strain values. The stress intensity factors at the specimen surfaces were considerably lower than at the midplanes. For the center-crack tension specimens with large thickness to crack-length ratios, the stress-intensity factor reached a maximum near the surface of the specimen. In all other specimens considered the maximum stress intensity occurred at the midplane.

Instability of enclosed horizons

NASA Astrophysics Data System (ADS)

Kay, Bernard S.

2015-03-01

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

k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner-Rusk Formulations

NASA Astrophysics Data System (ADS)

Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia

2012-06-01

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner-Rusk formulation on classical mechanics.

The generic unfolding of a codimension-two connection to a two-fold singularity of planar Filippov systems

NASA Astrophysics Data System (ADS)

Novaes, Douglas D.; Teixeira, Marco A.; Zeli, Iris O.

2018-05-01

Generic bifurcation theory was classically well developed for smooth differential systems, establishing results for k-parameter families of planar vector fields. In the present study we focus on a qualitative analysis of 2-parameter families, , of planar Filippov systems assuming that Z 0,0 presents a codimension-two minimal set. Such object, named elementary simple two-fold cycle, is characterized by a regular trajectory connecting a visible two-fold singularity to itself, for which the second derivative of the first return map is nonvanishing. We analyzed the codimension-two scenario through the exhibition of its bifurcation diagram.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)

1988-01-01

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

The magnetic field of a permanent hollow cylindrical magnet

NASA Astrophysics Data System (ADS)

Reich, Felix A.; Stahn, Oliver; Müller, Wolfgang H.

2016-09-01

Based on the rational version of M AXWELL's equations according to T RUESDELL and T OUPIN or KOVETZ, cf. (Kovetz in Electromagnetic theory, Oxford University Press, Oxford, 2000; Truesdell and Toupin in Handbuch der Physik, Bd. III/1, Springer, Berlin, pp 226-793; appendix, pp 794-858, 2000), we present, for stationary processes, a closed-form solution for the magnetic flux density of a hollow cylindrical magnet. Its magnetization is constant in axial direction. We consider M AXWELL's equations in regular and singular points that are obtained by rational electrodynamics, adapted to stationary processes. The magnetic flux density is calculated analytically by means of a vector potential. We obtain a solution in terms of complete elliptic integrals. Therefore, numerical evaluation can be performed in a computationally efficient manner. The solution is written in dimensionless form and can easily be applied to cylinders of arbitrary shape. The relation between the magnetic flux density and the magnetic field is linear, and an explicit relation for the field is presented. With a slight modification the result can be used to obtain the field of a solid cylindrical magnet. The mathematical structure of the solution and, in particular, singularities are discussed.

Fine-tuning free paradigm of two-measures theory: k-essence, absence of initial singularity of the curvature, and inflation with graceful exit to the zero cosmological constant state

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

Guendelman, E. I.; Kaganovich, A. B.

2007-04-15

The dilaton-gravity sector of the two-measures field theory (TMT) is explored in detail in the context of spatially flat Friedman-Robertson-Walker (FRW) cosmology. The model possesses scale invariance which is spontaneously broken due to the intrinsic features of the TMT dynamics. The dilaton {phi} dependence of the effective Lagrangian appears only as a result of the spontaneous breakdown of the scale invariance. If no fine-tuning is made, the effective {phi}-Lagrangian p({phi},X) depends quadratically upon the kinetic term X. Hence TMT represents an explicit example of the effective k-essence resulting from first principles without any exotic term in the underlying action intendedmore » for obtaining this result. Depending of the choice of regions in the parameter space (but without fine-tuning), TMT exhibits different possible outputs for cosmological dynamics: (a) Absence of initial singularity of the curvature while its time derivative is singular. This is a sort of sudden singularities studied by Barrow on purely kinematic grounds. (b) Power law inflation in the subsequent stage of evolution. Depending on the region in the parameter space the inflation ends with a graceful exit either into the state with zero cosmological constant (CC) or into the state driven by both a small CC and the field {phi} with a quintessencelike potential. (c) Possibility of resolution of the old CC problem. From the point of view of TMT, it becomes clear why the old CC problem cannot be solved (without fine-tuning) in conventional field theories. (d) TMT enables two ways for achieving small CC without fine-tuning of dimensionful parameters: either by a seesaw type mechanism or due to a correspondence principle between TMT and conventional field theories (i.e. theories with only the measure of integration {radical}(-g) in the action). (e) There is a wide range of the parameters such that in the late time universe: the equation of state w=p/{rho}<-1; w asymptotically (as t{yields}{infinity}) approaches -1 from below; {rho} approaches a constant, the smallness of which does not require fine-tuning of dimensionful parameters.« less

Rare regions and Griffiths singularities at a clean critical point: the five-dimensional disordered contact process.

PubMed

Vojta, Thomas; Igo, John; Hoyos, José A

2014-07-01

We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type, i.e., identical to that of the clean five-dimensional contact process. It is accompanied by off-critical power-law Griffiths singularities whose dynamical exponent z' saturates at a finite value as the transition is approached. These findings resolve the apparent contradiction between the Harris criterion, which implies that weak disorder is renormalization-group irrelevant, and the rare-region classification, which predicts unconventional behavior. We confirm and illustrate our theory by large-scale Monte Carlo simulations of systems with up to 70(5) sites. We also relate our results to a recently established general relation between the Harris criterion and Griffiths singularities [Phys. Rev. Lett. 112, 075702 (2014)], and we discuss implications for other phase transitions.

Generation of phase edge singularities by coplanar three-beam interference and their detection.

PubMed

Patorski, Krzysztof; Sluzewski, Lukasz; Trusiak, Maciej; Pokorski, Krzysztof

2017-02-06

In recent years singular optics has gained considerable attention in science and technology. Up to now optical vortices (phase point dislocations) have been of main interest. This paper presents the first general analysis of formation of phase edge singularities by coplanar three-beam interference. They can be generated, for example, by three-slit interference or self-imaging in the Fresnel diffraction field of a sinusoidal grating. We derive a general condition for the ratio of amplitudes of interfering beams resulting in phase edge dislocations, lateral separation of dislocations depends on this ratio as well. Analytically derived properties are corroborated by numerical and experimental studies. We develop a simple, robust, common path optical self-imaging configuration aided by a coherent tilted reference wave and spatial filtering. Finally, we propose an automatic fringe pattern analysis technique for detecting phase edge dislocations, based on the continuous wavelet transform. Presented studies open new possibilities for developing grating based sensing techniques for precision metrology of very small phase differences.

Cosmological solutions and finite time singularities in Finslerian geometry

NASA Astrophysics Data System (ADS)

Paul, Nupur; de, S. S.; Rahaman, Farook

2018-03-01

We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter γ which for isotropic limit is simply the barotropic equation of state p = (γ ‑ 1)ρ (γ ∈ ℝ being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows: (i) only an exponential expansion, or (ii) a finite time past singularity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We also discuss several energy conditions and the possibility of cosmic bounce. Finally, we establish the first law of thermodynamics in such spacetime.

The Euler-Poisson-Darboux equation for relativists

NASA Astrophysics Data System (ADS)

Stewart, John M.

2009-09-01

The Euler-Poisson-Darboux (EPD) equation is the simplest linear hyperbolic equation in two independent variables whose coefficients exhibit singularities, and as such must be of interest as a paradigm to relativists. Sadly it receives scant treatment in the textbooks. The first half of this review is didactic in nature. It discusses in the simplest terms possible the nature of solutions of the EPD equation for the timelike and spacelike singularity cases. Also covered is the Riemann representation of solutions of the characteristic initial value problem, which is hard to find in the literature. The second half examines a few of the possible applications, ranging from explicit computation of the leading terms in the far-field backscatter from predominantly outgoing radiation in a Schwarzschild space-time, to computing explicitly the leading terms in the matter-induced singularities in plane symmetric space-times. There are of course many other applications and the aim of this article is to encourage relativists to investigate this underrated paradigm.

Path optimization method for the sign problem

NASA Astrophysics Data System (ADS)

Ohnishi, Akira; Mori, Yuto; Kashiwa, Kouji

2018-03-01

We propose a path optimization method (POM) to evade the sign problem in the Monte-Carlo calculations for complex actions. Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method are promising and extensively discussed. In these methods, real field variables are complexified and the integration manifold is determined by the flow equations or stochastically sampled. When we have singular points of the action or multiple critical points near the original integral surface, however, we have a risk to encounter the residual and global sign problems or the singular drift term problem. One of the ways to avoid the singular points is to optimize the integration path which is designed not to hit the singular points of the Boltzmann weight. By specifying the one-dimensional integration-path as z = t +if(t)(f ɛ R) and by optimizing f(t) to enhance the average phase factor, we demonstrate that we can avoid the sign problem in a one-variable toy model for which the complex Langevin method is found to fail. In this proceedings, we propose POM and discuss how we can avoid the sign problem in a toy model. We also discuss the possibility to utilize the neural network to optimize the path.

Self-organized composites of multiwalled carbon nanotubes and nematic liquid crystal 5CB: optical singularities and percolation behavior in electrical conductivity

NASA Astrophysics Data System (ADS)

Ponevchinsky, V. V.; Goncharuk, A. I.; Vasil'ev, V. I.; Lebovka, N. I.; Soskin, M. S.

2009-10-01

This work discusses optical singularities and electrical conductivity behavior in a thin electrooptical cell filled with composites including multi-walled carbon nanotubes (MWCNTs) and nematic liquid crystal (LC). The MWCNTs with high aspect ratio L/d~300 ÷ 1000 and nematic LC 5CB (4-pentyl-40-cyanobiphenyl) were used. The composites were prepared by introduction of MWCNTs (0.0001÷0.1% wt) into LC solvent with subsequent sonication. The increase of MWCNT concentration (between 0.005÷0.05 % wt) resulted in self-organization of MWCNTs and formation of micronsized aggregates with fractal boundaries. The visually observed formation of spanning MWCNT networks near the percolation threshold at ~0.025 % wt was accompanied with transition from non-conductive to conductive state and generation of optical singularities. The observed effects were explained by the strong interactions between MWCNTs and LC medium and planar orientation of 5CB molecules near the lateral surface of MWCNTs. It was speculated that optical singularities arose as a results of interaction of an incident laser beam with LC perturbed interfacial shells covering the MWCNT clusters. Behavior of the interfacial shell thickness in external electric field and in the vicinity of the nematic to isotropic transition was discussed.

Fast higher-order MR image reconstruction using singular-vector separation.

PubMed

Wilm, Bertram J; Barmet, Christoph; Pruessmann, Klaas P

2012-07-01

Medical resonance imaging (MRI) conventionally relies on spatially linear gradient fields for image encoding. However, in practice various sources of nonlinear fields can perturb the encoding process and give rise to artifacts unless they are suitably addressed at the reconstruction level. Accounting for field perturbations that are neither linear in space nor constant over time, i.e., dynamic higher-order fields, is particularly challenging. It was previously shown to be feasible with conjugate-gradient iteration. However, so far this approach has been relatively slow due to the need to carry out explicit matrix-vector multiplications in each cycle. In this work, it is proposed to accelerate higher-order reconstruction by expanding the encoding matrix such that fast Fourier transform can be employed for more efficient matrix-vector computation. The underlying principle is to represent the perturbing terms as sums of separable functions of space and time. Compact representations with this property are found by singular-vector analysis of the perturbing matrix. Guidelines for balancing the accuracy and speed of the resulting algorithm are derived by error propagation analysis. The proposed technique is demonstrated for the case of higher-order field perturbations due to eddy currents caused by diffusion weighting. In this example, image reconstruction was accelerated by two orders of magnitude.

Optics of short-pitch deformed-helix ferroelectric liquid crystals: Symmetries, exceptional points, and polarization-resolved angular patterns

NASA Astrophysics Data System (ADS)

Kiselev, Alexei D.; Chigrinov, Vladimir G.

2014-10-01

In order to explore electric-field-induced transformations of polarization singularities in the polarization-resolved angular (conoscopic) patterns emerging after deformed-helix ferroelectric liquid crystal (DHFLC) cells with subwavelength helix pitch, we combine the transfer matrix formalism with the results for the effective dielectric tensor of biaxial FLCs evaluated using an improved technique of averaging over distorted helical structures. Within the framework of the transfer matrix method, we deduce a number of symmetry relations and show that the symmetry axis of L lines (curves of linear polarization) is directed along the major in-plane optical axis which rotates under the action of the electric field. When the angle between this axis and the polarization plane of incident linearly polarized light is above its critical value, the C points (points of circular polarization) appear in the form of symmetrically arranged chains of densely packed star-monstar pairs. We also emphasize the role of phase singularities of a different kind and discuss the enhanced electro-optic response of DHFLCs near the exceptional point where the condition of zero-field isotropy is fulfilled.

Exotic ferromagnetism in the two-dimensional quantum material C3N

NASA Astrophysics Data System (ADS)

Huang, Wen-Cheng; Li, Wei; Liu, Xiaosong

2018-04-01

The search for and study of exotic quantum states in novel low-dimensional quantum materials have triggered extensive research in recent years. Here, we systematically study the electronic and magnetic structures in the newly discovered two-dimensional quantum material C3N within the framework of density functional theory. The calculations demonstrate that C3N is an indirect-band semiconductor with an energy gap of 0.38 eV, which is in good agreement with experimental observations. Interestingly, we find van Hove singularities located at energies near the Fermi level, which is half that of graphene. Thus, the Fermi energy easily approaches that of the singularities, driving the system to ferromagnetism, under charge carrier injection, such as electric field gating or hydrogen doping. These findings not only demonstrate that the emergence of magnetism stems from the itinerant electron mechanism rather than the effects of local magnetic impurities, but also open a new avenue to designing field-effect transistor devices for possible realization of an insulator-ferromagnet transition by tuning an external electric field.

Modern Quantum Field Theory II - Proceeeings of the International Colloquium

NASA Astrophysics Data System (ADS)

Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.

1995-08-01

The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory * Finite Quantum Physics and Noncommutative Geometry * Higgs as Gauge Field and the Standard Model * Canonical Quantisation of an Off-Conformal Theory * Deterministic Quantum Mechanics in One Dimension * Spin-Statistics Relations for Topological Geons in 2+1 Quantum Gravity * Generalized Fock Spaces * Geometrical Expression for Short Distance Singularities in Field Theory * 5. Mathematics and Quantum Field Theory * Knot Invariants from Quantum Field Theories * Infinite Grassmannians and Moduli Spaces of G-Bundles * A Review of an Algebraic Geometry Approach to a Model Quantum Field Theory on a Curve (Abstract) * 6. Integrable Models * Spectral Representation of Correlation Functions in Two-Dimensional Quantum Field Theories * On Various Avatars of the Pasquier Algebra * Supersymmetric Integrable Field Theories and Eight Vertex Free Fermion Models (Abstract) * 7. Lattice Field Theory * From Kondo Model and Strong Coupling Lattice QCD to the Isgur-Wise Function * Effective Confinement from a Logarithmically Running Coupling (Abstract)

Global-Local Finite Element Analysis of Bonded Single-Lap Joints

NASA Technical Reports Server (NTRS)

Kilic, Bahattin; Madenci, Erdogan; Ambur, Damodar R.

2004-01-01

Adhesively bonded lap joints involve dissimilar material junctions and sharp changes in geometry, possibly leading to premature failure. Although the finite element method is well suited to model the bonded lap joints, traditional finite elements are incapable of correctly resolving the stress state at junctions of dissimilar materials because of the unbounded nature of the stresses. In order to facilitate the use of bonded lap joints in future structures, this study presents a finite element technique utilizing a global (special) element coupled with traditional elements. The global element includes the singular behavior at the junction of dissimilar materials with or without traction-free surfaces.

Probabilistic finite elements for fracture mechanics

NASA Technical Reports Server (NTRS)

Besterfield, Glen

1988-01-01

The probabilistic finite element method (PFEM) is developed for probabilistic fracture mechanics (PFM). A finite element which has the near crack-tip singular strain embedded in the element is used. Probabilistic distributions, such as expectation, covariance and correlation stress intensity factors, are calculated for random load, random material and random crack length. The method is computationally quite efficient and can be expected to determine the probability of fracture or reliability.

Changing image of correlation optics: introduction.

PubMed

Angelsky, Oleg V; Desyatnikov, Anton S; Gbur, Gregory J; Hanson, Steen G; Lee, Tim; Miyamoto, Yoko; Schneckenburger, Herbert; Wyant, James C

2016-04-20

This feature issue of Applied Optics contains a series of selected papers reflecting recent progress of correlation optics and illustrating current trends in vector singular optics, internal energy flows at light fields, optical science of materials, and new biomedical applications of lasers.

The dynamics of a shear band

NASA Astrophysics Data System (ADS)

Giarola, Diana; Capuani, Domenico; Bigoni, Davide

2018-03-01

A shear band of finite length, formed inside a ductile material at a certain stage of a continued homogeneous strain, provides a dynamic perturbation to an incident wave field, which strongly influences the dynamics of the material and affects its path to failure. The investigation of this perturbation is presented for a ductile metal, with reference to the incremental mechanics of a material obeying the J2-deformation theory of plasticity (a special form of prestressed, elastic, anisotropic, and incompressible solid). The treatment originates from the derivation of integral representations relating the incremental mechanical fields at every point of the medium to the incremental displacement jump across the shear band faces, generated by an impinging wave. The boundary integral equations (under the plane strain assumption) are numerically approached through a collocation technique, which keeps into account the singularity at the shear band tips and permits the analysis of an incident wave impinging a shear band. It is shown that the presence of the shear band induces a resonance, visible in the incremental displacement field and in the stress intensity factor at the shear band tips, which promotes shear band growth. Moreover, the waves scattered by the shear band are shown to generate a fine texture of vibrations, parallel to the shear band line and propagating at a long distance from it, but leaving a sort of conical shadow zone, which emanates from the tips of the shear band.

Quantum dynamics in phase space: Moyal trajectories 2

NASA Astrophysics Data System (ADS)

Braunss, G.

2013-01-01

Continuing a previous paper [G. Braunss, J. Phys. A: Math. Theor. 43, 025302 (2010), 10.1088/1751-8113/43/2/025302] where we had calculated ℏ2-approximations of quantum phase space viz. Moyal trajectories of examples with one and two degrees of freedom, we present in this paper the calculation of ℏ2-approximations for four examples: a two-dimensional Toda chain, the radially symmetric Schwarzschild field, and two examples with three degrees of freedom, the latter being the nonrelativistic spherically Coulomb potential and the relativistic cylinder symmetrical Coulomb potential with a magnetic field H. We show in particular that an ℏ2-approximation of the nonrelativistic Coulomb field has no singularity at the origin (r = 0) whereas the classical trajectories are singular at r = 0. In the third example, we show in particular that for an arbitrary function γ(H, z) the expression β ≡ pz + γ(H, z) is classically (ℏ = 0) a constant of motion, whereas for ℏ ≠ 0 this holds only if γ(H, z) is an arbitrary polynomial of second order in z. This statement is shown to extend correspondingly to a cylinder symmetrical Schwarzschild field with a magnetic field. We exhibit in detail a number of properties of the radially symmetric Schwarzschild field. We exhibit finally the problems of the nonintegrable Hénon-Heiles Hamiltonian and give a short review of the regular Hilbert space representation of Moyal operators.

A multi-material topology optimization approach for wrinkle-free design of cable-suspended membrane structures

NASA Astrophysics Data System (ADS)

Luo, Yangjun; Niu, Yanzhuang; Li, Ming; Kang, Zhan

2017-06-01

In order to eliminate stress-related wrinkles in cable-suspended membrane structures and to provide simple and reliable deployment, this study presents a multi-material topology optimization model and an effective solution procedure for generating optimal connected layouts for membranes and cables. On the basis of the principal stress criterion of membrane wrinkling behavior and the density-based interpolation of multi-phase materials, the optimization objective is to maximize the total structural stiffness while satisfying principal stress constraints and specified material volume requirements. By adopting the cosine-type relaxation scheme to avoid the stress singularity phenomenon, the optimization model is successfully solved through a standard gradient-based algorithm. Four-corner tensioned membrane structures with different loading cases were investigated to demonstrate the effectiveness of the proposed method in automatically finding the optimal design composed of curved boundary cables and wrinkle-free membranes.

The crack problem for a half plane stiffened by elastic cover plates

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

An elastic half plane containing a crack and stiffened by a cover plate is discussed. The asymptotic nature of the stress state in the half plane around an end point of the stiffener to determine the likely orientation of a possible fracture initiation and growth was studied. The problem is formulated for an arbitrary oriented radial crack in a system of singular integral equations. For an internal crack and for an edge crack, the problem is solved and the stress intensity factors at the crack tips and the interface stress are calculated. A cracked half plane with two symmetrically located cover plates is also considered. It is concluded that the case of two stiffeners appears to be more severe than that of a single stiffener.

Tensile cracking of a brittle conformal coating on a rough substrate

DOE PAGES

Reedy, Jr., E. D.

2016-04-07

This note examines the effect of interfacial roughness on the initiation and growth of channel cracks in a brittle film. A conformal film with cusp-like surface flaws that replicate the substrate roughness is investigated. This type of surface flaw is relatively severe in the sense that stress diverges as the cusp-tip is approached (i.e., there is a power-law stress singularity). For the geometry and range of film properties considered, the analysis suggests that smoothing the substrate could substantially increase the film’s resistance to the formation of the through-the-thickness cracks that precede channel cracking. Furthermore, smoothing the substrate’s surface has amore » relatively modest effect on the film stress needed to propagate a channel crack.« less

Rock Fracture Toughness Under Mode II Loading: A Theoretical Model Based on Local Strain Energy Density

NASA Astrophysics Data System (ADS)

Rashidi Moghaddam, M.; Ayatollahi, M. R.; Berto, F.

2018-01-01

The values of mode II fracture toughness reported in the literature for several rocks are studied theoretically by using a modified criterion based on strain energy density averaged over a control volume around the crack tip. The modified criterion takes into account the effect of T-stress in addition to the singular terms of stresses/strains. The experimental results are related to mode II fracture tests performed on the semicircular bend and Brazilian disk specimens. There are good agreements between theoretical predictions using the generalized averaged strain energy density criterion and the experimental results. The theoretical results reveal that the value of mode II fracture toughness is affected by the size of control volume around the crack tip and also the magnitude and sign of T-stress.

Singularities and the geometry of spacetime

NASA Astrophysics Data System (ADS)

Hawking, Stephen

2014-11-01

The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove the occurrence of singularities are discussed and then a number of theorems are presented which prove the occurrence of singularities in most cosmological solutions. A procedure is given which could be used to describe and classify the singularites and their expected nature is discussed. Sections 2 and 3 are reviews of standard work. In Section 4, the deviation equation is standard but the matrix method used to analyse it is the author's own as is the decomposition given of the Bianchi identities (this was also obtained independently by Trümper). Variation of curves and conjugate points are standard in a positive-definite metric but this seems to be the first full account for timelike and null curves in a Lorentz metric. Except where otherwise indicated in the text, Sections 5 and 6 are the work of the author who, however, apologises if through ignorance or inadvertance he has failed to make acknowledgements where due. Some of this work has been described in [Hawking S.W. 1965b. Occurrence of singularities in open universes. Phys. Rev. Lett. 15: 689-690; Hawking S.W. and G.F.R. Ellis. 1965c. Singularities in homogeneous world models. Phys. Rev. Lett. 17: 246-247; Hawking S.W. 1966a. Singularities in the universe. Phys. Rev. Lett. 17: 444-445; Hawking S.W. 1966c. The occurrence of singularities in cosmology. Proc. Roy. Soc. Lond. A 294: 511-521]. Undoubtedly, the most important results are the theorems in Section 6 on the occurrence of singularities. These seem to imply either that the General Theory of Relativity breaks down or that there could be particles whose histories did not exist before (or after) a certain time. The author's own opinion is that the theory probably does break down, but only when quantum gravitational effects become important. This would not be expected to happen until the radius of curvature of spacetime became about 10-14 cm.

Vacuum stress energy density and its gravitational implications

NASA Astrophysics Data System (ADS)

Estrada, Ricardo; Fulling, Stephen A.; Kaplan, Lev; Kirsten, Klaus; Liu, Zhonghai; Milton, Kimball A.

2008-04-01

In nongravitational physics the local density of energy is often regarded as merely a bookkeeping device; only total energy has an experimental meaning—and it is only modulo a constant term. But in general relativity the local stress-energy tensor is the source term in Einstein's equation. In closed universes, and those with Kaluza-Klein dimensions, theoretical consistency demands that quantum vacuum energy should exist and have gravitational effects, although there are no boundary materials giving rise to that energy by van der Waals interactions. In the lab there are boundaries, and in general the energy density has a nonintegrable singularity as a boundary is approached (for idealized boundary conditions). As pointed out long ago by Candelas and Deutsch, in this situation there is doubt about the viability of the semiclassical Einstein equation. Our goal is to show that the divergences in the linearized Einstein equation can be renormalized to yield a plausible approximation to the finite theory that presumably exists for realistic boundary conditions. For a scalar field with Dirichlet or Neumann boundary conditions inside a rectangular parallelepiped, we have calculated by the method of images all components of the stress tensor, for all values of the conformal coupling parameter and an exponential ultraviolet cutoff parameter. The qualitative features of contributions from various classes of closed classical paths are noted. Then the Estrada-Kanwal distributional theory of asymptotics, particularly the moment expansion, is used to show that the linearized Einstein equation with the stress-energy near a plane boundary as source converges to a consistent theory when the cutoff is removed. This paper reports work in progress on a project combining researchers in Texas, Louisiana and Oklahoma. It is supported by NSF Grants PHY-0554849 and PHY-0554926.

Critically Theorizing the Global

ERIC Educational Resources Information Center

Gaudelli, William

2013-01-01

Globalization has unleashed profound changes in education. These include positivistic international school comparisons, a singular focus on schools as drivers of economic development, and the adoption of neoliberal market principles in school. These changes, however, generally go unexamined within the field and literature of global education.…

Functional renormalization group approach to the Yang-Lee edge singularity

DOE PAGES

An, X.; Mesterházy, D.; Stephanov, M. A.

2016-07-08

Here, we determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ = 6 - d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O(∂more » 4) truncations of the scale-dependent effective action.« less

Functional renormalization group approach to the Yang-Lee edge singularity

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

An, X.; Mesterházy, D.; Stephanov, M. A.

Here, we determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ = 6 - d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O(∂more » 4) truncations of the scale-dependent effective action.« less

Is it really naked? On cosmic censorship in string theory

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

Frolov, Andrei V.

We investigate the possibility of cosmic censorship violation in string theory using a characteristic double-null code, which penetrates horizons and is capable of resolving the spacetime all the way to the singularity. We perform high-resolution numerical simulations of the evolution of negative mass initial scalar field profiles, which were argued to provide a counterexample to cosmic censorship conjecture for AdS-asymptotic spacetimes in five-dimensional supergravity. In no instances formation of naked singularity is seen. Instead, numerical evidence indicates that black holes form in the collapse. Our results are consistent with earlier numerical studies, and explicitly show where the 'no black hole'more » argument breaks.« less

Cohomogeneity-one solutions in Einstein-Maxwell-dilaton gravity

NASA Astrophysics Data System (ADS)

Lim, Yen-Kheng

2017-05-01

The field equations for Einstein-Maxwell-dilaton gravity in D dimensions are reduced to an effective one-dimensional system under the influence of exponential potentials. Various cases where exact solutions can be found are explored. With this procedure, we present interesting solutions such as a one-parameter generalization of the dilaton-Melvin spacetime and a three-parameter solution that interpolates between the Reissner-Nordström and Bertotti-Robinson solutions. This procedure also allows simple, alternative derivations of known solutions such as the Lifshitz spacetime and the planar anti-de Sitter naked singularity. In the latter case, the metric is cast in a simpler form which reveals the presence of an additional curvature singularity.

New Metrics from a Fractional Gravitational Field

NASA Astrophysics Data System (ADS)

El-Nabulsi, Rami Ahmad

2017-09-01

Agop et al. proved in Commun. Theor. Phys. (2008) that, a Reissner-Nordstrom type metric is obtained, if gauge gravitational field in a fractal spacetime is constructed by means of concepts of scale relativity. We prove in this short communication that similar result is obtained if gravity in D-spacetime dimensions is fractionalized by means of the Glaeske-Kilbas-Saigo fractional. Besides, non-singular gravitational fields are obtained without using extra-dimensions. We present few examples to show that these gravitational fields hold a number of motivating features in spacetime physics.

Dissipation, intermittency, and singularities in incompressible turbulent flows

NASA Astrophysics Data System (ADS)

Debue, P.; Shukla, V.; Kuzzay, D.; Faranda, D.; Saw, E.-W.; Daviaud, F.; Dubrulle, B.

2018-05-01

We examine the connection between the singularities or quasisingularities in the solutions of the incompressible Navier-Stokes equation (INSE) and the local energy transfer and dissipation, in order to explore in detail how the former contributes to the phenomenon of intermittency. We do so by analyzing the velocity fields (a) measured in the experiments on the turbulent von Kármán swirling flow at high Reynolds numbers and (b) obtained from the direct numerical simulations of the INSE at a moderate resolution. To compute the local interscale energy transfer and viscous dissipation in experimental and supporting numerical data, we use the weak solution formulation generalization of the Kármán-Howarth-Monin equation. In the presence of a singularity in the velocity field, this formulation yields a nonzero dissipation (inertial dissipation) in the limit of an infinite resolution. Moreover, at finite resolutions, it provides an expression for local interscale energy transfers down to the scale where the energy is dissipated by viscosity. In the presence of a quasisingularity that is regularized by viscosity, the formulation provides the contribution to the viscous dissipation due to the presence of the quasisingularity. Therefore, our formulation provides a concrete support to the general multifractal description of the intermittency. We present the maps and statistics of the interscale energy transfer and show that the extreme events of this transfer govern the intermittency corrections and are compatible with a refined similarity hypothesis based on this transfer. We characterize the probability distribution functions of these extreme events via generalized Pareto distribution analysis and find that the widths of the tails are compatible with a similarity of the second kind. Finally, we make a connection between the topological and the statistical properties of the extreme events of the interscale energy transfer field and its multifractal properties.

Inclined edge crack in two bonded elastic quarter planes under out-of-plane loading

NASA Astrophysics Data System (ADS)

Hwang, E. H.; Choi, S. R.; Earmme, Y. Y.

1992-08-01

The problem of the interfacial edge crack in which the crack-inclination angle = zero is solved analytically by means of the Wiener-Hopf technique with the Mellin transform. The results are found to confirm the result by Bassani and Erdogan (1979) showing that there is no stress singularity for the interface perpendicular to the free boundary at the junction with a straight inclined interface with no crack.

Cotton fibre cross-section properties

USDA-ARS?s Scientific Manuscript database

From a structural perspective the cotton fibre is a singularly discrete, elongated plant cell with no junctions or inter-cellular boundaries. Its form in nature is essentially unadulterated from the field to the spinning mill where its cross-section properties, as for any textile fibre, are central ...

Transitions in Pediatrics: A Segmental Analysis.

ERIC Educational Resources Information Center

Pawluch, Dorothy.

1983-01-01

Examines how, as medical advances drastically reduced infant and child mortality rates, the field of pediatrics expanded from singular concern with treating children's diseases to include involvement in managing troublesome behavior. Considers the continued involvement of pediatricians in ministering to the psychosocial and behavioral needs of…

Analysis of log-periodic power law singularity patterns in time series related to credit risk

NASA Astrophysics Data System (ADS)

Wosnitza, Jan Henrik; Sornette, Didier

2015-04-01

The log-periodic (super-exponential) power law singularity (LPPLS) has become a promising tool for predicting extreme behavior of self-organizing systems in natural sciences and finance. Some researchers have recently proposed to employ the LPPLS on credit risk markets. The review article at hand summarizes four papers in this field and shows how they are linked. After structuring the research questions, we collect the corresponding answers from the four articles. This eventually gives us an overall picture of the application of the LPPLS to credit risk data. Our literature review begins with grounding the view that credit default swap (CDS) spreads are hotbeds for LPPLS patterns and it ends up with drawing attention to the recently proposed alarm index for the prediction of institutional bank runs. By presenting a new field of application for the LPPLS, the reviewed strand of literature further substantiates the LPPLS hypothesis. Moreover, the results suggest that CDS spread trajectories belong to a different universality class than, for instance, stock prices.

On singular and highly oscillatory properties of the Green function for ship motions

NASA Astrophysics Data System (ADS)

Chen, Xiao-Bo; Xiong Wu, Guo

2001-10-01

The Green function used for analysing ship motions in waves is the velocity potential due to a point source pulsating and advancing at a uniform forward speed. The behaviour of this function is investigated, in particular for the case when the source is located at or close to the free surface. In the far field, the Green function is represented by a single integral along one closed dispersion curve and two open dispersion curves. The single integral along the open dispersion curves is analysed based on the asymptotic expansion of a complex error function. The singular and highly oscillatory behaviour of the Green function is captured, which shows that the Green function oscillates with indefinitely increasing amplitude and indefinitely decreasing wavelength, when a field point approaches the track of the source point at the free surface. This sheds some light on the nature of the difficulties in the numerical methods used for predicting the motion of a ship advancing in waves.

Coplanar three-beam interference and phase edge dislocations

NASA Astrophysics Data System (ADS)

Patorski, Krzysztof; SłuŻewski, Łukasz; Trusiak, Maciej; Pokorski, Krzysztof

2016-12-01

We present a comprehensive analysis of grating three-beam interference to discover a broad range of the ratio of amplitudes A of +/-1 diffraction orders and the zero order amplitude C providing phase edge dislocations. We derive a condition A/C > 0.5 for the occurrence of phase edge dislocations in three-beam interference self-image planes. In the boundary case A/C = 0.5 singularity conditions are met in those planes (once per interference field period), but the zero amplitude condition is not accompanied by an abrupt phase change. For A/C > 0.5 two adjacent singularities in a single field period show opposite sign topological charges. The occurrence of edge dislocations for selected values of A/C was verified by processing fork fringes obtained by introducing the fourth beam in the plane perpendicular to the one containing three coplanar diffraction orders. Two fork pattern processing methods are described, 2D CWT (two-dimensional continuous wavelet transform) and 2D spatial differentiation.

The Emergent Universe scheme and tunneling

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

Labraña, Pedro

We present an alternative scheme for an Emergent Universe scenario, developed previously in Phys. Rev. D 86, 083524 (2012), where the universe is initially in a static state supported by a scalar field located in a false vacuum. The universe begins to evolve when, by quantum tunneling, the scalar field decays into a state of true vacuum. The Emergent Universe models are interesting since they provide specific examples of non-singular inflationary universes.

Possible antigravity regions in F(R) theory?

NASA Astrophysics Data System (ADS)

Bamba, Kazuharu; Nojiri, Shin'ichi; Odintsov, Sergei D.; Sáez-Gómez, Diego

2014-03-01

We construct an F(R) gravity theory corresponding to the Weyl invariant two scalar field theory. We investigate whether such F(R) gravity can have the antigravity regions where the Weyl curvature invariant does not diverge at the Big Bang and Big Crunch singularities. It is revealed that the divergence cannot be evaded completely but can be much milder than that in the original Weyl invariant two scalar field theory.

Exact solutions to Brans-Dicke cosmologies in flat Friedmann universes.

NASA Technical Reports Server (NTRS)

Morganstern, R. E.

1971-01-01

The Brans-Dicke cosmological equations for flat Friedmann-type expanding universes are solved parametrically for time, density, expansion parameter, and scalar field. These results reduce to a previously obtained exact solution to the radiation cosmology. Although the scalar field may be undetectable at the present epoch, it is felt that, if it exists, it must play an important role as one approaches the initial singularity of the cosmology.

Bouncing cosmologies from quantum gravity condensates

NASA Astrophysics Data System (ADS)

Oriti, Daniele; Sindoni, Lorenzo; Wilson-Ewing, Edward

2017-02-01

We show how the large-scale cosmological dynamics can be obtained from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.

Remarks on non-BPS string amplitudes and their all order α' contact interactions in IIB, IIA

NASA Astrophysics Data System (ADS)

Hatefi, Ehsan

2017-03-01

We explore the entire form of S-Matrix elements of a potential C n-1 Ramond-Ramond (RR) form field, a tachyon and two transverse scalar fields on both world volume and transverse directions of type IIB and IIA superstring theories. Apart from < {V}_{C^{-2}}{V}_{φ^0}{V}_{φ^0}{V}_{T^0}\\rangle the other scattering amplitude, namely < {V}_{C^{-1}}{V}_{φ^{-1}}{V}_{φ^0}{V}_{T^0}\\rangle is also revealed. We then start to compare all singularity structures of symmetric and asymmetric analysis, generating all infinite singularity structures as well as all order α' contact interactions on the whole directions. This leads to deriving various new contact terms and several new restricted Bianchi identities in both type IIB and IIA. It is also shown that just some of the new couplings of type IIB (IIA) string theory can be re-verified in an Effective Field Theory (EFT) by pull-back of branes. To construct the rest of S-matrix elements one needs to first derive restricted world volume (or bulk) Bianchi identities and then discover new EFT couplings in both type IIB and IIA. Finally the presence of commutator of scalar fields inside the exponential of Wess-Zumino action for non-BPS branes has been confirmed as well.

Physical subspace in a model of the quantized electromagnetic field coupled to an external field with an indefinite metric

NASA Astrophysics Data System (ADS)

Suzuki, Akito

2008-04-01

We study a model of the quantized electromagnetic field interacting with an external static source ρ in the Feynman (Lorentz) gauge and construct the quantized radiation field Aμ (μ=0,1,2,3) as an operator-valued distribution acting on the Fock space F with an indefinite metric. By using the Gupta subsidiary condition ∂μAμ(x)(+)Ψ=0, one can select the physical subspace Vphys. According to the Gupta-Bleuler formalism, Vphys is a non-negative subspace so that elements of Vphys, called physical states, can be probabilistically interpretable. Indeed, assuming that the external source ρ is infrared regular, i.e., ρ̂/∣k∣3/2ɛL2(R3), we can characterize the physical subspace Vphys and show that Vphys is non-negative. In addition, we find that the Hamiltonian of the model is reduced to the Hamiltonian of the transverse photons with the Coulomb interaction. We, however, prove that the physical subspace is trivial, i.e., Vphys={0}, if and only if the external source ρ is infrared singular, i.e., ρ̂/∣k∣3/2∉L2(R3). We also discuss a representation different from the above representation such that the physical subspace is not trivial under the infrared singular condition.

The Semantics of Plurals: A Defense of Singularism

ERIC Educational Resources Information Center

Florio, Salvatore

2010-01-01

In this dissertation, I defend "semantic singularism", which is the view that syntactically plural terms, such as "they" or "Russell and Whitehead", are semantically singular. A semantically singular term is a term that denotes a single entity. Semantic singularism is to be distinguished from "syntactic singularism", according to which…

Dark sector impact on gravitational collapse of an electrically charged scalar field

NASA Astrophysics Data System (ADS)

Nakonieczna, Anna; Rogatko, Marek; Nakonieczny, Łukasz

2015-11-01

Dark matter and dark energy are dominating components of the Universe. Their presence affects the course and results of processes, which are driven by the gravitational interaction. The objective of the paper was to examine the influence of the dark sector on the gravitational collapse of an electrically charged scalar field. A phantom scalar field was used as a model of dark energy in the system. Dark matter was modeled by a complex scalar field with a quartic potential, charged under a U(1)-gauge field. The dark components were coupled to the electrically charged scalar field via the exponential coupling and the gauge field-Maxwell field kinetic mixing, respectively. Complete non-linear simulations of the investigated process were performed. They were conducted from regular initial data to the end state, which was the matter dispersal or a singularity formation in a spacetime. During the collapse in the presence of dark energy dynamical wormholes and naked singularities were formed in emerging spacetimes. The wormhole throats were stabilized by the violation of the null energy condition, which occurred due to a significant increase of a value of the phantom scalar field function in its vicinity. The square of mass parameter of the dark matter scalar field potential controlled the formation of a Cauchy horizon or wormhole throats in the spacetime. The joint impact of dark energy and dark matter on the examined process indicated that the former decides what type of an object forms, while the latter controls the amount of time needed for the object to form. Additionally, the dark sector suppresses the natural tendency of an electrically charged scalar field to form a dynamical Reissner-Nordström spacetime during the gravitational collapse.

Self-similar dynamics of air film entrained by a solid disk in confined space: A simple prototype of topological transitions

NASA Astrophysics Data System (ADS)

Nakazato, Hana; Yamagishi, Yuki; Okumura, Ko

2018-05-01

In hydrodynamic topological transitions, one mass of fluid breaks into two or two merge into one. For example, in honey-drop formation when honey is dripping from a spoon, honey is extended to separate into two masses as the liquid neck bridging them thins down to the micron scale. At the moment when the topology changes due to the breakup, physical observables such as surface curvature locally diverge. Such singular dynamics has widely attracted physicists, revealing universality in self-similar dynamics, which shares much in common with critical phenomena in thermodynamics. Many experimental examples have been found, including an electric spout and vibration-induced jet eruption. However, only a few cases have been physically understood on the basis of equations that govern the singular dynamics and even in such a case the physical understanding is mathematically complicated, inevitably involving delicate numerical calculations. Here we study the breakup of air film entrained by a solid disk into viscous liquid in a confined space, which leads to formation, thinning, and breakup of the neck of air. As a result, we unexpectedly find that equations governing the neck dynamics can be solved analytically by virtue of two remarkable experimental features: Only a single length scale linearly dependent on time remains near the singularity and two universal scaling functions describing the singular neck shape and velocity field are both analytic. The present solvable case would be essential for a better understanding of the singular dynamics and will help reveal the physics of unresolved examples intimately related to daily-life phenomena and diverse practical applications.

Theoretical constraints on dynamic pulverization of fault zone rocks

NASA Astrophysics Data System (ADS)

Xu, Shiqing; Ben-Zion, Yehuda

2017-04-01

We discuss dynamic rupture results aiming to elucidate the generation mechanism of pulverized fault zone rocks (PFZR) observed in 100-200 m wide belts distributed asymmetrically across major strike-slip faults separating different crustal blocks. Properties of subshear and supershear ruptures are considered using analytical results of Linear Elastic Fracture Mechanics and numerical simulations of Mode-II ruptures along faults between similar or dissimilar solids. The dynamic fields of bimaterial subshear ruptures are expected to produce off-fault damage primarily on the stiff side of the fault, with tensile cracks having no preferred orientation, in agreement with field observations. Subshear ruptures in a homogeneous solid are expected to produce off-fault damage with high-angle tensile cracks on the extensional side of the fault, while supershear ruptures between similar or dissimilar solids are likely to produce off-fault damage on both sides of the fault with preferred tensile crack orientations. One or more of these features are not consistent with properties of natural samples of PFZR. At a distance of about 100 m from the fault, subshear and supershear ruptures without stress singularities produce strain rates up to 1 s-1. This is less than required for rock pulverization in laboratory experiments with centimetre-scale intact rock samples, but may be sufficient for pulverizing larger samples with pre-existing damage.