Stress-energy tensors for vector fields outside a static black hole
International Nuclear Information System (INIS)
Barrios, F.A.; Vaz, C.
1989-01-01
We obtain new, approximate stress-energy tensors to describe gauge fields in the neighborhood of a Schwarzschild black hole. We assume that the coefficient of ∇ 2 R in the trace anomaly is correctly given by ζ-function regularization. Our approximation differs from that of Page and of Brown and Ottewill and relies upon a new, improved ansatz for the form of the stress-energy tensor in the ultrastatic optical metric of the black hole. The Israel-Hartle-Hawking thermal tensor is constructed to be regular on the horizon and possess the correct asymptotic behavior. Our approximation of Unruh's tensor is likewise constructed to be regular on the future horizon and exhibit a luminosity which agrees with Page's numerically obtained value. Geometric expressions for the approximate tensors are given, and the approximate energy density of the thermal tensor on the horizon is compared with recent numerical estimates
Study of the characteristics of crust stress field in East China by inversion of stress tensor
International Nuclear Information System (INIS)
Huilan, Z.; Rugang, D.
1991-12-01
This paper combines the search procedure with the optimization procedure to inverse the average stress tensor, and applies this method to study the crustal stress field using data of the solution of P wave first motion. By dealing with the data of Haicheng, Tangshan, Xingtai, Anyang, Liyang, Taiwan, Fujian and Guangdong areas, we obtain the characteristics of crust stress field of East China. The directions of the principal pressure stress always possess a small dip angle, but the azimuths vary from NEE (in north part of East China) to SEE (in the south part). This frame probably is related to the push-extrusive effects of the northwestern Pacific plate from NEE and the Philippine plate from SEE. (author). 5 refs, 8 figs, 4 tabs
Stress-energy tensor of quantized massive fields in static wormhole spacetimes
Kocuper, Ewa; Matyjasek, Jerzy; Zwierzchowska, Kasia
2017-11-01
In order to be traversable, the static Lorentzian wormhole must be made out of some exotic matter that violates the weak energy condition. The quantized fields are the natural candidates as their stress-energy tensor, in many cases, possesses desired properties. In this paper we construct and examine the stress-energy tensor of the quantized massive scalar, spinor and vector fields in six static wormhole spacetimes. We find that in all considered cases the quantum fields violate the Morris-Thorne conditions and do not have the form necessary to support the wormhole throat. This is in concord with the previous results and indicates that the massive quantum fields make the wormholes less operable.
The stress-energy tensor of flavor fields from AdS/CFT
Karch, Andreas; O'Bannon, Andy; Thompson, Ethan
2009-04-01
We use the AdS/CFT correspondence to study the transport properties of massive Script N = 2 hypermultiplet fields in an Script N = 4 SU(Nc) super-Yang-Mills theory plasma in the large Nc, large 't Hooft coupling limit, and in the presence of a baryon number chemical potential and external electric and magnetic fields. In particular, we compute the flavor fields' contribution to the stress-energy tensor. We find infrared divergences in the stress-energy tensor, arising from the flavor fields' constant rate of energy and momentum loss. We regulate these divergences and extract the energy and momentum loss rates from the divergent terms. We also check our result in various limits in which the divergences are absent. The supergravity dual is a system of D7-branes, with a particular configuration of worldvolume fields, probing an AdS-Schwarzschild background. The supergravity calculation amounts to computing the stress-energy tensor of the D7-branes.
Quantum stress tensor fluctuations of a conformal field and inflationary cosmology
International Nuclear Information System (INIS)
Ford, L. H.; Miao, S. P.; Ng, Kin-Wang; Woodard, R. P.; Wu, C.-H.
2010-01-01
We discuss the additional perturbation introduced during inflation by quantum stress tensor fluctuations of a conformally invariant field such as the photon. We consider both a kinematical model, which deals only with the expansion fluctuations of geodesics, and a dynamical model which treats the coupling of the stress tensor fluctuations to a scalar inflaton. In neither model do we find any growth at late times, in accordance with a theorem due to Weinberg. What we find instead is a correction which becomes larger the earlier one starts inflation. This correction is non-Gaussian and highly scale dependent, so the absence of such effects from the observed power spectra may imply a constraint on the total duration of inflation. We discuss different views about the validity of perturbation theory at very early times during which currently observable modes are trans-Planckian.
Vacuum stress tensor of a scalar field in a rectangular waveguide
International Nuclear Information System (INIS)
Rodrigues, R.B.; Svaiter, N.F.; Paola, R.D.M. de
2001-11-01
Using the heat Kernel method and the analytical continuation of the zeta function, we calculate the canonical and improved vacuum stress tensors, {T μν (vector x)} and {Θ μν (vector x)}, associated with a massless scalar field confined in the interior of an infinity long rectangular waveguide. The local depence of the renormalized energy for two special configurations when the total energy is positive and negative are presented using {T 00 (vector x)} and {Θ 00 (vector x)}. From the stress tensors we obtain the local casimir forces in all walls by introducing a particular external configuration. It is hown that this external configuration cannot give account of the edge divergences of the local forces. The local form of the forces is obtained for three special configurations. (author)
Quantum fields interacting with colliding plane waves: the stress-energy tensor and backreaction
International Nuclear Information System (INIS)
Dorca, M.; Verdaguer, E.
1997-01-01
Following a previous work on the quantization of a massless scalar field in a space-time representing the head on collision of two plane waves which focus into a Killing-Cauchy horizon, we compute the renormalized expectation value of the stress-energy tensor of the quantum field near that horizon in the physical state which corresponds to the Minkowski vacuum before the collision of the waves. It is found that for minimally coupled and conformally coupled scalar fields the respective stress-energy tensors are unbounded in the horizon. The specific form of the divergences suggests that when the semiclassical Einstein equations describing the backreaction of the quantum fields on the space-time geometry are taken into account, the horizon will acquire a curvature singularity. Thus the Killing-Cauchy horizon which is known to be unstable under ''generic'' classical perturbations is also unstable by vacuum polarization. The calculation is done following the point-splitting regularization technique. The dynamical colliding wave space-time has four quite distinct space-time regions, namely, one flat region, two single plane wave regions, and one interaction region. Exact mode solutions of the quantum field equation cannot be found exactly, but the blueshift suffered by the initial modes in the plane wave and interaction regions makes the use of the WKB expansion a suitable method of solution. To ensure the correct regularization of the stress-energy tensor, the initial flat modes propagated into the interaction region must be given to a rather high adiabatic order of approximation. (orig.)
Milton, Kimball A.; Fulling, Stephen A.; Parashar, Prachi; Kalauni, Pushpa; Murphy, Taylor
2016-04-01
Motivated by a desire to understand quantum fluctuation energy densities and stress within a spatially varying dielectric medium, we examine the vacuum expectation value for the stress tensor of a scalar field with arbitrary conformal parameter, in the background of a given potential that depends on only one spatial coordinate. We regulate the expressions by incorporating a temporal-spatial cutoff in the (imaginary) time and transverse-spatial directions. The divergences are captured by the zeroth- and second-order WKB approximations. Then the stress tensor is "renormalized" by omitting the terms that depend on the cutoff. The ambiguities that inevitably arise in this procedure are both duly noted and restricted by imposing certain physical conditions; one result is that the renormalized stress tensor exhibits the expected trace anomaly. The renormalized stress tensor exhibits no pressure anomaly, in that the principle of virtual work is satisfied for motions in a transverse direction. We then consider a potential that defines a wall, a one-dimensional potential that vanishes for z 0 , for z >0 . Previously, the stress tensor had been computed outside of the wall, whereas now we compute all components of the stress tensor in the interior of the wall. The full finite stress tensor is computed numerically for the two cases where explicit solutions to the differential equation are available, α =1 and 2. The energy density exhibits an inverse linear divergence as the boundary is approached from the inside for a linear potential, and a logarithmic divergence for a quadratic potential. Finally, the interaction between two such walls is computed, and it is shown that the attractive Casimir pressure between the two walls also satisfies the principle of virtual work (i.e., the pressure equals the negative derivative of the energy with respect to the distance between the walls).
Local recovery of lithospheric stress tensor from GOCE gravitational tensor
Eshagh, Mehdi
2017-04-01
The sublithospheric stress due to mantle convection can be computed from gravity data and propagated through the lithosphere by solving the boundary-value problem of elasticity for the Earth's lithosphere. In this case, a full tensor of stress can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a tensor from gravitational tensor measured at satellite altitudes. The mathematical relations will be much simpler in this way than the case of using gravity data as no derivative of spherical harmonics (SHs) or Legendre polynomials is involved in the expressions. Here, new relations between the SH coefficients of the stress and gravitational tensor elements are presented. Thereafter, integral equations are established from them to recover the elements of stress tensor from those of the gravitational tensor. The integrals have no closed-form kernels, but they are easy to invert and their spatial truncation errors are reducible. The integral equations are used to invert the real data of the gravity field and steady-state ocean circulation explorer mission (GOCE), in 2009 November, over the South American plate and its surroundings to recover the stress tensor at a depth of 35 km. The recovered stress fields are in good agreement with the tectonic and geological features of the area.
International Nuclear Information System (INIS)
Dappiagi, Claudio; Hack, Thomas-Paul; Pinamonti, Nicola
2009-03-01
We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We explicitly calculate its trace anomaly in particular. (orig.)
The Topology of Symmetric Tensor Fields
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.
The geomagnetic field gradient tensor
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Olsen, Nils
2012-01-01
We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination...
The stress energy tensor of a locally supersymmetric quantum field on a curved spacetime
International Nuclear Information System (INIS)
Koehler, M.
1995-04-01
For an analogon of the free Wess-Zumino model on Ricci flat spacetimes, the relation between a conserved 'supercurrent' and the point-separated improved energy momentum tensor is investigated and a similar relation as on Minkowski space is established. The expectation value of the latter in any globally Hadamard product state is found to be a priori finite in the coincidence limit if the theory is massive. On arbitrary globally hyperbolic spacetimes the 'supercurrent' is shown to be a well defined operator valued distribution on the GNS Hilbertspace of any globally Hadamard product state. Viewed as a new field, all n-point distributions exist, giving a new example for a Wightman field on that manifold. Moreover, it is shown that this field satisfies a new wave front set spectrum condition in a nontrivial way. (orig.)
Radiation Forces and Torques without Stress (Tensors)
Bohren, Craig F.
2011-01-01
To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce…
Magnetic hydrodynamics with asymmetric stress tensor
Billig, Yuly
2005-04-01
In this paper we study equations of magnetic hydrodynamics with a stress tensor. We interpret this system as the generalized Euler equation associated with an Abelian extension of the Lie algebra of vector fields with a nontrivial 2-cocycle. We use the Lie algebra approach to prove the energy conservation law and the conservation of cross-helicity.
Magnetic hydrodynamics with asymmetric stress tensor
Billig, Yuly
2004-01-01
In this paper we study equations of magnetic hydrodynamics with a stress tensor. We interpret this system as the generalized Euler equation associated with an abelian extension of the Lie algebra of vector fields with a non-trivial 2-cocycle. We use the Lie algebra approach to prove the energy conservation law and the conservation of cross-helicity.
Antisymmetric tensor generalizations of affine vector fields.
Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro
2016-02-01
Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.
Holographic stress tensor for non-relativistic theories
International Nuclear Information System (INIS)
Ross, Simon F.; Saremi, Omid
2009-01-01
We discuss the calculation of the field theory stress tensor from the dual geometry for two recent proposals for gravity duals of non-relativistic conformal field theories. The first of these has a Schroedinger symmetry including Galilean boosts, while the second has just an anisotropic scale invariance (the Lifshitz case). For the Lifshitz case, we construct an appropriate action principle. We propose a definition of the non-relativistic stress tensor complex for the field theory as an appropriate variation of the action in both cases. In the Schroedinger case, we show that this gives physically reasonable results for a simple black hole solution and agrees with an earlier proposal to determine the stress tensor from the familiar AdS prescription. In the Lifshitz case, we solve the linearised equations of motion for a general perturbation around the background, showing that our stress tensor is finite on-shell.
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot...... transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...
Inflationary cosmology and 4-index tensor fields
International Nuclear Information System (INIS)
Moorhouse, R.G.; Nixon, J.
1985-01-01
We show how an arbitrarily large expansion of the ordinary dimensions in the very early universe can be achieved in the d=11 supergravity theory where the 4-index anti-symmetric tensor field supplies the energy-momentum tensor. However, the decrease of the extra dimensions is too fast to give a satisfactory inflationary cosmology. If a 4-index tensor field is similar used to provide the energy-momentum tensor in dimensions significantly greater than 11 the inflationary outlook is more hopeful. (orig.)
Electromagnetic stress tensor for an amorphous metamaterial medium
Wang, Neng; Wang, Shubo; Ng, Jack
2018-03-01
We analytically and numerically investigated the internal optical forces exerted by an electromagnetic wave inside an amorphous metamaterial medium. We derived, by using the principle of virtual work, the Helmholtz stress tensor, which takes into account the electrostriction effect. Several examples of amorphous media are considered, and different electromagnetic stress tensors, such as the Einstein-Laub tensor and Minkowski tensor, are also compared. It is concluded that the Helmholtz stress tensor is the appropriate tensor for such systems.
Abelian gauge theories with tensor gauge fields
International Nuclear Information System (INIS)
Kapuscik, E.
1984-01-01
Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)
Conformal field theories and tensor categories. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics
2014-08-01
First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot......To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create "seams" or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template...
Why are tensor field theories asymptotically free?
Rivasseau, V.
2015-09-01
In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a 1/p2 propagator and quartic interactions and on the comparison between the intermediate field representations of the vector, matrix and tensor cases. The transition from asymptotic freedom (tensor case) to asymptotic safety (matrix case) is related to the crossing symmetry of the matrix vertex, whereas in the vector case, the lack of asymptotic freedom (“Landau ghost”), as in the ordinary scalar φ^44 case, is simply due to the absence of any wave function renormalization at one loop.
(Ln-bar, g)-spaces. Special tensor fields
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces
Tensor Fields for Use in Fractional-Order Viscoelasticity
Freed, Alan D.; Diethelm, Kai
2003-01-01
To be able to construct viscoelastic material models from fractional0order differentegral equations that are applicable for 3D finite-strain analysis requires definitions for fractional derivatives and integrals for symmetric tensor fields, like stress and strain. We define these fields in the body manifold. We then map them ito spatial fields expressed in terms of an Eulerian or Lagrangian reference frame where most analysts prefer to solve boundary problems.
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...
Visualization and processing of tensor fields
Weickert, Joachim
2007-01-01
Presents information on the visualization and processing of tensor fields. This book serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as a textbook for specialized classes and seminars for graduate and doctoral students.
Ye, Qian; Lin, Haoze
2017-07-01
Though extensively used in calculating optical force and torque acting on a material object illuminated by laser, the Maxwell stress tensor (MST) method follows the electromagnetic linear and angular momentum balance that is usually derived in most textbooks for a continuous volume charge distribution in free space, if not resorting to the application of Noether’s theorem in electrodynamics. To cast the conservation laws into a physically appealing form involving the current densities of linear and angular momentum, on which the MST method is based, the divergence theorem is employed to transform a volume integral into a surface integral. When a material object of finite volume is put into the field, it brings about a discontinuity of field across its surface, due to the presence of induced surface charge and surface current. Ambiguity arises among students in whether the divergence theorem can still be directly used without any justification. By taking into account the effect of the induced surface charge and current, we present a simple pedagogical derivation for the MST method for calculating the optical force and torque on an object immersed in monochromatic optical field, without resorting to Noether’s theorem. Although the results turn out to be identical to those given in the standard textbooks, our derivation avoids the direct use of the divergence theorem on a discontinuous function.
Lithospheric Stress Tensor from Gravity and Lithospheric Structure Models
Eshagh, Mehdi; Tenzer, Robert
2017-07-01
In this study we investigate the lithospheric stresses computed from the gravity and lithospheric structure models. The functional relation between the lithospheric stress tensor and the gravity field parameters is formulated based on solving the boundary-value problem of elasticity in order to determine the propagation of stresses inside the lithosphere, while assuming the horizontal shear stress components (computed at the base of the lithosphere) as lower boundary values for solving this problem. We further suppress the signature of global mantle flow in the stress spectrum by subtracting the long-wavelength harmonics (below the degree of 13). This numerical scheme is applied to compute the normal and shear stress tensor components globally at the Moho interface. The results reveal that most of the lithospheric stresses are accumulated along active convergent tectonic margins of oceanic subductions and along continent-to-continent tectonic plate collisions. These results indicate that, aside from a frictional drag caused by mantle convection, the largest stresses within the lithosphere are induced by subduction slab pull forces on the side of subducted lithosphere, which are coupled by slightly less pronounced stresses (on the side of overriding lithospheric plate) possibly attributed to trench suction. Our results also show the presence of (intra-plate) lithospheric loading stresses along Hawaii islands. The signature of ridge push (along divergent tectonic margins) and basal shear traction resistive forces is not clearly manifested at the investigated stress spectrum (between the degrees from 13 to 180).
Relativistic particles with spin and antisymmetric tensor fields
International Nuclear Information System (INIS)
Sandoval Junior, L.
1990-09-01
A study is made on antisymmetric tensor fields particularly on second order tensor field as far as his equivalence to other fields and quantization through the path integral are concerned. Also, a particle model is studied which has been recently proposed and reveals to be equivalent to antisymmetric tensor fields of any order. (L.C.J.A.)
Theoretical study of lithium clusters by electronic stress tensor
International Nuclear Information System (INIS)
Ichikawa, Kazuhide; Nozaki, Hiroo; Komazawa, Naoya; Tachibana, Akitomo
2012-01-01
We study the electronic structure of small lithium clusters Li n (n = 2 ∼ 8) using the electronic stress tensor. We find that the three eigenvalues of the electronic stress tensor of the Li clusters are negative and degenerate, just like the stress tensor of liquid. This leads us to propose that we may characterize a metallic bond in terms of the electronic stress tensor. Our proposal is that in addition to the negativity of the three eigenvalues of the electronic stress tensor, their degeneracy characterizes some aspects of the metallic nature of chemical bonding. To quantify the degree of degeneracy, we use the differential eigenvalues of the electronic stress tensor. By comparing the Li clusters and hydrocarbon molecules, we show that the sign of the largest eigenvalue and the differential eigenvalues could be useful indices to evaluate the metallicity or covalency of a chemical bond.
Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.
Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene
2016-03-01
Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.
Glyph-Based Comparative Visualization for Diffusion Tensor Fields.
Zhang, Changgong; Schultz, Thomas; Lawonn, Kai; Eisemann, Elmar; Vilanova, Anna
2016-01-01
Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging modality that enables the in-vivo reconstruction and visualization of fibrous structures. To inspect the local and individual diffusion tensors, glyph-based visualizations are commonly used since they are able to effectively convey full aspects of the diffusion tensor. For several applications it is necessary to compare tensor fields, e.g., to study the effects of acquisition parameters, or to investigate the influence of pathologies on white matter structures. This comparison is commonly done by extracting scalar information out of the tensor fields and then comparing these scalar fields, which leads to a loss of information. If the glyph representation is kept, simple juxtaposition or superposition can be used. However, neither facilitates the identification and interpretation of the differences between the tensor fields. Inspired by the checkerboard style visualization and the superquadric tensor glyph, we design a new glyph to locally visualize differences between two diffusion tensors by combining juxtaposition and explicit encoding. Because tensor scale, anisotropy type, and orientation are related to anatomical information relevant for DTI applications, we focus on visualizing tensor differences in these three aspects. As demonstrated in a user study, our new glyph design allows users to efficiently and effectively identify the tensor differences. We also apply our new glyphs to investigate the differences between DTI datasets of the human brain in two different contexts using different b-values, and to compare datasets from a healthy and HIV-infected subject.
Quantum stress tensor in Schwarzschild space-time
International Nuclear Information System (INIS)
Howard, K.W.; Candelas, P.
1984-01-01
The vacuum expectation value of the stress-energy tensor for the Hartle-Hawking state in Schwartzschild space-time has been calculated for the conformal scalar field. separates naturally into the sum of two terms. The first coincides with an approximate expression suggested by Page. The second term is a ''remainder'' that may be evaluated numerically. The total expression is in good qualitative agreement with Page's approximation. These results are at variance with earlier results given by Fawcett whose error is explained
Energy-momentum tensor of the electromagnetic field
International Nuclear Information System (INIS)
Horndeski, G.W.; Wainwright, J.
1977-01-01
In this paper we investigate the energy-momentum tensor of the most general second-order vector-tensor theory of gravitation and electromagnetism which has field equations which are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, and (iii) compatible with Maxwell's equations in a flat space. This energy-momentum tensor turns out to be quadratic in the first partial derivatives of the electromagnetic field tensor and depends upon the curvature tensor. The asymptotic behavior of this energy-momentum tensor is examined for solutions to Maxwell's equations in Minkowski space, and it is demonstrated that this energy-momentum tensor predicts regions of negative energy density in the vicinity of point sources
Energy-momentum tensor in the quantum field theory
International Nuclear Information System (INIS)
Azakov, S.I.
1977-01-01
An energy-momentum tensor in the scalar field theory is built. The tensor must satisfy the finiteness requirement of the Green function. The Green functions can always be made finite by renormalizations in the S-matrix by introducing counter terms into the Hamiltonian (or Lagrangian) of the interaction. Such a renormalization leads to divergencies in the Green functions. Elimination of these divergencies requires the introduction of new counter terms, which must be taken into account in the energy-momentum tensor
Renormalization of nonabelian gauge theories with tensor matter fields
Energy Technology Data Exchange (ETDEWEB)
Lemes, Vitor; Renan, Ricardo [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Sorella, Silvio Paolo [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica
1996-03-01
The renormalizability of a nonabelian model describing the coupling between antisymmetric second rank tensor matter fields and Yang-Mills gauge fields is discussed within the BRS algebraic framework. (author). 12 refs.
Renormalization of nonabelian gauge theories with tensor matter fields
International Nuclear Information System (INIS)
Lemes, Vitor; Renan, Ricardo; Sorella, Silvio Paolo
1996-03-01
The renormalizability of a nonabelian model describing the coupling between antisymmetric second rank tensor matter fields and Yang-Mills gauge fields is discussed within the BRS algebraic framework. (author). 12 refs
Gravity waves from quantum stress tensor fluctuations in inflation
International Nuclear Information System (INIS)
Wu, Chun-Hsien; Hsiang, Jen-Tsung; Ford, L. H.; Ng, Kin-Wang
2011-01-01
We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a nonscale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditions. If the initial time is taken to be sufficiently early, the fluctuating gravity waves are potentially observable both in the CMB radiation and in gravity wave detectors, and could offer a probe of trans-Planckian physics. The fact that they have not yet been observed might be used to constrain the duration and energy scale of inflation. However, this conclusion is contingent upon including the contribution of modes which were trans-Planckian at the beginning of inflation.
Gravity waves from quantum stress tensor fluctuations in inflation
Wu, Chun-Hsien; Hsiang, Jen-Tsung; Ford, L. H.; Ng, Kin-Wang
2011-11-01
We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a nonscale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditions. If the initial time is taken to be sufficiently early, the fluctuating gravity waves are potentially observable both in the CMB radiation and in gravity wave detectors, and could offer a probe of trans-Planckian physics. The fact that they have not yet been observed might be used to constrain the duration and energy scale of inflation. However, this conclusion is contingent upon including the contribution of modes which were trans-Planckian at the beginning of inflation.
DUCASSE , Eric; YAACOUBI , Slah
2010-01-01
International audience; A tensor Hankel transform'' (THT) is defined for vector fields, such as displacement, and second-order tensor fields, such as stress or strain. The THT establishes a bijection between the real space and the wave-vector domain, and, remarkably, cannot be reduced to a scalar transform applied separately to each component. One of the advantages of this approach is that some standard elasticity problems can be concisely rewritten by applying this tensor integral transform ...
On energy-momentum tensors of gravitational field
International Nuclear Information System (INIS)
Nikishov, A.I.
2001-01-01
The phenomenological approach to gravitation is discussed in which the 3-graviton interaction is reduced to the interaction of each graviton with the energy-momentum tensor of two others. If this is so, (and in general relativity this is not so), then the problem of choosing the correct energy-momentum tensor comes to finding the right 3-graviton vertex. Several energy-momentum tensors od gravitational field are considered and compared in the lowest approximation. Each of them together with the energy-momentum tensor of point-like particles satisfies the conservation laws when equations of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from other in the way their energy density is distributed between energy density of interaction (nonzero only at locations of particles) and energy density of gravitational field. Stating from Lorentz invariance, the Lagrangians for spin-2, mass-0 field are considered [ru
Effective field theory approaches for tensor potentials
Energy Technology Data Exchange (ETDEWEB)
Jansen, Maximilian
2016-11-14
Effective field theories are a widely used tool to study physical systems at low energies. We apply them to systematically analyze two and three particles interacting via tensor potentials. Two examples are addressed: pion interactions for anti D{sup 0}D{sup *0} scattering to dynamically generate the X(3872) and dipole interactions for two and three bosons at low energies. For the former, the one-pion exchange and for the latter, the long-range dipole force induce a tensor-like structure of the potential. We apply perturbative as well as non-perturbative methods to determine low-energy observables. The X(3872) is of major interest in modern high-energy physics. Its exotic characteristics require approaches outside the range of the quark model for baryons and mesons. Effective field theories represent such methods and provide access to its peculiar nature. We interpret the X(3872) as a hadronic molecule consisting of neutral D and D{sup *} mesons. It is possible to apply an effective field theory with perturbative pions. Within this framework, we address chiral as well as finite volume extrapolations for low-energy observables, such as the binding energy and the scattering length. We show that the two-point correlation function for the D{sup *0} meson has to be resummed to cure infrared divergences. Moreover, next-to-leading order coupling constants, which were introduced by power counting arguments, appear to be essential to renormalize the scattering amplitude. The binding energy as well as the scattering length display a moderate dependence on the light quark masses. The X(3872) is most likely deeper bound for large light quark masses. In a finite volume on the other hand, the binding energy significantly increases. The dependence on the light quark masses and the volume size can be simultaneously obtained. For bosonic dipoles we apply a non-perturbative, numerical approach. We solve the Lippmann-Schwinger equation for the two-dipole system and the Faddeev
Stress tensor computations at Mount St. Helens (1995-1998
Directory of Open Access Journals (Sweden)
S. Gresta
2000-06-01
Full Text Available Fault plane solutions of 459 events occurring between 1995 and 1998 at Mount St. Helens (State of Washington, Northwest U.S.A. were considered in order to infer the state of stress beneath the volcano. These events occurred in two distinct depth zones. The shallower zone is between 2 and 5.5 km, with shocks clustering in a tight cylindrical distribution about 1 km in radius directly beneath the crater. The deeper events are spread over a larger volume from 5.5 to 10 km depth and surround an aseismic zone below and slightly west of the lava dome. Faulting is characterized by a mixture of strike-slip, reverse and normal faults with maximum compression axes which do not cluster around a single direction. In the deep zone, between 5.5 and 10 km, P axes define a wheel-spoke pattern pointing radially away from the center of the aseismic zone. The 459 fault plane solutions were inverted for stress tensor parameters using the algorithm of Gephart and Forsyth. The inversion of the whole data set revealed that faulting was not produced by a uniform stress distribution. The subdivision of the zone into smaller volumes significantly reduced misfit and confidence areas of the solutions, whereas temporal subdivision of the sample did not lead to significant improvements in terms of stress uniformity. We suggest that the inhomogeneous stress field is consistent with a varying pressure source originating from the inferred crustal magma chamber and a thin conduit extending above it.
Tensor fields on orbits of quantum states and applications
Energy Technology Data Exchange (ETDEWEB)
Volkert, Georg Friedrich
2010-07-19
On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces H, we identify two classes of tensor field constructions. First, as pull-back tensor fields of order two from modified Hermitian tensor fields, constructed on Hilbert spaces by means of the property of having the vertical distributions of the C{sub 0}-principal bundle H{sub 0} {yields} P(H) over the projective Hilbert space P(H) in the kernel. And second, directly constructed on the Lie group, as left-invariant representation-dependent operator-valued tensor fields (LIROVTs) of arbitrary order being evaluated on a quantum state. Within the NP-hard problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable (Gurvits, 2003), we show that both tensor field constructions admit a geometric approach to this problem, which evades the traditional ambiguity on defining metrical structures on the convex set of mixed states. In particular by considering manifolds associated to orbits passing through a selected state when acted upon by the local unitary group U(n) x U(n) of Schmidt coefficient decomposition inducing transformations, we find the following results: In the case of pure states we show that Schmidt-equivalence classes which are Lagrangian submanifolds define maximal entangled states. This implies a stronger statement as the one proposed by Bengtsson (2007). Moreover, Riemannian pull-back tensor fields split on orbits of separable states and provide a quantitative characterization of entanglement which recover the entanglement measure proposed by Schlienz and Mahler (1995). In the case of mixed states we highlight a relation between LIROVTs of order two and a class of computable separability criteria based on the Bloch-representation (de Vicente, 2007). (orig.)
Electromagnetic energy density and stress tensor in a warm plasma with finite flow velocity
International Nuclear Information System (INIS)
Choi, Cheong R.; Lee, Nam C.
2004-01-01
The expressions of the average of energy density and the average stress tensor of the electromagnetic field in a warm collisionless plasma moving with a finite velocity are obtained by using a microscopic method that uses the fluid description of plasma. The result contains terms involved with derivatives of the dielectric tensor with respect to the velocity, which explicitly represent the effects of the finite velocity of the medium. In the zero-velocity limit, the results reduce to the well-known expressions for a plasma at rest with temporal and spatial dispersion
Energy-momentum tensor in quantum field theory
International Nuclear Information System (INIS)
Fujikawa, Kazuo.
1980-12-01
The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight 1/2 should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat space-time limit, all the Ward-Takahashi identities associate with space-time transformations including the global dilatation become free from anomalies, reflecting the general covariance of the integral measure; the trace of this energy-momentum tensor is thus finite at the zero momentum transfer. The Jacobian for the local conformal transformation however becomes non-trivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at the vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization group β-function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at the vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise. (author)
Causal structure in the scalar–tensor theory with field derivative coupling to the Einstein tensor
Directory of Open Access Journals (Sweden)
Masato Minamitsuji
2015-04-01
Full Text Available We investigate the causal structure in the scalar–tensor theory with the field derivative coupling to the Einstein tensor, which is a class of the Horndeski theory in the four-dimensional spacetime. We show that in general the characteristic hypersurface is non-null, which admits the superluminal propagations. We also derive the conditions that the characteristic hypersurface becomes null and show that a Killing horizon can be the causal edge for all the propagating degrees of freedom, if the additional conditions for the scalar field are satisfied. Finally, we find the position of the characteristic hypersurface in the dynamical spacetime with the maximally symmetric space, and that the fastest propagation can be superluminal, especially if the coupling constant becomes positive. We also argue that the superluminality itself may not lead to the acausality of the theory.
Dilaton and second-rank tensor fields as supersymmetric compensators
International Nuclear Information System (INIS)
Nishino, Hitoshi; Rajpoot, Subhash
2007-01-01
We formulate a supersymmetric theory in which both a dilaton and a second-rank tensor play roles of compensators. The basic off-shell multiplets are a linear multiplet (B μν ,χ,φ) and a vector multiplet (A μ ,λ;C μνρ ), where φ and B μν are, respectively, a dilaton and a second-rank tensor. The third-rank tensor C μνρ in the vector multiplet is ''dual'' to the conventional D field with 0 on-shell or 1 off-shell degree of freedom. The dilaton φ is absorbed into one longitudinal component of A μ , making it massive. Initially, B μν has 1 on-shell or 3 off-shell degrees of freedom, but it is absorbed into the longitudinal components of C μνρ . Eventually, C μνρ with 0 on-shell or 1 off-shell degree of freedom acquires in total 1 on-shell or 4 off-shell degrees of freedom, turning into a propagating massive field. These basic multiplets are also coupled to chiral multiplets and a supersymmetric Dirac-Born-Infeld action. Some of these results are also reformulated in superspace. The proposed mechanism may well provide a solution to the long-standing puzzle of massless dilatons and second-rank tensors in supersymmetric models inspired by string theory
Stress tensor correlators of CCFT{sub 2} using flat-space holography
Energy Technology Data Exchange (ETDEWEB)
Asadi, Mohammad; Baghchesaraei, Omid; Fareghbal, Reza [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of)
2017-11-15
We use the correspondence between three-dimensional asymptotically flat spacetimes and two-dimensional contracted conformal field theories (CCFTs) to derive the stress tensor correlators of CCFT{sub 2}. On the gravity side we use the metric formulation instead of the Chern-Simons formulation of three-dimensional gravity. This method can also be used for the four-dimensional case, where there is no Chern-Simons formulation for the bulk theory. (orig.)
Stress-tensor OPE in N=2 superconformal theories
International Nuclear Information System (INIS)
Liendo, Pedro; Ramírez, Israel; Seo, Jihye
2016-01-01
We carry out a detailed superspace analysis of the OPE of two N=2 stress-tensor multiplets. Knowledge of the multiplets appearing in the expansion, together with the two-dimensional chiral algebra description of N=2 SCFTs, imply an analytic bound on the central charge c. This bound is valid for any N=2 SCFT regardless of its matter content and flavor symmetries, and is saturated by the simplest Argyres-Douglas fixed point. We also present a partial conformal block analysis for the scalar superconformal primary of the multiplet.
Radiative processes for Rindler and accelerating observers and the stress-tensor detector
International Nuclear Information System (INIS)
Paola, R. De; Svaiter, N.F.
1996-04-01
It is considered a monopole detector interacting with a massive scalar field. Using the rotating wave approximation the radiative processes is discussed from the accelerated frame point of view. After this, it is obtained the Minkowski vacuum stress tensor measured by the accelerated observer using a non-gravitational stress sensor detector. Finally we analyse radiative processes of the monopole detector travelling in a world line that is inertial in the infinite past and has a constant proper acceleration in the infinite future. (author). 30 refs
Tensor gauge field localization on a string-like defect
Sousa, L. J. S.; Cruz, W. T.; Almeida, C. A. S.
2012-05-01
This work is devoted to the study of tensor gauge fields on a string-like defect in six dimensions. This model is very successful in localizing fields of various spins only by gravitational interaction. Due to problems of field localization in membrane models we are motivated to investigate if a string-like defect localizes the Kalb-Ramond field. In contrast to what happens in Randall-Sundrum and thick brane scenarios we find a localized zero mode without the addition of other fields in the bulk. Considering the local string defect we obtain analytical solutions for the massive modes. Also, we take the equations of motion in a supersymmetric quantum mechanics scenario in order to analyze the massive modes. The influence of the mass as well as the angular quantum number in the solutions is described. An additional analysis on the massive modes is performed by the Kaluza-Klein decomposition, which provides new details about the KK masses.
A new deteriorated energy-momentum tensor
International Nuclear Information System (INIS)
Duff, M.J.
1982-01-01
The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)
International Nuclear Information System (INIS)
Christensen, S.M.
1976-01-01
A method known as covariant geodesic point separation is developed to calculate the vacuum expectation value of the stress tensor for a massive scalar field in an arbitrary gravitational field. The vacuum expectation value will diverge because the stress-tensor operator is constructed from products of field operators evaluated at the same space-time point. To remedy this problem, one of the field operators is taken to a nearby point. The resultant vacuum expectation value is finite and may be expressed in terms of the Hadamard elementary function. This function is calculated using a curved-space generalization of Schwinger's proper-time method for calculating the Feynman Green's function. The expression for the Hadamard function is written in terms of the biscalar of geodetic interval which gives a measure of the square of the geodesic distance between the separated points. Next, using a covariant expansion in terms of the tangent to the geodesic, the stress tensor may be expanded in powers of the length of the geodesic. Covariant expressions for each divergent term and for certain terms in the finite portion of the vacuum expectation value of the stress tensor are found. The properties, uses, and limitations of the results are discussed
A Review of Tensors and Tensor Signal Processing
Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.
Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.
Minamitsuji, Masato
2014-01-01
We investigate the quasinormal modes of a test massless, minimally coupled scalar field on a static and spherically symmetric black hole in the scalar-tensor theory with field derivative coupling to the Einstein tensor, which is a part of the Horndeski theory with the shift symmetry. In our solution, the spacetime is asymptotically AdS (anti-de Sitter), where the effective AdS curvature scale is determined solely by the derivative coupling constant. The metric approaches the AdS spacetime in ...
Realizability conditions for the turbulent stress tensor in large-eddy simulation
Vreman, A.W.; Geurts, Bernardus J.; Kuerten, Johannes G.M.
1994-01-01
The turbulent stress tensor in large-eddy simulation is examined from a theoretical point of view. Realizability conditions for the components of this tensor are derived, which hold if and only if the filter function is positive. The spectral cut-off, one of the filters frequently used in large-eddy
Characteristics of the Residual Stress tensor when filter width is larger than the Ozmidov scale
de Bragança Alves, Felipe Augusto; de Bruyn Kops, Stephen
2017-11-01
In stratified turbulence, the residual stress tensor is statistically anisotropic unless the smallest resolved length scale is smaller than the Ozmidov scale and the buoyancy Reynolds number is sufficiently high for there to exist a range of scales that is statistically isotropic. We present approximations to the residual stress tensor that are derived analytically. These approximations are evaluated by filtering data from direct numerical simulations of homogeneous stratified turbulence, with unity Prandtl number, resolved on up to 8192 × 8192 × 4096 grid points along with an isotropic homogeneous case resolved on 81923 grid points. It is found that the best possible scaling of the strain rate tensor yields a residual stress tensor (RST) that is less well statistically aligned with the exact RST than a randomly generated tensor. It is also found that, while a scaling of the strain rate tensor can dissipate the right amount of energy, it produces incorrect anisotropic dissipation, removing energy from the wrong components of the velocity vector. We find that a combination of the strain rate tensor and a tensor related to energy redistribution caused by a Newtonian fluid viscous stress yields an excellent tensorial basis for modelling the RST.
Frames, the Loewner order and eigendecomposition for morphological operators on tensor fields
van de Gronde, Jasper; Roerdink, Jos B. T. M.
2014-01-01
Rotation invariance is an important property for operators on tensor fields, but up to now, most methods for morphology on tensor fields had to either sacrifice rotation invariance, or do without the foundation of mathematical morphology: a lattice structure. Recently, we proposed a framework for
Membrane stress tensor in the presence of lipid density and composition inhomogeneities.
Bitbol, A-F; Peliti, L; Fournier, J-B
2011-05-01
We derive the expression of the stress tensor for one- and two-component lipid membranes with density and composition inhomogeneities. We first express the membrane stress tensor as a function of the free-energy density by means of the principle of virtual work. We then apply this general result to a monolayer model which is shown to be a local version of the area-difference elasticity (ADE) model. The resulting stress tensor expression generalizes the one associated with the Helfrich model, and can be specialized to obtain the one associated with the ADE model. Our stress tensor directly gives the force exchanged through a boundary in a monolayer with density and composition inhomogeneities. Besides, it yields the force density, which is also directly obtained in covariant formalism. We apply our results to study the forces induced in a membrane by a local perturbation.
Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields
International Nuclear Information System (INIS)
Anco, Stephen C.
2003-01-01
A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here
On the energy-momentum tensors for field theories in spaces with affine connection and metric
International Nuclear Information System (INIS)
Manoff, S.
1991-01-01
Generalized covariant Bianchi type identities are obtained and investigated for Lagrangian densities, depending on co- and contravariant tensor fields and their first and second covariant derivatives in spaces with affine connection and metric (L n -space). The notions of canonical, generalized canonical, symmetric and variational energy-momentum tensor are introduced and necessary and sufficient conditions for the existence of the symmetric energy-momentum tensor as a local conserved quantity are obtained. 19 refs.; 1 tab
Migration transformation of two-dimensional magnetic vector and tensor fields
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2012-01-01
We introduce a new method of rapid interpretation of magnetic vector and tensor field data, based on ideas of potential field migration which extends the general principles of seismic and electromagnetic migration to potential fields. 2-D potential field migration represents a direct integral...... to the downward continuation of a well-behaved analytical function. We present case studies for imaging of SQUID-based magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from magnetic tensor field migration agree very well with both Euler deconvolution and the known...
The fermionic energy-momentum tensor in terms of currents in an external gauge field
International Nuclear Information System (INIS)
Bos, M.
1986-01-01
It is shown that for two-dimensional massless Dirac fields interacting with external gauge fields, the energy-momentum tensor can be expressed in terms of the current via the Sugawara-Sommerfield formula. (orig.)
Field of a charged particle in a scalar-tensor theory of gravitation
Reddy, D. R. K.; Vidyasagar, T.; Satyanarayana, B.
2012-11-01
Field equations in the scalar-tensor theory of gravitation, proposed by Saez and Ballester (Phys. Lett. A 113: 467, 1986), are obtained for a static charged point mass with the aid of a spherically symmetric metric. A closed form exact solution of the field equations is presented and may be considered as describing the field due to a charged mass point at the origin surrounded by a scalar-tensor field.
Renormalized Stress-Energy Tensor of an Evaporating Spinning Black Hole.
Levi, Adam; Eilon, Ehud; Ori, Amos; van de Meent, Maarten
2017-04-07
We provide the first calculation of the renormalized stress-energy tensor (RSET) of a quantum field in Kerr spacetime (describing a stationary spinning black hole). More specifically, we employ a recently developed mode-sum regularization method to compute the RSET of a minimally coupled massless scalar field in the Unruh vacuum state, the quantum state corresponding to an evaporating black hole. The computation is done here for the case a=0.7M, using two different variants of the method: t splitting and φ splitting, yielding good agreement between the two (in the domain where both are applicable). We briefly discuss possible implications of the results for computing semiclassical corrections to certain quantities, and also for simulating dynamical evaporation of a spinning black hole.
Energy-momentum tensor of the gravitational field for material spheres
International Nuclear Information System (INIS)
Sokolov, S.N.
1990-01-01
Density of the energy-momentum tensor of a gravitational field which can be defined in the general relativity theory with the help of ideas of the relativistic gravitational theory is found for the case of material spheres. A relationship of this quantity with the Riemann tensor R αβγδ is discussed
Tensor categories and the mathematics of rational and logarithmic conformal field theory
International Nuclear Information System (INIS)
Huang, Yi-Zhi; Lepowsky, James
2013-01-01
We review the construction of braided tensor categories and modular tensor categories from representations of vertex operator algebras, which correspond to chiral algebras in physics. The extensive and general theory underlying this construction also establishes the operator product expansion for intertwining operators, which correspond to chiral vertex operators, and more generally, it establishes the logarithmic operator product expansion for logarithmic intertwining operators. We review the main ideas in the construction of the tensor product bifunctors and the associativity isomorphisms. For rational and logarithmic conformal field theories, we review the precise results that yield braided tensor categories, and in the rational case, modular tensor categories as well. In the case of rational conformal field theory, we also briefly discuss the construction of the modular tensor categories for the Wess–Zumino–Novikov–Witten models and, especially, a recent discovery concerning the proof of the fundamental rigidity property of the modular tensor categories for this important special case. In the case of logarithmic conformal field theory, we mention suitable categories of modules for the triplet W-algebras as an example of the applications of our general construction of the braided tensor category structure. (review)
arXiv Tensor to scalar ratio from single field magnetogenesis
Giovannini, Massimo
2017-08-10
The tensor to scalar ratio is affected by the evolution of the large-scale gauge fields potentially amplified during an inflationary stage of expansion. After deriving the exact evolution equations for the scalar and tensor modes of the geometry in the presence of dynamical gauge fields, it is shown that the tensor to scalar ratio is bounded from below by the dominance of the adiabatic contribution and it cannot be smaller than one thousands whenever the magnetogenesis is driven by a single inflaton field.
Point defects dynamics in a stress field
International Nuclear Information System (INIS)
Smetniansky de De Grande, Nelida.
1989-01-01
The dependence of anisotropic defect diffusion on stress is studied for a hexagonal close packed (hcp) material under irradiation and uniaxially stressed. The diffusion is described as a discrete process of thermally activated jumps. It is shown that the presence of an external stress field enhances the intrinsic anisotropic diffusion, being this variation determined by the defect dipole tensors' symmetry in the equilibrium and saddle point configurations. Also, the point defect diffusion equations to sinks, like edge dislocations and spherical cavities, are solved and the sink strengths are calculated. The conclusion is that the dynamics of the interaction between defects and sinks is controlled by the changes in diffusivity induced by stress fields. (Author) [es
Analytic continuation of tensor fields along geodesics by means of covariant Taylor series
International Nuclear Information System (INIS)
Tsirulev, A.N.
1995-01-01
It is shown that covariant derivatives of all orders of arbitrary tensor field, curvature and torsion on a submanifold in the directions of normal geodesics to the submanifold, together with analytical conditions, define the tensor field in a normal neighbourhood of the submanifold introduced analogously to a normal neighbourhood of a point, by means of Taylor series with tensor coefficients. Evident formulae defined a recurrent procedure for calculation of the series coefficient in any order are obtain. Particular cases of the expansions of a pseudo-Riemannian metric by relation to the metric connection without torsion are considered for a point and a hypersurface. 6 refs
New topological invariants for non-abelian antisymmetric tensor fields from extended BRS algebra
International Nuclear Information System (INIS)
Boukraa, S.; Maillet, J.M.; Nijhoff, F.
1988-09-01
Extended non-linear BRS and Gauge transformations containing Lie algebra cocycles, and acting on non-abelian antisymmetric tensor fields are constructed in the context of free differential algebras. New topological invariants are given in this framework. 6 refs
On the equivalence among stress tensors in a gauge-fluid system
Mitra, Arpan Krishna; Banerjee, Rabin; Ghosh, Subir
2017-12-01
In this paper, we bring out the subtleties involved in the study of a first-order relativistic field theory with auxiliary field variables playing an essential role. In particular, we discuss the nonisentropic Eulerian (or Hamiltonian) fluid model. Interactions are introduced by coupling the fluid to a dynamical Maxwell (U(1)) gauge field. This dynamical nature of the gauge field is crucial in showing the equivalence, on the physical subspace, of the stress tensor derived from two definitions, i.e. the canonical (Noether) one and the symmetric one. In the conventional equal-time formalism, we have shown that the generators of the space-time transformations obtained from these two definitions agree modulo the Gauss constraint. This equivalence in the physical sector has been achieved only because of the dynamical nature of the gauge fields. Subsequently, we have explicitly demonstrated the validity of the Schwinger condition. A detailed analysis of the model in lightcone formalism has also been done where several interesting features are revealed.
Beijeren, H. van
1984-01-01
It is conjectured that the large values at intermediate times of the stress tensor autocorrelation function, found in computer simulations, may be caused by a coupling of the stress tensor to pairs of slowly decaying extended heat modes of large wave number. Approximate expressions, amenable to
Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows
Vermeulen, B.; Hoitink, A.J.F.; Sassi, M.G.
2011-01-01
We introduce a new technique to measure profiles of each term in the Reynolds stress tensor using coupled acoustic Doppler current profilers (ADCPs). The technique is based on the variance method which is extended to the case with eight acoustic beams. Methods to analyze turbulence from a single
Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography
International Nuclear Information System (INIS)
Christensen, Morten H.; Hartong, Jelle; Obers, Niels A.; Rollier, Blaise
2014-01-01
For a specific action supporting z=2 Lifshitz geometries we identify the Lifshitz UV completion by solving for the most general solution near the Lifshitz boundary. We identify all the sources as leading components of bulk fields which requires a vielbein formalism. This includes two linear combinations of the bulk gauge field and timelike vielbein where one asymptotes to the boundary timelike vielbein and the other to the boundary gauge field. The geometry induced from the bulk onto the boundary is a novel extension of Newton-Cartan geometry that we call torsional Newton-Cartan (TNC) geometry. There is a constraint on the sources but its pairing with a Ward identity allows one to reduce the variation of the on-shell action to unconstrained sources. We compute all the vevs along with their Ward identities and derive conditions for the boundary theory to admit conserved currents obtained by contracting the boundary stress-energy tensor with a TNC analogue of a conformal Killing vector. We also obtain the anisotropic Weyl anomaly that takes the form of a Hořava-Lifshitz action defined on a TNC geometry. The Fefferman-Graham expansion contains a free function that does not appear in the variation of the on-shell action. We show that this is related to an irrelevant deformation that selects between two different UV completions
Noether symmetries, energy-momentum tensors, and conformal invariance in classical field theory
International Nuclear Information System (INIS)
Pons, Josep M.
2011-01-01
In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. With this baggage on board, we next discuss in detail, for Poincare invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of Poincare symmetries and it is a basic ingredient of the generators of other eventual spacetime symmetries which may happen to exist. Instead, Hilbert tensors are the means to test whether a theory contains other spacetime symmetries beyond Poincare. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincare invariant Lagrangians, that the realization of scale invariance selects a unique Hilbert tensor which allows for an easy test as to whether conformal invariance is also realized. Finally we make some basic remarks on metric generally covariant theories and classical field theory in a fixed curved background.
Ducasse, Éric; Yaacoubi, Slah
2010-01-01
A tensor Hankel transform (THT) is defined for vector fields, such as displacement, and second-order tensor fields, such as stress or strain. The THT establishes a bijection between the real space and the wave-vector domain, and, remarkably, cannot be reduced to a scalar transform applied separately to each component. One of the advantages of this approach is that some standard elasticity problems can be concisely rewritten by applying this tensor integral transform coupled with an azimuthal Fourier series expansion. A simple and compact formulation of the boundary conditions is also achieved. Thanks to the THT, we obtain for each azimuthal wavenumber and each azimuthal direction exactly the same wave equation as for a standard 2D model of elastic wave propagation. Thus, waves similar to the standard plane P, SV and SH waves are naturally found. Lastly, the THT is used to calculate the ultrasonic field in an isotropic cylindrical leaky waveguide, the walls of which radiating into a surrounding elastic medium, by using a standard scattering approach.
The existence of a symmetric stress tensor in a non-local description of continuum mechanics
Schwarz, G.
1993-12-01
Among the foundations of continuum mechanics is the description of the constitutive forces in terms of a symmetric tensor. Noll showed that this is a consequence of the axiom of material frame indifference, what in turn means a local invariance of the system under the Euclidean group. Here we will prove, in order to obtain the same result, that the assumption of locality in this axiom is redundant. We model a non-local system by means of a virtual work principle. Under the global demand that the corresponding functional does not respond on rigid infinitesimal motions, we show the existence of a symmetric stress tensor as a local result.
Study of the tensor correlation in oxygen isotopes using mean-field-type and shell model methods
International Nuclear Information System (INIS)
Sugimoto, Satoru
2007-01-01
The tensor force plays important roles in nuclear structure. Recently, we have developed a mean-field-type model which can treat the two-particle-two-hole correlation induced by the tensor force. We applied the model to sub-closed-shell oxygen isotopes and found that an sizable attractive energy comes from the tensor force. We also studied the tensor correlation in 16O using a shell model including two-particle-two-hole configurations. In this case, quite a large attractive energy is obtained for the correlation energy from the tensor force
Pajevic, Sinisa; Aldroubi, Akram; Basser, Peter J
2002-01-01
The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.
Naohito, NAKAZAWA; Research Institute for Theoretical Physics Hiroshima University
1985-01-01
We formulate a field-theoretical method at finite temperature to calculate a thermal energy-momentum tensor in arbitrary curved space-times using a momentum-space representation of the thermal Green's function in terms of Riemann normal coordinates. In particular, the thermal energy-momentum tensor for a massive scalar field is calculated by the high-temperature expansion. A locally observed temperature is obtained by requiring the conservation law of the thermal energy-momentum tensor.
Four-point correlation function of stress-energy tensors in N=4 superconformal theories
Korchemsky, G P
2015-01-01
We derive the explicit expression for the four-point correlation function of stress-energy tensors in four-dimensional N=4 superconformal theory. We show that it has a remarkably simple and suggestive form allowing us to predict a large class of four-point correlation functions involving the stress-energy tensor and other conserved currents. We then apply the obtained results on the correlation functions to computing the energy-energy correlations, which measure the flow of energy in the final states created from the vacuum by a source. We demonstrate that they are given by a universal function independent of the choice of the source. Our analysis relies only on N=4 superconformal symmetry and does not use the dynamics of the theory.
International Nuclear Information System (INIS)
Iwanicki, T.; Maurer, W.; Heinz, W.
1983-01-01
For the calculation of mechanical properties of large magnet systems in 3-dimensional space, a very fine subdivision of the magnet structure is necessary. In the finite element programmes, this will lead to unacceptable long computing times and to the limits of computer-storage capacity. This limitation requires a simplification of the structure model. This problem can be solved by the numerical method, called ''numerical simulation'', by which an effective elasticity tensor will be obtained for a composite material. The structure has to perform a homogeneity condition, i.e. it must be possible to define a ''representative volume element'' (RVE). With the effective elasticity tensor, which can be found for such RVE, it is possible to calculate the average stress and with the interpolation of a surface displacement also the peak stresses in each point of the structure. A good agreement is found between experimental and theoretical moduli of elasticity. (author)
Visualizing MR diffusion tensor fields by dynamic fiber tracking and uncertainty mapping
Ehricke, HH; Klose, U; Grodd, W
Recent advances in magnetic resonance imaging have provided methods for the acquisition of high-resolution diffusion tensor fields. Their 3D-visualization with streamline-based techniques-called fiber tracking-allow analysis of cerebral white matter tracts for diagnostic, therapeutic as well as
An analysis of the intermediate field theory of T{sup 4} tensor model
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Viet Anh [Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris 11, Bat 210, Faculté des Sciences, Orsay Cedex, 91405 (France); IPhT, Institut de Physique Théorique, CEA/DSM/IPhT, CEA/Saclay,Orme des Merisiers batiment 774, Point courrier 136, Gif-sur-Yvette Cedex, 91191 (France); LAREMA, CNRS UMR 6093, Université d’Anger, Département de mathématiques,Faculté des Sciences, 2 Boulevard Lavoisier, Angers, 49045 (France); Dartois, Stéphane [Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris 11, Bat 210, Faculté des Sciences, Orsay Cedex, 91405 (France); LIPN, Institut Galilée, CNRS UMR, Université Paris 13,99 avenue Jean Baptiste Clément, Villetaneuse, 93430 (France); Eynard, Bertrand [IPhT, Institut de Physique Théorique, CEA/DSM/IPhT, CEA/Saclay,Orme des Merisiers batiment 774, Point courrier 136, Gif-sur-Yvette Cedex, 91191 (France); Centre de Recherches Mathématiques, Université de Montréal, Pavillon André-Aisenstadt,2920, Chemin de la tour, bur. 5357, Montréal, Québec, H3T 1J4 (Canada)
2015-01-07
In this paper we analyze the multi-matrix model arising from the intermediate field representation of the tensor model with all quartic melonic interactions. We derive the saddle point equation and the Schwinger-Dyson constraints. We then use them to describe the leading and next-to-leading eigenvalues distribution of the matrices.
Lattice energy-momentum tensor from the Yang-Mills gradient flow -- inclusion of fermion fields
Makino, Hiroki; Suzuki, Hiroshi
2014-01-01
Local products of fields deformed by the so-called Yang--Mills gradient flow become renormalized composite operators. This fact has been utilized to construct a correctly normalized conserved energy--momentum tensor in the lattice formulation of the pure Yang--Mills theory. In the present paper, this construction is further generalized for vector-like gauge theories containing fermions.
Two-Dimensional Interactions in a Class of Tensor Gauge Fields from Local BRST Cohomology
Babalic, E M; Cioroianu, E M; Negru, I; Sararu, S C
2003-01-01
Lagrangian interactions in a class of two-dimensional tensor gauge field theory are derived by means of deforming the solution to the master equation with specific cohomological techniques. Both the gauge transformations and their algebra are deformed. The gauge algebra of the coupled model is open.
Estimation of the magnetic field gradient tensor using the Swarm constellation
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Finlay, Chris; Olsen, Nils
2014-01-01
For the first time, part of the magnetic field gradient tensor is estimated in space by the Swarm mission. We investigate the possibility of a more complete estimation of the gradient tensor exploiting the Swarm constellation. The East-West gradients can be approximated by observations from...... the lower pair of Swarm satellites, whereas the North-South gradients can be approximated by the first differences in the along-track direction. As a preliminary test, here we will present an analysis of along track differences of CHAMP vector observations. These show considerably smaller standard...
International Nuclear Information System (INIS)
Adler, S.L.; Lieberman, J.
1978-01-01
We reanalyze the problem of regularization of the stress-energy tensor for massless vector particles propating in a general background metric, using covariant point separation techniques applied to the Hadamard elementary solution. We correct an error, point out by Wald, in the earlier formulation of Adler, Lieberman, and Ng, and find a stress-energy tensor trace anomaly agreeing with that found by other regularization methods
Large tensor mode, field range bound and consistency in generalized G-inflation
Energy Technology Data Exchange (ETDEWEB)
Kunimitsu, Taro; Suyama, Teruaki; Watanabe, Yuki; Yokoyama, Jun' ichi, E-mail: kunimitsu@resceu.s.u-tokyo.ac.jp, E-mail: suyama@resceu.s.u-tokyo.ac.jp, E-mail: watanabe@resceu.s.u-tokyo.ac.jp, E-mail: yokoyama@resceu.s.u-tokyo.ac.jp [Research Center for the Early Universe, Graduate School of Science, The University of Tokyo, Tokyo 113-0033 (Japan)
2015-08-01
We systematically show that in potential driven generalized G-inflation models, quantum corrections coming from new physics at the strong coupling scale can be avoided, while producing observable tensor modes. The effective action can be approximated by the tree level action, and as a result, these models are internally consistent, despite the fact that we introduced new mass scales below the energy scale of inflation. Although observable tensor modes are produced with sub-strong coupling scale field excursions, this is not an evasion of the Lyth bound, since the models include higher-derivative non-canonical kinetic terms, and effective rescaling of the field would result in super-Planckian field excursions. We argue that the enhanced kinetic term of the inflaton screens the interactions with other fields, keeping the system weakly coupled during inflation.
Large tensor mode, field range bound and consistency in generalized G-inflation
International Nuclear Information System (INIS)
Kunimitsu, Taro; Suyama, Teruaki; Watanabe, Yuki; Yokoyama, Jun'ichi
2015-01-01
We systematically show that in potential driven generalized G-inflation models, quantum corrections coming from new physics at the strong coupling scale can be avoided, while producing observable tensor modes. The effective action can be approximated by the tree level action, and as a result, these models are internally consistent, despite the fact that we introduced new mass scales below the energy scale of inflation. Although observable tensor modes are produced with sub-strong coupling scale field excursions, this is not an evasion of the Lyth bound, since the models include higher-derivative non-canonical kinetic terms, and effective rescaling of the field would result in super-Planckian field excursions. We argue that the enhanced kinetic term of the inflaton screens the interactions with other fields, keeping the system weakly coupled during inflation
Stress field reconstruction in an active mudslide
Baroň, Ivo; Kernstocková, Markéta; Melichar, Rostislav
2017-07-01
Meso-scale structures from gravitational slope deformation observed in landslides and deep-seated gravitational slope failures are very similar to those of endogenous ones. Therefore we applied palaeostress analysis of fault-slip data for reconstructing the stress field of an active mudslide in Pechgraben, Austria. This complex compound landslide has developed in clayey colluvium and shale and was activated after a certain period of dormancy in June 2013. During the active motion on June 12, 2013, 73 fault-slip traces at 9 locations were measured within the landslide body. The heterogeneous fault-slip data were processed in term of palaeostresses, the reconstructed palaeostress tensor being characterized by the orientations of the three principal stress axes and the stress ratio (which provides the shape of the stress ellipsoid). The results of the palaeostress analysis were compared to airborne laser scan digital terrain models that revealed dynamics and superficial displacements of the moving mass prior and after our survey. The results were generally in good agreement with the observed landslide displacement pattern and with the anticipated stress regime according to Mohr-Coulomb failure criteria and Anderson's theory. The compressional regime was mostly registered at the toe in areas, where a compressional stress field is expected during previous mass-movement stages, or at margins loaded by subsequent landslide bodies from above. On the other hand, extension regimes were identified at the head scarps of secondary slides, subsequently on bulged ridges at the toe and in the zone of horst-and-graben structures in the lower central part of the main landslide body, where the basal slip surface probably had locally convex character. Strike-slip regimes, as well as oblique normal or oblique reverse regimes were observed at the lateral margins of the landslide bodies. The directions of principal stresses could be used as markers of landslide movement directions
International Nuclear Information System (INIS)
Beleggia, M.; Graef, M. de
2003-01-01
A method is presented to compute the demagnetization tensor field for uniformly magnetized particles of arbitrary shape. By means of a Fourier space approach it is possible to compute analytically the Fourier representation of the demagnetization tensor field for a given shape. Then, specifying the direction of the uniform magnetization, the demagnetizing field and the magnetostatic energy associated with the particle can be evaluated. In some particular cases, the real space representation is computable analytically. In general, a numerical inverse fast Fourier transform is required to perform the inversion. As an example, the demagnetization tensor field for the tetrahedron will be given
Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector
Wu, Jie-Zhi; Zhou, Ye; Wu, Jian-Ming
1996-01-01
We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and computation may be achieved. For turbulent flows, this strategy immediately implies that a given Reynolds stress model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds stress tensor can be reduced to that of the mean turbulent Lamb vector alone, which is much simpler. As a first step of this alternative modeling development, we derive the governing equations for the Lamb vector and its square. These equations form a basis of new second-order closure schemes and, we believe, should be favorably compared to that of traditional Reynolds stress transport equation.
Notes on Translational and Rotational Properties of Tensor Fields in Relativistic Quantum Mechanics
Dvoeglazov, V. V.
Recently, several discussions on the possible observability of 4-vector fields have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 fundamental field. We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We study the massless limits. In fact, a theoretical motivation for this venture is the old papers of Ogievetskiĭ and Polubarinov, Hayashi, and Kalb and Ramond. Ogievetskiĭ and Polubarinov proposed the concept of the notoph, whose helicity properties are complementary to those of the photon. We analyze the quantum field theory with taking into account mass dimensions of the notoph and the photon. It appears to be possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the general relativity. Thus, in fact we deduced the gravitational field equations from relativistic quantum mechanics. The relations of this theory with the scalar-tensor theories of gravitation and f(R) are discussed. Particular attention has been paid to the correct definitions of the energy-momentum tensor and other Nöther currents in the electromagnetic theory, the relativistic theory of gravitation, the general relativity, and their generalizations. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph, and we conclude that they can probably be seen in experiments in the next few years.
Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity
Sato, N.; Yoshida, Z.
2018-02-01
Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.
The total energy-momentum tensor for electromagnetic fields in a dielectric
Crenshaw, Michael E.
2017-08-01
Radiation pressure is an observable consequence of optically induced forces on materials. On cosmic scales, radiation pressure is responsible for the bending of the tails of comets as they pass near the sun. At a much smaller scale, optically induced forces are being investigated as part of a toolkit for micromanipulation and nanofabrication technology [1]. A number of practical applications of the mechanical effects of light-matter interaction are discussed by Qiu, et al. [2]. The promise of the nascent nanophotonic technology for manufacturing small, low-power, high-sensitivity sensors and other devices has likely motivated the substantial current interest in optical manipulation of materials at the nanoscale, see, for example, Ref. [2] and the references therein. While substantial progress toward optical micromanipulation has been achieved, e.g. optical tweezers [1], in this report we limit our consideration to the particular issue of optically induced forces on a transparent dielectric material. As a matter of electromagnetic theory, these forces remain indeterminate and controversial. Due to the potential applications in nanotechnology, the century-old debate regarding these forces, and the associated momentums, has ramped up considerably in the physics community. The energy-momentum tensor is the centerpiece of conservation laws for the unimpeded, inviscid, incompressible flow of non-interacting particles in the continuum limit in an otherwise empty volume. The foundations of the energy-momentum tensor and the associated tensor conservation theory come to electrodynamics from classical continuum dynamics by applying the divergence theorem to a Taylor series expansion of a property density field of a continuous flow in an otherwise empty volume. The dust tensor is a particularly simple example of an energy-momentum tensor that deals with particles of matter in the continuum limit in terms of the mass density ρm, energy density ρmc 2 , and momentum density
Tensor hierarchy and generalized Cartan calculus in SL(3)×SL(2) exceptional field theory
Energy Technology Data Exchange (ETDEWEB)
Hohm, Olaf; Wang, Yi-Nan [Center for Theoretical Physics, Massachusetts Institute of Technology,77 Massachusetts Avenue, Cambridge, MA 02139 (United States)
2015-04-10
We construct exceptional field theory for the duality group SL(3)×SL(2). The theory is defined on a space with 8 ‘external’ coordinates and 6 ‘internal’ coordinates in the (3,2) fundamental representation, leading to a 14-dimensional generalized spacetime. The bosonic theory is uniquely determined by gauge invariance under generalized external and internal diffeomorphisms. The latter invariance can be made manifest by introducing higher form gauge fields and a so-called tensor hierarchy, which we systematically develop to much higher degree than in previous studies. To this end we introduce a novel Cartan-like tensor calculus based on a covariant nil-potent differential, generalizing the exterior derivative of conventional differential geometry. The theory encodes the full D=11 or type IIB supergravity, respectively.
Directory of Open Access Journals (Sweden)
C. Musumeci
1997-06-01
Full Text Available Fault-plane solutions of some tens of local earthquakes which occurred at Mt. Etna volcano during 1983-1986 have been inverted for stress tensor parameters by the algorithm of Gephart and Forsyth (1984. Three seismic sequences were focused on which respectively occurred during a flank eruption (June 1983, just after the end of a subterminal eruption (October 1984 and during an inter-eruptive period (May 1986. The application to the three sets of data of both the "approximate" and the "exact" methods evidenced the stability of results, and the stress directions are well defined in spite of the small number of events used for the inversion. The s1 obtained agrees with the regional tectonic framework, nearly horizontal and oriented N-S, only in the shallow crust, and just after the 1984 eruption. This supports the hypothesis of a tectonic control on the end of the eruptive activities at Mt. Etna. Conversely, results concerning the depth range 10-30 km are in apparent disagreement with other investigations (Cocina et al., 1997, as well as with the regional tectonics. The stress was here found homogeneous, but with s1 respectively trending ENE-WSW (June 1983 and E-W (May 1986. We suggest that the stress field could be temporarily modified by a local stress regime driven by the intrusion of uprising magma.
Energy momentum tensor and marginal deformations in open string field theory
International Nuclear Information System (INIS)
Sen, Ashoke
2004-01-01
Marginal boundary deformations in a two dimensional conformal field theory correspond to a family of classical solutions of the equations of motion of open string field theory. In this paper we develop a systematic method for relating the parameter labelling the marginal boundary deformation in the conformal field theory to the parameter labelling the classical solution in open string field theory. This is done by first constructing the energy-momentum tensor associated with the classical solution in open string field theory using Noether method, and then comparing this to the answer obtained in the conformal field theory by analysing the boundary state. We also use this method to demonstrate that in open string field theory the tachyon lump solution on a circle of radius larger than one has vanishing pressure along the circle direction, as is expected for a co-dimension one D-brane. (author)
International Nuclear Information System (INIS)
Stachel, J.
1977-01-01
A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensor Rsub(μνkappalambda) in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational 'superpotentials' closely connected with the Komar conservation laws (Phys. Rev.; 113:934 (1959)). Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational 'superpotentials'. (author)
Wu, Bofeng; Huang, Chao-Guang
2018-04-01
The 1 /r expansion in the distance to the source is applied to the linearized f (R ) gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular momentum in the gravitational waves are provided for linearized f (R ) gravity. All of these results have two parts, which are associated with the tensor part and the scalar part in the multipole expansion of linearized f (R ) gravity, respectively. The former is the same as that in General Relativity, and the latter, as the correction to the result in General Relativity, is caused by the massive scalar degree of freedom and plays an important role in distinguishing General Relativity and f (R ) gravity.
Earthquakes focal mechanism and stress field pattern in the northeastern part of Egypt
Directory of Open Access Journals (Sweden)
Emad K. Mohamed
2015-12-01
The inversion technique scheme is used also in the present study for determining the regional stress field parameters for earthquake focal mechanism solutions based on the grid search method of Gephart and Forsyth (1984. The Results of the stress tensor using focal mechanisms of recent earthquakes show a prevailed tension stress field in N52°E, N41°E and N52°E for the northern Red Sea, Gulf of Suez and Gulf of Aqaba zone respectively.
Tao, Chenyang; Nichols, Thomas E; Hua, Xue; Ching, Christopher R K; Rolls, Edmund T; Thompson, Paul M; Feng, Jianfeng
2017-01-01
We propose a generalized reduced rank latent factor regression model (GRRLF) for the analysis of tensor field responses and high dimensional covariates. The model is motivated by the need from imaging-genetic studies to identify genetic variants that are associated with brain imaging phenotypes, often in the form of high dimensional tensor fields. GRRLF identifies from the structure in the data the effective dimensionality of the data, and then jointly performs dimension reduction of the covariates, dynamic identification of latent factors, and nonparametric estimation of both covariate and latent response fields. After accounting for the latent and covariate effects, GRLLF performs a nonparametric test on the remaining factor of interest. GRRLF provides a better factorization of the signals compared with common solutions, and is less susceptible to overfitting because it exploits the effective dimensionality. The generality and the flexibility of GRRLF also allow various statistical models to be handled in a unified framework and solutions can be efficiently computed. Within the field of neuroimaging, it improves the sensitivity for weak signals and is a promising alternative to existing approaches. The operation of the framework is demonstrated with both synthetic datasets and a real-world neuroimaging example in which the effects of a set of genes on the structure of the brain at the voxel level were measured, and the results compared favorably with those from existing approaches. Copyright © 2016. Published by Elsevier Inc.
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.
International Nuclear Information System (INIS)
Barber, D.P.
2015-10-01
I extend and update earlier work, summarised in an earlier paper (D.P. Barber, M. Voigt, AIP Conference Proceedings 1149 (28)), whereby the invariant polarisation-tensor field (ITF) for deuterons in storage rings was introduced to complement the invariant spin field (ISF). Taken together, the ITF and the ISF provide a definition of the equilibrium spin density-matrix field which, in turn, offers a clean framework for describing equilibrium spin-1 ensembles in storage rings. I show how to construct the ITF by stroboscopic averaging, I give examples, I discuss adiabatic invariance and I introduce a formalism for describing the effect of noise and damping.
International Nuclear Information System (INIS)
Bull, James N.; Fitchett, Christopher M.; Tennant, W. Craighead
2010-01-01
This paper reports the determination of the electric-field-gradient and mean-squared-displacement tensors in 57 Fe symmetry-related sites of 1-bar Laue class in monoclinic FeCl 2 .4H 2 O at room temperature by single-crystal Mössbauer spectroscopy. Contrary to all previous work, the mean-squared-displacement matrix (tensor), , is not constrained to be isotropic resulting in the determination of physically meaningful estimates of microscopic (local) electric-field gradient (efg) and tensors. As a consequence of anisotropy in the tensor the absorber recoilless fractions are also anisotropic. As expected of a low-symmetry site, Laue class 1-bar in this case, no two principal axes of the efg and tensors are coaxial, within the combined errors in the two. Further, no principal direction of the efg tensor seems related to bond directions in the unit cell. Within error, and in agreement with an earlier study of sodium nitroprusside, it appears that the tensor principal directions lie close to the crystallographic axes suggesting that they are determined by long wavelength (phonon) vibrations in the crystal rather than by approximate local symmetry about the 57 Fe nucleus. Concurrent with the Mössbauer measurements, we determined as part of a new X-ray structural determination, precise atomic displacement parameters (ADPs) leading to an alternative determination of the matrix (tensor). The average of the eigenvalues of the Mössbauer-determined exceeds that of the average of the X-ray-determined eigenvalues by a factor of around 2.2. Assuming isotropic absorber recoilless fractions leads to substantially the same (macroscopic) efg tensor as had been determined in earlier work. Taking 1/3 x the trace of the anisotropic absorber recoilless fractions leads to an isotropic value of 0.304 in good agreement with earlier single crystal studies where isotropy was assumed.
International Nuclear Information System (INIS)
Beig, Robert; Krammer, Werner
2004-01-01
For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York
Stress field modelling from digital geological map data
Albert, Gáspár; Barancsuk, Ádám; Szentpéteri, Krisztián
2016-04-01
To create a model for the lithospheric stress a functional geodatabase is required which contains spatial and geodynamic parameters. A digital structural-geological map is a geodatabase, which usually contains enough attributes to create a stress field model. Such a model is not accurate enough for engineering-geological purposes because simplifications are always present in a map, but in many cases maps are the only sources for a tectonic analysis. The here presented method is designed for field geologist, who are interested to see the possible realization of the stress field over the area, on which they are working. This study presents an application which can produce a map of 3D stress vectors from a kml-file. The core application logic is implemented on top of a spatially aware relational database management system. This allows rapid and geographically accurate analysis of the imported geological features, taking advantage of standardized spatial algorithms and indexing. After pre-processing the map features in a GIS, according to the Type-Property-Orientation naming system, which was described in a previous study (Albert et al. 2014), the first stage of the algorithm generates an irregularly spaced point cloud by emitting a pattern of points within a user-defined buffer zone around each feature. For each point generated, a component-wise approximation of the tensor field at the point's position is computed, derived from the original feature's geodynamic properties. In a second stage a weighted moving average method calculates the stress vectors in a regular grid. Results can be exported as geospatial data for further analysis or cartographic visualization. Computation of the tensor field's components is based on the implementation of the Mohr diagram of a compressional model, which uses a Coulomb fracture criterion. Using a general assumption that the main principal stress must be greater than the stress from the overburden, the differential stress is
Correlation functions of the chiral stress-tensor multiplet in $ \\mathcal{N}=4 $ SYM
Chicherin, Dmitry; Eden, Burkhard; Heslop, Paul; Korchemsky, Gregory P.; Mason, Lionel; Sokatchev, Emery
2015-01-01
We give a new method for computing the correlation functions of the chiral part of the stress-tensor supermultiplet that relies on the reformulation of N=4 SYM in twistor space. It yields the correlation functions in the Born approximation as a sum of Feynman diagrams on twistor space that involve only propagators and no integration vertices. We use this unusual feature of the twistor Feynman rules to compute the correlation functions in terms of simple building blocks which we identify as a new class of N=4 off-shell superconformal invariants. Making use of the duality between correlation functions and planar scattering amplitudes, we demonstrate that these invariants represent an off-shell generalisation of the on-shell invariants defining tree-level scattering amplitudes in N=4 SYM.
Correlation functions of the chiral stress-tensor multiplet in N=4 SYM
Energy Technology Data Exchange (ETDEWEB)
Chicherin, Dmitry [LAPTH (Laboratoire d’Annecy-le-Vieux de Physique Théorique, UMR 5108),Université de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux (France); Doobary, Reza [Science Laboratories, Mathematics Department, Durham University, South Rd, Durham DH1 3LE (United Kingdom); Eden, Burkhard [Institut für Mathematik und Physik, Humboldt-Universität,Zum großen Windkanal 6, 12489 Berlin (Germany); Heslop, Paul [Science Laboratories, Mathematics Department, Durham University, South Rd, Durham DH1 3LE (United Kingdom); Korchemsky, Gregory P. [Institut de Physique Théorique, Unité Mixte de Recherche du CNRS, UMR 3681,CEA Saclay, 91191 Gif-sur-Yvette Cedex (France); Mason, Lionel [Mathematics Department, Oxford University,Woodstock Road, OX2 6GG (United Kingdom); Sokatchev, Emery [LAPTH (Laboratoire d’Annecy-le-Vieux de Physique Théorique, UMR 5108),Université de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux (France); Physics Department, Theory Unit, CERN,CH -1211, Geneva 23 (Switzerland); Institut Universitaire de France,103, bd Saint-Michel F-75005 Paris (France)
2015-06-29
We give a new method for computing the correlation functions of the chiral part of the stress-tensor supermultiplet that relies on the reformulation of N=4 SYM in twistor space. It yields the correlation functions in the Born approximation as a sum of Feynman diagrams on twistor space that involve only propagators and no integration vertices. We use this unusual feature of the twistor Feynman rules to compute the correlation functions in terms of simple building blocks which we identify as a new class of N=4 off-shell superconformal invariants. Making use of the duality between correlation functions and planar scattering amplitudes, we demonstrate that these invariants represent an off-shell generalisation of the on-shell invariants defining tree-level scattering amplitudes in N=4 SYM.
Hess, Siegfried
2015-01-01
This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...
Jongschaap, R.J.J.
1987-01-01
The so-called generalized Kramers-Kirkwood expression for the average stress tensor of a system of interacting point particles, derived by Bird and Curtiss on using a phase-space-kinetic formalism has been reconsidered from different points of view. First a derivation based upon volume averaging is
Dilaton, antisymmetric tensor and gauge fields in string effective theories at the one-loop level
International Nuclear Information System (INIS)
Mayr, P.; Stieberger, S.
1994-01-01
We investigate the dependence of the gauge couplings on the dilaton field in string effective theories at the one-loop level. First we resolve the discrepancies between statements based on symmetry considerations and explicit calculations in string effective theories on this subject. A calculation of the relevant one-loop scattering amplitudes in string theory gives us further information and allows us to derive the exact form of the corresponding effective lagrangian. In particular there is no dilaton dependent one-loop correction to the holomorphic f - function arising from massive string modes in the loop. In addition we address the coupling of the antisymmetric tensor field to the gauge bosons at one loop. While the string S-matrix elements are not reproduced using the usual supersymmetric lagrangian with the chiral superfield representation for the dilaton field, the analogue lagrangian with the dilaton in a linear multiplet naturally gives the correct answer. (orig.)
International Nuclear Information System (INIS)
Joglekar, S.D.; Misra, A.
1989-01-01
In this paper, we generalize our earlier discussion of renormalization of the energy-momentum tensor in scalar QED to that in non-Abelian gauge theories involving scalar fields. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be derived from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/)
International Nuclear Information System (INIS)
Ikhdair, Sameer M.; Hamzavi, Majid
2013-01-01
Approximate analytical solutions of the Dirac equation for Tietz—Hua (TH) potential including Coulomb-like tensor (CLT) potential with arbitrary spin—orbit quantum number κ are obtained within the Pekeris approximation scheme to deal with the spin—orbit coupling terms κ(κ ± 1)r −2 . Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov—Uvarov (NU) method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated. (general)
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning. Written in Python, it aims at following the same standard adopted by the main projects of the Python scientific community and fully integrating with these. It allows for fast and straightforward tensor d...
Stress tensor and viscosity of water: Molecular dynamics and generalized hydrodynamics results
Bertolini, Davide; Tani, Alessandro
1995-08-01
The time correlation functions (CF's) of diagonal and off-diagonal components of the stress tensor of water have been calculated at 245 and 298 K in a molecular dynamics (MD) study on 343 molecules in the microcanonical ensemble. We present results obtained at wave number k=0 and at a few finite values of k, in the atomic and molecular formalism. In all cases, more than 98% of these functions are due to the potential term of the stress tensor. At k=0, their main features are a fast oscillatory initial decay, followed by a long-time tail more apparent in the supercooled region. Bulk and shear viscosities, calculated via Green-Kubo integration of the relevant CF at k=0, are underestimated with respect to experimental data, mainly at low temperature, but their ratio (~=2) is correctly reproduced. Both shear and bulk viscosity decrease as a function of k, the latter more rapidly, so that they become almost equal at ~=1 Å-1. Also, both viscosities drop rapidly from their maximum at ω=0. This behavior has been related to the large narrowing observed in the acoustic band, mainly in the supercooled region. The infinite frequency bulk and shear rigidity moduli have been shown to be in fair agreement with the experimental data, provided the MD value used for comparison is that corresponding to the frequency range relevant to ultrasonic measurements. The MD results of stress-stress CF's compare well with those predicted by Bertolini and Tani [Phys. Rev. E 51, 1091 (1995)] at k=0, by an application of generalized hydrodynamics [de Schepper et al., Phys. Rev. A 38, 271 (1988)] in the molecular formalism, to the same model of water (TIP4P) [Jorgensen et al., J. Chem. Phys. 79, 926 (1983)]. These CF's are essentially equal in the atomic and molecular formalism, the only minor difference being restricted to the high frequency librational region of the shear function. By a comparison of atomic and molecular results, we show here that neglecting libration has no effect on the
Dudarev, S. L.; Ma, Pui-Wai
2018-03-01
Density functional theory (DFT) calculations show that self-interstitial atom (SIA) defects in nonmagnetic body-centered-cubic (bcc) metals adopt strongly anisotropic configurations, elongated in the direction [S. Han et al., Phys. Rev. B 66, 220101 (2002), 10.1103/PhysRevB.66.220101; D. Nguyen-Manh et al., Phys. Rev. B 73, 020101 (2006), 10.1103/PhysRevB.73.020101; P. M. Derlet et al., Phys. Rev. B 76, 054107 (2007), 10.1103/PhysRevB.76.054107; S. L. Dudarev, Annu. Rev. Mater. Res. 43, 35 (2013), 10.1146/annurev-matsci-071312-121626]. Elastic distortions, associated with such anisotropic atomic structures, appear similar to distortions around small prismatic dislocation loops, although the extent of this similarity has never been quantified. We derive analytical formulas for the dipole tensors of SIA defects, which show that, in addition to the prismatic dislocation looplike character, the elastic field of a SIA defect also has a significant isotropic dilatation component. Using empirical potentials and DFT calculations, we parametrize dipole tensors of defects for all the nonmagnetic bcc transition metals. This enables a quantitative evaluation of the energy of elastic interaction between the defects, which also shows that in a periodic three-dimensional simple cubic arrangement of crowdions, long-range elastic interactions between a defect and all its images favor a orientation of the defect.
Hamilton, Nicholas; Cal, Raúl Bayoán
2015-01-01
A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear stress - v w ¯ . The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds stress anisotropy tensor (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy tensor are composed with the eigenvalues yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates trends in the streamwise coordinate following the rotors, especially trailing the top-tip of the rotor and below the hub. Direction of rotation of rotor blades is shown by the orientation of characteristic spheroids according to principle axes. In the inflows of exit row turbines, the normalized Reynolds stress anisotropy tensor shows cumulative effects of the upstream turbines, tending toward prolate shapes for uniform rotational sense, oblate spheroids for streamwise organization of rotational senses, and a mixture of characteristic shapes when the rotation varies by row. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean
Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI
Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.
2015-01-01
Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085
Currents and the energy-momentum tensor in classical field theory: a fresh look at an old problem
International Nuclear Information System (INIS)
Forger, Michael; Roemer, Hartmann
2004-01-01
We give a comprehensive review of various methods to define currents and the energy-momentum tensor in classical field theory, with emphasis on a geometric point of view. The necessity of 'improving' the expressions provided by the canonical Noether procedure is addressed and given an adequate geometric framework. The main new ingredient is the explicit formulation of a principle of 'ultralocality' with respect to the symmetry generators, which is shown to fix the ambiguity inherent in the procedure of improvement and guide it towards a unique answer: when combined with the appropriate splitting of the fields into sectors, it leads to the well-known expressions for the current as the variational derivative of the matter field Lagrangian with respect to the gauge field and for the energy-momentum tensor as the variational derivative of the matter field Lagrangian with respect to the metric tensor. In the second case, the procedure is shown to work even when the matter field Lagrangian depends explicitly on the curvature, thus establishing the correct relation between scale invariance, in the form of local Weyl invariance 'on shell', and tracelessness of the energy-momentum tensor, required for a consistent definition of the concept of a conformal field theory
Bossa, Matías Nicolás; Zacur, Ernesto; Olmos, Salvador
2009-01-01
Tensor-based morphometry (TBM) is an analysis technique where anatomical information is characterized by means of the spatial transformations between a customized template and observed images. Therefore, accurate inter-subject non-rigid registration is an essential prerrequisite. Further statistical analysis of the spatial transformations is used to highlight some useful information, such as local statistical differences among populations. With the new advent of recent and powerful non-rigid registration algorithms based on the large deformation paradigm, TBM is being increasingly used. In this work we evaluate the statistical power of TBM using stationary velocity field diffeomorphic registration in a large population of subjects from Alzheimer's Disease Neuroimaging Initiative project. The proposed methodology provided atrophy maps with very detailed anatomical resolution and with a high significance compared with results published recently on the same data set.
Direct tensor rendering using a bidirectional reflectance model
Nagasawa, Mikio; Suzuki, Yoshio
2000-02-01
For the multi variable volumetric tensor field visualization, an efficient direct rendering technique without using geometrical primitive is proposed. The bi- directional reflectance shading model is used to map the anisotropy stress shear tensor components in direct volume rendering. We model the sub-pixel-sized microfacet at tensor sampling points. The nine component of 3D tensor field are mapped onto grid deformation, opacity mapping, color specification, and normal directions of these microfacets. The ray integration is executed though these irregular infinitesimal microfacets distribution. This direct tensor rendering was applied for at-a-glance tensor visualization of earthquake simulation. That realized a view of deformed structure, stress distribution, local shear discontinuity and the shock front, integrated in a single image. The characteristic P- and S-wave modes are distinguished in the rendered earthquake simulations. Compared with the glyph representation of tensor features, the direct tensor rendering gives the general and total image of tensor field even for the low resolution pixel planes, because the sampling object is assumed as infinitesimally small. the computational cost of direct tensor rendering is not so high than that of scalar volume rendering because the modifications are only ins hading calculation but not in the ray integration.
Choi, Bup Kyung; Oh, Tong In; Sajib, Saurav Zk; Kim, Jin Woong; Kim, Hyung Joong; Kwon, Oh In; Woo, Eung Je
2017-04-01
To realistically map the electric fields of biological tissues using a diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT) method to estimate tissue response during electrical stimulation. Imaging experiments were performed using chunks of bovine muscle. Two silver wire electrodes were positioned inside the muscle tissue for electrical stimulation. Electric pulses were applied with a 100-V amplitude and 100-μs width using a voltage stimulator. During electrical stimulation, we collected DT-MREIT data from a 3T magnetic resonance imaging scanner. We adopted the projected current density method to calculate the electric field. Based on the relation between the water diffusion tensor and the conductivity tensor, we computed the position-dependent scale factor using the measured magnetic flux density data. Then, a final conductivity tensor map was reconstructed using the multiplication of the water diffusion tensor and the scale factor. The current density images from DT-MREIT data represent the internal current flows that exist not only in the electrodes but also in surrounding regions. The reconstructed electric filed map from our anisotropic conductivity tensor with the projected current density shows coverage that is more than 2 times as wide, and higher signals in both the electrodes and surrounding tissues, than the previous isotropic method owing to the consideration of tissue anisotropy. An electric field map obtained by an anisotropic reconstruction method showed different patterns from the results of the previous isotropic reconstruction method. Since accurate electric field mapping is important to correctly estimate the coverage of the electrical treatment, future studies should include more rigorous validations of the new method through in vivo and in situ experiments.
Continuity equations for bound electromagnetic field and the electromagnetic energy-momentum tensor
International Nuclear Information System (INIS)
Kholmetskii, A L; Missevitch, O V; Yarman, T
2011-01-01
We analyze the application of the Poynting theorem to the bound (velocity-dependent) electromagnetic (EM) field and show that an often-used arbitrary elimination of the term of self-interaction in the product j·E (where j is the current density and E the electric field) represents, in general, an illegitimate operation, which leads to incorrect physical consequences. We propose correct ways of eliminating the terms of self-interaction from the Poynting theorem to transform it into the form that is convenient for problems with bound EM field, which yield the continuity equations for the proper EM energy density, the interaction part of EM energy density and the total EM energy density of bound fields, respectively. These equations indicate the incompleteness of the common EM energy-momentum tensor, and in our analysis, we find a missed term in its structure, which makes its trace non-vanished. Some implications of these results are discussed, in particular, in view of the notion of EM mass of charged particles.
Continuity equations for bound electromagnetic field and the electromagnetic energy-momentum tensor
Energy Technology Data Exchange (ETDEWEB)
Kholmetskii, A L [Department of Physics, Belarusian State University, 4 Nezavisimosti Avenue, 220030 Minsk (Belarus); Missevitch, O V [Institute for Nuclear Problems, Belarusian State University, 11 Bobruiskaya Street, 220030 Minsk (Belarus); Yarman, T, E-mail: khol123@yahoo.com [Department of Engineering, Okan University, Akfirat, Istanbul, Turkey and Savronik, Eskisehir (Turkey)
2011-05-01
We analyze the application of the Poynting theorem to the bound (velocity-dependent) electromagnetic (EM) field and show that an often-used arbitrary elimination of the term of self-interaction in the product j{center_dot}E (where j is the current density and E the electric field) represents, in general, an illegitimate operation, which leads to incorrect physical consequences. We propose correct ways of eliminating the terms of self-interaction from the Poynting theorem to transform it into the form that is convenient for problems with bound EM field, which yield the continuity equations for the proper EM energy density, the interaction part of EM energy density and the total EM energy density of bound fields, respectively. These equations indicate the incompleteness of the common EM energy-momentum tensor, and in our analysis, we find a missed term in its structure, which makes its trace non-vanished. Some implications of these results are discussed, in particular, in view of the notion of EM mass of charged particles.
International Nuclear Information System (INIS)
Choudhury, Sayantan
2015-01-01
In this paper my prime objective is to explain the generation of large tensor-to-scalar ratio from the single field sub-Planckian inflationary paradigm within Randall–Sundrum (RS) single braneworld scenario in a model independent fashion. By explicit computation I have shown that the effective field theory prescription of brane inflation within RS single brane setup is consistent with sub-Planckian excursion of the inflaton field, which will further generate large value of tensor-to-scalar ratio, provided the energy density for inflaton degrees of freedom is high enough compared to the brane tension in high energy regime. Finally, I have mentioned the stringent theoretical constraint on positive brane tension, cut-off of the quantum gravity scale and bulk cosmological constant to get sub-Planckian field excursion along with large tensor-to-scalar ratio as recently observed by BICEP2 or at least generates the tensor-to-scalar ratio consistent with the upper bound of Planck (2013 and 2015) data and Planck+BICEP2+Keck Array joint constraint
International Nuclear Information System (INIS)
Sohnius, M.; West, P.
1982-01-01
The tensor calculus for the new alternative minimal auxiliary field formulation of N = 1 supergravity is given. It is used to construct the couplings of this formulation of supergravity to matter. These couplings are found to be different, in several respects to those of the old minimal formulation of N = 1 supergravity. (orig.)
Electromagnetic Field Theory in (N+1)-Space-Time : AModern Time-Domain Tensor/Array Introduction
De Hoop, A.T.
2012-01-01
In this paper, a modern time-domain introduction is presented for electromagnetic field theory in (N+1)-spacetime. It uses a consistent tensor/array notation that accommodates the description of electromagnetic phenomena in N-dimensional space (plus time), a requirement that turns up in present-day
International Nuclear Information System (INIS)
Aghazadeh, Mustafa; Mirzaei, Mahmoud
2008-01-01
Hydrogen bond (HB) interactions are studied in the real crystalline structure of sulfamerazine by density functional theory (DFT) calculations of the electric field gradient (EFG) tensors at the sites of O-17, N-14, and H-2 nuclei. One-molecule (single) and four-molecule (cluster) models of sulfamerazine are created by available crystal coordinates and the EFG tensors are calculated in both models to indicate the influence of HB interactions on the tensors. Directly relate to the experiments, the calculated EFG tensors are converted to the experimentally measurable nuclear quadrupole resonance (NQR) parameters, quadrupole coupling constant (qcc) and asymmetry parameter (η Q ). The evaluated NQR parameters reveal that due to contribution of the target molecule to N-H...N and N-H...O types of HB interactions, the EFG tensors at the sites of various nuclei are influenced from single model to the target molecule in cluster. Additionally, O2, N4, and H2 nuclei of the target molecule are significantly influenced by HB interactions, consequently, they have the major contributions to HB interactions in cluster model of sulfamerazine. The calculations are performed employing B3LYP method and 6-311++G** basis set using GAUSSIAN 98 suite of program
Energy Technology Data Exchange (ETDEWEB)
Bongaarts, P.J.M.
1977-07-01
An approach to the investigation of the Maxwell field in the framework of axiomatic quantum field theory is presented which employs Borchers' algebraic reformulation of Wightman theory in a modified form adapted to the special features of the electromagnetic field. This makes it possible to clarify the relation between tensor and potential field operators, the meaning and properties of different gauges, the sense in which field equations hold and the properties of state spaces with their special subspaces.
Anderson, David; Yunes, Nicolás
2017-09-01
Scalar-tensor theories of gravity modify general relativity by introducing a scalar field that couples nonminimally to the metric tensor, while satisfying the weak-equivalence principle. These theories are interesting because they have the potential to simultaneously suppress modifications to Einstein's theory on Solar System scales, while introducing large deviations in the strong field of neutron stars. Scalar-tensor theories can be classified through the choice of conformal factor, a scalar that regulates the coupling between matter and the metric in the Einstein frame. The class defined by a Gaussian conformal factor with a negative exponent has been studied the most because it leads to spontaneous scalarization (i.e. the sudden activation of the scalar field in neutron stars), which consequently leads to large deviations from general relativity in the strong field. This class, however, has recently been shown to be in conflict with Solar System observations when accounting for the cosmological evolution of the scalar field. We here study whether this remains the case when the exponent of the conformal factor is positive, as well as in another class of theories defined by a hyperbolic conformal factor. We find that in both of these scalar-tensor theories, Solar System tests are passed only in a very small subset of coupling parameter space, for a large set of initial conditions compatible with big bang nucleosynthesis. However, while we find that it is possible for neutron stars to scalarize, one must carefully select the coupling parameter to do so, and even then, the scalar charge is typically 2 orders of magnitude smaller than in the negative-exponent case. Our study suggests that future work on scalar-tensor gravity, for example in the context of tests of general relativity with gravitational waves from neutron star binaries, should be carried out within the positive coupling parameter class.
Levashov, V A
2016-03-07
It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids' structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ1 ≥ λ2 ≥ λ3 ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ2/λ1) and (λ3/λ2) are essentially identical to each other in the liquids state. We also found that λ2 tends to be equal to the geometric average of λ1 and λ3. In our view, correlations between the eigenvalues may represent "the Poisson ratio effect" at the atomic scale.
Higher groupoid bundles, higher spaces, and self-dual tensor field equations
Energy Technology Data Exchange (ETDEWEB)
Jurco, Branislav [Charles University in Prague, Faculty of Mathematics and Physics, Mathematical Institute, Prague (Czech Republic); Saemann, Christian [Maxwell Institute for Mathematical Sciences, Department of Mathematics, Heriot-Watt University, Edinburgh (United Kingdom); Wolf, Martin [Department of Mathematics, University of Surrey, Guildford (United Kingdom)
2016-08-15
We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general class of (higher) spaces comprising presentable differentiable stacks, as e.g. orbifolds. We start off with a self-contained review on simplicial sets as models of (∞, 1)-categories. We then discuss principal bundles in terms of simplicial maps and their homotopies. We explain in detail a differentiation procedure, suggested by Severa, that maps higher groupoids to L{sub ∞}-algebroids. Generalising this procedure, we define connections for higher groupoid bundles. As an application, we obtain six-dimensional superconformal field theories via a Penrose-Ward transform of higher groupoid bundles over a twistor space. This construction reduces the search for non-Abelian self-dual tensor field equations in six dimensions to a search for the appropriate (higher) gauge structure. The treatment aims to be accessible to theoretical physicists. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Equations of motion for anisotropic nonlinear elastic continuum in gravitational field
International Nuclear Information System (INIS)
Sokolov, S.N.
1994-01-01
Equations of motion for anisotropic nonlinear elastic continuum in the gravitational field are written in the form convenient for numerical calculations. The energy-stress tensor is expressed through scalar and tensor products of three vectors frozen in the continuum. Examples of expansion of the energy-stress tensor into scalar and tensor invariants corresponding to some crystal classes are given. 47 refs
Bossa, Matias; Zacur, Ernesto; Olmos, Salvador
2010-07-01
Tensor-based morphometry (TBM) is an analysis technique where anatomical information is characterized by means of the spatial transformations mapping a customized template with the observed images. Therefore, accurate inter-subject non-rigid registration is an essential prerequisite for both template estimation and image warping. Subsequent statistical analysis on the spatial transformations is performed to highlight voxel-wise differences. Most of previous TBM studies did not explore the influence of the registration parameters, such as the parameters defining the deformation and the regularization models. In this work performance evaluation of TBM using stationary velocity field (SVF) diffeomorphic registration was performed in a subset of subjects from Alzheimer's Disease Neuroimaging Initiative (ADNI) study. A wide range of values of the registration parameters that define the transformation smoothness and the balance between image matching and regularization were explored in the evaluation. The proposed methodology provided brain atrophy maps with very detailed anatomical resolution and with a high significance level compared with results recently published on the same data set using a non-linear elastic registration method. Copyright (c) 2010 Elsevier Inc. All rights reserved.
On the large N limit, Wilson Loops, Confinement and Composite Antisymmetric Tensor Field theories
Castro, C
2004-01-01
A novel approach to evaluate the Wilson loops asociated with a $ SU ( \\infty )$ gauge theory in terms of pure string degrees of freedom is presented. It is based on the Guendelman-Nissimov-Pacheva formulation of composite antisymmetric tensor field theories of area (volume ) preserving diffeomorphisms which admit $p$-brane solutions and which provide a $new$ route to scale symmetry breaking and confinement in Yang-Mills theory. The quantum effects are discussed and we evaluate the vacuum expectation values (vev) of the Wilson loops in the large $N$ limit of the $quenched$ reduced $SU(N)$ Yang-Mills theory in terms of a path integral involving pure string degrees of freedom. The $quenched$ approximation is necessary to avoid a crumpling of the string world-sheet giving rise to very large Hausdorff dimensions as pointed out by Olesen. The approach is also consistent with the recent results based on the AdS/CFT correspondence and dual QCD models (dual Higgs model with dual Dirac strings ). More general Loop wav...
Tensor spherical harmonics and tensor multipoles. II. Minkowski space
International Nuclear Information System (INIS)
Daumens, M.; Minnaert, P.
1976-01-01
The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation
Stress field of a dislocating inclined fault
Energy Technology Data Exchange (ETDEWEB)
Huang, F.; Wang, T.
1980-02-01
Analytical expressions are derived for the stress field caused by a rectangular dislocating fault of an arbitrary dip in a semi-infinite elastic medium for the case of unequal Lame constants. The results of computations for the stress fields on the ground surface of an inclined strike-slip and an inclined dip-slip fault are represented by contour maps. The effects of Poisson Ratio of the medium, the dip angle, upper and lower boundaries of the faults on the stress field at surface have been discussed. As an application, the contour maps for shear stress and hydrostatic stress of near fields of the Tonghai (1970), Haicheng (1975) and Tangshan (1976) earthquakes have been calculated and compared with the spatial distributions of strong aftershocks of these earthquakes. It is found that most of the strong aftershocks are distributed in the regions of tensional stress, where the hydrostatic stress is positive.
Stress field of a dislocating inclined fault
Energy Technology Data Exchange (ETDEWEB)
Huang, F.; Wang, T.
1980-02-01
In this paper, analytical expressions of the stress field given rise by a rectangular dislocating fault of an arbitrary dip in a semi-infinite elastic medium for the case of unequal Lame constants are derived. The results of computations for the stress fields on the ground surface of an inclined strike-slip and an inclined dip-slip fault are represented by contour maps. The effects of the Poisson Ratio of the medium, the dip angle, upper and lower boundaries of the faults on the stress field at the surface have been discussed. As an application, the contour maps for shear stress and hydrostatic stress of near fields of the Tonghai (1970), Haicheng, (1975) and Tangshan (1976) earthquakes have been calculated and compared with the spatial distributions of strong aftershocks of these earthquakes. It is found that most of the strong aftershocks are distributed in the regions of tensional stress where the hydrostatic stress is positive.
Global Geopotential Energy & Stress Field
DEFF Research Database (Denmark)
Schiffer, Christian; Nielsen, S.B.
and stress induced geological structures. Quantifying single stress sources however remains a difficult and not uncommonly vague procedure. Modelling stress contributions can provide principle insight into the total and relative stress composition. One contribution is the internal gravitational stress...... in the lithosphere, induced by lateral density variation. The leading quantity is the Geopotential Energy, the integrated lithostatic pressure in a rock column, which is related to horizontal stresses by the Equations of Equilibrium. The Geopotential Energy can be furthermore linearly related to the Geoid under...... of the oceanic lithosphere. An entire modelling of the shallow Geopotential Energy is hereby approached, not taking into account possible deeper signals but all lithospheric signals for the subsequent stress calculation. Therefore a global lithospheric density model is necessary to calculate the corresponding...
Jenkins, Samantha; Blancafort, Lluís; Kirk, Steven R; Bearpark, Michael J
2014-04-21
New insights into the double bond isomerization of fulvene in the ground and excited electronic states are provided by newly developed QTAIM and stress tensor tools. The S0 and S1 states follow the 'biradical' torsion model, but the double bond is stiffer in the S0 state; by contrast, the S2 state follows the 'zwitterionic' torsion. Differences are explained in terms of the ellipticity and bond critical point (BCP) stiffness for both QTAIM and the stress tensor. Overall, the wave-function based analysis is found to be in agreement with the work of Bonačić-Koutecký and Michl that the bond-twisted species can have biradical or zwitterionic character, depending on the state. Using QTAIM and the stress tensor a new understanding of bond torsion is revealed; the electronic charge density around the twisted bond is found not to rotate in concert with the nuclei of the rotated -CH2 methylene group. The ability to visualize how the bond stiffness varies between individual electronic states and how this correlates with the QTAIM and stress tensor bond stiffness is highlighted. In addition, the most and least preferred morphologies of bond-path torsion are visualized. Briefly we discuss the prospects for using this new QTAIM and stress tensor analysis for excited state chemistry.
A Test for Tensor Lorentz Violating Fields Using a Rotating Comagnetometer
Smiciklas, Marc; Brown, Justin; Romalis, Michael
2011-05-01
The effective low-energy model of Lorentz violation described by the Standard Model Extension (SME) includes a number of tensor spin interactions that violate Lorentz symmetry but not CPT. Such interactions could be induced in popular Lorentz-violating theories, such as Horava theory of gravity and doubly-special relativity. We are performing a search for Lorentz-violating tensor spin interactions using a K-Rb-21Ne comagnetometer. Compared to our previous work with a K-3He comagnetometer, we expect to achieve significant improvements in energy sensitivity due to the smaller magnetic moment of 21Ne and use of hybrid optical pumping. Preliminary results searching for semisidereal modulations of the comagnetometer signal indicate that limits on tensor Lorentz violation can be improved by more than an order of magnitude. This research funded by NSF grant PHY-0969862
De Hoop, A.T.; Abubakar, A.; Habashy, T.M.
2009-01-01
The contrast-source stress-velocity integral-equation formulation of three-dimensional time-domain elastodynamic scattering problems is discussed. A novel feature of the formulation is a tensor partitioning of the relevant dynamic stress and the contrast source volume density of deformation rate.
Visualizing Tensor Normal Distributions at Multiple Levels of Detail.
Abbasloo, Amin; Wiens, Vitalis; Hermann, Max; Schultz, Thomas
2016-01-01
Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.
International Nuclear Information System (INIS)
Witalis, E.A.
1965-12-01
Rigorous derivations are given of the basic equations and methods available for the analysis of transverse MHD flow when Hall currents are not suppressed. The gas flow is taken to be incompressible and viscous with uniform tensor conductivity and arbitrary magnetic Reynold's number. The magnetic field is perpendicular to the flow and has variable strength. Analytical solutions can be obtained either in terms of the induced magnetic field or from two types of electric potential. The relevant set of suitable simplifications, restrictive conditions and boundary value considerations for each method is given
International Nuclear Information System (INIS)
Antoci, S.; Mihich, L.
1997-01-01
Given the present status of the problem of the electromagnetic energy tensor in matter, there is perhaps use in recalling a forgotten argument given in 1923 by W. Gordon. Let us consider a material medium which is homogeneous and isotropic when observed in its rest frame. For such a medium, Gordon's argument allows to reduce the above-mentioned problem to an analogous one, defined in a general relativistic vacuum. For the latter problem the form of the Lagrangian is known already, hence the determination of the energy tensor is a straightforward matter. One just performs the Hamiltonian derivative of the Lagrangian chosen in this way with respect to the true metric g ik . Abraham's tensor is thus selected as the electromagnetic energy tensor for a medium which is homogeneous and isotropic in its rest frame
Analysis and interpretation of stress indicators in deviated wells of the Coso Geothermal Field
Schoenball, Martin; Glen, Jonathan M. G.; Davatzes, Nicholas C.
2016-04-01
Characterizing the tectonic stress field is an integral part for the development of hydrothermal systems, especially enhanced geothermal systems (EGS). With a known stress field, critically stressed faults can be identified. Faults that are critically oriented with respect to the in-situ stress field exhibit a high tendency for slip, and thus are likely candidates for reactivation during the creation of an EGS. Reactivated faults are known to serve as dominant fluid pathways during hydrothermal circulation and the characteristics of this process determine the potential for damaging earthquakes; should extensive portions of well-oriented, large features be reactivated. As part of the FORGE initiative at the West Flank of the Coso Geothermal Field, we analyze a large set of image logs obtained from wells distributed across the geothermal field for details about the stress state revealed by indicators such as borehole breakouts and drilling-induced tensile fractures. Previous stress analyses at Coso have ignored deviated well sections, since their interpretation for the orientation of the stress tensor is non-unique with respect to varying stress magnitudes. Using interpreted borehole-induced structures, we perform a grid search over all possible Andersonian stress states and find a best fitting vertical stress tensor for each stress state characterized by principal stress magnitudes. By including deviated well sections and recently drilled wells, we considerably expand the suite of stress measurements in the Coso Geothermal Field. Along individual wells, this analysis also reveals local meter length-scale deviations from the best-fitting mean stress orientation. While most wells show consistent horizontal principal stress orientations with standard deviations of about 10°, other wells show large standard deviations on the order of 25°. Several regions have logged well trajectories with lateral spacing below 1 km. This enables us to trace changes of the stress
Soibelman, Yan
1997-01-01
We introduce the notion of meromorphic tensor category and illustrate it in several examples. They include representations of quantum affine algebras, chiral algebras of Beilinson and Drinfeld, G-vertex algebras of Borcherds, and representations of GL over a local field. Hopefully the formalism will accomodate various tensor structures arising in relation to the quantized Knizhnik-Zamolodchikov equations and deformed CFT
Bianchi Type-II String Cosmological Model with Magnetic Field in Scalar-tensor Theory of Gravitation
Sharma, N. K.; Singh, J. K.
2015-03-01
The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of scalar-tensor theory of gravitation formulated by Saez and Ballester (Phys. Lett. A 113:467, 1986). With the help of special law of variation for Hubble's parameter proposed by Berman (Nuovo Cimento B 74:182, 1983) string cosmological model is obtained in this theory. Some physical and kinematical properties of the model are also discussed.
Li, Jiahui; Xu, Tianlv; Ping, Yang; van Mourik, Tanja; Früchtl, Herbert; Kirk, Steven R.; Jenkins, Samantha
2018-03-01
QTAIM and the stress tensor were used to provide a detailed analysis of the topology of the molecular graph, BCP and bond-path properties, including the new introduced helicity length H, of a Tyr-Gly dipeptide conformer subjected to a torsion with four levels of theory; MP2, M06-2X, B3LYP-D3 and B3LYP and a modest-sized basis set, 6-31+G(d). Structural effects and bonding properties are quantified and reflect differences in the BSSE and lack of inclusion of dispersion effects in the B3LYP calculations. The helicity length H demonstrated that MP2 produced a unique response to the torsion suggesting future use as a diagnostic tool.
Zhong, Ji-Mao; Cheng, Wan-Zheng
2006-07-01
Based on the spatial orientation and slip direction of the fault plane solutions, we present the expression of corresponding mechanical axis tensor in geographic coordinate system, and then put forward a method for calculating average mechanical axis tensor and its eigenvalues, which involves solving the corresponding eigenequation. The method for deducing mean stress field from T, B, and P axes parameters of a number of focal mechanism solutions has been verified by inverting data of mean stress fields in Fuyun region and in Tangshan region with fitting method of slip direction, and both results are consistent. To study regional average stress field, we need to choose a population of focal mechanism solutions of earthquakes in the massifs where there are significant tectonic structures. According to the focal mechanism solutions of 256 moderate-strong earthquakes occurred in 13 seismic zones of Sichuan-Yunnan region, the quantitative analysis results of stress tensor in each seismic zone have been given. The algorithm of such method is simple and convenient, which makes the method for analyzing tectonic stress field with large amount of focal mechanism solution data become quantified.
Levitas, Valery I; Attariani, Hamed
2013-01-01
Si is a promising anode material for Li-ion batteries, since it absorbs large amounts of Li. However, insertion of Li leads to 334% of volumetric expansion, huge stresses, and fracture; it can be suppressed by utilizing nanoscale anode structures. Continuum approaches to stress relaxation in LixSi, based on plasticity theory, are unrealistic, because the yield strength of LixSi is much higher than the generated stresses. Here, we suggest that stress relaxation is due to anisotropic (tensorial) compositional straining that occurs during insertion-extraction at any deviatoric stresses. Developed theory describes known experimental and atomistic simulation data. A method to reduce stresses is predicted and confirmed by known experiments. Chemical potential has an additional contribution due to deviatoric stresses, which leads to increases in the driving force both for insertion and extraction. The results have conceptual and general character and are applicable to any material systems.
Mapping residual stress fields from Vickers hardness indents using Raman microprobe spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Sparks, R.G.; Enloe, W.S.; Paesler, M.A.
1988-12-01
Micro-Raman spectroscopy is used to map the residual stress fields in the vicinity of Vickers hardness indents. Both 514.5 and 488.0 nm, light is used to excite the effect and the resulting shifted and broadened Raman peaks are analyzed using computer deconvolution. Half-wave plates are used to vary the orientation of the incident later light`s polarization state with respect to crystal orientation. The Raman scattered light is then analyzed for polarization dependences which are indicative of the various components of the Raman scattering tensor. Such studies can yield valuable information about the orientation of stress components in a well known stress field. The results can then be applied to the determination of stress components in machined semiconductor materials.
Moran, S.C.
2003-01-01
The volcanological significance of seismicity within Katmai National Park has been debated since the first seismograph was installed in 1963, in part because Katmai seismicity consists almost entirely of high-frequency earthquakes that can be caused by a wide range of processes. I investigate this issue by determining 140 well-constrained first-motion fault-plane solutions for shallow (depth regions within the park. Earthquakes removed by several kilometers from the volcanic axis occur in a stress field characterized by horizontally oriented ??1 and ??3 axes, with ??1 rotated slightly (12??) relative to the NUVELIA subduction vector, indicating that these earthquakes are occurring in response to regional tectonic forces. On the other hand, stress tensors for earthquake clusters beneath several Katmai cluster volcanoes have vertically oriented ??1 axes, indicating that these events are occuring in response to local, not regional, processes. At Martin-Mageik, vertically oriented ??1 is most consistent with failure under edifice loading conditions in conjunction with localized pore pressure increases associated with hydrothermal circulation cells. At Trident-Novarupta, it is consistent with a number of possible models, including occurence along fractures formed during the 1912 eruption that now serve as horizontal conduits for migrating fluids and/or volatiles from nearby degassing and cooling magma bodies. At Mount Katmai, it is most consistent with continued seismicity along ring-fracture systems created in the 1912 eruption, perhaps enhanced by circulating hydrothermal fluids and/or seepage from the caldera-filling lake.
Tensor surgery and tensor rank
M. Christandl (Matthias); J. Zuiddam (Jeroen)
2018-01-01
textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices
PDX toroidal field coils stress analysis
International Nuclear Information System (INIS)
Nikodem, Z.D.; Smith, R.A.
1975-01-01
A method used in the stress analysis of the PDX toroidal field coil is developed. A multilayer coil design of arbitrary dimensions in the shape of either a circle or an oval is considered. The analytical model of the coil and the supporting coil case with connections to the main support structure is analyzed using the finite element technique. The three dimensional magnetic fields and the non-uniform body forces which are a loading condition on a coil due to toroidal and poloidal fields are calculated. The method of analysis permits rapid and economic evaluations of design changes in coil geometry as well as in coil support structures. Some results pertinent to the design evolution and their comparison are discussed. The results of the detailed stress analysis of the final coil design due to toroidal field, poloidal field and temperature loads are presented
Residual stress field of ballised holes
International Nuclear Information System (INIS)
Lai, Man On; He, Zhimin
2012-01-01
Ballising, involving pushing a slightly over-sized ball made of hard material through a hole, is a kind of cold working process. Applying ballising process to fastener holes produces compressive residual stress on the edge of the holes, and therefore increases the fatigue life of the components or structures. Quantification of the residual stress field is critical to define and precede the ballising process. In this article, the ballised holes are modeled as cold-expanded holes. Elastic-perfectly plastic theory is employed to analyze the holes with cold expansion process. For theoretical simplification, an axially symmetrical thin plate with a cold expanded hole is assumed. The elasticplastic boundaries and residual stress distribution surrounding the cold expanded hole are derived. With the analysis, the residual stress field can be obtained together with actual cold expansion process in which only the diameters of hole before and after cold expansion need to be measured. As it is a non-destructive method, it provides a convenient way to estimate the elastic-plastic boundaries and residual stresses of cold worked holes. The approach is later extended to the case involving two cold-worked holes. A ballised hole is looked upon as a cold expanded hole and therefore is investigated by the approach. Specimens ballised with different interference levels are investigated. The effects of interference levels and specimen size on residual stresses are studied. The overall residual stresses of plates with two ballised holes are obtained by superposing the residual stresses induced on a single ballised hole. The effects of distance between the centers of the two holes with different interference levels on the residual stress field are revealed
DEFF Research Database (Denmark)
Pessah, Martin Elias; Chan, Chi-kwan; Psaltis, Dimitrios
2006-01-01
The magnetorotational instability is thought to be responsible for the generation of magnetohydrodynamic turbulence that leads to enhanced outward angular momentum transport in accretion discs. Here, we present the first formal analytical proof showing that, during the exponential growth...... of the instability, the mean (averaged over the disc scale-height) Reynolds stress is always positive, the mean Maxwell stress is always negative, and hence the mean total stress is positive and leads to a net outward flux of angular momentum. More importantly, we show that the ratio of the Maxwell to the Reynolds...
Lu, Biao; Luo, Zhicai; Zhong, Bo; Zhou, Hao; Flechtner, Frank; Förste, Christoph; Barthelmes, Franz; Zhou, Rui
2017-11-01
Based on tensor theory, three invariants of the gravitational gradient tensor (IGGT) are independent of the gradiometer reference frame (GRF). Compared to traditional methods for calculation of gravity field models based on the gravity field and steady-state ocean circulation explorer (GOCE) data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. The IGGT approach as studied in this paper is a quadratic function of the gravity field model's spherical harmonic coefficients. The linearized observation equations for the least squares method are obtained using a Taylor expansion, and the weighting equation is derived using the law of error propagation. We also investigate the linearization errors using existing gravity field models and find that this error can be ignored since the used a-priori model EIGEN-5C is sufficiently accurate. One problem when using this approach is that it needs all six independent gravitational gradients (GGs), but the components V_{xy} and V_{yz} of GOCE are worse due to the non-sensitive axes of the GOCE gradiometer. Therefore, we use synthetic GGs for both inaccurate gravitational gradient components derived from the a-priori gravity field model EIGEN-5C. Another problem is that the GOCE GGs are measured in a band-limited manner. Therefore, a forward and backward finite impulse response band-pass filter is applied to the data, which can also eliminate filter caused phase change. The spherical cap regularization approach (SCRA) and the Kaula rule are then applied to solve the polar gap problem caused by GOCE's inclination of 96.7° . With the techniques described above, a degree/order 240 gravity field model called IGGT_R1 is computed. Since the synthetic components of V_{xy} and V_{yz} are not band-pass filtered, the signals outside the measurement bandwidth are replaced by the a-priori model EIGEN-5C. Therefore, this model is practically a
Stress tensor analysis in the Taiwan area from focal mechanisms of earthquakes
Yih-Hsiung, Yeh; Eric, Barrier; Cheng-Horng Lin; Jacques, Angelier
1991-12-01
We produce a map of the stress pattern in and around Taiwan based on 200 earthquake focal mechanism solutions. These solutions were determined by using data from Taiwan Telemetered Seismographic Network, microearthquake surveys and WWSSN. The stresses are derived through a minimization of angles between the slip vector and the shear stress on each nodal plane considered as a fault, employing appropriate weighting factors. The whole set of focal mechanisms is divided into several groups, mainly according to apparent clustering of the event locations. The results show that the direction of maximum principal stress in Taiwan area is nearly horizontal and SE-NW on average. This is in good agreement with the direction of relative motion between the Philippine Sea plate and the Eurasian plate. In western Taiwan, the fan-shaped distribution of the maximum principal stress is consistent with the direction of Philippine Sea-Eurasian plate convergence through a simple model of viscous material indented by a rigid wedge. In the northeastern part of Taiwan, a nearly horizontal minimum principal stress oriented N-S is found for shallow depths; it occurs in a region of low seismic velocities, probably related to the back-arc activity of the Okinawa Trough. Down-dip compressional and down-dip extensional stresses have been identified in different depth ranges within the subducting slab of the Philippine Sea plate in the northern Taiwan; this may reflect the slab characteristics in this area. A complex stress pattern prevails in the Hualien area, at the junction between the Ryukyu subduction system and the Taiwan collision zone.
Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdSd space
International Nuclear Information System (INIS)
Buchbinder, I.L.; Krykhtin, V.A.; Ryskina, L.L.
2009-01-01
We apply the BRST approach, developed for higher spin field theories, to Lagrangian construction for totally antisymmetric massive fermionic fields in AdS d space. As well as generic higher spin massive theories, the obtained Lagrangian theory is a reducible gauge model containing, besides the basic field, a number of auxiliary (Stueckelberg) fields and the order of reducibility grows with the value of the rank of the antisymmetric field. However, unlike the generic higher spin theory, for the special case under consideration we show that one can get rid of all the auxiliary fields and the final Lagrangian for fermionic antisymmetric field is formulated only in terms of basic field.
Diffusion tensor image registration using hybrid connectivity and tensor features.
Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang
2014-07-01
Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc.
Evaluation of Bayesian tensor estimation using tensor coherence
Kim, Dae-Jin; Kim, In-Young; Jeong, Seok-Oh; Park, Hae-Jeong
2009-06-01
Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion tensor MRI by interconnecting voxels according to the propagation direction defined by the diffusion tensor. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a tensor estimation method using a Bayesian framework, which includes an a priori probability distribution based on tensor coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed tensor estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic tensor fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple tensor regression.
Evaluation of Bayesian tensor estimation using tensor coherence
Energy Technology Data Exchange (ETDEWEB)
Kim, Dae-Jin; Park, Hae-Jeong [Laboratory of Molecular Neuroimaging Technology, Brain Korea 21 Project for Medical Science, Yonsei University, College of Medicine, Seoul (Korea, Republic of); Kim, In-Young [Department of Biomedical Engineering, Hanyang University, Seoul (Korea, Republic of); Jeong, Seok-Oh [Department of Statistics, Hankuk University of Foreign Studies, Yongin (Korea, Republic of)], E-mail: parkhj@yuhs.ac
2009-06-21
Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion tensor MRI by interconnecting voxels according to the propagation direction defined by the diffusion tensor. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a tensor estimation method using a Bayesian framework, which includes an a priori probability distribution based on tensor coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed tensor estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic tensor fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple tensor regression.
Stress Field and Seismicity in the Basin of Mexico
Huesca-Perez, E.; Quintanar, L.; Garcia-Palomo, A.
2007-12-01
Mexico City is located in the basin of Mexico, inside the so called Trans-Mexican Volcanic Belt. The region in general and the basin in particular, is characterized by local low magnitude seismicity (Mc risk to the city due of the nearness from epicenters. We can distinguish three main areas of local activity: 1).- surrounding the old basin of Texcoco lake, 2)- Chalco and 3)- Juchitepec - Milpa Alta outside Mexico City; the rest of the basin presents lower seismic activity. We recorded and located 336 earthquakes with digital seismograms between 1996 and 2007. From them, just 23 focal mechanisms could be evaluated because of low magnitude that creates recording problems in the seismological networks and high frequency background noise. The focal mechanisms are mainly strike-slip and dip-slip (normal) faulting. We used three different techniques (when possible) to calculate the focal mechanisms: simple and composite first motion focal mechanism, Hash's S/P amplitude rate focal mechanism and time domain moment tensor inversion using broadband three components seismograms. The final goal is to find the local and regional stress field for the whole basin.
Reynolds and Maxwell stress measurements in the reversed field pinch experiment Extrap-T2R
Vianello, N.; Antoni, V.; Spada, E.; Spolaore, M.; Serianni, G.; Cavazzana, R.; Bergsåker, H.; Cecconello, M.; Drake, J. R.
2005-08-01
The complete Reynolds stress (RS) has been measured in the edge region of the Extrap-T2R reversed field pinch experiment. The RS exhibits a strong gradient in the region where a high E × B shear takes place. Experimental results show this gradient to be almost entirely due to the electrostatic contribution. This has been interpreted as experimental evidence of flow generation via turbulence mechanism. The scales involved in flow generation are deduced from the frequency decomposition of RS tensor. They are found related to magnetohydrodynamic activity but are different with respect to the scales responsible for turbulent transport.
Electromagnetic field and mechanical stress analysis code
International Nuclear Information System (INIS)
1978-01-01
Analysis TEXMAGST is a two stage linear finite element code for the analysis of static magnetic fields in three dimensional structures and associated mechanical stresses produced by the anti J x anti B forces within these structures. The electromagnetic problem is solved in terms of magnetic vector potential A for a given current density anti J as curl 1/μ curl anti A = anti J considering the magnetic permeability as constant. The Coulombian gauge (div anti A = o) was chosen and was implemented through the use of Lagrange multipliers. The second stage of the problem - the calculation of mechanical stresses in the same three dimensional structure is solved by using the same code with few modifications - through a restart card. Body forces anti J x anti B within each element are calculated from the solution of the first stage run and represent the input to the second stage run which will give the solution for the stress problem
Tensors and their applications
Islam, Nazrul
2006-01-01
About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces
Gu, Chen; Marzouk, Youssef M.; Toksöz, M. Nafi
2018-03-01
Small earthquakes occur due to natural tectonic motions and are induced by oil and gas production processes. In many oil/gas fields and hydrofracking processes, induced earthquakes result from fluid extraction or injection. The locations and source mechanisms of these earthquakes provide valuable information about the reservoirs. Analysis of induced seismic events has mostly assumed a double-couple source mechanism. However, recent studies have shown a non-negligible percentage of non-double-couple components of source moment tensors in hydraulic fracturing events, assuming a full moment tensor source mechanism. Without uncertainty quantification of the moment tensor solution, it is difficult to determine the reliability of these source models. This study develops a Bayesian method to perform waveform-based full moment tensor inversion and uncertainty quantification for induced seismic events, accounting for both location and velocity model uncertainties. We conduct tests with synthetic events to validate the method, and then apply our newly developed Bayesian inversion approach to real induced seismicity in an oil/gas field in the sultanate of Oman—determining the uncertainties in the source mechanism and in the location of that event.
Charged tensor matter fields and Lorentz symmetry violation via spontaneous symmetry breaking
International Nuclear Information System (INIS)
Colatto, L.P.; Penna, A.L.A.; Santos, W.C.
2003-10-01
We consider a model with a charged vector field along with a Cremmer-Scherk-Kalb-Ramond (CSKR) matter field coupled to a U(1) gauge potential. We obtain a natural Lorentz symmetry violation due to the local U(1) spontaneous symmetry breaking mechanism triggered by the imaginary part of the vector matter. The choice of the unitary gauge leads to the decoupling of the gauge-Kr sector from the Higgs-Kr sector. The excitation spectrum is carefully analyzed and the physical modes are identified. We propose an identification of the neutral massive spin-1 Higgs-like field with the massive Z' boson of the so-called mirror matter models. (author)
Weyl tensors for asymmetric complex curvatures
International Nuclear Information System (INIS)
Oliveira, C.G.
Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt
The 'gravitating' tensor in the dualistic theory
International Nuclear Information System (INIS)
Mahanta, M.N.
1989-01-01
The exact microscopic system of Einstein-type field equations of the dualistic gravitation theory is investigated as well as an analysis of the modified energy-momentum tensor or so called 'gravitating' tensor is presented
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
Roman, D.C.; Moran, S.C.; Power, J.A.; Cashman, K.V.
2004-01-01
We searched for changes in local stress-field orientation at Mount Spurr volcano, Alaska, between August 1991 and December 2001. This study focuses on the stress-field orientation beneath Crater Peak vent, the site of three eruptions in 1992, and beneath the summit of Mount Spurr. Local stress tensors were calculated by inverting subsets of 140 fault-plane solutions for earthquakes beneath Crater Peak and 96 fault-plane solutions for earthquakes beneath Mount Spurr. We also calculated an upper-crustal regional stress tensor by inverting fault-plane solutions for 66 intraplate earthquakes located near Mount Spurr during 1991-2001. Prior to the 1992 eruptions, and for 11 months beginning with a posteruption seismic swarm, the axis of maximum compressive stress beneath Crater Peak was subhorizontal and oriented N67-76??E, approximately perpendicular to the regional axis of maximum compressive stress (N43??W). The strong temporal correlation between this horizontal stress-field rotation (change in position of the ??1/ ??3 axes relative to regional stress) and magmatic activity indicates that the rotation was related to magmatic activity, and we suggest that the Crater Peak stress-field rotation resulted from pressurization of a network of dikes. During the entire study period, the stress field beneath the summit of Mount Spurr also differed from the regional stress tensor and was characterized by a vertical axis of maximum compressive stress. We suggest that slip beneath Mount Spurr's summit occurs primarily on a major normal fault in response to a combination of gravitational loading, hydrothermal circulation, and magmatic processes beneath Crater Peak. Online material: Regional and local fault-plane solutions.
Compartmentalization of the Coso East Flank geothermal field imaged by 3-D full-tensor MT inversion
Lindsey, Nathaniel J.; Kaven, Joern; Davatzes, Nicholas C.; Newman, Gregory A.
2017-01-01
Previous magnetotelluric (MT) studies of the high-temperature Coso geothermal system in California identified a subvertical feature of low resistivity (2–5 Ohm m) and appreciable lateral extent (>1 km) in the producing zone of the East Flank field. However, these models could not reproduce gross 3-D effects in the recorded data. We perform 3-D full-tensor inversion and retrieve a resistivity model that out-performs previous 2-D and 3-D off-diagonal models in terms of its fit to the complete 3-D MT data set as well as the degree of modelling bias. Inclusion of secondary Zxx and Zyy data components leads to a robust east-dip (60†) to the previously identified conductive East Flank reservoir feature, which correlates strongly with recently mapped surface faults, downhole well temperatures, 3-D seismic reflection data, and local microseismicity. We perform synthetic forward modelling to test the best-fit dip of this conductor using the response at a nearby MT station. We interpret the dipping conductor as a fractured and fluidized compartment, which is structurally controlled by an unmapped blind East Flank fault zone.
Compartmentalization of the Coso East Flank geothermal field imaged by 3-D full-tensor MT inversion
Lindsey, Nathaniel J.; Kaven, Joern Ole; Davatzes, Nicholas; Newman, Gregory A.
2017-02-01
Previous magnetotelluric (MT) studies of the high-temperature Coso geothermal system in California identified a subvertical feature of low resistivity (2-5 Ohm m) and appreciable lateral extent (>1 km) in the producing zone of the East Flank field. However, these models could not reproduce gross 3-D effects in the recorded data. We perform 3-D full-tensor inversion and retrieve a resistivity model that out-performs previous 2-D and 3-D off-diagonal models in terms of its fit to the complete 3-D MT data set as well as the degree of modelling bias. Inclusion of secondary Zxx and Zyy data components leads to a robust east-dip (60†) to the previously identified conductive East Flank reservoir feature, which correlates strongly with recently mapped surface faults, downhole well temperatures, 3-D seismic reflection data, and local microseismicity. We perform synthetic forward modelling to test the best-fit dip of this conductor using the response at a nearby MT station. We interpret the dipping conductor as a fractured and fluidized compartment, which is structurally controlled by an unmapped blind East Flank fault zone.
Tensor calculus for physics a concise guide
Neuenschwander, Dwight E
2015-01-01
Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...
Analysis and interpretation of stress indicators in deviated wells of the Coso Geothermal Field
Schoenball, Martin; Glen, Jonathan M. G.; Davatzes, Nicholas C.
2016-01-01
Characterizing the tectonic stress field is an integral part of the development of hydrothermal systems and especially for enhanced geothermal systems (EGS). With a well characterized stress field the propensity of fault slip on faults with known location and orientation can be identified. Faults that are critically oriented for faulting with respect to the stress field are known to provide natural fluid pathways. A high slip tendency makes a fault a likely candidate for reactivation during the creation of an EGS. Similarly, the stress state provides insight for the potential of larger, damaging earthquakes should extensive portions of well-oriented, larger faults be reactivated.The analysis of stress indicators such as drilling-induced fractures and borehole breakouts is the main tool to infer information on the stress state of a geothermal reservoir. The standard procedure is applicable to sub-vertical wellbore sections and highly deviated sections have to be discarded. However, in order to save costs and reduce the environmental impact most recent wells are directionally drilled with deviations that require appropriate consideration of the deviated trajectory. Here we present an analysis scheme applicable to arbitrary well trajectories or a combination of wells to infer the stress state. Through the sampling of the stress tensor along several directions additional information on the stress regime and even relative stress magnitudes can be obtained. We apply this method on image logs from the pair of wells 58-10 and 58A-10 that were drilled from the same well pad. Both wells have image logs of about 2km of their trajectories that are separated by less than 300m. For both wells we obtain a mean orientation of SHmax of N23° with large standard deviations of locations of stress indicators of 24° and 26°, respectively. While the local stress direction is highly variable along both wells with dominant wavelengths from around 50 to 500m, the mean directions are very
Robust tensor estimation in diffusion tensor imaging
Maximov, Ivan I.; Grinberg, Farida; Jon Shah, N.
2011-12-01
The signal response measured in diffusion tensor imaging is subject to detrimental influences caused by noise. Noise fields arise due to various contributions such as thermal and physiological noise and sources related to the hardware imperfection. As a result, diffusion tensors estimated by different linear and non-linear least squares methods in absence of a proper noise correction tend to be substantially corrupted. In this work, we propose an advanced tensor estimation approach based on the least median squares method of the robust statistics. Both constrained and non-constrained versions of the method are considered. The performance of the developed algorithm is compared to that of the conventional least squares method and of the alternative robust methods proposed in the literature. Two examples of simulated diffusion attenuations and experimental in vivo diffusion data sets were used as a basis for comparison. The robust algorithms were shown to be advantageous compared to the least squares method in the cases where elimination of the outliers is desirable. Additionally, the constraints were applied in order to prevent generation of the non-positive definite tensors and reduce related artefacts in the maps of fractional anisotropy. The developed method can potentially be exploited also by other MR techniques where a robust regression or outlier localisation is required.
Energy Technology Data Exchange (ETDEWEB)
Armas-Pérez, Julio C.; Londono-Hurtado, Alejandro [Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637 (United States); Guzmán, Orlando [Departamento de Física, Universidad Autónoma Metropolitana, Iztapalapa, DF 09340, México (Mexico); Hernández-Ortiz, Juan P. [Departamento de Materiales y Minerales, Universidad Nacional de Colombia, Sede Medellín, Medellín (Colombia); Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637 (United States); Pablo, Juan J. de, E-mail: depablo@uchicago.edu [Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637 (United States); Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States)
2015-07-28
A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.
Energy Technology Data Exchange (ETDEWEB)
Armas-Perez, Julio C.; Londono-Hurtado, Alejandro; Guzman, Orlando; Hernandez-Ortiz, Juan P.; de Pablo, Juan J.
2015-07-27
A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.
International Nuclear Information System (INIS)
Rowland, D R
2007-01-01
The physical analysis of a uniformly accelerating point charge provides a rich problem to explore in advanced courses in electrodynamics and relativity since it brings together fundamental concepts in relation to electromagnetic radiation, Einstein's equivalence principle and the inertial mass of field energy in ways that reveal subtleties in each of these concepts. By first exploring the heuristic value of Maxwell's and Faraday's idea that the electromagnetic field is like a stressed material medium, it is shown in this paper that the problem also provides an interesting application of the electromagnetic stress-energy-momentum tensor and that an analysis using this tensor provides clear physical insight into this highly subtle and contentious problem and the so-called '4/3 problem' of classical electromagnetic theory. In particular, it is shown that the stress force on a uniformly accelerating, uniformly charged spherical shell due to its own field is simply the (relativistic) inertial mass of the charge's electrostatic field times the acceleration. Since the inertial mass of the electromagnetic field forms part of the observed rest mass of a charged particle, it is argued that the results are therefore consistent with the Lorentz-Abraham-Dirac equation of motion for an accelerating point charge, which implies that for uniform acceleration, the work done by the force acting on the charge only goes into increasing the kinetic energy of the charge, none goes into the creation of radiation
Buchner, Abel-John; Lozano-Durán, Adrián; Kitsios, Vassili; Atkinson, Callum; Soria, Julio
2016-04-01
Previous works have shown that momentum transfer in the wall-normal direction within turbulent wall-bounded flows occurs primarily within coherent structures defined by regions of intense Reynolds stress [1]. Such structures may be classified into wall-attached and wall-detached structures with the latter being typically weak, small-scale, and isotropically oriented, while the former are larger and carry most of the Reynolds stresses. The mean velocity fluctuation within each structure may also be used to separate structures by their dynamic properties. This study aims to extract information regarding the scales, kinematics and dynamics of these structures within the topological framework of the invariants of the velocity gradient tensor (VGT). The local topological characteristics of these intense Reynolds stress structures are compared to the topological characteristics of vortex clusters defined by the discriminant of the velocity gradient tensor. The alignment of vorticity with the principal strain directions within these structures is also determined, and the implications of these findings are discussed.
Nayak, Avinash; Taira, Taka'aki; Dreger, Douglas S.; Gritto, Roland
2018-04-01
We retrieve empirical Green's functions in the frequency range (˜0.2-0.9 Hz) for interstation distances ranging from ˜1 to ˜30 km (˜0.22 to ˜6.5 times the wavelength) at The Geysers geothermal field, Northern California, from coherency of ambient seismic noise being recorded by a variety of sensors (broad-band, short-period surface and borehole sensors, and one accelerometer). The applied methodology preserves the intercomponent relative amplitudes of the nine-component Green's tensor that allows us to directly compare noise-derived Green's functions (NGFs) with normalized displacement waveforms of complete single-force synthetic Green's functions (SGFs) computed with various 1-D and 3-D velocity models using the frequency-wavenumber integration method and a 3-D finite-difference wave propagation method, respectively. These comparisons provide an effective means of evaluating the suitability of different velocity models to different regions of The Geysers, and assessing the quality of the sensors and the NGFs. In the T-Tangential, R-Radial, Z-Vertical reference frame, the TT, RR, RZ, ZR and ZZ components (first component: force direction, second component: response direction) of NGFs show clear surface waves and even body-wave phases for many station pairs. They are also broadly consistent in phase and intercomponent relative amplitudes with SGFs for the known local seismic velocity structure that was derived primarily from body-wave traveltime tomography, even at interstation distances less than one wavelength. We also find anomalous large amplitudes in TR, TZ, RT and ZT components of NGFs at small interstation distances (≲4 km) that can be attributed to ˜10°-30° sensor misalignments at many stations inferred from analysis of longer period teleseismic waveforms. After correcting for sensor misalignments, significant residual amplitudes in these components for some longer interstation distance (≳8 km) paths are better reproduced by the 3-D velocity
The tectonic stress field evolution of India since the Oligocene
Digital Repository Service at National Institute of Oceanography (India)
Müller, R.D.; Yatheesh, V.; Shuhail, M.
strengths, enabling the modelling of stress field deflections along interfaces between relatively strong and weak tectonic elements through time. At 33 Ma a roughly NNW–SSE oriented band of relatively high maximum horizontal compressive stress (S...
Analysis of fracture patterns and local stress field variations in fractured reservoirs
Deckert, Hagen; Drews, Michael; Fremgen, Dominik; Wellmann, J. Florian
2010-05-01
independently estimated regional stress tensor is put as a boundary condition into the BE Model. The computed BE model allows to recognize local 3D stress tensor perturbations caused by the larger faults that act as mechanical inhomogeneities. The geometry of the fracture network from field work together with the local stress tensors derived from the 3D BE models allows examining normal and shear stresses on single fractures in different domains of the investigated area. This in turn is used to evaluate, which of the fractures might preferably act as fluid conduits by describing the dilation potential of single fractures. The combination of an improved understanding of the fracture network along with local stress tensors variations from mechanical models will provide a sound evaluation of fluid pathways in fractured reservoirs. In future applications the accurate investigation of large discontinuity pattern in outcrops might be used for a better mathematical definition of fracture networks which could be implemented into numerical simulations of fluid flow.
Conformal correlators of mixed-symmetry tensors
Costa, Miguel S
2015-01-01
We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to mixed-symmetry tensors by introducing a new commuting or anticommuting polarization vector for each row or column in the Young diagram that describes the index symmetries of the tensor. We determine the tensor structures that are allowed in n-point conformal correlation functions and give an algorithm for counting them in terms of tensor product coefficients. We show, with an example, how the new formalism can be used to compute conformal blocks of arbitrary external fields for the exchange of any conformal primary and its descendants. The matching between the number of tensor structures in conformal field theory correlators of operators in d dimensions and massive scattering amplitudes in d+1 dimensions is also seen to carry over to mixed-symmetry tensors.
Seif, Dariush; Po, Giacomo; Mrovec, Matous; Lazar, Markus; Elsässer, Christian; Gumbsch, Peter
2015-05-01
The stress fields of dislocations predicted by classical elasticity are known to be unrealistically large approaching the dislocation core, due to the singular nature of the theory. While in many cases this is remedied with the approximation of an effective core radius, inside which ad hoc regularizations are implemented, such approximations lead to a compromise in the accuracy of the calculations. In this work an anisotropic nonsingular elastic representation of dislocation fields is developed to accurately represent the near-core stresses of dislocations in α -iron. The regularized stress field is enabled through the use of a nonsingular Green's tensor function of Helmholtz-type gradient anisotropic elasticity, which requires only a single characteristic length parameter in addition to the material's elastic constants. Using a magnetic bond-order potential to model atomic interactions in iron, molecular statics calculations are performed, and an optimization procedure is developed to extract the required length parameter. Results show the method can accurately replicate the magnitude and decay of the near-core dislocation stresses even for atoms belonging to the core itself. Comparisons with the singular isotropic and anisotropic theories show the nonsingular anisotropic theory leads to a substantially more accurate representation of the stresses of both screw and edge dislocations near the core, in some cases showing improvements in accuracy of up to an order of magnitude. The spatial extent of the region in which the singular and nonsingular stress differ substantially is also discussed. The general procedure we describe may in principle be applied to accurately model the near-core dislocation stresses of any arbitrarily shaped dislocation in anisotropic cubic media.
Geometric decomposition of the conformation tensor in viscoelastic turbulence
Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.
2018-05-01
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.
The Physical Interpretation of the Lanczos Tensor
Roberts, Mark D.
1999-01-01
The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall...
International Nuclear Information System (INIS)
Darling, T.W.; Migliori, A.; Moshopoulou, E.G.; Trugman, S.A.; Neumeier, J.J.; Sarrao, J.L.; Bishop, A.R.; Thompson, J.D.
1998-01-01
We have measured the (cubic-lattice-approximation) elastic moduli of optical melt-zone-grown single-crystal La 0.83 Sr 0.17 MnO 3 using resonant ultrasound spectroscopy. We observe the structural transition at 285 K to be hysteretic in the ambient (almost zero) magnetic field. A second elastic feature at the ferromagnetic T c 265 K, a third at 252 K, and a fourth in magnetic field at 220 K are also observed in this sample, which sits in a particularly complex region in composition space. The application of a magnetic field changes some of the elastic moduli significantly between 220 K and 285 K. By determining the complete elastic tensor, we identify which cubic crystallographic distortions are strongest at each elastic anomaly and which are sensitive to magnetic field. We also determine which bonds play a role in each of the observed features. copyright 1998 The American Physical Society
Phase transition in tensor models
Energy Technology Data Exchange (ETDEWEB)
Delepouve, Thibault [Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris Sud,91405 Orsay Cedex (France); Centre de Physique Théorique, CNRS UMR 7644, École Polytechnique,91128 Palaiseau Cedex (France); Gurau, Razvan [Centre de Physique Théorique, CNRS UMR 7644, École Polytechnique,91128 Palaiseau Cedex (France); Perimeter Institute for Theoretical Physics,31 Caroline St. N, N2L 2Y5, Waterloo, ON (Canada)
2015-06-25
Generalizing matrix models, tensor models generate dynamical triangulations in any dimension and support a 1/N expansion. Using the intermediate field representation we explicitly rewrite a quartic tensor model as a field theory for a fluctuation field around a vacuum state corresponding to the resummation of the entire leading order in 1/N (a resummation of the melonic family). We then prove that the critical regime in which the continuum limit in the sense of dynamical triangulations is reached is precisely a phase transition in the field theory sense for the fluctuation field.
The maximum possible stress intensity factor for a crack in an unknown residual stress field
International Nuclear Information System (INIS)
Coules, H.E.; Smith, D.J.
2015-01-01
Residual and thermal stress fields in engineering components can act on cracks and structural flaws, promoting or inhibiting fracture. However, these stresses are limited in magnitude by the ability of materials to sustain them elastically. As a consequence, the stress intensity factor which can be applied to a given defect by a self-equilibrating stress field is also limited. We propose a simple weight function method for determining the maximum stress intensity factor which can occur for a given crack or defect in a one-dimensional self-equilibrating stress field, i.e. an upper bound for the residual stress contribution to K I . This can be used for analysing structures containing defects and subject to residual stress without any information about the actual stress field which exists in the structure being analysed. A number of examples are given, including long radial cracks and fully-circumferential cracks in thick-walled hollow cylinders containing self-equilibrating stresses. - Highlights: • An upper limit to the contribution of residual stress to stress intensity factor. • The maximum K I for self-equilibrating stresses in several geometries is calculated. • A weight function method can determine this maximum for 1-dimensional stress fields. • Simple MATLAB scripts for calculating maximum K I provided as supplementary material.
Wéber, Zoltán
2016-01-01
We have successfully estimated the full moment tensors of 22 local earthquakes with local magnitude ranging from 1.2 to 4.8 that occurred in the Hungarian part of the Pannonian basin between 1995 and 2014. We used a probabilistic waveform inversion procedure that takes into account the effects of the random noise contained in the seismograms, the uncertainty of the hypocentre determined from arrival times and the inaccurate knowledge of the velocity structure, while estimating the error affecting the derived focal parameters. The applied probabilistic approach maps the posterior probability density functions (PPDFs) for both the hypocentral coordinates and the moment tensor components. The final estimates are given by the maximum likelihood points of the PPDFs, while solution uncertainties are presented by histogram plots. The estimated uncertainties in the moment tensor components are plotted on the focal sphere in such a way, that the significance of the double couple (DC), the compensated linear vector dipole (CLVD) and the isotropic (ISO) parts of the source can be assessed. We have shown that the applied waveform inversion method is equally suitable to recover the source mechanism for low-magnitude events using short-period local waveforms as well as for moderate-size earthquakes using long-period seismograms. The non-DC components of the retrieved focal mechanisms are statistically insignificant for all the analysed earthquakes. The negligible amount of the ISO component implies the tectonic nature of the investigated events. The moment tensor solutions reported by other agencies for five of the ML > 4 earthquakes studied in this paper are very similar to those calculated by the applied waveform inversion algorithm. We have found only strike-slip and thrust faulting events, giving further support to the hypothesis that the Pannonian basin is currently experiencing a compressional regime of deformation. The orientations of the obtained focal mechanisms are in
Energy-Momentum Conservation Laws in Hamiltonian Field Theory
Sardanashvily, G.
1994-01-01
In the Lagrangian field theory, one gets different identities for different stress energy-momentum tensors, e.g., canonical energy-momentum tensors. Moreover, these identities are not conservation laws of the above-mentioned energy-momentum tensors in general. In the framework of the multimomentum Hamiltonian formalism, we have the fundamental identity whose restriction to a constraint space can be treated the energy-momentum conservation law. In standard field models, this appears the metric...
Chicherin, Dmitry
2017-03-09
We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N=4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators differ only slightly from those for the chiral correlators. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper \\cite{PartI}. In this approach only the chiral half of the supersymmetry is manifest. The other half is realized by nonlinear and nonlocal transformations of the LHC superfields. However, at Born level only the simple linear part of the transformations is relevant. It corresponds to effectively working in the self-dual sector of the theory. Our method is also applicable to a wider class of supermultiplets like all the half-BPS operators and the Konishi multiplet.
THE FIELD OF RECENT TECTONIC STRESSES IN CENTRAL AND SOUTH-EASTERN ASIA
Directory of Open Access Journals (Sweden)
Yu. L. Rebetsky
2014-01-01
Full Text Available The publication presents results of the study aimed at reconstruction of recent crustal stresses for Central and South-Eastern Asia with application of the method of cataclastic analysis of displacements caused by ruptures, which was proposed by Yu.L. Rebetsky. Two sources of seismic data were referred to: (1 the catalog comprising data from publications covering the period from 1904 to 1992, and (2 the Global Centroid Moment Tensor (CMT Database of earthquake mechanisms (http://earthquake.usgs.gov/eqarchives/sopor, which covers the period from 1978 to 2010. The method of cataclastic analysis in its earliest version was applied in 1996 and 1997 when seismic data from the first catalog were analyzed, and it yielded only parameters of stress ellipsoids; the reconstructions were published in a Russian-Chinese journal (it does not exist now. In this paper, these reconstructions are presented in new graphical formats of GIS. Data from the Global CMT Database were analyzed by the method of cataclastic analysis in the new revision with application of its stages 1 and 2. Based on the calculations, orientations of axes of principal stresses, types of ellipsoids, correlations between spherical and deviatoric components of stress tensors, and reduced stresses were determined. The two sets of reconstructions are compared in this paper. The catalog of earthquake focal mechanisms for the period from 1904 to 1992 consolidated information provided by different authors, and thus focal data for many seismic events were highly inconsistent; therefore, the reliability of reconstructions based on such data seems to be lower than that on the basis the Global CMT Database for the period from 1978 to 2010. Some of the reconstructed stress tensor parameters are mapped. For the areas which data are given in the Global CMT Database and considered as more reliable, mapping is based on stress parameters calculated from such data. For the areas that are not covered by the
The energy–momentum tensor(s in classical gauge theories
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2016-11-01
Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
The energy–momentum tensor(s) in classical gauge theories
Energy Technology Data Exchange (ETDEWEB)
Blaschke, Daniel N., E-mail: dblaschke@lanl.gov [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Gieres, François, E-mail: gieres@ipnl.in2p3.fr [Institut de Physique Nucléaire de Lyon, Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Bat. P. Dirac, 4 rue Enrico Fermi, F-69622 Villeurbanne (France); Reboud, Méril, E-mail: meril.reboud@ens-lyon.fr [Institut de Physique Nucléaire de Lyon, Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Bat. P. Dirac, 4 rue Enrico Fermi, F-69622 Villeurbanne (France); Ecole Normale Supérieure de Lyon, 46 allée d' Italie, F-69364 Lyon CEDEX 07 (France); Schweda, Manfred, E-mail: mschweda@tph.tuwien.ac.at [Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna (Austria)
2016-11-15
We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
Superposition of Stress Fields in Diametrically Compressed Cylinders
Directory of Open Access Journals (Sweden)
João Augusto de Lima Rocha
Full Text Available Abstract The theoretical analysis for the Brazilian test is a classical plane stress problem of elasticity theory, where a vertical force is applied to a horizontal plane, the boundary of a semi-infinite medium. Hypothesizing a normal radial stress field, the results of that model are correct. Nevertheless, the superposition of three stress fields, with two being based on prior results and the third based on a hydrostatic stress field, is incorrect. Indeed, this work shows that the Cauchy vectors (tractions are non-vanishing in the parallel planes in which the two opposing vertical forces are applied. The aim of this work is to detail the process used in the construction of the theoretical model for the three stress fields used, with the objective being to demonstrate the inconsistency often stated in the literature.
Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...
Tensor Transpose and Its Properties
Pan, Ran
2014-01-01
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.
Colored Tensor Models - a Review
Directory of Open Access Journals (Sweden)
Razvan Gurau
2012-04-01
Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.
The Energy-Momentum Tensor(s) in Classical Gauge Theories
Blaschke, Daniel N.; Gieres, Francois; Reboud, Meril; Schweda, Manfred
2016-01-01
We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from t...
International Nuclear Information System (INIS)
Montesinos, M.; Flores, E.
2006-01-01
The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral Proca field, the same procedure yields also the symmetric energy-momentum tensor. In all cases, the key point to get the right expressions for the energy-momentum tensors is the appropriate handling of their equations of motion and the Bianchi identities. It must be stressed that these results are obtained without using Belinfante's symmetrization techniques which are usually employed to this end. (Author)
Investigations of some rock stress measuring techniques and the stress field in Norway
Energy Technology Data Exchange (ETDEWEB)
Hanssen, Tor Harald
1997-12-31
Rock stresses are important to the safe construction and operation of all man-made structures in rock, whether In mining, civil or petroleum engineering. The crucial issue is their relative magnitude and orientation. This thesis develops equipment and methods for further rock stress assessment and reevaluates existing overcoring rock stress measurements, and relates this information to the present geological setting. Both laboratory work and field work are involved. In the field, rock stresses are measured by the overcoring and the hydraulic fracturing technique. An observation technique for assessing likely high stresses is developed. The field data refer to several hydropower projects and to some offshore hydrocarbon fields. The principal sections are: (1) Tectonic setting in the western Fennoscandia, (2) Triaxial rock stress measurements by overcoring using the NTH cell (a strain gauge cell developed at the Norwegian technical university in Trondheim and based on the CSIR cell of the South African Council for Scientific and Industrial Research), (3) Laboratory testing of the NTH cell, (4) Quality ranking of stresses measured by the NTH cell, (4) Recalculated rock stresses and implications to the regional stress field, (5) Hydraulic fracturing stress measurements. 113 refs., 98 figs., 62 tabs.
De Guidi, Giorgio; Caputo, Riccardo; Scudero, Salvatore; Perdicaro, Vincenzo
2013-04-01
tensors at all the investigated sites. Indeed, the maximum principal stress axis σ1 is vertical or subvertical, while the intermediate and the least axes (σ2 and σ3) lie on the horizontal plane or show low plunging values. The main direction of extension (σ3) at each site is in general agreement with the first-order regional stress field (WNW-ESE) even though some local perturbations have been recognized. These are interpreted as due to interferences between large active faults and their particular geometrical arrangement. In particular local stress deflections and stress swaps systematically occur in zones characterized by two overlapping fault segments or close to their tips.
3D reconstruction of tensors and vectors
Energy Technology Data Exchange (ETDEWEB)
Defrise, Michel; Gullberg, Grant T.
2005-02-17
Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields.
Modelling of the Global Geopotential Energy & Stress Field
DEFF Research Database (Denmark)
Schiffer, Christian; Nielsen, S.B.
Lateral density and topography variations yield in and important contribution to the lithospheric stress field. The leading quantity is the Geopotential Energy, the integrated lithostatic pressure in a rock column. The horizontal gradient of this quantity is related to horizontal stresses through...... the Equations of equilibrium of stresses. The Geopotential Energy furthermore can be linearly related to the Geoid under assumption of local isostasy. Satellite Geoid measurements contain, however, also non-isostatic deeper mantle responses of long wavelength. Unfortunately, high-pass filtering of the Geoid...... flow in the presence of local isostasy and a steady state geotherm. Subsequently we use a FEM code to solve the Equations of equilibrium of stresses for a three dimensional elastic shell. The modelled results are shown and compared with the global stress field and other publications....
Active stress field and seismotectonic features in Intra-Carpathian region of Romania
Oros, Eugen; Popa, Mihaela; Diaconescu, Mihai; Radulian, Mircea
2017-04-01
The Romanian Intra-Carpathian Region is located on the eastern half of Tisa-Dacia geodynamic block from the Neogene Carpathian-Pannonian Basin. The distribution of seismicity displays clear clusters and narrower zones with seismogenic potential confirmed by the damaging earthquakes recoded in the region, e.g. July 01, 1829 (Mw=6.2), October 10, 1834 (Mw=5.6), January 26, 1916 (Mw=6.4), July 12, 1991 (Mw=5.7), December 2, 1991 (Mw=5.5). The state of recent stress and deformation appears to be controlled by the interaction of plate-boundary and intraplate forces, which include the counterclockwise rotation and N-NE-directed indentation of the Adria microplate and buoyancy forces associated with differential topography and lithospheric heterogeneities. The stress field and tectonic regime are investigated at regional and local scales by the formal inversion of focal mechamisms. There can be observed short-scale lateral changes of i) tectonic regimes from compressive (reverse and strike-slip faultings) to pure extensive (normal faultings) and ii) variation of stress directions (SHmax) from NE-SW to EW and WNW-ESE towards Southern Carpathians and NS within Easter Carpathians. The changes in stress directions occur over a distance that is comparable to or smaller than the thickness of the lithosphere. A comparative analysis of stress tensor with GPS velocity/displacememt vectors shows variations from paralellism to orthogonality, suggesting different mechanisms of crustal deformations.The major seismic activity (Mw≥5.0) appears to be generally concentrated along the faults systems bordering de Tisa-Dacia Block, intersections of faults of different ages, internal shear zones and with the border of the former structural terrains, old rifts and neostructures.
Tensor rank is not multiplicative under the tensor product
M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)
2018-01-01
textabstractThe tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the
Tensor rank is not multiplicative under the tensor product
M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)
2017-01-01
textabstractThe tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor (not to be confused with the "tensor Kronecker product" used in
Directory of Open Access Journals (Sweden)
Lijing Shao
2017-10-01
Full Text Available Pulsar timing and laser-interferometer gravitational-wave (GW detectors are superb laboratories to study gravity theories in the strong-field regime. Here, we combine these tools to test the mono-scalar-tensor theory of Damour and Esposito-Farèse (DEF, which predicts nonperturbative scalarization phenomena for neutron stars (NSs. First, applying Markov-chain Monte Carlo techniques, we use the absence of dipolar radiation in the pulsar-timing observations of five binary systems composed of a NS and a white dwarf, and eleven equations of state (EOSs for NSs, to derive the most stringent constraints on the two free parameters of the DEF scalar-tensor theory. Since the binary-pulsar bounds depend on the NS mass and the EOS, we find that current pulsar-timing observations leave scalarization windows, i.e., regions of parameter space where scalarization can still be prominent. Then, we investigate if these scalarization windows could be closed and if pulsar-timing constraints could be improved by laser-interferometer GW detectors, when spontaneous (or dynamical scalarization sets in during the early (or late stages of a binary NS (BNS evolution. For the early inspiral of a BNS carrying constant scalar charge, we employ a Fisher-matrix analysis to show that Advanced LIGO can improve pulsar-timing constraints for some EOSs, and next-generation detectors, such as the Cosmic Explorer and Einstein Telescope, will be able to improve those bounds for all eleven EOSs. Using the late inspiral of a BNS, we estimate that for some of the EOSs under consideration, the onset of dynamical scalarization can happen early enough to improve the constraints on the DEF parameters obtained by combining the five binary pulsars. Thus, in the near future, the complementarity of pulsar timing and direct observations of GWs on the ground will be extremely valuable in probing gravity theories in the strong-field regime.
Bayesian regularization of diffusion tensor images
DEFF Research Database (Denmark)
Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif
2007-01-01
Diffusion tensor imaging (DTI) is a powerful tool in the study of the course of nerve fibre bundles in the human brain. Using DTI, the local fibre orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along...... several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. In this paper we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing...
International Nuclear Information System (INIS)
Malyshev, C
2007-01-01
A translational gauge approach of the Einstein type is proposed for obtaining the stresses that are due to non-singular screw dislocation. The stress distribution of the second order around the screw dislocation is classically known for the hollow circular cylinder with traction-free external and internal boundaries. The inner boundary surrounds the dislocation's core, which is not captured by the conventional solution. The present gauge approach enables us to continue the classically known quadratic stresses inside the core. The gauge equation is chosen in the Hilbert-Einstein form, and it plays the role of non-conventional incompatibility law. The stress function method is used, and it leads to the modified stress potential given by two constituents: the conventional one, say, the 'background' and a short-ranged gauge contribution. The latter just causes additional stresses, which are localized. The asymptotic properties of the resulting stresses are studied. Since the gauge contributions are short-ranged, the background stress field dominates sufficiently far from the core. The outer cylinder's boundary is traction-free. At sufficiently moderate distances, the second-order stresses acquire regular continuation within the core region, and the cut-off at the core does not occur. Expressions for the asymptotically far stresses provide self-consistently new length scales dependent on the elastic parameters. These lengths could characterize an exteriority of the dislocation core region
DEFF Research Database (Denmark)
Oddershede, Jette; Camin, Bettina; Schmidt, Søren
2012-01-01
The stress field around a notch in a coarse grained Mg AZ31 sample has been measured under tensile load using the individual grains as probes in an in situ high energy synchrotron diffraction experiment. The experimental set-up, a variant of three-dimensional X-ray diffraction microscopy, allows...... the position, orientation and full stress tensor of each illuminated grain to be determined and, hence, enables the study of evolving stress fields in coarse grained materials with a spatial resolution equal to the grain size. Grain resolved information like this is vital for understanding what happens when...... the traditional continuum mechanics approach breaks down and fracture is governed by local heterogeneities (e.g. phase or stress differences) between grains. As a first approximation the results obtained were averaged through the thickness of the sample and compared with an elastic–plastic continuum finite...
Taguchi, Y-H
2017-12-21
Although post-traumatic stress disorder (PTSD) is primarily a mental disorder, it can cause additional symptoms that do not seem to be directly related to the central nervous system, which PTSD is assumed to directly affect. PTSD-mediated heart diseases are some of such secondary disorders. In spite of the significant correlations between PTSD and heart diseases, spatial separation between the heart and brain (where PTSD is primarily active) prevents researchers from elucidating the mechanisms that bridge the two disorders. Our purpose was to identify genes linking PTSD and heart diseases. In this study, gene expression profiles of various murine tissues observed under various types of stress or without stress were analyzed in an integrated manner using tensor decomposition (TD). Based upon the obtained features, ∼ 400 genes were identified as candidate genes that may mediate heart diseases associated with PTSD. Various gene enrichment analyses supported biological reliability of the identified genes. Ten genes encoding protein-, DNA-, or mRNA-interacting proteins-ILF2, ILF3, ESR1, ESR2, RAD21, HTT, ATF2, NR3C1, TP53, and TP63-were found to be likely to regulate expression of most of these ∼ 400 genes and therefore are candidate primary genes that cause PTSD-mediated heart diseases. Approximately 400 genes in the heart were also found to be strongly affected by various drugs whose known adverse effects are related to heart diseases and/or fear memory conditioning; these data support the reliability of our findings. TD-based unsupervised feature extraction turned out to be a useful method for gene selection and successfully identified possible genes causing PTSD-mediated heart diseases.
Radiative corrections in a vector-tensor model
International Nuclear Information System (INIS)
Chishtie, F.; Gagne-Portelance, M.; Hanif, T.; Homayouni, S.; McKeon, D.G.C.
2006-01-01
In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by computing the one-loop contributions of the tensor field to the self-energy of the vector field. It is shown that despite the large number of Feynman diagrams in which the tensor field contributes, the sum of these diagrams vanishes, confirming that it is not physical. Furthermore, if the tensor field were to couple with a spinor field, it is shown at one-loop order that the spinor self-energy is not renormalizable, and hence this coupling must be excluded. In principle though, this tensor field does couple to the gravitational field
Schwab, Drew R.; Bidgoli, Tandis S.; Taylor, Michael H.
2017-12-01
Kansas, like other parts of the central U.S., has experienced a recent increase in seismicity. Correlation of these events with brine disposal operations suggests pore fluid pressure increases are reactivating preexisting faults, but rigorous evaluation at injection sites is lacking. Here we determine the suitability of CO2 injection into the Cambrian-Ordovician Arbuckle Group for long-term storage and into a Mississippian reservoir for enhanced oil recovery in Wellington Field, Sumner County, Kansas. To determine the potential for injection-induced earthquakes, we map subsurface faults and estimate in situ stresses, perform slip and dilation tendency analyses to identify well-oriented faults relative to the estimated stress field, and determine the pressure changes required to induce slip at reservoir and basement depths. Three-dimensional seismic reflection data reveal 12 near-vertical faults, mostly striking NNE, consistent with nodal planes from moment tensor solutions from recent earthquakes in the region. Most of the faults cut both reservoirs and several clearly penetrate the Precambrian basement. Drilling-induced fractures (N = 40) identified from image logs and inversion of earthquake moment tensor solutions (N = 65) indicate that the maximum horizontal stress is approximately EW. Slip tendency analysis indicates that faults striking reservoir conditions, whereas faults striking 020°-049° may be prone to reactivation with increasing pore fluid pressure. Although the proposed injection volume (40,000 t) is unlikely to reactive faults at reservoir depths, high-rate injection operations could reach pressures beyond the critical threshold for slip within the basement, as demonstrated by the large number of injection-induced earthquakes west of the study area.
Field instrumentation for hydrofracturing stress measurements
International Nuclear Information System (INIS)
Bjarnason, Bjarni; Torikka, Arne.
1989-08-01
A recently developed system for rock stress measurements by the hydraulic fracturing method is documented in detail. The new equipment is intended for measurement in vertical or nearvertical boreholes, down to a maximum depth of 1000 m. The minimum borehole, diameter required is 56 mm. Downhole instrumentation comprises a straddle packer assembly for borehole fracturing, equipment for determination of fracture orientations and a pressure transducer. The downhole tools are operated by means of a multihose system, containing high pressure hydraulic tubings, signal cable and carrying wire into one hose unit. The surface components of the equipment include a system for generation and control of water pressures up to approximately 75 MPa, an hydraulically operated drum for the multihose and a data acquisition system. All surface instrumentation is permanently mounted on a truck, which also serves as power source for the instrumentation. In addition to the description of instrumentation, the theoretical fundament and the testing procedures associated with the hydraulic fracturing method are briefly outlined
Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji
2017-11-15
Spin-orbit contributions to the zero-field splitting (ZFS) tensor (D SO tensor) of M III (acac) 3 complexes (M = V, Cr, Mn, Fe and Mo; acac = acetylacetonate anion) are evaluated by means of ab initio (a hybrid CASSCF/MRMP2) and DFT (Pederson-Khanna (PK) and natural orbital-based Pederson-Khanna (NOB-PK)) methods, focusing on the behaviour of DFT-based approaches to the D SO tensors against the valence d-electron configurations of the transition metal ions in octahedral coordination. Both the DFT-based approaches reproduce trends in the D tensors. Significantly, the differences between the theoretical and experimental D (D = D ZZ - (D XX + D YY )/2) values are smaller in NOB-PK than in PK, emphasising the usefulness of the natural orbital-based approach to the D tensor calculations of transition metal ion complexes. In the case of d 2 and d 4 electronic configurations, the D SO (NOB-PK) values are considerably underestimated in the absolute magnitude, compared with the experimental ones. The D SO tensor analysis based on the orbital region partitioning technique (ORPT) revealed that the D SO contributions attributed to excitations from the singly occupied region (SOR) to the unoccupied region (UOR) are significantly underestimated in the DFT-based approaches to all the complexes under study. In the case of d 3 and d 5 configurations, the (SOR → UOR) excitations contribute in a nearly isotropic manner, which causes fortuitous error cancellations in the DFT-based D SO values. These results indicate that more efforts to develop DFT frameworks should be directed towards the reproduction of quantitative D SO tensors of transition metal complexes with various electronic configurations and local symmetries around metal ions.
A multi-stage 3-D stress field modelling approach exemplified in the Bavarian Molasse Basin
Ziegler, Moritz O.; Heidbach, Oliver; Reinecker, John; Przybycin, Anna M.; Scheck-Wenderoth, Magdalena
2016-09-01
The knowledge of the contemporary in situ stress state is a key issue for safe and sustainable subsurface engineering. However, information on the orientation and magnitudes of the stress state is limited and often not available for the areas of interest. Therefore 3-D geomechanical-numerical modelling is used to estimate the in situ stress state and the distance of faults from failure for application in subsurface engineering. The main challenge in this approach is to bridge the gap in scale between the widely scattered data used for calibration of the model and the high resolution in the target area required for the application. We present a multi-stage 3-D geomechanical-numerical approach which provides a state-of-the-art model of the stress field for a reservoir-scale area from widely scattered data records. Therefore, we first use a large-scale regional model which is calibrated by available stress data and provides the full 3-D stress tensor at discrete points in the entire model volume. The modelled stress state is used subsequently for the calibration of a smaller-scale model located within the large-scale model in an area without any observed stress data records. We exemplify this approach with two-stages for the area around Munich in the German Molasse Basin. As an example of application, we estimate the scalar values for slip tendency and fracture potential from the model results as measures for the criticality of fault reactivation in the reservoir-scale model. The modelling results show that variations due to uncertainties in the input data are mainly introduced by the uncertain material properties and missing SHmax magnitude estimates needed for a more reliable model calibration. This leads to the conclusion that at this stage the model's reliability depends only on the amount and quality of available stress information rather than on the modelling technique itself or on local details of the model geometry. Any improvements in modelling and increases
(Ln-bar, g)-spaces. Ordinary and tensor differentials
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
Different types of differentials as special cases of differential operators acting on tensor fields over (L n bar, g)-spaces are considered. The ordinary differential, the covariant differential as a special case of the covariant differential operator, and the Lie differential as a special case of the Lie differential operator are investigated. The tensor differential and its special types (Covariant tensor differential, and Lie tensor differential) are determined and their properties are discussed. Covariant symmetric and antisymmetric (external) tensor differentials, Lie symmetric, and Lie antisymmetric (external) tensor differentials are determined and considered over (L n bar, g)-spaces
Energy Technology Data Exchange (ETDEWEB)
Chicherin, Dmitry [LAPTH, Université de Savoie, CNRS,B.P. 110, F-74941 Annecy-le-Vieux (France); Sokatchev, Emery [LAPTH, Université de Savoie, CNRS,B.P. 110, F-74941 Annecy-le-Vieux (France); Theoretical Physics Department, CERN,CH-1211, Geneva 23 (Switzerland)
2017-03-09
We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N=4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators are obtained from those for the chiral correlators by a simple Grassmann shift of the space-time variables. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper arXiv:1601.06803. In this approach only the chiral half of the supersymmetry is manifest. The other half is realized by nonlinear and nonlocal transformations of the LHC superfields. However, at Born level only the simple linear part of the transformations is relevant. It corresponds to effectively working in the self-dual sector of the theory. Our method is also applicable to a wider class of supermultiplets like all the half-BPS operators and the Konishi multiplet.
Chicherin, Dmitry; Sokatchev, Emery
2017-03-01
We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N = 4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators are obtained from those for the chiral correlators by a simple Grassmann shift of the space-time variables. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper arXiv:1601.06803. In this approach only the chiral half of the supersymmetry is manifest. The other half is realized by nonlinear and nonlocal transformations of the LHC superfields. However, at Born level only the simple linear part of the transformations is relevant. It corresponds to effectively working in the self-dual sector of the theory. Our method is also applicable to a wider class of supermultiplets like all the half-BPS operators and the Konishi multiplet.
Determining the stress field in active volcanoes using focal mechanisms
Directory of Open Access Journals (Sweden)
Bruno Massa
2016-11-01
Full Text Available Stress inversion of seismological datasets became an essential tool to retrieve the stress field of active tectonics and volcanic areas. In particular, in volcanic areas, it is able to put constrains on volcano-tectonics and in general in a better understanding of the volcano dynamics. During the last decades, a wide range of stress inversion techniques has been proposed, some of them specifically conceived to manage seismological datasets. A modern technique of stress inversion, the BRTM, has been applied to seismological datasets available at three different regions of active volcanism: Mt. Somma-Vesuvius (197 Fault Plane Solutions, FPSs, Campi Flegrei (217 FPSs and Long Valley Caldera (38,000 FPSs. The key role of stress inversion techniques in the analysis of the volcano dynamics has been critically discussed. A particular emphasis was devoted to performances of the BRTM applied to volcanic areas.
Tensor rank is not multiplicative under the tensor product
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2017-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...
Roman, D. C.
2003-12-01
A complete understanding of the initiation, evolution, and termination of volcanic eruptions requires reliable monitoring techniques to detect changes in the conduit system during periods of activity, as well as corresponding knowledge of conduit structure and of magma physical properties. Case studies of stress field orientation prior to, during, and after magmatic activity can be used to relate changes in stress field orientation to the state of the magmatic conduit system. These relationships may be tested through modeling of induced stresses. Here I present evidence from case studies and modeling that horizontal rotation of the axis of maximum compressive stress at an active volcano indicates pressurization of a magmatic conduit, and that this rotation, when observed, may also be indicative of the physical properties of the ascending magma. Changes in the local stress field orientation during the 1992 eruption sequence at Crater Peak (Mt. Spurr), Alaska were analyzed by calculating and inverting subsets of over 150 fault-plane solutions. Local stress tensors for four time periods, corresponding approximately to changes in activity at the volcano, were calculated based on the misfit of individual fault-plane solutions to a regional stress tensor. Results indicate that for nine months prior to the eruption, local maximum compressive stress was oriented perpendicular to regional maximum compressive stress. A similar horizontal rotation was observed beginning in November of 1992, coincident with an episode of elevated earthquake and tremor activity indicating intrusion of magma into the conduit. During periods of quiescence the local stress field was similar to the regional stress field. Similar horizontal rotations have been observed at Mt. Ruapehu, New Zealand (Miller and Savage 2001, Gerst 2003), Usu Volcano, Japan (Fukuyama et al. 2001), Unzen Volcano, Japan (Umakoshi et al. 2001), and Mt. St. Helens Volcano, USA (Moran 1994) in conjunction with eruptive
Weyl curvature tensor in static spherical sources
International Nuclear Information System (INIS)
Ponce de Leon, J.
1988-01-01
The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed
Levitas, Valery I.; Warren, James A.
2016-06-01
A thermodynamically consistent, large-strain, multi-phase field approach (with consequent interface stresses) is generalized for the case with anisotropic interface (gradient) energy (e.g. an energy density that depends both on the magnitude and direction of the gradients in the phase fields). Such a generalization, if done in the "usual" manner, yields a theory that can be shown to be manifestly unphysical. These theories consider the gradient energy as anisotropic in the deformed configuration, and, due to this supposition, several fundamental contradictions arise. First, the Cauchy stress tensor is non-symmetric and, consequently, violates the moment of momentum principle, in essence the Herring (thermodynamic) torque is imparting an unphysical angular momentum to the system. In addition, this non-symmetric stress implies a violation of the principle of material objectivity. These problems in the formulation can be resolved by insisting that the gradient energy is an isotropic function of the gradient of the order parameters in the deformed configuration, but depends on the direction of the gradient of the order parameters (is anisotropic) in the undeformed configuration. We find that for a propagating nonequilibrium interface, the structural part of the interfacial Cauchy stress is symmetric and reduces to a biaxial tension with the magnitude equal to the temperature- and orientation-dependent interface energy. Ginzburg-Landau equations for the evolution of the order parameters and temperature evolution equation, as well as the boundary conditions for the order parameters are derived. Small strain simplifications are presented. Remarkably, this anisotropy yields a first order correction in the Ginzburg-Landau equation for small strains, which has been neglected in prior works. The next strain-related term is third order. For concreteness, specific orientation dependencies of the gradient energy coefficients are examined, using published molecular dynamics
Tensor structure for Nori motives
Barbieri-Viale, Luca; Huber, Annette; Prest, Mike
2018-01-01
We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.
Tensor eigenvalues and their applications
Qi, Liqun; Chen, Yannan
2018-01-01
This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.
Dislocations, the elastic energy momentum tensor and crack propagation
International Nuclear Information System (INIS)
Lung, Chi-wei
1979-07-01
Based upon dislocation theory, some stress intensity factors can be calculated for practical cases. The results obtained by this method have been found to agree fairly well with the results obtained by the conventional fracture mechanics. The elastic energy momentum tensor has been used to calculate the force acting on the crack tip. A discussion on the kinetics of migration of impurities to the crack tip was given. It seems that the crack tip sometimes may be considered as a singularity in an elastic field and the fundamental law of classical field theory is applicable on the problem in fracture of materials. (author)
Comon, Pierre
2014-01-01
International audience; Tensor decompositions are at the core of many Blind Source Separation (BSS) algorithms, either explicitly or implicitly. In particular, the Canonical Polyadic (CP) tensor decomposition plays a central role in identification of underdetermined mixtures. Despite some similarities, CP and Singular value Decomposition (SVD) are quite different. More generally, tensors and matrices enjoy different properties, as pointed out in this brief survey.
Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Kitagawa, Masahiro; Takui, Takeji
2014-05-21
The CASSCF and the hybrid CASSCF-MRMP2 methods are applied to the calculations of spin-spin and spin-orbit contributions to the zero-field splitting tensors (D tensors) of the halogen-substituted spin-septet 2,4,6-trinitrenopyridines, focusing on the heavy atom effects on the spin-orbit term of the D tensors (D(SO) tensors). The calculations reproduced experimentally determined |D| values within an error of 15%. Halogen substitutions at the 3,5-positions are less influential in the spin-spin dipolar (D(SS)) term of 2,4,6-trinitrenopyridines, although the D(SO) terms are strongly affected by the introduction of heavier halogens. The absolute sign of the D(SO) value (D = D(ZZ) - (D(XX) + D(YY))/2) of 3,5-dibromo derivative 3 is predicted to be negative, which contradicts the Pederson-Khanna (PK) DFT result previously reported. The large negative contributions to the D(SO) value of 3 arise from the excited spin-septet states ascribed mainly to the excitations of in-plane lone pair of bromine atoms → SOMO of π nature. The importance of the excited states involving electron transitions from the lone pair orbital of the halogen atom is also confirmed in the D(SO) tensors of halogen-substituted para-phenylnitrenes. A new scheme based on the orbital region partitioning is proposed for the analysis of the D(SO) tensors as calculated by means of the PK-DFT approach.
Massless and massive quanta resulting from a mediumlike metric tensor
International Nuclear Information System (INIS)
Soln, J.
1985-01-01
A simple model of the ''primordial'' scalar field theory is presented in which the metric tensor is a generalization of the metric tensor from electrodynamics in a medium. The radiation signal corresponding to the scalar field propagates with a velocity that is generally less than c. This signal can be associated simultaneously with imaginary and real effective (momentum-dependent) masses. The requirement that the imaginary effective mass vanishes, which we take to be the prerequisite for the vacuumlike signal propagation, leads to the ''spontaneous'' splitting of the metric tensor into two distinct metric tensors: one metric tensor gives rise to masslesslike radiation and the other to a massive particle. (author)
Hunt, Katharine L. C.; Harris, Robert A.
1991-06-01
Motion of nuclei within a molecule induces a magnetic moment me in the electronic charge distribution, giving a nonzero electronic contribution to the magnetic transition dipole that produces vibrational circular dichroism. In this paper, we develop a new susceptibility density theory for the induced magnetic moment. The theory is based on the response of the electrons to changes in the nuclear Coulomb field, due to shifts in nuclear positions. The electronic response to these changes depends on the same susceptibility densities that determine response to external fields. Our analysis suggests a new physical picture of vibrational circular dichroism. It yields an equation for the density of the induced electronic magnetic moment within a molecule; it also yields a new relation connecting the electric-field shielding at nucleus I of a molecule in an applied magnetic field of frequency ω to the derivative of me with respect to the velocity of nucleus I, regarded as a parameter in the electronic wave function. Within our theory, the derivative of me with respect to nuclear velocity separates into quantum-mechanical and classical components in close analogy with the Hellmann-Feynman theorem for forces on nuclei. In matrix-element form, results from our theory are identical to those obtained with nonadiabatic perturbation theory, to leading order. In general, the leading nonadiabatic corrections to electronic properties are determined directly by the electrons' response to the changes in the nuclear Coulomb field, when the nuclei move.
Local Tensor Radiation Conditions For Elastic Waves
DEFF Research Database (Denmark)
Krenk, S.; Kirkegaard, Poul Henning
2001-01-01
A local boundary condition is formulated, representing radiation of elastic waves from an arbitrary point source. The boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point....... The tensor relation generalizes the traditional normal incidence impedance condition by accounting for the angle between wave propagation and the surface normal and by including a generalized stiffness term due to spreading of the waves. The effectiveness of the local tensor radiation condition...
Energy Technology Data Exchange (ETDEWEB)
Montesinos, M. [CINVESTAV-IPN, 07360 Mexico D.F. (Mexico); Flores, E. [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)]. E-mail: merced@fis.cinvestav.mx
2006-07-01
The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral Proca field, the same procedure yields also the symmetric energy-momentum tensor. In all cases, the key point to get the right expressions for the energy-momentum tensors is the appropriate handling of their equations of motion and the Bianchi identities. It must be stressed that these results are obtained without using Belinfante's symmetrization techniques which are usually employed to this end. (Author)
Photoelastic analyses of stresses in toroidal magnetic field coils
International Nuclear Information System (INIS)
Pih, H.
1977-02-01
Several two-dimensional photoelastic stress analyses were made on models of circular and oval toroidal magnetic field coils for fusion reactors. The circumferential variation of each coil's in-plane magnetic force was simulated by applying different pressures to 16 segmented regions of the inner surface of the models. One special loading fixture was used for the model of each shape and size. Birefringence and isoclinic angles were measured in a transmission polariscope at selected points on the loaded model. Boundary stresses in the cases of known boundary conditions were determined directly from the isochromatics. Separate principal stresses were calculated using the combination of photoelastic information and isopachic data obtained by the electrical analogy method from the solution of Laplace's equation. Comparisons were made between experimental results and those computed using the finite element method. The stress distribution between theoretical and experimental agrees very well, although the finite element method yielded slightly higher stresses than the photoelastic method; further work is needed to resolve this difference. In this investigation several variations of coil geometry and methods of support were evaluated. Based on experimental results, optimum structural designs of toroidal field coils were recommended
Crustal stress heterogeneity in the vicinity of a geothermal field: Coso Geothermal Field, CA
Blake, Kelly
Borehole induced structures seen in image logs from the Coso Geothermal Field, CA record variation in the azimuth of principal stress. Image logs of these structures from five boreholes were analyzed to quantify the stress heterogeneity for three geologically distinct locations: two boreholes within the Coso Geothermal Field (one in an actively produced volume), two on the margin of the Coso Geothermal Field and outside the production area, and a control borehole several tens of kilometers south of the Coso Geothermal Field. Average directions of Shmin and its standard deviation are similar along the eastern portion of the geothermal field at ˜107 +/- 28°; this is distinct from the western portion which has an azimuth of 081 +/- 18° and also distinct from outside the geothermal field where the average azimuth is 092 +/- 47°. These relationships suggest a correlation of stress orientation and heterogeneity with slip on the Coso Wash fault, suggesting that ˜20 years of production has not affected the Shmin.orientation. The slope of power spectrum quantifies the length-scale dependence of stress rotations for the volume of the brittle crust penetrated by each borehole. Spectral analysis was applied to the depth variation of stress direction and it demonstrates that: (1) the data set contains distinct wavelengths of stress rotation, (2) that the relative power of these wavelengths in the total scaling of stress directions demonstrates a fractal distribution and (3) in a manner consistent with earthquakes causing the stress rotations. While the vertically averaged Shmin orientation for the three eastern boreholes varied by as little as 1°, the spectral slopes varied by 0.4 log (deg2 *m)(m) from the inside to the margin unproduced areas of the Coso Geothermal Field. The two boreholes inside the field had spectral slopes within one standard deviation, even though Shmin orientations were not parallel. These results suggest that at the kilometer length scale, the
DEFF Research Database (Denmark)
Nevald, Rolf; Hansen, P. E.
1978-01-01
The fluorine and lithium NMR line shifts have been followed in temperature from 300 to 1.3 K and in fields up to 40 kG for LiTbF4 and LiHoF4. The Tb3+ and Ho3+ ionic moments cause these shifts. The Li shifts are dominated by dipole interactions, whereas the F shifts also have transferred hyperfine...... contributions of comparable sizes. The transferred hyperfine interactions turn out to be almost isotropic and exhibiting no temperature or field dependence. In LiHoF4 the line shifts are detectable within the entire temperature range. In LiTbF4 the fluorine and lithium lines broaden to such an extent...
Effect of pulsed electromagnetic fields on endoplasmic reticulum stress.
Keczan, E; Keri, G; Banhegyi, G; Stiller, I
2016-10-01
The maintenance of protein homeostasis in the endoplasmic reticulum (ER) is crucial in cell life. Disruption of proteostasis results in ER stress that activates the unfolded protein response (UPR); a signalling network assigned to manage the accumulated misfolded or unfolded proteins. Prolonged or unresolved ER stress leads to apoptotic cell death that can be the basis of many serious diseases. Our aim was to study the effect of pulsed electromagnetic fields (PEMF), an alternative, non-invasive therapeutic method on ER stressed cell lines. First, the effect of PEMF treatment on the expression of ER stress markers was tested in three different cell lines. PEMF had no remarkable effect on ER stress protein levels in human embryonic kidney (HEK293T) and human liver carcinoma (HepG2) cell lines. However, the expression of BiP, Grp94 and CHOP were increased in HeLa cells upon PEMF exposure. Therefore, HepG2 cell line was selected for further experiments. Cells were stressed by tunicamycin and exposed to PEMF. Grp94, PDI, CHOP and PARP expression as markers of stress were monitored by Western blot and cell viability was also investigated. Tunicamycin treatment, as expected, increased the expression of Grp94, PDI, CHOP and inactivated PARP. Analysis of protein expression showed that PEMF was able to decrease the elevated level of ER chaperons Grp94, PDI and the apoptosis marker CHOP. The truncated, inactive form of PARP was also decreased. Accordingly, cell viability was also improved by PEMF exposure. These results indicate that PEMF is able to moderate ER stress induced by tunicamycin in HepG2 cells. However, our results clearly draw attention to that different cell lines may vary in the response to PEMF treatment.
Poloidal field coil stress analysis for the ZTH machine
International Nuclear Information System (INIS)
Girrens, S.P.; Bennett, J.G.; Murphy, D.M.
1988-02-01
Three-dimensional finite element analysis of representative equilibrium field and ohmic heating coils for the Los Alamos ZTH air core machine was performed to determine static stress levels developed within the coil structure caused by Lorentz-force loading. Because of the complex coil configuration in cross section (copper conductors embedded in an epoxy insulating matrix), the study was performed in three steps: a bulk orthotropic material property determination, a bulk material coil section analysis, and a detailed composite cross section of selected thickness analysis. Computational procedures used with coil stress and displacement results that were obtained are presented. Extensive work was performed to investigate the magnitude of the error in coil stress predictions arising from the use of the three-step analysis procedure. Analytical and numerical procedures used to perform the estimate of error study are also presented. 34 figs
Algebraic and computational aspects of real tensor ranks
Sakata, Toshio; Miyazaki, Mitsuhiro
2016-01-01
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...
Analysis of stress and deformation fields of shape complex beams
Directory of Open Access Journals (Sweden)
Pástor Miroslav
2018-01-01
Full Text Available In this paper is investigated the analysis of stress and deformation fields of shape complex beams. The shape complex beams are made from load-bearing sheet (trapezoidal sheet circumferentially connected with strips of sheet metal, these beams are a substitute for more complex and heavier beams. The numerical analysis with static load are performed for these beams. The effect of three different types of connections between load-bearing sheet and strips of sheet metal is investigated. The first type of connection is represented by the trapezoidal sheet perfectly welded to the strips of sheet metal, the second type of connection is represented by the trapezoidal sheet welded to the strips of sheet metal only on the base sides of the trapezoidal sheet. The third one is represented by point welds. The stress and deformation fields for all types of the connections are compared and the suitable variant is chosen.
Stress field determination in an alloy 600 stress corrosion crack specimen
International Nuclear Information System (INIS)
Rassineux, B.; Labbe, T.
1995-05-01
In the context of EDF studies on stress corrosion cracking rates in the Alloy 600 steam generators tubes, we studied the influence of strain hardened surface layers on the different stages of cracking for a tensile smooth specimen (TLT). The stress field was notably assessed to try and explain the slow/rapid-propagation change observed beyond the strain hardened layers. The main difficulty is to simulate in a finite element model the inner and outer surfaces of these strain hardened layers, produced by the final manufacturing stages of SG tubes which have not been heat treated. In the model, the strain hardening is introduced by simulating a multi-layer material. Residual stresses are simulated by an equivalent fictitious thermomechanical calculation, realigned with respect to X-ray measurements. The strain hardening introduction method was validated by an analytical calculation giving identical results. Stress field evolution induced by specimen tensile loading were studied using an elastoplastic 2D finite element calculations performed with the Aster Code. The stress profile obtained after load at 660 MPa shows no stress discontinuity at the boundary between the strain hardened layer and the rest of the tube. So we propose that a complementary calculation be performed, taking into account the multi-cracked state of the strain hardened zones by means of a damage variable. In fact, this state could induce stress redistribution in the un-cracked area, which would perhaps provide an explanation of the crack-ground rate change beyond the strain hardened zone. The calculations also evidence the harmful effects of plastic strains on a strain hardened layer due to the initial state of the tube (not heat-treated), to grit blasting or to shot peening. The initial compressive stress condition of this surface layer becomes, after plastic strain, a tensile stress condition. These results are confirmed by laboratory test. (author). 10 refs., 18 figs., 9 tabs., 2 appends
Study On Aftershock Triggering In Consideration Of Tectonic Stress Field
Hu, C.; Cai, Y.
2007-12-01
: The occurrence of earthquake is related to the strength of rock and tectonic stress field. The seismic risk factor (SRF),D=\\left|{τn }\\right|/(μσn ) is proposed to describe the dangerous status of aftershock triggering in this paper. Dearthquakes, velocity field from GPS as well as geological survey. As one order of approximation, the magnitudes of the regional tectonic stress field can be estimated by the Coulomb failure criterion. Finite element method (FEM) and the concept of the factor D are used to study the aftershock triggering of the 1976 Tangshan Ms=7.8 earthquake. The results show that: (1) Most of the aftershocks triggered by the Tangshan earthquake occurred in the two-leaf-shaped regions of D≥ 1 near the north-east end of the main-shock fault. The largest leaf is about 100km long and 40km wide. (2) The areas of aftershock triggering predicted by the seismic risk factorD and Δ CFS (the changes in the Coulomb failure stress) are almost the same near the fault. The difference between them is that the aftershock area predicted by Δ CFS≥ 0 is too large and the area predicted by the factor D≥ 1 is limited. The areas of aftershock triggering predicted by Δ CFS≥ 0.04 MPa are nearly the same as those of D≥ 1 obtained by the study. (3) Sometimes Δ CFS =0.01MPa is taken as a low threshold of aftershock triggering. However, Δ CFS≥ 0 only means the probability increase of the earthquake triggering, not means the earthquake will occur. The earthquake occurrence is not only related to Δ CFS, but also to the tectonic stress field before the main-shock.
Gauge theories, duality relations and the tensor hierarchy
Bergshoeff, Eric A.; Hartong, Jelle; Hohm, Olaf; Huebscher, Mechthild; Ortin, Tomas; Hübscher, Mechthild
We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of
a tensor theory of gravitation in a curved metric on a flat background
International Nuclear Information System (INIS)
Drummond, J.E.
1979-01-01
A theory of gravity is proposed using a tensor potential for the field on a flat metric. This potential cannot be isolated by local observations, but some details can be deduced from measurements at a distance. The requirement that the field equations for the tensor potential shall be deducible from an action integral, that the action and field equations are gauge invariant, and, conversely, that the Lagrangian in the action integral can be integrated from the field equations leads to Einstein's field equations. The requirement that the field energy-momentum tensor exists leads to a constraint on the tensor potential. If the constraint is a differential gauge condition, then it can only be the Hilbert condition giving a unique background tensor, metric tensor and tensor potential. For a continuous field inside a solid sphere the metric must be homogeneous in the spatial coordinates, and the associated field energy-momentum tensor has properties consistent with Newtonian dynamics. (author)
Energy Technology Data Exchange (ETDEWEB)
Yang, Xiaobin, E-mail: yangxb@lzu.edu.cn; Li, Xiuhong; He, Yafeng; Wang, Xiaojun; Xu, Bo
2017-04-15
Highlights: • The differential equation including temperature and magnetic field was derived for a long cylindrical superconductor. • Thermal stress and electromagnetic stress were studied at the same time under pulse field magnetizing. • The distributions of the magnetic field, the temperature and stresses are studied and compared for two pulse fields of the different duration. • The Role thermal stress and electromagnetic stress play in the process of pulse field magnetizing is discussed. - Abstract: A multiphysics model for the numerical computation of stresses, trapped field and temperature distribution of a infinite long superconducting cylinder is proposed, based on which the stresses, including the thermal stresses and mechanical stresses due to Lorentz force, and trapped fields in the superconductor subjected to pulsed magnetic fields are analyzed. By comparing the results under pulsed magnetic fields with different pulse durations, it is found that the both the mechanical stress due to the electromagnetic force and the thermal stress due to temperature gradient contribute to the total stress level in the superconductor. For pulsed magnetic field with short durations, the thermal stress is the dominant contribution to the total stress, because the heat generated by AC-loss builds up significant temperature gradient in such short durations. However, for a pulsed field with a long duration the gradient of temperature and flux, as well as the maximal tensile stress, are much smaller. And the results of this paper is meaningful for the design and manufacture of superconducting permanent magnets.
Esrafili, Mehdi D.; Behzadi, Hadi; Hadipour, Nasser L.
2008-06-01
Nuclear quadrupole coupling tensors of 14N and 17O nuclei in benzamide clusters (up to n = 6) were calculated via density functional theory. Results revealed that N-H⋯O hydrogen bonds around the benzamide molecule in crystalline lattice have significant influence on 14N and 17O nuclear quadrupole coupling tensors. n-dependent trend in 14N quadrupole coupling tensors significantly correlates with cooperative effects of R(N-H⋯O) hydrogen bond distance. Natural bonding orbital analysis, NBO, was used to rationalize the quadrupole coupling results in terms of substantial n→σN-H∗ charge transfer in (benzamide) n=1-6 clusters. It was found that intermolecular n→σN-H∗ interactions play a key role in cooperative change of 14N and 17O quadrupole coupling tensors. There is an acceptable linear correlation between 14N or 17O quadrupole coupling tensors with strength of Fock matrix elements (Fij). This suggests that both 14N and 17O quadrupole coupling measurements can provide a useful probe for electron delocalization effects in both gaseous and condensed media.
Tensor rank is not multiplicative under the tensor product
DEFF Research Database (Denmark)
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2018-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection...... between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specifically, if a tensor t has border rank strictly smaller than its rank, then the tensor rank of t...... is not multiplicative under taking a sufficiently hight tensor product power. The “tensor Kronecker product” from algebraic complexity theory is related to our tensor product but different, namely it multiplies two k-tensors to get a k-tensor. Nonmultiplicativity of the tensor Kronecker product has been known since...
Cartesian tensors an introduction
Temple, G
2004-01-01
This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t
Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.
Stress Field in Brazil with Focal Mechanism: Regional and Local Patterns
Dias, F.; Assumpcao, M.
2013-05-01
The knowledge of stress field is fundamental not only to understand driving forces and plate deformation but also in the study of intraplate seismicity. The stress field in Brazil has been determined mainly using focal mechanisms and a few breakout data and in-situ measurements. However the stress field still is poorly known in Brazil. The focal mechanisms of recent earthquakes (magnitude lower than 5 mb) were studied using waveform modeling. We stacked the record of several teleseismic stations ( delta > 30°) stacked groups of stations separated according to distance and azimuth. Every record was visually inspected and those with a good signal/noise ratio (SNR) were grouped in windows of ten degrees distance and stacked. The teleseismic P-wave of the stacked signals was modeled using the hudson96 program of Herrmann seismology package (Herrmann, 2002) and the consistency of focal mechanism with the first-motion was checked. Some events in central Brazil were recorded by closer stations (~ 1000 km) and the moment tensor was determined with the ISOLA code (Sokos & Zahradnik, 2008). With the focal mechanisms available in literature and those obtained in this work, we were able to identify some patterns: the central region shows a purely compressional pattern (E-W SHmax), which is predicted by regional theoretical models (Richardson & Coblentz, 1996 and the TD0 model of Lithgow & Bertelloni, 2004). Meanwhile in the Amazon we find an indication of SHmax oriented in the SE-NW direction, probably caused by the Caribbean plate interaction (Meijer, 1995). In northern coastal region, the compression rotates following the coastline, which indicates an important local component related to spreading effects at the continental/oceanic transition (Assumpção, 1998) and flexural stresses caused by sedimentary load in Amazon Fan. We determine the focal mechanism of several events in Brazil using different techniques according to the available data. The major difficulty is to
Scattering of charged tensor bosons in gauge and superstring theories
Antoniadis, Ignatios
2010-01-01
We calculate the leading-order scattering amplitude of one vector and two tensor gauge bosons in a recently proposed non-Abelian tensor gauge field theory and open superstring theory. The linear in momenta part of the superstring amplitude has identical Lorentz structure with the gauge theory, while its cubic in momenta part can be identified with an effective Lagrangian which is constructed using generalized non-Abelian field strength tensors.
Secondary Traumatic Stress in Postdisaster Field Research Interviewers.
McLennan, Jim; Evans, Lynette; Cowlishaw, Sean; Pamment, Lindsay; Wright, Lyndsey
2016-02-01
Numerous studies show that those involved in disaster response may develop posttraumatic stress disorder or experience secondary traumatic stress (STS). There are few reports about the experiences of postdisaster field research interviewers. We report findings from a follow-up study of researchers who conducted postwildfire field research interviews with residents affected by 5 severe wildfire events in Australia over the period 2009-2014. There were 33 postwildfire research interviewers who reported their experiences, and 18 of them (54.5%) described distressing interviews involving deaths, surviving severe threats to life, and destruction of houses. There were 27 (81.6%) who reported having experienced 1 or more STS symptoms on a 20-item measure. Those who conducted interviews following a multifatality wildfire event reported higher levels of STS symptoms compared with researchers whose interviews followed nonfatal wildfires. There were 21 (63.6%) researchers who reported that their interviewing experiences had positive effects on their lives. This indicates that the researcher role of gathering information so that future wildfire risk could be mitigated may have served a protective function. Copyright © 2016 International Society for Traumatic Stress Studies.
Numerical analysis of stress fields generated by quenching process
Directory of Open Access Journals (Sweden)
A. Bokota
2011-04-01
Full Text Available In work the presented numerical models of tool steel hardening processes take into account mechanical phenomena generated by thermalphenomena and phase transformations. In the model of mechanical phenomena, apart from thermal, plastic and structural strain, alsotransformations plasticity was taken into account. The stress and strain fields are obtained using the solution of the Finite Elements Method of the equilibrium equation in rate form. The thermophysical constants occurring in constitutive relation depend on temperature and phase composite. For determination of plastic strain the Huber-Misses condition with isotropic strengthening was applied whereas fordetermination of transformation plasticity a modified Leblond model was used. In order to evaluate the quality and usefulness of thepresented models a numerical analysis of stresses and strains associated hardening process of a fang lathe of cone shaped made of tool steel was carried out.
Electric field exposure and evidence of stress in mice
Energy Technology Data Exchange (ETDEWEB)
De Bruyn, L.; De Jager, L. (Univ. of the Orange Free State, Bloemfontein (South Africa))
1994-04-01
The effect of stress induced by an electric field on the adrenal gland cortex of mice was examined by means of corticosterone serum assay and evaluation of the lipid profile of the different zones of the cortex. Six generations of experimental mice were exposed to a 10 kV/m electric field from conception and corresponding control groups were sham exposed. Mice were sacrificed at 35 days (n = 10), as adults (n = 20) and at 18 months (old mice) (n = 10). Blinded lipid estimates were performed on histological preparations of the adrenals, serum corticosterone levels were determined, and the results were statistically analyzed. The mean lipid volume in the zona glomerulosa of the exposed adult male group was significantly higher than that of the control group (P = 0.004). The median daytime corticosterone level of the exposed male mice was also significantly higher than that in the controls (P = 0.02). The lipid profiles and corticosterone values in the other subgroups did not differ significantly. As chronic stress increases the lipid volume of all the zones of the adrenal cortex and stimulates the zona glomerulosa to corticosterone secretion, the data suggest that the electric field acted as a chronic stressor in the adult male mice. 21 refs., 6 figs., 2 tabs.
Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul M.
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor...
Failure of Ceramic Composites in Non-Uniform Stress Fields
Rajan, Varun P.
Continuous-fiber ceramic matrix composites (CMCs) are of interest as hot-section components in gas turbine engines due to their refractoriness and low density relative to metallic alloys. In service, CMCs will be subjected to spatially inhomogeneous temperature and stress fields. Robust tools that enable prediction of deformation and fracture under these conditions are therefore required for component design and analysis. Such tools are presently lacking. The present work helps to address this deficiency by developing models for CMC mechanical behavior at two length scales: that of the constituents and that of the components. Problems of interest are further divided into two categories: '1-D loadings,' in which the stresses are aligned with the fiber axes, and '2-D loadings,' in which the stress state is more general. For the former class of problems, the major outstanding issue is material fracture, not deformation. A fracture criterion based on the attainment of a global load maximum is developed, which yields results for pure bending of CMCs in reasonable agreement with available experimental data. For the latter class of problems, the understanding of both the micro-scale and macro-scale behavior is relatively immature. An approach based upon analysis of a unit cell (a single fiber surrounded by a matrix jacket) is pursued. Stress fields in the constituents of the composite are estimated using analytical models, the accuracy of which is confirmed using finite element analysis. As part of a fracture mechanics analysis, these fields enable estimation of the steady-state matrix cracking stress for arbitrary in-plane loading of a unidirectional ply. While insightful at the micro-scale, unit cell models are difficult to extend to coarser scales. Instead, material deformation is typically predicted using phenomenological constitutive models. One such model for CMC laminates is investigated and found to predict material instability where none should exist. Remedies to
Couplings of self-dual tensor multiplet in six dimensions
Bergshoeff, E.; Sezgin, E.; Sokatchev, E.
1996-01-01
The (1, 0) supersymmetry in six dimensions admits a tensor multiplet which contains a second-rank antisymmetric tensor field with a self-dual field strength and a dilaton. We describe the fully supersymmetric coupling of this multiplet to a Yangâ€“Mills multiplet, in the absence of supergravity. The
Spectral Tensor-Train Decomposition
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.
2016-01-01
discretizations of the target function. We assess the performance of the method on a range of numerical examples: a modified set of Genz functions with dimension up to 100, and functions with mixed Fourier modes or with local features. We observe significant improvements in performance over an anisotropic......The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT.......e., the “cores”) comprising the functional TT decomposition. This result motivates an approximation scheme employing polynomial approximations of the cores. For functions with appropriate regularity, the resulting spectral tensor-train decomposition combines the favorable dimension-scaling of the TT...
Herman, Matthew W.; Herrmann, Robert B.; Benz, Harley M.; Furlong, Kevin P.
2014-01-01
On September 3, 2010, a MW 7.0 (U.S. Geological Survey moment magnitude) earthquake ruptured across the Canterbury Plains in South Island, New Zealand. Since then, New Zealand GNS Science has recorded over 10,000 aftershocks ML 2.0 and larger, including three destructive ~ MW 6.0 earthquakes near Christchurch. We treat the Canterbury earthquake sequence as an intraplate earthquake sequence, and compare its kinematics to an Andersonian model for fault slip in a uniform stress field. We determined moment magnitudes and double couple solutions for 150 earthquakes having MW 3.7 and larger through the use of a waveform inversion technique using data from broadband seismic stations on South Island, New Zealand. The majority (126) of these double couple solutions have strike-slip focal mechanisms, with right-lateral slip on ENE fault planes or equivalently left-lateral slip on SSE fault planes. The remaining focal mechanisms indicate reverse faulting, except for two normal faulting events. The strike-slip segments have compatible orientations for slip in a stress field with a horizontal σ1 oriented ~ N115°E, and horizontal σ3. The preference for right lateral strike-slip earthquakes suggests that these structures are inherited from previous stages of deformation. Reverse slip is interpreted to have occurred on previously existing structures in regions with an absence of existing structures optimally oriented for strike-slip deformation. Despite the variations in slip direction and faulting style, most aftershocks had nearly the same P-axis orientation, consistent with the regional σ1. There is no evidence for significant changes in these stress orientations throughout the Canterbury earthquake sequence.
Measuring Nematic Susceptibilities from the Elastoresistivity Tensor
Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian
The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....
Directory of Open Access Journals (Sweden)
E. V. Shmatok
2015-01-01
Full Text Available Nowadays mathematical modeling of peculiar features of a stress-strain state is considered as a perspective direction of research. In this regard the aim of this paper has been to make calculations of the stress-strain state initiated by a system of parallel lenticular residual mechanical twins that occur due to local surface deformation of Ni2MnGa single crystal martensitic phase.The method is applied while using a superposition principle of fields and approximation of a continuous distribution of twinning dislocations on twin boundaries in a continuous elastic medium.The calculations have made it possible to obtain distribution graphs of displacement fields and stresses and point out the fact that a configuration of displacement component distribution uy is significantly different from the displacement of components ux and uz having a displacement distribution similar to each other. The highest value of displacement occurs in the component uy in twins peaks.The paper also presents results of calculations for six components of a stress field the tensor. The obtained results have revealed similarity in stress distribution character of the components sxz and szz, but they differ numerically from each other about in two times. The largest value of the stresses occurring in the lenticular twins has been observed in components sxx, sxz, syy, syz and it has been focused mainly at the borders and peaks of twins.A common feature of the obtained components of displacement and stresses in a lenticular twins system is symmetry with regard to OY. In addition, the stress distribution of all obtained tensor components has been mainly localized at the borders and at the tops of twins where the highest values of stresses capable of exerting a significant impact on dislocation and diffusion processes are generally concentrated.
International Nuclear Information System (INIS)
Scheunert, M.
1982-10-01
We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)
Restrictions on Possible Forms of Classical Matter Fields Carrying no Energy
International Nuclear Information System (INIS)
Sokolowski, L.M.
2004-01-01
It is postulated in general relativity that the matter energy-momentum tensor vanishes if and only if all the matter fields vanish. In classical Lagrangian field theory the energy and momentum density are described by the variational (symmetric) energy-momentum tensor (named the stress tensor) and a priori it might occur that for some systems the tensor is identically to zero for all field configurations whereas evolution of the system is subject to deterministic Lagrange equations of motion. Such a system would not generate its own gravitational field. To check if these systems can exist in the framework of classical field theory we find a relationship between the stress tensor and the Euler operator (i.e. the Lagrange field equations). We prove that if a system of interacting scalar fields (the number of fields cannot exceed the spacetime dimension d) or a single vector field (in spacetimes with d even) has the stress tensor such that its divergence is identically zero (i.e. ''on and of shell''), then the Lagrange equations of motion hold identically too. These systems have then no propagation equations at all and should be regarded as unphysical. Thus nontrivial field equations require the stress tensor be nontrivial too. This relationship between vanishing (of divergence) of the stress tensor and of the Euler operator breaks down if the number of fields is greater than d. We show on concrete examples that a system of n > d interacting scalars or two interacting vector fields can have the stress tensor equal identically to zero while their propagation equations are nontrivial. This means that non-self-gravitating (and yet detectable) field systems are in principle admissible. Their equations of motion are, however, in some sense degenerate. We also show, that for a system of arbitrary number of interacting scalar fields or for a single vector field (in some specific spacetimes in the latter case), if the stress tensor is not identically zero, then it cannot
Field Phenotyping of Soybean Roots for Drought Stress Tolerance
Directory of Open Access Journals (Sweden)
Berhanu A. Fenta
2014-08-01
Full Text Available Root architecture was determined together with shoot parameters under well watered and drought conditions in the field in three soybean cultivars (A5409RG, Jackson and Prima 2000. Morphology parameters were used to classify the cultivars into different root phenotypes that could be important in conferring drought tolerance traits. A5409RG is a drought-sensitive cultivar with a shallow root phenotype and a root angle of <40°. In contrast, Jackson is a drought-escaping cultivar. It has a deep rooting phenotype with a root angle of >60°. Prima 2000 is an intermediate drought-tolerant cultivar with a root angle of 40°–60°. It has an intermediate root phenotype. Prima 2000 was the best performing cultivar under drought stress, having the greatest shoot biomass and grain yield under limited water availability. It had abundant root nodules even under drought conditions. A positive correlation was observed between nodule size, above-ground biomass and seed yield under well-watered and drought conditions. These findings demonstrate that root system phenotyping using markers that are easy-to-apply under field conditions can be used to determine genotypic differences in drought tolerance in soybean. The strong association between root and nodule parameters and whole plant productivity demonstrates the potential application of simple root phenotypic markers in screening for drought tolerance in soybean.
On the energy-momentum tensor in Moyal space
International Nuclear Information System (INIS)
Balasin, Herbert; Schweda, Manfred; Blaschke, Daniel N.; Gieres, Francois
2015-01-01
We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line. (orig.)
(2, 0) tensor multiplets and conformal supergravity in D = 6
Bergshoeff, Eric; Sezgin, Ergin; Proeyen, Antoine Van
1999-01-01
We construct the supercurrent multiplet that contains the energyâ€“momentum tensor of the (2, 0) tensor multiplet. By coupling this multiplet of currents to the fields of conformal supergravity, we first construct the linearized superconformal transformations rules of the (2, 0) Weyl multiplet.
A tensor approach to the estimation of hydraulic conductivities in ...
African Journals Online (AJOL)
Based on the field measurements of the physical properties of fractured rocks, the anisotropic properties of hydraulic conductivity (HC) of the fractured rock aquifer can be assessed and presented using a tensor approach called hydraulic conductivity tensor. Three types of HC values, namely point value, axial value and flow ...
Tensor analysis for physicists
Schouten, J A
1989-01-01
This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...
Tensor algebra and tensor analysis for engineers with applications to continuum mechanics
Itskov, Mikhail
2015-01-01
This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.
Killing tensors and conformal Killing tensors from conformal Killing vectors
International Nuclear Information System (INIS)
Rani, Raffaele; Edgar, S Brian; Barnes, Alan
2003-01-01
Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors
What have we learned from quantum field theory in curved space-time
International Nuclear Information System (INIS)
Fulling, S.A.
1984-01-01
The paper reviews the quantum field theory in curved space-time. Field quantization in gravitational backgrounds; particle creation by black holes; Hawking radiation; quantum field theory in curved space-time; covariant renormalization of the stress-energy-momentum tensor; quantum field theory and quantum gravity; are all discussed. (U.K.)
Tensor network state correspondence and holography
Singh, Sukhwinder
2018-01-01
In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.
Tensors, relativity, and cosmology
Dalarsson, Mirjana
2015-01-01
Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...
DEFF Research Database (Denmark)
Ziegel, Johanna; Nyengaard, Jens Randel; Jensen, Eva B. Vedel
In the present paper, statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles are developed. The focus of this work is on the case where the particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle...... shape and orientation, and stereological estimators of the tensors are derived. It is shown that these estimators can be combined to provide consistent estimators of the moments of the so-called particle cover density. The covariance structure associated with the particle cover density depends...... may be analysed using a generalized methods of moments in which the volume tensors enter. The developed methods are used to study the cell organization in the human brain cortex....
Quantifying the heterogeneity of the tectonic stress field using borehole data
Schoenball, Martin; Davatzes, Nicholas C.
2017-08-01
The heterogeneity of the tectonic stress field is a fundamental property which influences earthquake dynamics and subsurface engineering. Self-similar scaling of stress heterogeneities is frequently assumed to explain characteristics of earthquakes such as the magnitude-frequency relation. However, observational evidence for such scaling of the stress field heterogeneity is scarce. We analyze the local stress orientations using image logs of two closely spaced boreholes in the Coso Geothermal Field with subvertical and deviated trajectories, respectively, each spanning about 2 km in depth. Both the mean and the standard deviation of stress orientation indicators (borehole breakouts, drilling-induced fractures, and petal-centerline fractures) determined from each borehole agree to the limit of the resolution of our method although measurements at specific depths may not. We find that the standard deviation in these boreholes strongly depends on the interval length analyzed, generally increasing up to a wellbore log length of about 600 m and constant for longer intervals. We find the same behavior in global data from the World Stress Map. This suggests that the standard deviation of stress indicators characterizes the heterogeneity of the tectonic stress field rather than the quality of the stress measurement. A large standard deviation of a stress measurement might be an expression of strong crustal heterogeneity rather than of an unreliable stress determination. Robust characterization of stress heterogeneity requires logs that sample stress indicators along a representative sample volume of at least 1 km.
Superstrings with tensor degrees of freedom
Energy Technology Data Exchange (ETDEWEB)
Amorim, R. (Inst. de Fisica, Univ. Federal do Rio de Janeiro, Rio de Janeiro, RJ (Brazil)); Barcelos-Neto, J. (Inst. de Fisica, Univ. Federal do Rio de Janeiro, Rio de Janeiro, RJ (Brazil))
1994-10-01
We add antisymmetric tensor degrees of freedom to the usual superstring coordinates. We show that super and kappa symmetries are only achieved for the spacetime dimension D = 4. We also address problems related to the quantization of the model and discuss the influences of this extended spacetime in the usual quantum field theory. (orig.)
Tensor modes in pure natural inflation
Nomura, Yasunori; Yamazaki, Masahito
2018-05-01
We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.
Susceptibility tensor imaging (STI) of the brain.
Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu
2017-04-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Tensor calculus for engineers and physicists
de Souza Sánchez Filho, Emil
2016-01-01
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of N dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without need...
Tensor Calculus: Unlearning Vector Calculus
Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita
2018-01-01
Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…
The evolution of tensor polarization
International Nuclear Information System (INIS)
Huang, H.; Lee, S.Y.; Ratner, L.
1993-01-01
By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake
Locus of Control, Field Dependence, and Stress Reactivity in Young Adult Males.
Schweibinz, Janet S.
This study examined the potential relationships between locus of control, field dependence, and stress reactivity in a sample of young adult males (N=40). Locus of control, field dependence, and stress reactivity were measured by the Rotter Locus of Control Scale, the Embedded Figures Test, and the Life Events Survey, respectively. State stress…
Tensor B mode and stochastic Faraday mixing
Giovannini, Massimo
2014-01-01
This paper investigates the Faraday effect as a different source of B mode polarization. The E mode polarization is Faraday rotated provided a stochastic large-scale magnetic field is present prior to photon decoupling. In the first part of the paper we discuss the case where the tensor modes of the geometry are absent and we argue that the B mode recently detected by the Bicep2 collaboration cannot be explained by a large-scale magnetic field rotating, through the Faraday effect, the well established E mode polarization. In this case, the observed temperature autocorrelations would be excessively distorted by the magnetic field. In the second part of the paper the formation of Faraday rotation is treated as a stationary, random and Markovian process with the aim of generalizing a set of scaling laws originally derived in the absence of the tensor modes of the geometry. We show that the scalar, vector and tensor modes of the brightness perturbations can all be Faraday rotated even if the vector and tensor par...
Hall, Jennifer B; Fushman, David
2006-06-21
We applied a combination of 15N relaxation and CSA/dipolar cross-correlation measurements at five magnetic fields (9.4, 11.7, 14.1, 16.4, and 18.8 T) to determine the 15N chemical shielding tensors for backbone amides in protein G in solution. The data were analyzed using various model-independent approaches and those based on Lipari-Szabo approximation, all of them yielding similar results. The results indicate a range of site-specific values of the anisotropy (CSA) and orientation of the 15N chemical shielding tensor, similar to those in ubiquitin (Fushman, et al. J. Am. Chem. Soc. 1998, 120, 10947; J. Am. Chem. Soc. 1999, 121, 8577). Assuming a Gaussian distribution of the 15N CSA values, the mean anisotropy is -173.9 to -177.2 ppm (for 1.02 A NH bond length) and the site-to-site CSA variability is +/-17.6 to +/-21.4 ppm, depending on the method used. This CSA variability is significantly larger than derived previously for ribonuclease H (Kroenke, et al. J. Am. Chem. Soc. 1999, 121, 10119) or recently, using "meta-analysis" for ubiquitin (Damberg, et al. J. Am. Chem. Soc. 2005, 127, 1995). Standard interpretation of 15N relaxation studies of backbone dynamics in proteins involves an a priori assumption of a uniform 15N CSA. We show that this assumption leads to a significant discrepancy between the order parameters obtained at different fields. Using the site-specific CSAs obtained from our study removes this discrepancy and allows simultaneous fit of relaxation data at all five fields to Lipari-Szabo spectral densities. These findings emphasize the necessity of taking into account the variability of 15N CSA for accurate analysis of protein dynamics from 15N relaxation measurements.
Impact of fabric, microcracks and stress field on shale anisotropy
Energy Technology Data Exchange (ETDEWEB)
Dewhurst, D.N.; Siggins, A.F. [CSIRO Petroleum, Australian Petrolium Co-operative Research Centre, Kensington, WA (Australia)
2006-04-15
Few data are available on shales in terms of seismic to ultrasonic properties and anisotropy, although all are important with regards to imaging problems often encountered in such lithologies. Additionally, mechanisms causing changes in these properties are not well documented due to the fine grain size of such materials and time required for testing under controlled pore pressure conditions. The results presented here are derived from a set of experiments run on Muderong Shale with pore pressure control in order to evaluate the effect of stress magnitude and stress anisotropy on ultrasonic response. This shale was noted to have a linear velocity-mean effective stress response and extremely high anisotropy, both likely the result of the presence of fluid-filled cracks in a low permeability porous medium. Changes in velocity and V{sub p}/V{sub s} ratios are dependent on both stress and smectite content. S-wave velocity is significantly affected by the presence of smectite in this and other shales and at low stress (<20 MPa) is less sensitive to stress change than P-wave velocity. V{sub p}/V{sub s} ratios are noted to increase in this shale up to 20 MPa effective stress, then decrease slightly due to stress-induced loss of interlayer water in smectite. Intrinsic anisotropy comes from composition, a strong compaction fabric and the presence of microfractures; changes to ultrasonic anisotropy are the result of the magnitude of the stresses, their orientation with respect to the fractures and the degree of stress anisotropy. (author)
Vectors, tensors and the basic equations of fluid mechanics
Aris, Rutherford
1962-01-01
Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.
A generalization of tensor calculus and its application to physics
International Nuclear Information System (INIS)
Ashtekar, A.
1982-01-01
Penrose's abstract index notation and axiomatic introduction of covariant derivatives in tensor calculus is generalized to fields with internal degrees of freedom. The result provides, in particular, an intrinsic formulation of gauge theories without the use of bundles. (author)
Tensor modes on the string theory landscape
Energy Technology Data Exchange (ETDEWEB)
Westphal, Alexander
2012-06-15
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
Tensor modes on the string theory landscape
International Nuclear Information System (INIS)
Westphal, Alexander
2012-06-01
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
Analysis of HRR stress field at the three-dimensional crack tip, 1
International Nuclear Information System (INIS)
Kikuchi, Masanori; Yano, Kazunori.
1989-01-01
CT specimens with different thickness and a CCT specimen are analyzed precisely using the three-dimensional finite element method in the elastic-plastic stress states. The stress and displacement fields at the crack tip are compared with the HRR singular stress field and discussed. It is found that in the CT specimens, the thicknesses are larger than those recommended by the standard of fracture toughness testing; the stress and displacement fields agree very well with those of HRR fields. For the CT specimen, the thickness of which is a little smaller than the recommended value, the HRR field exists only on the inside of the specimen. It is shown that there are no HRR fields in the CCT specimen although its thickness in not small. (author)
Coordinate independent expression for transverse trace-free tensors
International Nuclear Information System (INIS)
Conboye, Rory
2016-01-01
The transverse and trace-free (TT) part of the extrinsic curvature represents half of the dynamical degrees of freedom of the gravitational field in the 3 + 1 formalism. As such, it is part of the freely specifiable initial data for numerical relativity. Though TT tensors in three-space possess only two component degrees of freedom, they cannot ordinarily be given solely by two scalar potentials. Such expressions have been derived, however, in coordinate form, for all TT tensors in flat space which are also translationally or axially symmetric (Conboye and Murchadha 2014 Class. Quantum Grav. 31 085019). Since TT tensors are conformally covariant, these also give TT tensors in conformally flat space. In this article, the work above has been extended by giving a coordinate-independent expression for these TT tensors. The translational and axial symmetry conditions have also been generalized to invariance along any hypersurface orthogonal Killing vector. (paper)
Coupling the antisymmetric tensor to the supergravity-matter system
International Nuclear Information System (INIS)
Binetruy, P.; Girardi, G.; Mueller, M.
1987-06-01
The description of the antisymmetric tensor gauge field with Chern-Simons forms in Kaehler superspace is used to derive a particular coupling of the antisymmetric tensor to the general supergravity-matter system in terms of superfields as well as component fields. The construction is performed directly in terms of the linear multiplet. The proper duality transformations are presented at the full superfield level. General couplings are shortly discussed
Gogny interactions with tensor terms
Energy Technology Data Exchange (ETDEWEB)
Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)
2016-07-15
We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)
Do Capacity Coupled Electric Fields Accelerate Tibial Stress Fracture Healing?
National Research Council Canada - National Science Library
Hoffman, Andrew
2004-01-01
A convenience sample based on availability of tibial stress fracture cases a% local Sports Medicine Clinics will be selected over 4 years until forty subjects (20 male, 20 female) have been treated...
Do Capacitively Coupled Electric Fields Accelerate Tibial Stress Fracture Healing
National Research Council Canada - National Science Library
Hoffman, Andrew
2002-01-01
A convenience sample based on availability of tibial stress fracture cases at local Sports Medicine Clinics will be selected over 2-3 years until forty subjects (20 male, 20 female) have been treated...
Do Capacitively Coupled Electric Fields Accelerate Tibial Stress Fracture Healing
National Research Council Canada - National Science Library
Hoffman, Andrew
2003-01-01
A convenience sample based on availability of tibial stress fracture cases at local Sports Medicine Clinics will be selected over 2-3 years until forty subjects (20 male, 20 female) have been treated...
Do Capacity Coupled Electric Fields Accelerate Tibial Stress Fracture Healing
2006-12-01
USA Corresponding author Belinda R. Beck, Ph.D. Griffith University School of Physiotherapy and Exercise Science, PMB 50 Gold Coast Mail Centre Q...accelerate tibial stress fracture healing? Medicine and Science in Sport and Exercise , 31(5, Suppl. 1): 2006 2. Beck B.R., Bergman G., Arendt E...Predicting Recovery from Tibial Stress Fracture Medicine and Science in Sport and Exercise , 31(5, Suppl. 1): 2007 (submitted) 15 Presentations
Prevention of brittle fracture of steel structures by controlling the local stress and strain fields
Directory of Open Access Journals (Sweden)
Moyseychik Evgeniy Alekseevich
Full Text Available In the article the author offers a classification of the methods to increase the cold resistance of steel structural shapes with a focus on the regulation of local fields of internal stresses and strains to prevent brittle fracture of steel structures. The need of a computer thermography is highlighted not only for visualization of temperature fields on the surface, but also to control the fields of residual stresses and strains in a controlled element.
End Late Paleozoic tectonic stress field in the southern edge of Junggar Basin
Directory of Open Access Journals (Sweden)
Wei Ju
2012-09-01
Full Text Available This paper presents the end Late Paleozoic tectonic stress field in the southern edge of Junggar Basin by interpreting stress-response structures (dykes, folds, faults with slickenside and conjugate joints. The direction of the maximum principal stress axes is interpreted to be NW–SE (about 325°, and the accommodated motion among plates is assigned as the driving force of this tectonic stress field. The average value of the stress index R′ is about 2.09, which indicates a variation from strike-slip to compressive tectonic stress regime in the study area during the end Late Paleozoic period. The reconstruction of the tectonic field in the southern edge of Junggar Basin provides insights into the tectonic deformation processes around the southern Junggar Basin and contributes to the further understanding of basin evolution and tectonic settings during the culmination of the Paleozoic.
Diffusion tensor smoothing through weighted Karcher means
Carmichael, Owen; Chen, Jun; Paul, Debashis; Peng, Jie
2014-01-01
Diffusion tensor magnetic resonance imaging (MRI) quantifies the spatial distribution of water Diffusion at each voxel on a regular grid of locations in a biological specimen by Diffusion tensors– 3 × 3 positive definite matrices. Removal of noise from DTI is an important problem due to the high scientific relevance of DTI and relatively low signal to noise ratio it provides. Leading approaches to this problem amount to estimation of weighted Karcher means of Diffusion tensors within spatial neighborhoods, under various metrics imposed on the space of tensors. However, it is unclear how the behavior of these estimators varies with the magnitude of DTI sensor noise (the noise resulting from the thermal e!ects of MRI scanning) as well as the geometric structure of the underlying Diffusion tensor neighborhoods. In this paper, we combine theoretical analysis, empirical analysis of simulated DTI data, and empirical analysis of real DTI scans to compare the noise removal performance of three kernel-based DTI smoothers that are based on Euclidean, log-Euclidean, and affine-invariant metrics. The results suggest, contrary to conventional wisdom, that imposing a simplistic Euclidean metric may in fact provide comparable or superior noise removal, especially in relatively unstructured regions and/or in the presence of moderate to high levels of sensor noise. On the contrary, log-Euclidean and affine-invariant metrics may lead to better noise removal in highly structured anatomical regions, especially when the sensor noise is of low magnitude. These findings emphasize the importance of considering the interplay of sensor noise magnitude and tensor field geometric structure when assessing Diffusion tensor smoothing options. They also point to the necessity for continued development of smoothing methods that perform well across a large range of scenarios. PMID:25419264
D=4, N=2 Gauged Supergravity coupled to Vector-Tensor Multiplets
Andrianopoli, Laura; D'Auria, Riccardo; Sommovigo, Luca; Trigiante, Mario
2011-01-01
We construct the general four-dimensional N=2 supergravity theory coupled to vector and vector-tensor multiplets only. Consistency of the construction requires the introduction of the vector fields dual to those sitting in the same supermultiplets as the antisymmetric tensors, as well as the scalar fields dual to the tensors themselves. Gauge symmetries also involving these additional fields guarantee the correct counting of the physical degrees of freedom.
Heat induced fracturing of rock in an existing uniaxial stress field
International Nuclear Information System (INIS)
Mathis, J.; Stephansson, O.; Bjarnason, B.; Hakami, H.; Herdocia, A.; Mattila, U.; Singh, U.
1986-01-01
This study was initiated under the premise that it may be possible to determine the state of stress in the earth's crust by heat induced fracturing of the rock surrounding a borehole. The theory involved is superficially simple, involving the superposition of the stress field around a borehole due to the existing virgin stresses and the uniform stress field of thermally loaded rock as induced by a heater. Since the heat stress field is uniform, varying only in magnitude and gradient as a function of heater input, fracturing should be controlled by the non-uniform virgin stress field. To determine if the method was, in fact, feasible, a series of laboratory test were conducted. These tests consisted of physically loading center drilled cubes of rock, 0.3 m on a side, uniaxially from 0 to 25 MPa. The blocks were then thermally loaded with a nominally rated 3.7 kW heater until failure occurred. Results from these laboratory tests were then compared to analytical studies of the problem, i.e., finite element and discrete theoretical analysis. Overall, results were such that the method is likely eliminated as a stress measurement technique. The immediate development of a thermal compressive zone on the borehole wall overlaps the tensile zone created by the uniaxial stress field, forcing the failure is thus controlled largely by the power input of the heater, being retarded by the small compressive stresses genrated by the uniaxial stress field. This small retardation effect is of such low magnitude that the retardation effect is of such low magnitude that the fracture time is relatively insensitive to the local virgin stress field. (authors)
Lee, Junhyung; Hong, Tae-Kyung; Chang, Chandong
2017-10-01
Seismic activity and focal mechanisms are governed by the effective stress field that is a combined result of regional tectonic processes and local stress perturbation. This study investigates the regional variation in the stress field in the eastern continental margin of the Eurasian plate around the Korean Peninsula and Japanese islands using a damped stress inversion technique based on the focal mechanism solutions of regional earthquakes. The dominant compressional stress is directed ENE-WSW around the Korean Peninsula and eastern China, E-W at the central East Sea and northern and southern Japan, NW-SE at central Japan, and N-S around the northern Nankai trough. The dominant compression direction changes rapidly in the East Sea and Japanese islands, which may be due to the combined effects of tectonic loading in the subduction zones off the Japanese islands and the India-Eurasia plate boundary. The crustal stress fields around the subduction zones off the Japanese islands present characteristic depth-dependent orientations. The orientations of the largest horizontal stress components, σH, in the subduction zones are subparallel with the plate convergence directions at shallow depths. The σH orientations are observed to rotate clockwise with the depth owing to slab subduction and lithospheric deformation. The regional stress field around the Japanese islands was perturbed temporally by the 2011 M9.0 Tohoku-Oki megathrust earthquake. The regional stress field was recovered in a couple of years. The stress field and tectonic structures are mutually affected, causing stress field distortion and a localized mixture of earthquakes in different faulting types.
Dillon, Joshua V.; Langmore, Ian; Tran, Dustin; Brevdo, Eugene; Vasudevan, Srinivas; Moore, Dave; Patton, Brian; Alemi, Alex; Hoffman, Matt; Saurous, Rif A.
2017-01-01
The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable...
Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region
Directory of Open Access Journals (Sweden)
Igor Vigdorovich
2015-01-01
Full Text Available The purpose of this paper is to establish the admitted region for five simultaneous, functionally independent invariants of the strain rate tensor S and rotation rate tensor Ω and calculate some simultaneous invariants of these tensors which are encountered in the theory of constitutive relations for turbulent flows. Such a problem, as far as we know, has not yet been considered, though it is obviously an integral part of any problem in which scalar functions of the tensors S and Ω are studied. The theory provided inside this paper is the building block for a derivation of new algebraic constitutive relations for three-dimensional turbulent flows in the form of expansions of the Reynolds-stress tensor in a tensorial basis formed by the tensors S and Ω, in which the scalar coefficients depend on simultaneous invariants of these tensors.
Tensor Permutation Matrices in Finite Dimensions
Christian, Rakotonirina
2005-01-01
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...
Directory of Open Access Journals (Sweden)
S. M. Abo-Dahab
2014-01-01
Full Text Available We estimated an analytical solution of the displacement, stress, and temperature in a rotating isotropic homogeneous elastic medium hollow sphere subjected to periodic loading and magnetic field. The coupled theory of thermoelasticity is applied to determine an infinite velocity of heat propagation. The numerical calculations are carried out for the displacement, temperature, and stresses. The results obtained are displayed graphically to illustrate the effect of initial stress, rotation, and magnetic field which indicate to pronounce influence of rotation and magnetic field.
The stress system generated by an electromagnetic field in a suspension of drops
Erdogan, M. E.
1982-01-01
The stress generated in a suspension of drops in the presence of a uniform electric field and a pure straining motion, taking into account that the magnetohydrodynamic effects are dominant was calculated. It was found that the stress generated in the suspension depended on the direction of the applied electric field, the dielectric constants, the vicosity coefficients, the conductivities, and the permeabilities of fluids inside and outside the drops. The expression of the particle stress shows that for fluids which are good conductors and poor dielectrics, especially for larger drops, magnetohydrodynamic effects end to reduce the dependence on the direction of the applied electric field.
Measurement of the stress field of a tunnel through its rock EMR
Qiu, Liming; Wang, Enyuan; Song, Dazhao; Liu, Zhentang; Shen, Rongxi; Lv, Ganggang; Xu, Zhaoyong
2017-08-01
In order to quantitatively study the relationship between the disturbance stress of coal mine roadways and the electromagnetic radiation (EMR) of rocks, and further evaluate their internal stress distributions, we first examined the characteristics of EMR signals emitted from rock mass under uniaxial compression, analyzed the relationship between the stress inside the rock mass and its emitted EMR intensity, and put forward a new disturbance stress testing method by monitoring the EMR from the rock mass to retrieve its surrounding stress field. Then, we applied the method to monitor EMR intensity from the no.11803 rock roadway of the Nuodong coal mine, China, and inversely retrieved its stress field. Lastly, we analyzed the causes of local stress anomalies in the Nuodong area by testing the EMR intensity of its nearby areas, and we examined the geology of the whole region. The results showed that: (1) in the rock roadway and the surrounding area of the Nuodong coal mine, the disturbance stress was in the range of 4.8 ˜ 9.1 MPa, the angle between the direction of the stress field and the horizontal plane of the roadway was 35 ± 2.5°, the lateral pressure coefficient was 1.30 ˜ 1.57 (2) the Laoguishan and Yulong anticlines in the vicinity of the Nuodong coal mine caused great horizontal tectonic stress in the region, and the existence of the auxiliary roadway and F12 normal fault resulted in the formation of two high stress zones in the no.11803 rock roadway. Overall, monitoring the EMR from rock mass could ascertain the state, direction, size and distribution of disturbance stress in a roadway and further obtain the distribution of the stress field of an underground structure.
Tensor Factorization for Low-Rank Tensor Completion.
Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao
2018-03-01
Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.
Vector Magnetic Fields, Sub surface Stresses and Evolution of ...
Indian Academy of Sciences (India)
tribpo
Abstract. Observations of the strength and spatial distribution of vector magnetic fields in active regions have revealed several fundamental properties of the twist of their magnetic fields. First, the handedness of this twist obeys a hemispheric rule: left handed in the northern hemis phere, right handed in the southern. Second ...
Fouré, Alexandre; Ogier, Augustin C; Le Troter, Arnaud; Vilmen, Christophe; Feiweier, Thorsten; Guye, Maxime; Gondin, Julien; Besson, Pierre; Bendahan, David
2018-05-01
Purpose To demonstrate the reproducibility of the diffusion properties and three-dimensional structural organization measurements of the lower leg muscles by using diffusion-tensor imaging (DTI) assessed with ultra-high-field-strength (7.0-T) magnetic resonance (MR) imaging and tractography of skeletal muscle fibers. On the basis of robust statistical mapping analyses, this study also aimed at determining the sensitivity of the measurements to sex difference and intramuscular variability. Materials and Methods All examinations were performed with ethical review board approval; written informed consent was obtained from all volunteers. Reproducibility of diffusion tensor indexes assessment including eigenvalues, mean diffusivity, and fractional anisotropy (FA) as well as muscle volume and architecture (ie, fiber length and pennation angle) were characterized in lower leg muscles (n = 8). Intramuscular variability and sex differences were characterized in young healthy men and women (n = 10 in each group). Student t test, statistical parametric mapping, correlation coefficients (Spearman rho and Pearson product-moment) and coefficient of variation (CV) were used for statistical data analysis. Results High reproducibility of measurements (mean CV ± standard deviation, 4.6% ± 3.8) was determined in diffusion properties and architectural parameters. Significant sex differences were detected in FA (4.2% in women for the entire lower leg; P = .001) and muscle volume (21.7% in men for the entire lower leg; P = .008), whereas architecture parameters were almost identical across sex. Additional differences were found independently of sex in diffusion properties and architecture along several muscles of the lower leg. Conclusion The high-spatial-resolution DTI assessed with 7.0-T MR imaging allows a reproducible assessment of structural organization of superficial and deep muscles, giving indirect information on muscle function. © RSNA, 2018 Online supplemental material is
Dark energy in scalar-tensor theories
International Nuclear Information System (INIS)
Moeller, J.
2007-12-01
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of σ-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
Dark energy in scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Moeller, J.
2007-12-15
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of {sigma}-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
Fermionic topological quantum states as tensor networks
Wille, C.; Buerschaper, O.; Eisert, J.
2017-06-01
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.
Response of Velocity Anisotropy of Shale Under Isotropic and Anisotropic Stress Fields
Li, Xiaying; Lei, Xinglin; Li, Qi
2018-03-01
We investigated the responses of P-wave velocity and associated anisotropy in terms of Thomsen's parameters to isotropic and anisotropic stress fields on Longmaxi shales cored along different directions. An array of piezoelectric ceramic transducers allows us to measure P-wave velocities along numerous different propagation directions. Anisotropic parameters, including the P-wave velocity α along a symmetry axis, Thomsen's parameters ɛ and δ, and the orientation of the symmetry axis, could then be extracted by fitting Thomsen's weak anisotropy model to the experimental data. The results indicate that Longmaxi shale displays weakly intrinsic velocity anisotropy with Thomsen's parameters ɛ and δ being approximately 0.05 and 0.15, respectively. The isotropic stress field has only a slight effect on velocity and associated anisotropy in terms of Thomsen's parameters. In contrast, both the magnitude and orientation of the anisotropic stress field with respect to the shale fabric are important in controlling the evolution of velocity and associated anisotropy in a changing stress field. For shale with bedding-parallel loading, velocity anisotropy is enhanced because velocities with smaller angles relative to the maximum stress increase significantly during the entire loading process, whereas those with larger angles increase slightly before the yield stress and afterwards decrease with the increasing differential stress. For shale with bedding-normal loading, anisotropy reversal is observed, and the anisotropy is progressively modified by the applied differential stress. Before reaching the yield stress, velocities with smaller angles relative to the maximum stress increase more significantly and even exceed the level of those with larger angles. After reaching the yield stress, velocities with larger angles decrease more significantly. Microstructural features such as the closure and generation of microcracks can explain the modification of the velocity anisotropy
The stress field in an edge cracked plate in antiplane deformation
Li, V. C.; Lim, H. S.
1988-01-01
The antiplane strain problem of an edge cracked elastic plate subjected to a surface displacement load is solved, and the surface line loads are obtained using conformal mapping techniques. Results are presented for the yield, stress, strain and displacement distributions, and stress intensity factors in the plate. A superposition technique and Green's functions are used to determine the strain field on the upper plate surface due to arbitrarily applied tensile stress on the lower plate surface.
National Research Council Canada - National Science Library
Jones, D
1995-01-01
.... Pulsing electromagnetic fields (PEMFs)have been shown to speed the healing of non-union fractures and we have used them successfully to treat stress fractures in the lower limbs. All women at Ft...
Biofeedback systems for stress reduction: Towards a Bright Future for a Revitalized Field
van den Broek, Egon; Westerink, Joyce H.D.M.; Conchon, E.; Correia, C.; Fred, A.; Gamboa, H.
2012-01-01
Stress has recently been baptized as the black death of the 21st century, which illustrates its threat to current health standards. This article proposes biofeedback systems as a means to reduce stress. A concise state-ofthe-art introduction on biofeedback systems is given. The field of mental
Evaluation of debonding strength of single lap joint by the intensity of singular stress field
Miyazaki, Tatsujiro; Noda, Nao-Aki
2017-05-01
In this paper, the similarity of the singular stress field of the single lap joint (SLJ) is discussed to evaluate the debonding fracture by the intensity of the singular stress field (ISSF). The practical method is proposed for analyzing the ISSF for the SLJ. The analysis method focuses on the FEM stress at the interface end by applying the same mesh pattern to the unknown and reference models. It is found that the independent technique useful for the bonded plate and butt joint cannot be applied to the SLJ because the singular stress field of the SLJ consists of two singular stress terms. The FEM stress is divided to two FEM stresses by applying the unknown and reference models to different minimum element sizes. Then, the practicality of the present method is examined by applying to the previous tensile test results of the SLJ composed of the aluminum alloy and the epoxy resin. The ISSFs for the SLJ were calculated by changing the adhesive thickness t 2 and the overlap length l 2. In the case of the SLJ with 225 mm in total length and 7 mm in adherend thickness, it was found that the similar singular stress fields are formed in the range of 0.15 mm ≤ t 2 ≤ 0.9mm and 15 mm ≤ l 2 ≤ 50 mm. It is shown that the critical ISSFs at the fracture are constant in the range.
Biofeedback for stress reduction: towards a brigth future for a revitalized field
Van den Broek, E.L.; Westerink, J.H.D.
2012-01-01
Stress has recently been baptized as the black death of the 21st century, which illustrates its threat to current health standards. Thisarticle proposes biofeedback systems as a means to reduce stress. Aconcise state-ofthe-art introduction on biofeedback systems is given. The field of mental health
A satellite based crop water stress index for irrigation scheduling in sugarcane fields
Veysi, Shadman; Naseri, Abd Ali; Hamzeh, Saeid; Bartholomeus, Harm
2017-01-01
In this study, the capability of crop water stress index (CWSI) based on satellite thermal infrared data for estimating water stress and irrigation scheduling in sugarcane fields was evaluated. For this purpose, eight Landsat 8 satellite images were acquired during the sugarcane growing season
Biofeedback systems for stress reduction : Towards a bright future for a revitalized field
Broek, E.L. van den; Westerink, J.H.D.M.
2012-01-01
Stress has recently been baptized as the black death of the 21st century, which illustrates its threat to current health standards. This article proposes biofeedback systems as a means to reduce stress. A concise state-of-the-art introduction on biofeedback systems is given. The field of mental
International Nuclear Information System (INIS)
Rao, J.R.; Tiwari, R.N.
1974-01-01
A theorem on obtaining exact solutions for a particular field structure from those of vacuum field equations of general theory as well as from some simpler solutions of unified theories is derived. With the help of this result the most general solution for the particular field structure is developed from the already known simpler solutions. The physical implications of this theorem in relation to some of the parallel work of other authors is discussed. (author)
Ford, S. R.; Dreger, D. S.; Walter, W. R.
2006-12-01
Seismic moment tensor analysis at regional distances commonly involves solving for the deviatoric moment tensor and decomposing it to characterize the tectonic earthquake source. The full seismic moment tensor solution can also recover the isotropic component of the seismic source, which is theoretically dominant in explosions and collapses, and present in volcanic events. Analysis of events with demonstrably significant isotropic energy can aid in understanding the source processes of volcanic and geothermal seismic events and the monitoring of nuclear explosions. Using a regional time-domain waveform inversion for the complete moment tensor we calculate the deviatoric and isotropic source components for several explosions at the Nevada Test Site (NTS) and earthquakes, collapses, and volcanic events in the surrounding region of the NTS (Western US). The events separate into specific populations according to their deviation from a pure double-couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination of explosions, earthquakes, and collapses. Analysis of the source principal axes can characterize the regional stress field, and tectonic release due to explosions. Error in the moment tensor solutions and source parameters is also calculated. We investigate the sensitivity of the moment tensor solutions to Green's functions calculated with imperfect Earth models, inaccurate event locations, and data with a low signal-to-noise ratio. We also test the performance of the method under a range of recording conditions from excellent azimuthal coverage to cases of sparse coverage as might be expected for smaller events. This analysis will be used to determine the magnitude range where well-constrained solutions can be obtained.
Tensor norms and operator ideals
Defant, A; Floret, K
1992-01-01
The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer
Notes on super Killing tensors
Energy Technology Data Exchange (ETDEWEB)
Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)
2016-03-14
The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.
Tensor Train Neighborhood Preserving Embedding
Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin
2018-05-01
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.
Canonical forms of tensor representations and spontaneous symmetry breaking
International Nuclear Information System (INIS)
Cummins, C.J.
1986-01-01
An algorithm for constructing canonical forms for any tensor representation of the classical compact Lie groups is given. This method is used to find a complete list of the symmetry breaking patterns produced by Higgs fields in the third-rank antisymmetric representations of U(n), SU(n) and SO(n) for n<=7. A simple canonical form is also given for kth-rank symmetric tensor representations. (author)
Asymptotic tensor rank of graph tensors: beyond matrix multiplication
M. Christandl (Matthias); P. Vrana (Péter); J. Zuiddam (Jeroen)
2016-01-01
textabstractWe present an upper bound on the exponent of the asymptotic behaviour of the tensor rank of a family of tensors defined by the complete graph on $k$ vertices. For $k\\geq4$, we show that the exponent per edge is at most 0.77, outperforming the best known upper bound on the exponent per
Improved modeling techniques for turbomachinery flow fields
Energy Technology Data Exchange (ETDEWEB)
Lakshminarayana, B.; Fagan, J.R. Jr.
1995-12-31
This program has the objective of developing an improved methodology for modeling turbomachinery flow fields, including the prediction of losses and efficiency. Specifically, the program addresses the treatment of the mixing stress tensor terms attributed to deterministic flow field mechanisms required in steady-state Computational Fluid Dynamic (CFD) models for turbomachinery flow fields. These mixing stress tensors arise due to spatial and temporal fluctuations (in an absolute frame of reference) caused by rotor-stator interaction due to various blade rows and by blade-to-blade variation of flow properties. This will be accomplished in a cooperative program by Penn State University and the Allison Engine Company. These tasks include the acquisition of previously unavailable experimental data in a high-speed turbomachinery environment, the use of advanced techniques to analyze the data, and the development of a methodology to treat the deterministic component of the mixing stress tenor.
International Nuclear Information System (INIS)
Allen, A.J.; Hutchings, M.T.; Windsor, C.G.
1987-01-01
The paper describes and illustrates the capability of neutron diffraction to measure the complete internal lattice macrostrain field, and hence the stress field, within steel components and weldments arising from their fabrication. A brief outline is given of the theory of the neutron method. The experimental considerations are discussed. The method is illustrated by its application to the measurement of the stress distribution in a:- uniaxially stressed mild steel rod, a double - V test weld, a tube-plate weld, and a cracked fatigue test specimen. (U.K.)
Tests for the determination of the stress condition in tension fields
Lahde, R; Wagner, H
1936-01-01
The present experiments treat the stress of actual tension fields within the elastic range. They give the magnitude of the flexural stresses due to wrinkling. They also disclose, particularly by slightly exceeded buckling load, the marked unloading - as compared with the tension-field theory - of the uprights as a result of the flexural stiffness of the web plate. The test sheets were clamped at the edges and brought to buckling through shearing and compressive stresses applied in the direction of the long sides.
Shielding Flowers Developing under Stress: Translating Theory to Field Application
Directory of Open Access Journals (Sweden)
Noam Chayut
2014-07-01
Full Text Available Developing reproductive organs within a flower are sensitive to environmental stress. A higher incidence of environmental stress during this stage of a crop plants’ developmental cycle will lead to major breaches in food security. Clearly, we need to understand this sensitivity and try and overcome it, by agricultural practices and/or the breeding of more tolerant cultivars. Although passion fruit vines initiate flowers all year round, flower primordia abort during warm summers. This restricts the season of fruit production in regions with warm summers. Previously, using controlled chambers, stages in flower development that are sensitive to heat were identified. Based on genetic analysis and physiological experiments in controlled environments, gibberellin activity appeared to be a possible point of horticultural intervention. Here, we aimed to shield flowers of a commercial cultivar from end of summer conditions, thus allowing fruit production in new seasons. We conducted experiments over three years in different settings, and our findings consistently show that a single application of an inhibitor of gibberellin biosynthesis to vines in mid-August can cause precocious flowering of ~2–4 weeks, leading to earlier fruit production of ~1 month. In this case, knowledge obtained on phenology, environmental constraints and genetic variation, allowed us to reach a practical solution.
Algebraic Rainich conditions for the fourth rank tensor V
International Nuclear Information System (INIS)
So, Lau Loi
2011-01-01
Algebraic conditions on the Ricci tensor in the Rainich-Misner-Wheeler unified field theory are known as the Rainich conditions. Penrose and more recently Bergqvist and Lankinen made an analogy from the Ricci tensor to the Bel-Robinson tensor B αβμν , a certain fourth rank tensor quadratic in the Weyl curvature, which also satisfies algebraic Rainich-like conditions. However, we found that not only does the tensor B αβμν fulfill these conditions, but so also does our recently proposed tensor V αβμν , which has many of the desirable properties of B αβμν . For the quasilocal small sphere limit restriction, we found that there are only two fourth rank tensors, B αβμν and V αβμν , which form a basis for good energy expressions. Both of them have the completely trace free and causal properties, these two form necessary and sufficient conditions. Surprisingly either completely traceless or causal is enough to fulfill the algebraic Rainich conditions.
A study of interply layer effects on the free-edge stress field of angleplied laminates
Murthy, P. L. N.; Chamis, C. C.
1984-01-01
The general-purpose finite-element program MSC/NASTRAN is used to study the interply layer effects on the free-edge stress field of symmetric angleplied laminates subjected to uniform tensile stress. The free-edge region is modeled as a separate substructure (superelement) which enables easy mesh refinement and provides the flexibility to move the superelement along the edge. The results indicate that the interply layer reduces the stress intensity significantly at the free edge. Another important observation of the study is that the failures observed near free edges of these types of laminates could have been caused by the interlaminar shear stresses.
Vector Magnetic Fields, Sub surface Stresses and Evolution of ...
Indian Academy of Sciences (India)
tribpo
Arendt 1996). Bogdan (1984) found that flux tubes of the same sense of twist will merge if their relative velocities are slow enough to allow their magnetic fields to reconnect. Zweibel & Rhoads (1995) estimated an upper limit to the critical velocity and concluded that colliding twisted flux tubes may coalesce at the base of the ...
Kodera, Masako; Iguchi, Tadashi; Tsuchiya, Norihiko; Tamura, Mizuki; Kakinuma, Shigeru; Naka, Nobuyuki; Kashiwagi, Shinsuke
2008-04-01
Stress engineering related to the LSI process is required. With shallow trench isolation (STI) structures, a high stress field causes a variation in electrical characteristics. Although stress fields in a Si substrate can be detected by Raman spectroscopy, no effective technique has been reported for the measurement of nanoscale stress fields in a dielectric material used for STI filling. Recently, we have reported that “cathodoluminescence (CL) spectroscopy” enables us to detect nanometer-scale stress fields in LSI structures. In this study, we performed the first estimation of the stress fields with a STI structure by CL and Raman spectroscopy, as well as finite element method (FEM) calculation. We were able to repeatedly acquire clear stress distributions by CL and Raman spectroscopy. Moreover, CL, Raman, and FEM results showed excellent agreement with one another, revealing that a large variation in stresses along the AA/STI boundary was induced by the intrinsic tensile stress of the SiO2 film.
Directory of Open Access Journals (Sweden)
Y. Prawoto
2012-01-01
Full Text Available Through an investigation of the field failure analysis and laboratory experiment, a study on (stress corrosion cracking SCC behavior of steel and aluminum was performed. All samples were extracted from known operating conditions from the field failures. Similar but accelerated laboratory test was subsequently conducted in such a way as to mimic the field failures. The crack depth and behavior of the SCC were then analyzed after the laboratory test and the mechanism of stress corrosion cracking was studied. The results show that for the same given stress relative to ultimate tensile strength, the susceptibility to SCC is greatly influenced by heat treatment. Furthermore, it was also concluded that when expressed relative to the (ultimate tensile strength UTS, aluminum has similar level of SCC susceptibility to that of steel, although with respect to the same absolute value of applied stress, aluminum is more susceptible to SCC in sodium hydroxide environment than steel.
EINSTEIN EQUATIONS FOR TETRAD FIELDS ECUACIONES DE EINSTEIN PARA CAMPOS TETRADOS
Directory of Open Access Journals (Sweden)
Héctor Torres-Silva
2008-11-01
Full Text Available Every metric tensor can be expressed by the inner product of tetrad fields. We prove that Einstein's equations for these fields have the same form as the stress-energy tensor of electromagnetism if the total external current . Using the Evans' unified field theory, we show that the true unification of gravity and electromagnetism is with source-free Maxwell equations.Todo tensor métrico puede ser expresado por el producto interno de campos tetrados. Se prueba que las ecuaciones de Einstein para esos campos tienen la misma forma que el tensor electromagnético de momento-energía si la corriente externa total es igual a cero. Usando la teoría de campo unificado de Evans se muestra que la verdadera unificación de la gravedad y el electromagnetismo es con las ecuaciones de Maxwell sin fuentes.
Perez-Flores, P.; Cembrano, J. M.; Sanchez-Alfaro, P.
2014-12-01
The northern termination of Liquiñe-Ofqui Fault System (LOFS) is characterized by major NNE-striking dextral strike-slip faults and several second and third-order NE-to-ENE-striking oblique-slip faults. This geometry forms a transtensional duplex structure. The LOFS has a complex crosscutting relationship with inherited NW-striking structures of the Arc-oblique long-lived Fault System (ALFS). We conducted a structural mapping of fault and vein populations at key structural sites representative of each regional structural system. Field observations were combined with different methods of inversion of fault-slip heterogeneous data and with the use of different open-source computer programs that calculate resolved stress tensors and P-T axes for each structural site in order to unravel the significance of this complex architecture. The results of the inversion of fault-slip analysis show that a transtensional strike-slip regime, with NE-SW-trending subhorizontal σ1, predominate in the first and second order faults in the northern termination of the duplex. A more local tensional regime was calculated for the same area. The inversion solutions are compatible with NE-trending subvertical veins system and dilational jogs and breccia. In contrast, within the central area of the duplex fault slip inversion of fault populations shows both transpressional and compressional regimes. The first tectonic regime is compatible with ENE-striking veins and dikes. In the southern part of the duplex, fault populations are compatible with either a local transtensional stress field with an ESE-trending subhorizontal σ1 or with a tensional regime with a SW-trending, steeply plunging σ1. Our results show the complexity in the nature and spatial distribution of stress fields within strike-slip duplexes and its role in the geometrical distribution of paleo-fluid flow, part of which may account for the reactivation of inherited faults or strain incompatibilities at fault intersections.
Full-field stress determination in photoelasticity with phase shifting technique
Guo, Enhai; Liu, Yonggang; Han, Yongsheng; Arola, Dwayne; Zhang, Dongsheng
2018-04-01
Photoelasticity is an effective method for evaluating the stress and its spatial variations within a stressed body. In the present study, a method to determine the stress distribution by means of phase shifting and a modified shear-difference is proposed. First, the orientation of the first principal stress and the retardation between the principal stresses are determined in the full-field through phase shifting. Then, through bicubic interpolation and derivation of a modified shear-difference method, the internal stress is calculated from the point with a free boundary along its normal direction. A method to reduce integration error in the shear difference scheme is proposed and compared to the existing methods; the integration error is reduced when using theoretical photoelastic parameters to calculate the stress component with the same points. Results show that when the value of Δx/Δy approaches one, the error is minimum, and although the interpolation error is inevitable, it has limited influence on the accuracy of the result. Finally, examples are presented for determining the stresses in a circular plate and ring subjected to diametric loading. Results show that the proposed approach provides a complete solution for determining the full-field stresses in photoelastic models.
Indicial tensor manipulation on MACSYMA
International Nuclear Information System (INIS)
Bogen, R.A.; Pavelle, R.
1977-01-01
A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The authors outline the capabilities of the system and describe some of the physical problems considered as well as others being examined at this time. (Auth.)
Displacement and stress fields around rock fractures opened by irregular overpressure variations
Directory of Open Access Journals (Sweden)
Shigekazu eKusumoto
2014-05-01
Full Text Available Many rock fractures are entirely driven open by fluids such as ground water, geothermal water, gas, oil, and magma. These are a subset of extension fractures (mode I cracks; e.g., dikes, mineral veins and joints referred to as hydrofractures. Field measurements show that many hydrofractures have great variations in aperture. However, most analytical solutions for fracture displacement and stress fields assume the loading to be either constant or with a linear variation. While these solutions have been widely used, it is clear that a fracture hosted by heterogeneous and anisotropic rock is normally subject to loading that is neither constant nor with a linear variation. Here we present new general solutions for the displacement and stress fields around hydrofractures, modelled as two-dimensional elastic cracks, opened by irregular overpressure variations given by the Fourier cosine series. Each solution has two terms. The first term gives the displacement and stress fields due to the average overpressure acting inside the crack; it is given by the initial term of the Fourier coefficients expressing the overpressure variation. The second term gives the displacement and stress fields caused by the overpressure variation; it is given by general terms of the Fourier coefficients and solved through numerical integration. Our numerical examples show that the crack aperture variation closely reflects the overpressure variation. Also, that the general displacement and stress fields close to the crack follow the overpressure variation but tend to be more uniform far from the crack. The present solutions can be used to estimate the displacement and stress fields around any fluid-driven crack, that is, any hydrofracture, as well as its aperture, provided the variation in overpressure can be described by Fourier series. The solutions add to our understanding of local stresses, displacements, and fluid transport associated with hydrofractures in the crust.
Killing-Yano tensors and Nambu mechanics
International Nuclear Information System (INIS)
Baleanu, D.
1998-01-01
Killing-Yano tensors were introduced in 1952 by Kentaro-Yano from mathematical point of view. The physical interpretation of Killing-Yano tensors of rank higher than two was unclear. We found that all Killing-Yano tensors η i 1 i 2 . .. i n with covariant derivative zero are Nambu tensors. We found that in the case of flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT and Kerr-Newmann metric Killing-Yano tensors of order two generate Nambu tensors of rank 3
Directory of Open Access Journals (Sweden)
Kang Ma
2017-01-01
Full Text Available Coherent gradient sensing (CGS method can be used to measure the slope of a reflective surface, and has the merits of full-field, non-contact, and real-time measurement. In this study, the thermal stress field of thermal barrier coating (TBC structures is measured by CGS method. Two kinds of powders were sprayed onto Ni-based alloy using a plasma spraying method to obtain two groups of film–substrate specimens. The specimens were then heated with an oxy-acetylene flame. The resulting thermal mismatch between the film and substrate led to out-of-plane deformation of the specimen. The deformation was measured by the reflective CGS method and the thermal stress field of the structure was obtained through calibration with the help of finite element analysis. Both the experiment and numerical results showed that the thermal stress field of TBC structures can be successfully measured by CGS method.
Mohammed, R. A.; Khatibi, S.
2017-12-01
One of the major concerns in producing from oil and gas reservoirs in North American Basins is the disposal of high salinity salt water. It is a misconception that Hydro frack triggers Earthquakes, but due to the high salinity and density of water being pumped to the formation that has pore space of the rock already filled, which is not the case in Hydro-frack or Enhanced Oil Recovery in which fracturing fluid is pumped into empty pore space of rocks in depleted reservoirs. A review on the Bakken history showed that the concerns related to induce seismicity has increased over time due to variations in Pore pressure and In-situ stress that have shown steep changes in the region over the time. In this study, we focused on Pore pressure and field Stress variations in lower Cretaceous Inyan Kara and Mississippian Devonian Bakken, Inyan Kara is the major source for class-II salt-water disposal in the basin. Salt-water disposal is the major cause for induced seismicity. A full field study was done on Beaver Lodge Field, which has many salt-water disposal wells Adjacent to Oil and Gas Wells. We analyzed formation properties, stresses, pore-pressure, and fracture gradient profile in the field and. The constructed Mechanical Earth Model (MEM) revealed changes in pore pressure and stresses over time due to saltwater injection. Well drilled in the past were compared to recently drilled wells, which showed much stress variations. Safe mud weight Window of wells near proximity of injection wells was examined which showed many cases of wellbore instabilities. Results of this study will have tremendous impact in studying environmental issues and the future drilling and Fracking operations.
Analyzing vortex breakdown flow structures by assignment of colors to tensor invariants.
Rütten, Markus; Chong, Min S
2006-01-01
Topological methods are often used to describe flow structures in fluid dynamics and topological flow field analysis usually relies on the invariants of the associated tensor fields. A visual impression of the local properties of tensor fields is often complex and the search of a suitable technique for achieving this is an ongoing topic in visualization. This paper introduces and assesses a method of representing the topological properties of tensor fields and their respective flow patterns with the use of colors. First, a tensor norm is introduced, which preserves the properties of the tensor and assigns the tensor invariants to values of the RGB color space. Secondly, the RGB colors of the tensor invariants are transferred to corresponding hue values as an alternative color representation. The vectorial tensor invariants field is reduced to a scalar hue field and visualization of iso-surfaces of this hue value field allows us to identify locations with equivalent flow topology. Additionally highlighting by the maximum of the eigenvalue difference field reflects the magnitude of the structural change of the flow. The method is applied on a vortex breakdown flow structure inside a cylinder with a rotating lid.
Renormalized energy-momentum tensor of λΦ4 theory in curved ...
Indian Academy of Sciences (India)
Renormalization of the energy-momentum tensor for λΦΦ4 theory. Our aim is to obtain finite expression for the energy-momentum tensor of a quantized scalar field interacting with classical Einstein gravitational field using momentum cut-off regular- ization technique. We have chosen the λΦ4 model of self-interaction, and ...
Cavitation microstreaming and stress fields created by microbubbles.
Collis, James; Manasseh, Richard; Liovic, Petar; Tho, Paul; Ooi, Andrew; Petkovic-Duran, Karolina; Zhu, Yonggang
2010-02-01
Cavitation microstreaming plays a role in the therapeutic action of microbubbles driven by ultrasound, such as the sonoporative and sonothrombolytic phenomena. Microscopic particle-image velocimetry experiments are presented. Results show that many different microstreaming patterns are possible around a microbubble when it is on a surface, albeit for microbubbles much larger than used in clinical practice. Each pattern is associated with a particular oscillation mode of the bubble, and changing between patterns is achieved by changing the sound frequency. Each microstreaming pattern also generates different shear stress and stretch/compression distributions in the vicinity of a bubble on a wall. Analysis of the micro-PIV results also shows that ultrasound-driven microstreaming flows around bubbles are feasible mechanisms for mixing therapeutic agents into the surrounding blood, as well as assisting sonoporative delivery of molecules across cell membranes. Patterns show significant variations around the bubble, suggesting sonoporation may be either enhanced or inhibited in different zones across a cellular surface. Thus, alternating the patterns may result in improved sonoporation and sonothrombolysis. The clear and reproducible delineation of microstreaming patterns based on driving frequency makes frequency-based pattern alternation a feasible alternative to the clinically less desirable practice of increasing sound pressure for equivalent sonoporative or sonothrombolytic effect. Surface divergence is proposed as a measure relevant to sonoporation.
In situ Weak Magnetic-Assisted Thermal Stress Field Reduction Effect in Laser Welding
Liang, Lvjie; Pang, Shengyong; Shao, Xinyu; Wang, Chunming; Jiang, Ping; Chen, Xin
2018-01-01
For decades, post-welding magnetic treatment has been used to reduce residual stress of welds by improving the crystal structure of solid-state welds. In this paper, we propose a new magnetic treatment method, which can reduce the time-dependent thermal stress field in situ and reduce the final residual stress of welds by simply exerting an assisted weak magnetic field perpendicular to the welding direction and workpiece during laser welding. A new finite-element model is developed to understand the thermal-mechanical physical process of the magnetic-assisted laser welding. For the widely used 304 austenite stainless steel, we theoretically observed that this method can reduce around 10 pct of the time-dependent thermal stress field, and finally reduce approximately 20 MPa of residual stress near the heat-affected zone with a 415-mT magnetic field for typical welding process parameters. A new mechanism based on magneto-fluid dynamics is proposed to explain the theoretical predications by combining high-speed imaging experiments of the transient laser welding process. The developed method is very simple but surprisingly effective, which opens new avenues for thermal stress reduction in laser welding of metals, particularly heat-sensitive metallic materials.
Tensor analysis and elementary differential geometry for physicists and engineers
Nguyen-Schäfer, Hung
2017-01-01
This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics. Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum m...
Vacuum fluctuations of twisted fields in the space time of cosmic strings
International Nuclear Information System (INIS)
Matsas, G.E.A.
1990-01-01
A twisted scalar field conformally coupled to gravitation is used to calculate the vacuum stress-energy tensor in the background spacetime generated by an infinite straight gauge cosmic string. The result has an absolute numerical value close to the one obtained with a non-twisted conformal scalar field but their signals are opposite. (author) [pt
X-ray strain tensor imaging: FEM simulation and experiments with a micro-CT.
Kim, Jae G; Park, So E; Lee, Soo Y
2014-01-01
In tissue elasticity imaging, measuring the strain tensor components is necessary to solve the inverse problem. However, it is impractical to measure all the tensor components in ultrasound or MRI elastography because of their anisotropic spatial resolution. The objective of this study is to compute 3D strain tensor maps from the 3D CT images of a tissue-mimicking phantom. We took 3D micro-CT images of the phantom twice with applying two different mechanical compressions to it. Applying the 3D image correlation technique to the CT images under different compression, we computed 3D displacement vectors and strain tensors at every pixel. To evaluate the accuracy of the strain tensor maps, we made a 3D FEM model of the phantom, and we computed strain tensor maps through FEM simulation. Experimentally obtained strain tensor maps showed similar patterns to the FEM-simulated ones in visual inspection. The correlation between the strain tensor maps obtained from the experiment and the FEM simulation ranges from 0.03 to 0.93. Even though the strain tensor maps suffer from high level noise, we expect the x-ray strain tensor imaging may find some biomedical applications such as malignant tissue characterization and stress analysis inside the tissues.
Cosmological magnetic fields - V
Indian Academy of Sciences (India)
Introduction. Magnetic fields seem to be everywhere that we can look in the universe, from our own sun out to high-redshift Lyman-« systems. The fields we ... is the field tensor, is the four-potential, and В is the four-current. The field tensor is observer-independent, while the electric and magnetic fields depend on the ...
MATLAB tensor classes for fast algorithm prototyping.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2004-10-01
Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.
Random SU(2) invariant tensors
Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei
2018-04-01
SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n = 4. In this paper, we show that for n > 4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.
Vilanova, Anna; Burgeth, Bernhard; Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data
2014-01-01
Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and...
THEORETICAL COMPUTATION OF A STRESS FIELD IN A CYLINDRICAL GLASS SPECIMEN
Directory of Open Access Journals (Sweden)
NORBERT KREČMER
2011-03-01
Full Text Available This work deals with the computation of the stress field generated in an infinitely high glass cylinder while cooling. The theory of structural relaxation is used in order to compute the heat capacity, the thermal expansion coefficient, and the viscosity. The relaxation of the stress components is solved in the frame of the Maxwell viscoelasticity model. The obtained results were verified by the sensitivity analysis and compared with some experimental data.
Retinal Vessel Segmentation via Structure Tensor Coloring and Anisotropy Enhancement
Directory of Open Access Journals (Sweden)
Mehmet Nergiz
2017-11-01
Full Text Available Retinal vessel segmentation is one of the preliminary tasks for developing diagnosis software systems related to various retinal diseases. In this study, a fully automated vessel segmentation system is proposed. Firstly, the vessels are enhanced using a Frangi Filter. Afterwards, Structure Tensor is applied to the response of the Frangi Filter and a 4-D tensor field is obtained. After decomposing the Eigenvalues of the tensor field, the anisotropy between the principal Eigenvalues are enhanced exponentially. Furthermore, this 4-D tensor field is converted to the 3-D space which is composed of energy, anisotropy and orientation and then a Contrast Limited Adaptive Histogram Equalization algorithm is applied to the energy space. Later, the obtained energy space is multiplied by the enhanced mean surface curvature of itself and the modified 3-D space is converted back to the 4-D tensor field. Lastly, the vessel segmentation is performed by using Otsu algorithm and tensor coloring method which is inspired by the ellipsoid tensor visualization technique. Finally, some post-processing techniques are applied to the segmentation result. In this study, the proposed method achieved mean sensitivity of 0.8123, 0.8126, 0.7246 and mean specificity of 0.9342, 0.9442, 0.9453 as well as mean accuracy of 0.9183, 0.9442, 0.9236 for DRIVE, STARE and CHASE_DB1 datasets, respectively. The mean execution time of this study is 6.104, 6.4525 and 18.8370 s for the aforementioned three datasets respectively.
3D MODELING OF STRESS FIELDS IN MILLING
Directory of Open Access Journals (Sweden)
Wadii YOUSFI
2015-05-01
Full Text Available Given the complexity of the physical phenomena present in machining, orthogonal cutting was the most exploited configuration in the analytical modelling of cutting. This configuration is no longer valid if we consider the orientations of the tool in space such as the milling process. A along the cutting edge the geometric and kinematic parameters vary greatly and the speed vector of each point is very sensitive to the position [1]. This study incorporates the kinematic evolutions in the volume, with significant gradients of speeds, in 3D machining configuration and this in each shear zone. These gradients velocity generate additional displacements of the chip, in three dimensions, therefore a new force component with the appearance of cutting moments. This study presents a brief description of orthogonal cutting model developed followed by the determination of the velocity field in each shear zone. From the overall expression of the velocity vector, the contributions of the kinematic variations to the strain and the strain rate between the two extreme points of the edge are determined.
Self-Organization of Polymeric Fluids in Strong Stress Fields
Directory of Open Access Journals (Sweden)
A. V. Semakov
2015-01-01
Full Text Available Analysis of literature data and our own experimental observations have led to the conclusion that, at high deformation rates, viscoelastic liquids come to behave as rubbery materials, with strong domination by elastic deformations over flow. This can be regarded as a deformation-induced fluid-to-rubbery transition. This transition is accompanied by elastic instability, which can lead to the formation of regular structures. So, a general explanation for these effects requires the treatment of viscoelastic liquids beyond critical deformation rates as rubbery media. Behaviouristic modeling of their behaviour is based on a new concept, which considers the medium as consisting of discrete elastic elements. Such a type of modeling introduces a set of discrete rotators settled on a lattice with two modes of elastic interaction. The first of these is their transformation from spherical to ellipsoidal shapes and orientation in an external field. The second is elastic collisions between rotators. Computer calculations have demonstrated that this discrete model correctly describes the observed structural effects, eventually resulting in a “chaos-to-order” transformation. These predictions correspond to real-world experimental data obtained under different modes of deformation. We presume that the developed concept can play a central role in understanding strong nonlinear effects in the rheology of viscoelastic liquids.
Development of the Stress of Immigration Survey (SOIS): a Field Test among Mexican Immigrant Women
Sternberg, Rosa Maria; Nápoles, Anna Maria; Gregorich, Steven; Paul, Steven; Lee, Kathryn A.; Stewart, Anita L.
2016-01-01
The Stress of Immigration Survey (SOIS) is a screening tool used to assess immigration-related stress. The mixed methods approach included concept development, pretesting, field-testing, and psychometric evaluation in a sample of 131 low-income women of Mexican descent. The 21-item SOIS screens for stress related to language; immigrant status; work issues; yearning for family and home country; and cultural dissonance. Mean scores ranged from 3.6 to 4.4 (1-5 scale, higher is more stress). Cronbach's alphas >.80 for all sub-scales. The SOIS may be a useful screening tool for detecting high levels of immigration-related stress in low-income Mexican immigrant women. PMID:26605954
Development of the Stress of Immigration Survey: A Field Test Among Mexican Immigrant Women.
Sternberg, Rosa Maria; Nápoles, Anna Maria; Gregorich, Steven; Paul, Steven; Lee, Kathryn A; Stewart, Anita L
2016-01-01
The Stress of Immigration Survey (SOIS) is a screening tool used to assess immigration-related stress. The mixed methods approach included concept development, pretesting, field testing, and psychometric evaluation in a sample of 131 low-income women of Mexican descent. The 21-item SOIS screens for stress related to language, immigrant status, work issues, yearning for family and home country, and cultural dissonance. Mean scores ranged from 3.6 to 4.4 (a scale of 1-5, higher is more stress). Cronbach α values were more than 0.80 for all subscales. The SOIS may be a useful screening tool for detecting high levels of immigration-related stress in low-income Mexican immigrant women.
DEFF Research Database (Denmark)
Larsen, Finn; Ormarsson, Sigurdur
2013-01-01
shrinkage and the inhomogeneity of the material. To obtain a better understanding of how stresses develop during climatic variations, the field histories of stresses (and strains) in cross sections in their entirety need to be studied. The present paper reports on experiments and numerical simulations......When solid wood dries from a green condition to a moisture content used for further processing, moisture-induced fracture and stresses can occur. The drying stresses arise because of internal deformation constraints that are strongly affected by the cross-sectional moisture gradient differential...... concerned with analysing the development of strains and stresses during the drying of 15-mm-thick discs of Norway spruce timber log. The samples were dried at 23 °C and relative humidity of 64 % from a green condition to equilibrium moisture content. The moisture gradient in the longitudinal direction...
Calculating contracted tensor Feynman integrals
International Nuclear Information System (INIS)
Fleischer, J.; Riemann, T.
2011-01-01
A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this Letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with external momenta. This is based on sums over signed minors weighted with scalar products of the external momenta. With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently.
Metric Tensor Vs. Metric Extensor
Fernández, V. V.; Moya, A. M.; Rodrigues Jr, Waldyr A.
2002-01-01
In this paper we give a comparison between the formulation of the concept of metric for a real vector space of finite dimension in terms of \\emph{tensors} and \\emph{extensors}. A nice property of metric extensors is that they have inverses which are also themselves metric extensors. This property is not shared by metric tensors because tensors do \\emph{not} have inverses. We relate the definition of determinant of a metric extensor with the classical determinant of the corresponding matrix as...
Calculating contracted tensor Feynman integrals
International Nuclear Information System (INIS)
Fleischer, J.
2011-05-01
A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with externalmomenta. This is based on sums over signedminors weighted with scalar products of the external momenta. With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently. (orig.)
A tensor approach to the estimation of hydraulic conductivities in ...
African Journals Online (AJOL)
2006-07-03
Jul 3, 2006 ... coefficients, i.e. the fracture roughness and combined stress conditions, are adapted to calibrate the tensor model application. The application ... Darcy's law is always used to estimate the groundwater flow in both porous and ... Inverse analysis on continuous or discontinuous problems dependent on ...
Multivariate Tensor-based Brain Anatomical Surface Morphometry via Holomorphic One-Forms
Wang, Yalin; Chan, Tony F.; Toga, Arthur W.; Thompson, Paul M.
2009-01-01
Here we introduce multivariate tensor-based surface morphometry using holomorphic one-forms to study brain anatomy. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We introduce two different holomorphic one-forms that induce different surface conformal parameterizations. We applied this framework to 3D MRI data to analyze hippocampal surface morphometry in Alzheimer’s Disease (AD; 26 subjects), lateral ventricula...
A quantum gravity tensor equation formally integrating general relativity with quantum mechanics
Duan, Xu
2016-01-01
Extending black-hole entropy to ordinary objects, we propose kinetic entropy tensor, based on which a quantum gravity tensor equation is established. Our investigation results indicate that if N=1, the quantum gravity tensor equation returns to Schrodinger integral equation. When N becomes sufficiently large, it is equivalent to Einstein field equation. This illustrates formal unification and intrinsic compatibility of general relativity with quantum mechanics. The quantum gravity equation ma...
Full-field measurement of dynamic stress by mechanoluminescence sensing film
Li, Chenshu; Xu, Chao-Nan; Imai, Yusuke; Bu, Nan
2009-07-01
Full-field measurement of dynamic stress has been realized by coating the surface of the test object metal with a upgrade mechanoluminescence sensing film of SrAl2O4:Eu (SAOE). Mechanoluminescent materials are attractive smart materials that can emit light induced by mechanical deformation. The ML sensing film of SAOE has been developed to make possible to visualize dynamic stress. Consequently this visualization technique has been become a promising experimental technique to investigate full-field stress analysis. In this paper we report the applications of the SAO ML sensing film for full-field stress analysis in aluminum alloy 5052 samples. Using the SAOE ML sensing film, the stress concentration produced by a circular hole was observed with the naked eyes in real time and the two-dimensional stress distribution was quantitatively measured; the complex and dynamic Portevin-Le Chatelier (PLC) effect, known as instability during plastic deformation, has been visualized, and the propagating characteristics of PLC bands were precisely investigated.
Stress analysis in high-temperature superconductors under pulsed field magnetization
Wu, Haowei; Yong, Huadong; Zhou, Youhe
2018-04-01
Bulk high-temperature superconductors (HTSs) have a high critical current density and can trap a large magnetic field. When bulk superconductors are magnetized by the pulsed field magnetization (PFM) technique, they are also subjected to a large electromagnetic stress, and the resulting thermal stress may cause cracking of the superconductor due to the brittle nature of the sample. In this paper, based on the H-formulation and the law of heat transfer, we can obtain the distributions of electromagnetic field and temperature, which are in qualitative agreement with experiment. After that, based on the dynamic equilibrium equations, the mechanical response of the bulk superconductor is determined. During the PFM process, the change in temperature has a dramatic effect on the radial and hoop stresses, and the maximum radial and hoop stress are 24.2 {{MPa}} and 22.6 {{MPa}}, respectively. The mechanical responses of a superconductor for different cases are also studied, such as the peak value of the applied field and the size of bulk superconductors. Finally, the stresses are also presented for different magnetization methods.
International Nuclear Information System (INIS)
Hack, Thomas-Paul; Moretti, Valter
2012-01-01
We review a few rigorous and partly unpublished results on the regularization of the stress–energy in quantum field theory on curved spacetimes: (1) the symmetry of the Hadamard/Seeley–DeWitt coefficients in smooth Riemannian and Lorentzian spacetimes, (2) the equivalence of the local ζ-function and the Hadamard-point-splitting procedure in smooth static spacetimes and (3) the equivalence of the DeWitt–Schwinger- and the Hadamard-point-splitting procedure in smooth Riemannian and Lorentzian spacetimes. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (paper)
Extreme of random field over rectangle with application to concrete rupture stresses
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2000-01-01
on the carrying capacity of theelement when the local material properties vary as a random field over the element, evaluation of the riskof floods or draughts in connection with river and reservoir management, etc. Only for some very few specialcases of process and field models it is possible to obtain exact...... to the area of the rectangle and the side lengths of therectangle. Published rupture stress data for plain concrete beams illustrate the applicability of the derivedclosed form extreme value distributions as models for distributions of rupture stresses related to weakest linkmechanisms....
Tensor Product of Polygonal Cell Complexes
Chien, Yu-Yen
2017-01-01
We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.
The normal conformal Cartan connection and the Bach tensor
International Nuclear Information System (INIS)
Korzynski, Mikolaj; Lewandowski, Jerzy
2003-01-01
The goal of this paper is to express the Bach tensor of a four-dimensional conformal geometry of an arbitrary signature by the Cartan normal conformal (CNC) connection. We show that the Bach tensor can be identified with the Yang-Mills current of the connection. It follows from that result that a conformal geometry whose CNC connection is reducible in an appropriate way has a degenerate Bach tensor. As an example we study the case of a CNC connection which admits a twisting covariantly constant twistor field. This class of conformal geometries of this property is known as given by the Fefferman metric tensors. We use our result to calculate the Bach tensor of an arbitrary Fefferman metric and show that it is proportional to the tensorial square of the four-fold eigenvector of the Weyl tensor. Finally, we solve the Yang-Mills equations imposed on the CNC connection for all the homogeneous Fefferman metrics. The only solution is the Nurowski-Plebanski metric
Effect of the induced magnetic field on peristaltic flow of a couple stress fluid
International Nuclear Information System (INIS)
Mekheimer, Kh.S.
2008-01-01
We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter γ, the Hartmann number M, the magnetic Reynolds number R m and the time averaged mean flow rate θ. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed
Stress Response to High Magnetic Fields in Transgenic Arabidopsis thaliana Plants.
Morgan, A. N.; Watson, B. C.; Maloney, J. R.; Meisel, M. W.; Brooks, J. S.; Paul, A.-L.; Ferl, R. J.
2000-03-01
With increasingly greater strength magnetic fields becoming available in research and medicine, the response of living tissue exposed to high magnetic fields has come under investigation. In this experiment, genetically engineered arabidopsis plants were exposed to homogeneous magnetic fields of varying strengths using a superconducting NMR magnet (0 to 9 T) at UF and a resistive magnet (0 to 25 T) at the NHMFL. The engineered plants produce the enzyme β-glucaronidase (GUS) when under stressful environmental conditions. The level of GUS activity is determined through qualitative histochemical assays and quantitative fluorometric assays. The control group of plants experienced baseline levels of GUS activity, but some of the plants that were exposed to magnetic fields in excess of 9 T show increased stress response. Additional information is available at http://www.phys.ufl.edu/ ~meisel/maglev.htm.
Magnetopriming - an alternate strategy for crop stress management of field crops
International Nuclear Information System (INIS)
Anand, Anjali
2014-01-01
Abiotic stresses are major deterrent to sustainable crop production worldwide. Seed germination and early seedling growth are considered as the most critical stages of plant growth under stress conditions. Maximising stress tolerance of crop species by breeding is an integral part of development of strategies for improving sustainable food production under stressed environment but the unprecedented rate at which stress is increasing vis-a-vis the time taken for development of a tolerant variety, necessitates exploring alternate strategies of crop stress management. Seed priming has emerged as a promising crop stress management technique that increases the speed of germination thus ensuring synchronized field emergence of the crop. Magnetopriming (exposure of seeds to magnetic field) is a non invasive physical stimulant used for improving seedling vigour that helps in establishment of crop stand under stress. In our experiments on maize; chickpea and wheat under water deficit and salinity, respectively, improved seed water absorption characteristics resulted in faster hydration of enzymes (amylases, protease and dehydrogenase) leading to early germination and enhanced vigour of seedlings under stress. Increased levels of hydrogen peroxide in faster germinating - magnetoprimed seeds, under both the growing conditions, suggested its role in oxidative signaling during seed germination process. An 'oxidative window' for reactive oxygen species ensured that faster germination rate in magnetoprimed seeds led to vigourous seedlings. Improved root system integrated with higher photosynthetic efficiency and efficient partitioning of Na + increased yield from magnetoprimed seeds under salinity in controlled experiments. Magnetopriming can be effectively used as a pre-sowing treatment for mitigating adverse effects of water deficit and salinity at seed germination and early seedling growth. Unlike other conventional priming techniques it avoids seed hydration and
Swim stress, motion, and deformation of active matter: effect of an external field
Takatori, Sho C.; Brady, John F.
2014-01-01
We analyze the stress, dispersion, and average swimming speed of self-propelled particles subjected to an external field that affects their orientation and speed. The swimming trajectory is governed by a competition between the orienting influence (i.e., taxis) associated with the external (e.g., magnetic, gravitational, thermal, nutrient concentration) field versus the effects that randomize the particle orientations (e.g., rotary Brownian motion and/or an intrinsic tumbling mechanism like t...
International Nuclear Information System (INIS)
Wenman, M.R.; Price, A.J.; Steuwer, A.; Chard-Tuckey, P.R.; Crocombe, A.
2009-01-01
The aim of the work is to elucidate the influence of plasticity behaviour on the residual stress field in a ferritic reactor pressure vessel steel. To this end, we investigate two compressively pre-loaded compact tension (CT) specimens to generate a mechanical residual stress field. One specimen was subsequently pre-cracked by fatigue before both specimens were measured using high-energy synchrotron X-ray diffraction. A fine grain size microstructure (∼5-10 μm grain size) allowed a small X-ray beam slit size and therefore gauge volume. The results provide an excellent data set for validation of finite element (FE) modelling predictions against which they have been compared. The results of both mechanical testing and modelling suggest that the use of a combined hardening model is needed to accurately predict the residual stress field present in the specimen after pre-loading. Some discrepancy between the modelled crack tip stress values and those found by X-ray diffraction remain which can be partly explained by volume averaging effects in the presence of very high stress/strain gradients.
Stress field analysis around vortex in elastic layer of viscoelastic turbulent channel flow
International Nuclear Information System (INIS)
Minegishi, T; Tsukahara, T; Kawaguchi, Y
2014-01-01
It is important from an engineering aspect to understand drag-reducing viscoelastic flow, since comprehension of the drag-reduction mechanism may facilitate designs with better additive types and/or channel configurations. In this study, we investigated the attenuation of vortices in fully-developed turbulence of viscoelastic fluid between parallel planes by DNS (Direct Numerical Simulation). We discussed how the viscoelastic stress play a role in the reduction of the turbulent motions around vortices and how it influences the entire flow field. For determining the major effect of viscoelasticity, we classified three stages of vortex evolution and examined statistical data for each stage. We clarified the relation between the velocity field and viscoelastic stress field using a product, or a correlation, between vorticity and rotational viscoelastic stress. We found that the inhibition of turbulence would be caused by the following aspects: damping longitudinal vortex by viscoelastic stress over a wide range in the channel, and relaxing development of vortex by the stress in vortex growing state.
Early field performance of drought-stressed scots pine (pinus sylvestris l.) seedlings
International Nuclear Information System (INIS)
Kulac, S.; Clcek, E.; Tasdemir, U.
2015-01-01
Scots pine (Pinus sylvestris) has a large natural distribution throughout the world, including semi-arid areas of Turkey, where it is being used for afforestation. Determining the drought resistance of Scots pine provenances can increase the success of afforestation efforts in semi-arid regions. In the first stage of this study, water-stress treatments were applied to ten provenances of one-year-old Scots pine seedlings in their second vegetation period (between April and November). The diameter and height of the seedlings were evaluated in the nursery in order to determine their morphology. The four drought-stress treatments consisted of once-weekly irrigation (IR1), twice-weekly irrigation (IR2-Control), biweekly irrigation (IR3) and open field conditions (IR4). Later, the water-stressed seedlings were planted in a semi-arid district in Bayburt, Turkey, and their survival and growth performances were evaluated over a five-year period. The nursery study showed that drought stress and provenance as well as the interaction of the two significantly affected the morphological characteristics of the seedlings. Under water-stress conditions, the best growth performance was found in the Dokurcun, Degirmendere and Dirgine provenance seedlings. Water-stress and provenance factors and their interaction also affected the open field performance of the seedlings, where the Degirmendere, Dirgine and Dokurcun provenances again exhibited the best performance. Consequently, these Scots pine provenances can be recommended for afforestation sites having conditions similar to those of the study site. (author)
Analytical model of stress field in submerged arc welding butt joint with thorough penetration
Directory of Open Access Journals (Sweden)
Winczek Jerzy
2018-01-01
Full Text Available Analytical model of temporary and residual stresses for butt welding with thorough penetration was described assuming planar section hypothesis and using integral equations of stress equilibrium of the bar and simple Hooke’s law. In solution the effect of phase transformations (structure changes and structural strains has been taken into account. Phase transformations during heating are limited by temperature values at the beginning and at the end of austenitic transformation, depending on chemical composition of steel while the progress of phase transformations during cooling is determined on the basis of TTT-welding diagram. Temperature values at the beginning and at the end of transformation are conditioned by the speed of heating. Kinetics of diffusional transformation is described basing on Johnson-Mehl-Avrami-Kolmogorov equation, while martensitic transformation, basing on Koistinen-Marburger equation. Stresses in elasto-plastic state are determined by iteration, using elastic solutions method with changeable longitudinal modulus of elasticity, conditioned by stress-strain curve. Computations of stress field have been conducted for one-side butt welded of two steel flats made from S235 steel. It has enabled a clear interpretation of influence of temperature field and phase transformation on stresses caused by welding using Submerged Arc Welding (SAW method.
Demountable low stress high field toroidal field magnet system for tokamak fusion reactors
International Nuclear Information System (INIS)
Powell, J.; Hsieh, D.; Lehner, J.; Suenaga, M.
1977-01-01
A new type of superconducting magnet system for large fusion reactors is described in this report. Instead of winding large planar or multi-axis coils, as has been proposed in previous fusion reactor designs, the superconducting coils are made by joining together several prefabricated conductor sections. The joints can be unmade and sections removed if they fail. Conductor sections can be made at a factory and shipped to the reactor site for assembly. The conductor stress level in the assembled coil can be kept small by external support of the coil at a number of points along its perimeter, so that the magnetic forces are transmitted to an external warm reinforcement structure. This warm reinforcement structure can also be the primary containment for the fusion reactor, constructed similar to a PCRV (Prestressed Concrete Reactor Vessel) used in fission reactors. Low thermal conductivity, high strength supports are used to transfer the magnetic forces to the external reinforcement through a hydraulic system. The hydraulic supports are movable and can be programmed to accommodate thermal contraction and to minimize stress in the superconducting coil
Demountable low stress high field toroidal field magnet system for tokamak fusion reactors
International Nuclear Information System (INIS)
Powell, J.; Hsieh, D.; Lehner, J.; Suenaga, M.
1978-01-01
A new type of superconducting magnet system for large fusion reactors is described. Instead of winding large planar or multi-axis coils, as has been proposed in previous fusion reactor designs, the superconducting coils are made by joining together several prefabricated conductor sections. The joints can be unmade and sections removed if they fail. Conductor sections can be made at a factory and shipped to the reactor site for assembly. The conductor stress level in the assembled coil can be kept small by external support of the coil at a number of points along its perimeter, so that the magnetic forces are transmitted to an external warm reinforcement structure. This warm reinforcement structure can also be the primary containment for the fusion reactor, constructed similar to a PCRV (Prestressed Concrete Reactor Vessel) used in fission reactors. Low thermal conductivity, high strength supports are used to transfer the magnetic forces to the external reinforcement through a hydraulic system. The hydraulic supports are movable and can be programmed to accommodate thermal contraction and to minimize stress in the superconducting coil. (author)
International Nuclear Information System (INIS)
Stegemann, Robert; Cabeza, Sandra; Lyamkin, Viktor; Bruno, Giovanni; Pittner, Andreas; Wimpory, Robert; Boin, Mirko; Kreutzbruck, Marc
2017-01-01
The residual stress distribution of tungsten inert gas welded S235JRC+C plates was determined by means of neutron diffraction (ND). Large longitudinal residual stresses with maxima around 600 MPa were found. With these results as reference, the evaluation of residual stress with high spatial resolution GMR (giant magneto resistance) sensors was discussed. The experiments performed indicate a correlation between changes in residual stresses (ND) and the normal component of local residual magnetic stray fields (GMR). Spatial variations in the magnetic field strength perpendicular to the welds are in the order of the magnetic field of the earth. - Highlights: • Comparison of magnetic microstructure with neutron diffraction stress analysis. • High spatial resolution magnetic stray field images of hypereutectoid TIG welds. • Spatial variations of the stray fields are below the magnetic field of the earth. • GMR spin valve gradiometer arrays adapted for the evaluation of magnetic microstructures. • Magnetic stray fields are closely linked to microstructure of the material.
Energy Technology Data Exchange (ETDEWEB)
Stegemann, Robert, E-mail: Robert.Stegemann@bam.de [Bundesanstalt für Materialforschung und -prüfung (BAM), Unter den Eichen 87, 12200 Berlin (Germany); Cabeza, Sandra; Lyamkin, Viktor; Bruno, Giovanni; Pittner, Andreas [Bundesanstalt für Materialforschung und -prüfung (BAM), Unter den Eichen 87, 12200 Berlin (Germany); Wimpory, Robert; Boin, Mirko [HZB Helmholtz-Zentrum Berlin, Hahn-Meitner-Platz 1, 14109 Berlin (Germany); Kreutzbruck, Marc [Bundesanstalt für Materialforschung und -prüfung (BAM), Unter den Eichen 87, 12200 Berlin (Germany); IKT, University of Stuttgart, Pfaffenwaldring 32, 70569 Stuttgart (Germany)
2017-03-15
The residual stress distribution of tungsten inert gas welded S235JRC+C plates was determined by means of neutron diffraction (ND). Large longitudinal residual stresses with maxima around 600 MPa were found. With these results as reference, the evaluation of residual stress with high spatial resolution GMR (giant magneto resistance) sensors was discussed. The experiments performed indicate a correlation between changes in residual stresses (ND) and the normal component of local residual magnetic stray fields (GMR). Spatial variations in the magnetic field strength perpendicular to the welds are in the order of the magnetic field of the earth. - Highlights: • Comparison of magnetic microstructure with neutron diffraction stress analysis. • High spatial resolution magnetic stray field images of hypereutectoid TIG welds. • Spatial variations of the stray fields are below the magnetic field of the earth. • GMR spin valve gradiometer arrays adapted for the evaluation of magnetic microstructures. • Magnetic stray fields are closely linked to microstructure of the material.
Black holes in vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland); Kase, Ryotaro; Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Minamitsuji, Masato, E-mail: lavinia.heisenberg@eth-its.ethz.ch, E-mail: r.kase@rs.tus.ac.jp, E-mail: masato.minamitsuji@tecnico.ulisboa.pt, E-mail: shinji@rs.kagu.tus.ac.jp [Centro Multidisciplinar de Astrofisica—CENTRA, Departamento de Fisica, Instituto Superior Tecnico—IST, Universidade de Lisboa—UL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)
2017-08-01
We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.
Dynamic Response in Transient Stress-Field Behavior Induced by Hydraulic Fracturing
Jenkins, Andrew
Hydraulic fracturing is a technique which is used to exploit geologic features and subsurface properties in an effort to increase production in low-permeability formations. The process of hydraulic fracturing provides a greater surface contact area between the producing formation and the wellbore and thus increases the amount of recoverable hydrocarbons from within the reservoir. The use of this stimulation technique has brought on massive applause from the industry due to its widespread success and effectiveness, however the dynamic processes that take part in the development of hydraulic fractures is a relatively new area of research with respect to the massive scale operations that are seen today. The process of hydraulic fracturing relies upon understanding and exploiting the in-situ stress distribution throughout the area of study. These in-situ stress conditions are responsible for directing fracture orientation and propagation paths throughout the period of injection. The relative magnitude of these principle stresses is key in developing a successful stimulation plan. In horizontal well plan development the interpretation of stress within the reservoir is required for determining the azimuth of the horizontal well path. These horizontal laterals are typically oriented in a manner such that the well path lies parallel to the minimum horizontal stress. This allows for vertical fractures to develop transversely to the wellbore, or normal to the least principle stress without the theoretical possibility of fractures overlapping, creating the most efficient use of the fluid energy during injection. The orientation and magnitude of these in-situ stress fields however can be dynamic, controlled by the subsequent fracture propagation and redistribution of the surrounding stresses. That is, that as the fracture propagates throughout the reservoir, the relative stress fields surrounding the fractures may see a shift and deviate from their original direction or
New apparatus for ceramic texturing working under uniaxial stress and in a magnetic field
International Nuclear Information System (INIS)
Noudem, J.G.; Beille, J.; Draperi, A.; Sulpice, A.; Tournier, R.
1993-01-01
We have developed a new versatile apparatus combining the effect of hot pressing and the effect of magnetic field to texture HTSC (high-temperature superconductor) ceramics. The experimental set-up allows application of uniaxial stress up to 1100 degrees C under a maximum pressure of 60 MPa, in a controlled atmosphere and a magnetic field of 8 T. We have optimized the cycle for stress application along with the thermal cycle to produce highly-textured ceramics. In this paper, we describe the stress and thermal cycles used to texture Bi-Pb-Sr-Ca-Cu-O (2223 phase) ceramics. We present the physical and chemical characterizations of the samples which show a strong degree of crystallite orientation. (author)
Quantifying the stress fields due to a delta-hydride precipitate in alpha-Zr matrix
Energy Technology Data Exchange (ETDEWEB)
Tummala, Hareesh [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Capolungo, Laurent [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Tome, Carlos N. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-10-19
This report is a preliminary study on δ-hydride precipitate in zirconium alloy performed using 3D discrete dislocation dynamics simulations. The ability of dislocations in modifying the largely anisotropic stress fields developed by the hydride particle in a matrix phase is addressed for a specific dimension of the hydride. The influential role of probable dislocation nucleation at the hydride-matrix interface is reported. Dislocation nucleation around a hydride was found to decrease the shear stress (S_{13}) and also increase the normal stresses inside the hydride. We derive conclusions on the formation of stacks of hydrides in zirconium alloys. The contribution of mechanical fields due to dislocations was found to have a non-negligible effect on such process.
Bi-Metallic Composite Structures With Designed Internal Residual Stress Field
Brice, Craig A.
2014-01-01
Shape memory alloys (SMA) have a unique ability to recover small amounts of plastic strain through a temperature induced phase change. For these materials, mechanical displacement can be accomplished by heating the structure to induce a phase change, through which some of the plastic strain previously introduced to the structure can be reversed. This paper introduces a concept whereby an SMA phase is incorporated into a conventional alloy matrix in a co-continuous reticulated arrangement forming a bi-metallic composite structure. Through memory activation of the mechanically constrained SMA phase, a controlled residual stress field is developed in the interior of the structure. The presented experimental data show that the memory activation of the SMA composite component significantly changes the residual stress distribution in the overall structure. Designing the structural arrangement of the two phases to produce a controlled residual stress field could be used to create structures that have much improved durability and damage tolerance properties.
Field performance of timber bridges. 11, Spearfish Creek stress-laminated box-beam bridge
J. P. Wacker; M. A. Ritter; K. Stanfill-McMillan
The Spearfish Creek bridge was constructed in 1992 in Spearfish, South Dakota. It is a single-span, stress-laminated, box-beam superstructure. Performance of the bridge is being monitored for 5 years, beginning at installation. This report summarizes results for the first 3-1/2 years of monitoring and includes information on the design, construction, and field...
The University of California Institute of Environmental Stress Marathon Field Studies
Maron, Michael B.
2014-01-01
In 1973, the Institute of Environmental Stress of the University of California-Santa Barbara, under the direction of Steven M. Horvath, began a series of field and laboratory studies of marathon runners during competition. As one of Horvath's graduate students, many of these studies became part of my doctoral dissertation. The rationale for…
Field performance of stress-laminated highway bridges constructed with glued laminated timber
J.P. Wacker
2004-01-01
This paper summarizes the field performance of three stress-laminated deck timber bridges located in Wisconsin, New York, and Arizona. The deck superstructures of these single-span highway bridges is comprised of full-span glued laminated timber (glulam) beam laminations manufactured with southern pine, hem fir/red maple combination, and/or Douglas fir lumber species....
Analysis of the stress field and strain rate in Zagros-Makran transition zone
Ghorbani Rostam, Ghasem; Pakzad, Mehrdad; Mirzaei, Noorbakhsh; Sakhaei, Seyed Reza
2018-01-01
Transition boundary between Zagros continental collision and Makran oceanic-continental subduction can be specified by two wide limits: (a) Oman Line is the seismicity boundary with a sizeable reduction in seismicity rate from Zagros in the west to Makran in the east; and (b) the Zendan-Minab-Palami (ZMP) fault system is believed to be a prominent tectonic boundary. The purpose of this paper is to analyze the stress field in the Zagros-Makran transition zone by the iterative joint inversion method developed by Vavrycuk (Geophysical Journal International 199:69-77, 2014). The results suggest a rather uniform pattern of the stress field around these two boundaries. We compare the results with the strain rates obtained from the Global Positioning System (GPS) network stations. In most cases, the velocity vectors show a relatively good agreement with the stress field except for the Bandar Abbas (BABS) station which displays a relatively large deviation between the stress field and the strain vector. This deviation probably reflects a specific location of the BABS station being in the transition zone between Zagros continental collision and Makran subduction zones.
Degradation of Au–Ti contacts of SiGe HBTs during electromagnetic field stress
International Nuclear Information System (INIS)
Alaeddine, A; Genevois, C; Cuvilly, F; Daoud, K; Kadi, M
2011-01-01
This paper addresses electromagnetic field stress effects on SiGe heterojunction bipolar transistors (HBTs)' reliability issues, focusing on the relationship between the stress-induced current and device structure degradations. The origin of leakage currents and electrical parameter shifts in failed transistors has been studied by complementary failure analysis techniques. Characterization of the structure before and after ageing was performed by transmission electron microscopy (TEM) and energy dispersive spectroscopy (EDS). For the stressed samples, interface deformations of the titanium (Ti) thin film around all gold (Au) contacts have been clearly detected. These degradations include localized interface reaction between Au and Ti layers as well as their lateral atomic migration causing a significant reduction of Ti thickness. EDS analysis of the disordered region which is near the Si 3 N 4 interface has shown significant signals from Au. These observations could be attributed to the coupling between high current densities induced by stress and thermal effects due to local heating effects
Identification of natural fractures and in situ stress at Rantau Dedap geothermal field
Artyanto, Andika; Sapiie, Benyamin; Idham Abdullah, Chalid; Permana Sidik, Ridwan
2017-12-01
Rantau Dedap Area is a geothermal field which is located in Great Sumatra Fault (GSF). The fault and fracture are main factor in the permeability of the geothermal system. However, not all faults and fractures have capability of to flow the fluids. Borehole image log is depiction of the borehole conditions, it is used to identify the natural fractures and drilling induced fracture. Both of them are used to identify the direction of the fracture, direction of maximum horizontal stress (SHmax), and geomechanics parameters. The natural fractures are the results of responses to stress on a rock and permeability which controlling factor in research area. Breakouts is found in this field as a trace of drilling induced fracture due to in situ stress work. Natural fractures are strongly clustered with true strike trending which first, second, and third major direction are N170°E – N180°E (N-S), N60°E – N70°E (NE-SW), and N310°E – N320°E (NW-SE), while the dominant dip is 80° –90°. Based on borehole breakout analysis, maximum horizontal stress orientation is identified in N162°E – N204°E (N-S) and N242°E (NE-SW) direction. It’s constantly similar with regional stress which is affected by GSF. Several parameters have been identified and analyzed are SHmax, SHmin, and Sy. It can be concluded that Rantau Dedap Geothermal Field is affected by strike-slip regime. The determination of in situ stress and natural fractures are important to study the pattern of permeability which is related to the fault in reservoir of this field.
Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature
Loveridge, Lee C.
2004-01-01
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.
The effect of a tectonic stress field on coal and gas outbursts.
An, Fenghua; Cheng, Yuanping
2014-01-01
Coal and gas outbursts have always been a serious threat to the safe and efficient mining of coal resources. Ground stress (especially the tectonic stress) has a notable effect on the occurrence and distribution of outbursts in the field practice. A numerical model considering the effect of coal gas was established to analyze the outburst danger from the perspective of stress conditions. To evaluate the outburst tendency, the potential energy of yielded coal mass accumulated during an outburst initiation was studied. The results showed that the gas pressure and the strength reduction from the adsorbed gas aggravated the coal mass failure and the ground stress altered by tectonics would affect the plastic zone distribution. To demonstrate the outburst tendency, the ratio of potential energy for the outburst initiation and the energy consumption was used. Increase of coal gas and tectonic stress could enhance the potential energy accumulation ratio, meaning larger outburst tendency. The component of potential energy for outburst initiation indicated that the proportion of elastic energy was increased due to tectonic stress. The elastic energy increase is deduced as the cause for a greater outburst danger in a tectonic area from the perspective of stress conditions.
Directory of Open Access Journals (Sweden)
Xianming Shi
2017-12-01
Full Text Available The use of chemicals for snow and ice control operations is a common practice for improving the safety and mobility of roadways in cold climate, but brings significant concerns over their risks including the corrosive effects on transportation infrastructure and motor vehicles. The vast majority of existing studies and methods to test the deicer corrosivity have been restricted to laboratory environments and unstressed metals, which may not reliably simulate actual service conditions. As such, we report a case study in which stainless steel SS 304 (unstressed and externally tensile stressed, aluminum (Al 1100 and low carbon steel (C1010 coupons were exposed to 25% MgCl2 under field conditions for six weeks. A new corrosion test-bed was developed in Montana to accelerate the field exposure to this deicer. To further investigate the observed effect of tensile stress on the corrosion of stainless steel, SS 304 (unstressed and externally stressed coupons were exposed to 25% MgCl2 solution under the laboratory conditions. The C 1010 exhibited the highest percentage of rust area and suffered the most weight loss as a result of field exposure and MgCl2 sprays. In terms of ultimate tensile strength, the Al 1100 coupons saw the greatest reduction and the unstressed and externally stressed SS 304 coupons saw the least. The ability of MgCl2 to penetrate deep into the matrix of aluminum alloy poses great risk to such structural material. Tensile stressed SS 304 suffered more corrosion than unstressed SS 304 in both the field and laboratory conditions. Results from this case study may shed new light on the deicer corrosion issue and help develop improved field testing methods to evaluate the deicer corrosivity to metals in service.
Directory of Open Access Journals (Sweden)
Gongfa Li
2015-04-01
Full Text Available With the development of metallurgical industry and the improvement of continuous casting technology, the processing properties of casting technology equipment are being paid more attention. Ladle is one of the most representatives of the furnace equipment; higher requirements of ladle are put forward in response to the call for national energy-saving and emission reduction. According to the requirements of actual operator and working condition, a lining structure of a new type of ladle with nanometer adiabatic material is put forward. Based on heat transfer theory and finite element technology, the three-dimensional finite element model of a new type of ladle is established. Temperature field and stress field of the new type of ladle with the nanometer adiabatic material in lining structure after baking are analyzed. The results indicate that the distributions of temperature and thermal stress level of working layer, permanent layer, and nanometer heat insulating layer are similar, and they are in the permissible stress and temperature range of each material for the new type of ladle. Especially heat preservation effect of nanometer adiabatic material is excellent. Furthermore, the maximum temperature of shell for the new type of ladle drops to 114°C than the traditional ladle, and the maximum stress of shell for the new type of ladle is lower than the traditional ladle, that is, 114 MPa. It can provide reliable theory for energy-saving and emission reduction of metallurgy industry, which also points out the right direction for the future development of the iron and steel industry.
Poisson-Jacobi reduction of homogeneous tensors
International Nuclear Information System (INIS)
Grabowski, J; Iglesias, D; Marrero, J C; Padron, E; Urbanski, P
2004-01-01
The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold M, homogeneous with respect to a vector field Δ on M, and first-order polydifferential operators on a closed submanifold N of codimension 1 such that Δ is transversal to N. This correspondence relates the Schouten-Nijenhuis bracket of multivector fields on M to the Schouten-Jacobi bracket of first-order polydifferential operators on N and generalizes the Poissonization of Jacobi manifolds. Actually, it can be viewed as a super-Poissonization. This procedure of passing from a homogeneous multivector field to a first-order polydifferential operator can also be understood as a sort of reduction; in the standard case-a half of a Poisson reduction. A dual version of the above correspondence yields in particular the correspondence between Δ-homogeneous symplectic structures on M and contact structures on N
Directory of Open Access Journals (Sweden)
A. V. Livshits
2014-01-01
Full Text Available The article is devoted to non-stationary temperature field blanks from aluminum alloys during heat treatment. It consists of the introduction and two smaller paragraphs. In the introduction the author concerns the influence of residual stresses arising in the manufacturing process of details, on the strength of the whole aircraft construction and, consequently, on their technical and economic parameters, such as weight, reliability, efficiency, and cost. He also notes that the residual stresses appeared during the production of parts change their location, size and direction under the influence of the elastic deformations that occur during the exploitation of aircraft. Redistributed residual stresses may have a chaotic distribution that may cause overlap of these stresses on the stresses caused by the impact of workload of constructions and destruction or damage of aircraft components.The first paragraph is devoted to the existing methods and techniques for determining the residual stresses. The presented methods and techniques are analyzed to show the advantages and disadvantages of each of them. The conclusion is drawn that the method to determine the residual stresses is necessary, its cost is less than those of existing ones, and an error does not exceed 10%.In the second section, the author divides the problem of determining the residual stresses into two parts, and describes the solution methods of the first one. The first problem is to define the temperature field of the work piece. The author uses a Fourier equation with the definition of initial and boundary conditions to describe a mathematical model of the heat cycle of work piece cooling. He draws special attention here to the fact that it is complicated to determine the heat transfer coefficient, which characterizes the process of cooling the work piece during hardening because of its dependence on a number of factors, such as changing temperature-dependent material properties of
Directory of Open Access Journals (Sweden)
Gongfa Li
2015-06-01
Full Text Available With the development of metallurgical industry and the improvement of kiln technology, the processing properties of kiln equipment are being paid more attention. The rotary kiln is one of the most representatives of the furnace equipment; higher requirements of the rotary kiln are put forward in response to the call of the national energy saving and emission reduction. That is, the new designed equipment has the characteristics of the optimal energy consumption and stable performance. In order to analyze the energy consumption of the rotary kiln, it is necessary to study the heat transfer process of the rotary kilns. The three-dimensional numerical model of the rotary kiln is set up by using the finite element technology. After analyzing the data, it is found that different thicknesses of the kiln crust and different working conditions have certain influence on the rotary kiln’s temperature field and stress field. After analyzing the result of the simulation, the temperature of the rotary kiln’s outer wall has an approximate linear relationship with the thickness of the kiln crust. Changing the thickness of the kiln crust will not only alter the value of the maximum stress but also have influence on the position of maximum stress. The increase in the thickness of the kiln crust can reduce the extreme value of stress. When the wind speed of induce fan inside the kiln is larger, the temperature of each layer will be relatively high as well, and the temperature curve is softer, and the temperature variation is more stable. It has also been found that when the comprehensive coefficient of heat exchange outside the kiln surface is larger, the thermal stress created by the body of kiln is smaller. The phenomenon of excessive thermal stress can be improved by changing the outer surface ventilation conditions of the rotary kiln. In order to ensure that the high temperature of the kiln wall has no influence on working wheels, and make sure the
The tensor rank of tensor product of two three-qubit W states is eight
Chen, Lin; Friedland, Shmuel
2017-01-01
We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.
Numerical analysis of branched cracks in bi-axial stress fields
International Nuclear Information System (INIS)
Kovac, M.; Cizelj, L.
1998-01-01
The stress corrosion cracks as seen for example in PWR steam generator tubing made of Inconel 600 are usually found to be of highly irregular kinked and branched shapes. Numerical analysis of kinked and branched cracks in bi-axial plane stress fields using methods such as finite or boundary element method may provide useful and cost effective solutions. However, accurate analysis of complex shaped cracks requires very fine meshes and, consequently, excessively high computational efforts. This paper discusses some possible strategies of numerical modeling of kinked and branched cracks in general bi-axial stress field using the general-purpose finite element code ABAQUS. The strategies discussed include J-integral and stress intensity factor solutions with different mesh densities. The accuracy of the numerical results obtained is compared with reference solutions from the literature. The main result of the paper is an optimal numerical strategy, which maximizes the accuracy of the result at as low computational efforts as feasible. The selected optimal strategy is expected to be used in the future simulations of large networks of inter-granular stress corrosion cracks at the grain-size scale using incomplete random tessellation.(author)
Directory of Open Access Journals (Sweden)
Sunita Deswal
2013-01-01
Full Text Available The aim of this paper is to study magneto-thermoelastic interactions in an initially stressed isotropic homogeneous half-space in the context of fractional order theory of generalized thermoelasticity. State space formulation with the Laplace transform technique is used to obtain the general solution, and the resulting formulation is applied to the ramp type increase in thermal load and zero stress. Solutions of the problem in the physical domain are obtained by using a numerical method of the Laplace inverse transform based on the Fourier expansion technique, and the expressions for the displacement, temperature, and stress inside the half-space are obtained. Numerical computations are carried out for a particular material for illustrating the results. Results obtained for the field variables are displayed graphically. Some comparisons have been shown in figures to present the effect of fractional parameter, ramp parameter, magnetic field, and initial stress on the field variables. Some particular cases of special interest have been deduced from the present investigation.
Energy Technology Data Exchange (ETDEWEB)
Lermo, Javier; Antayhua, Yanet [Instituto de Ingenieria, Universidad Nacional Autonoma de Mexico, Mexico D.F (Mexico)]. E-Mail: jles@pumas.iingen.unam.mx; Quintanar, Luis [Instituto de Geofisica, Universidad Nacional Autonoma de Mexico, Mexico D.F (Mexico); Lorenzo, Cecilia [Gerencia de Proyectos Geotermoelectricos, Comision Federal de Electricidad, Michoacan (Mexico)
2008-01-15
The distribution of earthquakes at the surface and at depth in the Los Humeros geothermal field, Puebla (Mexico), is analyzed from 1997-2004. Data for 95 earthquakes were registered at more than five permanent and temporary stations installed by the Comision Federal de Electricidad and the Instituto de Ingenieria of the Universidad Nacional Autonoma de Mexico. The duration magnitudes of the quakes are equal to or lower than 3.6 Md and the focal depths do not exceed 4.0 km. Simple focal mechanisms and moment tensor inversions were made, and the number of earthquakes registered by two stations of the permanent network (numbers S05, S06) was compared with water-injection and steam-production volumes over a certain period. The results at the surface and at depth show seismic activity occurring in the northern zone of the field around injection wells I29 (well H-29) and I38 (well H-38); whereas, the simple focal mechanisms and moment tensors demonstrate stresses of heterogeneous origin, suggesting that part of the seismic activity in Los Humeros is probably induced, mainly by injecting water. [Spanish] Se analiza la distribucion en superficie y en profundidad de los sismos ocurridos en el campo geotermico de Los Humeros, Puebla (Mexico), durante el periodo 1997-2004. Los datos corresponden a 95 sismos registrados por mas de cinco estaciones permanentes y temporales instaladas por la Comision Federal de Electricidad y el Instituto de Ingenieria de la Universidad Nacional Autonoma de Mexico, cuyas magnitudes de duracion son menores o iguales a 3.6 Md y profundidades focales que no sobrepasan los 4.0 km. Asimismo, se realizaron mecanismos focales simples y de inversion de tensor de momento, y se comparo el numero de sismos registrados por dos estaciones de la red permanente (numeros S05, S06) con la inyeccion de agua y la produccion de vapor durante cierto tiempo. Los resultados en superficie y en profundidad muestran actividad sismica en la zona norte del campo, alrededor
He, Yan; Guo, Hao
2016-07-01
Respecting the conservation laws of momentum and energy in a many body theory is very important for understanding the transport phenomena. The previous conserving approximation requires that the self-energy of a single particle could be written as a functional derivative of a full dressed Green's function. This condition can not be satisfied in the G0 G t-matrix or pair fluctuation theory which emphasizes the fermion pairing with a stronger than the Bardeen-Cooper-Schrieffer (BCS) attraction. In the previous work [1], we have shown that when the temperature is above the superfluid transition temperature Tc, the G0 G t-matrix theory can be put into a form that satisfies the stress tensor Ward identity (WI) or local form of conservation laws by introducing a new type of vertex correction. In this paper, we will extend the above conservation approximation to the superfluid phase in the BCS mean field level. To establish the stress tensor WI, we have to include the fluctuation of the order parameter or the contribution from the Goldstone mode. The result will be useful for understanding the transport properties such as the behavior of the viscosity of Fermionic gases in the superfluid phases.
Einstein gravity 3-point functions from conformal field theory
Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein
2017-12-01
We study stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter suggests that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions 〈 T T T 〉, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy a ≈ c as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.
Tensor Target Polarization at TRIUMF
Energy Technology Data Exchange (ETDEWEB)
Smith, G
2014-10-27
The first measurements of tensor observables in $\\pi \\vec{d}$ scattering experiments were performed in the mid-80's at TRIUMF, and later at SIN/PSI. The full suite of tensor observables accessible in $\\pi \\vec{d}$ elastic scattering were measured: $T_{20}$, $T_{21}$, and $T_{22}$. The vector analyzing power $iT_{11}$ was also measured. These results led to a better understanding of the three-body theory used to describe this reaction. %Some measurements were also made in the absorption and breakup channels. A direct measurement of the target tensor polarization was also made independent of the usual NMR techniques by exploiting the (nearly) model-independent result for the tensor analyzing power at 90$^\\circ _{cm}$ in the $\\pi \\vec{d} \\rightarrow 2p$ reaction. This method was also used to check efforts to enhance the tensor polarization by RF burning of the NMR spectrum. A brief description of the methods developed to measure and analyze these experiments is provided.
Mechanical stress calculations for toroidal field coils by the finite element method
International Nuclear Information System (INIS)
Soell, M.; Jandl, O.; Gorenflo, H.
1976-09-01
After discussing fundamental relationships of the finite element method, this report describes the calculation steps worked out for mechanical stress calculations in the case of magnetic forces and forces produced by thermal expansion or compression of toroidal field coils using the SOLID SAP IV computer program. The displacement and stress analysis are based on the 20-node isoparametric solid element. The calculation of the nodal forces produced by magnetic body forces are discussed in detail. The computer programs, which can be used generally for mesh generation and determination of the nodal forces, are published elsewhere. (orig.) [de
Effects of the stress field induced by a running tyre on the soil pore system
DEFF Research Database (Denmark)
Berisso, Feto Esimo; Schjønning, Per; Lamandé, Mathieu
2013-01-01
repeated wheelings were performed by a forage harvester (wheel load 6100 kg; tyre width 80 cm). Mean normal and horizontal stresses were measured with Bolling probes (at 10, 20 and 40 cm depth) and load cells (at 40, 50, 60 cm lateral distance from the centreline of the wheel rut at 10, 30 and 50 cm depth...... state in the soil profile beneath the harvester tyre was calculated using the SoilFlex model. Pore continuity index (N) and blocked air-filled porosity (εb) were estimated from the relationship between ka and air-filled porosity (εa) for a range of matric potentials. Calculated and measured stresses...... of the wheel rut. Simulations of the stress field in the soil beneath the tyre indicated that the trends in ka were determined by both the mean normal stress and the shear stress, while the trend in εa was determined by the mean normal stress only. At 10 cm depth, the index of pore continuity (N) supported...
Link prediction via generalized coupled tensor factorisation
DEFF Research Database (Denmark)
Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.
2012-01-01
and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....
Holographic duality from random tensor networks
Energy Technology Data Exchange (ETDEWEB)
Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)
2016-11-02
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main
Stegemann, Robert; Cabeza, Sandra; Lyamkin, Viktor; Bruno, Giovanni; Pittner, Andreas; Wimpory, Robert; Boin, Mirko; Kreutzbruck, Marc
2017-03-01
The residual stress distribution of tungsten inert gas welded S235JRC+C plates was determined by means of neutron diffraction (ND). Large longitudinal residual stresses with maxima around 600 MPa were found. With these results as reference, the evaluation of residual stress with high spatial resolution GMR (giant magneto resistance) sensors was discussed. The experiments performed indicate a correlation between changes in residual stresses (ND) and the normal component of local residual magnetic stray fields (GMR). Spatial variations in the magnetic field strength perpendicular to the welds are in the order of the magnetic field of the earth.
Directory of Open Access Journals (Sweden)
Jorge Gago
2017-10-01
Full Text Available Abstract Background There is currently a high requirement for field phenotyping methodologies/technologies to determine quantitative traits related to crop yield and plant stress responses under field conditions. Methods We employed an unmanned aerial vehicle equipped with a thermal camera as a high-throughput phenotyping platform to obtain canopy level data of the vines under three irrigation treatments. High-resolution imagery (< 2.5 cm/pixel was employed to estimate the canopy conductance (g c via the leaf energy balance model. In parallel, physiological stress measurements at leaf and stem level as well as leaf sampling for primary and secondary metabolome analysis were performed. Results Aerial g c correlated significantly with leaf stomatal conductance (g s and stem sap flow, benchmarking the quality of our remote sensing technique. Metabolome profiles were subsequently linked with g c and g s via partial least square modelling. By this approach malate and flavonols, which have previously been implicated to play a role in stomatal function under controlled greenhouse conditions within model species, were demonstrated to also be relevant in field conditions. Conclusions We propose an integrative methodology combining metabolomics, organ-level physiology and UAV-based remote sensing of the whole canopy responses to water stress within a vineyard. Finally, we discuss the general utility of this integrative methodology for broad field phenotyping.
Directory of Open Access Journals (Sweden)
Lucie MALÍKOVÁ
2013-12-01
Full Text Available The paper deals with an analysis of the stress and displacement fields in various cracked specimens (loaded in mode I as well as in mode II. The main goal is to determine an accurate approximation of the near-crack-tip fields which can be subsequently used e.g. in the case of quasi-brittle materials for estimation of the extent of a nonlinear zone at the crack tip in general, the fracture process zone in particular. Values of coefficients of the so-called higher-order terms of the power expansion by which the fields can be expressed are determined via regression from results of numerical simulations. The analysis is conducted using 2D numerical models and ANSYS FE computational system is employed. Various aspects regarding the description of the stress/displacement fields by means of the Williams expansion are discussed; especially the convergence of the coefficients of the first several terms of the series expansion, their absolute values and importance for an accurate stress approximation.
Quantum field theory in spaces with closed time-like curves
Energy Technology Data Exchange (ETDEWEB)
Boulware, D.G.
1992-12-31
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27{pi}. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Quantum field theory in spaces with closed time-like curves
International Nuclear Information System (INIS)
Boulware, D.G.
1992-01-01
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon
Axially Symmetric Cosmological Model with Bulk Stress in Saez-Ballester Theory of Gravitation
Mete, V. G.; Nimkar, A. S.; Elkar, V. D.
2016-01-01
An Axially symmetric non-static space time is considered in presence of bulk stress in scalar tensor theory formulated by Saez and Ballester (Phys. Lett. A113, 467 1985). For solving the field equations, relation between metric potential and shear velocity is proportional to scale expansion are used. Also various physical and geometrical properties of the model have been discussed.
Negative power spectra in quantum field theory
International Nuclear Information System (INIS)
Hsiang, Jen-Tsung; Wu, Chun-Hsien; Ford, L.H.
2011-01-01
We consider the spatial power spectra associated with fluctuations of quadratic operators in field theory, such as quantum stress tensor components. We show that the power spectrum can be negative, in contrast to most fluctuation phenomena where the Wiener-Khinchin theorem requires a positive power spectrum. We show why the usual argument for positivity fails in this case, and discuss the physical interpretation of negative power spectra. Possible applications to cosmology are discussed. -- Highlights: → Wiener-Khinchin theorem usually implies a positive power spectrum of fluctuations. → We show this is not always the case in quantum field theory. → Quantum stress tensor fluctuations can have a negative power spectrum. → Negative power interchanges correlations and anticorrelations.
Compact stars in vector-tensor-Horndeski theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Momeni, Davood; Myrzakulov, Kairat; Myrzakulov, Ratbay [Eurasian National University, Department of General and Theoretical Physics, Eurasian International Center for Theoretical Physics, Astana (Kazakhstan); Faizal, Mir [University of British Columbia-Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada)
2017-01-15
In this paper, we will analyze a theory of modified gravity, in which the field content of general relativity will be increased to include a vector field. We will use the Horndeski formalism to non-minimally couple this vector field to the metric. As we will be using the Horndeski formalism, this theory will not contain Ostrogradsky ghost degree of freedom. We will analyze compact stars using this vector-tensor-Horndeski theory. (orig.)
Otsubo, Makoto; Miyakawa, Ayumu; Imanishi, Kazutoshi
2018-03-01
Spatial and temporal variations in inland crustal stress prior to the 2011 Mw 9.0 Tohoku earthquake are investigated using focal mechanism solutions for shallow seismicity in Iwaki City, Japan. The multiple inverse method of stress tensor inversion detected two normal-faulting stress states that dominate in different regions. The stress field around Iwaki City changed from a NNW-SSE-trending triaxial extensional stress (stress regime A) to a NW-SE-trending axial tension (stress regime B) between 2005 and 2008. These stress changes may be the result of accumulated extensional stress associated with co- and post-seismic deformation due to the M7 class earthquakes. In this study we suggest that the stress state around Iwaki City prior to the 2011 Tohoku earthquake may have been extensional with a low differential stress. High pore pressure is required to cause earthquakes under such small differential stresses.
Gao, Yang; Wang, Xuesong; Cheng, Yuhu; Wang, Z Jane
2015-08-01
To take full advantage of hyperspectral information, to avoid data redundancy and to address the curse of dimensionality concern, dimensionality reduction (DR) becomes particularly important to analyze hyperspectral data. Exploring the tensor characteristic of hyperspectral data, a DR algorithm based on class-aware tensor neighborhood graph and patch alignment is proposed here. First, hyperspectral data are represented in the tensor form through a window field to keep the spatial information of each pixel. Second, using a tensor distance criterion, a class-aware tensor neighborhood graph containing discriminating information is obtained. In the third step, employing the patch alignment framework extended to the tensor space, we can obtain global optimal spectral-spatial information. Finally, the solution of the tensor subspace is calculated using an iterative method and low-dimensional projection matrixes for hyperspectral data are obtained accordingly. The proposed method effectively explores the spectral and spatial information in hyperspectral data simultaneously. Experimental results on 3 real hyperspectral datasets show that, compared with some popular vector- and tensor-based DR algorithms, the proposed method can yield better performance with less tensor training samples required.
International Nuclear Information System (INIS)
Mace, R.L.
1996-01-01
We report on a new form for the dielectric tensor for a plasma containing superthermal particles. The individual particle components are modelled by 3-dimensional isotropic kappa, or generalized Lorentzian, distributions with arbitrary real-valued index κ. The new dielectric tensor is valid for arbitrary wavevectors. The dielectric tensor, which resembles Trubnikov's dielectric tensor for a relativistic plasma, is compared with the familiar Maxwellian form. When the dielectric tensor is used in the plasma dispersion relation for waves propagating parallel to the magnetic field it reproduces previously derived dispersion relations for various electromagnetic and electrostatic waves in plasmas modelled by Lorentzian particle distributions. Within the constraints of propagation parallel to the ambient magnetic field, we extend the above results to incorporate loss-cone Lorentzian particle distributions, which have important applications in laboratory mirror devices, as well as in space and astrophysical environments. (orig.)
Prediction of modal properties of circular disc with pre-stressed fields
Directory of Open Access Journals (Sweden)
Naď Milan
2018-01-01
Full Text Available Many structural elements in technical devices, as well as some tools in manufacturing equipment, such as saw blade or, have a geometric shape similar to a circular disc. In many cases, these circular discs must meet the required dynamic properties. One of the techniques to achieve the required dynamic properties of circular disc is based on initiating pre-stressed fields in the disc plane. In-plane residual stresses are created by appropriate technological treatments in selected disc part, for example by rolling of annulus leading to plastic deformation which causes the change of volume distribution in this disc part. The effects of in-plane residual stresses on modal properties of circular disc are analysed. The natural frequencies modifications depending on position and width and also on the change in thickness of the roll-prestressed annulus are investigated in this paper.
Stress analysis of three-dimensional roadway layout of stagger arrangement with field observation
Cui, Zimo; Chanda, Emmanuel; Zhao, Jingli; Wang, Zhihe
2018-01-01
Longwall top-coal caving (LTCC) has been a popular, more productive and cost-effective method for extracting thick (> 5 m) to ultra-thick coal seams in recent years. However, low-level recovery ratio of coal resources and top-coal loss above the supports at both ends of working face are long-term problems. Geological factors, such as large dip angle, soft rock, mining depth further complicate the problems. This paper proposes addressing this issue by adopting three-dimensional roadway layout of stagger arrangement (3-D RLSA). In this study, the first step was to analyse the stress environment surrounding head entry in the replacing working face based on the stress distribution characteristics at the triangular coal-pillar side in gob and the stress slip line field theory. In the second step, filed observation was conducted. Finally, an economic evaluation of the 3-D RLSA for extracting thick to ultra-thick seams was conducted.
Quasilocal energy and the Bel-Robinson tensor
International Nuclear Information System (INIS)
Krishnasamy, Ilangkovan
1985-01-01
The general-relativistic field equations are examined from the point of view of a local inertial observer and a quasilocal definitions of energy-momentum is thereby obtained. This definition relates to the Bel-Robinson tensor and the approach is shown to be consistent with the result obtained from the definition of energy given by Hawking. (author)
Tensor product of quantum logics
Pulmannová, Sylvia
1985-01-01
A quantum logic is the couple (L,M) where L is an orthomodular σ-lattice and M is a strong set of states on L. The Jauch-Piron property in the σ-form is also supposed for any state of M. A ``tensor product'' of quantum logics is defined. This definition is compared with the definition of a free orthodistributive product of orthomodular σ-lattices. The existence and uniqueness of the tensor product in special cases of Hilbert space quantum logics and one quantum and one classical logic are studied.
Mignan, Arnaud
2018-03-01
The aftershock productivity law is an exponential function of the form K ∝ exp(αM), with K being the number of aftershocks triggered by a given mainshock of magnitude M and α ≈ ln(10) being the productivity parameter. This law remains empirical in nature although it has also been retrieved in static stress simulations. Here, we parameterize this law using the solid seismicity postulate (SSP), the basis of a geometrical theory of seismicity where seismicity patterns are described by mathematical expressions obtained from geometric operations on a permanent static stress field. We first test the SSP that relates seismicity density to a static stress step function. We show that it yields a power exponent q = 1.96 ± 0.01 for the power-law spatial linear density distribution of aftershocks, once uniform noise is added to the static stress field, in agreement with observations. We then recover the exponential function of the productivity law with a break in scaling obtained between small and large M, with α = 1.5ln(10) and ln(10), respectively, in agreement with results from previous static stress simulations. Possible biases of aftershock selection, proven to exist in epidemic-type aftershock sequence (ETAS) simulations, may explain the lack of break in scaling observed in seismicity catalogues. The existence of the theoretical kink, however, remains to be proven. Finally, we describe how to estimate the solid seismicity parameters (activation density δ+, aftershock solid envelope r∗ and background stress amplitude range Δo∗) for large M values.
Validation of buoyancy driven spectral tensor model using HATS data
DEFF Research Database (Denmark)
Chougule, A.; Mann, Jakob; Kelly, Mark C.
2016-01-01
We present a homogeneous spectral tensor model for wind velocity and temperature fluctuations, driven by mean vertical shear and mean temperature gradient. Results from the model, including one-dimensional velocity and temperature spectra and the associated co-spectra, are shown in this paper....... The model also reproduces two-point statistics, such as coherence and phases, via cross-spectra between two points separated in space. Model results are compared with observations from the Horizontal Array Turbulence Study (HATS) field program (Horst et al. 2004). The spectral velocity tensor in the model...
Tensor calculus for supergravity on a manifold with boundary
Energy Technology Data Exchange (ETDEWEB)
Belyaev, D.V. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Van Nieuwenhuizen, P. [New York State Univ., Stony Brook, NY (United States). C.N. Yang Institute for Theoretical Physics
2007-11-15
Using the simple setting of 3D N=1 supergravity, we show how the tensor calculus of supergravity can be extended to manifolds with boundary. We present an ex- tension of the standard F-density formula which yields supersymmetric bulk-plus-boundary actions. To construct additional separately supersymmetric boundary actions, we decompose bulk supergravity and bulk matter multiplets into co-dimension one submultiplets. As an illustration we obtain the supersymmetric extension of the York-Gibbons-Hawking extrinsic curvature boundary term. We emphasize that our construction does not require any boundary conditions on off-shell fields. This gives a significant improvement over the existing orbifold supergravity tensor calculus. (orig.)
Tensor calculus for supergravity on a manifold with boundary
International Nuclear Information System (INIS)
Belyaev, Dmitry V.; Nieuwenhuizen, Peter van
2008-01-01
Using the simple setting of 3D N = 1 supergravity, we show how the tensor calculus of supergravity can be extended to manifolds with boundary. We present an extension of the standard F-density formula which yields supersymmetric bulk-plus-boundary actions. To construct additional separately supersymmetric boundary actions, we decompose bulk supergravity and bulk matter multiplets into co-dimension one submultiplets. As an illustration we obtain the supersymmetric extension of the York-Gibbons-Hawking extrinsic curvature boundary term. We emphasize that our construction does not require any boundary conditions on off-shell fields. This gives a significant improvement over the existing orbifold supergravity tensor calculus
International Nuclear Information System (INIS)
Makhnovskiy, D. P.; Panina, L. V.; Mapps, D. J.
2001-01-01
This article concerns the investigation of the magnetic behavior of the surface impedance tensor cflx var-sigma in CoSiB amorphous wires having a residual torsion stress and a helical anisotropy. The full tensor cflx var-sigma involving three different components is found by measuring the S 21 parameter at a required excitation with a Hewlett-Packard network/spectrum analyzer at MHz frequencies. In general, the impedance plots versus axial magnetic field H ex exhibit a hysteresis related to that for the case of static magnetization. The diagonal components of cflx var-sigma (longitudinal var-sigma zz and circular var-sigma v ar-phi v ar-phi) show a sharp peak in a narrow field interval where the domain walls form and contribute to the ac magnetization dynamics. This peak is not seen for the off-diagonal component var-sigma zv ar-phi (var-sigma v ar-phi z ) since the existence of the domain structure suppresses it. Applying a dc bias current results in a gradual transition to a nonhysteretic asymmetrical behavior with an enhanced sensitivity. The portions of the experimental plots associated with the rotational dynamic process are in qualitative agreement with the theory based on a single-domain model. [copyright] 2001 American Institute of Physics
Photoelastic and analytical investigation of stress in toroidal magnetic field coils
International Nuclear Information System (INIS)
Pih, H.; Gray, W.H.
1975-01-01
A series of two-dimensional photoelastic stress analyses on circular and oval toroidal magnetic field coils for fusion reactors were made. The circumferential variation of the coil's magnetic force was simulated by applying different pressures to sixteen segmented regions of the inner surface of the models. Isochromatics and isoclinics were measured at selected points on the loaded model in a transmission polariscope using a microphotometer. Separate principal stresses were obtained using the combination of photoelastic information and isopachic data measured from the solution of Laplace's equation by the electrical analog method. Analysis of the same coil geometries, loadings, and boundary conditions were made using the finite element method. General agreement between theory and experiment was realized. From this investigation several variations of coil geometry and methods of support were evaluated. Based upon this experiment, suggestions for optimum structural design of toroidal field coils are presented
Distributions of temperature and stress fields on penetration assembly during multi-pass welding
International Nuclear Information System (INIS)
Li Hong; Li Li
2010-01-01
Welding is a fundamental manufacturing technique used to join metal components. They cause errors during the assembly of the structure and reduce the strength of the structure. Based on an elastic-plastic-model, a three-dimensional finite element numerical simulation of a stainless steel penetration assembly during multi-pass welding with girth welds is carried out in this paper. And then the transient temperature field and the real-time dynamic stresses field of the structure are obtained. The heat source is modeled as a moving heat flux along girth welds following a double ellipsoid distribution. The 'birth and death' element method is applied to simulate the gradual growth of welding pass metal. The way of predicting the residual stresses in this paper can prepare an error-minimizing guide at design stage and can be used in accuracy management.
Analytical Solution for Stress Field and Intensity Factor in CSTBD under Mixed Mode Conditions
Directory of Open Access Journals (Sweden)
Najaf Ali Ghavidel
2014-06-01
Full Text Available Considering the fact that rocks fail faster under tensile stress, rock tensile strength is of greatimportance in applications such as blasting, rock fragmentation, slope stability, hydraulic fracturing,caprock integrity, and geothermal energy extraction. There are two direct and indirect methods tomeasure tensile strength. Since direct methods always encompass difficulties in test setup, indirectmethods, specifically the Brazilian test, have often been employed for tensile strength measurement.Tensile failure is technically attributed to crack propagation in rock. Fracture mechanics hassignificant potential for the determination of crack behaviour as well as propagation pattern. To applyBrazilian tests, cracked disc geometry has been suggested by the International Society for RockMechanics ISRM. Accordingly, a comprehensive study is necessary to evaluate stress field and stressintensity factor (SIF around the crack in the centre of the specimen. In this paper, superpositionprinciple is employed to solve the problem of cracked straight-through Brazilian disc (CSTBD, usingtwo methods of dislocation and complex stress function. Stress field and SIF in the vicinity of thecrack tip are then calculated. With the proposed method, the magnitude of critical load for crackinitiation in structures can be predicted. This method is valid for any crack of any arbitrary length andangle. In addition, numerical modelling has been carried out for the Brazilian disc. Finally, theanalytical solution has been compared with numerical modelling results showing the same outcomefor both methods.
Influence of the lithosphere-asthenosphere boundary on the stress field northwest of the Alps
Maury, J.; Cornet, F. H.; Cara, M.
2014-11-01
In 1356, a magnitude 6-7 earthquake occurred near Basel, in Switzerland. But recent compilations of GPS measurements reveal that measured horizontal deformation rates in northwestern continental Europe are smaller than error bars on the measurements, proving present tectonic activity, if any, is very small in this area. We propose to reconcile these apparently antinomic observations with a mechanical model of the lithosphere that takes into account the geometry of the lithosphere-asthenosphere boundary, assuming that the only loading mechanism is gravity. The lithosphere is considered to be an elastoplastic material satisfying a Von Mises plasticity criterion. The model, which is 400 km long, 360 km wide and 230 km thick, is centred near Belfort in eastern France, with its width oriented parallel to the N145°E direction. It also takes into account the real topography of both the ground surface and that of the Moho discontinuity. Not only does the model reproduce observed principal stress directions orientations, it also identifies a plastic zone that fits roughly the most seismically active domain of the region. Interestingly, a somewhat similar stress map may be produced by considering an elastic lithosphere and an ad-hoc horizontal `tectonic' stress field. However, for the latter model, examination of the plasticity criterion suggests that plastic deformation should have taken place. It is concluded that the present-day stress field in this region is likely controlled by gravity and rheology, rather than by active Alpine tectonics.
FOCAL MECHANISMS OF EARTHQUAKES AND STRESS FIELD OF THE CRUST IN MONGOLIA AND ITS SURROUNDINGS
Directory of Open Access Journals (Sweden)
N. A. Radziminovich
2016-01-01
Full Text Available We have compiled and analyzed earthquake focal solutions for the territory of Mongolia and its surroundings in order to reveal a spatial variability of stress orientation and stress regimes of the crust. According to the stress inversion results, the SHmax is turning from W-E in the eastern Mongolia to SW-NE in the Gobi Altay and the central Mongolia, and then to S-N in the western part of the region. Comparison with data derived from GPS measurements shows that directions of the strain axes revealed by the geodetic and seismological observations are generally consistent. A contradiction is found for the Bolnai zone where results of GPS estimation indicate the predominance of extension (in the SE-NW direction, whereas earthquake data for the longer period of seismic observations reveal compression. Compression in this zone is mainly due to the Tsetserleg-Bolnai earthquakes contribution; however, a part of the recent data on focal mechanisms fits an extensional stress field with the NNW orientated extension axis. These data are in accordance with some published works which suggest a transtensive field from some structural geology studies in the eastern part of the Bolnai zone.The paper is supplemented with a list of M≥4.5 earthquake fault plane solutions and unpublished focal mechanisms for some M≤4.5 earthquakes of the northern Mongolia and the southern Baikal region.
International Nuclear Information System (INIS)
Freynik, H.S. Jr.; Roach, D.R.; Deis, D.W.; Hirzel, D.G.
1977-01-01
Evaluation and calibration measurements were performed on commercial nickel-chromium metal-foil strain gages in a high-magnetic-field (12 T), liquid-helium (4.2 K) environment. The purpose was to fully characterize strain gages for use at cryogenic temperatures in high magnetic fields. In this study, the magnetoresistance of a number of strain gages was measured in three orthogonal directions at mechanical strain levels to 8900 μm/m. As a result, a unique calibration curve was defined for magnetoresistance strain errors that is independent of strain level and field direction to 12 T at 4.2 K. A current strain-gage application is the measurement of superconductor mechanical properties. These gages will soon be used in the stress analysis of superconducting fusion magnets during cooldown from ambient temperatures and during operation at 4.2 K with magnetic fields to 12 T
1995-08-11
activities. Pulsing electromagnetic fields ( PEMFs )have been shown to speed the healing of non-union fractures and we have used them successfully to...and then randomized into actual PEMF and placebo PEMF groups and treated for one hour per day until they return to duty. Changes in the bone scan are...musculoskeletal groups. Results to date indicate that pelvic stress fractures are being misdiagnosed. If these results are confirmed, treatments for
Post-paleozoic crustal responses to the contemporary stress field in the eastern United States
International Nuclear Information System (INIS)
Staub, W.P.; Hardee, H.K.
1993-01-01
This paper summarizes the current state of knowledge with respect to post-Paleozoic tectonic features and their relationship to the contemporary stress field outside coastal plain regions of the eastern United States. Until the early 1970s very little was known about such features. By the end of 1992 post-Paleozoic faults had been observed in at least five widely separated regions. Pleistocene-Holocene surface ruptures and liquefaction features had been observed over a steadily increasing area of the upper Mississippi embayment and adjacent regions. Ages of most recent ruptures of post-Paleozoic faults range from uncertain to Holocene and their senses of motion are compatible with the contemporary stress field. The cumulative amount of post-Paleozoic displacement on these faults is generally less than three meters. Fracture systems in Paleozoic rocks also are compatible with the contemporary stress field over a wide region of Indiana. The apparent compatibility of these widely scattered tectonic features with the contemporary stress field suggests that larger earthquakes may have occurred during Pleistocene-Holocene time and over a wider region of the eastern United States than implied by the historical record of seismicity. With the exception of the New Madrid fault system and possibly the Meers fault, small lengths and small cumulative displacements on these features place limits on the magnitude and frequency of strong-motion earthquakes in a give region. Therefore, the potential exists for limited fault reactivation and surface rupture throughout the eastern United States. Quaternary offsets also have been observed along branches of the Kentucky River fault system in eastern Kentucky. Currently, there is insufficient evidence from which to conclude that any of these faults is active in a regulatory sense
Nonperturbative loop quantization of scalar-tensor theories of gravity
International Nuclear Information System (INIS)
Zhang Xiangdong; Ma Yongge
2011-01-01
The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter ω(φ). In the sector of ω(φ)=-(3/2), the feasible theories are restricted and a new primary constraint generating conformal transformations of spacetime is obtained, while in the other sector of ω(φ)≠-(3/2), the canonical structure and constraint algebra of the theories are similar to those of general relativity coupled with a scalar field. By canonical transformations, we further obtain the connection-dynamical formalism of the scalar-tensor theories with real su(2) connections as configuration variables in both sectors. This formalism enables us to extend the scheme of nonperturbative loop quantum gravity to the scalar-tensor theories. The quantum kinematical framework for the scalar-tensor theories is rigorously constructed. Both the Hamiltonian constraint operator and master constraint operator are well defined and proposed to represent quantum dynamics. Thus the loop quantum gravity method is also valid for general scalar-tensor theories.
Tensor analysis and elementary differential geometry for physicists and engineers
Nguyen-Schäfer, Hung
2014-01-01
Tensors and methods of differential geometry are very useful mathematical tools in many fields of modern physics and computational engineering including relativity physics, electrodynamics, computational fluid dynamics (CFD), continuum mechanics, aero and vibroacoustics, and cybernetics. This book comprehensively presents topics, such as bra-ket notation, tensor analysis, and elementary differential geometry of a moving surface. Moreover, authors intentionally abstain from giving mathematically rigorous definitions and derivations that are however dealt with as precisely as possible. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors and differential geometry and to use them in the physical and engineering world. The target audience primarily comprises graduate students in physics and engineering, research scientists, and practicing engineers.
Generalized stress field in granular soils heap with Rayleigh–Ritz method
Directory of Open Access Journals (Sweden)
Gang Bi
2017-02-01
Full Text Available The stress field in granular soils heap (including piled coal will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations. Because the former method is not reliable as pressure cells instrumented on the interface between piled coal and the underlying soft soil do not work well, results from numerical methods alone are necessary to be doubly checked with one more method before they are extended to more complex cases. The generalized stress field in granular soils heap is analyzed with Rayleigh–Ritz method. The problem is divided into two cases: case A without horizontal constraint on the base and case B with horizontal constraint on the base. In both cases, the displacement functions u(x, y and v(x, y are assumed to be cubic polynomials with 12 undetermined parameters, which will satisfy the Cauchy's partial differential equations, generalized Hooke's law and boundary equations. A function is built with the Rayleigh–Ritz method according to the principle of minimum potential energy, and the problem is converted into solving two undetermined parameters through the variation of the function, while the other parameters are expressed in terms of these two parameters. By comparison of results from the Rayleigh–Ritz method and numerical simulations, it is demonstrated that the Rayleigh–Ritz method is feasible to study the generalized stress field in granular soils heap. Solutions from numerical methods are verified before being extended to more complicated cases.
Peculiarities of stress field formation during cutting isotropic material by mining machine cutters
Gabov, V. V.; Zadkov, D. A.
2017-10-01
Peculiarities of the cutting process of isotropic material by mining machine cutters are considered. The objective of the studies is revealing regularities of the process of stress field formation in the pre-cutter zone of the breakable massif and assessment of the possibility of purposeful control of cutting process parameters. Taking into account the multifactorial nature and randomness of the process of elementary chippage formation, an experimental method of studies with the use of full-sized cutters was accepted as a determining principle. A stand for cutting an isotropic transparent material with an optical method of observing stress fields in the under-cutter zone, the procedure of conducting studies and results were presented in the paper. The use of quasi-isotropic acryl glass as an object for destruction allowed reducing the influence of multifactorial nature and randomness on the process of formation of the stress field and elementary chippage. The modes, excluding continuous chip formation, determined by, on the one hand, the phenomenon of material creep – at low cutting speeds, and, on the other hand – cutting speed modes by the terms of thermal conditions, were determined. Continuation of experimental studies of the cutting process of quasi-isotropic materials is aimed at revealing the most significant factors and determination of their influence on the change of phase parameters of elementary chippage and at revealing the very opportunity of formation of elementary chippage characteristics.
Reciprocal mass tensor : a general form
International Nuclear Information System (INIS)
Roy, C.L.
1978-01-01
Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)
Tensor-based spatiotemporal saliency detection
Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen
2018-03-01
This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.
Akkerman, Erik M.
2010-01-01
Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional
The Chevreton tensor and Einstein-Maxwell spacetimes conformal to Einstein spaces
International Nuclear Information System (INIS)
Bergqvist, Goeran; Eriksson, Ingemar
2007-01-01
In this paper, we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure radiation type and that it restricts the spacetimes to Petrov type N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on a closed form, we settle by giving the integrability conditions in the general case, but we do give new explicit examples of Einstein-Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a C-space. The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are conformally C-spaces, but none of them are conformal to Einstein spaces
The space generated by metric and torsion tensors, derivation of Einstein-Hilbert equation
Directory of Open Access Journals (Sweden)
Николай Иванович Яременко
2014-11-01
Full Text Available This paper is devoted to the derivation of field equations in space with the geometric structure generated by metric and torsion tensors. We also study the geometry of the space are generated jointly and agreed by the metric tensor and the torsion tensor. We showed that in such space the structure of the curvature tensor has special features and for this tensor obtained analog Ricci - Jacobi identity; was evaluated gap that occurs at the transition from the original to the image and vice versa, in the case of an infinitely small contours. We have researched the geodesic lines equation. We introduce the tensor π_αβ which is similar to the second fundamental tensor of hypersurfaces Y^n-1, but the structure of this tensor is substantially different from the case of Riemannian spaces with zero torsion. Then we obtained formulas which characterize the change of vectors in accompanying basis relative to this basis itself in the small. Taking into considerations our results about the structure of such space we derived from the variation principle the general field equations (electromagnetic and gravitational.
Local nematic susceptibility in stressed BaFe2As2 from NMR electric field gradient measurements
Kissikov, T.; Sarkar, R.; Lawson, M.; Bush, B. T.; Timmons, E. I.; Tanatar, M. A.; Prozorov, R.; Bud'ko, S. L.; Canfield, P. C.; Fernandes, R. M.; Goh, W. F.; Pickett, W. E.; Curro, N. J.
2017-12-01
The electric field gradient (EFG) tensor at the 75As site couples to the orbital occupations of the As p orbitals and is a sensitive probe of local nematicity in BaFe2As2 . We use nuclear magnetic resonance to measure the nuclear quadrupolar splittings and find that the EFG asymmetry responds linearly to the presence of a strain field in the paramagnetic phase. We extract the nematic susceptibility from the slope of this linear response as a function of temperature and find that it diverges near the structural transition, in agreement with other measures of the bulk nematic susceptibility. Our work establishes an alternative method to extract the nematic susceptibility which, in contrast to transport methods, can be extended inside the superconducting state.
Vector and tensor analysis with applications
Borisenko, A I; Silverman, Richard A
1979-01-01
Concise and readable, this text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. It also includes a systematic study of the differential and integral calculus of vector and tensor functions of space and time. Worked-out problems and solutions. 1968 edition.
Permeability tensor and representative elementary volume of fractured rock masses
Rong, Guan; Peng, Jun; Wang, Xiaojiang; Liu, Guang; Hou, Di
2013-11-01
Based on a simulation of three-dimensional fracture networks and a superposition principle of liquid dissipation energy for fractured rock masses, a model of the fracture permeability tensor is proposed. An elastic constitutive model of rock fractures, considering fracture closure and dilation during shearing, is also proposed, based on the dilation angle of the fracture. Algorithms of flow-path searching and calculation of the effective flow coefficients for fracture networks are presented, together with a discussion on the influence of geometric parameters of the fractures (trace length, spacing, aperture, orientation and the number of fracture sets) on magnitude, anisotropy of hydraulic permeability and the size of a representative elementary volume (REV). The anisotropy of hydraulic permeability of fractured rock masses is mainly affected by orientation and the number of fracture sets, and the REV size is mainly influenced by trace length, spacing and the number of fracture sets. The results of studies on REV size and the influence of in-situ stress on hydraulic conductivity of the rock mass on the slope of Jinping-I hydropower station, China, are presented using the developed models and methods. The simulation results agreed well with the results obtained from field water-pressure measurements, with an error of less than 10 %.
International Nuclear Information System (INIS)
Huang, H.Y.; Chu, W.Y.; Su, Y.J.; Qiao, L.J.; Gao, K.W.
2005-01-01
The combined effect of electric field and residual stress on propagation of unloaded indentation cracks in a PZT-5 ceramic has been studied. The results show that residual stress itself is too small to induce delayed propagation of the indentation cracks in silicon oil. If applied constant electric field is larger than 0.2 kV/cm, the combined effect of electric field and residual stress can cause delayed propagation of the indentation crack after passing an incubation time in silicon oil, but the crack will arrest after propagating for 10-30 μm because of decrease of the resultant stress intensity factor induced by the field and residual stress with increasing the crack length. The threshold electric field for delayed propagation of the indentation crack in silicon oil is E DP = 0.2 kV/cm. If the applied electric field is larger than 5.25 kV/cm, combined effect of the electric field and residual stress can cause instant propagation of the indentation crack, and under sustained electric field, the crack which has propagated instantly can propagate continuously, until arrest at last. The critical electric field for instant propagation of the indentation crack is E P = 5.25 kV/cm. If the applied electric field is larger than 12.6 kV/cm, the microcracks induced by the electric field initiate everywhere, grow and connect in a smooth specimen, resulting in delayed failure, even without residual stress. The threshold electric field for delayed failure of a smooth specimen in silicon oil is E DF = 12.6 kV/cm and the critical electric field for instant failure is E F = 19.1 kV/cm
Bowman, R E; Ferguson, D; Luine, V N
2002-01-01
Twenty-one days of chronic restraint stress impairs male rat performance on the radial arm maze [Luine et al. (1994) Brain Res. 639, 167-170], but enhances female rat performance [Bowman et al. (2001) Brain Res. 904, 279-289]. To assess possible ovarian hormone mechanisms underlying this sexually dimorphic response to stress, we examined chronic stress effects in ovariectomized rats. Ovariectomized rats received Silastic capsule implants containing cholesterol or estradiol and were assigned to a daily restraint stress (21 days, 6 h/day) or non-stress group. Following the stress period, subjects were tested for open field activity and radial arm maze performance. Stress and estradiol treatment affected open field activity. All stressed animals, with or without estradiol treatment, made fewer total outer sector crossings. In contrast, estradiol-treated animals, with or without stress, made more inner sector visits, an indication that estradiol decreased anxious behavior on the open field across time. As measured by the total number of visits required to complete the task, stress did not affect radial arm maze performance in ovariectomized rats, but estradiol-treated animals, with or without stress, performed better than non-treated animals on the radial arm maze. Stressed subjects receiving estradiol showed the best radial arm maze performance. Following killing, tissue samples were obtained from various brain regions known to contribute to learning and memory, and monoamine and metabolite levels were measured. Several changes were observed in response to both stress and estradiol. Most noteworthy, stress treatment decreased homovanillic acid levels in the prefrontal cortex, an effect not previously observed in stressed intact females. Estradiol treatment increased norepinephrine levels in CA3 region of the hippocampus, mitigating stress-dependent changes. Both stress and estradiol decreased dentate gyrus levels of 5-hydroxyindole acetic acid. In summary, the current
Projectors and seed conformal blocks for traceless mixed-symmetry tensors
Energy Technology Data Exchange (ETDEWEB)
Costa, Miguel S. [Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Theory Division, Department of Physics, CERN, CH-1211 Genève 23 (Switzerland); Hansen, Tobias [Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D-22761 Hamburg (Germany); Penedones, João [Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Theory Division, Department of Physics, CERN, CH-1211 Genève 23 (Switzerland); Fields and Strings Laboratory, Institute of Physics, EPFL, CH-1015 Lausanne (Switzerland); Trevisani, Emilio [Centro de Física do Porto, Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal)
2016-07-05
In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length l{sub 1} of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in l{sub 1} for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.
Projectors and seed conformal blocks for traceless mixed-symmetry tensors
Costa, Miguel S.; Penedones, João; Trevisani, Emilio
2016-01-01
In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in $l_1$ for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.
Proof of a decomposition theorem for symmetric tensors on spaces with constant curvature
Energy Technology Data Exchange (ETDEWEB)
Straumann, N. [Institute for Theoretical Physics, University of Zurich (Switzerland)
2008-08-15
In cosmological perturbation theory a first major step consists in the decomposition of the various perturbation amplitudes into scalar, vector and tensor perturbations, which mutually decouple. In performing this decomposition one uses - beside the Hodge decomposition for one-forms - an analogous decomposition of symmetric tensor fields of second rank on Riemannian manifolds with constant curvature. While the uniqueness of such a decomposition follows from Gauss' theorem, a rigorous existence proof is not obvious. In this note we establish this for smooth tensor fields, by making use of some important results for linear elliptic differential equations. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
Proof of a decomposition theorem for symmetric tensors on spaces with constant curvature
International Nuclear Information System (INIS)
Straumann, N.
2008-01-01
In cosmological perturbation theory a first major step consists in the decomposition of the various perturbation amplitudes into scalar, vector and tensor perturbations, which mutually decouple. In performing this decomposition one uses - beside the Hodge decomposition for one-forms - an analogous decomposition of symmetric tensor fields of second rank on Riemannian manifolds with constant curvature. While the uniqueness of such a decomposition follows from Gauss' theorem, a rigorous existence proof is not obvious. In this note we establish this for smooth tensor fields, by making use of some important results for linear elliptic differential equations. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.
Li, Wei; Liu, Chunlei
2013-10-01
Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity.
Evaluation of the tensor polynomial failure criterion for composite materials
Tennyson, R. C.; Macdonald, D.; Nanyaro, A. P.
1978-01-01
A comprehensive experimental and analytical evaluation of the tensor polynomial failure criterion was undertaken to determine its capability for predicting the ultimate strength of laminated composite structures subject to a plane stress state. Results are presented demonstrating that a quadratic formulation is too conservative and a cubic representation is required. Strength comparisons with test data derived from glass/epoxy and graphite/epoxy tubular specimens are also provided to validate the cubic strength criterion.
DEFF Research Database (Denmark)
Regel, Jeppe Bendix; Orozova-Bekkevold, Ivanka; Andreassen, Katrine Alling
2017-01-01
We propose a combination of Biot's equations for effective stress and the expression for shear failure in a rock to obtain an expression for minimum pore pressure in a stable vertical well bore. We show that a Biot's coefficient calculated from logging data in the Hejre Field, North Sea, is signi......We propose a combination of Biot's equations for effective stress and the expression for shear failure in a rock to obtain an expression for minimum pore pressure in a stable vertical well bore. We show that a Biot's coefficient calculated from logging data in the Hejre Field, North Sea......, is significantly different from 1. The log-derived Biot's coefficient is above 0.8 in the Shetland Chalk Group and in the Tyne Group, and 0.6-0.8 in the Heno Sandstone Formation. We show that the effective vertical and horizontal stresses obtained using the log-derived Biot's coefficient result in a drilling...... window for a vertical well larger than if approximating Biot's coefficient by 1. The estimation of the Biot's coefficient is straightforward in formations with a stiff frame, whereas in formations such as shales, caution has to be taken. We discuss the consequence of assumptions made on the mineral...
Directory of Open Access Journals (Sweden)
Fukada Saiji
2015-01-01
Full Text Available The prestressed concrete (PC stress ribbon footbridge is a type of suspension bridge without towers, which has been applied in Japan and all over the world for years in light of its low construction cost and aesthetic merit. It generally consists of the precast concrete slabs with embedded cables. However, the walking-induced lateral vibration trouble of the Millennium Bridge in London in 2000 gave a lesson to the engineers that the lateral vibration feature must be taken into consideration for the footbridge vibration evaluation. In this sense, the field investigations on the lateral vibration features of 14 pre-stressed concrete stress ribbon footbridge in Japan was carried out by artificial impact and damping free vibration tests. According to the investigations, the larger the bridge span, the lower the frequencies of lateral-related vibration modes. In addition, based on the damping-free vibration field tests, there was a tendency toward the damping constant degradation when bridge span became larger.
Engineering stress in thin films for the field of bistable MEMS
Ratnayake, Dilan; Martin, Michael D.; Gowrishetty, Usha R.; Porter, Daniel A.; Berfield, Thomas A.; McNamara, Shamus P.; Walsh, Kevin M.
2015-12-01
While stress-free and tensile films are well-suited for released in-plane MEMS designs, compressive films are needed for released out-of-plane MEMS structures such as buckled beams and diaphragms. This study presents a characterization of stress on a variety of sputtered and plasma-enhanced chemical vapour deposition (PECVD)-deposited films, including titanium tungsten, invar, silicon nitride and amorphous silicon, appropriate for the field of bistable MEMS. Techniques and strategies are presented (including varying substrate bias, pressure, temperature, and frequency multiplexing) for tuning internal stress across the spectrum from highly compressive (-2300 MPa) to highly tensile (1500 MPa). Conditions for obtaining stress-free films are also presented in this work. Under certain conditions during the PECVD deposition of amorphous silicon, interesting ‘micro-bubbles’ formed within the deposited films. Strategies to mitigate their formation are presented, resulting in a dramatic improvement in surface roughness quality from 667 nm root mean square (RMS) to 16 nm RMS. All final deposited films successfully passed the traditional ‘tape test’ for adhesion.
Simultaneous wall-shear-stress and wide-field PIV measurements in a turbulent boundary layer
Gomit, Guillaume; Fourrie, Gregoire; de Kat, Roeland; Ganapathisubramani, Bharathram
2015-11-01
Simultaneous particle image velocimetry (PIV) and hot-film shear stress sensor measurements were performed to study the large-scale structures associated with shear stress events in a flat plate turbulent boundary layer at a high Reynolds number (Reτ ~ 4000). The PIV measurement was performed in a streamwise-wall normal plane using an array of six high resolution cameras (4 ×16MP and 2 ×29MP). The resulting field of view covers 8 δ (where δ is the boundary layer thickness) in the streamwise direction and captures the entire boundary layer in the wall-normal direction. The spatial resolution of the measurement is approximately is approximately 70 wall units (1.8 mm) and sampled each 35 wall units (0.9 mm). In association with the PIV setup, a spanwise array of 10 skin-friction sensors (spanning one δ) was used to capture the footprint of the large-scale structures. This combination of measurements allowed the analysis of the three-dimensional conditional structures in the boundary layer. Particularly, from conditional averages, the 3D organisation of the wall normal and streamwise velocity components (u and v) and the Reynolds shear stress (-u'v') related to a low and high shear stress events can be extracted. European Research Council Grant No-277472-WBT.
Full-field fabric stress mapping by micro Raman spectroscopy in a yarn push-out test.
Lei, Z K; Qin, F Y; Fang, Q C; Bai, R X; Qiu, W; Chen, X
2018-02-01
The full-field stress distribution of a two-dimensional plain fabric was mapped using micro Raman spectroscopy (MRS) through a novel yarn push-out test, simulating a quasi-static projectile impact on the fabric. The stress-strain relationship for a single yarn was established using a digital image correlation method in a single-yarn tensile test. The relationship between Raman peak shift and aramid Kevlar 49 yarn stress was established using MRS in a single-yarn tensile test. An out-of-plane loading test was conducted on an aramid Kevlar 49 plain fabric, and the yarn stress was measured using MRS. From the full-field fabric stress distribution, it can be observed that there is a cross-shaped distribution of high yarn stress; this result would be helpful in further studies on load transfer on a fabric during a projectile impact.
Bioeffects of Static Magnetic Fields: Oxidative Stress, Genotoxic Effects, and Cancer Studies
Ghodbane, Soumaya; Lahbib, Aida; Sakly, Mohsen; Abdelmelek, Hafedh
2013-01-01
The interaction of static magnetic fields (SMFs) with living organisms is a rapidly growing field of investigation. The magnetic fields (MFs) effect observed with radical pair recombination is one of the well-known mechanisms by which MFs interact with biological systems. Exposure to SMF can increase the activity, concentration, and life time of paramagnetic free radicals, which might cause oxidative stress, genetic mutation, and/or apoptosis. Current evidence suggests that cell proliferation can be influenced by a treatment with both SMFs and anticancer drugs. It has been recently found that SMFs can enhance the anticancer effect of chemotherapeutic drugs; this may provide a new strategy for cancer therapy. This review focuses on our own data and other data from the literature of SMFs bioeffects. Three main areas of investigation have been covered: free radical generation and oxidative stress, apoptosis and genotoxicity, and cancer. After an introduction on SMF classification and medical applications, the basic phenomena to understand the bioeffects are described. The scientific literature is summarized, integrated, and critically analyzed with the help of authoritative reviews by recognized experts; international safety guidelines are also cited. PMID:24027759
Directory of Open Access Journals (Sweden)
Kaplan David L
2011-01-01
Full Text Available Abstract Background Electric fields are integral to many biological events, from maintaining cellular homeostasis to embryonic development to healing. The application of electric fields offers substantial therapeutic potential, while optimal dosing regimens and the underlying mechanisms responsible for the positive clinical impact are poorly understood. Methods The purpose of this study was to track the differentiation profile and stress response of human bone marrow derived mesenchymal stem cells (hMSCs undergoing osteogenic differentiation during exposure to a 20 mV/cm, 60 kHz electric field. Morphological and biochemical changes were imaged using endogenous two-photon excited fluorescence (TPEF and quantitatively assessed through eccentricity calculations and extraction of the redox ratio from NADH, FAD and lipofuscin contributions. Real time reverse transcriptase-polymerase chain reactions (RT-PCR were used to track osteogenic differentiation markers, namely alkaline phosphatase (ALP and collagen type 1 (col1, and stress response markers, such as heat shock protein 27 (hsp27 and heat shock protein 70 (hsp70. Comparisons of collagen deposition between the stimulated hMSCs and controls were examined through second harmonic generation (SHG imaging. Results Quantitative differences in cell morphology, as described through an eccentricity ratio, were found on days 2 and days 5 (p Conclusions Electrical stimulation is a useful tool to improve hMSC osteogenic differentiation, while heat shock proteins may reveal underlying mechanisms, and optical non-invasive imaging may be used to monitor the induced morphological and biochemical changes.
Bioeffects of Static Magnetic Fields: Oxidative Stress, Genotoxic Effects, and Cancer Studies
Directory of Open Access Journals (Sweden)
Soumaya Ghodbane
2013-01-01
Full Text Available The interaction of static magnetic fields (SMFs with living organisms is a rapidly growing field of investigation. The magnetic fields (MFs effect observed with radical pair recombination is one of the well-known mechanisms by which MFs interact with biological systems. Exposure to SMF can increase the activity, concentration, and life time of paramagnetic free radicals, which might cause oxidative stress, genetic mutation, and/or apoptosis. Current evidence suggests that cell proliferation can be influenced by a treatment with both SMFs and anticancer drugs. It has been recently found that SMFs can enhance the anticancer effect of chemotherapeutic drugs; this may provide a new strategy for cancer therapy. This review focuses on our own data and other data from the literature of SMFs bioeffects. Three main areas of investigation have been covered: free radical generation and oxidative stress, apoptosis and genotoxicity, and cancer. After an introduction on SMF classification and medical applications, the basic phenomena to understand the bioeffects are described. The scientific literature is summarized, integrated, and critically analyzed with the help of authoritative reviews by recognized experts; international safety guidelines are also cited.
Modeling flow and shear stress fields over unsteady three dimensional dunes
Hardy, Richard; Parsons, Dan; Ashworth, Phil; Reesink, Arjan; Best, Jim
2014-05-01
The flow field over dunes has been extensively measured in laboratory conditions and there is general understanding on the nature of the flow over dunes formed under equilibrium flow conditions. This has allowed an understanding of bed shear stress to be derived and the development of morpho-dynamic models. However, fluvial systems typically experience unsteady flow and therefore the sediment-water interface is constantly responding and reorganizing to these unsteady flows and stresses, over a range of both spatial and temporal scales. This is primarily through the adjustment of bed forms (including ripples, dunes and bar forms) which then subsequently alter the flow field. This paper investigates, through the application of a numerical model, the influence of these roughness elements on the overall flow and bed shear stress. A series of physical experiments were undertaken in a flume, 16m long and 2m wide, where a fine sand (D50 of 239µm) was water worked under a range of unsteady hydraulic conditions to generate a series of quasi-equilibrium three dimensional bed forms. During the experiments flow was measured with acoustic Doppler velocimeters, (aDv's). On four occasions the flume was drained and the bed topography measured with terrestrial LiDAR to create digital elevation models. This data provide the necessary boundary conditions and validation data for a numerical three dimensional flow model. The prediction of flow over the four static beds demonstrates the spatial distribution of shear stress and the potential sediment transport paths between the dune crests. These appear to be associated with coherent flow structures formed by localized shear flow. These flow predictions are currently being used to develop a fully three dimensional morphodynamic model to further understand dune dynamics under unsteady flow conditions.
Therapeutic Ultrasound in Navicular Stress Injuries in Elite Track and Field Athletes.
Malliaropoulos, Nikolaos; Alaseirlis, Dimosthenis; Konstantinidis, George; Papalada, Agapi; Tsifountoudis, Ioannis; Petras, Kosmas; Maffulli, Nicola
2017-05-01
To ascertain whether therapeutic ultrasound (TUS) can be used to assess the progression of conservative management in navicular stress injuries. This is a prospective, clinical case series. Level of evidence IV. All participants were examined and followed up in a private Sports Injury Clinic. Ten elite track and field athletes with severe dorsal midfoot pain over the navicular bone participated in this study. All patients underwent both TUS and magnetic resonance imaging (MRI) evaluation. The painful threshold of TUS on initial evaluation was a mean of 0.707 ± 149 W/cm, and MRI detected a navicular stress injury in all patients. The athletes received conservative treatment and underwent sequential TUS evaluations at 4, 8, 12 and 16 weeks. Therapeutic ultrasound pain threshold values were recorded, and the patients were additionally asked to grade local tenderness on a Visual Analogue Scale. Time to return to play was also recorded. The level of pain produced by the application of TUS on a navicular stress fracture seemed to correlate well with Visual Analogue Scale scores and the grade of fracture demonstrated on MRI. The initial low TUS painful mean value increased to a normal mean value of 1.97 ± 0.067 W/cm by 16 weeks. When clinical and TUS findings had returned to normal, the patients were allowed to return to sports activities, with no recurrences experienced during the study period. The production of pain associated with the application of TUS on a navicular stress fracture is a safe and reproducible method of monitoring the resolution of these fractures. We have used it successfully in making return-to-play decisions for elite level track and field athletes.
Mixed symmetry tensors in the worldline formalism
Energy Technology Data Exchange (ETDEWEB)
Corradini, Olindo [Dipartimento di Scienze Fisiche, Informatiche e Matematiche,Università degli Studi di Modena e Reggio Emilia, via Campi 213/A, I-41125 Modena (Italy); INFN - Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Edwards, James P. [Department of Mathematical Sciences, University of Bath,Claverton Down, Bath BA2 7AY (United Kingdom)
2016-05-10
We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which — by adding a suitable Chern-Simons term to the particle action — can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) “flavour” symmetry on the worldline particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young tableau. In particular the occupation numbers of the wavefunction — i.e. the lengths of the columns (rows) of the Young tableau — are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.
Koch, Saskia B. J.; van Zuiden, Mirjam; Nawijn, Laura; Frijling, Jessie L.; Veltman, Dick J.; Olff, Miranda
2017-01-01
Background: Posttraumatic stress disorder (PTSD) is a disabling psychiatric disorder that has been associated with lower white matter integrity of tracts connecting the prefrontal cortex with limbic regions. However, previous diffusion tensor imaging (DTI) findings have been inconsistent, showing
Teh, Irvin; McClymont, Darryl; Zdora, Marie-Christine; Whittington, Hannah J; Davidoiu, Valentina; Lee, Jack; Lygate, Craig A; Rau, Christoph; Zanette, Irene; Schneider, Jürgen E
2017-03-10
Diffusion tensor imaging (DTI) is widely used to assess tissue microstructure non-invasively. Cardiac DTI enables inference of cell and sheetlet orientations, which are altered under pathological conditions. However, DTI is affected by many factors, therefore robust validation is critical. Existing histological validation is intrinsically flawed, since it requires further tissue processing leading to sample distortion, is routinely limited in field-of-view and requires reconstruction of three-dimensional volumes from two-dimensional images. In contrast, synchrotron radiation imaging (SRI) data enables imaging of the heart in 3D without further preparation following DTI. The objective of the study was to validate DTI measurements based on structure tensor analysis of SRI data. One isolated, fixed rat heart was imaged ex vivo with DTI and X-ray phase contrast SRI, and reconstructed at 100 μm and 3.6 μm isotropic resolution respectively. Structure tensors were determined from the SRI data and registered to the DTI data. Excellent agreement in helix angles (HA) and transverse angles (TA) was observed between the DTI and structure tensor synchrotron radiation imaging (STSRI) data, where HA DTI-STSRI = -1.4° ± 23.2° and TA DTI-STSRI = -1.4° ± 35.0° (mean ± 1.96 standard deviation across all voxels in the left ventricle). STSRI confirmed that the primary eigenvector of the diffusion tensor corresponds with the cardiomyocyte long-axis across the whole myocardium. We have used STSRI as a novel and high-resolution gold standard for the validation of DTI, allowing like-with-like comparison of three-dimensional tissue structures in the same intact heart free of distortion. This represents a critical step forward in independently verifying the structural basis and informing the interpretation of cardiac DTI data, thereby supporting the further development and adoption of DTI in structure-based electro-mechanical modelling and routine clinical
Composite antisymmetric tensor bosons in a four-fermion interaction model
International Nuclear Information System (INIS)
Dmitrasinovic, V.
2000-01-01
We discuss the phenomenological consequences of the U A (1) symmetry-breaking two-flavour four-fermion antisymmetric (AS) Lorentz tensor interaction Lagrangians. We use the recently developed methods that respect the 'duality' symmetry of this interaction. Starting from the Fierz transform of the two-flavour 't Hooft interaction (a four-fermion Lagrangian with AS tensor interaction terms augmented by Nambu and Jona-Lasinio (NJL)-type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we find the following. (a) Four antisymmetric tensor and four AS pseudotensor bosons exist which satisfy a mass relation previously derived for scalar and pseudoscalar mesons from the 't Hooft interaction. (b) Antisymmetric tensor bosons mix with vector bosons via one-fermion-loop effective couplings so that both kinds of bosons have their masses shifted and the fermions (quarks) acquire anomalous magnetic moment form factors that explicitly violate chiral symmetry. (c) The mixing of massive AS tensor fields with vector fields leads to two sets of spin-1 states. The second set of spin-1 mesons is heavy and has not been observed. Moreover, at least one member of this second set is tachyonic, under standard assumptions about the source and strength of the AS tensor interaction. The tachyonic state also shows up as a pole in the space-like region of the electromagnetic form factors. (d) The mixing of axial-vector fields with antisymmetric tensor bosons is proportional to the (small) isospin-breaking up-down quark mass difference, so the mixing-induced mass shift is negligible. (e) The AS tensor version of the Veneziano-Witten U A (1) symmetry-breaking interaction does not lead to tachyons, or any AS tensor field propagation to leading order in N C . (author)
International Nuclear Information System (INIS)
Ramos, Tomas; Rubilar, Guillermo F.; Obukhov, Yuri N.
2011-01-01
Highlights: → The definition of the momentum of light inside matter is studied. → Fully relativistic analysis of the dielectric 'Einstein box' thought experiment. → Minkowski, Abraham and the total energy-momentum tensors are derived in detail. → Some assumptions hidden in the usual Einstein box argument are identified. → The Abraham momentum is not uniquely selected as the momentum of light in this case. - Abstract: We analyse the 'Einstein box' thought experiment and the definition of the momentum of light inside matter. We stress the importance of the total energy-momentum tensor of the closed system (electromagnetic field plus material medium) and derive in detail the relativistic expressions for the Abraham and Minkowski momenta, together with the corresponding balance equations for an isotropic and homogeneous medium. We identify some assumptions hidden in the Einstein box argument, which make it weaker than it is usually recognized. In particular, we show that the Abraham momentum is not uniquely selected as the momentum of light in this case.
Directory of Open Access Journals (Sweden)
J. Olakunle Onaolapo
2016-07-01
Conclusion: Repeated caffeine consumption and/or acute sleep-deprivation led to significant changes in pattern of open-field behaviour and stress/antioxidant response in mice. Responses seen in the study are probably due to modulatory effects of caffeine on the total body response to stressful stimuli.
Effects of 60 Hz electric fields on operant and social stress behaviors of nonhuman primates
Energy Technology Data Exchange (ETDEWEB)
Rogers, W.R.; Coelho, A.M. Jr.; Easley, S.P.; Lucas, J.H.; Moore, G.T.; Orr, J.L.; Smith, H.D.; Taylor, L.L.; Tuttle, M.L.
1987-10-24
The objective of this program is to investigate, using the baboon as a nonhuman primate surrogate for the human, possible behavioral effects associated with exposure to high intensity 60 Hz electric fields. Results from this program, along with information from experiments conducted elsewhere, will be used by the Department of Energy (DOE) to estimate and evaluate the likelihood of deleterious consequences resulting from exposure of humans to the electric fields associated with power transmission over high voltage lines. This research program consists of four major research projects, all of which have been successfully completed. The first project evaluated the potentially aversive character of exposure to 60 Hz electric fields by determining the threshold intensity that produces escape or avoidance responses. The second project estimated the threshold intensity for detection threshold was 12 kV/m; the range of means was 6 to 16 kV/m. The third project assessed, in separate experiments conducted at 30 and 60 kV/m, effects of chronic exposure to electric fields on the performance of two operant conditioning tasks, fixed ratio (FR), and differential reinforcement of low rate (DRL). In the same two experiments, the fourth project investigated, using the systematic quantitative observational sampling methods of primatology, the possible stress-inducing effects of chronic exposure to 60 Hz electric fields on the behavior of baboons living in small social groups. 131 refs., 87 figs., 123 tabs.
Enders, Laramy S; Nunney, Leonard
2012-09-22
Recent meta-analyses conducted across a broad range of taxa have demonstrated a strong linear relationship between the change in magnitude of inbreeding depression under stress and stress level, measured as fitness loss in outbred individuals. This suggests that a general underlying response may link stress and inbreeding depression. However, this relationship is based primarily on laboratory data, and it is unknown whether natural environments with multiple stressors and fluctuating stress levels alter how stress affects inbreeding depression. To test whether the same pattern persists in the field, we investigated the effect of seasonal variation on stress level and inbreeding depression in a 3-year field study measuring the productivity of captive populations of inbred and outbred Drosophila melanogaster. We found cold winter temperatures were most stressful and induced the greatest inbreeding depression. Furthermore, these data, collected under natural field conditions, conformed to the same predictive linear relationship seen in Drosophila laboratory studies, with inbreeding depression increasing by 0.17 lethal equivalents for every 10 per cent increase in stress level. Our results suggest that under natural conditions stress level is a primary determinant of the magnitude of inbreeding depression and should be considered when assessing extinction vulnerability in small populations.
Diffusion tensor optical coherence tomography
Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.
2018-01-01
In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.
Transposes, L-Eigenvalues and Invariants of Third Order Tensors
Qi, Liqun
2017-01-01
Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order t...
Directory of Open Access Journals (Sweden)
Dhaneshwar Mishra
2017-07-01
Full Text Available Exact closed-form expressions have been derived for the stresses and the electric fields induced in piezoelectric multilayers deposited on a substrate with lattice misfit and thermal expansion coefficient mismatch. The derived formulations can model any number of layers using recursive relations that minimize the computation time. A proper rotation matrix has been utilized to generalize the expressions so that they can be used for various growth orientations with each layer having hexagonal crystal symmetry. As an example, the influence of lattice misfit and thermal expansion coefficient mismatch on the state of electroelastic fields in different layers of GaN multi quantum wells has been examined. A comparison with the finite element analysis results showed very close agreement. The analytical expressions developed herein will be useful in designing optoelectronic devices as well as in predicting defect density in multi quantum wells.