Academic literature on the topic 'Intrinsic field tensors'
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Journal articles on the topic "Intrinsic field tensors"
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CIARLET, PHILIPPE G., LILIANA GRATIE, CRISTINEL MARDARE, and MING SHEN. "SAINT VENANT COMPATIBILITY EQUATIONS ON A SURFACE APPLICATION TO INTRINSIC SHELL THEORY." Mathematical Models and Methods in Applied Sciences 18, no. 02 (February 2008): 165–94. http://dx.doi.org/10.1142/s0218202508002644.
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We first establish that the linearized change of metric and change of curvature tensors, with components in L2 and H-1 respectively, associated with a displacement field, with components in H1, of a surface S immersed in ℝ3 must satisfy in the distributional sense compatibility conditions that may be viewed as the linear version of the Gauss and Codazzi-Mainardi equations. These compatibility conditions, which are analogous to the familiar Saint Venant equations in three-dimensional elasticity, constitute the Saint Venant equations on the surface S. We next show that these compatibility conditions are also sufficient, i.e. that they in fact characterize the linearized change of metric and the linearized change of curvature tensors in the following sense: If two symmetric matrix fields of order two defined over a simply-connected surface S ⊂ ℝ3 satisfy the above compatibility conditions, then they are the linearized change of metric and linearized change of curvature tensors associated with a displacement field of the surface S, a field whose existence is thus established. The proof provides an explicit algorithm for recovering such a displacement field from the linearized change of metric and linearized change of curvature tensors. This algorithm may be viewed as the linear counterpart of the reconstruction of a surface from its first and second fundamental forms. Finally, we show how these results can be applied to the "intrinsic theory" of linearly elastic shells, where the linearized change of metric and change of curvature tensors are the new unknowns. These new unknowns solve a quadratic minimization problem over a space of tensor fields whose components, which are only in L2, satisfy the Saint Venant compatibility conditions on a surface in the sense of distributions.
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Niedermaier, Max. "Nonstandard Action of Diffeomorphisms and Gravity’s Anti-Newtonian Limit." Symmetry 12, no. 5 (May 6, 2020): 752. http://dx.doi.org/10.3390/sym12050752.
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A tensor calculus adapted to the Anti-Newtonian limit of Einstein gravity is developed. The limit is defined in terms of a global conformal rescaling of the spatial metric. This enhances spacelike distances compared to timelike ones and in the limit effectively squeezes the lightcones to lines. Conventional tensors admit an analogous Anti-Newtonian limit, which however transforms according to a non-standard realization of the spacetime Diffeomorphism group. In addition to the type of the tensor the transformation law depends on, a set of integer-valued weights is needed to ensure the existence of a nontrivial limit. Examples are limiting counterparts of the metric, Einstein, and Riemann tensors. An adapted purely temporal notion of parallel transport is presented. By introducing a generalized Ehresmann connection and an associated orthonormal frame compatible with an invertible Carroll metric, the weight-dependent transformation laws can be mapped into a universal one that can be read off from the index structure. Utilizing this ‘decoupling map’ and a realization of the generalized Ehresmann connection in terms of scalar field, the limiting gravity theory can be endowed with an intrinsic Levi–Civita type notion of spatio-temporal parallel transport.
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Krawczuk, Anna, Daniel Pérez, and Piero Macchi. "PolaBer: a program to calculate and visualize distributed atomic polarizabilities based on electron density partitioning." Journal of Applied Crystallography 47, no. 4 (June 14, 2014): 1452–58. http://dx.doi.org/10.1107/s1600576714010838.
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This paper describes the program PolaBer, which calculates atomic polarizability tensors from electric field perturbations of a partitioned electron density distribution. Among many possible partitioning schemes, PolaBer is currently using the quantum theory of atoms in molecules and it is interfaced to programs that apply such a partitioning. The calculation of the atomic tensors follows the idea suggested by Keith [The Quantum Theory of Atoms in Molecules: From Solid State to DNA and Drug Design, (2007), edited by C. F. Matta & R. J. Boyd. Weinheim: Wiley-VCH], which enables the removal of the intrinsic origin dependence of the atomic charge contributions to the molecular dipole moment. This scheme allows the export, within chemically equivalent functional groups, of properties calculated from atomic dipoles, such as for example the atomic polarizabilities. The software permits visualization of the tensors and calculation of straightforward optical properties of a molecule (like the molar refractive index) or a crystal (assuming the molecule in a given crystal lattice).
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YOUSSEF, NABIL L., S. H. ABED, and A. SOLEIMAN. "CONCURRENT π-VECTOR FIELDS AND ENERGY β-CHANGE." International Journal of Geometric Methods in Modern Physics 06, no. 06 (September 2009): 1003–31. http://dx.doi.org/10.1142/s0219887809003904.
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The present paper deals with an intrinsic investigation of the notion of a concurrent π-vector field on the pullback bundle of a Finsler manifold (M, L). The effect of the existence of a concurrent π-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular β-change, namely the energy β-change ([Formula: see text]with[Formula: see text]; [Formula: see text] being a concurrent π-vector field), is established. The relation between the two Barthel connections Γ and [Formula: see text], corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy β-change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection, and the Hashiguchi connection. Moreover, the change of their curvature tensors is concluded. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.
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SOLEIMAN, A. "PARALLEL π-VECTOR FIELDS AND ENERGY β-CHANGE." International Journal of Geometric Methods in Modern Physics 08, no. 04 (June 2011): 753–72. http://dx.doi.org/10.1142/s0219887811005373.
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The present paper deals with an intrinsic investigation of the notion of a parallel π-vector field on the pullback bundle of a Finsler manifold (M, L). The effect of the existence of a parallel π-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular β-change, namely the energy β-change ([Formula: see text]with[Formula: see text] being a parallel π-vector field), is established. The relation between the two Barthel connections Γ and [Formula: see text], corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy β-change of the fundamental linear connection in Finsler geometry: The Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is concluded. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.
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VAN GOETHEM, NICOLAS, and FRANÇOIS DUPRET. "A distributional approach to 2D Volterra dislocations at the continuum scale." European Journal of Applied Mathematics 23, no. 3 (February 16, 2012): 417–39. http://dx.doi.org/10.1017/s0956792512000010.
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We develop a theory to represent dislocations and disclinations in single crystals at the continuum (or mesoscopic) scale by directly modelling the defect densities as concentrated effects governed by the distribution theory. The displacement and rotation multi-valuedness is resolved by introducing the intrinsic and single-valued Frank and Burgers tensors from the distributional gradients of the strain field. Our approach provides a new understanding of the theory of line defects as developed by Kröner [10] and other authors [6, 9]. The fundamental identity relating the incompatibility tensor to the Frank and Burgers vectors (and which is a cornerstone of the theory of dislocations in single crystals) is proved in the 2D case under appropriate assumptions on the strain and strain curl growth in the vicinity of the assumed isolated defect lines. In general, our theory provides a rigorous framework for the treatment of crystal line defects at the mesoscopic scale and a basis to strengthen the theory of homogenisation from mesoscopic to macroscopic scale.
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Lahoche, Vincent, Mohamed Ouerfelli, Dine Ousmane Samary, and Mohamed Tamaazousti. "Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra II: Tensorial Data." Entropy 23, no. 7 (June 23, 2021): 795. http://dx.doi.org/10.3390/e23070795.
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The tensorial principal component analysis is a generalization of ordinary principal component analysis focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative renormalization group formalism, based on a slight generalization of the covariance matrix, to investigate signal detection for the difficult issue of nearly continuous spectra. Renormalization group allows constructing an effective description keeping only relevant features in the low “energy” (i.e., large eigenvalues) limit and thus providing universal descriptions allowing to associate the presence of the signal with objectives and computable quantities. Among them, in this paper, we focus on the vacuum expectation value. We exhibit experimental evidence in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold, in agreement with our conclusions for matrices, providing a new step in the direction of a universal statement.
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SOLEIMAN, A. "ENERGY β-CONFORMAL CHANGE IN FINSLER GEOMETRY." International Journal of Geometric Methods in Modern Physics 09, no. 04 (May 6, 2012): 1250029. http://dx.doi.org/10.1142/s0219887812500296.
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The present paper deals with an intrinsic generalization of the conformal change and energy β-change on a Finsler manifold (M.L.), namely the energy β-conformal change ([Formula: see text] with [Formula: see text]; [Formula: see text] being a concurrent π-vector field and σ(x) is a function on M). The relation between the two Barthel connections Γ and [Formula: see text], corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy β-conformal change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is obtained. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.
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Ciarlet, Philippe G., and Cristinel Mardare. "The intrinsic theory of linearly elastic plates." Mathematics and Mechanics of Solids 24, no. 4 (May 28, 2018): 1182–203. http://dx.doi.org/10.1177/1081286518776047.
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In an intrinsic approach to a problem in elasticity, the only unknown is a tensor field representing an appropriate ‘measure of strain’, instead of the displacement vector field in the classical approach. The objective of this paper is to study the displacement traction problem in the special case where the elastic body is a linearly elastic plate of constant thickness, clamped over a portion of its lateral face. In this respect, we first explicitly compute the intrinsic three-dimensional boundary condition of place in terms of the Cartesian components of the linearized strain tensor field, thus avoiding the recourse to covariant components in curvilinear coordinates and providing an interesting example of actual computation of an intrinsic boundary condition of place in three-dimensional elasticity. Second, we perform a rigorous asymptotic analysis of the three-dimensional equations as the thickness of the plate, considered as a parameter, approaches zero. As a result, we identify the intrinsic two-dimensional equations of a linearly elastic plate modelled by the Kirchhoff–Love theory, with the linearized change of metric and change of curvature tensor fields of the middle surface of the plate as the new unknowns, instead of the displacement field of the middle surface in the classical approach.
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LU, H., C. N. POPE, S. SCHRANS, and X. J. WANG. "NEW REALIZATIONS OF W ALGEBRAS AND W STRINGS." Modern Physics Letters A 07, no. 20 (June 28, 1992): 1835–42. http://dx.doi.org/10.1142/s0217732392001543.
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We discuss new realizations of W algebras in which the currents are expressed in terms of two arbitrary commuting energy-momentum tensors together with a set of free scalar fields. This contrasts with the previously-known realizations, which involve only one energy-momentum tensor. Since realizations of nonlinear algebras are not easy to come by, the fact that this new class exists is of intrinsic interest. We use these new realizations to build the corresponding W-string theories and show that they are effectively described by two independent ordinary Virasoro-like strings.
Dissertations / Theses on the topic "Intrinsic field tensors"
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Kellermann, David Conrad Mechanical & Manufacturing Engineering Faculty of Engineering UNSW. "Strongly orthotropic continuum mechanics." Publisher:University of New South Wales. Mechanical & Manufacturing Engineering, 2008. http://handle.unsw.edu.au/1959.4/41454.
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The principal contribution of this dissertation is a theory of Strongly Orthotropic Continuum Mechanics that is derived entirely from an assertion of geometric strain indeterminacy. Implementable into the finite element method, it can resolve widespread kinematic misrepresentations and offer unique and purportedly exact strain-induced energies by removing the assumptions of strain tensor symmetry. This continuum theory births the proposal of a new class of physical tensors described as the Intrinsic Field Tensors capable of generalising the response of most classical mechanical metrics, a number of specialised formulations and the solutions shown to be kinematically intermediate. A series of numerical examples demonstrate Euclidean objectivity, material frame-indifference, patch test satisfaction, and agreement between the subsequent Material Principal Co-rotation and P??I??C decomposition methods that produce the intermediary stress/strain fields. The encompassing theory has wide applicability owing to its fundamental divergence from conventional mechanics, it offers non-trivial outcomes when applied to even very simple problems and its use of not the Eulerian, Lagrangian but the Intrinsic Frame generates previously unreported results in strongly orthotropic continua.
Books on the topic "Intrinsic field tensors"
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Deruelle, Nathalie, and Jean-Philippe Uzan. Differential geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0004.
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This chapter presents some elements of differential geometry, the ‘vector’ version of Euclidean geometry in curvilinear coordinates. In doing so, it provides an intrinsic definition of the covariant derivative and establishes a relation between the moving frames attached to a trajectory introduced in Chapter 2 and the moving frames of Cartan associated with curvilinear coordinates. It illustrates a differential framework based on formulas drawn from Chapter 2, before discussing cotangent spaces and differential forms. The chapter then turns to the metric tensor, triads, and frame fields as well as vector fields, form fields, and tensor fields. Finally, it performs some vector calculus.
Book chapters on the topic "Intrinsic field tensors"
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Oertel, Gerhard. "Stress." In Stress and Deformation. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195095036.003.0008.
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Stress is a tensor quantity that describes the mechanical force density (force per unit area) on the complete surface of a domain inside a material body. A stress exists wherever one part of a body exerts a force on neighboring parts. Its orientation is not tied to any particular directions that are intrinsic to the material like, say, crystallographic axes. It is thus distinct from the matter tensors that were discussed in the preceding chapter, all of which have definitive orientations within a crystal or other anisotropic material; it is called a field tensor (and so is strain). The definition of stress depends on the concept of a continuum. Let f(xi) be a single-valued function defined for every point xi in a region. This function is said to be continuous at the point xi if the following holds for all paths of approach of xi to °xi:. . . f(xi) → f(°xi) as xi → °xi (4.1)· . . . Equivalently, for any number ∊, no matter how small, there exists a neighborhood of nonzero radius around the point xi in which: . . . . 〈f(xi) − f(°xi)〉2 < ∊, (4.2) . . . for all points xi in that neighborhood. A continuum is an idealized material whose physical attributes are continuous functions of position. Thus neighboring points remain neighbors, and a continuum cannot have gaps or jumps (discontinuities) in its properties. Surfaces bounding gaps or defining discontinuities must be specially treated in continuum mechanics. Examples are surfaces between two fluids of differing density or viscosity, or between solids with different thermal conductivity or elastic properties. Real materials are never continua; they are discontinuous at the atomic scale, and often at larger scales as well. The notion of a continuum is, therefore, only a macroscopic approximation, but it allows useful mathematical approaches to the treatment of real phenomena.
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Nolte, David D. "The General Theory of Relativity and Gravitation." In Introduction to Modern Dynamics, 426–60. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198844624.003.0013.
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The intrinsic curvature of a metric space is captured by the Riemann curvature tensor, which can be contracted to the Ricci tensor and the Ricci scalar. Einstein took these curvature quantities and constructed the Einstein field equations that relate the curvature of space-time to energy and mass density. For an isotropic density, a solution to the field equations is the Schwarzschild metric, which contains mass terms that modify both the temporal and the spatial components of the invariant element. Consequences of the Schwarzschild metric include gravitational time dilation, length contraction, and redshifts. Trajectories in curved space-time are expressed as geodesics through the Schwarzschild metric space. Solutions to the geodesic equation lead to the precession of the perihelion of Mercury and to the deflection of light by the Sun.
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Fiorino, Daniel J. "Green Economy: Reframing Ecology, Economics, and Equity." In Conceptual Innovation in Environmental Policy. The MIT Press, 2017. http://dx.doi.org/10.7551/mitpress/9780262036580.003.0012.
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The real and perceived conflicts among economic growth and ecological protection define one of the central tensions in environmental policy. The premise of the concept of a green economy is that it is possible at some level to transform this assumed, traditional zero-sum into a positive relationship. Although its intellectual origins may be traced to the fields of ecological economics, business greening, and ecological modernization, the green economy concept gained particular visibility in the wake of the 2009 financial crisis. This chapter argues that the green economy concept may be influential both in policy framing and as a framework for guiding and carrying out economic and political change. Three modifications in treatments of the concept would make it more acceptable and relevant for future policy debates: rethinking the purpose of growth as well as how it is achieved; shedding more light on economic inequality and its ecological consequences; and emphasizing the intrinsic as well as the utilitarian value of ecological assets and services.
Conference papers on the topic "Intrinsic field tensors"
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Zhang, Tao, Xinhua Wang, Yingchun Chen, Zia Ullah, and Yizhen Zhao. "Non-Contact Geomagnetic Localization of Pipeline Defects Using Empirical Mode Decomposition and Magnetic Gradient Tensor." In 2018 12th International Pipeline Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/ipc2018-78258.
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Non-contact geomagnetic anomaly detection, as one of passive non-destructive testing (NDT) techniques, can be used to locate pipeline defects, while its accuracy is affected by random noise and detection orientation. In order to extract effective geomagnetic anomaly signals of pipeline defects, a method based on empirical mode decomposition (EMD) and magnetic gradient tensor was studied. In order to filter random noise, EMD was performed to self-adaptively decompose magnetic field signals into a series of intrinsic mode functions (IMFs), and then Hurst exponent was implemented to exclude false modes; The calculation method of magnetic gradient tensor modulus (MGTM) was proposed to obtain precise defect locations according to tensor symmetry; Subsequently, the remote pipeline defect model was built based on the magnetic dipole theory, and the relationship between detection orientation and MGTM was discussed. The experimental results showed that the proposed method could realize high precision and reliable non-contact geomagnetic localization of pipeline defects.
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Buryachenko, Valeriy A. "Micromechanics of Random Structure Thermoperistatic Composites." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65841.
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In contrast to the classical local and nonlocal theories, the peridynamic equation of motion introduced by Silling (J. Mech. Phys. Solids 2000; 48: 175–209) is free of any spatial derivatives of displacement. The new general integral equations (GIE) connecting the displacement fields in the point being considered and the surrounding points of random structure composite materials (CMs) is proposed. For statistically homogeneous thermoperistatic media subjected to homogeneous volumetric boundary loading, one proved that the effective behaviour of this media is governing by conventional effective constitutive equation which is intrinsic to the local thermoelasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional thermoelasticity of CMs and adapted to thermoperistatics. A generalization of the Hills equality to peri-static composites is proved. The classical representations of effective elastic moduli through the mechanical influence functions for elastic CMs are generalized to the case of peristatics, and the energetic definition of effective elastic moduli is proposed. The general results establishing the links between the effective properties (effective elastic moduli, effective thermal expansion) and the corresponding mechanical and transformation influence functions are obtained by the use of the decomposition of local fields into load and residual fields. Effective properties of thermoperistatic CM are expressed through the introduced local stress polarization tensor averaged over the extended inclusion phase. This similarity opens a way for straightforward expansion of analytical micromechanics tools for locally elastic CMs to the new area of random structure peri-dynamic CMs. Detailed numerical examples for 1D case are considered.