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CIARLET, PHILIPPE G., LILIANA GRATIE, CRISTINEL MARDARE i MING SHEN. "SAINT VENANT COMPATIBILITY EQUATIONS ON A SURFACE APPLICATION TO INTRINSIC SHELL THEORY". Mathematical Models and Methods in Applied Sciences 18, nr 02 (luty 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, nr 5 (6.05.2020): 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 i Piero Macchi. "PolaBer: a program to calculate and visualize distributed atomic polarizabilities based on electron density partitioning". Journal of Applied Crystallography 47, nr 4 (14.06.2014): 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 i A. SOLEIMAN. "CONCURRENT π-VECTOR FIELDS AND ENERGY β-CHANGE". International Journal of Geometric Methods in Modern Physics 06, nr 06 (wrzesień 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, nr 04 (czerwiec 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, i FRANÇOIS DUPRET. "A distributional approach to 2D Volterra dislocations at the continuum scale". European Journal of Applied Mathematics 23, nr 3 (16.02.2012): 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 i Mohamed Tamaazousti. "Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra II: Tensorial Data". Entropy 23, nr 7 (23.06.2021): 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, nr 04 (6.05.2012): 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., i Cristinel Mardare. "The intrinsic theory of linearly elastic plates". Mathematics and Mechanics of Solids 24, nr 4 (28.05.2018): 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 i X. J. WANG. "NEW REALIZATIONS OF W ALGEBRAS AND W STRINGS". Modern Physics Letters A 07, nr 20 (28.06.1992): 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.
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Verwoerd, Wynand S. "Iterative solution of quadratic tensor equations for mutual polarisation". International Journal of Mathematics and Mathematical Sciences 32, nr 5 (2002): 301–12. http://dx.doi.org/10.1155/s0161171202110246.
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To describe mutual polarisation in bulk materials containing high polarisability molecules, local fields beyond the linear approximation need to be included. A second order tensor equation is formulated, and it describes this in the case of crystalline or at least locally ordered materials such as an idealised polymer. It is shown that this equation is solved by a set of recursion equations that relate the induced dipole moment, linear polarisability, and first hyperpolarisability in the material to the intrinsic values of the same properties of isolated molecules. From these, macroscopic susceptibility tensors up to second order can be calculated for the material.
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CIARLET, PHILIPPE G., PATRICK CIARLET, OANA IOSIFESCU, STEFAN SAUTER i JUN ZOU. "LAGRANGE MULTIPLIERS IN INTRINSIC ELASTICITY". Mathematical Models and Methods in Applied Sciences 21, nr 04 (kwiecień 2011): 651–66. http://dx.doi.org/10.1142/s0218202511005167.
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In an intrinsic approach to three-dimensional linearized elasticity, the unknown is the linearized strain tensor field (or equivalently the stress tensor field by means of the constitutive equation), instead of the displacement vector field in the classical approach. We consider here the pure traction problem and the pure displacement problem and we show that, in each case, the intrinsic approach leads to a quadratic minimization problem constrained by Donati-like relations (the form of which depends on the type of boundary conditions considered). Using the Babuška-Brezzi inf-sup condition, we then show that, in each case, the minimizer of the constrained minimization problem found in an intrinsic approach is the first argument of the saddle-point of an ad hoc Lagrangian, so that the second argument of this saddle-point is the Lagrange multiplier associated with the corresponding constraints. Such results have potential applications to the numerical analysis and simulation of the intrinsic approach to three-dimensional linearized elasticity.
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Ciarlet, Philippe G., Cristinel Mardare i Xiaoqin Shen. "Donati compatibility conditions for membrane and flexural shells". Analysis and Applications 13, nr 06 (5.08.2015): 685–705. http://dx.doi.org/10.1142/s0219530514500237.
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Donati compatibility conditions on a surface allow to reformulate the minimization problem for a linearly elastic shell through the intrinsic approach, i.e. as a quadratic minimization problem with the linearized change of metric and change of curvature tensors of the middle surface of the shell as the new unknowns. Such compatibility conditions typically take the form of variational equations with divergence-free tensor fields as test-functions. In a previous work, the first author and Oana Iosifescu have identified and justified Donati compatibility conditions for shells modeled by Koiter's equations. In this paper, Donati compatibility conditions are identified and justified for two specific classes of linearly elastic shells, the so-called elliptic membrane shells and flexural shells.
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Ciarlet, Philippe G., i Cristinel Mardare. "Intrinsic formulation of the displacement-traction problem in linearized elasticity". Mathematical Models and Methods in Applied Sciences 24, nr 06 (28.03.2014): 1197–216. http://dx.doi.org/10.1142/s0218202513500814.
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The displacement-traction problem of linearized elasticity is a system of partial differential equations and boundary conditions whose unknown is the displacement field inside a linearly elastic body. We explicitly identify here the corresponding boundary conditions satisfied by the linearized strain tensor field associated with such a displacement field. Using this identification, we are then able to provide an intrinsic formulation of the displacement-traction problem of linearized elasticity, by showing how it can be recast into a boundary value problem whose unknown is the linearized strain tensor field.
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Summa, Francesco Ferdinando, i Paolo Lazzeretti. "Electronic Currents and Anapolar Response Induced in Molecules by Monochromatic Light". Chemistry 3, nr 3 (5.09.2021): 1022–36. http://dx.doi.org/10.3390/chemistry3030073.
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It is shown that the electric dipole- and electric quadrupole–anapole polarizabilities, denoted respectively by fαβ′ and gα,βγ′, and the anapole magnetizability aαβ, are intrinsic properties of the electron cloud of molecules responding to optical fields. fαβ′ is a nonvanishing property of chiral and achiral compounds, whereas aαβ is suitable for enantiomer discrimination of chiral species. They can conveniently be evaluated by numerical integration, employing a formulation complementary to that provided by perturbation theory and relying on the preliminary computation of electronic current density tensors all over the molecular domain. The origin dependence of the dynamic anapolar response is rationalized via related computational techniques employing numerical integration, as well as definitions of molecular property tensors, for example, electric dipole and electric quadrupole polarizabilties and magnetizability. A preliminary application of the theory is reported for the Ra enantiomer of the hydrogen peroxide molecule, evaluating tensor components of electric dipole-anapole polarizability and anapole magnetizability as functions of the dihedral angle ϕ≡∠ H-O-O-H in the range 0∘≤ϕ≤180∘.
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Hammond, Richard T. "Einstein’s dream". International Journal of Modern Physics D 28, nr 14 (październik 2019): 1943005. http://dx.doi.org/10.1142/s0218271819430053.
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It is shown the antisymmetric part of the metric tensor is the potential for the torsion field, which arises from intrinsic spin. To maintain gauge invariance, the nonsymmetric part of the metric tensor must be generalized to include the electromagnetic field. This result leads to a link between the cosmological constant and the electromagnetic field.
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BANDELLONI, GIUSEPPE. "UNCONSTRAINED HIGHER SPINS IN FOUR DIMENSIONS". International Journal of Geometric Methods in Modern Physics 08, nr 03 (maj 2011): 511–56. http://dx.doi.org/10.1142/s0219887811005269.
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The relativistic symmetric tensor fields are, in four dimensions, the right candidates to describe Higher Spin Fields. Their highest spin content is isolated with the aid of covariant conditions, discussed within a group theory framework, in which auxiliary fields remove the lower intrinsic angular momenta sectors. These conditions are embedded within a Lagrangian Quantum Field theory which describes an Higher Spin Field interacting with a Classical background. The model is invariant under a (B.R.S.) symmetric unconstrained tensor extension of the reparametrization symmetry, which include the Fang–Fronsdal algebra in a well defined limit. However, the symmetry setting reveals that the compensator field, which restore the Fang–Fronsdal symmetry of the free equations of motion, is in the existing in the framework and has a relevant geometrical meaning. The Ward identities coming from this symmetry are discussed. Our constraints give the result that the space of the invariant observables is restricted to the ones constructed with the Highest Spin Field content. The quantum extension of the symmetry reveals that no new anomaly is present. The role of the compensator field in this result is fundamental.
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Hernández-Lemus, Enrique. "On a Class of Tensor Markov Fields". Entropy 22, nr 4 (16.04.2020): 451. http://dx.doi.org/10.3390/e22040451.
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Here, we introduce a class of Tensor Markov Fields intended as probabilistic graphical models from random variables spanned over multiplexed contexts. These fields are an extension of Markov Random Fields for tensor-valued random variables. By extending the results of Dobruschin, Hammersley and Clifford to such tensor valued fields, we proved that tensor Markov fields are indeed Gibbs fields, whenever strictly positive probability measures are considered. Hence, there is a direct relationship with many results from theoretical statistical mechanics. We showed how this class of Markov fields it can be built based on a statistical dependency structures inferred on information theoretical grounds over empirical data. Thus, aside from purely theoretical interest, the Tensor Markov Fields described here may be useful for mathematical modeling and data analysis due to their intrinsic simplicity and generality.
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Bukusheva, A. V. "Geometry of Nonholonomic Kenmotsu Manifolds". Izvestiya of Altai State University, nr 1(117) (17.03.2021): 84–87. http://dx.doi.org/10.14258/izvasu(2021)1-13.
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The concept of the intrinsic geometry of a nonholonomic Kenmotsu manifold M is introduced. It is understood as the set of those properties of the manifold that depend only on the framing of the D^ distribution D of the manifold M, on the parallel transformation of vectors belonging to the distribution D along curves tangent to this distribution. The invariants of the intrinsic geometry of the nonholonomic Kenmotsu manifold are: the Schouten curvature tensor; 1-form η generating the distribution D; the Lie derivative of the metric tensor g along the vector field ; Schouten — Wagner tensor field P, whose components in adapted coordinates are expressed using the equalities . It is proved that, as in the case of the Kenmotsu manifold, the Schouten — Wagner tensor of the manifold M vanishes. It follows that the Schouten tensor of a nonholonomic Kenmotsu manifold has the same formal properties as the Riemann curvature tensor. It is proved that the alternation of the Ricci — Schouten tensor coincides with the differential of the structural form. This property of the Ricci — Schouten tensor is used in the proof of the main result of the article: a nonholonomic Kenmotsu manifold cannot carry the structure of an η-Einstein manifold.
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HAMMOND, RICHARD T. "SPIN FROM THE NONSYMMETRIC METRIC TENSOR". International Journal of Modern Physics D 22, nr 12 (październik 2013): 1342009. http://dx.doi.org/10.1142/s0218271813420091.
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A solution to the gravitational field equations based on a nonsymmetric metric tensor is examined. Unlike Einstein's interpretation of electromagnetism, or Moffat's generalized gravity, it is shown that the nonsymmetric part of the metric tensor is the potential of the spin field, and its intimate connection to string theory is established. This formulation solves the longstanding problem of electromagnetism and torsion, naturally showing how electromagnetism, through its intrinsic spin, can create torsion.
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Bezborodov, Mikhail A., Mikhail A. Eremin, Vitaly V. Korolev, Ilya G. Kovalenko i Elena V. Zhukova. "Visualization of the Anisotropy of the Velocity Dispersion and Characteristics of the Multi-Velocity Continuum in the Regions of Multi-Stream Flows of Gas-Dust Media with Polydisperse Dust". Journal of Imaging 6, nr 9 (17.09.2020): 98. http://dx.doi.org/10.3390/jimaging6090098.
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Collisionless media devoid of intrinsic stresses, for example, a dispersed phase in a multiphase medium, have a much wider variety of space-time structures and features formed in them than collisional media, for example, a carrier, gas, or liquid phase. This is a consequence of the fact that evolution in such media occurs in phase space, i.e., in a space of greater dimensions than the usual coordinate space. As a consequence, the process of the formation of features in collisionless media (clustering or vice versa, a loss of continuity) can occur primarily in the velocity space, which, in contrast to the features in the coordinate space (folds, caustics, or voids), is poorly observed directly. To identify such features, it is necessary to use visualization methods that allow us to consider, in detail, the evolution of the medium in the velocity space. This article is devoted to the development of techniques that allow visualizing the degree of anisotropy of the velocity fields of collisionless interpenetrating media. Simultaneously tracking the behavior of different fractions in such media is important, as their behavior can be significantly different. We propose three different techniques for visualizing the anisotropy of velocity fields using the example of two- and three-continuum dispersed media models. We proposed the construction of spatial distributions of eccentricity fields (scalar fields), or fields of principal directions of the velocity dispersion tensor (tensor fields). In the first case, we used some simple eccentricity functions for dispersion tensors for two fractions simultaneously, which we call surrogate entropy. In the second case, to visualize the anisotropy of the velocity fields of three fractions simultaneously, we used an ordered array (3-vector) of eccentricities for the color representation through decomposition in three basic colors. In the case of a multi-stream flow, we used cluster analysis methods to identify sections of a multi-stream flow (beams) and used glyphs to visualize the entire set of beams (vector-tensor fields).
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Mesarec, Luka, Aleš Iglič, Veronika Kralj-Iglič, Wojciech Góźdź, Epifanio G. Virga i Samo Kralj. "Curvature Potential Unveiled Topological Defect Attractors". Crystals 11, nr 5 (12.05.2021): 539. http://dx.doi.org/10.3390/cryst11050539.
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We consider the theoretical and positional assembling of topological defects (TDs) in effectively two-dimensional nematic liquid crystal films. We use a phenomenological Helfrich–Landau–de Gennes-type mesoscopic model in which geometric shapes and nematic orientational order are expressed in terms of a curvature tensor field and a nematic tensor order parameter field. Extrinsic, intrinsic, and total curvature potentials are introduced using the parallel transport concept. These potentials reveal curvature seeded TD attractors. To test ground configurations, we used axially symmetric nematic films exhibiting spherical topology.
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Guo, Si Lu, i Xiao Nian Wang. "Orientation-Independent Tensor Voting Analysis". Advanced Materials Research 756-759 (wrzesień 2013): 3286–92. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.3286.
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Tensor voting framework is an approach for perceptual organization. A tensor can provide more information than scalar or vector in image processing. However, the structure of tensor also makes it not unique but orientation dependent. In this paper, to quantify properly the intrinsic orientation-independent voting process, we proposed a new description of the tensor fields, which consists of three rotationally invariant quantities. Instead of coordinate transformation, this approach does not require tensor diagonalization or eigenvalue calculation. Therefore, our approach is not susceptible to potential artifacts induced during these number manipulations, meanwhile simplified the voting process at the same time.
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CIARLET, PHILIPPE G., LILIANA GRATIE i MICHELE SERPILLI. "CESÀRO–VOLTERRA PATH INTEGRAL FORMULA ON A SURFACE". Mathematical Models and Methods in Applied Sciences 19, nr 03 (marzec 2009): 419–41. http://dx.doi.org/10.1142/s0218202509003486.
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If a symmetric matrix field e = (eij) of order three satisfies the Saint-Venant compatibility relations in a simply-connected open subset Ω of ℝ3, then e is the linearized strain tensor field of a displacement field v of Ω, i.e. [Formula: see text] in Ω. A classical result, due to Cesàro and Volterra, asserts that, if the field e is smooth, the unknown displacement field v(x) at any point x ∈ Ω can be explicitly written as a path integral inside Ω with endpoint x, and whose integrand is an explicit function of the functions eij and their derivatives. Now let ω be a simply-connected open subset in ℝ2 and let θ : ω → ℝ3 be a smooth immersion. If two symmetric matrix fields (γαβ) and (ραβ) of order two satisfy appropriate compatibility relations in ω, then (γαβ) and (ραβ) are the linearized change of metric and change of curvature tensor field corresponding to a displacement vector field η of the surface θ(ω). We show here that a "Cesàro–Volterra path integral formula on a surface" likewise holds when the fields (γαβ) and (ραβ) are smooth. This means that the displacement vector η(y) at any point θ(y), y ∈ ω, of the surface θ(ω) can be explicitly computed as a path integral inside ω with endpoint y, and whose integrand is an explicit function of the functions γαβ and ραβ and their covariant derivatives. Such a formula has potential applications to the mathematical analysis and numerical simulation of linear "intrinsic" shell models.
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GAL'TSOV, D. V., i E. A. DAVYDOV. "YANG-MILLS CONDENSATES IN COSMOLOGY". International Journal of Modern Physics: Conference Series 14 (styczeń 2012): 316–25. http://dx.doi.org/10.1142/s201019451200743x.
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We discuss homogeneous and isotropic cosmological models driven by SU(2) gauge fields in the framework of Einstein gravity. There exists a Yang-Mills field configuration, parametrized by a single scalar function, which consists of parallel electric and magnetic fields and has the stress tensor mimicking an homogeneous and isotropic fluid. The unique SU(2) gauge theory with spontaneous symmetry breaking sharing the same property is the Yang-Mills coupled to the complex doublet Higgs, this exists only in the case of the closed universe. This model contains an intrinsic mechanism for inflation due to the Higgs potential. Our second goal is to show that a successful inflation can be achieved also within the pure Yang-Mills theory adding an appropriate theta-term.
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FERNÁNDEZ, V. V., A. M. MOYA i W. A. RODRIGUES. "GEOMETRIC AND EXTENSOR ALGEBRAS AND THE DIFFERENTIAL GEOMETRY OF ARBITRARY MANIFOLDS". International Journal of Geometric Methods in Modern Physics 04, nr 07 (listopad 2007): 1117–58. http://dx.doi.org/10.1142/s0219887807002478.
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We give in this paper which is the third in a series of four a theory of covariant derivatives of representatives of multivector and extensor fields on an arbitrary open set U ⊂ M, based on the geometric and extensor calculus on an arbitrary smooth manifold M. This is done by introducing the notion of a connection extensor field γ defining a parallelism structure on U ⊂ M, which represents in a well-defined way the action on U of the restriction there of some given connection ∇ defined on M. Also we give a novel and intrinsic presentation (i.e. one that does not depend on a chosen orthonormal moving frame) of the torsion and curvature fields of Cartan's theory. Two kinds of Cartan's connection operator fields are identified, and both appear in the intrinsic Cartan's structure equations satisfied by the Cartan's torsion and curvature extensor fields. We introduce moreover a metrical extensor g in U corresponding to the restriction there of given metric tensor g defined on M and also introduce the concept of a geometric structure(U, γ ,g) for U ⊂ M and study metric compatibility of covariant derivatives induced by the connection extensor γ. This permits the presentation of the concept of gauge (deformed) derivatives which satisfy noticeable properties useful in differential geometry and geometrical theories of the gravitational field. Several derivatives of operators in metric and geometrical structures, like ordinary and covariant Hodge co-derivatives and some duality identities are exhibited.
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LOHIYA, DAKSH. "ON GENERAL 'SPIN' CONNECTIONS, GRAVITATION AND ELECTRODYNAMICS". Modern Physics Letters A 04, nr 07 (10.04.1989): 681–93. http://dx.doi.org/10.1142/s0217732389000812.
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It is known that intrinsic spin-vector-field analysis on a manifold provides as beautiful a description of the underlying geometry as does the description in terms of "world-vectors" defined on the manifold. However, requiring that a spinor connection be compatible with a corresponding 4-vector connection still leaves enough additional structure in the former to incorporate a gauge field. The resulting spin-curvature tensor is related to the Riemann tensor as well as an "electromagnetic field tensor" so definable. We advocate that the most general linear combination of dimensionally extended "Euler characteristics", constructed out of the generalized spin-curvature two form, be considered as a candidate for a lagrangian. It turns out to be a "natural" way to construct a unified framework for studying gravitation and electromagnetism. The consistency of the theory signals a rich structure that the underlying manifold must possess. We develop arguments to suggest that the electromagnetic field cannot be associated with amplitude transformation of the local tangent spin space but rather is consistent with the phase transformations.
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An, Jinliang, Yuzhen Song, Yuwei Guo, Xiaoxiao Ma i Xiangrong Zhang. "Tensor Discriminant Analysis via Compact Feature Representation for Hyperspectral Images Dimensionality Reduction". Remote Sensing 11, nr 15 (4.08.2019): 1822. http://dx.doi.org/10.3390/rs11151822.
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Dimensionality reduction is of great importance which aims at reducing the spectral dimensionality while keeping the desirable intrinsic structure information of hyperspectral images. Tensor analysis which can retain both spatial and spectral information of hyperspectral images has caused more and more concern in the field of hyperspectral images processing. In general, a desirable low dimensionality feature representation should be discriminative and compact. To achieve this, a tensor discriminant analysis model via compact feature representation (TDA-CFR) was proposed in this paper. In TDA-CFR, the traditional linear discriminant analysis was extended to tensor space to make the resulting feature representation more informative and discriminative. Furthermore, TDA-CFR redefines the feature representation of each spectral band by employing the tensor low rank decomposition framework which leads to a more compact representation.
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DEHGHANI, M. "A NEW PHYSICAL STATE FOR DE SITTER LINEAR GRAVITY". International Journal of Modern Physics A 26, nr 02 (20.01.2011): 301–15. http://dx.doi.org/10.1142/s0217751x11051251.
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Based on conformal invariance and using Dirac's six-cone formalism, a new conformally invariant physical field equation for de Sitter (dS) linear gravity has been obtained, which corresponds to one of the unitary irreducible representations of the dS group and is denoted by [Formula: see text] in the sense of discrete series. Using ambient space notations, it has been shown that the solution to this new field equation can be written as the multiplication of a generalized symmetric polarization tensor of rank 2 and a massless conformally coupled scalar field in dS space–time. The physical tensor two-point function has been calculated in terms of the conformally coupled scalar two-point function in the ambient space formalism. It has been expressed in terms of dS intrinsic coordinates from its ambient space counterpart, which is dS-invariant and free of any divergences.
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Nitschke, Ingo, Sebastian Reuther i Axel Voigt. "Liquid crystals on deformable surfaces". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, nr 2241 (wrzesień 2020): 20200313. http://dx.doi.org/10.1098/rspa.2020.0313.
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Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk-free energies of the liquid crystal with geometric properties of the surface. We derive a thermodynamically consistent Landau-de Gennes-Helfrich model which considers the simultaneous relaxation of the Q -tensor field and the surface. The resulting system of tensor-valued surface partial differential equation and geometric evolution laws is numerically solved to tackle the rich dynamics of this system and to compute the resulting equilibrium shape. The results strongly depend on the intrinsic and extrinsic curvature contributions and lead to unexpected asymmetric shapes.
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FARHOUDI, M. "CLASSICAL TRACE ANOMALY". International Journal of Modern Physics D 14, nr 07 (lipiec 2005): 1233–50. http://dx.doi.org/10.1142/s0218271805006730.
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We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy–momentum tensor even in classical treatments. As an example, we take this analogy to any generic second order Lagrangian and exactly derive the trace anomaly relation suggested by Duff. This indicates that an intrinsic reason for the existence of such a relation should perhaps be, classically, somehow related to the covariance of the form of Einstein's equations.
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Malinin, V. G., N. A. Malinina, V. V. Malinin, A. A. Dimov i O. A. Malukhina. "Tensor characteristics of intrinsic scattering magnetic field as an effective tool for strength diagnostics of steel products". IOP Conference Series: Materials Science and Engineering 939 (8.10.2020): 012046. http://dx.doi.org/10.1088/1757-899x/939/1/012046.
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Schäppi, Daniel. "Which abelian tensor categories are geometric?" Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, nr 734 (1.01.2018): 145–86. http://dx.doi.org/10.1515/crelle-2014-0053.
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AbstractFor a large class of geometric objects, the passage to categories of quasi-coherent sheaves provides an embedding in the 2-category of abelian tensor categories. The notion of weakly Tannakian categories introduced by the author gives a characterization of tensor categories in the image of this embedding.However, this notion requires additional structure to be present, namely a fiber functor. For the case of classical Tannakian categories in characteristic zero, Deligne has found intrinsic properties—expressible entirely within the language of tensor categories—which are necessary and sufficient for the existence of a fiber functor. In this paper we generalize Deligne’s result to weakly Tannakian categories in characteristic zero. The class of geometric objects whose tensor categories of quasi-coherent sheaves can be recognized in this manner includes both the gerbes arising in classical Tannaka duality and more classical geometric objects such as projective varieties over a field of characteristic zero.Our proof uses a different perspective on fiber functors, which we formalize through the notion of geometric tensor categories. A second application of this perspective allows us to describe categories of quasi-coherent sheaves on fiber products.
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Bahmani, Bahador, Reza Abedi i Philip Clarke. "A Stochastic Bulk Damage Model Based on Mohr-Coulomb Failure Criterion for Dynamic Rock Fracture". Applied Sciences 9, nr 5 (26.02.2019): 830. http://dx.doi.org/10.3390/app9050830.
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We present a stochastic bulk damage model for rock fracture. The decomposition of strain or stress tensor to its negative and positive parts is often used to drive damage and evaluate the effective stress tensor. However, they typically fail to correctly model rock fracture in compression. We propose a damage force model based on the Mohr-Coulomb failure criterion and an effective stress relation that remedy this problem. An evolution equation specifies the rate at which damage tends to its quasi-static limit. The relaxation time of the model introduces an intrinsic length scale for dynamic fracture and addresses the mesh sensitivity problem of earlier damage models. The ordinary differential form of the damage equation makes this remedy quite simple and enables capturing the loading rate sensitivity of strain-stress response. The asynchronous Spacetime Discontinuous Galerkin (aSDG) method is used for macroscopic simulations. To study the effect of rock inhomogeneity, the Karhunen-Loeve method is used to realize random fields for rock cohesion. It is shown that inhomogeneity greatly differentiates fracture patterns from those of a homogeneous rock, including the location of zones with maximum damage. Moreover, as the correlation length of the random field decreases, fracture patterns resemble angled-cracks observed in compressive rock fracture.
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Gan’shina, Elena A., L. L. Golik, Z. E. Kun’kova, Vitaly I. Kovalev, Yury V. Markin, Andrey I. Novikov, Georgy S. Zykov i in. "Magneto-Optical Evidence for Intrinsic Ferromagnetism in (Ga,Mn)As Layers Grown by Pulsed Laser Deposition". Solid State Phenomena 233-234 (lipiec 2015): 101–4. http://dx.doi.org/10.4028/www.scientific.net/ssp.233-234.101.
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GaMnAs layers fabricated on GaAs(001) substrates by laser ablation technique were studied using the magneto-optical transversal Kerr effect (TKE) (E = 0.5 - 4.0 eV) and spectral ellipsometry (E = 1.4 - 4.5 eV). Obtained spectral, temperature and magnetic field TKE dependences shown that the used technique allowed us to obtain ferromagnetic (Ga,Mn)As layers, whose composition was close to single-phase one (without MnAs inclusions). Spectral dependences of the off-diagonal components (e’ = e’1 - ie’2) of the permittivity tensor and also of the magnetic circular dichroism (MCD) were calculated for ferromagnetic (Ga,Mn)As sample. The calculated dependences were compared with the published magneto-optical spectra of (Ga,Mn)As layers grown by molecular beam epitaxy.
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Rüdiger, Andreas, i Rainer Waser. "Nanoscale Ferroelectrics". Advances in Science and Technology 45 (październik 2006): 2392–99. http://dx.doi.org/10.4028/www.scientific.net/ast.45.2392.
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Ferroelectrics are among the most advanced materials for non-volatile storage applications. Their two thermodynamically equivalent groundstates of spontaneous polarization can be toggled between by an external electric field. We present recent progress in the fabrication, registration, manipulation and characterization of nanoscale ferroelectrics. Chemical solution deposition is adapted to a pre-registration process by e-beam lithography to fabricate registered ferroelectric nanostructures below 100 nm width. A post-processing by chemical mechanical polishing either for embedded or free grains modifies the aspect ratio thus controlling the coercive field distribution of nanoferroelectrics. We also discuss some very recent findings of the complex interaction of field and piezoelectric tensor in a real piezoresponse force microscope. This method requires a comprehensive treatment of all contributions to tell apart extrinsic from intrinsic effects.
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DEHGHANI, M. "EVALUATION OF THE GRAVITON TWO-POINT FUNCTION IN DE SITTER SPACE". International Journal of Modern Physics A 25, nr 18n19 (30.07.2010): 3749–64. http://dx.doi.org/10.1142/s0217751x1005010x.
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After a brief review of the linearized gravity in de Sitter (dS) four-dimensional space and ambient flat five-dimensional notations, the linearized field equation is written in terms of the Casimir operators of dS group. It is shown that the field equation is gauge invariant under some special gauge transformations. Because of this gauge freedom, a gauge-fixing parameter c is inserted in the field equation. It is shown that the solution to the field equation can be written as the multiplication of a generalized symmetric rank-2 polarization tensor and a massless minimally coupled scalar field in ambient space notations. The graviton two-point function has been thoroughly calculated, which is dS-invariant and free of any divergences. This two-point function has been expressed in terms of the intrinsic dS coordinates, from its ambient space counterpart, which is clearly dS-invariant and free of any divergences again.
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DEHGHANI, M. "COVARIANT TWO-POINT FUNCTION FOR MASSLESS SPIN-2 FIELD IN DE SITTER SPACE". Modern Physics Letters A 24, nr 40 (28.12.2009): 3283–94. http://dx.doi.org/10.1142/s0217732309031326.
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The linearized gravitational field equation in de Sitter (dS) four-dimensional space is gauge invariant under some special gauge transformations. It is also gauge invariant in ambient space notations in which the field equation is written in terms of the Casimir operators of dS group. In this paper the field equation is solved in terms of a gauge-fixed value (i.e. in the minimal case). It is shown that the solution can be written as the multiplication of a generalized symmetric rank-2 polarization tensor and a massless minimally coupled scalar field in ambient space notations. The two-point function is calculated in ambient space notations, which is dS-invariant and free of any divergences. This two-point function has been expressed in terms of dS intrinsic coordinates, from its ambient space counterpart, which is clearly dS-invariant and free of any divergences again.
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Ravishankar, Joshitha, Mansi Sharma i Pradeep Gopalakrishnan. "A Flexible Coding Scheme Based on Block Krylov Subspace Approximation for Light Field Displays with Stacked Multiplicative Layers". Sensors 21, nr 13 (4.07.2021): 4574. http://dx.doi.org/10.3390/s21134574.
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To create a realistic 3D perception on glasses-free displays, it is critical to support continuous motion parallax, greater depths of field, and wider fields of view. A new type of Layered or Tensor light field 3D display has attracted greater attention these days. Using only a few light-attenuating pixelized layers (e.g., LCD panels), it supports many views from different viewing directions that can be displayed simultaneously with a high resolution. This paper presents a novel flexible scheme for efficient layer-based representation and lossy compression of light fields on layered displays. The proposed scheme learns stacked multiplicative layers optimized using a convolutional neural network (CNN). The intrinsic redundancy in light field data is efficiently removed by analyzing the hidden low-rank structure of multiplicative layers on a Krylov subspace. Factorization derived from Block Krylov singular value decomposition (BK-SVD) exploits the spatial correlation in layer patterns for multiplicative layers with varying low ranks. Further, encoding with HEVC eliminates inter-frame and intra-frame redundancies in the low-rank approximated representation of layers and improves the compression efficiency. The scheme is flexible to realize multiple bitrates at the decoder by adjusting the ranks of BK-SVD representation and HEVC quantization. Thus, it would complement the generality and flexibility of a data-driven CNN-based method for coding with multiple bitrates within a single training framework for practical display applications. Extensive experiments demonstrate that the proposed coding scheme achieves substantial bitrate savings compared with pseudo-sequence-based light field compression approaches and state-of-the-art JPEG and HEVC coders.
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LISBOA, RONAI, MANOEL MALHEIRO, A. S. de CASTRO, P. ALBERTO i MANOEL FIOLHAIS. "PERTURBATIVE BREAKING OF THE PSEUDOSPIN SYMMETRY IN THE RELATIVISTIC HARMONIC OSCILLATOR". International Journal of Modern Physics D 13, nr 07 (sierpień 2004): 1447–51. http://dx.doi.org/10.1142/s0218271804005675.
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We show that relativistic mean fields theories with scalar S, and vector V, quadratic radial potentials can generate a harmonic oscillator with exact pseudospin symmetry and positive energy bound states when S=-V. The eigenenergies are quite different from those of the non-relativistic harmonic oscillator. We also discuss a mechanism for perturbatively breaking this symmetry by introducing a tensor potential. Our results shed light into the intrinsic relativistic nature of the pseudospin symmetry, which might be important in high density systems such as neutron stars.
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Zaouter, Tony, Didier Lasseux i Marc Prat. "Gas slip flow in a fracture: local Reynolds equation and upscaled macroscopic model". Journal of Fluid Mechanics 837 (21.12.2017): 413–42. http://dx.doi.org/10.1017/jfm.2017.868.
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The slightly compressible flow of a gas in the slip regime within a rough fracture featuring a heterogeneous aperture field is analysed in depth in this work. Starting from the governing Navier–Stokes, continuity and gas state law equations together with a first-order slip boundary condition at the impermeable walls of the fracture, the two-dimensional slip-corrected Reynolds model is first derived, which is shown to be second-order-accurate in the local slope of the roughness asperities while being first-order-accurate in the Knudsen number. Focusing the interest on the flow-rate to pressure-gradient relationship over a representative element of the fracture, an upscaling procedure is applied to the local Reynolds equation using the method of volume averaging, providing a macroscopic model for which the momentum conservation equation has a Reynolds-like form. The effective macroscopic transmissivity tensor, which is characteristic of the representative element, is shown to be given by a closure problem that is non-intrinsic to the geometrical structure of the fracture only due to the slip effect. An expansion to the first order in the Knudsen number is carried out on the closure, yielding a decomposition of the effective transmissivity tensor into its purely viscous part and its slip correction, both being given by the solution of intrinsic closure subproblems. Numerical validations of the solution to the closure problem are performed with analytical predictions for simple fracture geometries. Comparison between the macroscopic transmissivity tensor, obtained from the solution of the closure problem, and its first-order approximation is illustrated on a randomly rough correlated Gaussian fracture.
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Ali, Akram, Siraj Uddin i Wan Othman. "Geometry of warped product pointwise semi-slant submanifolds of Kaehler manifolds". Filomat 31, nr 12 (2017): 3771–88. http://dx.doi.org/10.2298/fil1712771a.
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In this paper, we study warped product pointwise semi-slant submanifolds of a Kaehler manifold. First, we prove some characterizations results in terms of the tensor fields T and F and then, we obtain a geometric inequality for the second fundamental form in terms of intrinsic invariants. Furthermore, the equality case is also discussed. Moreover, we give some applications for Riemannian and compact Remannian submanifolds as well, i.e., we construct necessary and sufficient conditions for the non-existence of compact warped product pointwise semi-slant submanifold in complex space forms.
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Hivet, G., i A. V. Duong. "A contribution to the analysis of the intrinsic shear behavior of fabrics". Journal of Composite Materials 45, nr 6 (27.10.2010): 695–716. http://dx.doi.org/10.1177/0021998310382315.
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The in-plane shear behavior of textile performs is the most studied mechanical property because this mode of deformation is necessary for forming on double curvature surfaces. The resulting mechanical behavior is complex and specific considering the possibilities of relative movements between yarns and fibers. Two main tests are used: the hinged framework or ‘picture frame’ and the tensile test at 45° or ‘bias test’. Nevertheless, the results obtained by different labs using these two tests on the same fabric can be significantly different. Using a simplified analytical model of the picture frame test and a specific instrumented picture frame that enables us to track and adjust yarns tensions and to measure the strain field through optical measurements, this article analyzes and explains the origin of these discrepancies and concludes in dealing with the association between the experimental test used and the intrinsic in-plane shear behavior of a fabric.
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Kim, Lily H., Edward H. Lee, Michelle Galvez, Murat Aksoy, Stefan Skare, Rafael O’Halloran, Michael S. B. Edwards, Samantha J. Holdsworth i Kristen W. Yeom. "Reduced field of view echo-planar imaging diffusion tensor MRI for pediatric spinal tumors". Journal of Neurosurgery: Spine 31, nr 4 (październik 2019): 607–15. http://dx.doi.org/10.3171/2019.4.spine19178.
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OBJECTIVESpine MRI is a diagnostic modality for evaluating pediatric CNS tumors. Applying diffusion-weighted MRI (DWI) or diffusion tensor imaging (DTI) to the spine poses challenges due to intrinsic spinal anatomy that exacerbates various image-related artifacts, such as signal dropouts or pileups, geometrical distortions, and incomplete fat suppression. The zonal oblique multislice (ZOOM)–echo-planar imaging (EPI) technique reduces geometric distortion and image blurring by reducing the field of view (FOV) without signal aliasing into the FOV. The authors hypothesized that the ZOOM-EPI method for spine DTI in concert with conventional spinal MRI is an efficient method for augmenting the evaluation of pediatric spinal tumors.METHODSThirty-eight consecutive patients (mean age 8 years) who underwent ZOOM-EPI spine DTI for CNS tumor workup were retrospectively identified. Patients underwent conventional spine MRI and ZOOM-EPI DTI spine MRI. Two blinded radiologists independently reviewed two sets of randomized images: conventional spine MRI without ZOOM-EPI DTI, and conventional spine MRI with ZOOM-EPI DTI. For both image sets, the reviewers scored the findings based on lesion conspicuity and diagnostic confidence using a 5-point Likert scale. The reviewers also recorded presence of tumors. Quantitative apparent diffusion coefficient (ADC) measurements of various spinal tumors were extracted. Tractography was performed in a subset of patients undergoing presurgical evaluation.RESULTSSixteen patients demonstrated spinal tumor lesions. The readers were in moderate agreement (kappa = 0.61, 95% CI 0.30–0.91). The mean scores for conventional MRI and combined conventional MRI and DTI were as follows, respectively: 3.0 and 4.0 for lesion conspicuity (p = 0.0039), and 2.8 and 3.9 for diagnostic confidence (p < 0.001). ZOOM-EPI DTI identified new lesions in 3 patients. In 3 patients, tractography used for neurosurgical planning showed characteristic fiber tract projections. The mean weighted ADCs of low- and high-grade tumors were 1201 × 10−6 and 865 × 10−6 mm2/sec (p = 0.002), respectively; the mean minimum weighted ADCs were 823 × 10−6 and 474 × 10−6 mm2/sec (p = 0.0003), respectively.CONCLUSIONSDiffusion MRI with ZOOM-EPI can improve the detection of spinal lesions while providing quantitative diffusion information that helps distinguish low- from high-grade tumors. By adding a 2-minute DTI scan, quantitative diffusion information and tract profiles can reliably be obtained and serve as a useful adjunct to presurgical planning for pediatric spinal tumors.
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Nagayama, Tsutomu, i Atsushi Sanada. "Broadband transmission-line illusions based on transformation electromagnetic". EPJ Applied Metamaterials 6 (2019): 23. http://dx.doi.org/10.1051/epjam/2019018.
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We demonstrate broadband transmission-line illusions based on transformation electromagnetics at microwave frequencies by using the distributed full-tensor anisotropic medium. Due to an intrinsic nature of the non-resonant unit cell of the medium, the illusions operate from DC to an upper limit frequency where the homogeneous medium approximation holds. Two-dimensional groove and bump illusion media mimicking scattered waves by an original groove and a bump are designed. Their broadband and incident angle independent operations are confirmed by circuit simulations. The groove illusion medium is implemented on a dielectric substrate with microstrip-line technology, and it is confirmed experimentally by near-field measurements that the illusion medium well mimics scattered waves by the original groove in the broadband frequency range from 2.60 GHz to 4.65 GHz.
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Goodman, Michael L. "Driven, dissipative, energy-conserving magnetohydrodynamic equilibria. Part 2. The screw pinch". Journal of Plasma Physics 49, nr 1 (luty 1993): 125–59. http://dx.doi.org/10.1017/s002237780001686x.
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A cylindrically symmetric, electrically driven, dissipative, energy-conserving magnetohydrodynamic equilibrium model is considered. The high-magneticfield Braginskii ion thermal conductivity perpendicular to the local magnetic field and the complete electron resistivity tensor are included in an energy equation and in Ohm's law. The expressions for the resistivity tensor and thermal conductivity depend on number density, temperature, and the poloidal and axial (z-component) magnetic field, which are functions of radius that are obtained as part of the equilibrium solution. The model has plasma-confining solutions, by which is meant solutions characterized by the separation of the plasma into two concentric regions separated by a transition region that is an internal boundary layer. The inner region is the region of confined plasma, and the outer region is the region of unconfined plasma. The inner region has average values of temperature, pressure, and axial and poloidal current densities that are orders of magnitude larger than in the outer region. The temperature, axial current density and pressure gradient vary rapidly by orders of magnitude in the transition region. The number density, thermal conductivity and Dreicer electric field have a global minimum in the transition region, while the Hall resistivity, Alfvén speed, normalized charge separation, Debye length, (ωλ)ion and the radial electric field have global maxima in the transition region. As a result of the Hall and electron-pressure-gradient effects, the transition region is an electric dipole layer in which the normalized charge separation is localized and in which the radial electric field can be large. The model has an intrinsic value of β, about 13·3%, which must be exceeded in order that a plasma-confining solution exist. The model has an intrinsic length scale that, for plasma-confining solutions, is a measure of the thickness of the boundary-layer transition region. If appropriate boundary conditions are given at R = 0 then the equilibrium is uniquely determined. If appropriate boundary conditions are given at any outer boundary R = a then the equilibrium exhibits a bifurcation into two states, one of which exhibits plasma confinement and carries a larger axial current than the other, which is almost homogeneous and cannot confine a plasma. Exact expressions for the two values of the axial current in the bifurcation are derived. If the boundary conditions are given at R = a then a solution exists if and only if the constant driving electric field exceeds a critical value. An exact expression for this critical electric field is derived. It is conjectured that the bifurcation is associated with an electric-field-driven transition in a real plasma, between states with different rotation rates, energy dissipation rates and confinement properties. Such a transition may serve as a relatively simple example of the L—H mode transition observed in tokamaks.
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Minas, Georgios, Emmanuel Saridakis, Panayiotis Stavrinos i Alkiviadis Triantafyllopoulos. "Bounce Cosmology in Generalized Modified Gravities". Universe 5, nr 3 (10.03.2019): 74. http://dx.doi.org/10.3390/universe5030074.
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We investigate the bounce realization in the framework of generalized modified gravities arising from Finsler and Finsler-like geometries. In particular, a richer intrinsic geometrical structure is reflected in the appearance of extra degrees of freedom in the Friedmann equations that can drive the bounce. We examine various Finsler and Finsler-like constructions. In the cases of general very special relativity, as well as of Finsler-like gravity on the tangent bundle, we show that a bounce cannot easily be obtained. However, in the Finsler–Randers space, induced scalar anisotropy can fulfil bounce conditions, and bouncing solutions are easily obtained. Finally, for the general class of theories that include a nonlinear connection, a new scalar field is induced, leading to a scalar–tensor structure that can easily drive a bounce. These features reveal the capabilities of Finsler and Finsler-like geometries.
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Calonne, N., C. Geindreau, F. Flin, S. Morin, B. Lesaffre, S. Rolland du Roscoat i P. Charrier. "3-D image-based numerical computations of snow permeability: links to specific surface area, density, and microstructural anisotropy". Cryosphere Discussions 6, nr 2 (19.03.2012): 1157–80. http://dx.doi.org/10.5194/tcd-6-1157-2012.
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Abstract. We used three-dimensional (3-D) images of snow microstructure to carry out numerical estimations of the full tensor of the intrinsic permeability of snow (K). This study was performed on 35 snow samples, spanning a wide range of seasonal snow types. Because the permeability is related to a characteristic length, we introduced a dimensionless tensor K*=K/ res2, where the equivalent sphere radius of ice grains (res) is computed from the specific surface area of snow (SSA) and the ice density (ρi) as follows: res=3/(SSA x ρi). Values of K*, the average of vertical and horizontal components of K*, were plotted vs. snow density (ρs) and compared to analytical models and data from the literature, showing generally a good agreement. The 35 values of K* were fitted to ρs and provide the following regression: K*=2.94 x exp(–0.013 ρs), with a correlation coefficient of 0.985. This indicates that permeability, if assumed isotropic, can be reasonably determined from SSA and ρs, which are both easily measurable in the field. However, the anisotropy coefficient of K, induced by the snow microstructure, ranges from 0.74 to 1.66 for the samples considered. This behavior is consistent with that of the effective thermal conductivity obtained in a previous work.
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Popov, Yu I. "Fields of geometric objects associated with compiled hyperplane-distribution in affine space". Differential Geometry of Manifolds of Figures, nr 51 (2020): 103–15. http://dx.doi.org/10.5922/0321-4796-2020-51-12.
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A compiled hyperplane distribution is considered in an n-dimensional projective space . We will briefly call it a -distribution. Note that the plane L(A) is the distribution characteristic obtained by displacement in the center belonging to the L-subbundle. The following results were obtained: a) The existence theorem is proved: -distribution exists with arbitrary (3n – 5) functions of n arguments. b) A focal manifold is constructed in the normal plane of the 1st kind of L-subbundle. It was obtained by shifting the center A along the curves belonging to the L-distribution. A focal manifold is also given, which is an analog of the Koenigs plane for the distribution pair (L, L). c) It is shown that a framed -distribution in the 1st kind normal field of H-distribution induces tangent and normal bundles. d) Six connection theorems induced by a framed -distribution in these bundles are proved. In each of the bundles , the framed -distribution induces an intrinsic torsion-free affine connection in the tangent bundle and a centro-affine connection in the corresponding normal bundle. e) In each of the bundles (d) in the differential neighborhood of the 2nd order, the covers of 2-forms of curvature and curvature tensors of the corresponding connections are constructed.
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Nabias, Julie, Aktham Asfour i Jean-Paul Yonnet. "Effect of Torsion Stress on the Offset and Sensitivity of Diagonal and Off-Diagonal GMI in Amorphous Wires". Sensors 18, nr 12 (24.11.2018): 4121. http://dx.doi.org/10.3390/s18124121.
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In this paper, the torsional stress effect on Giant Magneto-Impedance (GMI) was studied in Co-rich amorphous wires. The study, which was conducted in the context of the development of a current clamp based on GMI, considered torsion as a parameter of the influence of this sensor. Both diagonal, Z11, and off-diagonal, Z21, components of the impedance tensor were investigated. The samples were Co-rich wires with a 100 µ diameter. The wires were twisted positive and negative angles with respect to a reference position. For each component of the impedance, the intrinsic sensitivity and offset were measured as a function of the rotation angle. The results showed that the sensitivity of the diagonal component at a given working point slightly increased for angles between −90° to +90°, whereas the sensitivity was almost constant for the off-diagonal component at zero-field. The intrinsic offset in the diagonal configuration was almost unchanged for the rotation angles considered, whereas this offset increased in the off-diagonal configuration. Furthermore, the GMI ratio of Z11 was also measured as a function of the rotation angle for comparison purposes with known data. The maximum of this ratio was obtained for a rotation angle of about 50°.