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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

Jönsson, J., E. Svensson, and J. T. Christensen. "Strain gauge measurement of wheel-rail interaction forces." Journal of Strain Analysis for Engineering Design 32, no. 3 (April 1, 1997): 183–91. http://dx.doi.org/10.1243/0309324971513328.

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Анотація:

A theoretical basis for quasi static determination of wheel—rail interaction forces using strain measures in the foot of the rail is given. Vlasov's theory for thin-walled beams is used in combination with continuous translational and rotational elastic supports based on smoothing out the stiffness of the rail sleepers. The smoothing out of the rotational elastic support has traditionally not been done. The use of this model is validated by the decay lengths of the problem and through finite element analysis. The finite element analysis is performed using discrete sleeper stiffness and Vlasov beam elements. The sensitivity of the measuring technique to parameter variations is illustrated and an example shows the simplicity of the proposed direct measuring technique.

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2

Friberg, P. O. "Beam element matrices derived from Vlasov's theory of open thin-walled elastic beams." International Journal for Numerical Methods in Engineering 21, no. 7 (July 1985): 1205–28. http://dx.doi.org/10.1002/nme.1620210704.

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3

Kim, J. H., and Y. Y. Kim. "Analysis of Thin-Walled Closed Beams With General Quadrilateral Cross Sections." Journal of Applied Mechanics 66, no. 4 (December 1, 1999): 904–12. http://dx.doi.org/10.1115/1.2791796.

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This paper deals with the one-dimensional static and dynamic analysis of thin-walled closed beams with general quadrilateral cross sections. The coupled deformations of distortion as well as torsion and warping are investigated in this work. A new approach to determine the functions describing section deformations is proposed. In particular, the present distortion function satisfies all the necessary continuity conditions unlike Vlasov's distortion function. Based on these section deformation functions, a one-dimensional theory dealing with the coupled deformations is presented. The actual numerical work is carried out using two-node C0 finite element formulation. The present one-dimensional results for some static and free-vibration problems are compared with the existing and the plate finite element results.

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4

Höller, R., M. Aminbaghai, L. Eberhardsteiner, J. Eberhardsteiner, R. Blab, B. Pichler, and C. Hellmich. "Rigorous amendment of Vlasov's theory for thin elastic plates on elastic Winkler foundations, based on the Principle of Virtual Power." European Journal of Mechanics - A/Solids 73 (January 2019): 449–82. http://dx.doi.org/10.1016/j.euromechsol.2018.07.013.

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5

Treumann, Rudolf A., and Wolfgang Baumjohann. "Causal kinetic equation of non-equilibrium plasmas." Annales Geophysicae 35, no. 3 (May 24, 2017): 683–90. http://dx.doi.org/10.5194/angeo-35-683-2017.

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Abstract. Statistical plasma theory far from thermal equilibrium is subject to Liouville's equation, which is at the base of the BBGKY hierarchical approach to plasma kinetic theory, from which, in the absence of collisions, Vlasov's equation follows. It is also at the base of Klimontovich's approach which includes single-particle effects like spontaneous emission. All these theories have been applied to plasmas with admirable success even though they suffer from a fundamental omission in their use of the electrodynamic equations in the description of the highly dynamic interactions in many-particle conglomerations. In the following we extend this theory to taking into account that the interaction between particles separated from each other at a distance requires the transport of information. Action needs to be transported and thus, in the spirit of the direct-interaction theory as developed by Wheeler and Feynman (1945), requires time. This is done by reference to the retarded potentials. We derive the fundamental causal Liouville equation for the phase space density of a system composed of a very large number of charged particles. Applying the approach of Klimontovich (1967), we obtain the retarded time evolution equation of the one-particle distribution function in plasmas, which replaces Klimontovich's equation in cases when the direct-interaction effects have to be taken into account. This becomes important in all systems where the distance between two points |Δq| ∼ ct is comparable to the product of observation time and light velocity, a situation which is typical in cosmic physics and astrophysics.

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6

Perelmuter, Anatolii. "To the calculation of steel structures from thin-walled rods." Strength of Materials and Theory of Structures, no. 108 (May 30, 2022): 119–30. http://dx.doi.org/10.32347/2410-2547.2022.108.119-130.

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The article contains a brief historical essay on the main ideas for calculating systems composed of thin-walled rods of open profile. The main approaches to the calculation of these systems taking into account the inequality of nodal deplanations are analyzed. It is proposed to use the finite element method using thin finite rods and specially constructed superelements as finite elements, which take into account the participation of nodal joints. The stiffness matrix of a thin-walled rod of the 14th order, built on the basis of the classical Vlasov's non-slip theory for open-profile rods, when the cross-sectional displacement is taken into account. Nodal superelements consist of shell finite elements and have m deplanation degrees of freedom according to the number of rods that approach the node. With the help of the matrix of stiffness of the nodal superelement, the connection between the deplanai, which affect the node, and the reactive forces, which have the form of bimoments realized. The method of construction of the node stiffness matrix is indicated, which is based on the use of infinitely rigid bodies, displacements and rotations of which allow to simulate the influence of deplanations on the node. The peculiarities of the assembly operation in the presence of nodal superelements are indicated. Possible variants of inclusion of the considered technique in software complexes for calculation of building designs are specified.

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7

Birman, V. "Extension of Vlasov’s Semi-membrane Theory to Reinforced Composite Shells." Journal of Applied Mechanics 59, no. 2 (June 1, 1992): 462–64. http://dx.doi.org/10.1115/1.2899547.

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Governing equations for the statics and dynamics of reinforced composite shells are developed based on Vlasov’s semi-membrane shell theory. These equations have closed-form solutions illustrated for buckling and free vibration problems. The buckling solution converges to the known result for unstiffened isotropic shells.

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8

Epstein, Marcelo, and Reuven Segev. "Vlasov’s beam paradigm and multivector Grassmann statics." Mathematics and Mechanics of Solids 24, no. 10 (March 29, 2019): 3167–79. http://dx.doi.org/10.1177/1081286519839182.

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The theory of thin-walled beams proposed in 1940 by Vlasov is shown to emerge naturally within the framework of multivector statics. This circumstance is used as the basis for possible extensions of the theory to media with complex microstructures.

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9

Piccardo, Giuseppe, Alberto Ferrarotti, and Angelo Luongo. "Nonlinear Generalized Beam Theory for open thin-walled members." Mathematics and Mechanics of Solids 22, no. 10 (June 30, 2016): 1907–21. http://dx.doi.org/10.1177/1081286516649990.

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In the framework of the Generalized Beam Theory (GBT) a new cross-section analysis is proposed, specifically suited for nonlinear elastic thin-walled beams (TWB). The approach is developed according to the nonlinear Galerkin method (NGM), which calls for the evaluation of nonlinear (passive) trial functions, to be used in conjunction with linear (active) trial functions, in describing the displacement field. The set of (quadratic) trial functions is determined here by requiring that the classic Vlasov’s kinematic hypotheses of the linear theory (i.e. (a) transverse inextensibility and (b) unshearability) are satisfied also in the nonlinear sense. The linear field is described by the so-called conventional displacements, by neglecting non-conventional displacements, which violate Vlasov’s hypotheses. The nonlinear trial functions thus generated are innovative deformation fields, which describe extensional and shear displacements in a different way from that of the non-conventional fields of the linear theory. In particular, they consist of non-constant tangential and out-of-plane displacements of the cross-section profile, able to ensure inextensibility and unshearability of all the plate elements, by balancing the second-order strains induced by the conventional displacements. Since nonlinear trial functions do not increase the number of the unknowns, the GBT spirit, as a reduction method, is preserved. A very promising example is discussed, which shows that equilibrium paths can be determined by using few linear trial functions in conjunction with the corresponding nonlinear trial functions, supplying good results when compared with burdensome finite-element solutions.

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10

ELZE, H. TH, M. GYULASSY, D. VASAK, HANNELORE HEINZ, H. STÖCKER, and W. GREINER. "TOWARDS A RELATIVISTIC SELFCONSISTENT QUANTUM TRANSPORT THEORY OF HADRONIC MATTER." Modern Physics Letters A 02, no. 07 (July 1987): 451–60. http://dx.doi.org/10.1142/s0217732387000562.

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We derive the relativistic quantum transport- and constraint equations for a relativistic field theory of baryons coupled to scalar and vector mesons. We extract a selfconsistent momentum dependent Vlasov term and the structure of quantum corrections for the Vlasov-Uehling-Uhlenbeck approach. The inclusion of pions and deltas into this transport theory is discussed.

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11

Esen, Oğul, Miroslav Grmela, Hasan Gümral, and Michal Pavelka. "Lifts of Symmetric Tensors: Fluids, Plasma, and Grad Hierarchy." Entropy 21, no. 9 (September 18, 2019): 907. http://dx.doi.org/10.3390/e21090907.

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Geometrical and algebraic aspects of the Hamiltonian realizations of the Euler’s fluid and the Vlasov’s plasma are investigated. A purely geometric pathway (involving complete lifts and vertical representatives) is proposed, which establishes a link from particle motion to evolution of the field variables. This pathway is free from Poisson brackets and Hamiltonian functionals. Momentum realizations (sections on T * T * Q ) of (both compressible and incompressible) Euler’s fluid and Vlasov’s plasma are derived. Poisson mappings relating the momentum realizations with the usual field equations are constructed as duals of injective Lie algebra homomorphisms. The geometric pathway is then used to construct the evolution equations for 10-moments kinetic theory. This way the entire Grad hierarchy (including entropic fields) can be constructed in a purely geometric way. This geometric way is an alternative to the usual Hamiltonian approach to mechanics based on Poisson brackets.

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12

EROFEEV, V. I. "Derivation of an equation for three-wave interactions based on the Klimontovich–Dupree equation." Journal of Plasma Physics 57, no. 2 (February 1997): 273–98. http://dx.doi.org/10.1017/s0022377896004990.

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A collision integral for three-wave interactions in a collisionless plasma is derived from the full plasma description by means of the Klimontovich–Dupree and Maxwell equations. This collision integral differs from its traditional counterpart (calculated within the framework of Vlasov theory) by an additional functional factor. This means that the changes in the wave spectral density, which are induced by three-wave interactions, occur with a rate other than that calculated in Vlasov theory.

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13

Grmela, Miroslav, and Michal Pavelka. "Landau damping in the multiscale Vlasov theory." Kinetic & Related Models 11, no. 3 (2018): 521–45. http://dx.doi.org/10.3934/krm.2018023.

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14

Lacker, Daniel. "Limit Theory for Controlled McKean--Vlasov Dynamics." SIAM Journal on Control and Optimization 55, no. 3 (January 2017): 1641–72. http://dx.doi.org/10.1137/16m1095895.

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15

Tronci, Cesare, and Enrico Camporeale. "Neutral Vlasov kinetic theory of magnetized plasmas." Physics of Plasmas 22, no. 2 (February 2015): 020704. http://dx.doi.org/10.1063/1.4907665.

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16

Yu, Wenbin, Dewey H. Hodges, Vitali V. Volovoi, and Eduardo D. Fuchs. "A generalized Vlasov theory for composite beams." Thin-Walled Structures 43, no. 9 (September 2005): 1493–511. http://dx.doi.org/10.1016/j.tws.2005.02.003.

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17

Coghi, Michele, Jean-Dominique Deuschel, Peter K. Friz, and Mario Maurelli. "Pathwise McKean–Vlasov theory with additive noise." Annals of Applied Probability 30, no. 5 (October 2020): 2355–92. http://dx.doi.org/10.1214/20-aap1560.

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18

Griffin-Pickering, Megan, and Mikaela Iacobelli. "Global strong solutions in $ {\mathbb{R}}^3 $ for ionic Vlasov-Poisson systems." Kinetic & Related Models 14, no. 4 (2021): 571. http://dx.doi.org/10.3934/krm.2021016.

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<p style='text-indent:20px;'>Systems of Vlasov-Poisson type are kinetic models describing dilute plasma. The structure of the model differs according to whether it describes the electrons or positively charged ions in the plasma. In contrast to the electron case, where the well-posedness theory for Vlasov-Poisson systems is well established, the well-posedness theory for ion models has been investigated more recently. In this article, we prove global well-posedness for two Vlasov-Poisson systems for ions, posed on the whole three-dimensional Euclidean space <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^3 $\end{document}</tex-math></inline-formula>, under minimal assumptions on the initial data and the confining potential.</p>

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19

Erkmen, R. Emre, and Magdi Mohareb. "Nonorthogonal solution for thin-walled members – a finite element formulation." Canadian Journal of Civil Engineering 33, no. 4 (April 1, 2006): 421–39. http://dx.doi.org/10.1139/l05-116.

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Conventional solutions for the equations of equilibrium based on the well-known Vlasov thin-walled beam theory uncouple the equations by adopting orthogonal coordinate systems. Although this technique considerably simplifies the resulting field equations, it introduces several modelling complications and limitations. As a result, in the analysis of problems where eccentric supports or abrupt cross-sectional changes exist (in elements with rectangular holes, coped flanges, or longitudinal stiffened members, etc.), the Vlasov theory has been avoided in favour of a shell finite element that offer modelling flexibility at higher computational cost. In this paper, a general solution of the Vlasov thin-walled beam theory based on a nonorthogonal coordinate system is developed. The field equations are then exactly solved and the resulting displacement field expressions are used to formulate a finite element. Two additional finite elements are subsequently derived to cover the special cases where (a) the St.Venant torsional stiffness is negligible and (b) the warping torsional stiffness is negligible. Key words: open sections, warping effect, finite element,thin-walled beams, asymmetric sections.

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20

BRIZARD, A. J., and A. MISHCHENKO. "Guiding-center recursive Vlasov and Lie-transform methods in plasma physics." Journal of Plasma Physics 75, no. 5 (October 2009): 675–96. http://dx.doi.org/10.1017/s0022377809007946.

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AbstractThe gyrocenter phase-space transformation used to describe nonlinear gyrokinetic theory is rediscovered by a recursive solution of the Hamiltonian dynamics associated with the perturbed guiding-center Vlasov operator. The present work clarifies the relation between the derivation of the gyrocenter phase-space coordinates by the guiding-center recursive Vlasov method and the method of Lie-transform phase-space transformations.

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21

Bessi, Ugo. "Viscous aubby-mather theory and the vlasov equation." Discrete and Continuous Dynamical Systems 34, no. 2 (August 2013): 379–420. http://dx.doi.org/10.3934/dcds.2014.34.379.

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22

Hirvijoki, Eero, Joshua W. Burby, and Alain J. Brizard. "Metriplectic foundations of gyrokinetic Vlasov–Maxwell–Landau theory." Physics of Plasmas 29, no. 6 (June 2022): 060701. http://dx.doi.org/10.1063/5.0091727.

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This Letter reports on a metriplectic formulation of a collisional, nonlinear full- f electromagnetic gyrokinetic theory compliant with energy conservation and monotonic entropy production. In an axisymmetric background magnetic field, the toroidal angular momentum is also conserved. Notably, a new collisional current, contributing to the gyrokinetic Maxwell–Ampère equation and the gyrokinetic charge conservation law, is discovered.

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23

Brizard, Alain J., and Cesare Tronci. "Variational formulations of guiding-center Vlasov-Maxwell theory." Physics of Plasmas 23, no. 6 (June 2016): 062107. http://dx.doi.org/10.1063/1.4953431.

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24

Degond, Pierre. "Spectral theory of the linearized Vlasov-Poisson equation." Transactions of the American Mathematical Society 294, no. 2 (February 1, 1986): 435. http://dx.doi.org/10.1090/s0002-9947-1986-0825714-8.

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25

Holm, D. D., V. Putkaradze, and C. Tronci. "Double-bracket dissipation in kinetic theory for particles with anisotropic interactions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2122 (April 21, 2010): 2991–3012. http://dx.doi.org/10.1098/rspa.2010.0043.

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We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double-bracket approach (double-bracket Vlasov, or DBV). The moments of the DBV equation lead to a non-local form of Darcy’s law for the mass density. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the DBV form. The moment dynamics for these double-bracket kinetic equations is expressed as Lie–Darcy continuum equations for densities of mass and orientation. We also show how to obtain a Smoluchowski model from a cold plasma-like moment closure of DBV. Thus, the double-bracket kinetic framework serves as a unifying method for deriving different types of dynamics, from density-orientation to Smoluchowski equations. Extensions for more general physical systems are also discussed.

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26

CALOGERO, SIMONE. "A MATHEMATICAL THEORY OF ISOLATED SYSTEMS IN RELATIVISTIC PLASMA PHYSICS." Journal of Hyperbolic Differential Equations 04, no. 02 (June 2007): 267–94. http://dx.doi.org/10.1142/s0219891607001136.

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The existence and the properties of isolated solutions to the relativistic Vlasov–Maxwell system with initial data on the backward hyperboloid [Formula: see text] are investigated. Isolated solutions of Vlasov–Maxwell can be defined by the condition that the particle density is compactly supported on the initial hyperboloid and by imposing the absence of incoming radiation on the electromagnetic field. Various consequences of the mass-energy conservation laws are derived by assuming the existence of smooth isolated solutions which match the inital data. In particular, it is shown that the mass-energy of isolated solutions on the backward hyperboloids and on the surfaces of constant proper time are preserved and equal, while the mass-energy on the forward hyperboloids is non-increasing and uniformly bounded by the mass-energy on the initial hyperboloid. Moreover the global existence and uniqueness of classical solutions in the future of the initial surface is established for the one-dimensional version of the system.

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27

Gasser, I., P. E. Jabin, and B. Perthame. "Regularity and propagation of moments in some nonlinear Vlasov systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 6 (December 2000): 1259–73. http://dx.doi.org/10.1017/s0308210500000676.

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We introduce a new variant to prove the regularity of solutions to transport equations of the Vlasov type. Our approach is mainly based on the proof of propagation of velocity moments, as in a previous paper by Lions and Perthame. We combine it with moment lemmas which assert that, locally in space, velocity moments can be gained from the kinetic equation itself. We apply our theory to two cases. First, to the Vlasov–Poisson system, and we solve a long-standing conjecture, namely the propagation of any moment larger than two. Next, to the Vlasov–Stokes system, where we prove the same result for fairly singular kernels.

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28

Volovoi, V. V., and D. H. Hodges. "Theory of Anisotropic Thin-Walled Beams." Journal of Applied Mechanics 67, no. 3 (March 7, 2000): 453–59. http://dx.doi.org/10.1115/1.1312806.

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Анотація:

Asymptotically correct, linear theory is presented for thin-walled prismatic beams made of generally anisotropic materials. Consistent use of small parameters that are intrinsic to the problem permits a natural description of all thin-walled beams within a common framework, regardless of whether cross-sectional geometry is open, closed, or strip-like. Four “classical” one-dimensional variables associated with extension, twist, and bending in two orthogonal directions are employed. Analytical formulas are obtained for the resulting 4×4 cross-sectional stiffness matrix (which, in general, is fully populated and includes all elastic couplings) as well as for the strain field. Prior to this work no analytical theories for beams with closed cross sections were able to consistently include shell bending strain measures. Corrections stemming from those measures are shown to be important for certain cases. Contrary to widespread belief, it is demonstrated that for such “classical” theories, a cross section is not rigid in its own plane. Vlasov’s correction is shown to be unimportant for closed sections, while for open cross sections asymptotically correct formulas for this effect are provided. The latter result is an extension to a general contour of a result for I-beams previously published by the authors. [S0021-8936(00)03003-8]

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29

DOLBEAULT, J., and G. REIN. "TIME-DEPENDENT RESCALINGS AND LYAPUNOV FUNCTIONALS FOR THE VLASOV–POISSON AND EULER–POISSON SYSTEMS, AND FOR RELATED MODELS OF KINETIC EQUATIONS, FLUID DYNAMICS AND QUANTUM PHYSICS." Mathematical Models and Methods in Applied Sciences 11, no. 03 (April 2001): 407–32. http://dx.doi.org/10.1142/s021820250100091x.

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Анотація:

We investigate rescaling transformations for the Vlasov–Poisson and Euler–Poisson systems and derive in the plasma physics case Lyapunov functionals which can be used to analyze dispersion effects. The method is also used for studying the long time behavior of the solutions and can be applied to other models in kinetic theory (two-dimensional symmetric Vlasov–Poisson system with an external magnetic field), in fluid dynamics (Euler system for gases) and in quantum physics (Schrödinger–Poisson system, nonlinear Schrödinger equation).

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30

Hartnack, C., H. Stöcker, and W. Greiner. "Landau-Vlasov model versus Vlasov-Uehling-Uhlenbeck-approach. Different flow effects from the same theory?" Physics Letters B 215, no. 1 (December 1988): 33–35. http://dx.doi.org/10.1016/0370-2693(88)91064-7.

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31

Besse, Nicolas, Norbert Mauser, and Eric Sonnendrücker. "Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic Phenomena." International Journal of Applied Mathematics and Computer Science 17, no. 3 (October 1, 2007): 361–74. http://dx.doi.org/10.2478/v10006-007-0030-3.

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Анотація:

Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic PhenomenaWe present a new numerical method to solve the Vlasov-Darwin and Vlasov-Poisswell systems which are approximations of the Vlasov-Maxwell equation in the asymptotic limit of the infinite speed of light. These systems model low-frequency electromagnetic phenomena in plasmas, and thus "light waves" are somewhat supressed, which in turn allows the numerical discretization to dispense with the Courant-Friedrichs-Lewy condition on the time step. We construct a numerical scheme based on semi-Lagrangian methods and time splitting techniques. We develop a four-dimensional phase space algorithm for the distribution function while the electromagnetic field is solved on a two-dimensional Cartesian grid. Finally, we present two nontrivial test cases: (a) the wave Landau damping and (b) the electromagnetic beam-plasma instability. For these cases our numerical scheme works very well and is in agreement with analytic kinetic theory.

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32

Rein, Gerhard. "Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system." Banach Center Publications 41, no. 1 (1997): 179–94. http://dx.doi.org/10.4064/-41-1-179-194.

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33

Chiabó, L., and G. Sánchez-Arriaga. "Limitations of stationary Vlasov-Poisson solvers in probe theory." Journal of Computational Physics 438 (August 2021): 110366. http://dx.doi.org/10.1016/j.jcp.2021.110366.

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34

Kovalev, V. F., S. V. Krivenko, and V. V. Pustovalov. "Symmetry Group of Vlasov-Maxwell Equations in Plasma Theory." Journal of Nonlinear Mathematical Physics 3, no. 1-2 (January 1996): 175–80. http://dx.doi.org/10.2991/jnmp.1996.3.1-2.20.

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35

Popov, V. Yu, and V. P. Silin. "Vlasov modes in the theory of ion-acoustic turbulence." Plasma Physics Reports 40, no. 4 (April 2014): 298–305. http://dx.doi.org/10.1134/s1063780x14040060.

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36

Webb, Stephen D. "A Hamiltonian perturbation theory for the nonlinear Vlasov equation." Journal of Mathematical Physics 57, no. 4 (April 2016): 042905. http://dx.doi.org/10.1063/1.4947262.

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37

Fomichev, S. V., and D. F. Zaretsky. "Vlasov theory of Mie resonance broadening in metal clusters." Journal of Physics B: Atomic, Molecular and Optical Physics 32, no. 21 (October 15, 1999): 5083–102. http://dx.doi.org/10.1088/0953-4075/32/21/303.

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38

LIU, S. Q., and Y. LIU. "Kinetic theory of transverse plasmons in pair plasmas." Journal of Plasma Physics 77, no. 2 (April 16, 2010): 145–53. http://dx.doi.org/10.1017/s002237781000019x.

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Анотація:

AbstractA set of nonlinear governing equations for interactions of transverse plasmons with pair plasmas is derived from Vlasov–Maxwell equations. It is shown the ponderomotive force induced by high-frequency transverse plasmons will expel the pair particles away, resulting in the formation of density cavity in which transverse plasmons are trapped. Numerical results show the envelope of wave fields will collapse and break into a filamentary structure due to the spatially inhomogeneous growth rate. The results obtained would be useful for understanding the nonlinear propagation behavior of intense electromagnetic waves in pair plasmas.

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39

Zubair, Tamour, Muhammad Usman, Ilyas Khan, Nawaf N. Hamadneh, Tiao Lu, and Mulugeta Andualem. "Higher-Order Accurate and Conservative Hybrid Numerical Scheme for Relativistic Time-Fractional Vlasov-Maxwell System." Journal of Function Spaces 2022 (March 22, 2022): 1–12. http://dx.doi.org/10.1155/2022/7046579.

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The historical analysis demonstrates that plasma scientists produced a variety of numerical methods for solving “kinetic” models, i.e., the Vlasov-Maxwell (VM) system. Still, on the other hand, a significant fact or drawback of most algorithms is that they do not preserve conservation philosophies. This is a crucial fact that cannot be disregarded since the Vlasov Maxwell system is associated with conservation rules and is capable of assessing after the accomplishment of certain helpful mathematical actions. To examine the fractional-order routine of charged particles, we constructed a fractional-order plasma model and proposed a higher-order conservative numerical approach based on operational matrices theory and Shifted Gegenbauer estimations. Numerical convergence is investigated to confirm its competence and compatibility. This concept may be used in problems involving variable order and multidimensionality, such as those involving Vlasov and Boltzmann systems.

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40

Zhang, Xiang, Jing Jun Lou, and Shao Chun Ding. "Kinetic Analysis of a Cylindrical Shell Partially Treated with Constrained Layer Damping." Applied Mechanics and Materials 34-35 (October 2010): 1299–304. http://dx.doi.org/10.4028/www.scientific.net/amm.34-35.1299.

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This paper presents a transfer function method for a cylindrical shell with a partially passive constrained layer damping (PCLD) treatment. A thin shell theory based on Donnell-Mushtari-Vlasov assumption is employed to yield a mathematical model. The equation of motion and boundary conditions of a cylindrical shell with partially PCLD are derived. The paper provides theory supports for PCLD structure’s engineering applications in submarine weapon field.

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41

DAS, CHANDRA. "Evolution of magnetic moment in the interaction of waves with kinetically described plasmas." Journal of Plasma Physics 57, no. 2 (February 1997): 343–48. http://dx.doi.org/10.1017/s002237789600493x.

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The non-oscillating part of the magnetic moment field (called the inverse Faraday effect (IFE) for this field from a circularly polarized wave in a medium) is calculated for the interaction of an elliptically polarized wave with a weakly ionized magnetized plasma in a kinetic theory model and with unmagnetized Vlasov plasmas. For a weakly ionized magnetized plasma, the induced field increases with both temperature and ambient magnetic field. For an unmagnetized plasma, it increases parabolically with temperature. The induced magnetic field is found to vary parabolically with temperature in the case of an unmagnetized Vlasov plasma.

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42

Minardi, E. "The thermodynamics of the Vlasov equilibria." Journal of Plasma Physics 33, no. 3 (June 1985): 359–67. http://dx.doi.org/10.1017/s0022377800002567.

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A statistical procedure is applied for constructing an entropy functional associated with a collective Vlasov equilibrium described by a given coarse-grained current and charge distribution. The functional is not at a maximum if the magnetic or electrostatic equilibrium is not unique. This property connects the principle of maximum entropy with bifurcation theory and marginal stability analysis.

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43

Lazar, M., and R. Schlickeiser. "Relativistic kinetic theory of electromagnetic waves in equilibrium magnetized plasma. General dispersion equations." Canadian Journal of Physics 81, no. 12 (December 1, 2003): 1377–87. http://dx.doi.org/10.1139/p03-087.

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The relativistic kinetic theory of parallel propagating electromagnetic waves in a magnetized equilibrium plasma is presented. On the basis of relativistic VlasovMaxwell equations, a general explicit dispersion relation is derived by a correct analytical continuation for all complex frequencies of electromagnetic waves.PACS Nos.: 52.25.Dg, 52.25.Xz, 52.27.Ep, 52.27.Ny, 52.35.Hr, 52.35.Mw, 52.35.Py

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44

Wang, Zhao Qiang, Jin Cheng Zhao, and Jing Hai Gong. "A New Torsion Element of Thin-Walled Beams Including Shear Deformation." Applied Mechanics and Materials 94-96 (September 2011): 1642–45. http://dx.doi.org/10.4028/www.scientific.net/amm.94-96.1642.

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Restrained torsion analysis of open thin-walled beam is presented in this paper. A finite element model is developed. The element is based on the first-order torsion theory, which accounts for the warping deformation and shear deformation due to restrained torsion. The interpolation functions of total rotation and twist rate of free warping rotation of cross section are constructed respectively by using the relationship between these two rotations. Numerical example is illustrated to validate the current approach and the results of the current theory are compared with those obtained from classical Vlasov theory and first-order torsion theory.

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45

El-Nabulsi, Rami Ahmad. "Modified plasma–fluid equations from nonstandard Lagrangians with applications to nuclear fusion." Canadian Journal of Physics 93, no. 1 (January 2015): 55–67. http://dx.doi.org/10.1139/cjp-2014-0233.

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Nonstandard Lagrangian dynamics have gained great interest recently, in particular within the theory of nonlinear differential equations and dissipative dynamical systems. In this paper, we address their implications in plasma–fluid dynamics. The mathematical settings are constructed starting from the modified Vlasov–Boltzmann transport equation, which is derived from modified Euler–Lagrange equations of motion. Far from giving a self-consistent nonstandard Lagrangian theory of plasma–fluid dynamics, in this paper we have just introduced the basic settings and discussed some illustrative examples that such a modified theory should have in plasma–fluid theory and nuclear fusion.

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46

Redekop, D. "NATURAL FREQUENCIES OF A SHORT CURVED PIPE." Transactions of the Canadian Society for Mechanical Engineering 18, no. 1 (March 1994): 35–45. http://dx.doi.org/10.1139/tcsme-1994-0003.

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The natural frequencies are determine for a short curved pipe. A shell theory is developed in toroidal coordinates, based on the Mushtari-Vlasov-Donnell assumptions. The theory is specialized for the case of moderate curvature of the torus centre-line. To demonstrate the accuracy of the theory the end. exponential decay coefficients are calculated. These are compared with the corresponding coefficients for a straight pipe, and with values given previously for a curved pipe. The theory for the determination of the natural frequencies of vibration in symmetric and anti-symmetric modes is presented. Numerical results are computed using the theory, and these are compared with results for a comparable straight pipe.

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47

Mukherjee, Joydeep, and A. Roy Chowdhury. "Nonlinear Landau damping in a relativistic plasma." Journal of Plasma Physics 52, no. 1 (August 1994): 55–74. http://dx.doi.org/10.1017/s0022377800017773.

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Анотація:

A generalized non-local nonlinear Schrödinger equation describing the phenomenon of nonlinear Landau damping in a relativistic two-component plasma is deduced using the kinetic-theory approach of Vlasov. Parameters appearing in the equation are evaluated explicitly for the case of a Maxwellian distribution function.

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48

Silin, I., R. Sydora, and K. Sauer. "Electron beam-plasma interaction: Linear theory and Vlasov-Poisson simulations." Physics of Plasmas 14, no. 1 (January 2007): 012106. http://dx.doi.org/10.1063/1.2430518.

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49

Şen, Nevroz, and Peter E. Caines. "Nonlinear Filtering Theory for McKean--Vlasov Type Stochastic Differential Equations." SIAM Journal on Control and Optimization 54, no. 1 (January 2016): 153–74. http://dx.doi.org/10.1137/15m1013304.

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50

Choi, Soomin, and Yoon Young Kim. "Higher-order Vlasov torsion theory for thin-walled box beams." International Journal of Mechanical Sciences 195 (April 2021): 106231. http://dx.doi.org/10.1016/j.ijmecsci.2020.106231.

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