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Journal articles on the topic 'Vlasov theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

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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15

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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16

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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17

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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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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18

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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19

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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20

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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21

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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22

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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23

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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24

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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25

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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26

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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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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27

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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28

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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29

Molitoris, J. J., D. Hahn, C. Alonso, I. Collazo, P. D’Alessandris, T. McAbee, J. Wilson, and J. Zingman. "Relativistic nuclear fluid dynamics and Vlasov-Uehling-Uhlenbeck kinetic theory." Physical Review C 37, no. 3 (March 1, 1988): 1014–19. http://dx.doi.org/10.1103/physrevc.37.1014.

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30

Sircombe, N. J., T. D. Arber, and R. O. Dendy. "Kinetic effects in laser-plasma coupling: Vlasov theory and computations." Journal de Physique IV (Proceedings) 133 (June 2006): 277–81. http://dx.doi.org/10.1051/jp4:2006133055.

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31

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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32

Altenbach, J., H. Altenbach, and V. Matzdorf. "A generalized Vlasov theory for thin-walled composite beam structures." Mechanics of Composite Materials 30, no. 1 (1994): 43–54. http://dx.doi.org/10.1007/bf00612733.

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33

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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34

Wollman, Stephen. "Local existence and uniqueness theory of the Vlasov-Maxwell system." Journal of Mathematical Analysis and Applications 127, no. 1 (October 1987): 103–21. http://dx.doi.org/10.1016/0022-247x(87)90143-0.

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35

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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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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36

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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37

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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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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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

Pfirsch, Dieter. "Negative Energy Waves in the Frame work of Vlasov -Maxwell Theory." Zeitschrift für Naturforschung A 43, no. 6 (June 1, 1988): 533–37. http://dx.doi.org/10.1515/zna-1988-0603.

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Abstract On the basis of a variational formulation of the Vlasov-Maxwell theory it was recently shown that, for instance, all magnetically confined plasmas allow the existence of negative energy waves. Such waves can become nonlinearly and dissipatively unstable and might therefore be of importance in explaining anomalous transport. The proof of this result uses infinitely strongly localized perturbations. This is, however, not necessary: in this paper it is shown by discussing general, homogeneous, magnetized plasmas that the necessary localization is related to the average gyroradius rg of the relevant particle species. For unstable plasmas the extent or wavelengths of negative energy waves can be of the order of rg, whereas for linearly stable plasmas the extent can be a small fraction of rg.

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40

Kolomietz, V. M., V. A. Plujko, and S. Shlomo. "Collisional damping in heated nuclei within the Landau-Vlasov kinetic theory." Physical Review C 52, no. 5 (November 1, 1995): 2480–87. http://dx.doi.org/10.1103/physrevc.52.2480.

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41

Schindler, Karl, and Joachim Birn. "Models of two-dimensional embedded thin current sheets from Vlasov theory." Journal of Geophysical Research: Space Physics 107, A8 (August 2002): SMP 20–1—SMP 20–13. http://dx.doi.org/10.1029/2001ja000304.

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42

Sahraoui, F., G. Belmont, and M. L. Goldstein. "NEW INSIGHT INTO SHORT-WAVELENGTH SOLAR WIND FLUCTUATIONS FROM VLASOV THEORY." Astrophysical Journal 748, no. 2 (March 13, 2012): 100. http://dx.doi.org/10.1088/0004-637x/748/2/100.

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43

Zhang, Y. Z., and S. M. Mahajan. "Renormalized perturbation theory: Vlasov–Poisson system, weak turbulence limit, and gyrokinetics." Physics of Fluids 31, no. 10 (1988): 2894. http://dx.doi.org/10.1063/1.866998.

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44

DUAN, RENJUN, TONG YANG, and HUIJIANG ZHAO. "THE VLASOV–POISSON–BOLTZMANN SYSTEM FOR SOFT POTENTIALS." Mathematical Models and Methods in Applied Sciences 23, no. 06 (March 17, 2013): 979–1028. http://dx.doi.org/10.1142/s0218202513500012.

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An important physical model describing the dynamics of dilute weakly ionized plasmas in the collisional kinetic theory is the Vlasov–Poisson–Boltzmann system for which the plasma responds strongly to the self-consistent electrostatic force. This paper is concerned with the electron dynamics of kinetic plasmas in the whole space when the positive charged ion flow provides a spatially uniform background. We establish the global existence and optimal convergence rates of solutions near a global Maxwellian to the Cauchy problem on the Vlasov–Poisson–Boltzmann system for angular cutoff soft potentials with -2 ≤ γ < 0. The main idea is to introduce a time-dependent weight function in the velocity variable to capture the singularity of the cross-section at zero relative velocity.

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45

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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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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46

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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47

Zhang, Xiang, Jing Jun Lou, Gui Feng Liu, and Shao Chun Ding. "Spectral Finite Element Modeling of Cylindrical Shells with Passive Constrained Layer Damping." Advanced Materials Research 211-212 (February 2011): 695–99. http://dx.doi.org/10.4028/www.scientific.net/amr.211-212.695.

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This paper presents a spectral finite element method for a cylindriacl shell with a passive constrained layer damping treatment. A thin shell theory based on Donnell-Mushtari-Vlasov assumption is employed. The equation of spectral unit and the method of determination of natural frequency and modal loss factor are presented.

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48

Altman, Wolf, and Luiz Bevilacqua. "Nonconservative Components of Follower Forces in the Classical Shell Theory." Applied Mechanics Reviews 42, no. 11S (November 1, 1989): S13—S19. http://dx.doi.org/10.1115/1.3152383.

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An analysis of follower forces acting on shell structures is presented. Attention is focussed on the expressions of such forces as functions of the generalized displacements. Specific expressions for the follower forces are obtained, according to the order of magnitude of the strains and angles of rotation. For small strains the follower forces allow a decomposition into conservative and non-conservative components. This leads to the equations of dynamic stability of shell problems subjected to follower loads. The dynamic counterparts of Donnell-Mushtari-Vlasov stability equations are presented, by either retaining or omitting the prebuckling rotations.

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49

Roth, M., J. De Keyser, and M. M. Kuznetsova. "Vlasov theory of the equilibrium structure of tangential discontinuities in space plasmas." Space Science Reviews 76, no. 3-4 (May 1996): 251–317. http://dx.doi.org/10.1007/bf00197842.

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50

Chung, S. W., S. G. Hong, and G. S. Ju. "Extension and reduction of Donnell-Vlasov shell theory to hybrid anisotropic materials." Composite Structures 172 (July 2017): 190–97. http://dx.doi.org/10.1016/j.compstruct.2017.03.019.

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