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Academic literature on the topic 'Vlasov's theory'

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Published: 14 March 2023

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Journal articles on the topic "Vlasov's theory"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Vlasov's theory"

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CAMMARANO, SANDRO. "STATIC AND DYNAMIC ANALYSIS OF HIGH-RISE BUILDINGS." Doctoral thesis, Politecnico di Torino, 2014. http://hdl.handle.net/11583/2565549.

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This thesis is focused on the structural behaviour of high-rise buildings subjected to transversal loads expressed in terms of shears and torsional moments. As horizontal reinforcement, the resistant skeleton of the construction can be composed by different vertical bracings, such as shear walls, braced frames and thin-walled open section profiles, having constant or variable geometrical properties along the height. In this way, most of the traditional structural schemes can be modelled, from moment resisting frames up to outrigger and tubular systems. In particular, an entire chapter is addressed to the case of thin-walled open section shear walls which are defined by a coupled flexural-torsional behaviour, as described by Vlasov’s theory of the sectorial areas. From the analytical point of view, the three-dimensional formulation proposed by Al. Carpinteri and An. Carpinteri (1985) is considered and extended in order to perform dynamic analyses and encompass innovative structural solutions which can twist and taper from the bottom to the top of the building. Such approach is based on the hypothesis of in-plane infinitely rigid floors which assure the connection between the vertical bracings and, consequently, reduce the number of degrees of freedom being only three for each level. By means of it, relevant design information such as the floor displacements, the external load distribution between the structural components, the internal actions, the free vibrations as well as the mode shapes can be quickly obtained. The clearness and the conciseness of the matrix formulation allow to devise a simple computer program which, starting from basic information as the building geometry, the number and type of vertical stiffening, the material properties and the intensity of the external forces, provides essential results for preliminary designs.
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Tronci, Cesare. "Geometric dynamics of Vlasov kinetic theory and its moments." Thesis, Imperial College London, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486660.

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The Vlasov equation of kinetic theory is introduced and the Hamiltonian structure of its moments is presented. Then we focus on the geodesic evolution of the Vlasov moments [1.2]. As a first step, these moment equations generalize the Camassa-Holm equation [3] to its multi-component version [4]. Subsequently, adding electrostatic forces to the geodesic moment equations relates them to the Benney equations [5] and to the equations for beam dynamics in particle accelerators. Next, we develop a kinetic theory for self assembly in nano-particles. The Darcy law [6] is introduced as a general principle for aggregation dynamics in friction dominated systems (at different scales). Then, a kinetic equation is introduced [7,8] for the dissipative motion of isotropic nano-particles. The zeroth-moment dynamics of this equation recovers the classical Darcy law at the macroscopic level [7]. A kinetic-theory description for oriented nano-particles is also presented [9]. At the macroscopic level, the zeroth moments of this kinetic equation recover the magnetization dynamics of the Landau-Lifshitz-Gilbert equation [10]. The moment equations exhibit the spontaneous emergence of singular solutions (clumpons) that finally merge in one singularity. This behaviour represents aggregation and alignment of oriented nano-particles. Finally, the Smoluchowsky description is derived from the dissipative Vlasov equation for anisotropic interactions. Various levels of approximate Smoluchowsky descriptions are proposed as special cases of the general treatment. As a result, the macroscopic momentum emerges as an additional dynamical variable that in general cannot be neglected.
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Zhang, Mei. "Some problems on conservation laws and Vlasov-Poisson-Boltzmann equation /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b23749465f.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2009.
"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [90]-94)
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Rathsman, Karin. "Modeling of Electron Cooling : Theory, Data and Applications." Doctoral thesis, Uppsala universitet, Kärnfysik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-129686.

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The Vlasov technique is used to model the electron cooling force. Limitations of the applicability of the method is obtained by considering the perturbations of the electron plasma. Analytical expressions of the electron cooling force, valid beyond the Coulomb logarithm approximation, are derived and compared to numerical calculations using adaptive Monte Carlo integration. The calculated longitudinal cooling force is verified with measurements in CELSIUS. Transverse damping rates of betatron oscillations for a nonlinear cooling force is explored. Experimental data of the transverse monochromatic instability is used to determine the rms angular spread due to solenoid field imperfections in CELSIUS. The result, θrms= 0.16 ± 0.02 mrad, is in agreement with the longitudinal cooling force measurements. This verifies the internal consistency of the model and shows that the transverse and longitudinal cooling force components have different velocity dependences. Simulations of electron cooling with applications to HESR show that the momentum reso- lution ∆p/p smaller than 10−5 is feasible, as needed for the charmonium spectroscopy in the experimental program of PANDA. By deflecting the electron beam angle to make use of the monochromatic instability, a reasonable overlap between the circulating antiproton beam and the internal target can be maintained. The simulations also indicate that the cooling time is considerably shorter than expected.
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Maruca, Bennett Andrew. "Instability-Driven Limits on Ion Temperature Anisotropy in the Solar Wind: Observations and Linear Vlasov Theory." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10457.

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Kinetic microinstabilities in the solar wind arise when its non-thermal properties become too extreme. This thesis project focused specifically on the four instabilities associated with ion temperature anisotropy: the cyclotron, mirror, and parallel and oblique firehose instabilities. Numerous studies have provided evidence that proton temperature anisotropy in the solar wind is limited by the actions of these instabilities. For this project, a fully revised analysis of data from the Wind spacecraft's Faraday cups and calculations from linear Vlasov theory were used to extend these findings in two respects. First, theoretical thresholds were derived for the \(\alpha\)-particle temperature anisotropy instabilities, which were then found to be consistent with a statistical analysis of Wind \(\alpha\)-particle data. This suggests that \(\alpha\)-particles, which constitute only about 5% of ions in the solar wind, are nevertheless able to drive temperature anisotropy instabilities. Second, a statistical analysis of Wind proton data found that proton temperature was significantly enhanced in plasma unstable due to proton temperature anisotropy. This implies that extreme proton temperature anisotropies in solar wind at 1 AU arise from ongoing anisotropic heating (versus cooling from, e.g., CGL double adiabatic expansion). Together, these results provide further insight into the complex evolution of the solar wind's non-fluid properties.
Astronomy
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Allanson, Oliver Douglas. "Theory of one-dimensional Vlasov-Maxwell equilibria : with applications to collisionless current sheets and flux tubes." Thesis, University of St Andrews, 2017. http://hdl.handle.net/10023/11916.

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Vlasov-Maxwell equilibria are characterised by the self-consistent descriptions of the steady-states of collisionless plasmas in particle phase-space, and balanced macroscopic forces. We study the theory of Vlasov-Maxwell equilibria in one spatial dimension, as well as its application to current sheet and flux tube models. The ‘inverse problem' is that of determining a Vlasov-Maxwell equilibrium distribution function self-consistent with a given magnetic field. We develop the theory of inversion using expansions in Hermite polynomial functions of the canonical momenta. Sufficient conditions for the convergence of a Hermite expansion are found, given a pressure tensor. For large classes of DFs, we prove that non-negativity of the distribution function is contingent on the magnetisation of the plasma, and make conjectures for all classes. The inverse problem is considered for nonlinear ‘force-free Harris sheets'. By applying the Hermite method, we construct new models that can describe sub-unity values of the plasma beta (βpl) for the first time. Whilst analytical convergence is proven for all βpl, numerical convergence is attained for βpl = 0.85, and then βpl = 0.05 after a ‘re-gauging' process. We consider the properties that a pressure tensor must satisfy to be consistent with ‘asymmetric Harris sheets', and construct new examples. It is possible to analytically solve the inverse problem in some cases, but others must be tackled numerically. We present new exact Vlasov-Maxwell equilibria for asymmetric current sheets, which can be written as a sum of shifted Maxwellian distributions. This is ideal for implementations in particle-in-cell simulations. We study the correspondence between the microscopic and macroscopic descriptions of equilibrium in cylindrical geometry, and then attempt to find Vlasov-Maxwell equilibria for the nonlinear force-free ‘Gold-Hoyle' model. However, it is necessary to include a background field, which can be arbitrarily weak if desired. The equilibrium can be electrically non-neutral, depending on the bulk flows.
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Li, Li. "The asymptotic behavior for the Vlasov-Poisson-Boltzmann system & heliostat with spinning-elevation tracking mode /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b30082419f.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2009.
"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [84]-87)
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Liu, Yating. "Optimal Quantization : Limit Theorem, Clustering and Simulation of the McKean-Vlasov Equation." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS215.

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Cette thèse contient deux parties. Dans la première partie, on démontre deux théorèmes limites de la quantification optimale. Le premier théorème limite est la caractérisation de la convergence sous la distance de Wasserstein d’une suite de mesures de probabilité par la convergence simple des fonctions d’erreur de la quantification. Ces résultats sont établis en Rd et également dans un espace de Hilbert séparable. Le second théorème limite montre la vitesse de convergence des grilles optimales et la performance de quantification pour une suite de mesures de probabilité qui convergent sous la distance de Wasserstein, notamment la mesure empirique. La deuxième partie de cette thèse se concentre sur l’approximation et la simulation de l’équation de McKean-Vlasov. On commence cette partie par prouver, par la méthode de Feyel (voir Bouleau (1988)[Section 7]), l’existence et l’unicité d’une solution forte de l’équation de McKean-Vlasov dXt = b(t, Xt, μt)dt + σ(t, Xt, μt)dBt sous la condition que les fonctions de coefficient b et σ sont lipschitziennes. Ensuite, on établit la vitesse de convergence du schéma d’Euler théorique de l’équation de McKean-Vlasov et également les résultats de l’ordre convexe fonctionnel pour les équations de McKean-Vlasov avec b(t,x,μ) = αx+β, α,β ∈ R. Dans le dernier chapitre, on analyse l’erreur de la méthode de particule, de plusieurs schémas basés sur la quantification et d’un schéma hybride particule- quantification. À la fin, on illustre deux exemples de simulations: l’équation de Burgers (Bossy and Talay (1997)) en dimension 1 et le réseau de neurones de FitzHugh-Nagumo (Baladron et al. (2012)) en dimension 3
This thesis contains two parts. The first part addresses two limit theorems related to optimal quantization. The first limit theorem is the characterization of the convergence in the Wasserstein distance of probability measures by the pointwise convergence of Lp-quantization error functions on Rd and on a separable Hilbert space. The second limit theorem is the convergence rate of the optimal quantizer and the clustering performance for a probability measure sequence (μn)n∈N∗ on Rd converging in the Wasserstein distance, especially when (μn)n∈N∗ are the empirical measures with finite second moment but possibly unbounded support. The second part of this manuscript is devoted to the approximation and the simulation of the McKean-Vlasov equation, including several quantization based schemes and a hybrid particle-quantization scheme. We first give a proof of the existence and uniqueness of a strong solution of the McKean- Vlasov equation dXt = b(t, Xt, μt)dt + σ(t, Xt, μt)dBt under the Lipschitz coefficient condition by using Feyel’s method (see Bouleau (1988)[Section 7]). Then, we establish the convergence rate of the “theoretical” Euler scheme and as an application, we establish functional convex order results for scaled McKean-Vlasov equations with an affine drift. In the last chapter, we prove the convergence rate of the particle method, several quantization based schemes and the hybrid scheme. Finally, we simulate two examples: the Burger’s equation (Bossy and Talay (1997)) in one dimensional setting and the Network of FitzHugh-Nagumo neurons (Baladron et al. (2012)) in dimension 3
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Matsui, Tatsuki. "Kinetic theory and simulation of collisionless tearing in bifurcated current sheets." Diss., University of Iowa, 2008. http://ir.uiowa.edu/etd/38.

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Brigouleix, Nicolas. "Sur le système de Vlasov-Maxwell : régularité et limite non relativiste." Thesis, Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAX098.

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Cette thèse est consacrée à l'étude du système d'équations aux dérivées partielles de Vlasov-Maxwell qui décrit l'évolution au cours du temps de la fonction de distribution de particules chargées dans un plasma. Nos travaux portent plus particulièrement sur la régularité des solutions de ce système et le problème de la limite non-relativiste.Dans un premier temps, on étudie un modèle jouet combinant une équation de Vlasov et un système d'équations de transport. On utilise les méthodes utilisées pour obtenir et améliorer le critère de Glassey-Strauss qui donne une condition suffisante sous laquelle une solution forte du système de Vlasov-Maxwell ne développe pas de singularités. La perte de régularité se manifeste lorsque la vitesse des particules est proche de la vitesse de résonnance du système hyperbolique adjoint. Le même phénomène se produit pour les solutions de notre système jouet, mais il possède une structure moins complexe.Dans un deuxième temps, on aborde la question de la limite non relativiste. Après adimensionnement, la vitesse de la lumière peut être considérée comme un grand paramètre du système. Lorsque celui ci tend vers l'infini, on parle de limite non-relativiste. Au premier ordrer, la limite non relativiste du système de Vlasov-Maxwell est le système de Vlasov-Poisson. Dans un premier chapitre, on établit une méthode itérative qui permet formellement d'obtenir des systèmes couplant l'équation de Vlasov à un système elliptique et formant une approximation non relativiste d'ordre arbitrairement élevé du système de Vlasov-Maxwell. Ces systèmes sont de plus bien posés dans certains espaces de Sobolev. Dans un second chapitre on démontre un résultat de limite non relativiste vers le système de Vlasov-Poisson sous des conditions ne portant que sur la densité macroscopique de charges. Pour ce faire on étudie une fonctionnelle quantifiant la distance de Wasserstein entre les solutions faibles des deux systèmes
In this dissertation, we study the Vlasov-Maxwell system of partial differential equations, describing the evolution of the distribution function of charged particles in a plasma. More precisely, we study the regularity of solutions to this system, and the question of the non-relativstic limit.In the first part, we study a Toy-model, combining the Vlasov equation with a system of transport equations. We use the methods developed to obtain and imrpove the Glassey-Strauss criterion, which gives a sufficient condition under which strong solutions do not develop singularities. The loss of regularity occures when the speed of the particles is close to the characteristic speed of the joined hyperbolic system. The same phenomenon occures for the solutions of the Toy-model, but its structure is easier to handle.In the second part, we focus on the question of the non-relativistic limit. After a rescaling of the equations, the speed of light can be considered as a big parameter. When it tends to infinity, it is called the non-relativistic limit. At first order, the non-relativistic limit of the Vlasov-Maxwell system is the Vlasov-Poisson system. First, an iterative method giving arbitrary high non-relativistic approximations is established. These systems combine the Vlasov-equation with elliptic systems of equations, and are well-posed in some weigthed Sobolev spaces. We also prove a result on the non-relativistic limit to the Vlasov-Poisson system under the weaker assumption of boundedness of the macroscopic density. We study a functional quantifying the Wasserstein distance between weak solutions of both systems
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Books on the topic "Vlasov's theory"

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Vedenyapin, Victor. Kinetic Boltzmann, Vlasov and related equations. Waltham, MA: Elsevier Science, 2011.

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Allanson, Oliver. Theory of One-Dimensional Vlasov-Maxwell Equilibria. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97541-2.

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Vedenyapin, Victor, Alexander Sinitsyn, and Eugene Dulov. Kinetic Boltzmann, Vlasov and Related Equations. Elsevier, 2011.

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Vedenyapin, Victor, Alexander Sinitsyn, and Eugene Dulov. Kinetic Boltzmann, Vlasov and Related Equations. Elsevier, 2011.

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Deruelle, Nathalie, and Jean-Philippe Uzan. Kinetic theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0010.

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This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.
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Existence and Uniqueness Theory of the Vlasov Equation. Creative Media Partners, LLC, 2018.

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Existence and Uniqueness Theory of the Vlasov Equation. Franklin Classics, 2018.

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Theory of One-Dimensional Vlasov-Maxwell Equilibria: With Applications to Collisionless Current Sheets and Flux Tubes. Springer, 2018.

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Allanson, Oliver. Theory of One-Dimensional Vlasov-Maxwell Equilibria: With Applications to Collisionless Current Sheets and Flux Tubes. Springer, 2019.

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Book chapters on the topic "Vlasov's theory"

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Koskinen, Hannu E. J. "Vlasov Theory." In Physics of Space Storms, 141–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-00319-6_5.

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Babovsky, H., and H. Neunzert. "The Vlasov Equation: Some Mathematical Aspects." In Kinetic Theory and Gas Dynamics, 37–66. Vienna: Springer Vienna, 1988. http://dx.doi.org/10.1007/978-3-7091-2762-9_2.

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Bonitz, Michael. "Mean–Field Approximation. Quantum Vlasov Equation. Collective Effects." In Quantum Kinetic Theory, 83–117. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24121-0_4.

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Cercignani, Carlo, and Gilberto Medeiros Kremer. "The Vlasov Equation and Related Systems." In The Relativistic Boltzmann Equation: Theory and Applications, 347–69. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8165-4_13.

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Allanson, Oliver. "Introduction." In Theory of One-Dimensional Vlasov-Maxwell Equilibria, 1–40. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97541-2_1.

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Allanson, Oliver. "The Use of Hermite Polynomials for the Inverse Problem in One-Dimensional Vlasov-Maxwell Equilibria." In Theory of One-Dimensional Vlasov-Maxwell Equilibria, 41–67. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97541-2_2.

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Allanson, Oliver. "One-Dimensional Nonlinear Force-Free Current Sheets." In Theory of One-Dimensional Vlasov-Maxwell Equilibria, 69–112. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97541-2_3.

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Allanson, Oliver. "One-Dimensional Asymmetric Current Sheets." In Theory of One-Dimensional Vlasov-Maxwell Equilibria, 113–36. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97541-2_4.

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Allanson, Oliver. "Neutral and Non-neutral Flux Tube Equilibria." In Theory of One-Dimensional Vlasov-Maxwell Equilibria, 137–80. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97541-2_5.

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Allanson, Oliver. "Discussion." In Theory of One-Dimensional Vlasov-Maxwell Equilibria, 181–91. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97541-2_6.

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Conference papers on the topic "Vlasov's theory"

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Orynyak, Igor, and Yaroslav Dubyk. "Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory." In ASME 2018 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/pvp2018-84932.

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Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.
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Harrison, Michael G., Thomas Neukirch, and Eric Stempels. "Theory of 1D Vlasov-Maxwell Equilibria." In COOL STARS, STELLAR SYSTEMS AND THE SUN: Proceedings of the 15th Cambridge Workshop on Cool Stars, Stellar Systems and the Sun. AIP, 2009. http://dx.doi.org/10.1063/1.3099222.

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Xia, Wen-Zhong, Xiu-Gen Jiang, Min Ding, Hong-Zhi Wang, Xing-Hua Chen, Xiao-Ke Cheng, and Wei-Tong Guo. "Analytical element for torsion bar based on vlasov theory." In 2016 International Conference on Mechanics and Architectural Design. WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789813149021_0054.

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Yu, Wenbin, Dewey Hodges, Vitali Volovoi, and Eduardo Fuchs. "The Vlasov Theory of the Variational Asymptotic Beam Sectional Analysis." In 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2004. http://dx.doi.org/10.2514/6.2004-1520.

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Watanabe, T. H., H. Sugama, and S. Ferrando i Margalet. "Gyrokinetic-Vlasov simulations of the ion temperature gradient turbulence in tokamak and helical systems." In THEORY OF FUSION PLASMAS: Joint Varenna-Lausanne International Workshop. AIP, 2006. http://dx.doi.org/10.1063/1.2404557.

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WOODSON, MARSHALL, ERIC JOHNSON, and RAPHAEL HAFTKA. "A VLASOV THEORY FOR LAMINATED COMPOSITE CIRCULAR BEAMS WITH THIN-WALLED OPEN CROSS SECTIONS." In 34th Structures, Structural Dynamics and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1993. http://dx.doi.org/10.2514/6.1993-1619.

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Orynyak, Igor, and Andrii Oryniak. "Efficient Solution for Cylindrical Shell Based on Short and Long (Enhanced Vlasov’s) Solutions on Example of Concentrated Radial Force." In ASME 2018 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/pvp2018-85032.

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There is the general feeling among the scientists that everything what could be performed by theoretical analysis for cylindrical shell was already done in last century, or at least, would require so tremendous efforts, that it will have a little practical significance in our era of domination of powerful and simple to use commercial software. Present authors partly support this point of view. Nevertheless there is one significant mission of theory which is not exhausted yet, but conversely is increasingly required for engineering community. We mean the educational one, which would provide by rather simple means the general understanding of the patterns of deformational behavior, the load transmission mechanisms, and the dimensionless combinations of physical and geometrical parameters which governs these patterns. From practical consideration it is important for avoiding of unnecessary duplicate calculations, for reasonable restriction of the geometrical computer model for long structures, for choosing the correct boundary conditions, for quick evaluation of the correctness of results obtained. The main idea of work is expansion of solution in Fourier series in circumferential direction and subsequent consideration of two simplified differential equations of 4th order (biquadratic ones) instead of one equation of 8th order. The first equation is derived in assumption that all variables change more quickly in axial direction than in circumferential one (short solution), and the second solution is based on the opposite assumption (long solution). One of the most novelties of the work consists in modification of long solution which in fact is well known Vlasov’s semi-membrane theory. Two principal distinctions are suggested: a) hypothesis of inextensibility in circumferential direction is applied only after the elimination of axial force; b) instead of hypothesis zero shear deformation the differential dependence between circumferential displacement and axial one is obtained from equilibrium equation of circumferential forces by neglecting the forth order derivative. The axial force is transmitted to shell by means of short solution which gives rise (as main variables in it) to a radial displacement, its angle of rotation, bending radial moment and radial force. The shear force is also generated by it. The latter one is equilibrated by long solution, which operates by circumferential displacement, axial one, axial force and shear force. The comparison of simplified approach consisted from short solution and enhanced Vlasov’s (long) solution with FEA results for a variety of radius to wall thickness ratio from big values and up to 20 shows a good accuracy of this approach. So, this rather simple approach can be used for solution of different problems for cylindrical shells.
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Tzou, H. S., D. W. Wang, and I. Hagiwara. "Distributed Dynamic Signal Analysis of Piezoelectric Laminated Linear and Nonlinear Toroidal Shells." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/ad-23715.

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Abstract Toroidal shells belong to the shells of revolution family. Dynamic sensing signals and their distributed characteristics of spatially distributed sensors or neurons laminated on thin toroidal shell structures are investigated in this study. Spatially distributed modal voltages and signal patterns are related to the meridional and circumferential membrane/bending strains, based on the direct piezoelectricity, the Gauss theorem, the Maxwell principle and the open-circuit assumption. Linear and nonlinear toroidal shells are defined based on the thin shell theory and the von Karman geometric nonlinearity. With the simplified mode shape functions defined by the Donnell-Mushtari-Vlasov theory, modal dependent distributed signals and detailed signal components of spatially distributed sensors or neurons are defined and these signals are quantitatively illustrated. Signal distributions basically reveal distinct modal characteristics of toroidal shells. Parametric studies suggest that the dominating signal component originates from the meridional membrane strains. Shell dimensions, materials, boundary conditions, natural modes, sensor locations/distributions/sizes, modal strain components, etc. all influence the spatially distributed modal voltages and signal generations.
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Vogt, Mathias, and Philipp Amstutz. "Arbitrary Order Perturbation Theory for Time-Discrete Vlasov Systems with Drift Maps and Poisson Type Collective Kick Maps." In Nonlinear Dynamics and Collective Effects in Particle Beam Physics. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813279612_0015.

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Скубачевский, Александр, and Юлия Беляева. "Stationary solutions of the Vlasov--Poisson equations in torus and applications to the theory of high temperature plasma." In International scientific conference "Ufa autumn mathematical school - 2021". Baskir State University, 2021. http://dx.doi.org/10.33184/mnkuomsh2t-2021-10-06.37.

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Reports on the topic "Vlasov's theory"

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Blaskiewicz, Michael. 3D Vlasov theory of the plasma cascade instability. Office of Scientific and Technical Information (OSTI), October 2019. http://dx.doi.org/10.2172/1572289.

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LOCAL BUCKLING (WRINKLING) OF PROFILED METAL-FACED INSULATING SANDWICH PANELS – A PARAMETRIC STUDY. The Hong Kong Institute of Steel Construction, August 2022. http://dx.doi.org/10.18057/icass2020.p.248.

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This study aims to investigate the effects of various parameters including the height of the profiling region, spacing of profiling ribs, length of the panel, thickness and modulus of the foam core, and thickness of the profiled face sheet, on the local buckling capacity of profiled metal faced insulating sandwich panels. A simplified finite element (FE) modeling approach that models the profiled face sheet as a folded plate structure resting on elastic foundation is adopted. This modeling approach was validated through comparison with tests results and 3D FE modeling of the entire sandwich structure in a previous study conducted by the authors. The two-parameter elastic foundation properties are determined using a modified nonlinear Vlasov foundation model. The results show that all the above-mentioned parameters play important roles in controlling the buckling capacity of the panel. However, the slenderness ratio of the panel is the most dominant parameter among all. Understanding the influence of each of the aforementioned parameters aids in the design process of such panels and provides insight into their local buckling response.
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