Linear Boltzmann Equation
A gPC-intrusive Monte-Carlo scheme for the resolution of the uncertain linear Boltzmann equation
... the linear Boltzmann equa- tion: Bateman equations for neutronics [ 22 , 33 , 34 , 23 , 5 ], Stefan’s law for photonics [ 41 ] or even hydrody- namics with the resolution of the BGK [ 6 ] model, solved with ...
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Spectral convergence of the generalized Polynomial Chaos reduced model obtained from the uncertain linear Boltzmann equation
... 2 L 2 (I×Θ) = 0, the error can still grow quickly with time. It can be theoretically compensated with an increasing polynomial order P . The smoother the solution, the more efficient the increase of P . The fact the gPC ...
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QUANTITATIVE RATES OF CONVERGENCE TO EQUILIBRIUM FOR THE DEGENERATE LINEAR BOLTZMANN EQUATION ON THE TORUS
... [20] M. Hairer, J. Mattingly. Yet another look at Harris’s ergodic theorem for Markov chains Stochastic Analysis, Random fields and Applications VI 109-117 Prog. Probab. 63 Birkauser/Springer Basel AG Basel 2011 [21] D. ...
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From Newton's law to the linear Boltzmann equation without cut-off
... the linear Boltzmann equation without ...Landau equation (see [ 6 ] for a derivation of the Landau equation starting from a particle ...the linear Boltzmann ...
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An Unsplit Monte-Carlo scheme for the resolution of the linear Boltzmann equation coupled to (stiff) Bateman equations
... transport equation with a MC resolution with Bateman ...transport equation and another one for the Bateman system), it is stable and prevents from obtaining non physical ...non linear stochastic ...
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Hypocoercivity in Phi-entropy for the linear relaxation Boltzmann equation on the Torus
... 2019 BOLTZMANN EQUATION ON THE ...relaxation Boltzmann equation in Boltzmann entropy and related entropy functionals, the ...the linear Boltzmann equation with a ...
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Global Solutions of the Boltzmann Equation over R D near Global Maxwellians with Small Mass
... the linear Boltzmann equation, sketched for instance in section ...the linear Boltzmann equation considered by ...the equation of motion we describe defines a one-sided ...
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Q-discrete Painlevé equation and associated linear problem
... Boussinesq equation [12], Kadomstev-Petviashvilli (KP) equa- tion, sine-Gordon equation [50], Korteweg-de Vries (KdV) equation [10] and the modified Korteweg-de Vries (mKdV) equation ...
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The Boltzmann Equation for a Multi-species Mixture Close to Global Equilibrium
... The collision kernels B ij are nonnegative, moreover they contain all the informa- tion about the interaction between two particles and are determined by physics. We mention at this point that one can derive this type ...
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Moment preserving Fourier-Galerkin spectral methods and application to the Boltzmann equation
... 3. this solution in everywhere positive for time large enough; 4. this solution f N c (t, ·) converges to a solution f (t) of the truncated Boltzmann equation ( 2.7 ) with spectral accuracy, uniformly in ...
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A Fokker-Planck model of the Boltzmann equation with correct Prandtl number
... Fokker-Planck equation to get a correct Prandtl number: roughly speaking, the diffusion coefficient (which is the equilibrium temperature) is replaced by a non diagonal temperature ...
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Remarks on non-linear Schrödinger equation with magnetic fields
... seem easy to solve the Cauchy problem in magnetic Sobolev spaces of high degree. To overcome this difficulty, we work as in [5], [4] and approximate the solution of (1.1) by solution of a non-linear Schr¨odinger ...
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A hybrid kinetic-fluid model for solving the gas dynamics Boltzmann-BGK equation
... kinetic equation. Solving a kinetic equation requires the discretization of large number of variables (3 di- mensions in position, 3 dimensions in velocity plus the ...kinetic equation very often ...
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On the stability of equilibrium preserving spectral methods for the homogeneous Boltzmann equation
... Comput. 40, 5 (2018), A2858–A2882. [3] Cercignani, C., Illner, R., and Pulvirenti, M. The Mathematical Theory of Dilute Gases, vol. 106 of Applied Mathematical Sciences. Springer-Verlag, New York, 1994. [4] Dimarco, G., ...
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EQUILIBRIUM SOLUTION TO THE INELASTIC BOLTZMANN EQUATION DRIVEN BY A PARTICLES THERMAL BATH
... study of propagation of L p norms. Second, since the microscopic collision mechanism is affected by the mass ratio of the two involved media (thermal bath and granular material), Povzner-like estimates for G are not ...
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Construction and Analysis of Lattice Boltzmann Methods Applied to a 1D Convection-Diffusion Equation
... classical Boltzmann equation – is obtained with a Chapman-Enskog expansion and not with a Hilbert expansion which is too complicate to give the ...the linear operators are simple 2 × 2 ...
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Stability of global equilibrium for the multi-species Boltzmann equation in $L^\infty$ settings
... x,v (w), where the weight w is either polynomial or stretched exponential, and thus show the exponential stability of µ. The importance of polynomial weights relies on the physically relevant problems of initial data ...
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Resonant dynamics for the quintic non linear Schrödinger equation
... Very recently, Colliander, Keel, Staffilani, Takaoka and Tao [4] have proved a very nice result on the transfer of energy to high frequencies in the cubic defocusing nonlinear Schr¨ odinger equation on the 2 ...
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A new deviational Asymptotic Preserving Monte Carlo method for the homogeneous Boltzmann equation
... Consequently, the numerical techniques are often designed in such a way that the computa- tional cost is as low as possible. In this context, Monte Carlo methods have been the dominant approach to deal with rarefied ...
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Numerical modeling of the splitting of magnetic droplets by multiphase lattice Boltzmann equation
... / La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version acceptée du manuscrit ou la version de l’éditeur. For the publisher’[r] ...
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