The Experts below are selected from a list of 108 Experts worldwide ranked by ideXlab platform

Jérôme Pousin - One of the best experts on this subject based on the ideXlab platform.

Amol Aggarwal - One of the best experts on this subject based on the ideXlab platform.

  • Limit Shapes and Local Statistics for the Stochastic Six-Vertex Model
    Communications in Mathematical Physics, 2020
    Co-Authors: Amol Aggarwal
    Abstract:

    In this paper we consider the stochastic six-vertex model on a cylinder with arbitrary initial data. First, we show that it exhibits a limit shape in the thermodynamic limit, whose density profile is given by the entropy solution to an explicit, non-Linear Conservation Law that was predicted by Gwa–Spohn (Phys Rev Lett 68:725–728, 1992) and by Reshetikhin–Sridhar (Commun Math Phys 363:741–765, 2018). Then, we show that the local statistics of this model around any continuity point of its limit shape are given by an infinite-volume, translation-invariant Gibbs measure of the appropriate slope.

  • limit shapes and local statistics for the stochastic six vertex model
    arXiv: Probability, 2019
    Co-Authors: Amol Aggarwal
    Abstract:

    In this paper we consider the stochastic six-vertex model on a cylinder with arbitrary initial data. First, we show that it exhibits a limit shape in the thermodynamic limit, whose density profile is given by the entropy solution to an explicit, non-Linear Conservation Law that was predicted by Gwa-Spohn in 1992 and by Reshetikhin-Sridhar in 2018. Then, we show that the local statistics of this model around any continuity point of its limit shape are given by an infinite-volume, translation-invariant Gibbs measure of the appropriate slope.

Olivier Besson - One of the best experts on this subject based on the ideXlab platform.

Gerald Warnecke - One of the best experts on this subject based on the ideXlab platform.

  • Convergence of a splitting scheme applied to the Ruijgrok-Wu model of the Boltzmann equation
    Journal of Computational and Applied Mathematics, 2001
    Co-Authors: Hailiang Liu, Jinghua Wang, Gerald Warnecke
    Abstract:

    This paper deals with upwind splitting schemes for the Ruijgrok–Wu model (Physica A 113 (1982) 401– 416) of the kinetic theory of rare7ed gases in the 8uid-dynamic scaling.We prove the stability and the convergence for these schemes. The relaxation limit is also investigated and the limit equation is proved to be a 7rst-order quasi-Linear Conservation Law. The loss of quasi-monotonicity of the present model makes it necessary to give a more careful analysis of its structure. We also obtain global error estimates in the spaces W s;p for −16s61=p; 16p6∞ and pointwise error estimates for the approximate solution.The proof naturally uses the framework introduced by Nessyahu and Tadmor (SIAM J.Numer Anal.29 (1992) 1505 –1519) due to the convexity of the 8ux function. c

  • Convergence of a splitting scheme applied to the Ruijgrok–Wu model of the Boltzmann equation
    Journal of Computational and Applied Mathematics, 2001
    Co-Authors: Hailiang Liu, Jinghua Wang, Gerald Warnecke
    Abstract:

    AbstractThis paper deals with upwind splitting schemes for the Ruijgrok-Wu model (Physica A 113 (1982) 401–416) of the kinetic theory of rarefied gases in the fluid-dynamic scaling. We prove the stability and the convergence for these schemes. The relaxation limit is also investigated and the limit equation is proved to be a first-order quasi-Linear Conservation Law. The loss of quasi-monotonicity of the present model makes it necessary to give a more careful analysis of its structure. We also obtain global error estimates in the spaces Ws,p for −1⩽s⩽1/p,1⩽p⩽∞ and pointwise error estimates for the approximate solution. The proof naturally uses the framework introduced by Nessyahu and Tadmor (SIAM J. Numer Anal. 29 (1992) 1505–1519) due to the convexity of the flux function

Hailiang Liu - One of the best experts on this subject based on the ideXlab platform.

  • Computational high-frequency wave propogation using the level-set method with applications to the semi-classical limit of the Schrödinger equations
    Communications in Mathematical Sciences, 2003
    Co-Authors: Li-tien Cheng, Hailiang Liu, Stanley Osher
    Abstract:

    We introduce a level set method for computational high frequency wave propagation in dispersive media and consider the application to Linear Schrodinger equation with high frequency initial data. High frequency asymptotics of dispersive equations often lead to the well-known WKB system where the phase of the plane wave evolves according to a nonLinear Hamilton-Jacobi equation and the intensity is governed by a Linear Conservation Law. From the Hamilton-Jacobi equation, wave fronts with multiple phases are constructed by solving a Linear Liouville equation of a vector valued level set function in the phase space. The multi-valued phase itself can be constructed either from an additional Linear hyperbolic equation in phase space or an additional Linear homogeneous equation and component to the level set function in an augmented phase space. This phase is in fact valid in the entire physical domain, but one of the components of the level set function can be used to restrict it to a wave front of interest. The use of the level set method in this numerical approach provides an Eulerian framework that automatically resolves the multi-valued wave fronts and phase from the superposition of solutions of the equations in phase space.

  • Convergence of a splitting scheme applied to the Ruijgrok-Wu model of the Boltzmann equation
    Journal of Computational and Applied Mathematics, 2001
    Co-Authors: Hailiang Liu, Jinghua Wang, Gerald Warnecke
    Abstract:

    This paper deals with upwind splitting schemes for the Ruijgrok–Wu model (Physica A 113 (1982) 401– 416) of the kinetic theory of rare7ed gases in the 8uid-dynamic scaling.We prove the stability and the convergence for these schemes. The relaxation limit is also investigated and the limit equation is proved to be a 7rst-order quasi-Linear Conservation Law. The loss of quasi-monotonicity of the present model makes it necessary to give a more careful analysis of its structure. We also obtain global error estimates in the spaces W s;p for −16s61=p; 16p6∞ and pointwise error estimates for the approximate solution.The proof naturally uses the framework introduced by Nessyahu and Tadmor (SIAM J.Numer Anal.29 (1992) 1505 –1519) due to the convexity of the 8ux function. c

  • Convergence of a splitting scheme applied to the Ruijgrok–Wu model of the Boltzmann equation
    Journal of Computational and Applied Mathematics, 2001
    Co-Authors: Hailiang Liu, Jinghua Wang, Gerald Warnecke
    Abstract:

    AbstractThis paper deals with upwind splitting schemes for the Ruijgrok-Wu model (Physica A 113 (1982) 401–416) of the kinetic theory of rarefied gases in the fluid-dynamic scaling. We prove the stability and the convergence for these schemes. The relaxation limit is also investigated and the limit equation is proved to be a first-order quasi-Linear Conservation Law. The loss of quasi-monotonicity of the present model makes it necessary to give a more careful analysis of its structure. We also obtain global error estimates in the spaces Ws,p for −1⩽s⩽1/p,1⩽p⩽∞ and pointwise error estimates for the approximate solution. The proof naturally uses the framework introduced by Nessyahu and Tadmor (SIAM J. Numer Anal. 29 (1992) 1505–1519) due to the convexity of the flux function