The Experts below are selected from a list of 174 Experts worldwide ranked by ideXlab platform
Fabio Lucio Toninelli - One of the best experts on this subject based on the ideXlab platform.
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lozenge tiling dynamics and convergence to the Hydrodynamic Equation
Communications in Mathematical Physics, 2018Co-Authors: Benoit Laslier, Fabio Lucio ToninelliAbstract:We study a reversible continuous-time Markov dynamics of a discrete (2 + 1)-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the \({L\times L}\) torus, or as a conservative dynamics for a two-dimensional system of interlaced particles. The particle interlacement constraints imply that the equilibrium measures are far from being product Bernoulli: particle correlations decay like the inverse distance squared and interface height fluctuations behave on large scales like a massless Gaussian field. We consider a particular choice of the transition rates, originally proposed in Luby et al. (SIAM J Comput 31:167–192, 2001): in terms of interlaced particles, a particle jump of length n that preserves the interlacement constraints has rate 1/(2n). This dynamics presents special features: the average mutual volume between two interface configurations decreases with time (Luby et al. 2001) and a certain one-dimensional projection of the dynamics is described by the heat Equation (Wilson in Ann Appl Probab 14:274–325, 2004). In this work we prove a Hydrodynamic limit: after a diffusive rescaling of time and space, the height function evolution tends as \({L\to\infty}\) to the solution of a non-linear parabolic PDE. The initial profile is assumed to be C2 differentiable and to contain no “frozen region”. The explicit form of the PDE was recently conjectured (Laslier and Toninelli in Ann Henri Poincare Theor Math Phys 18:2007–2043, 2017) on the basis of local equilibrium considerations. In contrast with the Hydrodynamic Equation for the Langevin dynamics of the Ginzburg–Landau model (Funaki and Spohn in Commun Math Phys 85:1–36, 1997; Nishikawa in Commun Math Phys 127:205–227, 2003), here the mobility coefficient turns out to be a non-trivial function of the interface slope.
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lozenge tiling dynamics and convergence to the Hydrodynamic Equation
arXiv: Probability, 2017Co-Authors: Benoit Laslier, Fabio Lucio ToninelliAbstract:We study a reversible continuous-time Markov dynamics of a discrete $(2+1)$-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the $L\times L$ torus, or as a conservative dynamics for a two-dimensional system of interlaced particles. The particle interlacement constraints imply that the equilibrium measures are far from being product Bernoulli: particle correlations decay like the inverse distance squared and interface height fluctuations behave on large scales like a massless Gaussian field. We consider a particular choice of the transition rates, originally proposed in [Luby-Randall-Sinclair]: in terms of interlaced particles, a particle jump of length $n$ that preserves the interlacement constraints has rate $1/(2n)$. This dynamics presents special features: the average mutual volume between two interface configurations decreases with time and a certain one-dimensional projection of the dynamics is described by the heat Equation. In this work we prove a Hydrodynamic limit: after a diffusive rescaling of time and space, the height function evolution tends as $L\to\infty$ to the solution of a non-linear parabolic PDE. The initial profile is assumed to be $C^2$ differentiable and to contain no "frozen region". The explicit form of the PDE was recently conjectured on the basis of local equilibrium considerations. In contrast with the Hydrodynamic Equation for the Langevin dynamics of the Ginzburg-Landau model [Funaki-Spohn,Nishikawa], here the mobility coefficient turns out to be a non-trivial function of the interface slope.
Benoit Laslier - One of the best experts on this subject based on the ideXlab platform.
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lozenge tiling dynamics and convergence to the Hydrodynamic Equation
Communications in Mathematical Physics, 2018Co-Authors: Benoit Laslier, Fabio Lucio ToninelliAbstract:We study a reversible continuous-time Markov dynamics of a discrete (2 + 1)-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the \({L\times L}\) torus, or as a conservative dynamics for a two-dimensional system of interlaced particles. The particle interlacement constraints imply that the equilibrium measures are far from being product Bernoulli: particle correlations decay like the inverse distance squared and interface height fluctuations behave on large scales like a massless Gaussian field. We consider a particular choice of the transition rates, originally proposed in Luby et al. (SIAM J Comput 31:167–192, 2001): in terms of interlaced particles, a particle jump of length n that preserves the interlacement constraints has rate 1/(2n). This dynamics presents special features: the average mutual volume between two interface configurations decreases with time (Luby et al. 2001) and a certain one-dimensional projection of the dynamics is described by the heat Equation (Wilson in Ann Appl Probab 14:274–325, 2004). In this work we prove a Hydrodynamic limit: after a diffusive rescaling of time and space, the height function evolution tends as \({L\to\infty}\) to the solution of a non-linear parabolic PDE. The initial profile is assumed to be C2 differentiable and to contain no “frozen region”. The explicit form of the PDE was recently conjectured (Laslier and Toninelli in Ann Henri Poincare Theor Math Phys 18:2007–2043, 2017) on the basis of local equilibrium considerations. In contrast with the Hydrodynamic Equation for the Langevin dynamics of the Ginzburg–Landau model (Funaki and Spohn in Commun Math Phys 85:1–36, 1997; Nishikawa in Commun Math Phys 127:205–227, 2003), here the mobility coefficient turns out to be a non-trivial function of the interface slope.
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lozenge tiling dynamics and convergence to the Hydrodynamic Equation
arXiv: Probability, 2017Co-Authors: Benoit Laslier, Fabio Lucio ToninelliAbstract:We study a reversible continuous-time Markov dynamics of a discrete $(2+1)$-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the $L\times L$ torus, or as a conservative dynamics for a two-dimensional system of interlaced particles. The particle interlacement constraints imply that the equilibrium measures are far from being product Bernoulli: particle correlations decay like the inverse distance squared and interface height fluctuations behave on large scales like a massless Gaussian field. We consider a particular choice of the transition rates, originally proposed in [Luby-Randall-Sinclair]: in terms of interlaced particles, a particle jump of length $n$ that preserves the interlacement constraints has rate $1/(2n)$. This dynamics presents special features: the average mutual volume between two interface configurations decreases with time and a certain one-dimensional projection of the dynamics is described by the heat Equation. In this work we prove a Hydrodynamic limit: after a diffusive rescaling of time and space, the height function evolution tends as $L\to\infty$ to the solution of a non-linear parabolic PDE. The initial profile is assumed to be $C^2$ differentiable and to contain no "frozen region". The explicit form of the PDE was recently conjectured on the basis of local equilibrium considerations. In contrast with the Hydrodynamic Equation for the Langevin dynamics of the Ginzburg-Landau model [Funaki-Spohn,Nishikawa], here the mobility coefficient turns out to be a non-trivial function of the interface slope.
Teiji Kunihiro - One of the best experts on this subject based on the ideXlab platform.
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derivation of relativistic Hydrodynamic Equations consistent with relativistic boltzmann Equation by renormalization group method
European Physical Journal A, 2012Co-Authors: Kyosuke Tsumura, Teiji KunihiroAbstract:We review our work on the application of the renormalization-group method to obtain first- and second-order relativistic Hydrodynamics from the relativistic Boltzmann Equation (RBE) as a dynamical system, with some corrections and new unpublished results. For the first-order Equation, we explicitly obtain the distribution function in the asymptotic regime as the invariant manifold of the dynamical system, which turns out to be nothing but the matching condition defining the energy frame, i.e., the Landau-Lifshitz one. It is argued that the frame on which the flow of the relativistic Hydrodynamic Equation is defined must be the energy frame, if the dynamics should be consistent with the underlying RBE. A sketch is also given for derivation of the second-order Hydrodynamic Equation, i.e., extended thermodynamics, which is accomplished by extending the invariant manifold so that it is spanned by excited modes as well as the zero modes (Hydrodynamic modes) of the linearized collision operator. On the basis of thus constructed resummed distribution function, we propose a novel ansatz for the functional form to be used in Grad moment method; it is shown that our theory gives the same expressions for the transport coefficients as those given in the Chapman-Enskog theory as well as the novel expressions for the relaxation times and lengths allowing natural interpretation.
Claudio Landim - One of the best experts on this subject based on the ideXlab platform.
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large deviations for the boundary driven symmetric simple exclusion process
Mathematical Physics Analysis and Geometry, 2003Co-Authors: Lorenzo Bertini, A De Sole, Davide Gabrielli, Giovanni Jonalasinio, Claudio LandimAbstract:The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in nonequilibrium, namely for nonreversible systems. In this paper we consider a simple example of a nonequilibrium situation, the symmetric simple exclusion process in which we let the system exchange particles with the boundaries at two different rates. We prove a dynamical large deviation principle for the empirical density which describes the probability of fluctuations from the solutions of the Hydrodynamic Equation. The so-called quasi potential, which measures the cost of a fluctuation from the stationary state, is then defined by a variational problem for the dynamical large deviation rate function. By characterizing the optimal path, we prove that the quasi potential can also be obtained from a static variational problem introduced by Derrida, Lebowitz, and Speer.
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Hydrodynamic Equation of Symmetric Simple Exclusion Processes
Grundlehren der mathematischen Wissenschaften, 1999Co-Authors: Claude Kipnis, Claudio LandimAbstract:In this chapter we prove the Hydrodynamic behavior of nearest neighbor symmetric simple exclusion processes and show that the Hydrodynamic Equation is the heat Equation: $${\partial _t}\rho = \left( {1/2} \right)\Delta \rho .$$
Suparna Roychowdhury - One of the best experts on this subject based on the ideXlab platform.
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solving a relativistic Hydrodynamic Equation in the presence of a magnetic field for a phase transition in a neutron star
Journal of Physics G, 2012Co-Authors: Ritam Mallick, Rajesh Gopal, Sanjay K Ghosh, S Raha, Suparna RoychowdhuryAbstract:A hadronic to quark matter phase transition may occur inside neutron stars having the central densities of the order of three to ten times the normal nuclear matter saturation density (n0). The transition is expected to be a two-step process; transition from hadronic matter to two-flavour matter and two-flavour matter to β equilibrated charge neutral three-flavour matter. In this paper, we concentrate on the first step of the process and solve the relativistic Hydrodynamic Equations for the conversion front in the presence of a high magnetic field. The Lorentz force due to the magnetic field is included in the energy–momentum tensor by averaging over the polar angles. We find that for an initial dipole configuration of the magnetic field with a sufficiently high value at the surface, the velocity of the front increases considerably.