v - in t / 9 50 20 01 v 1 3 F eb 1 99 5 Shock waves in the dissipative Toda lattice
نویسندگان
چکیده
We consider the propagation of a shock wave (SW) in the damped Toda lattice. The SW is a moving boundary between two semi-infinite lattice domains with different densities. A steadily moving SW may exist if the damping in the lattice is represented by an “inner” friction, which is a discrete analog of the second viscosity in hydrodynamics. The problem can be considered analytically in the continuum approximation, and the analysis produces an explicit relation between the SW’s velocity and the densities of the two phases. Numerical simulations of the lattice equations of motion demonstrate that a stable SW establishes if the initial velocity is directed towards the less dense phase; in the opposite case, the wave gradually spreads out. The numerically found equilibrium velocity of the SW turns out to be in a very good agreement with the analytical formula even in a strongly discrete case. If the initial velocity is essentially different from the one determined by the densities (but has the correct sign), the velocity does not significantly alter, but instead the SW adjusts itself to the given velocity by sending another SW in the opposite direction.
منابع مشابه
v - in t / 9 90 20 05 v 1 5 F eb 1 99 9 Multiscale Analysis of Discrete Nonlinear
The method of multiscale analysis is constructed for dicrete systems of evolution equations for which the problem is that of the far behavior of an input boundary datum. Discrete slow space variables are introduced in a general setting and the related finite differences are constructed. The method is applied to a series of representative examples: the Toda lattice, the nonlinear Klein-Gordon ch...
متن کامل- qc / 9 50 20 05 v 1 1 F eb 1 99 5 CPP - 94 - 38 ON NON - RIEMANNIAN PARALLEL TRANSPORT IN REGGE
We discuss the possibility of incorporating non-Riemannian parallel transport into Regge calculus. It is shown that every Regge lattice is locally equivalent to a space of constant curvature. Therefore well known-concepts of differential geometry imply the definition of an arbitrary linear affine connection on a Regge lattice.
متن کاملar X iv : s ol v - in t / 9 70 80 01 v 1 4 A ug 1 99 7 Two - dimensional soliton cellular automaton of deautonomized Toda - type
A deautonomized version of the two-dimensional Toda lattice equation is presented. Its ultra-discrete analogue and soliton solutions are also discussed. PACS: 03.20.+i; 03.40.Kf; 04.60.Nc
متن کاملar X iv : h ep - t h / 99 07 01 9 v 1 5 J ul 1 99 9 SOLUTIONS WITH INTERSECTING P - BRANES RELATED TO TODA CHAINS
Solutions in multidimensional gravity with m p-branes related to Toda-like systems (of general type) are obtained. These solutions are defined on a product of n + 1 Ricci-flat spaces M 0 × M 1 ×. .. × M n and are governed by one harmonic function on M 0. The solutions are defined up to the solutions of Laplace and Toda-type equations and correspond to null-geodesics of the (sigma-model) target-...
متن کاملv - in t / 9 61 10 02 v 1 4 N ov 1 99 6 Small - amplitude excitations in a deformable discrete nonlinear Schrödinger equation
Small-amplitude excitations in a deformable discrete nonlinear Schrödinger equation. A detailed analysis of the small-amplitude solutions of a deformed discrete nonlin-ear Schrödinger equation is performed. For generic deformations the system possesses " singular " points which split the infinite chain in a number of independent segments. We show that small-amplitude dark solitons in the vicini...
متن کامل