26,515 research outputs found
A discrete linearizability test based on multiscale analysis
In this paper we consider the classification of dispersive linearizable
partial difference equations defined on a quad-graph by the multiple scale
reduction around their harmonic solution. We show that the A_1, A_2 and A_3
linearizability conditions restrain the number of the parameters which enter
into the equation. A subclass of the equations which pass the A_3
C-integrability conditions can be linearized by a Mobius transformation
The ontology of temperature in nonequilibrium systems
The laws of thermodynamics provide a clear concept of the temperature for an
equilibrium system in the continuum limit. Meanwhile, the equipartition theorem
allows one to make a connection between the ensemble average of the kinetic
energy and the uniform temperature. When a system or its environment is far
from equilibrium, however, such an association does not necessarily apply. In
small systems, the regression hypothesis may not even apply. Herein, we show
that in small nonequilibrium systems, the regression hypothesis still holds
though with a generalized definition of the temperature. The latter must now be
defined for each such manifestation.Comment: J.Chem.Phys. (in press); 23 pages, 3 figures, 1 tabl
The projection of a nonlocal mechanical system onto the irreversible generalized Langevin equation, II: Numerical simulations
The irreversible generalized Langevin equation (iGLE) contains a
nonstationary friction kernel that in certain limits reduces to the GLE with
space-dependent friction. For more general forms of the friction kernel, the
iGLE was previously shown to be the projection of a mechanical system with a
time-dependent Hamiltonian. [R. Hernandez, J. Chem. Phys. 110, 7701 (1999)] In
the present work, the corresponding open Hamiltonian system is further
explored. Numerical simulations of this mechanical system illustrate that the
time dependence of the observed total energy and the correlations of the
solvent force are in precise agreement with the projected iGLE.Comment: 8 pages, 9 figures, submitted to J. Chem. Phy
Magneto-optical imaging of magnetic deflagration in Mn12-Acetate
For the first time, the morphology and dynamics of spin avalanches in
Mn12-Acetate crystals using magneto-optical imaging has been explored. We
observe an inhomogeneous relaxation of the magnetization, the spins reversing
first at one edge of the crystal and a few milliseconds later at the other end.
Our data fit well with the theory of magnetic deflagration, demonstrating that
very slow deflagration rates can be obtained, which makes new types of
experiments possible.Comment: 5 two-column pages, 3 figures, EPL styl
Multiscale expansion and integrability properties of the lattice potential KdV equation
We apply the discrete multiscale expansion to the Lax pair and to the first
few symmetries of the lattice potential Korteweg-de Vries equation. From these
calculations we show that, like the lowest order secularity conditions give a
nonlinear Schroedinger equation, the Lax pair gives at the same order the
Zakharov and Shabat spectral problem and the symmetries the hierarchy of point
and generalized symmetries of the nonlinear Schroedinger equation.Comment: 10 pages, contribution to the proceedings of the NEEDS 2007
Conferenc
On the Integrability of the Discrete Nonlinear Schroedinger Equation
In this letter we present an analytic evidence of the non-integrability of
the discrete nonlinear Schroedinger equation, a well-known discrete evolution
equation which has been obtained in various contexts of physics and biology. We
use a reductive perturbation technique to show an obstruction to its
integrability.Comment: 4 pages, accepted in EP
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