161 research outputs found
Geometric discretization of the Koenigs nets
We introduce the Koenigs lattice, which is a new integrable reduction of the
quadrilateral lattice (discrete conjugate net) and provides natural integrable
discrete analogue of the Koenigs net. We construct the Darboux-type
transformations of the Koenigs lattice and we show permutability of
superpositions of such transformations, thus proving integrability of the
Koenigs lattice. We also investigate the geometry of the discrete Koenigs
transformation. In particular we characterize the Koenigs transformation in
terms of an involution determined by a congruence conjugate to the lattice.Comment: 17 pages, 2 figures; some spelling and typing errors correcte
Hopping in a Supercooled Lennard-Jones Liquid: Metabasins, Waiting Time Distribution, and Diffusion
We investigate the jump motion among potential energy minima of a
Lennard-Jones model glass former by extensive computer simulation. From the
time series of minima energies, it becomes clear that the energy landscape is
organized in superstructures, called metabasins. We show that diffusion can be
pictured as a random walk among metabasins, and that the whole temperature
dependence resides in the distribution of waiting times. The waiting time
distribution exhibits algebraic decays: for very short times and
for longer times, where near . We
demonstrate that solely the waiting times in the very stable basins account for
the temperature dependence of the diffusion constant.Comment: to be published in Phys. Rev.
What does the potential energy landscape tell us about the dynamics of supercooled liquids and glasses?
For a model glass-former we demonstrate via computer simulations how
macroscopic dynamic quantities can be inferred from a PEL analysis. The
essential step is to consider whole superstructures of many PEL minima, called
metabasins, rather than single minima. We show that two types of metabasins
exist: some allowing for quasi-free motion on the PEL (liquid-like), the others
acting as traps (solid-like). The activated, multi-step escapes from the latter
metabasins are found to dictate the slowing down of dynamics upon cooling over
a much broader temperature range than is currently assumed
Finite-Size Effects in a Supercooled Liquid
We study the influence of the system size on various static and dynamic
properties of a supercooled binary Lennard-Jones liquid via computer
simulations. In this way, we demonstrate that the treatment of systems as small
as N=65 particles yields relevant results for the understanding of bulk
properties. Especially, we find that a system of N=130 particles behaves
basically as two non-interacting systems of half the size.Comment: Proceedings of the III Workshop on Non Equilibrium Phenomena in
Supercooled Fluids, Glasses and Amorphous Materials, Sep 2002, Pis
Time scale for the onset of Fickian diffusion in supercooled liquids
We propose a quantitative measure of a time scale on which Fickian diffusion
sets in for supercooled liquids and use Brownian Dynamics computer simulations
to determine the temperature dependence of this onset time in a Lennard-Jones
binary mixture. The time for the onset of Fickian diffusion ranges between 6.5
and 31 times the relaxation time (the relaxation time is the
characteristic relaxation time of the incoherent intermediate scattering
function). The onset time increases faster with decreasing temperature than the
relaxation time. Mean squared displacement at the onset time increases
with decreasing temperature
Slow dynamics of a confined supercooled binary mixture II: Q space analysis
We report the analysis in the wavevector space of the density correlator of a
Lennard Jones binary mixture confined in a disordered matrix of soft spheres
upon supercooling. In spite of the strong confining medium the behavior of the
mixture is consistent with the Mode Coupling Theory predictions for bulk
supercooled liquids. The relaxation times extracted from the fit of the density
correlator to the stretched exponential function follow a unique power law
behavior as a function of wavevector and temperature. The von Schweidler
scaling properties are valid for an extended wavevector range around the peak
of the structure factor. The parameters extracted in the present work are
compared with the bulk values obtained in literature.Comment: 8 pages with 8 figures. RevTeX. Accepted for publication in Phys.
Rev.
Time evolution of dynamic propensity in a model glass former. The interplay between structure and dynamics
By means of the isoconfigurational method we calculate the change in the
propensity for motion that the structure of a glass-forming system experiences
during its relaxation dynamics. The relaxation of such a system has been
demonstrated to evolve by means of rapid crossings between metabasins of its
potential energy surface (a metabasin being a group of mutually similar,
closely related structures which differ markedly from other metabasins), as
collectively relaxing units (d-clusters) take place. We now show that the
spatial distribution of propensity in the system does not change significantly
until one of these d-clusters takes place. However, the occurrence of a
d-cluster clearly de-correlates the propensity of the particles, thus ending up
with the dynamical influence of the structural features proper of the local
metabasin. We also show an important match between particles that participate
in d-clusters and that which show high changes in their propensity.Comment: 7 pages, 8 figures, articl
Integrable dynamics of Toda-type on the square and triangular lattices
In a recent paper we constructed an integrable generalization of the Toda law
on the square lattice. In this paper we construct other examples of integrable
dynamics of Toda-type on the square lattice, as well as on the triangular
lattice, as nonlinear symmetries of the discrete Laplace equations on the
square and triangular lattices. We also construct the - function
formulations and the Darboux-B\"acklund transformations of these novel
dynamics.Comment: 22 pages, 4 figure
A geometric interpretation of the spectral parameter for surfaces of constant mean curvature
Considering the kinematics of the moving frame associated with a constant
mean curvature surface immersed in S^3 we derive a linear problem with the
spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral
parameter is related to the radius R of the sphere S^3. The application of the
Sym formula to this linear problem yields constant mean curvature surfaces in
E^3. Independently, we show that the Sym formula itself can be derived by an
appropriate limiting process R -> infinity.Comment: 12 page
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