214 research outputs found
Understanding and Controlling Regime Switching in Molecular Diffusion
Diffusion can be strongly affected by ballistic flights (long jumps) as well
as long-lived sticking trajectories (long sticks). Using statistical inference
techniques in the spirit of Granger causality, we investigate the appearance of
long jumps and sticks in molecular-dynamics simulations of diffusion in a
prototype system, a benzene molecule on a graphite substrate. We find that
specific fluctuations in certain, but not all, internal degrees of freedom of
the molecule can be linked to either long jumps or sticks. Furthermore, by
changing the prevalence of these predictors with an outside influence, the
diffusion of the molecule can be controlled. The approach presented in this
proof of concept study is very generic, and can be applied to larger and more
complex molecules. Additionally, the predictor variables can be chosen in a
general way so as to be accessible in experiments, making the method feasible
for control of diffusion in applications. Our results also demonstrate that
data-mining techniques can be used to investigate the phase-space structure of
high-dimensional nonlinear dynamical systems.Comment: accepted for publication by PR
(In)commensurability, scaling and multiplicity of friction in nanocrystals and application to gold nanocrystals on graphite
The scaling of friction with the contact size and (in)commensurabilty of
nanoscopic and mesoscopic crystals on a regular substrate are investigated
analytically for triangular nanocrystals on hexagonal substrates. The crystals
are assumed to be stiff, but not completely rigid. Commensurate and
incommensurate configurations are identified systematically. It is shown that
three distinct friction branches coexist, an incommensurate one that does not
scale with the contact size () and two commensurate ones which scale
differently (with and ) and are associated with various
combinations of commensurate and incommensurate lattice parameters and
orientations. This coexistence is a direct consequence of the two-dimensional
nature of the contact layer, and such multiplicity exists in all geometries
consisting of regular lattices. To demonstrate this, the procedure is repeated
for rectangular geometry. The scaling of irregularly shaped crystals is also
considered, and again three branches are found (). Based
on the scaling properties, a quantity is defined which can be used to classify
commensurability in infinite as well as finite contacts. Finally, the
consequences for friction experiments on gold nanocrystals on graphite are
discussed
Criticality in Dynamic Arrest: Correspondence between Glasses and Traffic
Dynamic arrest is a general phenomenon across a wide range of dynamic
systems, but the universality of dynamic arrest phenomena remains unclear. We
relate the emergence of traffic jams in a simple traffic flow model to the
dynamic slow down in kinetically constrained models for glasses. In kinetically
constrained models, the formation of glass becomes a true (singular) phase
transition in the limit . Similarly, using the Nagel-Schreckenberg
model to simulate traffic flow, we show that the emergence of jammed traffic
acquires the signature of a sharp transition in the deterministic limit \pp\to
1, corresponding to overcautious driving. We identify a true dynamical
critical point marking the onset of coexistence between free flowing and jammed
traffic, and demonstrate its analogy to the kinetically constrained glass
models. We find diverging correlations analogous to those at a critical point
of thermodynamic phase transitions.Comment: 4 pages, 4 figure
Chaotic properties of spin lattices near second-order phase transitions
We perform a numerical investigation of the Lyapunov spectra of chaotic
dynamics in lattices of classical spins in the vicinity of second-order
ferromagnetic and antiferromagnetic phase transitions. On the basis of this
investigation, we identify a characteristic of the shape of the Lyapunov
spectra, the "G-index", which exhibits a sharp peak as a function of
temperature at the phase transition, provided the order parameter is capable of
sufficiently strong dynamic fluctuations. As a part of this work, we also
propose a general numerical algorithm for determining the temperature in
many-particle systems, where kinetic energy is not defined.Comment: 9 pages, 11 figure
Lyapunov spectra of billiards with cylindrical scatterers: comparison with many-particle systems
The dynamics of a system consisting of many spherical hard particles can be
described as a single point particle moving in a high-dimensional space with
fixed hypercylindrical scatterers with specific orientations and positions. In
this paper, the similarities in the Lyapunov exponents are investigated between
systems of many particles and high-dimensional billiards with cylindrical
scatterers which have isotropically distributed orientations and homogeneously
distributed positions. The dynamics of the isotropic billiard are calculated
using a Monte-Carlo simulation, and a reorthogonalization process is used to
find the Lyapunov exponents. The results are compared to numerical results for
systems of many hard particles as well as the analytical results for the
high-dimensional Lorentz gas. The smallest three-quarters of the positive
exponents behave more like the exponents of hard-disk systems than the
exponents of the Lorentz gas. This similarity shows that the hard-disk systems
may be approximated by a spatially homogeneous and isotropic system of
scatterers for a calculation of the smaller Lyapunov exponents, apart from the
exponent associated with localization. The method of the partial stretching
factor is used to calculate these exponents analytically, with results that
compare well with simulation results of hard disks and hard spheres.Comment: Submitted to PR
Goldstone modes in Lyapunov spectra of hard sphere systems
In this paper, we demonstrate how the Lyapunov exponents close to zero of a
system of many hard spheres can be described as Goldstone modes, by using a
Boltzmann type of approach. At low densities, the correct form is found for the
wave number dependence of the exponents as well as for the corresponding
eigenvectors in tangent-space. The predicted values for the Lyapunov exponents
belonging to the transverse mode are within a few percent of the values found
in recent simulations, the propagation velocity for the longitudinal mode is
within 1%, but the value for the Lyapunov exponent belonging to the
longitudinal mode deviates from the simulations by 30%. For higher densities,
the predicted values deviate more from the values calculated in the
simulations. These deviations may be due to contributions from ring collisions
and similar terms, which, even at low densities, can contribute to the leading
order.Comment: 12 pages revtex, 5 figures, accepted by Physical Review
The Lyapunov spectrum of the many-dimensional dilute random Lorentz gas
For a better understanding of the chaotic behavior of systems of many moving
particles it is useful to look at other systems with many degrees of freedom.
An interesting example is the high-dimensional Lorentz gas, which, just like a
system of moving hard spheres, may be interpreted as a dynamical system
consisting of a point particle in a high-dimensional phase space, moving among
fixed scatterers. In this paper, we calculate the full spectrum of Lyapunov
exponents for the dilute random Lorentz gas in an arbitrary number of
dimensions. We find that the spectrum becomes flatter with increasing
dimensionality. Furthermore, for fixed collision frequency the separation
between the largest Lyapunov exponent and the second largest one increases
logarithmically with dimensionality, whereas the separations between Lyapunov
exponents of given indices not involving the largest one, go to fixed limits.Comment: 8 pages, revtex, 6 figures, submitted to Physical Review
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