291,739 research outputs found
Molecular free path distribution in rarefied gases
We present the results of investigations into the distribution of molecular free paths in rarefied gases using molecular dynamics simulations. Our tests on a range of different gas densities and confinements (unbounded, single bounding wall and parallel bounding walls) indicate that the molecules perform Lévy-type flights, irrespective of the presence of a bounding wall. The free paths most closely follow a power-law distribution. Simulations of gases confined by planar surfaces indicate that the local molecular mean free path varies sharply close to a solid surface. These results may yield new insight into diffusive transport in rarefied gases, in particular, the constitutive behaviour of gas flows in micro- and nanoscale devices
On the length of one-dimensional reactive paths
Motivated by some numerical observations on molecular dynamics simulations,
we analyze metastable trajectories in a very simplecsetting, namely paths
generated by a one-dimensional overdamped Langevin equation for a double well
potential. More precisely, we are interested in so-called reactive paths,
namely trajectories which leave definitely one well and reach the other one.
The aim of this paper is to precisely analyze the distribution of the lengths
of reactive paths in the limit of small temperature, and to compare the
theoretical results to numerical results obtained by a Monte Carlo method,
namely the multi-level splitting approach
Anomalous Paths in Quantum Mechanical Path-Integrals
We investigate modifications of the discrete-time lattice action, for a
quantum mechanical particle in one spatial dimension, that vanish in the
na\"ive continuum limit but which, nevertheless, induce non-trivial effects due
to quantum fluctuations. These effects are seen to modify the geometry of the
paths contributing to the path-integral describing the time evolution of the
particle, which we investigate through numerical simulations. In particular, we
demonstrate the existence of a modified lattice action resulting in paths with
any fractal dimension, d_f, between one and two. We argue that d_f=2 is a
critical value, and we exhibit a type of lattice modification where the
fluctuations in the position of the particle becomes independent of the time
step, in which case the paths are interpreted as superdiffusive L\'{e}vy
flights. We also consider the jaggedness of the paths, and show that this gives
an independent classification of lattice theories.Comment: 7 pages,6 figure
Equilibrium Sampling From Nonequilibrium Dynamics
We present some applications of an Interacting Particle System (IPS)
methodology to the field of Molecular Dynamics. This IPS method allows several
simulations of a switched random process to keep closer to equilibrium at each
time, thanks to a selection mechanism based on the relative virtual work
induced on the system. It is therefore an efficient improvement of usual
non-equilibrium simulations, which can be used to compute canonical averages,
free energy differences, and typical transitions paths
Wardrop Equilibrium in Discrete-Time Selfish Routing with Time-Varying Bounded Delays
This paper presents a multi-commodity, discrete-
time, distributed and non-cooperative routing algorithm, which is
proved to converge to an equilibrium in the presence of
heterogeneous, unknown, time-varying but bounded delays.
Under mild assumptions on the latency functions which describe
the cost associated to the network paths, two algorithms are
proposed: the former assumes that each commodity relies only on
measurements of the latencies associated to its own paths; the
latter assumes that each commodity has (at least indirectly) access
to the measures of the latencies of all the network paths. Both
algorithms are proven to drive the system state to an invariant set
which approximates and contains the Wardrop equilibrium,
defined as a network state in which no traffic flow over the
network paths can improve its routing unilaterally, with the latter
achieving a better reconstruction of the Wardrop equilibrium.
Numerical simulations show the effectiveness of the proposed
approach
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