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A probabilistic analysis of the direct simulation of a homogeneous gas is
given. A hierarchy of equations similar to the BBGKY hierarchy for the reduced
probability densities is derived. By invoking the molecular chaos assumption,
an equation similar to the Boltzmann equation for the single particle
probability density and the corresponding H-theorem is derived.
Comment: Based on a talk by A. M. J at international workshop MESODIS'06 (IIT
Kanpur,Dec-2006)
Comment: 23 pages, 13 figures
Comment: submitted to Physical Review E
The efficiency of path sampling simulations can be improved considerably
using the approach of path swapping. For this purpose, we have devised a new
algorithmic procedure based on the transition interface sampling technique. In
the same spirit of parallel tempering, paths between different ensembles are
swapped, but the role of temperature is here played by the interface position.
We have tested the method on the denaturation transition of DNA using the
Peyrard-Bishop-Dauxois model. We find that the new algorithm gives a reduction
of the computational cost by a factor 20.
We use a recently proved fluctuation theorem for the currents to develop the
response theory of nonequilibrium phenomena. In this framework, expressions for
the response coefficients of the currents at arbitrary orders in the
thermodynamic forces or affinities are obtained in terms of the fluctuations of
the cumulative currents and remarkable relations are obtained which are the
consequences of microreversibility beyond Onsager reciprocity relations.
A two-dimensional lattice gas of two species, driven in opposite directions
by an external force, undergoes a jamming transition if the filling fraction is
sufficiently high. Using Monte Carlo simulations, we investigate the growth of
these jams ("clouds"), as the system approaches a non-equilibrium steady state
from a disordered initial state. We monitor the dynamic structure factor
$S(k_x,k_y;t)$ and find that the $k_x=0$ component exhibits dynamic scaling, of
the form $S(0,k_y;t)=t^\beta \tilde{S}(k_yt^\alpha)$. Over a significant range
of times, we observe excellent data collapse with $\alpha=1/2$ and $\beta=1$.
The effects of varying filling fraction and driving force are discussed.
The blasting of brittle materials with sharp particles is an important
fabrication technology in many industrial processes. In particular, for
micro-systems, it allows the production of devices with feature sizes down to
few tens of microns. An important parameter of this process is the surface
roughness of post-blasted surfaces. In this work the scaling properties of
Pyrex glass and silicon surfaces after bombardment with alumina particles is
investigated. The targets were bombarded at normal incidence using alumina
particles with two different average sizes, $29\mu m$ and $9\mu m$,
respectively. This investigation indicates that the resulting surfaces have
multifractal properties. Applying multifractal detrended fluctuation analysis
(MFDFA) allowed us to determine the singularity spectrum of the surfaces. This
spectrum did not depe...
Comment: 35 pages, 10 figures, corresponding author: G. Le Caer
Comment: 78 pages, based on PhD thesis, see the Preface for more comments
