1,541 research outputs found
Transport Properties of the Diluted Lorentz Slab
We study the behavior of a point particle incident from the left on a slab of
a randomly diluted triangular array of circular scatterers. Various scattering
properties, such as the reflection and transmission probabilities and the
scattering time are studied as a function of thickness and dilution. We show
that a diffusion model satisfactorily describes the mentioned scattering
properties. We also show how some of these quantities can be evaluated exactly
and their agreement with numerical experiments. Our results exhibit the
dependence of these scattering data on the mean free path. This dependence
again shows excellent agreement with the predictions of a Brownian motion
model.Comment: 14 pages of text in LaTeX, 7 figures in Postscrip
Interaction energies of monosubstituted benzene dimers via nonlocal density functional theory
We present density-functional calculations for the interaction energy of
monosubstituted benzene dimers. Our approach utilizes a recently developed
fully nonlocal correlation energy functional, which has been applied to the
pure benzene dimer and several other systems with promising results. The
interaction energy as a function of monomer distance was calculated for four
different substituents in a sandwich and two T-shaped configurations. In
addition, we considered two methods for dealing with exchange, namely using the
revPBE generalized gradient functional as well as full Hartree-Fock. Our
results are compared with other methods, such as Moller-Plesset and
coupled-cluster calculations, thereby establishing the usefulness of our
approach. Since our density-functional based method is considerably faster than
other standard methods, it provides a computational inexpensive alternative,
which is of particular interest for larger systems where standard calculations
are too expensive or infeasible.Comment: submitted to J. Chem. Phy
Results of Evolution Supervised by Genetic Algorithms
A series of results of evolution supervised by genetic algorithms with
interest to agricultural and horticultural fields are reviewed. New obtained
original results from the use of genetic algorithms on structure-activity
relationships are reported.Comment: 6 pages, 1 Table, 2 figure
A real Lorentz-FitzGerald contraction
Many condensed matter systems are such that their collective excitations at
low energies can be described by fields satisfying equations of motion formally
indistinguishable from those of relativistic field theory. The finite speed of
propagation of the disturbances in the effective fields (in the simplest
models, the speed of sound) plays here the role of the speed of light in
fundamental physics. However, these apparently relativistic fields are immersed
in an external Newtonian world (the condensed matter system itself and the
laboratory can be considered Newtonian, since all the velocities involved are
much smaller than the velocity of light) which provides a privileged coordinate
system and therefore seems to destroy the possibility of having a perfectly
defined relativistic emergent world. In this essay we ask ourselves the
following question: In a homogeneous condensed matter medium, is there a way
for internal observers, dealing exclusively with the low-energy collective
phenomena, to detect their state of uniform motion with respect to the medium?
By proposing a thought experiment based on the construction of a
Michelson-Morley interferometer made of quasi-particles, we show that a real
Lorentz-FitzGerald contraction takes place, so that internal observers are
unable to find out anything about their `absolute ' state of motion. Therefore,
we also show that an effective but perfectly defined relativistic world can
emerge in a fishbowl world situated inside a Newtonian (laboratory) system.
This leads us to reflect on the various levels of description in physics, in
particular regarding the quest towards a theory of quantum gravity.Comment: 6 pages, no figures. Minor changes reflect published versio
Brownian motion and diffusion: from stochastic processes to chaos and beyond
One century after Einstein's work, Brownian Motion still remains both a
fundamental open issue and a continous source of inspiration for many areas of
natural sciences. We first present a discussion about stochastic and
deterministic approaches proposed in the literature to model the Brownian
Motion and more general diffusive behaviours. Then, we focus on the problems
concerning the determination of the microscopic nature of diffusion by means of
data analysis. Finally, we discuss the general conditions required for the
onset of large scale diffusive motion.Comment: RevTeX-4, 11 pages, 5 ps-figures. Chaos special issue "100 Years of
Brownian Motion
A Paradox of State-Dependent Diffusion and How to Resolve It
Consider a particle diffusing in a confined volume which is divided into two
equal regions. In one region the diffusion coefficient is twice the value of
the diffusion coefficient in the other region. Will the particle spend equal
proportions of time in the two regions in the long term? Statistical mechanics
would suggest yes, since the number of accessible states in each region is
presumably the same. However, another line of reasoning suggests that the
particle should spend less time in the region with faster diffusion, since it
will exit that region more quickly. We demonstrate with a simple microscopic
model system that both predictions are consistent with the information given.
Thus, specifying the diffusion rate as a function of position is not enough to
characterize the behaviour of a system, even assuming the absence of external
forces. We propose an alternative framework for modelling diffusive dynamics in
which both the diffusion rate and equilibrium probability density for the
position of the particle are specified by the modeller. We introduce a
numerical method for simulating dynamics in our framework that samples from the
equilibrium probability density exactly and is suitable for discontinuous
diffusion coefficients.Comment: 21 pages, 6 figures. Second round of revisions. This is the version
that will appear in Proc Roy So
Acceleration-Induced Nonlocality: Uniqueness of the Kernel
We consider the problem of uniqueness of the kernel in the nonlocal theory of
accelerated observers. In a recent work, we showed that the convolution kernel
is ruled out as it can lead to divergences for nonuniform accelerated motion.
Here we determine the general form of bounded continuous kernels and use
observational data regarding spin-rotation coupling to argue that the kinetic
kernel given by is the only physically acceptable
solution.Comment: LaTeX file, 2 figures, 14 page
Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two
We consider the billiard dynamics in a non-compact set of R^d that is
constructed as a bi-infinite chain of translated copies of the same
d-dimensional polytope. A random configuration of semi-dispersing scatterers is
placed in each copy. The ensemble of dynamical systems thus defined, one for
each global realization of the scatterers, is called `quenched random Lorentz
tube'. Under some fairly general conditions, we prove that every system in the
ensemble is hyperbolic and almost every system is recurrent, ergodic, and
enjoys some higher chaotic properties.Comment: Final version for J. Stat. Phys., 18 pages, 4 figure
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