2,129 research outputs found
Transport properties in chaotic and non-chaotic many particles systems
Two deterministic models for Brownian motion are investigated by means of
numerical simulations and kinetic theory arguments. The first model consists of
a heavy hard disk immersed in a rarefied gas of smaller and lighter hard disks
acting as a thermal bath. The second is the same except for the shape of the
particles, which is now square. The basic difference of these two systems lies
in the interaction: hard core elastic collisions make the dynamics of the disks
chaotic whereas that of squares is not. Remarkably, this difference is not
reflected in the transport properties of the two systems: simulations show that
the diffusion coefficients, velocity correlations and response functions of the
heavy impurity are in agreement with kinetic theory for both the chaotic and
the non-chaotic model. The relaxation to equilibrium, however, is very
sensitive to the kind of interaction. These observations are used to reconsider
and discuss some issues connected to chaos, statistical mechanics and
diffusion.Comment: 23 pgs with 8 Figure
Classical light dispersion theory in a regular lattice
We study the dynamics of an infinite regular lattice of classical charged
oscillators. Each individual oscillator is described as a point particle
subject to a harmonic restoring potential, to the retarded electromagnetic
field generated by all the other particles, and to the radiation reaction
expressed according to the Lorentz--Dirac equation. Exact normal mode
solutions, describing the propagation of plane electromagnetic waves through
the lattice, are obtained for the complete linearized system of infinitely many
oscillators. At variance with all the available results, our method is valid
for any values of the frequency, or of the ratio between wavelength and lattice
parameter. A remarkable feature is that the proper inclusion of radiation
reaction in the dynamics of the individual oscillators does not give rise to
any extinction coefficient for the global normal modes of the lattice. The
dispersion relations resulting from our solution are numerically studied for
the case of a simple cubic lattice. New predictions are obtained in this way
about the behavior of the crystal at frequencies near the proper oscillation
frequency of the dipoles.Comment: 15 pages, 1 figure; typos correcte
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
Swapping trajectories: a new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres
Binary encounters between spherical particles in shear flow are studied for a
system bounded by a single planar wall or two parallel planar walls under
creeping flow conditions. We show that wall proximity gives rise to a new class
of binary trajectories resulting in cross-streamline migration of the
particles. The spheres on these new trajectories do not pass each other (as
they would in free space) but instead they swap their cross-streamline
positions. To determine the significance of the wall-induced particle
migration, we have evaluated the hydrodynamic self-diffusion coefficient
associated with a sequence of uncorrelated particle displacements due to binary
particle encounters. The results of our calculations quantitatively agree with
the experimental value obtained by \cite{Zarraga-Leighton:2002} for the
self-diffusivity in a dilute suspension of spheres undergoing shear flow in a
Couette device. We thus show that the wall-induced cross-streamline particle
migration is the source of the anomalously large self-diffusivity revealed by
their experiments.Comment: submited to JF
Performance and selection of winter durum wheat genotypes in different European conventional and organic fields
Sustainability is a key factor for the future of agriculture. Productivity in agriculture has more than tripled in developed countries since the 1950s. Beyond the success of plant breeding, the increased use of inorganic fertilizers, application of pesticides, and spread of irrigation also contributed to this success. However, impressive yield increases started to decline in the 1980s because of the lack of sustainability. One of the most beneficial ways to increase sustainability is organic agriculture. In such agro-ecosystem-based holistic production systems the prerequisite of successful farming is the availability of crop genotypes that perform well. However, selection of winter durum wheat for sub-optimal growing conditions is still mainly neglected, and the organic seed market also lacks of information on credibly tested winter durum varieties suitable for organic agriculture
Persistent random walk on a one-dimensional lattice with random asymmetric transmittances
We study the persistent random walk of photons on a one-dimensional lattice
of random asymmetric transmittances. Each site is characterized by its
intensity transmittance t (t') for photons moving to the right (left)
direction. Transmittances at different sites are assumed independent,
distributed according to a given probability density Distribution. We use the
effective medium approximation and identify two classes of probability density
distribution of transmittances which lead to the normal diffusion of photons.
Monte Carlo simulations confirm our predictions.Comment: 7 pages, submitted to Phys. Rev.
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
Quantum corrections to the Larmor radiation formula in scalar electrodynamics
We use the semi-classical approximation in perturbative scalar quantum
electrodynamics to calculate the quantum correction to the Larmor radiation
formula to first order in Planck's constant in the non-relativistic
approximation, choosing the initial state of the charged particle to be a
momentum eigenstate. We calculate this correction in two cases: in the first
case the charged particle is accelerated by a time-dependent but
space-independent vector potential whereas in the second case it is accelerated
by a time-independent vector potential which is a function of one spatial
coordinate. We find that the corrections in these two cases are different even
for a charged particle with the same classical motion. The correction in each
case turns out to be non-local in time in contrast to the classical
approximation.Comment: 19 page
Signatures of Radiation Reaction in Ultra-Intense Laser Fields
We discuss radiation reaction effects on charges propagating in ultra-intense
laser fields. Our analysis is based on an analytic solution of the
Landau-Lifshitz equation. We suggest to measure radiation reaction in terms of
a symmetry breaking parameter associated with the violation of null translation
invariance in the direction opposite to the laser beam. As the Landau-Lifshitz
equation is nonlinear the energy transfer within the pulse is rather sensitive
to initial conditions. This is elucidated by comparing colliding and fixed
target modes in electron laser collisions.Comment: 8 pages, 6 figure
Self-energy of a scalar charge near higher-dimensional black holes
We study the problem of self-energy of charges in higher dimensional static
spacetimes. Application of regularization methods of quantum field theory to
calculation of the classical self-energy of charges leads to model-independent
results. The correction to the self-energy of a scalar charge due to the
gravitational field of black holes of the higher dimensional
Majumdar-Papapetrou spacetime is calculated exactly. It proves to be zero in
even dimensions, but it acquires non-zero value in odd dimensional spacetimes.
The origin of the self-energy correction in odd dimensions is similar to the
origin the conformal anomalies in quantum field theory in even dimensional
spacetimes.Comment: 9 page
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