3,814 research outputs found
Propagation and organization in lattice random media
We show that a signal can propagate in a particular direction through a model
random medium regardless of the precise state of the medium. As a prototype, we
consider a point particle moving on a one-dimensional lattice whose sites are
occupied by scatterers with the following properties: (i) the state of each
site is defined by its spin (up or down); (ii) the particle arriving at a site
is scattered forward (backward) if the spin is up (down); (iii) the state of
the site is modified by the passage of the particle, i.e. the spin of the site
where a scattering has taken place, flips (). We consider one dimensional and triangular lattices, for which we give a
microscopic description of the dynamics, prove the propagation of a particle
through the scatterers, and compute analytically its statistical properties. In
particular we prove that, in one dimension, the average propagation velocity is
, with the probability that a site has a spin
, and, in the triangular lattice, the average propagation velocity is
independent of the scatterers distribution: . In both cases, the
origin of the propagation is a blocking mechanism, restricting the motion of
the particle in the direction opposite to the ultimate propagation direction,
and there is a specific re-organization of the spins after the passage of the
particle. A detailed mathematical analysis of this phenomenon is, to the best
of our knowledge, presented here for the first time.Comment: 30 pages, 15 separate figures (in PostScript); submitted to J. Stat.
Phy
Dynamics of short polymer chains in solution
We present numerical and analytical results describing the effect of
hydrodynamic interactions on the dynamics of a short polymer chain in solution.
A molecular dynamics algorithm for the polymer is coupled to a direct
simulation Monte Carlo algorithm for the solvent. We give an explicit
expression for the velocity autocorrelation function of the centre of mass of
the polymer which agrees well with numerical results if Brownian dynamics,
hydrodynamic correlations and sound wave scattering are included
Statistics of precursors to fingering processes
We present an analysis of the statistical properties of hydrodynamic field
fluctuations which reveal the existence of precursors to fingering processes.
These precursors are found to exhibit power law distributions, and these power
laws are shown to follow from spatial -Gaussian structures which are
solutions to the generalized non-linear diffusion equation.Comment: 7 pages incl. 5 figs; tp appear in Europhysics Letter
Dynamic correlations in stochastic rotation dynamics
The dynamic structure factor, vorticity and entropy density dynamic
correlation functions are measured for Stochastic Rotation Dynamics (SRD), a
particle based algorithm for fluctuating fluids. This allows us to obtain
unbiased values for the longitudinal transport coefficients such as thermal
diffusivity and bulk viscosity. The results are in good agreement with earlier
numerical and theoretical results, and it is shown for the first time that the
bulk viscosity is indeed zero for this algorithm. In addition, corrections to
the self-diffusion coefficient and shear viscosity arising from the breakdown
of the molecular chaos approximation at small mean free paths are analyzed. In
addition to deriving the form of the leading correlation corrections to these
transport coefficients, the probabilities that two and three particles remain
collision partners for consecutive time steps are derived analytically in the
limit of small mean free path. The results of this paper verify that we have an
excellent understanding of the SRD algorithm at the kinetic level and that
analytic expressions for the transport coefficients derived elsewhere do indeed
provide a very accurate description of the SRD fluid.Comment: 33 pages including 16 figure
High frequency longitudinal and transverse dynamics in water
High-resolution, inelastic x-ray scattering measurements of the dynamic
structure factor S(Q,\omega) of liquid water have been performed for wave
vectors Q between 4 and 30 nm^-1 in distinctly different thermodynamic
conditions (T= 263 - 420 K ; at, or close to, ambient pressure and at P = 2
kbar). In agreement with previous inelastic x-ray and neutron studies, the
presence of two inelastic contributions (one dispersing with Q and the other
almost non-dispersive) is confirmed. The study of their temperature- and
Q-dependence provides strong support for a dynamics of liquid water controlled
by the structural relaxation process. A viscoelastic analysis of the
Q-dispersing mode, associated with the longitudinal dynamics, reveals that the
sound velocity undergoes the complete transition from the adiabatic sound
velocity (c_0) (viscous limit) to the infinite frequency sound velocity
(c_\infinity) (elastic limit). On decreasing Q, as the transition regime is
approached from the elastic side, we observe a decrease of the intensity of the
second, weakly dispersing feature, which completely disappears when the viscous
regime is reached. These findings unambiguously identify the second excitation
to be a signature of the transverse dynamics with a longitudinal symmetry
component, which becomes visible in the S(Q,\omega) as soon as the purely
viscous regime is left.Comment: 28 pages, 12 figure
Critical dynamics of ballistic and Brownian particles in a heterogeneous environment
The dynamic properties of a classical tracer particle in a random, disordered
medium are investigated close to the localization transition. For Lorentz
models obeying Newtonian and diffusive motion at the microscale, we have
performed large-scale computer simulations, demonstrating that universality
holds at long times in the immediate vicinity of the transition. The scaling
function describing the crossover from anomalous transport to diffusive motion
is found to vary extremely slowly and spans at least 5 decades in time. To
extract the scaling function, one has to allow for the leading universal
corrections to scaling. Our findings suggest that apparent power laws with
varying exponents generically occur and dominate experimentally accessible time
windows as soon as the heterogeneities cover a decade in length scale. We
extract the divergent length scales, quantify the spatial heterogeneities in
terms of the non-Gaussian parameter, and corroborate our results by a thorough
finite-size analysis.Comment: 14 page
Science and Film-making
The essay reviews the literature, mostly historical, on the relationship between science and film-making, with a focus on the science documentary. It then discusses the circumstances of the emergence of the wildlife making-of documentary genre. The thesis examined here is that since the early days of cinema, film-making has evolved from being subordinate to science, to being an equal partner in the production of knowledge, controlled by non-scientists
Spurious diffusion in particle simulations of the Kolmogorov flow
Particle simulations of the Kolmogorov flow are analyzed by the
Landau-Lifshitz fluctuating hydrodynamics. It is shown that a spurious
diffusion of the center of mass corrupts the statistical properties of the
flow. The analytical expression for the corresponding diffusion coefficient is
derived.Comment: 10 pages, no figure
High frequency dynamics in a monatomic glass
The high frequency dynamics of glassy Selenium has been studied by Inelastic
X-ray Scattering at beamline BL35XU (SPring-8). The high quality of the data
allows one to pinpoint the existence of a dispersing acoustic mode for
wavevectors () of nm, helping to clarify a previous
contradiction between experimental and numerical results. The sound velocity
shows a positive dispersion, exceeding the hydrodynamic value by 10%
at nm. The dependence of the sound attenuation
, reported for other glasses, is found to be the low- limit of a
more general law which applies also to the
higher region, where no longer holds.Comment: Phys. Rev. Lett. (Accepted
Realistic interpretation of a superposition state does not imply a mixture
Contrary to previous claims, it is shown that, for an ensemble of either
single-particle systems or multi-particle systems, the realistic interpretation
of a superposition state that mathematically describes the ensemble does not
imply that the ensemble is a mixture. Therefore it cannot be argued that the
realistic interpretation is wrong on the basis that some predictions derived
from the mixture are different from the corresponding predictions derived from
the superposition state
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