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 ($\uparrow \Leftrightarrow \downarrow$). 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 $= 1/(3-2q)$, with $q$ the probability that a site has a spin $\uparrow$, and, in the triangular lattice, the average propagation velocity is independent of the scatterers distribution: $= 1/8$. 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 $q$-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 ($Q$) of $1.5<Q<12.5$ nm$^{-1}$, helping to clarify a previous contradiction between experimental and numerical results. The sound velocity shows a positive dispersion, exceeding the hydrodynamic value by $\approx$ 10% at $Q<3.5$ nm$^{-1}$. The $Q^2$ dependence of the sound attenuation $\Gamma(Q)$, reported for other glasses, is found to be the low-$Q$ limit of a more general $\Gamma(Q) \propto \Omega(Q)^2$ law which applies also to the higher $Q$ region, where $\Omega(Q)\propto Q$ 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