From random walk to single-file diffusion

We report an experimental study of diffusion in a quasi-one-dimensional (q1D) colloid suspension which behaves like a Tonks gas. The mean squared displacement as a function of time is described well with an ansatz encompassing a time regime that is both shorter and longer than the mean time between collisions. This ansatz asserts that the inverse mean squared displacement is the sum of the inverse mean squared displacement for short time normal diffusion (random walk) and the inverse mean squared displacement for asymptotic single-file diffusion (SFD). The dependence of the single-file 1D mobility on the concentration of the colloids agrees quantitatively with that derived for a hard rod model, which confirms for the first time the validity of the hard rod SFD theory. We also show that a recent SFD theory by Kollmann leads to the hard rod SFD theory for a Tonks gas.Comment: 4 pages, 4 figure

Propagation Failure in Excitable Media

We study a mechanism of pulse propagation failure in excitable media where stable traveling pulse solutions appear via a subcritical pitchfork bifurcation. The bifurcation plays a key role in that mechanism. Small perturbations, externally applied or from internal instabilities, may cause pulse propagation failure (wave breakup) provided the system is close enough to the bifurcation point. We derive relations showing how the pitchfork bifurcation is unfolded by weak curvature or advective field perturbations and use them to demonstrate wave breakup. We suggest that the recent observations of wave breakup in the Belousov-Zhabotinsky reaction induced either by an electric field or a transverse instability are manifestations of this mechanism.Comment: 8 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm

Wave-number locking in spatially forced pattern-forming systems

Abstract -We use the Swift-Hohenberg model and normal-form equations to study wave-number locking in two-dimensional systems as a result of one-dimensional spatially periodic weak forcing. The freedom of the system to respond in a direction transverse to the forcing leads to wavenumber locking in a wide range of forcing wave-numbers, even for weak forcing, unlike the locking in a set of narrow Arnold tongues in one-dimensional systems. Multi-stability ranges of stripe, rectangular, and oblique patterns produce a variety of resonant patterns. The results shed new light on rehabilitation practices of banded vegetation in drylands. Copyright c EPLA, 2008 Frequency locking phenomena in temporally forced oscillators are well understood; a forced oscillator can adjust its frequency of oscillation to a rational fraction of the forcing frequency The spatial counterpart of frequency locking, wavenumber locking, is less well understood. Although much work has been devoted to pattern-forming systems that are subjected to spatially periodic forcing In this letter we analyze wave-number locking phenomena associated with a two-dimensional response to a one-dimensional forcing. We are interested in universal aspects of wave-number locking and therefore base our study on normal-form equations. We derive these equations using a periodically forced Swift-Hohenberg (SH) equation, which helps us motivate the problem and test our analysis using direct numerical solutions. The specific equation we consider is In this equation ε is the distance from the instability point of the unforced zero state to a stationary pattern with a wave-number k 0 ∼ O(1), k f is the forcing wave-number, γ is the intensity of multiplicative forcing and α is the intensity of additive forcing. In the absence of forcing (α = γ = 0) the unstable zero state u = 0 evolves towards a stripe pattern with wavenumber k 0 , the pattern that minimizes the Lyapunov function of the SH equation (se

Domain Walls in Non-Equilibrium Systems and the Emergence of Persistent Patterns

Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a variational principle far from equilibrium allows the coexistence of domain walls propagating in any direction. As a consequence, *persistent* patterns may emerge. We study this mechanism of pattern formation using a non-variational extension of Landau's model for second order phase transitions. PACS numbers: 05.70.Fh, 42.65.Pc, 47.20.Ky, 82.20MjComment: 12 pages LaTeX, 5 postscript figures To appear in Phys. Rev.

Phase Dynamics of Nearly Stationary Patterns in Activator-Inhibitor Systems

The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model are studied using a phase dynamics approach. A Cross-Newell phase equation describing slow and weak modulations of periodic stationary solutions is derived. The derivation applies to the bistable, excitable, and the Turing unstable regimes. In the bistable case stability thresholds are obtained for the Eckhaus and the zigzag instabilities and for the transition to traveling waves. Neutral stability curves demonstrate the destabilization of stationary planar patterns at low wavenumbers to zigzag and traveling modes. Numerical solutions of the model system support the theoretical findings

Atomic-scale surface demixing in a eutectic liquid BiSn alloy

Resonant x-ray reflectivity of the surface of the liquid phase of the Bi$_{43}$Sn$_{57}$ eutectic alloy reveals atomic-scale demixing extending over three near-surface atomic layers. Due to the absence of underlying atomic lattice which typically defines adsorption in crystalline alloys, studies of adsorption in liquid alloys provide unique insight on interatomic interactions at the surface. The observed composition modulation could be accounted for quantitatively by the Defay-Prigogine and Strohl-King multilayer extensions of the single-layer Gibbs model, revealing a near-surface domination of the attractive Bi-Sn interaction over the entropy.Comment: 4 pages (two-column), 3 figures, 1 table; Added a figure, updated references, discussion; accepted at Phys. Rev. Let

On the Origin of Traveling Pulses in Bistable Systems

The interaction between a pair of Bloch fronts forming a traveling domain in a bistable medium is studied. A parameter range beyond the nonequilibrium Ising-Bloch bifurcation is found where traveling domains collapse. Only beyond a second threshold the repulsive front interactions become strong enough to balance attractive interactions and asymmetries in front speeds, and form stable traveling pulses. The analysis is carried out for the forced complex Ginzburg-Landau equation. Similar qualitative behavior is found in the bistable FitzHugh-Nagumo model.Comment: 5 pages, RevTeX. Aric Hagberg: http://t7.lanl.gov/People/Aric/; Ehud Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm

Anomalous layering at the liquid Sn surface

X-ray reflectivity measurements on the free surface of liquid Sn are presented. They exhibit the high-angle peak, indicative of surface-induced layering, also found for other pure liquid metals (Hg, Ga and In). However, a low-angle peak, not hitherto observed for any pure liquid metal, is also found, indicating the presence of a high-density surface layer. Fluorescence and resonant reflectivity measurements rule out the assignment of this layer to surface-segregation of impurities. The reflectivity is modelled well by a 10% contraction of the spacing between the first and second atomic surface layers, relative to that of subsequent layers. Possible reasons for this are discussed.Comment: 8 pages, 9 figures; to be submitted to Phys. Rev. B; updated references, expanded discussio

Fluctuating "Pulled" Fronts: the Origin and the Effects of a Finite Particle Cutoff

Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed $v^*$ for $N \to \infty$ is extremely slow -- going only as $\ln^{-2}N$. In this paper, we study the front propagation in a simple stochastic lattice model. A detailed analysis of the microscopic picture of the front dynamics shows that for the description of the far tip of the front, one has to abandon the idea of a uniformly translating front solution. The lattice and finite particle effects lead to a ``stop-and-go'' type dynamics at the far tip of the front, while the average front behind it ``crosses over'' to a uniformly translating solution. In this formulation, the effect of stochasticity on the asymptotic front speed is coded in the probability distribution of the times required for the advancement of the ``foremost bin''. We derive expressions of these probability distributions by matching the solution of the far tip with the uniformly translating solution behind. This matching includes various correlation effects in a mean-field type approximation. Our results for the probability distributions compare well to the results of stochastic numerical simulations. This approach also allows us to deal with much smaller values of $N$ than it is required to have the $\ln^{-2}N$ asymptotics to be valid.Comment: 26 pages, 11 figures, to appear in Phys. rev.

Order Parameter Equations for Front Transitions: Planar and Circular Fronts

Near a parity breaking front bifurcation, small perturbations may reverse the propagation direction of fronts. Often this results in nonsteady asymptotic motion such as breathing and domain breakup. Exploiting the time scale differences of an activator-inhibitor model and the proximity to the front bifurcation, we derive equations of motion for planar and circular fronts. The equations involve a translational degree of freedom and an order parameter describing transitions between left and right propagating fronts. Perturbations, such as a space dependent advective field or uniform curvature (axisymmetric spots), couple these two degrees of freedom. In both cases this leads to a transition from stationary to oscillating fronts as the parity breaking bifurcation is approached. For axisymmetric spots, two additional dynamic behaviors are found: rebound and collapse.Comment: 9 pages. Aric Hagberg: http://t7.lanl.gov/People/Aric/; Ehud Meron: http://www.bgu.ac.il/BIDR/research/staff/meron.htm