Spinodal Decomposition and the Tomita Sum Rule

The scaling properties of a phase-ordering system with a conserved order parameter are studied. The theory developed leads to scaling functions satisfying certain general properties including the Tomita sum rule. The theory also gives good agreement with numerical results for the order parameter scaling function in three dimensions. The values of the associated nonequilibrium decay exponents are given by the known lower bounds.Comment: 15 pages, 6 figure

Dynamics of Ordering of Heisenberg Spins with Torque --- Nonconserved Case. I

We study the dynamics of ordering of a nonconserved Heisenberg magnet. The dynamics consists of two parts --- an irreversible dissipation into a heat bath and a reversible precession induced by a torque due to the local molecular field. For quenches to zero temperature, we provide convincing arguments, both numerically (Langevin simulation) and analytically (approximate closure scheme due to Mazenko), that the torque is irrelevant at late times. We subject the Mazenko closure scheme to systematic numerical tests. Such an analysis, carried out for the first time on a vector order parameter, shows that the closure scheme performs respectably well. For quenches to $T_c$, we show, to ${\cal O}(\epsilon^2)$, that the torque is irrelevant at the Wilson-Fisher fixed point.Comment: 13 pages, REVTEX, and 19 .eps figures, compressed, Submitted to Phys. Rev.

Effect of a magnetic flux on the critical behavior of a system with long range hopping

We study the effect of a magnetic flux in a 1D disordered wire with long range hopping. It is shown that this model is at the metal-insulator transition (MIT) for all disorder values and the spectral correlations are given by critical statistics. In the weak disorder regime a smooth transition between orthogonal and unitary symmetry is observed as the flux strength increases. By contrast, in the strong disorder regime the spectral correlations are almost flux independent. It is also conjectured that the two level correlation function for arbitrary flux is given by the dynamical density-density correlations of the Calogero-Sutherland (CS) model at finite temperature. Finally we describe the classical dynamics of the model and its relevance to quantum chaos.Comment: 5 pages, 4 figure

Coarsening Dynamics of a One-Dimensional Driven Cahn-Hilliard System

We study the one-dimensional Cahn-Hilliard equation with an additional driving term representing, say, the effect of gravity. We find that the driving field $E$ has an asymmetric effect on the solution for a single stationary domain wall (or `kink'), the direction of the field determining whether the analytic solutions found by Leung [J.Stat.Phys.{\bf 61}, 345 (1990)] are unique. The dynamics of a kink-antikink pair (`bubble') is then studied. The behaviour of a bubble is dependent on the relative sizes of a characteristic length scale $E^{-1}$, where $E$ is the driving field, and the separation, $L$, of the interfaces. For $EL \gg 1$ the velocities of the interfaces are negligible, while in the opposite limit a travelling-wave solution is found with a velocity $v \propto E/L$. For this latter case ($EL \ll 1$) a set of reduced equations, describing the evolution of the domain lengths, is obtained for a system with a large number of interfaces, and implies a characteristic length scale growing as $(Et)^{1/2}$. Numerical results for the domain-size distribution and structure factor confirm this behavior, and show that the system exhibits dynamical scaling from very early times.Comment: 20 pages, revtex, 10 figures, submitted to Phys. Rev.

Measurement of Lagrangian velocity in fully developed turbulence

We have developed a new experimental technique to measure the Lagrangian velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler tracking. This method yields a direct access to the velocity of a single particule at a turbulent Reynolds number $R_{\lambda} = 740$. Its dynamics is analyzed with two decades of time resolution, below the Lagrangian correlation time. We observe that the Lagrangian velocity spectrum has a Lorentzian form $E^{L}(\omega) = u_{rms}^{2} T_{L} / (1 + (T_{L}\omega)^{2})$, in agreement with a Kolmogorov-like scaling in the inertial range. The probability density function (PDF) of the velocity time increments displays a change of shape from quasi-Gaussian a integral time scale to stretched exponential tails at the smallest time increments. This intermittency, when measured from relative scaling exponents of structure functions, is more pronounced than in the Eulerian framework.Comment: 4 pages, 5 figures. to appear in PR

Overall time evolution in phase-ordering kinetics

The phenomenology from the time of the quench to the asymptotic behavior in the phase-ordering kinetics of a system with conserved order parameter is investigated in the Bray-Humayun model and in the Cahn-Hilliard-Cook model. From the comparison of the structure factor in the two models the generic pattern of the overall time evolution, based on the sequence ``early linear - intermediate mean field - late asymptotic regime'' is extracted. It is found that the time duration of each of these regimes is strongly dependent on the wave vector and on the parameters of the quench, such as the amplitude of the initial fluctuations and the final equilibrium temperature. The rich and complex crossover phenomenology arising as these parameters are varied can be accounted for in a simple way through the structure of the solution of the Bray-Humayun model.Comment: RevTeX, 14 pages, 18 figures, to appear in Phys. Rev.

Velocity Distribution of Topological Defects in Phase-Ordering Systems

The distribution of interface (domain-wall) velocities ${\bf v}$ in a phase-ordering system is considered. Heuristic scaling arguments based on the disappearance of small domains lead to a power-law tail, $P_v(v) \sim v^{-p}$ for large v, in the distribution of $v \equiv |{\bf v}|$. The exponent p is given by $p = 2+d/(z-1)$, where d is the space dimension and 1/z is the growth exponent, i.e. z=2 for nonconserved (model A) dynamics and z=3 for the conserved case (model B). The nonconserved result is exemplified by an approximate calculation of the full distribution using a gaussian closure scheme. The heuristic arguments are readily generalized to conserved case (model B). The nonconserved result is exemplified by an approximate calculation of the full distribution using a gaussian closure scheme. The heuristic arguments are readily generalized to systems described by a vector order parameter.Comment: 5 pages, Revtex, no figures, minor revisions and updates, to appear in Physical Review E (May 1, 1997

Bilayer Membrane in Confined Geometry: Interlayer Slide and Steric Repulsion

We derived free energy functional of a bilayer lipid membrane from the first principles of elasticity theory. The model explicitly includes position-dependent mutual slide of monolayers and bending deformation. Our free energy functional of liquid-crystalline membrane allows for incompressibility of the membrane and vanishing of the in-plane shear modulus and obeys reflectional and rotational symmetries of the flat bilayer. Interlayer slide at the mid-plane of the membrane results in local difference of surface densities of the monolayers. The slide amplitude directly enters free energy via the strain tensor. For small bending deformations the ratio between bending modulus and area compression coefficient, Kb/KA, is proportional to the square of monolayer thickness, h. Using the functional we performed self-consistent calculation of steric potential acting on bilayer between parallel confining walls separated by distance 2d. We found that temperature-dependent curvature at the minimum of confining potential is enhanced four times for a bilayer with slide as compared with a unit bilayer. We also calculate viscous modes of bilayer membrane between confining walls. Pure bending of the membrane is investigated, which is decoupled from area dilation at small amplitudes. Three sources of viscous dissipation are considered: water and membrane viscosities and interlayer drag. Dispersion has two branches. Confinement between the walls modifies the bending mode with respect to membrane in bulk solution. Simultaneously, inter-layer slipping mode, damped by viscous drag, remains unchanged by confinement.Comment: 23 pages,3 figures, pd

Phase Separation Kinetics in a Model with Order-Parameter Dependent Mobility

We present extensive results from 2-dimensional simulations of phase separation kinetics in a model with order-parameter dependent mobility. We find that the time-dependent structure factor exhibits dynamical scaling and the scaling function is numerically indistinguishable from that for the Cahn-Hilliard (CH) equation, even in the limit where surface diffusion is the mechanism for domain growth. This supports the view that the scaling form of the structure factor is "universal" and leads us to question the conventional wisdom that an accurate representation of the scaled structure factor for the CH equation can only be obtained from a theory which correctly models bulk diffusion.Comment: To appear in PRE, figures available on reques

Long time correlations in Lagrangian dynamics: a key to intermittency in turbulence

New aspects of turbulence are uncovered if one considers flow motion from the perspective of a fluid particle (known as the Lagrangian approach) rather than in terms of a velocity field (the Eulerian viewpoint). Using a new experimental technique, based on the scattering of ultrasounds, we have obtained a direct measurement of particle velocities, resolved at all scales, in a fully turbulent flow. It enables us to approach intermittency in turbulence from a dynamical point of view and to analyze the Lagrangian velocity fluctuations in the framework of random walks. We find experimentally that the elementary steps in the 'walk' have random uncorrelated directions but a magnitude that is extremely long-range correlated in time. Theoretically, we study a Langevin equation that incorporates these features and we show that the resulting dynamics accounts for the observed one- and two-point statistical properties of the Lagrangian velocity fluctuations. Our approach connects the intermittent statistical nature of turbulence to the dynamics of the flow.Comment: 4 pages, 4 figure