Lamellae Stability in Confined Systems with Gravity

The microphase separation of a diblock copolymer melt confined by hard walls and in the presence of a gravitational field is simulated by means of a cell dynamical system model. It is found that the presence of hard walls normal to the gravitational field are key ingredients to the formation of well ordered lamellae in BCP melts. To this effect the currents in the directions normal and parallel to the field are calculated along the interface of a lamellar domain, showing that the formation of lamellae parallel to the hard boundaries and normal to the field correspond to the stable configuration. Also, it is found thet the field increases the interface width.Comment: 4 pages, 2 figures, submitted to Physical Review

The role of the alloy structure in the magnetic behavior of granular systems

The effect of grain size, easy magnetization axis and anisotropy constant distributions in the irreversible magnetic behavior of granular alloys is considered. A simulated granular alloy is used to provide a realistic grain structure for the Monte Carlo simulation of the ZFC-FC curves. The effect of annealing and external field is also studied. The simulation curves are in good agreement with the FC and ZFC magnetization curves measured on melt spun Cu-Co ribbons.Comment: 13 pages, 10 figures, submitted to PR

Density mismatch in thin diblock copolymer films

Thin films of diblock copolymer subject to gravitational field are simulated by means of a cell dynamical system model. The difference in density of the two sides of the molecule and the presence of the field causes the formation of lamellar patterns with orientation parallel to the confining walls even when they are neutral. The concentration profile of those films is analyzed in the weak segregation regime and a functional form for the profile is proposed.Comment: 9 pages and 8 figures. Needs EPSF macros. Submitted to PR

A Comment on the Path Integral Approach to Cosmological Perturbation Theory

It is pointed out that the exact renormalization group approach to cosmological perturbation theory, proposed in Matarrese and Pietroni, JCAP 0706 (2007) 026, arXiv:astro-ph/0703563 and arXiv:astro-ph/0702653, constitutes a misnomer. Rather, having instructively cast this classical problem into path integral form, the evolution equation then derived comes about as a special case of considering how the generating functional responds to variations of the primordial power spectrum.Comment: 2 pages, v2: refs added, published in JCA

Coupled Maps on Trees

We study coupled maps on a Cayley tree, with local (nearest-neighbor) interactions, and with a variety of boundary conditions. The homogeneous state (where every lattice site has the same value) and the node-synchronized state (where sites of a given generation have the same value) are both shown to occur for particular values of the parameters and coupling constants. We study the stability of these states and their domains of attraction. As the number of sites that become synchronized is much higher compared to that on a regular lattice, control is easier to effect. A general procedure is given to deduce the eigenvalue spectrum for these states. Perturbations of the synchronized state lead to different spatio-temporal structures. We find that a mean-field like treatment is valid on this (effectively infinite dimensional) lattice.Comment: latex file (25 pages), 4 figures included. To be published in Phys. Rev.

Scaling in Late Stage Spinodal Decomposition with Quenched Disorder

We study the late stages of spinodal decomposition in a Ginzburg-Landau mean field model with quenched disorder. Random spatial dependence in the coupling constants is introduced to model the quenched disorder. The effect of the disorder on the scaling of the structure factor and on the domain growth is investigated in both the zero temperature limit and at finite temperature. In particular, we find that at zero temperature the domain size, $R(t)$, scales with the amplitude, $A$, of the quenched disorder as $R(t) = A^{-\beta} f(t/A^{-\gamma})$ with $\beta \simeq 1.0$ and $\gamma \simeq 3.0$ in two dimensions. We show that $\beta/\gamma = \alpha$, where $\alpha$ is the Lifshitz-Slyosov exponent. At finite temperature, this simple scaling is not observed and we suggest that the scaling also depends on temperature and $A$. We discuss these results in the context of Monte Carlo and cell dynamical models for phase separation in systems with quenched disorder, and propose that in a Monte Carlo simulation the concentration of impurities, $c$, is related to $A$ by $A \sim c^{1/d}$.Comment: RevTex manuscript 5 pages and 5 figures (obtained upon request via email [email protected]

Early stage scaling in phase ordering kinetics

A global analysis of the scaling behaviour of a system with a scalar order parameter quenched to zero temperature is obtained by numerical simulation of the Ginzburg-Landau equation with conserved and non conserved order parameter. A rich structure emerges, characterized by early and asymptotic scaling regimes, separated by a crossover. The interplay among different dynamical behaviours is investigated by varying the parameters of the quench and can be interpreted as due to the competition of different dynamical fixed points.Comment: 21 pages, latex, 7 figures available upon request from [email protected]

From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example

Derivation of the canonical (or Boltzmann) distribution based only on quantum dynamics is discussed. Consider a closed system which consists of mutually interacting subsystem and heat bath, and assume that the whole system is initially in a pure state (which can be far from equilibrium) with small energy fluctuation. Under the "hypothesis of equal weights for eigenstates", we derive the canonical distribution in the sense that, at sufficiently large and typical time, the (instantaneous) quantum mechanical expectation value of an arbitrary operator of the subsystem is almost equal to the desired canonical expectation value. We present a class of examples in which the above derivation can be rigorously established without any unproven hypotheses.Comment: LaTeX, 8 pages, no figures. The title, abstract and some discussions are modified to stress physical motivation of the work. References are added to [2]. This version will appear in Phys. Rev. Lett. There is an accompanying unpublished note (cond-mat/9707255

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

Scaling and Crossover in the Large-N Model for Growth Kinetics

The dependence of the scaling properties of the structure factor on space dimensionality, range of interaction, initial and final conditions, presence or absence of a conservation law is analysed in the framework of the large-N model for growth kinetics. The variety of asymptotic behaviours is quite rich, including standard scaling, multiscaling and a mixture of the two. The different scaling properties obtained as the parameters are varied are controlled by a structure of fixed points with their domains of attraction. Crossovers arising from the competition between distinct fixed points are explicitely obtained. Temperature fluctuations below the critical temperature are not found to be irrelevant when the order parameter is conserved. The model is solved by integration of the equation of motion for the structure factor and by a renormalization group approach.Comment: 48 pages with 6 figures available upon request, plain LaTe