We study classical Heisenberg spins on an infinite elastic cylinder. In the continuum limit the Hamiltonian of the system is given by the nonlinear o. model. We investigate the periodic, cylindrically symmetric solution of the sine-Gordon equation (the Euler-Lagrange equation for this Hamiltonian).

We study classical Heisenberg spins coupled by an isotropic or an anisotropic spin-spin interaction on an infinite elastic cylinder. In the continuum limit, the Hamiltonian of the system is given by a nonlinear o. model. We investigate the cylindrically symmetric solutions of the sine-Gordon equation (the Euler-Lagrange equation for this Hamiltonian). The periodic solution as well as the anisotropic one-soliton solution do not satisfy the self-dual equations of Bogomol'nyi [Sov. J. Nucl. Phys. 24, 449 (1976)j which are a necessary condition to reach the minimum energy configuration in each homotopy class. This generates geometrical frustration and produces a geometric eKect: a shrinking of the cylinder coupled with nontrivial spin distributions.

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Interfaces between lamellar and disordered phases, and grain boundaries within lamellar phases, are investigated employing a simple Landau free energy functional. The former are examined using analytic, approximate methods in the weak segregation limit, leading to density profiles which can extend over many wavelengths of the lamellar phase. The latter are studied numerically and exactly. We find a change from smooth chevron configurations typical of small tilt angles to distorted omega configurations at large tilt angles in agreement with experiment.

The Soret motion in binary liquids is shown to arise to a large extent from rectified velocity fluctuations. From a hard-bead model with elastic collisions in a nonuniform temperature, we derive a net force on each molecule, which is proportional to the temperature gradient and depends on the ratio of the molecular masses and moments of inertia. Our findings agree with previous numerical simulations and provide an explanation for the thermal diffusion isotope effect observed for several liquids.

We study the growth of a periodic pattern in one dimension for a model of spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on the intermediate region, where the nonlinearity cannot be neglected anymore, and before the coalescence dominates. The dynamics is captured through the standard technique of a solubility condition performed over a particular family of quasistatic solutions. The main result is that the dynamics along this particular class of solutions can be expressed in terms of a simple ordinary differential equation. The density profile of the stationary regime found at the end of the nonlinear growth is also well characterized. Numerical simulations correspond satisfactorily to the analytical results through three different methods and asymptotic dynamics are well recovered, even far from the region where the approximations hold.

We study interfacial behavior of a lamellar (stripe) phase coexisting with a disordered phase. Systematic analytical expansions are obtained for the interfacial profile in the vicinity of a tricritical point. They are characterized by a wide interfacial region involving a large number of lamellae. Our analytical results apply to systems with one dimensional symmetry in true thermodynamical equilibrium and are of relevance to metastable interfaces between lamellar and disordered phases in two and three dimensions. In addition, good agreement is found with numerical minimization schemes of the full free energy functional having the same one dimensional symmetry. The interfacial energy for the lamellar to disordered transition is obtained in accord with mean field scaling laws of tricritical points.

We present an approximate analytical solution of the Cahn-Hilliard equation describing the coalescence during a first order phase transition. We have identified all the intermediate profiles, stationary solutions of the noiseless Cahn-Hilliard equation. Using properties of the soliton lattices, periodic solutions of the Ginzburg-Landau equation, we have construct a family of ansatz describing continuously the process of destabilization and period doubling predicted in Langer's self similar scenario [1].