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.