Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models

We consider least energy solutions to the nonlinear equation $-\Delta_g u=f(r,u)$ posed on a class of Riemannian models $(M,g)$ of dimension $n\ge 2$ which include the classical hyperbolic space $\mathbb H^n$ as well as manifolds with unbounded sectional geometry. Partial symmetry and existence of least energy solutions is proved for quite general nonlinearities $f(r,u)$, where $r$ denotes the geodesic distance from the pole of $M$

Dynamical heterogeneities as fingerprints of a backbone structure in Potts models

We investigate slow non-equilibrium dynamical processes in two-dimensional $q$--state Potts model with both ferromagnetic and $\pm J$ couplings. Dynamical properties are characterized by means of the mean-flipping time distribution. This quantity is known for clearly unveiling dynamical heterogeneities. Using a two-times protocol we characterize the different time scales observed and relate them to growth processes occurring in the system. In particular we target the possible relation between the different time scales and the spatial heterogeneities originated in the ground state topology, which are associated to the presence of a backbone structure. We perform numerical simulations using an approach based on graphics processing units (GPUs) which permits to reach large system sizes. We present evidence supporting both the idea of a growing process in the preasymptotic regime of the glassy phases and the existence of a backbone structure behind this processes.Comment: 9 pages, 7 figures, Accepted for publication in PR

Short-time dynamics of finite-size mean-field systems

We study the short-time dynamics of a mean-field model with non-conserved order parameter (Curie-Weiss with Glauber dynamics) by solving the associated Fokker-Planck equation. We obtain closed-form expressions for the first moments of the order parameter, near to both the critical and spinodal points, starting from different initial conditions. This allows us to confirm the validity of the short-time dynamical scaling hypothesis in both cases. Although the procedure is illustrated for a particular mean-field model, our results can be straightforwardly extended to generic models with a single order parameter.Comment: accepted for publication in JSTA

Light Microscopy Measurements of Ice Recrystallization in Frozen Corn Starch Pastes Using Isothermal Freeze Fixation

Isothermal freeze fixation was used to analyze ice recrystallization by light microscopy in a 10 % (W/W) frozen corn starch paste during storage at temperatures in the range of -5 to -20 °C. Different formulations were tested in order to obtain a suitable fixative for this method of indirect observation of the ice crystals. A solution of formaldehyde, ethanol and water (10:45:45 V:V) was selected because it minimized substitution-induced distortion and contraction of the matrix. The diffusion coefficients of the selected fixative in the frozen system were measured at different temperatures in conditions of unidirectional mass transfer in a semi - infinite medium. The activation energy for diffusion was determined (Ea = 95.11 ± I. 15 KJ/mol). Fixation times for the frozen starch paste at different temperatures were predicted from a mathematical model for unidirectional mass transfer with a discontinuous diffusion coefficient. Matrix contraction during the different stages of the freeze fixation method was evaluated. Recrystallization of ice in frozen corn starch pastes during storage was analyzed by the measurement of the changes in ice crystal equivalent diameters on the micrographs. A kinetic equation for recrystallization was fitted to the experimental data to obtain the corresponding parameters. Contraction of the matrix affects the kinetic constants but has no effect on activation energy. The effect of recrystallization during fixation on ice crystal measurements was not significant

Phase separation of the Potts model in que square lattice

When the two dimensional q-color Potts model in the square lattice is quenched at zero temperature with Glauber dynamics, the energy decreases in time following an Allen-Cahn power law, and the system converges to a phase with energy higher than the ground state energy after an arbitrary large time when q>4. At low but finite temperature, it cesses to obey the power-law regime and orders after a very long time, which increases with q, and before which it performs a domain growth process which tends to be slower as q increases. We briefly present and comment numerical results on the ordering at nonzero temperature.Comment: 3 pages, 1 figure, proceedings of the "International Workshop on Complex sytems", June 2006 in Santander (Spain