On the solute coupling at the moving solid/liquid interface during equiaxed solidification

Integral mass conservation was widely accepted for the solute coupling to solve solute redistribution during equiaxed solidification so far. The present study revealed that the integral form was invalid for moving boundary problems as it could not represent the mass balance at the moving interface. Accordingly, differential mass conservation at the solid/liquid interface was used to solve solute diffusion for spherical geometry. The model was applied for hydrogen diffusion in solidification to validate that the hydrogen enrichment was significant and depended on the growth rate. (c) 2006 American Institute of Physics.

Metal-insulator transition and charge ordering in the extended Hubbard model at one-quarter filling

We study, with exact diagonalization, the zero temperature properties of the quarter-filled extended Hubbard model on a square lattice. We find that increasing the ratio of the intersite Coulomb repulsion, V, to the bandwidth drives the system from a metal to a charge ordered insulator. The evolution of the optical conductivity spectrum with increasing V is in agreement with the observed optical conductivity of several layered molecular crystals with the theta and beta crystal structures.

Simulation of the micro-physics of rocks using LSMearth

The particle-based Lattice Solid Model (LSM) was developed to provide a basis to study the physics of rocks and the nonlinear dynamics of earthquakes (MORA and PLACE, 1994; PLACE and MORA, 1999). A new modular and flexible LSM approach has been developed that allows different microphysics to be easily included in or removed from the model. The approach provides a virtual laboratory where numerical experiments can easily be set up and all measurable quantities visualised. The proposed approach provides a means to simulate complex phenomena such as fracturing or localisation processes, and enables the effect of different micro-physics on macroscopic behaviour to be studied. The initial 2-D model is extended to allow three-dimensional simulations to be performed and particles of different sizes to be specified. Numerical bi-axial compression experiments under different confining pressure are used to calibrate the model. By tuning the different microscopic parameters (such as coefficient of friction, microscopic strength and distribution of grain sizes), the macroscopic strength of the material and can be adjusted to be in agreement with laboratory experiments, and the orientation of fractures is consistent with the theoretical value predicted based on Mohr-Coulomb diagram. Simulations indicate that 3-D numerical models have different macroscopic properties than in 2-D and, hence, the model must be recalibrated for 3-D simulations. These numerical experiments illustrate that the new approach is capable of simulating typical rock fracture behaviour. The new model provides a basis to investigate nucleation, rupture and slip pulse propagation in complex fault zones without the previous model limitations of a regular low-level surface geometry and being restricted to two-dimensions.

Effect of Co addition on the lattice parameter, electrical conductivity and sintering of gadolinia-doped ceria

Co-sintering aid has been added to Ce1.9Gd0.1O1.95 (CGO) by treating a commercial powder with Co(NO3)(2) (COCGO), X-ray diffraction (XRD) measurements of lattice parameter indicated that the Co was located on the CGO particle surface after calcination at 650 degreesC. After heat treatment at temperatures above 650 degreesC, the room temperature lattice parameter of CGO was found to increase, indicating redistribution of the Gd. Compared to CGO, the lattice parameter of CGO + 2 cation% Co (2CoCGO) was lower for a given temperature (650-1100 degreesC), A.C. impedance revealed that the lattice conductivity of 2CoCGO was enhanced when densified at lower temperatures, Transmission electron microscopy (TEM) showed that, even after sintering for 4 h at 980 degreesC, most of the Co was located at grain boundaries. (C) 2002 Published by Elsevier Science B.V.

Lattice-gas model of particles with orientational and positional degrees of freedom: Mean-field treatment

We consider a lattice-gas model of particles with internal orientational degrees of freedom. In addition to antiferromagnetic nearest-neighbor (NN) and next-nearest-neighbor (NNN) positional interactions we also consider NN and NNN interactions arising from the internal state of the particles. The system then shows positional and orientational ordering modes with associated phase transitions at Tp and To temperatures at which long-range positional and orientational ordering are, respectively, lost. We use mean-field techniques to obtain a general approach to the study of these systems. By considering particular forms of the orientational interaction function we study coupling effects between both phase transitions arising from the interplay between orientational and positional degrees of freedom. In mean-field approximation coupling effects appear only for the phase transition taking place at lower temperatures. The strength of the coupling depends on the value of the long-range order parameter that remains finite at that temperature.

Lattice-gas model of orientable molecules: Application to liquid crystals

We have analyzed a two-dimensional lattice-gas model of cylindrical molecules which can exhibit four possible orientations. The Hamiltonian of the model contains positional and orientational energy interaction terms. The ground state of the model has been investigated on the basis of Karl¿s theorem. Monte Carlo simulation results have confirmed the predicted ground state. The model is able to reproduce, with appropriate values of the Hamiltonian parameters, both, a smectic-nematic-like transition and a nematic-isotropic-like transition. We have also analyzed the phase diagram of the system by mean-field techniques and Monte Carlo simulations. Mean-field calculations agree well qualitatively with Monte Carlo results but overestimate transition temperatures.

Temperature-dependent orientational ordering on a spherical surface modeled with a lattice spin model

We study the orientational ordering on the surface of a sphere using Monte Carlo and Brownian dynamics simulations of rods interacting with an anisotropic potential. We restrict the orientations to the local tangent plane of the spherical surface and fix the position of each rod to be at a discrete point on the spherical surface. On the surface of a sphere, orientational ordering cannot be perfectly nematic due to the inevitable presence of defects. We find that the ground state of four +1/2 point defects is stable across a broad range of temperatures. We investigate the transition from disordered to ordered phase by decreasing the temperature and find a very smooth transition. We use fluctuations of the local directors to estimate the Frank elastic constant on the surface of a sphere and compare it to the planar case. We observe subdiffusive behavior in the mean square displacement of the defect cores and estimate their diffusion constants.

Reply to “Comment on ‘Temperature-dependent orientational ordering on a spherical surface modeled with a lattice spin model’ ”

A reply to the comment of S. Romano, Phys. Rev. E 2015 on our previous paper is provided.

Glassy states in the stochastic Potts model

We have studied by numerical simulations the relaxation of the stochastic seven-state Potts model after a quench from a high temperature down to a temperature below the first-order transition. For quench temperatures just below the transition temperature the phase ordering occurs by simple coarsening under the action of surface tension. For sufficient low temperatures however the straightening of the interface between domains drives the system toward a metastable disordered state, identified as a glassy state. Escaping from this state occurs, if the quench temperature is nonzero, by a thermal activated dynamics that eventually drives the system toward the equilibrium state. (C) 2009 Elsevier B.V. All rights reserved.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

The n-site approximation for the triplet-creation model

The nonequilibrium phase transition of the one-dimensional triplet-creation model is investigated using the n-site approximation scheme. We find that the phase diagram in the space of parameters (gamma, D), where gamma is the particle decay probability and D is the diffusion probability, exhibits a tricritical point for n >= 4. However, the fitting of the tricritical coordinates (gamma(t), D(t)) using data for 4 <= n <= 13 predicts that gamma(t) becomes negative for n >= 26, indicating thus that the phase transition is always continuous in the limit n -> infinity. However, the large discrepancies between the critical parameters obtained in this limit and those obtained by Monte Carlo simulations, as well as a puzzling non-monotonic dependence of these parameters on the order of the approximation n, argue for the inadequacy of the n-site approximation to study the triplet-creation model for computationally feasible values of n.

Ordered phases in the extended Hubbard model

A novel method to probe the diverse phases for the extended Hubbard model (EHM), including the correlated hopping term, is presented. We extend an effective medium approach [1] to a bipartite lattice, allowing for charge- and/or spin-ordered phases. We calculate the necessary correlation functions to build the EHM phase diagram.

Two versions of the threshold contact model in two dimensions

Two versions of the threshold contact process ordinary and conservative - are studied on a square lattice. In the first, particles are created on active sites, those having at least two nearest neighbor sites occupied, and are annihilated spontaneously. In the conservative version, a particle jumps from its site to an active site. Mean-field analysis suggests the existence of a first-order phase transition, which is confirmed by Monte Carlo simulations. In the thermodynamic limit, the two versions are found to give the same results. (C) 2012 Elsevier B.V. All rights reserved.

Biaxial nematic phase in the Maier-Saupe model for a mixture of discs and cylinders

We analyze the global phase diagram of a Maier-Saupe lattice model with the inclusion of shape-disordered degrees of freedom to mimic a mixture of oblate and prolate molecules (discs and cylinders). In the neighborhood of a Landau multicritical point, solutions of the statistical problem can be written as a Landau-de Gennes expansion for the free energy. If the shape-disordered degrees of freedom are quenched, we confirm the existence of a biaxial nematic structure. If orientational and disorder degrees of freedom are allowed to thermalize, this biaxial solution becomes thermodynamically unstable. Also, we use a two-temperature formalism to mimic the presence of two distinct relaxation times, and show that a slight departure from complete thermalization is enough to stabilize a biaxial nematic phase.

Structure and anomalous solubility for hard spheres in an associating lattice gas model

In this paper we investigate the solubility of a hard-sphere gas in a solvent modeled as an associating lattice gas. The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated both through Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and is shown to exhibit a minimum as a function of temperature. The line of minimum solubility (TmS) coincides with the line of maximum density (TMD) for different solvent chemical potentials, in accordance with the literature on continuous realistic models and on the "cavity" picture. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4743635]