A Phase-field Model for Computer Simulation of Lamellar Structure Formation in y-TiAI

In the present paper, a phase-field model is developed to simulate the formation and evolution of lamellar microstructure in γ-TiAl alloys. The mechanism of formation of TiAl lamellae proposed by Denquin and Naka is incorporated into the model. The model describes the formation and evolution of the face-centered cubic (fcc) stacking lamellar zone followed by the subsequent appearance and growth of the γ-phase, involving both the chemical composition change by atom transfer and the ordering of the fcc lattice. The thermodynamics of the model system and the interaction between the displacive and diffusional transformations are described by a non-equilibrium free energy formulated as a function of concentration and structural order parameter fields. The long-range elastic interactions, arising from the lattice misfit between the α, fcc (A1) and the various orientation variants of the γ-phase are taken into account by incorporating of the elastic strain energy into the total free energy. Simulation studies based on the model successfully predicted some essential features of the lamellar structure. It is found that the formation and evolution of the lamellar structure are predominantly controlled by the minimization of the elastic energy of the interfaces between the different fcc stacking groups, low-symmetry product phase γ and the high-symmetry α-phase, as well as between the various orientation variants of the product phase.

Thermodynamic properties and atomistic structure of the dry amorphous silica surface from a reactive force field model

A force field model of the Keating type supplemented by rules to break, form, and interchange bonds is applied to investigate thermodynamic and structural properties of the amorphous SiO2 surface. A simulated quench from the liquid phase has been carried out for a silica sample made of 3888 silicon and 7776 oxygen atoms arranged on a slab similar to 40 angstrom thick, periodically repeated along two directions. The quench results into an amorphous sample, exposing two parallel square surfaces of similar to 42 nm(2) area each. Thermal averages computed during the quench allow us to determine the surface thermodynamic properties as a function of temperature. The surface tension turns out to be gamma=310 +/- 20 erg/cm(2) at room temperature and gamma=270 +/- 30 at T=2000 K, in fair agreement with available experimental estimates. The entropy contribution Ts-s to the surface tension is relatively low at all temperatures, representing at most similar to 20% of the surface energy. Almost without exceptions, Si atoms are fourfold coordinated and oxygen atoms are twofold coordinated. Twofold and threefold rings appear only at low concentration and are preferentially found in proximity of the surface. Above the glass temperature T-g=1660 +/- 50 K, the mobility of surface atoms is, as expected, slightly higher than that of bulk atoms. The computation of the height-height correlation function shows that the silica surface is rough in the equilibrium and undercooled liquid phase, becoming smooth below the glass temperature T-g.

Mean field approach for tracking similar objects

In this paper, we consider the problem of tracking similar objects. We show how a mean field approach can be used to deal with interacting targets and we compare it with Markov Chain Monte Carlo (MCMC). Two mean field implementations are presented. The first one is more general and uses particle filtering. We discuss some simplifications of the base algorithm that reduce the computation time. The second one is based on suitable Gaussian approximations of probability densities that lead to a set of self-consistent equations for the means and covariances. These equations give the Kalman solution if there is no interaction. Experiments have been performed on two kinds of sequences. The first kind is composed of a single long sequence of twenty roaming ants and was previously analysed using MCMC. In this case, our mean field algorithms obtain substantially better results. The second kind corresponds to selected sequences of a football match in which the interaction avoids tracker coalescence in situations where independent trackers fail.

Random neighbor sandpile model with constrained total energy

We propose as energy-constrained sandpile model with random neighbors. The critical behavior of the model is in the same universality class as the mean-field self-organized criticality sandpile. The critical energy E-c depends on the number of neighbors n of each site, but the various exponents do not. For n = 6, we got that E-c = 0.4545; and a self-similar structure of the energy distribution function with five major peaks is also observed. This is a natural result of system dynamics and the way the system is disturbed.

Universality and self-similarity of an energy-constrained sandpile model with random neighbors

We study an energy-constrained sandpile model with random neighbors. The critical behavior of the model is in the same universality class as the mean-field self-organized criticality sandpile. The critical energy E-c depends on the number of neighbors n for each site, but the various exponents are independent of n. A self-similar structure with n-1 major peaks is developed for the energy distribution p(E) when the system approaches its stationary state. The avalanche dynamics contributes to the major peaks appearing at E-Pk = 2k/(2n - 1) with k = 1,2,...,n-1, while the fine self-similar structure is a natural result of the way the system is disturbed. [S1063-651X(99)10307-6].

Case study of the uniaxial anisotropic spin-1 bilinear-biquadratic Heisenberg model on a triangular lattice

We study the spin-1 model on a triangular lattice in the presence of a uniaxial anisotropy field using a cluster mean-field (CMF) approach. The interplay among antiferromagnetic exchange, lattice geometry, and anisotropy forces Gutzwiller mean-field approaches to fail in a certain region of the phase diagram. There, the CMF method yields two supersolid phases compatible with those present in the spin-1/2 XXZ model onto which the spin-1 system maps. Between these two supersolid phases, the three-sublattice order is broken and the results of the CMF approach depend heavily on the geometry and size of the cluster. We discuss the possible presence of a spin liquid in this region.

A reactive force field simulation of liquid-liquid phase transitions in phosphorus

A force field model of phosphorus has been developed based on density functional (DF) computations and experimental results, covering low energy forms of local tetrahedral symmetry and more compact (simple cubic) structures that arise with increasing pressure. Rules tailored to DF data for the addition, deletion, and exchange of covalent bonds allow the system to adapt the bonding configuration to the thermodynamic state. Monte Carlo simulations in the N-P-T ensemble show that the molecular (P-4) liquid phase, stable at low pressure P and relatively low temperature T, transforms to a polymeric (gel) state on increasing either P or T. These phase changes are observed in recent experiments at similar thermodynamic conditions, as shown by the close agreement of computed and measured structure factors in the molecular and polymer phases. The polymeric phase obtained by increasing pressure has a dominant simple cubic character, while the polymer obtained by raising T at moderate pressure is tetrahedral. Comparison with DF results suggests that the latter is a semiconductor, while the cubic form is metallic. The simulations show that the T-induced polymerization is due to the entropy of the configuration of covalent bonds, as in the polymerization transition in sulfur. The transition observed with increasing P is the continuation at high T of the black P to arsenic (A17) structure observed in the solid state, and also corresponds to a semiconductor to metal transition. (C) 2004 American Institute of Physics.

Generalized compound transport of charged particles in turbulent magnetized plasmas

The transport of charged particles in partially turbulent magnetic systems is investigated from first principles. A generalized compound transport model is proposed, providing an explicit relation between the mean-square deviation of the particle parallel and perpendicular to a magnetic mean field, and the mean-square deviation which characterizes the stochastic field-line topology. The model is applied in various cases of study, and the relation to previous models is discussed.

Spontaneous spin polarization and charge localization in metal nanowires: the role of a geometric constriction

An idealized jellium model of conducting nanowires with a geometric constriction is investigated by density functional theory (DFT) in the local spin density (LSD) approximation. The results reveal a fascinating variety of spin and charge patterns arising in wires of sufficiently low (r(s) >= 15) average electron density, pinned at the indentation by an apparent attractive interaction with the constriction. The spin-resolved frequency-dependent conductivity shows a marked asymmetry in the two spin channels, reflecting the spontaneous spin polarization around the wire neck. The relevance of the computational results is discussed in relation to the so-called 0.7 anomaly found by experiments in the low-frequency conductivity of nanowires at near-breaking conditions (see 2008 J. Phys.: Condens Matter 20, special issue on the 0.7 anomaly). Although our mean-field approach cannot account for the intrinsic many-body effects underlying the 0.7 anomaly, it still provides a diagnostic tool to predict impending transitions in the electronic structure.

Robust nonadiabatic molecular dynamics for metals and insulators

We present a new formulation of the correlated electron-ion dynamics (CEID) scheme, which systematically improves Ehrenfest dynamics by including quantum fluctuations around the mean-field atomic trajectories. We show that the method can simulate models of nonadiabatic electronic transitions and test it against exact integration of the time-dependent Schrodinger equation. Unlike previous formulations of CEID, the accuracy of this scheme depends on a single tunable parameter which sets the level of atomic fluctuations included. The convergence to the exact dynamics by increasing the tunable parameter is demonstrated for a model two level system. This algorithm provides a smooth description of the nonadiabatic electronic transitions which satisfies the kinematic constraints (energy and momentum conservation) and preserves quantum coherence. The applicability of this algorithm to more complex atomic systems is discussed.

Nonlinear response of permanent dipoles in a uniaxial potential to alternating fields

It is shown how the existing theory of the dynamic Kerr effect and nonlinear dielectric relaxation based on the noninertial Brownian rotation of noninteracting rigid dipolar particles may be generalized to take into account interparticle interactions using the Maier-Saupe mean field potential. The results (available in simple closed form) suggest that the frequency dependent nonlinear response provides a method of measuring the Kramers escape rate (or in the analogous problem of magnetic relaxation of fine single domain ferromagnetic particles, the superparamagnetic relaxation time).

Time-dependent tight binding

Starting from a Lagrangian mean-field theory, a set of time-dependent tight-binding equations is derived to describe dynamically and self-consistently an interacting system of quantum electrons and classical nuclei. These equations conserve norm, total energy and total momentum. A comparison with other tight-binding models is made. A previous tight-binding result for forces on atoms in the presence of electrical current flow is generalized to the time-dependent domain and is taken beyond the limit of local charge neutrality.

The Influence of Point Defects and Inhomogeneous Strain on the Functional Behaviour of Thin film Ferroelectrics

An attempt has been made to unequivocally identify the influence that inhomogeneous strain fields, surrounding point defects, have on the functional properties of thin film ferroelectrics. Single crystal thin film lamellae of BaTiO3 have been integrated into capacitor structures, and the functional differences between those annealed in oxygen and those annealed in nitrogen have been mapped. Key features, such as the change in the paraelectric-ferroelectric phase transition from first to second order were noted and found to be consistent with mean field modeling predictions for the effects of inhomogeneous strain. Switching characteristics appeared to be unaffected, suggesting that point defects have a low efficacy in domain wall pinning.