Structural phase transitions in ionic molecular solids

An overview is presented of our studies on the nature of structural instabilities in relatively complex ionic solids. These are based on parameter-free interionic potentials based on the Gordon-Kim modified electron gas formalism extended to molecular ions.

We describe the manner in which there emerge from these studies quite general concepts of “size” and “shape” as structural determinants. In particular, we discuss how these, and the approximate symmetries that they can produce, can provide a relatively simple structure-based explanation of the origins of incommensurate phases in these systems. However, we also emphasize that the existence of such symmetries does not guarantee an incommensurate phase. This can only be realized if long-range correlations are sufficiently strong to overcome random local disordering. Thus, either the molecular units are partially linked and/or there exist long-range Coulomb interactions between individual units.     

Predicting XAFS scattering path cumulants and XAFS spectra for metals (Cu,Ni, Fe,Ti, Au) using molecular dynamics simulations

The ability of molecular dynamics (MD) simulations to support the analysis of X‐ray absorption fine‐structure (XAFS) data for metals is evaluated. The low‐order cumulants (ΔR, σ², C₃) for XAFS scattering paths are calculated for the metals Cu, Ni, Fe, Ti and Au at 300 K using 28 interatomic potentials of the embedded‐atom method type. The MD cumulant predictions were evaluated within a cumulant expansion XAFS fitting model, using global (path‐independent) scaling factors. Direct simulations of the corresponding XAFS spectra, χ(R), are also performed using MD configurational data in combination with the FEFFab initio code. The cumulant scaling parameters compensate for differences between the real and effective scattering path distributions, and for any errors that might exist in the MD predictions and in the experimental data. The fitted value of ΔR is susceptible to experimental errors and inadvertent lattice thermal expansion in the simulation crystallites. The unadjusted predictions of σ² vary in accuracy, but do not show a consistent bias for any metal except Au, for which all potentials overestimate σ². The unadjusted C₃ predictions produced by different potentials display only order‐of‐magnitude consistency. The accuracy of direct simulations of χ(R) for a given metal varies among the different potentials. For each of the metals Cu, Ni, Fe and Ti, one or more of the tested potentials was found to provide a reasonable simulation of χ(R). However, none of the potentials tested for Au was sufficiently accurate for this purpose.     

量子动力学的约化与自相似(英文)

推广少体问题中的 AGS约化理论 ,证明量子动力学在不同层次具有相同形式 ,称为量子动力学的自相似.By a generalized version of AGS reduction procedure we show that the forms of quantum dynamics at different strata are the same. This is the self similarity of quantum dynamics.     

Dynamics of the current-driven Josephson junction

The irreversible macroscopic dynamics of the Josephson junction coupled to external wires acting as a current source is derived rigorously from the underlying microscopic Hamiltonian quantum mechanics. The external systems are treated in the singular coupling limit. The use of this limit is explicitly justified via an interpretation of the singular coupling limit in terms of the relative magnitudes of system, reservoir, and coupling energies. The qualitative behavior of the macroscopic dynamical equations is shown to depend sensitively and crucially on the interaction between the wires and the superconductors and on the size of the wires: the dc Josephson effect only happens when one lets Cooper pairs be driven into the junction by collective (i.e., small) reservoirs.     

Equipartition and rate of energy exchanges in a model of a radiant cavity

Results of calculations on a model of a radiant cavity, performed in order to explore the relation between stochasticity and geometrical structure of phase space, are presented. The rate of energy exchanges, as indicator of stochasticity, is found to be quite effective. Furthermore, a trend to equipartition for such a quantity is observed at increasing energy, and this implies an increasing rigidity of high harmonic modes also in the stochastic regime of motion. Such a feature may be correlated to the shape of the spectrum which characterizes the radiant cavity with respect to nonlinear chains.     

Phase space density representations in fluid dynamics

Phase space density representations of inviscid fluid dynamics were recently discussed by Abarbanel and Rouhi. Here it is shown that such representations may be simply derived and interpreted by means of the Liouville equation corresponding to the dynamical system of ordinary differential equations that describes fluid particle trajectories. The Hamiltonian and Poisson bracket for the phase space density then emerge as immediate consequences of the corresponding structure of the dynamics. For barotropic fluids, this approach leads by direct construction to the formulation presented by Abarbanel and Rouhi. Extensions of this formulation to inhomogeneous incompressible fluids and to fluids in which the state equation involves an additional transported scalar variable are constructed by augmenting the single-particle dynamics and phase space to include the relevant additional variable.     

A perturbed martingale approach to global optimization

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization.     

Nonlinear hydrodynamic phenomena in Stokes flow regime

We investigate nonlinear phenomena in dispersed two-phase systems under creeping-flow conditions. We consider nonlinear evolution of a single deformed drop and collective dynamics of arrays of hydrodynamically coupled particles. To explore physical mechanisms of system instabilities, chaotic drop evolution, and structural transitions in particle arrays we use simple models, such as small-deformation equations and effective-medium theory. We find numerical and analytical solutions of the simplified governing equations. The small-deformation equations for drop dynamics are analyzed using results of dynamical systems theory. Our investigations shed new light on the dynamics of complex fluids, where the nonlinearity often stems from the evolving boundary conditions in Stokes flow.     

The growth and modification of materials via ion–surface processing

A wide variety of gas phase ions with kinetic energies from 1–10⁷ eV increasingly are being used for the growth and modification of state-of-the-art material interfaces. Ions can be used to deposit thin films; expose fresh interfaces by sputtering; grow mixed interface layers from ions, ambient neutrals, and/or surface atoms; modify the phases of interfaces; dope trace elements into interface regions; impart specific chemical functionalities to a surface; toughen materials; and create micron- and nanometer-scale interface structures. Several examples are developed which demonstrate the variety of technologically important interface modification that is possible with gas phase ions. These examples have been selected to demonstrate how the choice of the ion and its kinetic energy controls modification and deposition for several different materials. Examples are drawn from experiments, computer simulations, fundamental research, and active technological applications. Finally, a list of research areas is provided for which ion–surface modification promises considerable scientific and technological advances in the new millennium.     

Quasi-equilibrium lattice Boltzmann method

A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is developed. Lattice Boltzmann models for isothermal binary mixtures with a given Schmidt number, and for a weakly compressible flow with a given Prandtl number are derived and validated.