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.

Density functionals from many-body perturbation theory: The band gap for semiconductors and insulators

Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the derivative discontinuity of the exchange-correlation functional. In practice for semiconductors and insulators the band gap calculated within any local or semilocal density approximations underestimates severely the experimental energy gap. On the other hand, calculations with an "exact" exchange potential derived from many-body perturbation theory via the optimized effective potential suggest that improving the exchange-correlation potential approximation can yield a reasonable agreement between the Kohn-Sham band gap and the experimental gap. The results in this work show that this is not the case. In fact, we add to the exact exchange the correlation that corresponds to the dynamical (random phase approximation) screening in the GW approximation. This accurate exchange-correlation potential provides band structures similar to the local density approximation with the corresponding derivative discontinuity that contributes 30%-50% to the energy gap. Our self-consistent results confirm substantially the results for Si and other semiconductors obtained perturbatively [R. W. Godby , Phys. Rev. B 36, 6497 (1987)] and extend the conclusion to LiF and Ar, a wide-gap insulator and a noble-gas solid. (c) 2006 American Institute of Physics.

Universal tight binding model for chemical reactions in solution and at surfaces. I. Organic molecules

As is now well established, a first order expansion of the Hohenberg-Kohn total energy density functional about a trial input density, namely, the Harris-Foulkes functional, can be used to rationalize a non self consistent tight binding model. If the expansion is taken to second order then the energy and electron density matrix need to be calculated self consistently and from this functional one can derive a charge self consistent tight binding theory. In this paper we have used this to describe a polarizable ion tight binding model which has the benefit of treating charge transfer in point multipoles. This admits a ready description of ionic polarizability and crystal field splitting. It is necessary in constructing such a model to find a number of parameters that mimic their more exact counterparts in the density functional theory. We describe in detail how this is done using a combination of intuition, exact analytical fitting, and a genetic optimization algorithm. Having obtained model parameters we show that this constitutes a transferable scheme that can be applied rather universally to small and medium sized organic molecules. We have shown that the model gives a good account of static structural and dynamic vibrational properties of a library of molecules, and finally we demonstrate the model's capability by showing a real time simulation of an enolization reaction in aqueous solution. In two subsequent papers, we show that the model is a great deal more general in that it will describe solvents and solid substrates and that therefore we have created a self consistent quantum mechanical scheme that may be applied to simulations in heterogeneous catalysis.

Modeling relativistic soliton interactions in overdense plasmas: A perturbed nonlinear Schrodinger equation framework

We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrodinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrodinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude

Relativistic theory for localized electrostatic excitations in degenerate electron-ion plasmas

A self-consistent relativistic two-fluid model is proposed for electron-ion plasma dynamics. A one-dimensional geometry is adopted. Electrons are treated as a relativistically degenerate fluid, governed by an appropriate equation of state. The ion fluid is also allowed to be relativistic, but is cold, nondegenerate, and subject only to an electrostatic potential. Exact stationary-profile solutions are sought, at the ionic scale, via the Sagdeev pseudopotential method. The analysis provides the pulse existence region, in terms of characteristic relativistic parameters, associated with the (ultrahigh) particle density.

Free energy and molecular dynamics calculations for the cubic-tetragonal phase transition in zirconia

The high-temperature cubic-tetragonal phase transition of pure stoichiometric zirconia is studied by molecular dynamics (MD) simulations and within the framework of the Landau theory of phase transformations. The interatomic forces are calculated using an empirical, self-consistent, orthogonal tight-binding model, which includes atomic polarizabilities up to the quadrupolar level. A first set of standard MD calculations shows that, on increasing temperature, one particular vibrational frequency softens. The temperature evolution of the free-energy surfaces around the phase transition is then studied with a second set of calculations. These combine the thermodynamic integration technique with constrained MD simulations. The results seem to support the thesis of a second-order phase transition but with unusual, very anharmonic behavior above the transition temperature.

Development of complex classical force fields through force matching to ab initio data: Application to a room-temperature ionic liquid

Recent experimental neutron diffraction data and ab initio molecular dynamics simulation of the ionic liquid dimethylimidazolium chloride ([dmim]Cl) have provided a structural description of the system at the molecular level. However, partial radial distribution functions calculated from the latter, when compared to previous classical simulation results, highlight some limitations in the structural description offered by force fieldbased simulations. With the availability of ab initio data it is possible to improve the classical description of [dmim]Cl by using the force matching approach, and the strategy for fitting complex force fields in their original functional form is discussed. A self-consistent optimization method for the generation of classical potentials of general functional form is presented and applied, and a force field that better reproduces the observed first principles forces is obtained. When used in simulation, it predicts structural data which reproduces more faithfully that observed in the ab initio studies. Some possible refinements to the technique, its application, and the general suitability of common potential energy functions used within many ionic liquid force fields are discussed.

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.

Magnetic tight binding and the iron-chromium enthalpy anomaly

We describe a self-consistent magnetic tight-binding theory based in an expansion of the Hohenberg-Kohn density functional to second order, about a non-spin-polarized reference density. We show how a first order expansion about a density having a trial input magnetic moment leads to a fixed moment model. We employ a simple set of tight-binding parameters that accurately describes electronic structure and energetics, and show these to be transferable between first row transition metals and their alloys. We make a number of calculations of the electronic structure of dilute Cr impurities in Fe, which we compare with results using the local spin density approximation. The fixed moment model provides a powerful means for interpreting complex magnetic configurations in alloys; using this approach, we are able to advance a simple and readily understood explanation for the observed anomaly in the enthalpy of mixing.

Ring currents in azulene

We propose a self consistent polarisable ion tight binding theory for the study of push-pull processes in aromatic molecules. We find that the method quantitatively reproduces ab initio calculations of dipole moments and polarisability. We apply the scheme in a simulation which solves the time dependent Schroedinger equation to follow the relaxation of azulene from the second excited to the ground states. We observe rather spectacular oscillating ring currents which we explain in terms of interference between the HOMO and LUMO states.

Coherent X-ray production via pulse reflection from laser-driven dense electron sheets

A scheme to obtain brilliant x-ray sources by coherent reflection of a counter-propagating pulse from laser-driven dense electron sheets is theoretically and numerically investigated in a self-consistent manner. A radiation pressure acceleration model for the dynamics of the electron sheets blown out from laser-irradiated ultrathin foils is developed and verified by PIC simulations. The first multidimensional and integral demonstration of the scheme by 2D PIC simulations is presented. It is found that the reflected pulse undergoes Doppler-upshift by a factor 4?z2, where ?z = (1- vz2/c2)-1/2 is the effective Lorentz factor of the electron sheet al ong its normal direction. Meanwhile the pulse electric field is intensified by a factor depending on the electron density of the sheet in its moving frame ne/?, where ? is the full Lorentz factor.

Asymptotic modeling of short plane-parallel high-pressure glow discharge

Here a self-consistent continuum model is presented for a narrow gap plane-parallel dc glow discharge. The set of governing equations consisting of continuity and momentum equations for positive ions, fast (emitted by the cathode) and slow electrons (generated by fast electron impact ionization) coupled with Poisson's equation is treated by the technique of matched asymptotic expansions. Explicit results are obtained in the asymptotic limit: (chi delta) much less than 1, where chi = e Phi(a)/kT, delta = (r(D)/L)(2) (Phi(a) is the applied voltage, r(D) is the Debye radius) and pL much greater than 1(Hg mm cm), where p is the gas pressure and L is the gap length. In the case of high pressure, the electron energy relaxation length is much smaller than the gap length, and so the local field approximation is valid. The discharge space divides naturally into a cathode fall sheath, a quasineutral plasma region, and an anode fall sheath. The electric potential distribution obtained for each region in a (semi)analytical form is asymptotically matched to the adjoining regions in the region of overlap. The effects of the gas pressure, gap length, and applied voltage on the length of each region are investigated. (C) 2000 American Institute of Physics. [S1070-664X(00)01302-1].

Universal behaviour of shock precursors in the presence of efficient cosmic ray acceleration

The self-consistent interaction between energetic particles and self-generated hydromagnetic waves in a cosmic ray pressure dominated plasma is considered. Using a three-dimensional hybrid magnetohydrodynamics (MHD)-kinetic code, which utilizes a spherical harmonic expansion of the Vlasov-Fokker-Planck equation, high-resolution simulations of the magnetic field growth including feedback on the cosmic rays are carried out. It is found that for shocks with high cosmic ray acceleration efficiency, the magnetic fields become highly disorganized, resulting in near isotropic diffusion, independent of the initial orientation of the ambient magnetic field. The possibility of sub-Bohm diffusion is demonstrated for parallel shocks, while the diffusion coefficient approaches the Bohm limit from below for oblique shocks. This universal behaviour suggests that Bohm diffusion in the root-mean-squared field inferred from observation may provide a realistic estimate for the maximum energy acceleration time-scale in young supernova remnants. Although disordered, the magnetic field is not self-similar suggesting a non-uniform energy-dependent behaviour of the energetic particle transport in the precursor. Possible indirect radiative signatures of cosmic ray driven magnetic field amplification are discussed.

Universal tight binding model for chemical reactions in solution and at surfaces. II. Water

A revised water model intended for use in condensed phase simulations in the framework of the self consistent polarizable ion tight binding theory is constructed. The model is applied to water monomer, dimer, hexamers, ice, and liquid, where it demonstrates good agreement with theoretical results obtained by more accurate methods, such as DFT and CCSD(T), and with experiment. In particular, the temperature dependence of the self diffusion coefficient in liquid water predicted by the model, closely reproduces experimental curves in the temperature interval between 230 K and 350 K. In addition, and in contrast to standard DFT, the model properly orders the relative densities of liquid water and ice. A notable, but inevitable, shortcoming of the model is underestimation of the static dielectric constant by a factor of two. We demonstrate that the description of inter and intramolecular forces embodied in the tight binding approximation in quantum mechanics leads to a number of valuable insights which can be missing from ab initio quantum chemistry and classical force fields. These include a discussion of the origin of the enhanced molecular electric dipole moment in the condensed phases, and a detailed explanation for the increase of coordination number in liquid water as a function of temperature and compared with ice-leading to insights into the anomalous expansion on freezing. The theory holds out the prospect of an understanding of the currently unexplained density maximum of water near the freezing point. 

Nonreciprocal scattering by stacked nonlinear magneto-active semiconductor layers

The combinatorial frequency generation by the periodic stacks of magnetically biased semiconductor layers has been modelled in a self-consistent problem formulation, taking into account the nonlinear dynamics of carriers. It is shown that magnetic bias not only renders nonreciprocity of the three-wave mixing process but also significantly enhances the nonlinear interactions in the stacks, especially at the frequencies close to the intrinsic magneto-plasma resonances of the constituent layers. The main mechanisms and properties of the combinatorial frequency generation and emission from the stacks are illustrated by the simulation results, and the effects of the individual layer parameters and the structure arrangement on the stack nonlinear and nonreciprocal response are discussed. © 2014 Elsevier B.V. All rights reserved.