Particle Representation Research Articles

Charge transfer between fullerenes and highly charged noble gas ions

A semiclassical model for the description of charge-exchange processes in collisions between fullerenes and multiply charged ions is developed. It is based on the decay model combined with the impact-parameter representation for the heavy particles' relative motion. The charge-transfer process in our model is treated as a transition of the active electron over and under the quasistatic potential barrier formed by the electric fields of the target and projectile. Due to the high electron delocalization on the surface of fullerene we represent it as a perfectly conducting hard sphere, whose radius is determined by the dipole polarizability of C60. The energies of the active electrons are assumed to be equal to the corresponding ionization potentials including the Stark-shift effect. We have developed an efficient technique for the evaluation of the electron transmission coefficient through the asymmetric potential barrier. It is shown that our model provides a good agreement with the available experimental data on single-electron charge-exchange processes. Moreover, it allows us to get an adequate description of multi-electron transfer processes. The first theoretical results on charge exchange between the fullerene ions and highly charged ions have been obtained.

Regularization of the interaction and renormalization of the physical constants in the clothed particle representation within the quantum field theory

The possibility of covariant regularization of trilinear Yukawa-type interaction has been investigated within the simplified standard quantum field theory. The properties of the vertex functions, conditioned by the Lorentz invariance of particle mass shifts, and regularizing functions in the lowest interaction orders have been studied within the clothed-particle representation.

Single particle representation of parabose extension of conformal supersymmetry

AbstractWe consider generalized conformal supersymmetry constructed as parabose N = 4 algebra. It is shown that Green's ansatz representations have, in this context, natural interpretation as multi particle spaces. The simplest nontrivial representation is shown to correspond to a massless particle of arbitrary helicity, and some peculiar properties of this space are pointed out.

N-conserving Bogoliubov vacuum of a two-component Bose–Einstein condensate: density fluctuations close to a phase-separation condition

Two-component Bose–Einstein condensates are considered within a number conserving version of the Bogoliubov theory. We show that the Bogoliubov vacuum state can be obtained in the particle representation in a simple form. We predict considerable density fluctuations in finite systems close to the phase-separation regime. We analyze homogeneous condensates and condensates in a double-well potential.

Nonexplosion of a class of semilinear equations via branching particle representations

We consider a branching particle system where an individual particle gives birth to a random number of offspring at the place where it dies. The probability distribution of the number of offspring is given bypk,k= 2, 3, …. The corresponding branching process is related to the semilinear partial differential equationforx∈ ℝd, whereAis the infinitesimal generator of a multiplicative semigroup and thepks,k= 2, 3, …, are nonnegative functions such thatWe obtain sufficient conditions for the existence of global positive solutions to semilinear equations of this form. Our results extend previous work by Nagasawa and Sirao (1969) and others.

Nonexplosion of a class of semilinear equations via branching particle representations

We consider a branching particle system where an individual particle gives birth to a random number of offspring at the place where it dies. The probability distribution of the number of offspring is given by pk, k = 2, 3, …. The corresponding branching process is related to the semilinear partial differential equation for x ∈ ℝd, where A is the infinitesimal generator of a multiplicative semigroup and the pks, k = 2, 3, …, are nonnegative functions such that We obtain sufficient conditions for the existence of global positive solutions to semilinear equations of this form. Our results extend previous work by Nagasawa and Sirao (1969) and others.

Low-noise particle algorithms for extended magnetohydrodynamic closure

Two new low-noise particle closure methods are developed and tested. Closure of a small set of moment equations is accomplished with first or second order moments computed from a delta-f particle in cell (δf PIC) distribution. Conservation laws are developed and in one case apply to the discrete system, showing that squared weights are part of the system energy and therefore bounded for all time. Implicit time differencing and orbit averaging techniques are developed and implemented. Low-order moment constraints are satisfied exactly by a new particle representation. Numerical tests for one dimension, k⊥=0, and two dimension, k∥=0 show the successful application of both methods to damped waves and of the second order closure method to unstable gravitational modes. The methods described here are a natural and efficient way to close extended magnetohydrodynamic (MHD) equations to obtain a full kinetic description.

Solving shortest path problem using particle swarm optimization

This paper presents the investigations on the application of particle swarm optimization (PSO) to solve shortest path (SP) routing problems. A modified priority-based encoding incorporating a heuristic operator for reducing the possibility of loop-formation in the path construction process is proposed for particle representation in PSO. Simulation experiments have been carried out on different network topologies for networks consisting of 15–70 nodes. It is noted that the proposed PSO-based approach can find the optimal path with good success rates and also can find closer sub-optimal paths with high certainty for all the tested networks. It is observed that the performance of the proposed algorithm surpasses those of recently reported genetic algorithm based approaches for this problem.

A diagrammatic approach to response problems in composite systems

The bulk macroscopic response of a system of particles or inclusions with field-inducedforces is studied. The susceptibilities and transport coefficients in such a system areexpressed as averages of a multiple-scattering expansion. A special diagrammaticmethod is developed for analyzing the structure of the expansion. The concept ofirreducibility is discussed in detail and shown to be crucial in obtaining macroscopicequations characterizing the system response with coefficients depending solely onlocal properties of the medium. Due to the representation of particles by lines indiagrams, irreducibility is given a particularly simple topological interpretation in thediagrammatic language. The method is illustrated by a discussion of responseproblems in colloidal suspensions in the presence of hydrodynamic interactions.

Liquid phase sintering, II: Computer study of skeletal settling and solid phase extrication in a microgravity environment

A two-dimensional numerical method based on the Brownian motion model and on the Densification model for simulation of liquid phase sintering in microgravity environment will be developed. Both models will be based on domain topology (two-dimensional particle representation) and control volume methodology and on three submodels for domain translation, solid skeleton formation and domain extrication. This method will be tested in order to conduct a study of diffusion phenomena and microgravitational effects on microstructural evolution influenced by skeletal settling combined with solid-phase extrication during liquid phase sintering of porous W-Ni system.

Automatic kernel clustering with a Multi-Elitist Particle Swarm Optimization Algorithm

This article introduces a scheme for clustering complex and linearly non-separable datasets, without any prior knowledge of the number of naturally occurring groups in the data. The proposed method is based on a modified version of classical Particle Swarm Optimization (PSO) algorithm, known as the Multi-Elitist PSO (MEPSO) model. It also employs a kernel-induced similarity measure instead of the conventional sum-of-squares distance. Use of the kernel function makes it possible to cluster data that is linearly non-separable in the original input space into homogeneous groups in a transformed high-dimensional feature space. A new particle representation scheme has been adopted for selecting the optimal number of clusters from several possible choices. The performance of the proposed method has been extensively compared with a few state of the art clustering techniques over a test suit of several artificial and real life datasets. Based on the computer simulations, some empirical guidelines have been provided for selecting the suitable parameters of the PSO algorithm.

The IMPROVE-1 Storm of 1–2 February 2001. Part III: Sensitivity of a Mesoscale Model Simulation to the Representation of Snow Particle Types and Testing of a Bulk Microphysical Scheme with Snow Habit Prediction

Abstract A mesoscale model simulation of a wide cold-frontal rainband observed in the Pacific Northwest during the Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE-1) field study was used to test the sensitivity of the model-produced precipitation to varied representations of snow particles in a bulk microphysical scheme. Tests of sensitivity to snow habit type, by using empirical relationships for mass and velocity versus diameter, demonstrated the defectiveness of the conventional assumption of snow particles as constant density spheres. More realistic empirical mass–diameter relationships result in increased numbers of particles and shift the snow size distribution toward larger particles, leading to increased depositional growth of snow and decreased cloud water production. Use of realistic empirical mass–diameter relationships generally increased precipitation at the surface as the rainband interacted with the orography, with more limited increases occurring offshore. Changes in both the mass–diameter and velocity–diameter relationships significantly redistributed precipitation either windward or leeward when the rainband interacted with the mountain barrier. A method of predicting snow particle habit in a bulk microphysical scheme, and using predicted habit to dynamically determine snow properties in the scheme, was developed and tested. The scheme performed well at predicting the habits present (or not present) in aircraft observations of the rainband. Use of the scheme resulted in little change in the precipitation rate at the ground for the rainband offshore, but significantly increased precipitation when the rainband interacted with the windward slope of the Olympic Mountains. The study demonstrates the promise of the habit prediction approach to treating snow in bulk microphysical schemes.

Nonlinear polarization and dissipative correspondence between low-frequency fluid and gyrofluid equations

The correspondence between gyrofluid and low-frequency fluid equations is examined. The lowest-order conservative effects in E×B advection, parallel dynamics, and curvature match trivially. The principal concerns are polarization fluxes, and dissipative parallel viscosity and parallel heat fluxes. The emergence of the polarization heat flux in the fluid model and its contribution to the energy theorem is reviewed. It is shown that gyroviscosity and the polarization fluxes are matched by the finite gyroradius corrections to advection in the long-wavelength limit, provided that the differences between gyrocenter and particle representations are taken into account. The dissipative parallel viscosity is matched by the residual thermal anisotropy in the gyrofluid model in the collision-dominated limit. The dissipative parallel heat flux is matched by the gyrofluid parallel heat flux variables in the collision-dominated limit. Hence, the gyrofluid equations are a complete superset of the low-frequency fluid equations.

A Modified PSO Structure Resulting in High Exploration Ability With Convergence Guaranteed

Particle swarm optimization (PSO) is a population-based stochastic recursion procedure, which simulates the social behavior of a swarm of ants or a school of fish. Based upon the general representation of individual particles, this paper introduces a decreasing coefficient to the updating principle, so that PSO can be viewed as a regular stochastic approximation algorithm. To improve exploration ability, a random velocity is added to the velocity updating in order to balance exploration behavior and convergence rate with respect to different optimization problems. To emphasize the role of this additional velocity, the modified PSO paradigm is named PSO with controllable random exploration velocity (PSO-CREV). Its convergence is proved using Lyapunov theory on stochastic process. From the proof, some properties brought by the stochastic components are obtained such as "divergence before convergence" and "controllable exploration." Finally, a series of benchmarks is proposed to verify the feasibility of PSO-CREV.

Simulation of biological flow and transport in complex geometries using embedded boundary/volume-of-fluid methods

We have developed a simulation capability to model multiscale flow and transport in complex biological systems based on algorithms and software infrastructure developed under the SciDAC APDEC CET. The foundation of this work is a new hybrid fluid-particle method for modeling polymer fluids in irregular microscale geometries that enables long-time simulation of validation experiments. Both continuum viscoelastic and discrete particle representations have been used to model the constitutive behavior of polymer fluids. Complex flow environment geometries are represented on Cartesian grids using an implicit function. Direct simulation of flow in the irregular geometry is then possible using embedded boundary/volume-of-fluid methods without loss of geometric detail. This capability has been used to simulate biological flows in a variety of application geometries including biomedical microdevices, anatomical structures and porous media.

Clothed particle representation in quantum field theory: mass renormalization

The method of unitary clothing transformations is used to handling the so-called clothed particle representation (CPR) (see [A.V. Shebeko and M.I. Shirokov, Phys. Part. Nucl. 32 (2001) 31; nucl-th/0102037 , V.Yu. Korda and A.V. Shebeko, Phys. Rev. D 70 (2004) 085011, V.Yu. Korda, L. Canton and A.V. Shebeko, doi:10.1016/j.aop.2006.07.010 , Ann. Phys. (2006) in press; nucl-th/060325 ] and refs. therein), where the total field Hamiltonian H and the three boost operators in the instant form of relativistic dynamics take on the same sparse structure in the Hilbert space of hadronic states. In this approach the mass counterterms are cancelled by commutators of the generators of clothing transformations and the field interaction operator. This allows the pion and nucleon mass shifts to be expressed through the corresponding three-dimensional integrals whose integrands are proved to be dependent on certain covariant combinations of the relevant three-momenta. The property provides the momentum independence of mass renormalization.

Improved Velocity Projection for the Material Point Method

The standard velocity projection scheme for the Material Point Method (MPM) and a typical form of the GIMP Method are exam­ ined. It is demonstrated that the fidelity of in­ formation transfer from a particle representation to the computational grid is strongly dependent on particle density and location. In addition, use of non-uniform grids and even non-uniform par­ ticle sizes are shown to introduce error. An en­ hancement to the projection operation is devel­ oped which makes use of already available veloc­ ity gradient information. This enhancement facil­ itates exact projection of linear functions and re­ duces the dependence of projection accuracy on particle location and density for non-linear func­ tions. The efficacy of this formulation for reduc­ ing error is demonstrated in solid mechanics sim­ ulations in one and two dimensions.

A spatial point process model for solving the MEG inverse problem

Abstract We present a new approach for solving the MEG inverse problem. It is well known that it is an ill-posed inverse problem because of Maxwell's equations. Two main methods for solving the inverse problem exist: modelling based on dipoles (or higher order elements) and distributed approaches. We propose here a new modelling approach that mixes both types and permits the consideration of varying numbers of dipoles and allows the inclusion of a Bayesian prior model. We model cerebral activity by a random set of dipoles. We use a spatial Poisson point process distribution parameterized by its intensity measure. From a set of MEG measurements we estimate the intensity measure by formulating the inverse problem as an optimization problem in the space of measures. Using ideas from the work of Zuyev and Molchanov, we propose an algorithm to minimize the expected mean square error. The algorithm consists of a particle representation of the state (possible locations for dipoles) coupled with a stochastic gradient descent. We present results on a set of simulated data. We show that our approach outperforms existing methods based on dipole location in the case of numerous dipoles or correlated noise in terms of mean and maximum square error.

Galileo symmetries in polymer particle representation

To illustrate the conceptual problems for the low-energy symmetries in the continuum of spacetime emerging from the discrete quantum geometry, Galileo symmetries are investigated in the polymer particle representation of a non-relativistic particle as a simple toy model. The complete Galileo transformations (translation, rotation and Galileo boost) are naturally defined in the polymer particle Hilbert space and Galileo symmetries are recovered with highly suppressed deviations in the low-energy regime from the underlying polymer particle description.

Spin dependent masses and symmetry

Abstract Recently, Cohen and Glashow pointed out that all known experimental tests of relativistic kinematics are consistent with invariance of physics under the four-parameter subgroup Sim ( 2 ) of the Lorentz group. The massive one-particle irreducible representations of ISim ( 2 ) , that is Sim ( 2 ) times spacetime translations, are all one-dimensional, labeled by spin along a preferred axis. Consequently particle theories based on this symmetry can accommodate lepton number conserving masses for left-handed neutrinos without the need to introduce sterile states. The same property of massive particle representations, however, also leads to the possibility that particle masses may be split within the different spins of a representation of the ordinary Poincare group. In this Letter we investigate the low-energy structure of theories with spin dependent masses and comment on the bounds on such effects.