Annihilation of Brownian particles on randomly distributed traps during anisotropic diffusion

The effect of diffusion anisotropy on the long-time asymptotic behavior of the survival probability of a Brownian particle among randomly distributed traps is discussed. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 5, 362–365 (10 September 1997)     

Random walks on lattices with randomly distributed traps I. The average number of steps until trapping

For a random walk on a lattice with a random distribution of traps we derive an asymptotic expansion valid for smallq for the average number of steps until trapping, whereq is the probability that a lattice point is a trap. We study the case of perfect traps (where the walk comes to an end) and the extension obtained by letting the traps be imperfect (i.e., by giving the walker a finite probability to remain free when stepping on a trap). Several classes of random walks of varying dimensionality are considered and special care is taken to show that the expansion derived is exact up to and including the last term calculated. The numerical accuracy of the expansion is discussed.     

Survival probabilities for random walks on lattices with randomly distributed traps

I present here a numerical procedure to compute survival probabilities for random walks on lattices with randomly distributed traps. The procedure has some advantages over existing methods, and its performance is evaluated for the 1D simple random walk, for which some exact results are known. Thereafter, I apply the procedure to 1D random walks with variable step length and to 3D simple random walks.     

Probability density tomography of microcavity polaritons confined in cylindrical traps of various sizes

We present the optical tomography of the probability density of microcavity polaritons, confined in three dimensions by cylindrical traps of various sizes. Collecting the photoluminescence emitted by the quasimodes under continuous nonresonant laser excitation, we reconstruct a three dimensional mapping of the photoluminescence, from which we can extract the spatial distribution of the confined states at any energy. We discuss the impact of the confinement shape and size on the probability density patterns.     

Improving light trapping and conversion efficiency of amorphous silicon solar cell by modified and randomly distributed ZnO nanorods

Three-dimensional （3D） nanostructures in thin film solar cells have attracted significant attention due to their appli- cations in enhancing light trapping. Enhanced light trapping can result in more effective absorption in solar cells, thus leading to higher short-circuit current density and conversion efficiency. We develop randomly distributed and modified ZnO nanorods, which are designed and fabricated by the following processes： the deposition of a ZnO seed layer on sub- strate with sputtering, the wet chemical etching of the seed layer to form isolated islands for nanorod growth, the chemical bath deposition of the ZnO nanorods, and the sputtering deposition of a thin Al-doped ZnO （ZnO：Al） layer to improve the ZnO/Si interface. Solar cells employing the modified ZnO nanorod substrate show a considerable increase in solar energy conversion efficiency.     

随机取向双层椭球粒子偏振散射特性研究

基于T矩阵方法,给出了随机取向、轴对称、含核椭球粒子的散射计算方法.散射体的核和外壳均可为非球形粒子,整个粒子具有轴对称性.以含核椭球粒子为模型,计算了含有吸收性内核(黑炭,black carbon)的水凝物气溶胶的散射特性,分析了核的大小、形状对消光系数、散射系数、吸收系数、不对称因子、单次散射反照率以及Muller矩阵等的影响. 关键词： 光散射 T矩阵 Muller矩阵 椭球粒子     

Line interference of randomly distributed spectral components

The general theory of statistical processing of experimental spectra with very high line densities is presented. Application of the proposed correlation method to data on pressure broadening obtained with diode lasers verifies the local nature of the line interference (spectral-exchange effect) induced by collisions.     

Statistical theory of the pinning of Bloch walls by randomly distributed defects

The coercive force is calculated for a rigid and a one- or two-dimensionally vaulted Bloch wall on the basis of a statistical theory. It is shown that the validity of the various pinning models developed previously depends on the defect density, the interaction force, and the area and flexibility of the domain wall. Our theoretical results are confirmed by a computer simulation of the pinning problem. The study of the temperature dependence of the coercive force proves to be a sensitive test to decide which pinning model applies.     

Characterization of the light scattering by ensembles of randomly distributed soot aggregates

Soot particles formed in combustion processes commonly exist in the form of ensembles of randomly distributed aggregates of small, nearly spherical monomers. In this paper, these randomly distributed aggregates are numerically generated using a combination of the cluster–cluster aggregation algorithm with the Monte Carlo method. Moreover, an efficient and accurate numerical method is presented for characterizing the light scattering by these complex soot particles illuminated by plane wave and Gaussian beam. This method exploits the unique features of the hybrid finite element-boundary integral method and, more importantly, the unique features of soot aggregates. It is designed in such a manner that it first decomposes the original problem into many sub-regions, where each primary particle is regarded as a sub-region, and then it employs the edge-based finite element method to deal with each sub-region. The sub-regions communicate through the near-field Green’s function. To reduce computational burdens, an iterative domain decomposition method in combination with parallel conjugate gradient method is adopted to solve the coupling system of equations. As an illustration, we present some of our preliminary numerical results. The results are expected to provide useful insights into the optical properties of soot particles formed in combustion processes.     

On the strength distribution of a field created by randomly distributed dipoles

The probability distribution of the strength of a field created by parallel dipoles arranged randomly, on average, uniformly is considered. The problem of divergence at small distances is analyzed. It is shown that, for any, including an arbitrarily small, number of dipoles ε in the cutoff sphere, the average field value is zero. In the case ε ? 1, the field distribution consists of a central part, whose half-width is of an order of the average polarization of a medium, and a very wide and structured background. An interpolation formula for the Fourier image of the field distribution applicable for arbitrary values of ε is proposed. An analogy with the theory of spectral line broadening is established. The connection with the problems of molecular optics and inhomogeneous Stark broadening of spectral lines is discussed.     

Localization under the effect of randomly distributed decoherence

Electron transport through disordered quasi one-dimensional quantum systems is studied. Decoherence is taken into account by a spatial distribution of virtual reservoirs, which represent local interactions of the conduction electrons with their environment. We show that the decoherence distribution has observable effects on the transport. If the decoherence reservoirs are distributed randomly without spatial correlations, a minimal degree of decoherence is necessary to obtain Ohmic conduction. Below this threshold the system is localized and thus, a decoherence driven metal-insulator transition is found. In contrast, for homogenously distributed decoherence, any finite degree of decoherence is sufficient to destroy localization. Thus, the presence or absence of localization in a disordered one-dimensional system may give important insight about how the electron phase is randomized.     

Competitive trapping effects in a set of partially absorbing traps

This note contains a formalism for calculating properties of random walks in the presence of a set of partially absorbing traps. The properties that are considered are the probability of trapping at a specific point and the survival probability as a function of step number. The results are expressed in terms of determinants, but approximations to these can be found.     

Surface area of the domain visited by a spherical Brownian particle

A spatial domain swept out by a spherical particle, whose center follows a Wiener trajectory, is referred to as a Wiener sausage. The present study focuses on the surface area of the Wiener sausage. Using intuitive arguments we derive the mean and variance of the surface area, as well as the asymptotic behavior of its probability density in the limits when the area tends to zero and infinity.     

Velocity autocorrelation function of a Brownian particle

In this article, we present molecular dynamics study of the velocity autocorrelation function (VACF) of a Brownian particle. We compare the results of the simulation with the exact analytic predictions for a compressible fluid from [T.S. Chow, J.J. Hermans, Physica 65, 156 (1973)] and an approximate result combining the predictions from hydrodynamics at short and long times. The physical quantities which determine the decay were determined from separate bulk simulations of the Lennard-Jones fluid at the same thermodynamic state point. We observe that the long-time regime of the VACF compares well the predictions from the macroscopic hydrodynamics, but the intermediate decay is sensitive to the viscoelastic nature of the solvent.     

Transient enhancement and detuning of laser-driven parametric instabilities by particle trapping

Kinetic simulations of backward stimulated Raman scattering (BSRS), where the Langmuir wave coherence time is greater than the bounce time for trapped electrons, yield transient reflectivity levels far above those predicted by fluidlike models. Electron trapping reduces the Langmuir wave damping and lowers the Langmuir wave frequency, and leads to a secular phase shift between the Langmuir wave and the BSRS beat ponderomotive force. This phase shift detunes and saturates BSRS and a similar effect, due to ion trapping, is the saturation mechanism for backward stimulated Brillouin scattering. Competition with forward SRS is discussed.     

Mass-selective trapping of pulsed charged particle beams

The phase-space method is used to evaluate the mass-selective ion confinement properties of the radio-frequency (rf) quadrupole ion trap with phase-synchronized switching-on of the driving rf field for pulsed ion injection from an external source. The results are of interest for on-line investigations of both short-lived isotopes and stable highly charged ions. In particular, singly charged ions with an energy of 10 eV and a mass in the neighborhood of 100 amu, injected along the gap or through an aperture on one of the electrodes, are considered. Mass-selective storage of the injected ions is possible for any trap operation point within the stability region by allowing a field-free drift distance before ion injection. It is shown that after appropriate scaling the results apply to the trapping of any pulsed beam of charged particles.     

Electronic structure of titanium monoxide with randomly distributed vacancies

The electronic structure of titanium monoxide TiO _y (0.810 ≤ y ≤ 1.262) in the high-temperature cubic phase with vacancies randomly distributed over the titanium and oxygen sublattices is calculated in the coherent potential approximation. The changes in the electronic spectra with the concentration of vacancies are retraced. The calculated spectra are compared to the available experimental data.     

Nonlinear modulation of randomly distributed upper-hybrid modes in plasmas

A new type of modulations of an ensemble of random waves near the upper-hybrid resonance frequency is investigated. For the linearly unstable cases, the growth rates are obtained and exact nonlinear stationary distributions are presented.