Statistics of a coherent lidar signal in a turbulent atmosphere

Absolute and conditional statistical properties of a pulse coherent Doppler lidar signal in a turbulent atmosphere are studied. Upon coherent receiving of optical fields scattered by a large number of particles, the lidar signal is shown to be a nonstationary non-Gaussian random process with Gaussian conditional statistical characteristics. The appearance of non-Gaussian properties of the signal is caused by correlation of turbulent fluctuations of the wind velocity field within the scattering volume. For the considered signal model, which corresponds to the single scattering approximation and is a sum of a large number of random variables, the central limit theorem is found to be untrue due to the statistical dependence of particles’ positions in a turbulent atmosphere. The results of numerical calculations show that, for a homogeneous and isotropic turbulence, the behavior of the signal statistics significantly depends on the size of the scattering volume and on the state of atmospheric turbulence. A Gaussian statistics is observed at small heights; with an increase in height, the non-Gaussian component becomes considerable in fluctuations of the lidar signal.     

Energy fluctuation and correlation in Tsallis statistics

We investigate the fluctuation of the energy in the framework of Tsallis statistics and find the correlation plays an important role in energy fluctuations. In Tsallis statistics, the correlation is induced by the nonextensivity of Tsallis entropy and exists between particles even if the particles are dynamically independent. By taking the generalized ideal gas as an example, we get that when the particle number N is large enough, the relative fluctuation of the energy is proportional to 1/N instead of in Boltzmann statistics. Thus, the relative energy fluctuation is much smaller in Tsallis statistics than that in Boltzmann statistics. Besides, we demonstrate that the introduction of correlation between particle energies leads to smaller energy fluctuations in Tsallis statistics.     

Perturbation theory for large Stokes number particles in random velocity fields

We derive a perturbative approach to study, in the large inertia limit, the dynamics of solid particles in a smooth, incompressible and finite-time correlated random velocity field. We carry on an expansion in powers of the inverse square root of the Stokes number, defined as the ratio of the relaxation time for the particle velocities and the correlation time of the velocity field. We describe in this limit the residual concentration fluctuations of the particle suspension, and determine the contribution to the collision velocity statistics produced by clustering. For both concentration fluctuations and collision velocities, we analyze the differences with the compressible one-dimensional case.     

Suspension and fall of heavy particles in random two-dimensional flow

We investigate the settling of heavy particles in a steady, two-dimensional random velocity field, and find instances in which particle suspension occurs. This leads to a bimodal velocity distribution that may explain some apparently conflicting results reported in the literature. The bimodal distribution is typically smeared out by a time dependence of the ambient flow but, if the time variation is slow, the settling rates of some particles will be as well. The resulting broadbanded velocity distribution of the settling particles will have significance for processes such as rain drop formation, in which the spread of particle velocities affects the statistics of particle collisions.     

Density-PDFs and Lagrangian statistics of highly compressible turbulence

In isothermal, highly compressible turbulent flows, density fluctuations follow a log-normal distribution. We establish a connection between these density fluctuations and the probability-density-functions (PDF) of Lagrangian tracer particles advected with the flow. Our predicted particle statistics is tested against large scale numerical simulations, which were performed with 512³ collocation points and 2 million tracer particles integrated over several dynamical times.     

Correlations for the circular Dyson brownian motion model with Poisson initial conditions

The circular Dyson brownian motion model refers to the stochastic dynamics of the log-gas on a circle. It also specifies the eigenvalues of certain parameter-dependent ensembles of unitary random matrices. This model is considered with the initial condition that the particles are non-interacting (Poisson statistics). Jack polynomial theory is used to derive a simple exact expression for the density-density correlation with the position of one particle specified in the initial state, and the position of one particle specified at time τ, valid for all β > 0. The same correlation with two particles specified in the initial state is also derived exactly, and some special cases of the theoretical correlations are illustrated by comparison with the empirical correlations calculated from the eigenvalues of certain parameter-dependent Gaussian random matrices. Application to fluctuation formulas for time-displaced linear statistics in made.     

Signal statistics of laser light scattering

After a brief survey of number fluctuations, a topic of current interest in light scattering research, the theory is developed for a particular case of this type. A laser beam of Gaussian cross section illuminates a volume in which there is a fluctuating number of identical particles. For incoherent detection the scattered intensities are additive. The interest centers on the statistics of the total scattered intensity. Starting from the moment generating function, the distribution function of scattered intensity is computed using two different methods. In an experiment designed to test the computed distributions, agreement between theory and measurement is found if the mean particle number within the scattering volume exceeds 3. The experimental procedure is described and some difficulties are explained which so far did not permit application of the theory for particle numbers much below 3.     

Description of evaporation of a spherical liquid drop by a non-Markovian random process based on integral stochastic equations

Processes of evaporation (condensation) of vapor particles from the surface of a spherical drop and processes of their diffusion into surrounding volume are considered. Special features of evaporation are investigated taking into account vapor particle fluctuations caused by random changes in the temperature, concentration, etc. Statistical characteristics of fluctuations of the corresponding quantities, including the mass flow through the liquid-vapor boundary and concentration on the liquid surface, are presented. The distribution of completely evaporated drop number versus time is presented.     

Distribution of time-averaged observables for weak ergodicity breaking

We find a general formula for the distribution of time-averaged observables for systems modeled according to the subdiffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and Boltzmann's statistics, while for the anomalous subdiffusive case a weakly nonergodic statistical mechanical framework is constructed, which is based on Lévy's generalized central limit theorem. As an example we calculate the distribution of X, the time average of the position of the particle, for unbiased and uniformly biased particles, and show that X exhibits large fluctuations compared with the ensemble average .     

Fluctuations of the Maximal Particle Energy of the Quantum Ideal Gas and Random Partitions

We investigate the limiting distribution of the fluctuations of the maximal summand in a random partition of a large integer with respect to a multiplicative statistics. We show that for a big family of Gibbs measures on partitions (so-called generalized Bose–Einstein statistics) this distribution is the well-known Gumbel distribution which usually appears in the context of indepedent random variables. In particular, it means that the (properly rescaled) maximal energy of an individual particle in the grand canonical ensemble of the d-dimensional quantum ideal gas has the Gumbel distribution in the limit. We also apply our result to find the fluctuations of the height of a random 3D Young diagram (plane partition) and investigate the order statistics of random partitions under generalized Bose–Einstein statistics.     

Low-Concentration Photon Correlation Spectroscopy

Photon correlation spectroscopy (PCS) is a technique to measure rapidly particle size in the sub-micrometre region. The use of PCS is, however, limited by concentration. The upper limit is due to multiple scattering of the incident light and the lower limit is determined by the fact that fluctuations of the number of particles in the measuring zone have a significant influence on the apparent diffusion coefficient. In this paper a signal processing method is described which differentiates this influence. With this system the lower limit is no longer limited to about 100 particles in the measuring volume corresponding to a concentration of 10⁹ particles/cm³. The limitation is now the intensity of the scattered light, which becomes too weak at a concentration of about 50 particles/cm³. As a consequence of this work, a revision to the basic theory of PCS may be necessary. Moreover, the new processing method also permits the measurement of the particle concentration in the sample.     

Role of stochastic fluctuations in the charge on macroscopic particles in dusty plasmas

The currents which charge a macroscopic particle placed in a plasma consist of discrete charges; hence, the charge can undergo random fluctuations about its equilibrium value. These random fluctuations can be described by a simple model which, if the mechanisms for charging of macroscopic particles are known, makes it possible to determine the dependence of the temporal and amplitude characteristics of the fluctuations on the plasma parameters. This model can be used to study the effect of charge fluctuations on the dynamics of the macroscopic particles. The case of so-called plasma-dust crystals (i.e., highly ordered structures which develop because of strong interactions among macroscopic particles) in laboratory gaseous discharge plasmas is considered as an example. The molecular dynamics method shows that, under certain conditions, random fluctuations in the charge can effectively heat a system of macroscopic particles, thereby impeding the ordering process. Zh. éksp. Teor. Fiz. 115, 2067–2079 (June 1999)     

单势阱粒子溢流模型中热力学量的涨落效应

采用相空间积分方法严格导出了各态历经条件下单势阱粒子溢流模型中系统温度和阱内粒子数涨落的解析表达式,着重讨论了热力学量涨落与总粒子数和势阱体积之间的关系.研究表明,系统总粒子数越少以及势阱体积越小,热力学涨落越显著,并且热力学涨落与阱内粒子的溢出密切相关.粒子的溢出和系统负比热及热力学大幅涨落的发生存在一一对应的关系,这一对应关系的根源可以从表观能量逆均分来理解.     

Gravitational settling of a highly concentrated system of solid spherical particles

In the present paper, we report on the results of an experimental study of the process of gravity sedimentation of a cloud of monodispersed solid spherical particles with initial volume concentration C > 0.03, which was performed in a wide range of Reynolds numbers. An analytical estimate of the settling regimes of spherical particle clouds is presented. A new method for creating a spherical particle cloud with a high concentration of particles is proposed. A qualitative picture of the settling process of a highly concentrated particle cloud under gravity is revealed. A criterial dependence for the drag coefficient of a sedimenting spherical particle cloud as an entity is obtained.     

A subgrid model for clustering of high-inertia particles in large-eddy simulations of turbulence

Clustering (or preferential concentration) of inertial particles suspended in a homogeneous, isotropic turbulent flow is strongly influenced by the smallest scales of the turbulence. In particle-laden large-eddy simulations (LES) of turbulence, these small scales are not captured by the grid and hence their effect on particle motion needs to be modelled. In this paper, we use a subgrid model based on kinematic simulations of turbulence (Kinematic Simulation based SubGrid Model or KSSGM), for the first time in the context of predicting the clustering and the relative velocity statistics of inertial particles. This initial study focuses on the special case of inertial particles in the absence of gravitational settling. We show that the KSSGM gives excellent predictions for clustering in a priori tests for inertial particles with St ≥ 2.0, where St is the Stokes number, defined as the ratio of the particle response time to the Kolmogorov time-scale. To the best of our knowledge, the KSSGM represents the first model that has been shown to capture the effect of the subgrid scales on inertial particle clustering for St ≥ 2.0. We also show that the mean inward radial relative velocity between inertial particles (?w_r?^(?), which enters into the formula for the collision kernel) is accurately predicted by the KSSGM for all St. We explain why the model captures clustering at higher St?but not for lower St?, and provide new insights into the key statistical parameters of turbulence that a subgrid model would have to describe, in order to accurately predict clustering of low-St?particles in an LES.     

Hydrodynamic screening and axisymmetric turbulence in the transient sedimentation of a dilute suspension at small Reynolds number

A theory of settling of a dilute suspension of identical spherical particles in a viscous incompressible fluid is developed on the basis of the equations of transient Stokesian dynamics. The equations describe hydrodynamic interactions between particles moving under the influence of a constant force, starting to act at a particular instant of time. For a dilute suspension, a monopole approximation can be used. It is argued that the growth of velocity fluctuations is bounded by a combination of two effects, destructive interference of the flow patterns of individual particles, and a rearrangement of particle positions leading to a time-dependent microstructure of the suspension. After a long time, the microstructure tends to a steady state. The corresponding structure factor is described phenomenologically. The corresponding pair correlation function and the velocity correlation functions describing axisymmetric turbulence on the length scale of the mean distance between particles are evaluated.     

Single-shot two-dimensional measurement of nanoparticles in turbulent jet-diffusion flames using phase-selective laser-induced breakdown spectroscopy

In this work, we demonstrate a single-shot two-dimensional measurement of vanadic oxide (V₂O₅) nanoparticles in a turbulent jet-diffusion flame based on phase-selective laser-induced breakdown spectroscopy (PS-LIBS). By collecting the atomic spectra of vanadium near 439?nm from nano-sized plasmas within the ～30?ns lifetime, particle information can be revealed without interference from elastic scattering or Bremsstrahlung emissions. As the laser intensity increases, the signal intensity first increases and then saturates when the laser intensity reaches 0.5 GW/cm². In the saturation regime, a proportional correlation is established between the signal intensity and the particle volume fraction. Based on the parametric study in the laminar condition, we image the instantaneous distribution of particle volume fraction in the turbulent condition using single-shot PS-LIBS measurements. The snapshots show that vanadic oxide nanoparticles concentrate near the diffusion flame surface, which may be caused by the rapid formation of particles on the oxidizer/precursor side and quick dilution across the reaction layer. The Proper Orthogonal Decomposition (POD) analysis further indicates that the fluctuations of the particle volume fraction originate from the unsteady flame surface at the upstream positions and large-scale mixing at the downstream positions. The single-shot PS-LIBS measurement shows promising potential for resolving complex processes of particle formation in turbulent flame synthesis.     

An experimental investigation of three-dimensional particle aggregation using digital holographic microscopy

The tendency of particles to aggregate depends on particle-particle and particle-fluid interactions. These interactions can be characterized but it requires accurate 3D measurements of particle distributions. We introduce the application of an off-axis digital holographic microscopy for measuring distributions of dense micrometer (2 μm) particles in a liquid solution. We demonstrate that digital holographic microscopy is capable of recording the instantaneous 3D position of particles in a flow volume. A new reconstruction method that aids identification of particle images was used in this work. About 62% of the expected number of particles within the interrogated flow volume was detected. Based on the 3D position of individual particles, the tendency of particle to aggregate is investigated. Results show that relatively few particles (around 5–10 of a cohort of 1500) were aggregates. This number did not change significantly with time.