Arbitrary Size Distribution Research Articles

Magnetic Resonance Imaging of coarse sediment

Non-destructive observation methods for coarse sediments are usually limited to two dimensions, for instance in opened cores or at the surface. We report a trial of a promising new method for three-dimensional imaging of gravelly sediments: Magnetic Resonance Imaging (MRI). MRI maps contrasts in density and relaxation properties of protons, which are very different for sediment and water in the pores. Images of glass bead mixtures show that the local porosity varies with sorting patterns or imperfect sample mixing, illustrating the potential for this non-destructive imaging method. As a quantitative test, we verify that a macroscopic sediment property – porosity – compares well to a standard lab determination and a recent model for predicting porosity for arbitrary grain size distributions. Finally we discuss potential applications and limitations of MRI to porosity and permeability, sedimentary structures, benthic life and slow groundwater or mass flows.

A Numerical Procedure to Calculate Hydraulic Conductivity for an Arbitrary Pore Size Distribution

The ability to calculate soil hydraulic properties from soil physical data has been a dominant objective of soil physics research since the 1950s. The purpose of this study was to develop an approach based on modern physics to deal with an arbitrary porous medium. Some important advances resulted from applying critical path analysis from percolation theory and percolation scaling to a truncated random fractal model (Rieu and Sposito) of a soil. In fact, some of the perceived limitations of the fractal model at high and low saturations were reevaluated as strengths in the previous application. Nevertheless, it is not realistic to expect all media to be characterized accurately in such a simple fashion. We developed an appropriate generalization of the description of the medium to an arbitrary pore size distribution while maintaining the complications related to fluid connectivity at high and low saturations relating to percolation theory. It also maintains the relevance of the pore size distribution to the hydraulic conductivity through the application of critical path analysis. A numerical routine was constructed to apply these concepts to an arbitrary pore size distribution, which in our case was inferred from experimentally determined particle size data. Although more than 50 soils were investigated, our preliminary study does not indicate what the general relevance of fractal models is.

Effects of dust size distribution on dust acoustic waves in two-dimensional unmagnetized dusty plasma

For unmagnetized dusty plasma with many different dust grain species containing both hot isothermal electrons and ions, both the linear dispersion relation and the Kadomtsev–Petviashvili equation for small, but finite amplitude dust acoustic waves are obtained. The linear dispersion relation is investigated numerically. Furthermore, the variations of amplitude, width, and propagation velocity of the nonlinear solitary wave with an arbitrary dust size distribution function are studied as well. Moreover, both the power law distribution and the Gaussian distribution are approximately simulated by using appropriate arbitrary dust size distribution functions.

Modeling the Structure Formation of Particulate Langmuir Films: the Effect of Polydispersity

Two-dimensional molecular dynamics computer simulation has been developed to model the compression of Langmuir films composed of spherical nanoparticles with arbitrary size distribution. We demonstrate that the usual assumption in the determination of interparticle potentials from the surface pressure vs area isotherms (i.e., monodisperse particles in perfect hexagonal order) leads to a systematic overestimation of the characteristic length of the interaction. On the basis of the results of the simulation, we propose a correction method to improve the traditional way of determining the interparticle potentials. We use the corrected particle-particle interactions to explore the correlation between the broadness of the size distribution and several structural parameters (decay length of pair-correlation function, global orientational order parameter, mean, and standard deviation of number of neighbors). Due to the uniaxial compression and the stiffness of the particulate layer, the surface pressure is not a scalar field. We investigate the effect of polydispersity on the anisotropy and the fluctuation of the surface pressure tensor in Langmuir films during uniaxial compression.

Tail behavior of the queue size and waiting time in a queue with discrete autoregressive arrivals

Autoregressive arrival models are described by a few parameters and provide a simple means to obtain analytical models for matching the first- and second-order statistics of measured data. We consider a discrete-time queueing system where the service time of a customer occupies one slot and the arrival process is governed by a discrete autoregressive process of order 1 (a DAR(1) process) which is characterized by an arbitrary stationary batch size distribution and a correlation coefficient. The tail behaviors of the queue length and the waiting time distributions are examined. In particular, it is shown that, unlike in the classical queueing models with Markovian arrival processes, the correlation in the DAR(1) model results in nongeometric tail behavior of the queue length (and the waiting time) if the stationary distribution of the DAR(1) process has infinite support. A complete characterization of the geometric tail behavior of the queue length (and the waiting time) is presented, showing the impact of the stationary distribution and the correlation coefficient when the stationary distribution of the DAR(1) process has finite support. It is also shown that the stationary distribution of the queue length (and the waiting time) has a tail of regular variation with index -β − 1, by finding an explicit expression for the tail asymptotics when the stationary distribution of the DAR(1) process has a tail of regular variation with index -β.

Tail behavior of the queue size and waiting time in a queue with discrete autoregressive arrivals

Autoregressive arrival models are described by a few parameters and provide a simple means to obtain analytical models for matching the first- and second-order statistics of measured data. We consider a discrete-time queueing system where the service time of a customer occupies one slot and the arrival process is governed by a discrete autoregressive process of order 1 (a DAR(1) process) which is characterized by an arbitrary stationary batch size distribution and a correlation coefficient. The tail behaviors of the queue length and the waiting time distributions are examined. In particular, it is shown that, unlike in the classical queueing models with Markovian arrival processes, the correlation in the DAR(1) model results in nongeometric tail behavior of the queue length (and the waiting time) if the stationary distribution of the DAR(1) process has infinite support. A complete characterization of the geometric tail behavior of the queue length (and the waiting time) is presented, showing the impact of the stationary distribution and the correlation coefficient when the stationary distribution of the DAR(1) process has finite support. It is also shown that the stationary distribution of the queue length (and the waiting time) has a tail of regular variation with index -β-1, by finding an explicit expression for the tail asymptotics when the stationary distribution of the DAR(1) process has a tail of regular variation with index -β.

Mathematical simulation of mass transfer processes under heterogeneous reactions in polydisperse porous media

Submitted is a theoretical study of mass transfer processes in polydisperse porous media in the presence of chemical reactions. Kinetic regime of methane pyrolysis in a porous carbon skeleton considering external and internal diffusion resistances for different initial distributions of particles forming the porous medium is investigated. Derived is a general analytical expression describing the influence of the inner reaction surface variation on the degree of the pore filling for an arbitrary initial particle size distribution. Expressions defining the time of pores filling by pyrocarbon based on approximate and exact solutions of the equation for the probability density function (PDF) of particle size distribution are received. Dependence of pore filling time on effective diffusion coefficient and initial particle size distribution using both solutions for PDF-equation is compared. It is shown, that the dominant factor influencing the pore filling time is the dispersion of particle size distribution.

Correct Procedures for the Calculation of Heats of Adsorption for Heterogeneous Adsorbents from Molecular Simulation

Several procedures for calculating the heat of adsorption from Monte Carlo simulations for a heterogeneous adsorbent are presented. Simulations have been performed to generate isotherms for nitrogen at 77 K and methane at 273.15 K in graphitic slit pores of various widths. The procedures were then applied to calculate the heat of adsorption of an activated carbon with an arbitrary pore size distribution. The consistency of the different procedures shows them to be correct in calculating interaction energy contributions to the heat of adsorption. The currently favored procedure for this type of calculation, from the literature, is shown to be incorrect and in serious error when calculating the heat of adsorption of activated carbon.

Rotation rate and velocity dispersion of planetary ring particles with size distribution: I. Formulation and analytic calculation

We derive an equation for the evolution of rotational energy of Keplerian particles in a dilute disk due to mutual collisions. Three-dimensional Keplerian motion of particles is taken into account precisely, on the basis of Hill's approximation. The Rayleigh distribution of particles' orbital eccentricities and inclinations, and the Gaussian distribution of their rotation rates are also taken into account. Performing appropriate variable transformation, we show that the equation can be expressed with two terms. The first term, which we call collisional stirring term, represents energy exchange between rotation and random motion via collisions. The second term, which we call rotational friction term, tends to equalize the mean rotational energy of particles with different sizes. The equation can describe the evolution of rotational energy of Keplerian particles with an arbitrary size distribution. We analytically evaluate the rates of stirring and friction for the random kinetic energy and rotational energy due to inelastic collisions, for non-gravitating particles in a dilute disk. Using these results, we discuss equilibrium states in a disk of spinning, non-gravitating Keplerian particles.

A discrete nonlinear mass transfer equation with applications in solid-state sintering of ceramic materials

The evolution of grain structures in materials is a complex and multiscale process that determines the material's final properties. Understanding the dynamics of grain growth is a key factor for controlling this process. We propose a phenomenological approach, based on a nonlinear, discrete mass transfer equation for the evolution of an arbitrary initial grain size distribution. Transition rates for mass transfer across grains are assumed to follow the Arrhenius law, but the activation energy depends on the degree of amorphization of each grain. We argue that the magnitude of the activation energy controls the final (sintered) grain size distribution, and we verify this prediction by numerical simulation of mass transfer in a one-dimensional grain aggregate.

Size sorting of Au and Pt nanoparticles from arbitrary particle size distributions

A K 2BSPP (dipotassium bis( p-sulfonatophenyl)phenylphosphane dihydrate)-based method to sort and size refine Au and Pt nanoparticles has been developed. It makes use of K 2BSPP to impart graduated stability to the nanoparticles in a number of NaCl solutions. The method offers a systematic approach to preparing metal nanoparticles of small diameters and a narrow size distribution from an arbitrary particle size distribution. TEM investigations confirmed the size refinement efficacy of this treatment method: in a typical experiment, the mean particle size and relative standard deviation of Au nanoparticles after three successive treatments were 5.18 and 0.055 nm, respectively, down from the corresponding values of 8.22 and 0.26 nm from the initial untreated nanoparticle solution. The K 2BSPP-based size refinement procedure is a simple alternative to more complex chemical procedures and stringent process control that are currently required for the preparation of mono-dispersed systems.

Rotation Rates of Particles in Saturn's Rings

Rotational states of particles in Saturn's rings are not directly observable but have been inferred from spacecraft and ground-based observations of their thermal emission. A temperature contrast between night- and daysides of particles in Saturn's C ring during crossing of the planetary shadow has been detected and interpreted as indicating the particles' having spin rates comparable to or less than their orbital frequency. Previous numerical simulations showed such slow rotation when the particles' size distribution was not taken into account. Faster rotation of smaller particles has been suggested, but rotation of ring particles with a broad size distribution has been poorly understood. Here we derive an evolution equation for the rotational energy of ring particles with an arbitrary size distribution and show the results of calculations of rotation rates of particles with a broad size distribution, from centimeters to 10 m. Numerical results show that 10 cm-sized or smaller particles would spin several tens to hundreds of times in one orbital period, while large ones spin slowly. The spin axes of slowly rotating large particles have a tendency to be nearly aligned in the direction normal to the ring plane, while rapidly rotating small particles have random spin orientations. In optically thin rings such as Saturn's C ring, small particles with a spin axis pointing nearly toward the Sun are likely responsible for the observed temperature contrast, as recently pointed out by Morishima & Salo. Rapidly rotating small particles have larger orbital inclinations than slowly rotating large particles; thus, ring particles' rotational states have vertical heterogeneity.

On the theory of optical properties of fractal clusters

A theory of optical properties of clusters of spherical metal nanoparticles characterized by an arbitrary size distribution is developed in a quasi-static dipole approximation. The equations for coupled dipoles and general relations are formulated in terms of reduced dipole moments. It is shown that the dipole resonant frequencies and amplitudes, the absorbed power, and the acting-field magnitudes strongly depend on the ratios of particle radii in a cluster. Properties of linear, planar, and three-dimensional systems are examined.

Determination of the Particle Size Distribution of Quantum Nanocrystals from Absorbance Spectra

The optical absorbance spectrum for a suspension of quantum particles with an arbitrary particle size distribution is determined by the electronic transition and the distribution of bandgaps in the system. It is demonstrated that the particle size distribution obtained for a suspension of ZnO quantum particles is in excellent agreement with the distribution obtained from transmission electron microscope images.

Parameterization of cloud droplet formation in global climate models

An aerosol activation parameterization has been developed based on a generalized representation of aerosol size and composition within the framework of an ascending adiabatic parcel; this allows for parameterizing the activation of chemically complex aerosol with an arbitrary size distribution and mixing state. The new parameterization introduces the concept of “population splitting,” in which the cloud condensation nuclei (CCN) that form droplets are treated as two separate populations: those that have a size close to their critical diameter and those that do not. Explicit consideration of kinetic limitations on droplet growth is introduced. Our treatment of the activation process unravels much of its complexity. As a result of this, a substantial number of conditions of droplet formation can be treated completely free of empirical information or correlations; there are, however, some conditions of droplet activation for which an empirically derived correlation is utilized. Predictions of the parameterization are compared against extensive cloud parcel model simulations for a variety of aerosol activation conditions that cover a wide range of chemical variability and CCN concentrations. The parameterization tracks the parcel model simulations closely and robustly. The parameterization presented here is intended to allow for a comprehensive assessment of the aerosol indirect effect in general circulation models.

A unified approach to analyze multiple access protocols for buffered finite users

In this paper, a new approach is proposed to analyze the performance of buffered random multiple access protocols called tagged user analysis (TUA). In TUA, each user is modeled as an independent queueing system, which operates at its own equilibrium probability. As a result, the classical queueing theory can be employed to analyze the queueing behavior of each user. On the basis of the behavior of the tagged user, the performance of the whole system is analyzed. TUA is a unified method of analyzing most of random access methods including the heterogeneous random multiple access techniques that are difficult to analyze otherwise. Furthermore, TUA can also handle those systems where user terminals may have arbitrary packet size (in slots) distribution, arbitrary arrival processes such as batch packet arrivals in Bernoulli, arbitrary service principle such as priority queueing, last came first served, and random service. In this paper, in addition to analyzing for the distributions of several performance indices, their mean values are obtained.

Analytical Formulas for Film Thickness in Compacted Asphalt Mixture

Recently, several researchers have proposed asphalt film thickness as a criterion for ensuring the durability of asphalt mixtures. However, they suggested that the standard film thickness equation, which dates back to the 1940s, needs to be examined by modern technology and improved. A presumable background on which the Asphalt Institute surface area factors are based was recovered and analyzed in detail. A fundamentally sound model for film thickness calculation was developed using a model of asphalt concrete in which the aggregates are spherical but have an arbitrary size distribution. A recent result from statistical geometry is applied to determine the film thickness for any volume fraction of aggregates and any volume fraction of effective asphalt. The analytical formulas are presented, the details of the calculation are summarized, and examples are provided.

On the Exact Analysis of a Discrete-Time Queueing System with Autoregressive Inputs

In this paper, we provide an exact analysis of a discrete-time queueing system driven by a discrete autoregressive model of order 1 (DAR(1)) characterized by an arbitrary marginal batch size distribution and a correlation coefficient. Closed-form expressions for the probability generating function and mean queue length are derived. It is shown that the system performance is quite sensitive to the correlation of the arrival process. In addition, a comparison with traditional Markovian processes shows that arrival processes of DAR(1) type exhibit larger queue length as compared with the traditional Markovian processes when the marginal densities and correlation coefficients are matched.

Magnetic structure and hysteresis in hard magnetic nanocrystalline film: Computer simulation

Three-dimensional micromagnetic simulations are used to study the effect of crystallographic textures on the magnetic properties of uniaxial nanocrystalline films of hard magnetic materials with arbitrary grain shapes and size distributions. The correlation lengths (effective ferromagnetic exchange interaction radius and domain wall width) are assumed to be smaller than the typical grain size. The Landau–Lifshitz equations of magnetization dynamics are employed to describe the distribution of magnetization in ferromagnetic domains, domain evolution during magnetization switching, and the hysteresis curve. The equations are solved numerically in reciprocal space using the fast Fourier transform technique. Simulations are performed for films of different grain textures. The results show that magnetic coupling between grains in thin films significantly affects the morphology of the magnetic domains and their response to the magnetic field applied. The greater the deviation of the uniaxial directions of the grains from the film normal, the smaller the coercivity and the remanence magnetization. It is also shown that the remanence magnetization and coercivity respond differently to the variations in film texture and that the magnetic reversal process is a collective process involving groups of grains. In particular, it is found that the crystallographic texture of the grains has a more complicated effect on the coercivity than on the remanence magnetization and on the character of topological changes during the magnetization reversal process.

Largest claims reinsurance premiums under discrete claims sizes

The generalized largest claims reinsurance cover is reconsidered. Formulas for its net premium and loading are derived under assumption of an arbitrary discrete claims size distribution. The formula for the net premium is specialized to the assumption of Poisson-distributed claims number.