Velocity distribution for a dilute vibrated granular material

The velocity distribution for a vibrated granular material is determined in the dilute limit where the frequency of particle collisions with the vibrating surface is large compared to the frequency of binary collisions. The particle motion is driven by the source of energy due to particle collisions with the vibrating surface, and two dissipation mechanisms-inelastic collisions and air drag-are considered. In the latter case, a general form for the drag force is assumed. First, the distribution function for the vertical velocity for a single particle colliding with a vibrating surface is determined in the limit where the dissipation during a collision due to inelasticity or between successive collisions due to drag is small compared to the energy of a particle. In addition, two types of amplitude functions for the velocity of the surface, symmetric and asymmetric about zero velocity, are considered. In all cases, differential equations for the distribution of velocities at the vibrating surface are obtained using a flux balance condition in velocity space, and these are solved to determine the distribution function. It is found that the distribution function is a Gaussian distribution when the dissipation is due to inelastic collisions and the amplitude function is symmetric, and the mean square velocity scales as [[U-2](s)/(1 - e(2))], where [U-2](s) is the mean square velocity of the vibrating surface and e is the coefficient of restitution. The distribution function is very different from a Gaussian when the dissipation is due to air drag and the amplitude function is symmetric, and the mean square velocity scales as ([U-2](s)g/mu(m))(1/(m+2)) when the acceleration due to the fluid drag is -mu(m)u(y)\u(y)\(m-1), where g is the acceleration due to gravity. For an asymmetric amplitude function, the distribution function at the vibrating surface is found to be sharply peaked around [+/-2[U](s)/(1-e)] when the dissipation is due to inelastic collisions, and around +/-[(m +2)[U](s)g/mu(m)](1/(m+1)) when the dissipation is due to fluid drag, where [U](s) is the mean velocity of the surface. The distribution functions are compared with numerical simulations of a particle colliding with a vibrating surface, and excellent agreement is found with no adjustable parameters. The distribution function for a two-dimensional vibrated granular material that includes the first effect of binary collisions is determined for the system with dissipation due to inelastic collisions and the amplitude function for the velocity of the vibrating surface is symmetric in the limit delta(I)=(2nr)/(1 - e)much less than 1. Here, n is the number of particles per unit width and r is the particle radius. In this Limit, an asymptotic analysis is used about the Limit where there are no binary collisions. It is found that the distribution function has a power-law divergence proportional to \u(x)\((c delta l-1)) in the limit u(x)-->0, where u(x) is the horizontal velocity. The constant c and the moments of the distribution function are evaluated from the conservation equation in velocity space. It is found that the mean square velocity in the horizontal direction scales as O(delta(I)T), and the nontrivial third moments of the velocity distribution scale as O(delta(I)epsilon(I)T(3/2)) where epsilon(I) = (1 - e)(1/2). Here, T = [2[U2](s)/(1 - e)] is the mean square velocity of the particles.

Measurement of probability-distribution functions sensitive technique for the study of conduction phenomena in liquid dielectrics

The paper outlines a technique for sensitive measurement of conduction phenomena in liquid dielectrics. The special features of this technique are the simplicity of the electrical system, the inexpensive instrumentation and the high accuracy. Detection, separation and analysis of a random function of current that is superimposed on the prebreakdown direct current forms the basis of this investigation. In this case, prebreakdown direct current is the output data of a test cell with large electrodes immersed in a liquid medium subjected to high direct voltages. Measurement of the probability-distribution function of a random fluctuating component of current provides a method that gives insight into the mechanism of conduction in a liquid medium subjected to high voltages and the processes that are responsible for the existence of the fluctuating component of the current.

Statistical properties of entropy-consuming fluctuations in jammed states of laponite suspensions: Fluctuation relations and generalized Gumbel distribution

We report a universal large deviation behavior of spatially averaged global injected power just before the rejuvenation of the jammed state formed by an aging suspension of laponite clay under an applied stress. The probability distribution function (PDF) of these entropy consuming strongly non-Gaussian fluctuations follow an universal large deviation functional form described by the generalized Gumbel (GG) distribution like many other equilibrium and nonequilibrium systems with high degree of correlations but do not obey the Gallavotti-Cohen steady-state fluctuation relation (SSFR). However, far from the unjamming transition (for smaller applied stresses) SSFR is satisfied for both Gaussian as well as non-Gaussian PDF. The observed slow variation of the mean shear rate with system size supports a recent theoretical prediction for observing GG distribution.

A nested linear codes approach to distributed function computation over subspaces

In this paper, we consider a distributed function computation setting, where there are m distributed but correlated sources X1,...,Xm and a receiver interested in computing an s-dimensional subspace generated by [X1,...,Xm]Γ for some (m × s) matrix Γ of rank s. We construct a scheme based on nested linear codes and characterize the achievable rates obtained using the scheme. The proposed nested-linear-code approach performs at least as well as the Slepian-Wolf scheme in terms of sum-rate performance for all subspaces and source distributions. In addition, for a large class of distributions and subspaces, the scheme improves upon the Slepian-Wolf approach. The nested-linear-code scheme may be viewed as uniting under a common framework, both the Korner-Marton approach of using a common linear encoder as well as the Slepian-Wolf approach of employing different encoders at each source. Along the way, we prove an interesting and fundamental structural result on the nature of subspaces of an m-dimensional vector space V with respect to a normalized measure of entropy. Here, each element in V corresponds to a distinct linear combination of a set {Xi}im=1 of m random variables whose joint probability distribution function is given.

Spectral intensity distribution of trapped

To calculate static response properties of a many-body system, local density approximation (LDA) can be safely applied. But, to obtain dynamical response functions, the applicability of LDA is limited bacause dynamics of the system needs to be considered as well. To examine this in the context of cold atoms, we consider a system of non-interacting spin4 fermions confined by a harmonic trapping potential. We have calculated a very important response function, the spectral intensity distribution function (SIDF), both exactly and using LDA at zero temperature and compared with each other for different dimensions, trap frequencies and momenta. The behaviour of the SIDF at a particular momentum can be explained by noting the behaviour of the density of states (DoS) of the free system (without trap) in that particular dimension. The agreement between exact and LDA SIDFs becomes better with increase in dimensions and number of particles.

Kinetic theory for particle concentration distribution in two phase flow

The results of experiments in open channels and closed pipelines show two kinds of patterns for the vertical distribution of particle concentration (i.e., pattern I and pattern II). The former shows a pattern of maximum concentration at some location above the bottom and the downward decay of the concentration below the location. The latter always shows an increase of the particle concentration downward over the whole vertical, with the maximum value at the bottom. Many investigations were made on the pattern II, but few were made on pattern I. In this paper, a particle velocity distribution function is first obtained in the equilibrium state or in dilute steady state for the particle in two-phase flows, then a theoretical model for the particle concentration distribution is derived from the kinetic theory. More attention is paid to the predictions of the concentration distribution of pattern I and comparisons of the present model are made with the data measured by means of laser doppler anemometry (LDA). Very good agreements are obtained between the measured and calculated results.

双晶晶界在高温下的热稳定性的分子动力学研究

晶界结构在高温下的热稳定性问题是一个长期争论而又未能解决的问题，其争论的焦点是：在远低于熔点的温度下，晶界结构是否发生了可观察到的无序化，即是否存在一个远低于熔点的结构转化温度。为了能澄清这一争论，本文系统地研究了晶界结构的热稳定性。为了消除相互作用势的影响和系统误差，本文首先采用Morse势和经验多体势分别对铝、铜单晶的熔化过程进行了分子动力学模拟。在平衡态下，通过计算表征结构无序化的静态结构因子、径向分布函数和单晶原子位形图，获得了铝、铜单晶的熔点，结果表明：多体势计算的铝和铜的单晶熔点更接近实验值。因此，采用经验多体势应用分子动力学方法分别模拟了铝、铜Σ3、Σ5、Σ9、Σ11、Σ19、Σ33六种对称倾侧双晶晶界晶界结构由有序向无序转化的过程，计算了平衡态下的表征结构无序化的静态结构因子、径向分布函数和晶界原子位形图并将多体势获得的铝、铜单晶熔点作为晶界结构转化温度的约化熔点，获得了铝、铜Σ3、Σ5、Σ9、Σ11、Σ19、Σ33六种对称倾侧双晶晶界结构的转化温度和熔点，结果表明：1．Σ5、Σ9、Σ11、Σ19、Σ33五种对称倾侧双晶晶界均在远低于单晶熔点温度时，晶界结构发生了可观察到的无序化，而且双晶晶界结构的转变温度相差不大，双晶晶界熔点也低于单晶熔点。2．Σ3晶界在温度远低于熔点时，其晶界结构没有发生可观察到的无序化；Σ3晶界的转化温度与单晶熔点接近。所以，可以认为Σ3晶界不存在转化温度。这是由于Σ3晶界为共格孪晶，具有较低的能量。综上所述，除Σ3共格孪晶外，在远低于熔点温度下，晶界结构发生了可观察到的无序化，即：存在一个远低于熔点的转化温度，此时其静态结构因子约为0.5左右；晶界结构的熔点均低于单晶熔点，此时其静态结构因子约为0.15左右。从全文模拟结果可以看出，静态结构因子、径向分布函数、晶界原子位形图三种方法在确定晶界的结构转化温度和熔点时，静态结构因子是最有效、最准确的定量方法。

Effects of El Niño–Southern Oscillation events on catches of Bigeye Tuna (Thunnus obesus) in the eastern Indian Ocean off Java

The effects of El Niño–Southern Oscillation events on catches of Bigeye Tuna (Thunnus obesus) in the eastern Indian Ocean (EIO) off Java were evaluated through the use of remotely sensed environmental data (sea-surface-height anomaly [SSHA], sea-surface temperature [SST], and chlorophyll a concentration), and Bigeye Tuna catch data. Analyses were conducted for the period of 1997–2000, which included the 1997–98 El Niño and 1999–2000 La Niña events. The empirical orthogonal function (EOF) was applied to examine oceanographic parameters quantitatively. The relationship of those parameters to variations in catch distribution of Bigeye Tuna was explored with a generalized additive model (GAM). The mean hook rate was 0.67 during El Niño and 0.44 during La Niña, and catches were high where SSHA ranged from –21 to 5 cm, SST ranged from 24°C to 27.5°C, and chlorophyll-a concentrations ranged from 0.04 to 0.16 mg m–3. The EOF analysis confirmed that the 1997–98 El Niño affected oceanographic conditions in the EIO off Java. The GAM results indicated that SST was better than the other environmental factors (SSHA and chlorophyll-a concentration) as an oceanographic predictor of Bigeye Tuna catches in the region. According to the GAM predictions, the highest probabilities (70–80%) for Bigeye Tuna catch in 1997–2000 occurred during oceanographic conditions during the 1997–98 El Niño event.

Daily rainfall along the United States Pacific Coast appears to conform to a square-root normal probability distribution

EXTRACT (SEE PDF FOR FULL ABSTRACT): As part of a study of climatic influences on landslide initiation, a statistical analysis of long-term (>40 years) records of daily rainfall from 24 Pacific coastal stations, from San Diego to Cape Flattery, disclosed an unexpected result - the square root of the daily rainfall closely approximates a normal distribution function. ... This paper illustrates the use of the square-root-normal distribution to analyze variations in precipitation along the mainland United States Pacific Coast with examples of orographic enhancement, rain shadows, and increase in precipitation frequency with geographic latitude.

FIRST PASSAGE APPROXIMATION FOR NORMAL STATIONARY RANDOM PROCESSES.

A new approximate solution for the first passage probability of a stationary Gaussian random process is presented which is based on the estimation of the mean clump size. A simple expression for the mean clump size is derived in terms of the cumulative normal distribution function, which avoids the lengthy numerical integrations which are required by similar existing techniques. The method is applied to a linear oscillator and an ideal bandpass process and good agreement with published results is obtained. By making a slight modification to an existing analysis it is shown that a widely used empirical result for the asymptotic form of the first passage probability can be deduced theoretically.

Isotopic dependence of production cross sections of superheavy nuclei in hot fusion reactions

The dinuclear system model has been further developed by introducing the barrier distribution function method in the process of heavy-ion capture and fusion to synthesize superheavy nuclei. The capture of two colliding nuclei, formation and de-excitation process of compound nucleus are decribed by using empirical coupled channel model, solving master equation numerically and statistical evaporation model, respectively. Within the framework of the dinuclear system model, the fusion-evaporation excitation functions of the systems Ca-48(Am-243, 3n-5n) (288-286)115 and Ca-48(Cm-248, 3n-5n)(293-291)116 are calculated, which are used for synthesizing new superheavy nuclei at Dubna in recent years. Isotopic dependence of production cross sections with double magic nucleus Ca-48 bombarding actinide targets U, Np, Pu, Am, Cm to synthesize superheavy nuclei with charged numbers Z=112-116 is analyzed systematically. Based on these analysis, the optimal projectile-target combination and the optimal excitation energy are proposed. It is shown that shell correction energy and neutron separation energy will play an important role on the isotopic dependence of production cross sections of superheavy nuclei.

Modelling raindrop impact and splash erosion processes within a spatial cell: a stochastic approach

A new approach is proposed to simulate splash erosion on local soil surfaces. Without the effect of wind and other raindrops, the impact of free-falling raindrops was considered as an independent event from the stochastic viewpoint. The erosivity of a single raindrop depending on its kinetic energy was computed by an empirical relationship in which the kinetic energy was expressed as a power function of the equivalent diameter of the raindrop. An empirical linear function combining the kinetic energy and soil shear strength was used to estimate the impacted amount of soil particles by a single raindrop. Considering an ideal local soil surface with size of I m x I m, the expected number of received free-failing raindrops with different diameters per unit time was described by the combination of the raindrop size distribution function and the terminal velocity of raindrops. The total splash amount was seen as the sum of the impact amount by all raindrops in the rainfall event. The total splash amount per unit time was subdivided into three different components, including net splash amount, single impact amount and re-detachment amount. The re-detachment amount was obtained by a spatial geometric probability derived using the Poisson function in which overlapped impacted areas were considered. The net splash amount was defined as the mass of soil particles collected outside the splash dish. It was estimated by another spatial geometric probability in which the average splashed distance related to the median grain size of soil and effects of other impacted soil particles and other free-falling raindrops were considered. Splash experiments in artificial rainfall were carried out to validate the availability and accuracy of the model. Our simulated results suggested that the net splash amount and re-detachment amount were small parts of the total splash amount. Their proportions were 0.15% and 2.6%, respectively. The comparison of simulated data with measured data showed that this model could be applied to simulate the soil-splash process successfully and needed information of the rainfall intensity and original soil properties including initial bulk intensity, water content, median grain size and some empirical constants related to the soil surface shear strength, the raindrop size distribution function and the average splashed distance. Copyright (c) 2007 John Wiley & Sons, Ltd.

Resuspension and advection processes affecting suspended particulate matter concentrations in the central English Channel

Suspended particulate matter (SPM) measurements obtained along a cross-section in the central English Channel (Wight-Cotentin transect) indicate that the area may be differentiated into: (1) an English coastal zone, associated with the highest concentrations; (2) a French coastal zone, with intermediate concentrations; and (3) the offshore waters of the Channel, characterised by a very low suspended-sediment load. The SPM particle-size distribution was modal close to the English coast (main mode 10-12 mu m); the remainder of the area was characterised by flat SPM distributions. Examination of the diatom communities in the SPM suggest:; that material resuspended in the intertidal zone and the estuarine environments was advected towards the offshore waters of the English Channel. Considerable variations in SPM concentrations occurred during a tidal cycle: maximum concentrations were sometimes up to 3 times higher than the minimum concentrations, Empirical orthogonal function (EOF) analysis of the SPM concentration time series indicates that, although the bottom waters were more turbid than the surficial waters, this was not likely to be the result of in situ sediment resuspension. Instead, the observed variations appear to be controlled mainly by advective mechanisms. The limited resuspension was probably caused by: (1) the limited availability of fine-grained material within the bottom sediments, and (2) 'bed-armouring' processes which protect the finer-grained fractions of the seabed material from erosion and entrainment within the overlying flow during the less energetic stages of the tide.

Reconstruction of vertical thermal structure from several subsurface temperatures in the China Seas and adjacent waters

Empirical Orthogonal Function (EOF) analysis is used in this study to generate main eigenvector fields of historical temperature for the China Seas (here referring to Chinese marine territories) and adjacent waters from 1930 to 2002 (510 143 profiles). A good temperature profile is reconstructed based on several subsurface in situ temperature observations and the thermocline was estimated using the model. The results show that: 1) For the study area, the former four principal components can explain 95% of the overall variance, and the vertical distribution of temperature is most stable using the in situ temperature observations near the surface. 2) The model verifications based on the observed CTD data from the East China Sea (ECS), South China Sea (SCS) and the areas around Taiwan Island show that the reconstructed profiles have high correlation with the observed ones with the confidence level > 95%, especially to describe the characteristics of the thermocline well. The average errors between the reconstructed and observed profiles in these three areas are 0.69A degrees C, 0.52A degrees C and 1.18A degrees C respectively. It also shows the model RMS error is less than or close to the climatological error. The statistical model can be used to well estimate the temperature profile vertical structure. 3) Comparing the thermocline characteristics between the reconstructed and observed profiles, the results in the ECS show that the average absolute errors are 1.5m, 1.4 m and 0.17A degrees C/m, and the average relative errors are 24.7%, 8.9% and 22.6% for the upper, lower thermocline boundaries and the gradient, respectively. Although the relative errors are obvious, the absolute error is small. In the SCS, the average absolute errors are 4.1 m, 27.7 m and 0.007A degrees C/m, and the average relative errors are 16.1%, 16.8% and 9.5% for the upper, lower thermocline boundaries and the gradient, respectively. The average relative errors are all < 20%. Although the average absolute error of the lower thermocline boundary is considerable, but contrast to the spatial scale of average depth of the lower thermocline boundary (165 m), the average relative error is small (16.8%). Therefore the model can be used to well estimate the thermocline.

Distribution of the nonlinear random ocean wave period

Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37A degrees 27.6' N, 122A degrees 15.1' E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (nu=0.3-0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional statistical wave theory.