Cluster dynamics and cluster size distributions in systems of self-propelled particles

Systems of self-propelled particles (SPP) interacting by a velocity alignment mechanism in the presence of noise exhibit rich clustering dynamics. Often, clusters are responsible for the distribution of (local) information in these systems. Here, we investigate the properties of individual clusters in SPP systems, in particular the asymmetric spreading behavior of clusters with respect to their direction of motion. In addition, we formulate a Smoluchowski-type kinetic model to describe the evolution of the cluster size distribution (CSD). This model predicts the emergence of steady-state CSDs in SPP systems. We test our theoretical predictions in simulations of SPP with nematic interactions and find that our simple kinetic model reproduces qualitatively the transition to aggregation observed in simulations.     

Electron-hole droplets size at equilibrium

A finite lifetime τ implies that the liquid phase can only form droplets of finite size. Introducing this finite τ in the usual nucleation theory, one can obtain analytical expressions for the electron-hole droplets size, number and exciton density at steady state, in the limit of large τ. This equilibrium size results, in fact, from a Maxwell construction on an appropriate chemical potential.     

Multidimensionally resolved pore size distributions

A novel method of determining median pore size and pore size distributions as a function of spatial position inside a porous sample is described. Pore sizes have been measured with 1-, 2- and 3-dimensional spatial resolution, using NMR cryoporometry in conjunction with magnetic resonance imaging techniques. The method is suitable for pore diameters in the range of 30 Å to over 2000 Å pore diameter, and is based on the technique of freezing a liquid in the pores and measuring the melting temperature by nuclear magnetic resonance. Since the melting point is depressed for crystals of small size, the melting point depression gives a measurement of pore size.     

Cluster size distribution at criticality

Monte Carlo studies of the cluster size distribution for the site percolation problem on the triangular lattice are extended to lattices with up to 4 × 10¹¹ sites. Agreement with the predictions of scaling theory at p_c is excellent over a range of cluster sizes spanning five orders of magnitude.     

Variations in raindrop size distributions measured at Rome

Summary The knowledge of raindrop size distributions is of great interest to cloud physicists, radar meteorologists and communication engineers. Beginning from the Winter 1986–87, the Precipitation Group of the Atmospheric Physics Institute installed on the roof of the Institute building in Roma-Eur a disdrometer RD-69. The sensor is an electromechanical device with surface of 50 cm² able to measure the raindrop diameter with a precision of 5% and a resolution (delay between two drops hitting the sensor) of one millisecond. After the calibration, significant precipitations were recorded continuously, with a sample period of 1 minute, during the whole life of the storms. It can be expected that a knowledge of the drop size distributions, and in particular of the differences between distrubitions, can be used to infer details of the storm and the environment. In this work the first results of the analyses are presented. Particular attention was conferred to the variation characteristics of the precipitation type (thunderstorm and widespread) as well as to the variations of the distributions in short time intervals, that may be caused by different effects, for example the growth and decay of a precipitation cell or the movement of a cell combined with the different fall velocities of small and large drops. Paper presented at the IV Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 22–24, 1987, Rome.     

Aggregate size distributions in migration driven growth models

The kinetics of aggregate growth through reversible migrations between any two aggregates is studied. We propose a simple model with the symmetrical migration rate kernel at which the monomers migrate from the aggregates of size k to those of size j. The results show that for the case, the aggregate size distribution approaches a conventional scaling form; moreover, the typical aggregate size grows as in the case and as in the case. We also investigate another simple model with the asymmetrical rate kernel ( ), which exhibits some scaling properties quite different from the symmetrical one. The aggregate size distribution satisfies the conventional scaling form only in the case of and , and the typical aggregate size grows as .Received: 14 October 2003, Published online: 23 December 2003PACS: 82.20.-w Chemical kinetics and dynamics - 68.43.Jk Diffusion of adsorbates, kinetics of coarsening and aggregation - 89.75.Da Systems obeying scaling laws     

An NMR protocol for determining ice crystal size distributions during freezing and pore size distributions during freeze-drying

Nuclear magnetic resonance water proton relaxometry is widely used to investigate pore size distributions and pore connectivity in brine-saturated porous rocks and construction materials. In this paper we show that, by replacing water with acetone, a similar method can be used to probe the porous structure of freeze-dried starch gels and therefore the ice crystal size distribution in frozen starch gels. The method relies on the observation that the starch surface acts as a powerful relaxation sink for acetone proton transverse magnetization so that Brownstein-Tarr theory can be used to extract the pore size distribution from the relaxation data. In addition the relaxation time distribution is found to depend on the spectrometer frequency and the Carr-Purcell-Meiboom-Gill pulse spacing, consistent with the existence of large susceptibility-induced field gradients within the pores. The potential of this approach for noninvasively measuring ice crystal size distributions during freezing and pore size distributions during freeze-drying in other food systems is discussed.     

On non‐equilibrium photon distributions in the Casimir effect

The electromagnetic field in a typical geometry of the Casimir effect is described in the Schwinger–Keldysh formalism. The main result is the photon distribution function (Keldysh Green function) in any stationary state of the field. A two‐plate geometry with a sliding interface in local equilibrium is studied in detail, and full agreement with the results of Rytov fluctuation electrodynamics is found.     

Log-normal size distributions of ultrafine metal particles

We have produced particles with median diameters well below 5 nm of Al, Fe, Co and Sn, using inert gas evaporation. The logarithm of the particle volume has a Gaussian distribution which can be explained by a theoretical model for coalescence of liquid particles. The standard deviations of these log-normal distributions, as inferred from electron microscopy, always lie close to a common value regardless of the kind of metal or method of evaporation.     

Simulation of bimodal size distributions for coarsening

We introduce two very simple models to decribe coarsening. Both models possesses two characteristics: long range diffusive interaction and fluctuations. Computer simulations show that they lead to bimodal particle size distributions. The appearance of bimodal distribution can be related to a discontinuous particle growth rate.     

City size distributions for India and China

This paper studies the size distributions of urban agglomerations for India and China. We have estimated the scaling exponent for Zipf’s law with the Indian census data for the years of 1981-2001 and the Chinese census data for 1990 and 2000. Along with the biased linear fit estimate, the maximum likelihood estimate for the Pareto and Tsallis q-exponential distribution has been computed. For India, the scaling exponent is in the range of [1.88, 2.06] and for China, it is in the interval [1.82, 2.29]. The goodness-of-fit tests of the estimated distributions are performed using the Kolmogorov-Smirnov statistic.     

Grain size distributions for competitive growth with nucleation

The paper introduces and discusses an idealized competitive growth model with nucleation for the microstructure formation during dense branching phase separation in thin Al/Ge films. Grain size and grain length distributions for the new model are obtained analytically and by simulation. These distributions exhibit a characteristic scaling form similar to cluster size distributions in many other growth models. The cutoff functions in these scaling forms and their influence on the determination of effective exponents are studied in detail. It is found that nucleation introduces a new length scale into the other-wise selfsimilar competitive growth model. This length scale appears only inside the cutoff function and diverges algebraically as the nucleation rate vanishes. We find both analytically and by simulation that the cutoff functions can exhibit stretched exponential behaviour exp(–x ) for large arguments. Our analytical and simulation results for grain size and grain length distributions are in excellent quantitative agreement.     

Droplet size and velocity distributions for spray modelling

Methods for constructing droplet size distributions and droplet velocity profiles are examined as a basis for the Eulerian spray model proposed in Beck and Watkins (2002,2003) [5], [6]. Within the spray model, both distributions must be calculated at every control volume at every time-step where the spray is present and valid distributions must be guaranteed. Results show that the Maximum Entropy formalism combined with the Gamma distribution satisfy these conditions for the droplet size distributions. Approximating the droplet velocity profile is shown to be considerably more difficult due to the fact that it does not have compact support. An exponential model with a constrained exponent offers plausible profiles.     

Use of elemental size distributions in identifying particle formation modes

The chemical composition of particles generated during pulverized coal combustion is the consequence of their formation processes. This work aims to use the size resolved elemental composition of coal-derived particles to identify their formation modes. A size-classified bituminous coal is burnt in a laboratory drop tube furnace at 1150, 1250, and 1350 °C, respectively. The elemental composition of the size-segregated particles from coal combustion is analyzed and the total mass fraction size distributions of Si and Al are obtained. Three particle formation modes are observed in these distribution profiles. The coarse mode has the highest value of the total mass fraction of Si and Al while the ultrafine mode has the lowest one. The total mass fraction of Si and Al in these two modes is nearly independent of particle size. It is believed that the coarse mode is formed by the mineral coalescence mechanism and the ultrafine mode by the vaporization–condensation mechanism. The difference in the total mass fraction of Si and Al between the central mode and the other two indicates that the central mode is formed by different mechanisms. Based on the observation that the total mass fraction of Si and Al in this mode increases with increasing particle size, heterogeneous condensation of vaporized species on existing fine residual ash particles is proposed to account for the formation of these particles. The study of the elemental composition of the three modes represented in five categories verifies the proposed formation mechanisms for them to some extent.     

Small sample size effects in statistical analyses of eigenvalue distributions

The effects of small sample sizes on the statistical analysis of eigenvalue distributions were analyzed numerically. The behavior of the nearest-neighbor spacing distribution, the ₃ statistic, and the linear correlation coefficient between adjacent spacings was studied, and the effects of missing or spurious levels and of unfolding an energy-dependent level density were explored. For small sample sizes the nearest-neighbor spacing distribution appears to be the most reliable of these three statistics.We wish to thank T. Guhr for his computer code to calculate GOE spectra and T. von Egidy for discussions concerning the energy dependence of level densities. This work was supported in part by the US Department of Energy under Grant Nos. DE-FG05-87ER40353 and DE-FG05-88ER40441.     

The size dependence of equilibrium elastic strain in finite epitaxial islands

The equilibrium elastic strain in epitaxial islands of small size is shown to have a sawtooth dependence on island width by minimizing the systems energy as calculated from a periodic interaction potential between substrate and overgrowth. Such a sawtooth variation is consistent with Vincent's observations and idea that a given misfit between island and substrate may not be entirely accommodated by an integral number of identical misfit dislocations, and hence, the remaining misfit, which depends in part on island width, will be accommodated by residual elastic strain. The present calculations of mechanical equilibrium support these ideas and further reveal that in some cases misfit dislocations may over compensate for the misfit, thereby introducing an elastic strain of opposite sign to that normally expected. Other results of the calculations are in agreement with earlier theoretical and experimental observations.     

Determining aerosol particle size distributions using time-resolved laser-induced incandescence

The particle size distribution within an aerosol containing refractory nanoparticles can be inferred using time-resolved laser-induced incandescence (TR-LII). In this procedure, a small volume of aerosol is heated to incandescent temperatures by a short laser pulse, and the incandescence of the aerosol particles is then measured as they return to the ambient gas temperature by conduction heat transfer. Although the cooling rate of an individual particle depends on its volume-to-area ratio, recovering the particle size distribution from the observed temporal decay of the LII signal is complicated by the fact that the LII signal is due to the incandescence of all particle size classes within the sample volume, and because of this, the particle size distribution is related to the time-resolved LII signal through a mathematically ill-posed equation. This paper reviews techniques proposed in the literature for recovering particle size distributions from TR-LII data. The characteristics of this problem are then discussed in detail, with a focus on the effect of ill-posedness on the stability and uniqueness of the recovered particle size distributions. Finally, the performance of each method is evaluated and compared based on the results of a perturbation analysis. PACS  44.05.+e; 47.70.Pq; 78.70.-g; 65.80.+n; 78.20.Ci     

Bubble dynamics and size distributions during focused ultrasound insonation

The deposition of ultrasonic energy in tissue can cause tissue damage due to local heating. For pressures above a critical threshold, cavitation will occur, inducing a much larger thermal energy deposition in a local region. The present work develops a nonlinear bubble dynamics model to numerically investigate bubble oscillations and bubble-enhanced heating during focused ultrasound (HIFU) insonation. The model is applied to calculate two threshold-dependent phenomena occurring for nonlinearly oscillating bubbles: Shape instability and growth by rectified diffusion. These instabilities in turn are shown to place physical boundaries on the time-dependent bubble size distribution, and thus the thermal energy deposition.