单体迁移驱使的聚集体生长

本文提出了一个可解的聚集体生长模型。在系统中，在质量为l的B聚集体的作用下，一个单体从质量为i的A聚集体迁移到质量为j的A聚集体，这个迁移反应速率核为K(i;j;l) i^μ j^ν l^varpi（ω≥0）。利用平均场速率方程方法，本文得到了几种不同情况下的聚集体质量分布的解析解。对μ=ν的系统，在μ<3/2的情况下系统的聚集体质量分布a_k(t)具有一种普适的标度形式。对于μ≠ν的系统，只有在μ<ν和μ+ν<2的情况下a_k(t)才满足标度形式。同时，在μ+ν>2（μ≠ν）或者μ>3/2（μ=ν）的情况下，系统将发生类凝胶相变。此外，本文也研究了反应核为K(i;j;l)μ(i^μ j^ν+ i^νj^μ )lω的系统的动力学标度行为。结果表明，聚集体质量分布只有在μ+ν<3的情况下才遵循标度律，而在其他情况下系统将在足够长的时间后发生类凝胶相变。     

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.     

Interfacial growth in driven Ginzburg-Landau models: Short and long-time dynamics

Interfacial growth in driven systems is studied from the initial stage to the longtime regime. Numerical integrations of a Ginzburg-Landan type equation with a new flux term introduced by an external field are presented. The interfacial instabilities are induced by the external field. From the numerical results, we obtain the dispersion relation for the initial growth. During the intermediate temporal regime, fingers of a characteristic triangular shape could grow. Depending on the boundary conditions, the final state corresponds to strips, multifinger states, or a one-finger state. The results for the initial growth are interpreted by means of surface-driven and Mullins-Sekerka instabilities. The shape of the one-finger state is explained in terms of the characteristic length introduced by the external field.     

Rate-equation approach to island capture zones and size distributions in epitaxial growth

Understanding and predicting the effects of correlations between island size and the rate of monomer capture has been shown to be the central problem in predicting the island-size distribution in submonolayer growth. Here we summarize a method which involves a self-consistent coupling of evolution equations for the capture-zone distributions with rate equations for the island-size distribution. The method has been successfully applied to irreversible submonolayer growth in both one and two dimensions to predict the size-dependent capture numbers and island-size distributions.     

Cluster size distributions in equilibrium

Equilibrium size distributions for finite system containingM monomers in a volumeV undergoing coagulation (polymerization)/fragmentation, are determined for coagulation rateK _ij and fragmentation rateF _ij , corresponding to the processA _i +A _j A _i+j (hereA _k denotes a cluster containingk monomeric units). It is shown that microscopic detailed balance impliesF _ij /K _ij =a _i a _j /a _i+j , where anda _k are arbitrary. The mean and most probable size distributionc _k = ^–1 a _k e ^–k coincide in the thermodynamic limitM, V, =M/V fixed. If , 2<<3, then the theory predicts a (solgel) phase transition at a well defined value ofq = ^–1, with critical exponents = and = –2. The gel fraction exponent assumes its classical value unity, probably due to the neglect of spatial fluctuations. Finally it is indicated how the theory can in principle be extended to account for isomerism and cyclization.     

Effects on generalized growth models driven by a non-Poissonian dichotomic noise

In this paper we consider a general growth model with stochastic growth rate modelled via a symmetric non-poissonian dichotomic noise. We find an exact analytical solution for its probability distribution. We consider the, as yet, unexplored case where the deterministic growth rate is perturbed by a dichotomic noise characterized by a waiting time distribution in the two state that is a power law with power 1 < μ < 2. We apply the results to two well-known growth models; Malthus-Verhulst and Gompertz.     

Velocity distributions in glottal models

Velocity distributions within three models of the human larynx, namely, a rigid plexiglas model, an excised canine larynx, and a computational model are investigated with experimental and theoretical analyses. A plexiglas wind tunnel with interchangeable glottal constrictions was used as a two-dimensional steady-flow model to measure velocity and pressure for various glottal shapes. A canine excised larynx was used as a prototype pulsatile flow model to study pressure and velocity variations during phonation. Results of the plexiglas modelling indicated a parabolic laminar velocity profile upstream of the glottal constriction and turbulent and asymmetric velocity profiles downstream of the glottal constriction. The time-averaged velocities of the excised larynx had similarities with the plexiglas model results, and instabilities and asymmetries were also demonstrated by the computational method.     

Asymptotics of work distributions in a stochastically driven system

We determine the asymptotic forms of work distributions at arbitrary times T, in a class of driven stochastic systems using a theory developed by Nickelsen and Engel (EN theory) [D. Nickelsen and A. Engel, Eur. Phys. J. B 82, 207 (2011)], which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in path integral form, are characterised by having quadratic augmented actions. We first illustrate EN theory, for a deterministically driven system – the breathing parabola model, and show that within its framework, the Crooks fluctuation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial, which also determines the exact moment-generating-function at arbitrary times. We then extend our analysis to a stochastically driven system, studied in references [S. Sabhapandit, EPL 89, 60003 (2010); A. Pal, S. Sabhapandit, Phys. Rev. E 87, 022138 (2013); G. Verley, C. Van den Broeck, M. Esposito, New J. Phys. 16, 095001 (2014)], for both equilibrium and non-equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary T. For dissipated work in the steady state, we compare the large T asymptotic behaviour of our solution to the functional form obtained in reference [New J. Phys. 16, 095001 (2014)]. In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with numerical simulations. Our solutions are exact in the low noise (β →?∞) limit.     

Wealth distributions in asset exchange models

A model for the evolution of the wealth distribution in an economically interacting population is introduced, in which a specified amount of assets are exchanged between two individuals when they interact. The resulting wealth distributions are determined for a variety of exchange rules. For “random” exchange, either individual is equally likely to gain in a trade, while “greedy” exchange, the richer individual gains. When the amount of asset traded is fixed, random exchange leads to a Gaussian wealth distribution, while greedy exchange gives a Fermi-like scaled wealth distribution in the long-time limit. Multiplicative processes are also investigated, where the amount of asset exchanged is a finite fraction of the wealth of one of the traders. For random multiplicative exchange, a steady state occurs, while in greedy multiplicative exchange a continuously evolving power law wealth distribution arises. Received: 13 August 1997 / Revised: 31 December 1997 / Accepted: 26 January 1998     

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.     

Fast-ionic-conductor behavior of driven lattice-gas models

We discuss driven diffusive lattice-gas systems as a model for fast ionic conductors, derive associated hydrodynamic equations and expressions for transport coefficients, and compare mean-field theory, Monte Carlo results and experimental observations. The comparison between model and real behaviours helps to understand some properties of those materials which seem to be characterized by the occurrence of nonequilibrium steady states and phase transitions. In particular, our study suggests the existence in Nature of a novel (nonequilibrium) universality class.     

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.     

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.     

Size selected growth of nanodots: effects of growth kinetics and energetics on the formation of stationary size distributions

The size selection of nanodots during the growth is studied by using a reaction kinetic model, where reaction rates depend on the dot size. The characteristic feature of the reaction rates is the energetics, where the free energy of dots has a minimum at the certain dot size. The model equations are solved by using a particle coalescence simulation method. We find phenomenologically three distinct stages of growth. First, during the initial deposition stage, distributions with high density of small dots occur. Second, there is an intermediate and short-lived stationary state, which is controlled by kinetics of growth. Third, a long-lived stationary state is obtained, with nearly Gaussian size distributions, mostly determined by the energetics of the growth but also significantly affected by the kinetics. In the final stage, size selection and narrowing of the distributions occur. It is also shown that in the final stage of growth the Fokker-Planck type continuum model describes well the evolution of the distributions and the size selection.     

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.     

Eigenvalue distributions in matrix models for Chern-Simons-matter theories

The eigenvalue distribution is investigated for matrix models related via the localization to Chern-Simons-matter theories. An integral representation of the planar resolvent is used to derive the positions of the branch points of the planar resolvent in the large ?t Hooft coupling limit. Various known exact results on eigenvalue distributions and the expectation value of Wilson loops are reproduced.     

Helicity-dependent generalized parton distributions in constituent quark models

Helicity-dependent generalized parton distributions of the nucleon are derived from the overlap representation of generalized parton distributions using light-cone wave functions obtained in constituent quark models. Results from two different quark models are used also to study the angular momentum sum rule and the spin asymmetry in polarized electron scattering.     

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.