共查询到20条相似文献,搜索用时 62 毫秒
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Robert M. Ziff 《Journal of statistical physics》1980,23(2):241-263
It is shown that three basic models of the Flory-Stockmayer theory of polymerization may all be described directly by means of a kinetic rate equation of a form first discussed by Smoluchowski, and correspond to the three known classes of solutions to this equation. The kinetics of gelation are discussed from the rate equation; the nature of both the Flory and the Stockmayer gelation theories is shown, and a new model of gelation is proposed. Some new solutions to Smoluchowski's equation are given in an appendix.Supported by the U.S. DOE, the National Science Foundation, and the Petroleum Research Fund. 相似文献
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We present an application of a growth model for a system of cities. This computer model simulates the evolution of systems with measurable entities (e.g. city size), and takes into account the growth of the entities in terms of size and number. It includes a random multiplicative process for the growth of individual entities and for the creation of new ones. We use a new mathematical expression with a positive exponent α (which we call the ‘shape exponent’) and additional three parameters, to describe the dynamics of the systems’ size distributions through time. We compare the changes of a real system of cities and the model’s results quantitatively and qualitatively. Our findings suggest that there is a good agreement at the macro level between the model and the real data. 相似文献
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Elodie Leveugle Aaron Sellinger James M. Fitz-Gerald 《Applied Surface Science》2007,253(15):6456-6460
A combined experimental and computational study is performed to investigate the origin and characteristics of the surface features observed in SEM images of thin polymer films deposited in matrix-assisted pulsed laser evaporation (MAPLE). Analysis of high-resolution SEM images of surface morphologies of the films deposited at different fluences reveals that the mass distributions of the surface features can be well described by a power-law, Y(N) ∝ N−t, with exponent −t ≈ −1.6. Molecular dynamic simulations of the MAPLE process predict a similar size distribution for large clusters observed in the ablation plume. A weak dependence of the cluster size distributions on fluence and target composition suggests that the power-law cluster size distribution may be a general characteristic of the ablation plume generated as a result of an explosive decomposition of a target region overheated above the limit of its thermodynamic stability. Based on the simulation results, we suggest that the ejection of large matrix-polymer clusters, followed by evaporation of the volatile matrix, is responsible for the formation of the surface features observed in the polymer films deposited in MAPLE experiments. 相似文献
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This paper proposes a controlled particle deposition model
for cluster growth on the substrate surface and then presents exact
results for the cluster (island) size distribution. In the system,
at every time step a fixed number of particles are injected into the
system and immediately deposited onto the substrate surface. It
investigates the cluster size distribution by employing the
generalized rate equation approach. The results exhibit that the
evolution behaviour of the system depends crucially on the details
of the adsorption rate kernel. The cluster size distribution can
take the Poisson distribution or the conventional scaling form in
some cases, while it is of a quite complex form in other cases. 相似文献
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In this paper,the(2+1)-dimensional Hunter-Saxton equation is proposed and studied.It is shown that the(2+1)-dimensional Hunter–Saxton equation can be transformed to the Calogero–Bogoyavlenskii–Schiff equation by reciprocal transformations.Based on the Lax-pair of the Calogero–Bogoyavlenskii–Schiff equation,a non-isospectral Lax-pair of the(2+1)-dimensional Hunter–Saxton equation is derived.In addition,exact singular solutions with a finite number of corners are obtained.Furthermore,the(2+1)-dimensional μ-Hunter–Saxton equation is presented,and its exact peaked traveling wave solutions are derived. 相似文献
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均匀磁场中氢原子低能级简并度的解除 总被引:1,自引:0,他引:1
讨论了均匀强磁场中氢原子哈密顿量中B^2项的影响,指出在忽略自旋-轨道相互作用的情况下,该项可使氢原子低能级简并度完全解除。 相似文献
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Seeking a travelling wave solution of the classical Boussinesq system and making an ansatz for the solution,we obtain a nonlinear system of algebraic equations.We solve the system using an effective algorithm and then two general explicit solutions are obtained which are of physical interest. 相似文献
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用数学软件Mathematica研究正交非均匀电场中氢原子两个高激发态(n=4和5)的能级和波函数.讨论能级分裂,并绘制零级近似下氢原子的电子概率角分布图. 相似文献
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An asymptotic solving method for the periodic solution of a class of disturbed nonlinear evolution equation 下载免费PDF全文
<正>A class of disturbed evolution equation is considered using a simple and valid technique.We first introduce the periodic traveling-wave solution of a corresponding typical evolution equation.Then the approximate solution for an original disturbed evolution equation is obtained using the asymptotic method.We point out that the series of approximate solution is convergent and the accuracy of the asymptotic solution is studied using the fixed point theorem for the functional analysis. 相似文献
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带电细圆环与导体球壳系统的场分布 总被引:1,自引:0,他引:1
先依电象法,推导均匀带电圆环在金属导体球壳内的"象电荷";再在球坐标系下,根据电场强度的计算公式与Tay-lor展开式,计算出均匀带电细圆环在全空间的电场分布的级数形式解;进而结合唯一性定理和电场的叠加原理,获得带电细圆环与导体球壳系统的空间场分布. 相似文献
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We use a simple spring-block system as a qualitative analogous of a seismic fault. The role of the asperities present in a real seismic fault is played by sandpapers of several grades. With this experimental array Gutenberg-Richter type-laws are obtained. We also observed that the maximum characteristic event in each experimental run depends on both the mass of the sliding blocks and the age of the sandpapers used at the interface between the blocks and the rough track. 相似文献
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It is rigorously proved that the analog of the free energy for the bond and site percolation problem on
in arbitrary dimension (> 1) has a singularity at zero external field as soon as percolation appears, whereas it is analytic for small concentrations. For large concentrations at least, it remains, however, infinitely differentiable and Borel-summable. Results on the asymptotic behavior of the cluster size distribution and its moments, and on the average surface-to-size ratio, are also obtained. Analogous results hold for the cluster generating function of any equilibrium state of a lattice model, including, for example, the Ising model, but infinite-range andn-body interactions are also allowed.Supported by the Fonds National Suisse de la Recherche Scientifique (to HK). 相似文献
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《Physica A》2005,356(1):100-106
Clusters of infected individuals are defined on data from health laboratories, but this quantity has not been defined and characterized by epidemy models on statistical physics. For a system of mobile agents we simulate a model of infection without immunization and show that all the moments of the cluster size distribution at the critical rate of infection are characterized by only one exponent, which is the same exponent that determines the behavior of the total number of infected agents. No giant cluster survives independent of the magnitude of the rate of infection. 相似文献
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In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example. 相似文献
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An exact expression of the stationary distribution is found for a particular chemical model without detailed balance. An analytical approximation of this solution is obtained for small values of the concentration. It is shown that the WKB continuous approximation of the distribution is valid for all values of the concentration. 相似文献