We investigate aggregation driven by mass injection. In this stochastic process, mass is added with constant rate r and clusters merge at a constant total rate 1 , so that both the total number of clusters and the total mass steadily grow with time. Analytic results are presented for the three classic aggregation rates K{i,j} between clusters of size i and j . When K{i,j}=const , the cluster size distribution decays exponentially. When K{i,j} proportional, i+j or K{i,j} proportional, ixj , there are two phases: (i) a condensate phase with a condensate containing a finite fraction of the mass in the system as well as finite clusters and (ii) a cluster phase with finite clusters only. For K{i,j} proportional, i+j , the cluster size distribution, c{k} , has a power-law tail, c{k} approximately k;{-gamma} in either phase. The exponent is a nonmonotonic function of the injection rate gamma=r(r-1) in the condensate phase r<2 and gamma=r in the cluster phase r>2 .
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.75.011103 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Vibrational modes and spectrum of oscillators on a scale-free network.
Phys Rev E Stat Nonlin Soft Matter Phys
March 2005
We study vibrational modes and spectrum of a model system of atoms and springs on a scale-free network where we assume that the atoms and springs are distributed as nodes and links of a scale-free network. To understand the nature of excitations with many degrees of freedom on the scale-free network, we adopt a particular model that we assign the mass M(i) and the specific oscillation frequency omega(i) of the ith atom and the spring constant K(ij) between the ith and jth atoms. We show that the density of states of the spectrum follows a scaling law P (omega(2)) proportional, variant (omega(2))(-gamma), where gamma = 3 and that as the number of nodes N is increasing, the maximum eigenvalue grows as fast as sqrt[N].
View Article and Find Full Text PDFNormal modes and frequencies from covariances in molecular dynamics or Monte Carlo simulations.
J Chem Phys
January 2004
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
We propose a simple method to obtain normal modes (NMs) and their characteristic frequencies from molecular dynamics or Monte Carlo simulations at any temperature. The resulting NM are consistent with the vibrational density of states (DOS) (every feature of the DOS can be attributed to one or few NMs). At low temperatures they coincide with the ones obtained from the Hessian matrix.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!