Related papers: Cluster size distribution in the autocatalytic gro…
A notion of measure solution is formulated for a coagulation-diffusion equation, which is the natural counterpart of Smoluchowski's coagulation equation in a spatially inhomogeneous setting. Some general properties of such solutions are…
We prove well-posedness of global solutions for a class of coagulation equations which exhibit the gelation phase transition. To this end, we solve an associated partial differential equation involving the generating functions before and…
The Sweeny algorithm for the $Q$-state random-cluster model in two dimensions is shown to exhibit a rich mixture of critical dynamical scaling behaviors. As $Q$ decreases, the so-called critical speeding-up for non-local quantities becomes…
The formation of self assembled structures such as micelles has been intensively studied and is well understood. The ability of a solution of amphiphilic molecules to develop micelles is depending on the concentration and characterized by…
A two species reaction-diffusion model, in which particles diffuse on a one-dimensional lattice and annihilate when meeting each other, has been investigated. Mean field equations for general choice of reaction rates have been solved…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
The crystallization proceeds by the advance of the crystal faces into the disordered phase at the expense of the supersaturation which is not sustained in our model. Using a conservation constraint for the transformation ratio and a kinetic…
Nucleation and growth of crystal in an oxide glass was studied in a Si B Al Zr Nd Ca Na O system. The nucleation and growth process was monitored by thermal analysis and isothermal experiments. For the Ca sample the crystallization is…
We study numerically a coagulation-fragmentation model derived by Niwa and further elaborated by Degond et al., where a unique equilibrium distribution of group sizes is shown to exist in both cases of continuous and discrete group size…
Modeling of aggregation processes in space-inhomogeneous systems is extremely numerically challenging since complicated aggregation equations -- Smoluchowski equations are to be solved at each space point along with the computation of…
The paper compares the statistical description of physical-metallurgical processes and ceramic-polycrystalline evolutions, termed the normal grain growth (NGG), as adopted to soft- and chemically-reactive grains, with a Smoluchowski's…
We present a simple theory for the evolution of initially compact clusters in a tidal field. The fundamental ingredient of the model is that a cluster conducts a constant fraction of its own energy through the half-mass radius by two-body…
Most classification methods are based on the assumption that data conforms to a stationary distribution. The machine learning domain currently suffers from a lack of classification techniques that are able to detect the occurrence of a…
We investigate the influence of a shear flow on the process of nucleation. Mesoscopic nonequilibrium thermodynamics is used to derive the Fokker-Planck equation governing the evolution of the cluster size distribution in a metastable phase…
We analyse time evolution of spread complexity (SC) in an isolated interacting quantum many-body system when it is subjected to a sudden quench. The differences in characteristics of the time evolution of the SC for different time scales is…
We propose a new type of diffuse interface model describing the evolution of a tumor mass under the effects of a chemical substance (e.g., a nutrient or a drug). The process is described by utilizing the variables $\varphi$, an order…
The new approach outlined in Paper I (Spurzem \& Giersz 1996) to follow the individual formation and evolution of binaries in an evolving, equal point-mass star cluster is extended for the self-consistent treatment of relaxation and close…
In this paper, temporal growth and morphological evolution of ZnO nano-colloids were studied by in-situ UV-Vis absorption spectroscopy and Transmission Electron Microscopy (TEM) respectively. Nucleation of the nanoparticles was observed to…
We study the nucleation of crystalline cluster phases in the generalized exponential model with exponent n=4. Due to the finite value of this pair potential for zero separation, at high densities the system forms cluster crystals with…
Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process…