The formation of a distribution of cluster sizes is a common feature in a wide variety of situations. Examples include astrophysics, atmospheric physics and polymer science, [2, 3, 8]. In this paper we discuss some mathematical aspects of the Smoluchowski coagulation equation which is a model for the dynamics of cluster growth. This model involves a coupled infinite system of ordinary different...

We describe a linear network that models correlations between real-valued visible variables using one or more real-valued hidden variables-a factor analysis model. This model can be seen as a linear version of the Helmholtz machine, and its parameters can be learned using the wake-sleep method, in which learning of the primary generative model is assisted by a recognition model, whose role is t...

We have explored the role of electrokinetics in the spontaneous motion of platinum-gold nanorods suspended in hydrogen peroxide (H2O2) solutions that may arise from the bimetallic electrochemical decomposition of H2O2. The electrochemical decomposition pathway was confirmed by measuring the steady-state short-circuit current between platinum and gold interdigitated microelectrodes (IMEs) in the...

We consider a generalized class of Keller-Segel models describing the chemo-taxis of biological populations (bacteria, amoebae, endothelial cells, social insects ,...). We show the analogy with nonlinear mean field Fokker-Planck equations and generalized thermodynamics. As an illustration, we introduce a new model of chemotaxis incorporating both effects of anomalous diffusion and exclusion pri...

We classify the equilibrium solutions of the Smoluchowski equation for dipolar (extended) rigid nematic polymers under imposed elongational flow. The Smoluchowski equation couples theMaier-Saupe short-range interaction, dipole-dipole interaction, and an external elongational flow. We show that all stable equilibria of rigid, dipolar rod dispersions under imposed uniaxial elongational flow field...

We show that the Perron-Frobenius equation of microscopic chaos based on double symmetric maps leads to an inhomogeneous Smoluchowski equation with a source term. Our perturbative analysis reveals that the source term gives rise to a directed current for a strongly damped particle in a spatially periodic potential. In addition, our result proves that in the zeroth-order limit, the position dist...

We present an approach for text analysis, especially for topic words extraction and document classification, based on a probabilistic generative model. Generative models are useful since they can extract the underlying causal structure of data objects. For this model, a stochastic Helmholtz machine is used and it is fitted using the wake-sleep algorithm, a simple stochastic learning algorithm. ...

This paper describes the modifications and evolution of a thermal pulse combustionmodel for predicting the combustion oscillations of an aerovalved 250 kW pulse combustorincorporating a soot formation-combustion model. Validation of the model is carried out from theexperimental data of an aerovalved Helmholtz type pulse combustor, where a sinusoidal air inlet massflow coupled with pressure osci...

The aim of this work was to find a relationship between electroosmotic flow (EOF) velocity of the mobile phase in pressurized planar electrochromatography (PPEC) and physicochemical properties like zeta potential, dielectric constant, and viscosity of the mobile phase as well as its composition. The study included different types of organic modifiers (acetonitrile, methanol, ethanol, acetone, f...