Continuous-time birth-death Markov processes serve as useful models in population biology. When the birth-death rates are nonlinear, the time evolution of the first n order moments of the population is not closed, in the sense that it depends on moments of order higher than n. For analysis purposes, the time evolution of the first n order moments is often made to be closed by approximating thes...

The closure problem of the stellar hydrodynamic equations is studied in a general case by describing the family of phase space density functions for which the collisionless Boltzmann equation is strictly equivalent to a finite subset of moment equations. The method is based on the use of maximum entropy distributions, which are afterwards generalised to phase space density functions depending o...

As stochastic simulations become increasingly common in biological research, tools for analysis of such systems are in demand. The deterministic analogue to stochastic models, a set of probability moment equations equivalent to the Chemical Master Equation (CME), offers the possibility of a priori analysis of systems without the need for computationally costly Monte Carlo simulations. Despite t...

Kinetic equations containing terms for spatial transport, gravity, fluid drag and particleparticle collisions can be used to model dilute gas-particle flows. However, the enormity of independent variables makes direct numerical simulation of these equations almost impossible for practical problems. A viable alternative is to reformulate the problem in terms of moments of velocity distribution. ...

This work applies the moment method onto a generic form of kinetic equations, given by the Boltzmann equation, to simplify kinetic models of particle systems. This leads to the moment closure problem which is addressed using entropy-based moment closure techniques utilizing entropy minimization. The resulting moment closure system forms a system of partial differential equations that retain str...

This paper discusses the application of moment closures to continuous Markov chains derived from process algebras such as GPEPA and MASSPA. Two related approaches are being investigated. Firstly we re-formulate normal moment closure in a process algebra framework using Isserlis’ theorem. Secondly we apply a mixture of this normal closure and less precise moment closures for the purpose of reduc...

We present a population density and moment-based description of the stochastic dynamics of domain Ca-mediated inactivation of L-type Ca channels. Our approach accounts for the effect of heterogeneity of local Ca signals on whole cell Ca currents; however, in contrast with prior work, e.g., Sherman et al. (1990), we do not assume that Ca domain formation and collapse are fast compared to channel...

We consider condensing flow with droplets that nucleate and grow, but do not slip with respect to the surrounding gas phase. To compute the local droplet size distribution, one could solve the general dynamic equation and the fluid dynamics equations simultaneously. To reduce the overall computational effort of this procedure by roughly an order of magnitude, we propose an alternative procedure...

In this paper parabolic random partial differential equations and parabolic stochastic partial differential equations driven by a Wiener process are considered. A deterministic, tensorized evolution equation for the second moment and the covariance of the solutions of the parabolic stochastic partial differential equations is derived. Well-posedness of a space-time weak variational formulation ...

We investigate the dynamics of a deterministic finite-sized network of synaptically coupled spiking neurons and present a formalism for computing the network statistics in a perturbative expansion. The small parameter for the expansion is the inverse number of neurons in the network. The network dynamics are fully characterized by a neuron population density that obeys a conservation law analog...