Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear bou...

In the stochastic formulation of chemical reactions, the time evolution of the first M order statistical moments for the number of molecules of the different species involved is generally not closed, in the sense that they depend on moments of order higher than M. For analysis purposes, the time evolution of the first M order moments is often made to be closed by approximating the higher order ...

An efficient method is presented as a means of an approximate, analytic timedependent solution of the Fokker-Planck equation (FPE) for the linear Langevin model subjected to additive and multiplicative noise. We have assumed that the dynamical distribution has the same structure as the exact stationary one and that its parameters are expressed in terms of first and second moments, whose equatio...

Steel Plate Shear Wall (SPSW) is an emerging seismic load-resistant system that, compared to other systems, enjoys the advantages of stable ductile behavior, fewer detailing requirements, rapid constructability, and economy. American seismic provisions decree that a SPSW should be designed as a moment frame with a web infill plate. Specifically, in case of buildings taller than 160 ft, it decre...

A second-order total variation diminishing (TVD) method with variable flux limiters is proposed to overcome the non-realizability issue, which has been one of major obstacles in applying conventional TVD schemes moment transport equations. In present method, a realizable set at cell face reconstructed by allowing flexible selection limiter values within region. Necessary conditions for scheme s...

We propose a hybrid method for the multi-scale kinetic equations in framework of hyperbolic moment (Cai and Li SIAM J Sci Comput 32(5):2875–2907, 2010). In this method, fourth order system is chosen as governing fluid region, while with arbitrary region. When transiting from regime to regime, maximum entropy principle adopted reconstruct distribution function, so that information region can be ...

In the stochastic description of biochemical reaction systems, the time evolution of statistical moments for species population counts is described by a linear dynamical system. However, except for some ideal cases (such as zero- and first-order reaction kinetics), the moment dynamics is underdetermined as lower-order moments depend upon higher-order moments. Here, we propose a novel method to ...