The solution of population balance equations is a function f(t, r, x) describing a population density of particles of the property x at time t and space r. For instance, the additional independent variable x may denote the mass of the particle. The describing equation contains additional sink and source terms involving integral operators. Since the coordinate x adds at least one further dimensi...

In this work we develop, demonstrate, and distribute the code for a new Simulink block that models the dynamic evolution of the population density function for a physical system which can be modeled by a population balance equation. The name of the block is PCSS, for population balance modeling using the conservation element/solution element method in Simulink. The block interfaces with an auxi...

We investigate the phenomenon of extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling (scenario A) or attracting (scenario B) point of the deterministic rate equation. In scenario A the metastable stochastic population resides in ...

In a conformational nonequilibrium steady state (cNESS), enzyme turnover is modulated by the underlying conformational dynamics. On the basis of a discrete kinetic network model, we use an integrated probability flux balance method to derive the cNESS turnover rate for a conformation-modulated enzymatic reaction. The traditional Michaelis-Menten (MM) rate equation is extended to a generalized f...

In the past, the kinetics of aggregation has been extensively studied. Aggregation rates were measured and calculated thanks to a population balance. Aggregate morphologies were measured or got by computer simulations. However, the link between the aggregation kinetics and the morphology changes with time is not so clear. The modelling of aggregation may be even more complex as restructuring of...

The dynamics of Ostwald ripening is treated by cluster distribution kinetics represented by a population balance equation that also describes growth or dissolution. Unlike simple crystal growth driven by supersaturation, the smaller, more soluble clusters in the distribution dissolve during ripening near equilibrium and vanish when they reach the critical nucleus size. Larger clusters according...

The interfacial area per unit volume is one of the key parameters for the design of multiphase reactors. In this work a population balance approach is applied to calculate the interfacial area density in a bubble column. The resulting transport equation for the arithmetic bubble volume is coupled with the balance equations for mass and momentum. In addition the physical absorption of the gas ph...

We address the issue of state estimation of an aggregation process through (i) using model reduction to obtain a tractable approximation of the governing dynamics, and (ii) designing a fast moving-horizon estimator for the reduced-order model. We first use the method of moments to reduce the governing integro-differential equation down to a nonlinear ordinary differential equation (ODE). This r...

the homogeneous balance method can be used to construct exact traveling wave solutions of nonlinear partial differential equations. in this paper, this method is used to construct newsoliton solutions of the (3+1) jimbo--miwa equation.

‎In this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-‎dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method‎, homogeneous balance method, extended F-expansion method‎. ‎By ‎using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...