We introduce a gray-box approach for modeling the molecular weight distribution in step-growth polymerization reactions using aggregation population balance equation. The is based on extracting data-based kernel function from in-process measurements of distribution. method applied to historical data an industrial batch reactor. resulting model used decision support production by predicting reac...

A PDAE model of a multicomponent gas pipeline has been formulated and solved using the ode15s solver of Matlab. The model with boundary conditions allows for reactions and di usion. Also, general cubic equations of state for pressure and enthalpy are described. To simplify the implementation at this stage, a non-reactive, non-di usional model with fixed feed composition is considered, and multi...

This paper deals with the diffusion approximation of a semiconductor BoltzmannPoisson system. The statistics of collisions we are considering here, is the Fermi-Dirac operator with the Pauli exclusion term and without the detailed balance principle. Our study generalizes, the result of Goudon and Mellet [14], to the multi-dimensional case. keywords: Semiconductor, Boltzmann-Poisson, diffusion a...

The Hamiltonian approach of the Pauli-Fierz model is studied by Derezinski and Jaksic (cf. [7]). In this paper, we give the Markovian description of this model. Using the weak coupling limit, we derive the quantum Markovian semigroup of the Pauli-Fierz system from its Hamiltonian description. Also, we give the explicit form of the associated Lindblad generator. As a consequence, we study the pr...

The local mass of weak solutions to the discrete diffusive coagulation-fragmentation equation is proved to converge, in the fast reaction limit, to the solution of a nonlinear diffusion equation, the coagulation and fragmentation rates enjoying a detailed balance condition.

Population balance modeling has received an unprecedented amount of attention during the past few years from both academic and industrial quarters because of its applicability to a wide variety of particulate processes. In this article, a fresh look is taken of the basic issues of the application of population balances towards strengthening the approach as well as widening the scope of their ap...

In this paper we report on a study of a two level preemptive priority queue with balking and reneging for lower priority level. The inter-arrival and the service times for both levels follow exponential distribution. We use a finite difference equation approach for solving the balance equations of the governing queuing model whose states are described by functions of one independent variable. H...

We study a XY model which consists of a spin chain coupled to heat baths. We give a repeated quantum interaction Hamiltonian describing this model. We compute the explicit form of the associated Lindblad generator in the case of the spin chain coupled to one, two and several heat baths. We further study the properties of quantum master equation such as approach to equilibrium, local equilibrium...

limitation of water resources in iran motivates sustaining and preserving of the resources in order to supply future water needs. fulfilling these objectives will not be possible unless having accurate water balance of watersheds. the purpose of this study is to estimate the water balance parameters using a distributed method. the large number of distributed models and methods was studied and “...

Abstract. In Part 1, I considered the zero-dimensional heat equation, showing quite generally that conductive–radiative surface boundary conditions lead to half-ordered derivative relationships between fluxes and temperatures: energy balance equation (HEBE). The real Earth, even when averaged in time over weather scales (up ≈ 10 d), is highly heterogeneous. this 2, treatment extended horizontal...