On the Solution of the Smoluchowski Coagulation Equation Using a Conservative Discretization Approach (CDA)

2019 ◽  
pp. 691-696
Author(s):  
Menwer Attarakih ◽  
Hans-Jörg Bart
Keyword(s):  
Smoluchowski Coagulation Equation ◽  
Conservative Discretization ◽  
Coagulation Equation

scholarly journals The Approximation of Entropy for Smoluchowski Coagulation Equation With TEMOM

2021 ◽  
Author(s):  
Mingliang Xie
Keyword(s):  
Average Particle ◽  
Particle Volume ◽  
Principle Of Maximum Entropy ◽  
Global Properties ◽  
Smoluchowski Coagulation Equation ◽  
Coagulation Equation ◽  
Definition Of ◽  
Definition Of Information ◽  
Increasing Function ◽  
Principle Of Maximum

In this paper, the definition of information entropy of Smoluchowski coagulation equation for Brownian motion is introduced based on coagulation probability. The expression of entropy is the function of geometric average particle volume and standard deviation with lognormal distribution assumption. The asymptotic solution with moment method shows that the entropy is a monotone increasing function of time, which is equivalence to the entropy based on particle size distribution. the result reveals that the present definition of entropy of Smoluchowski coagulation equation are inadequate because the particle average volume at equilibrium cannot be determined from the principle of maximum entropy. This provides a basis for further exploring the global properties of Smoluchowski coagulation equation.

Tensor train versus Monte Carlo for the multicomponent Smoluchowski coagulation equation

2016 ◽  
Vol 316 ◽  
pp. 164-179 ◽  
Author(s):  
Sergey A. Matveev ◽  
Dmitry A. Zheltkov ◽  
Eugene E. Tyrtyshnikov ◽  
Alexander P. Smirnov
Keyword(s):  
Monte Carlo ◽  
Smoluchowski Coagulation Equation ◽  
Coagulation Equation

scholarly journals Generalized sensitivity functions for size-structured population models

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Dustin D. Keck ◽  
David M. Bortz
Keyword(s):  
Differential Equation ◽  
Parameter Estimation ◽  
Population Models ◽  
Structured Population Models ◽  
Sensitivity Functions ◽  
Structured Population ◽  
Smoluchowski Coagulation Equation ◽  
Generalized Sensitivity ◽  
Coagulation Equation ◽  
The Impact

AbstractSize-structured population models provide a popular means to mathematically describe phenomena such as bacterial aggregation, schooling fish, and planetesimal evolution. For parameter estimation, a generalized sensitivity function (GSF) provides a tool that quantifies the impact of data from specific regions of the experimental domain. This function helps to identify the most relevant data subdomains, which enhances the optimization of experimental design. To our knowledge, GSFs have not been used in the partial differential equation (PDE) realm, so we provide a novel PDE extension of the discrete and continuous ordinary differential equation (ODE) concepts of Thomaseth and Cobelli and Banks et al. respectively. We analyze a GSF in the context of size-structured population models, and specifically analyze the Smoluchowski coagulation equation to determine the most relevant time and volume domains for three, distinct aggregation kernels. Finally, we provide evidence that parameter estimation for the Smoluchowski coagulation equation does not require post-gelation data.

A bank merger predictive model using the Smoluchowski stochastic coagulation equation and reverse engineering

2018 ◽  
Vol 36 (4) ◽  
pp. 634-662
Author(s):  
Zahra Banakar ◽  
Madjid Tavana ◽  
Brian Huff ◽  
Debora Di Caprio
Keyword(s):  
Reverse Engineering ◽  
Matrix Equation ◽  
Estimation Method ◽  
Financial Behavior ◽  
Future Research ◽  
Bank Mergers ◽  
Content Type ◽  
Smoluchowski Coagulation Equation ◽  
Coagulation Equation ◽  
Dynamic Stochastic

Purpose The purpose of this paper is to provide a theoretical framework for predicting the next period financial behavior of bank mergers within a statistical-oriented setting. Design/methodology/approach Bank mergers are modeled combining a discrete variant of the Smoluchowski coagulation equation with a reverse engineering method. This new approach allows to compute the correct merging probability values via the construction and solution of a multi-variable matrix equation. The model is tested on real financial data relative to US banks collected from the National Information Centre. Findings Bank size distributions predicted by the proposed method are much more adherent to real data than those derived from the estimation method. The proposed method provides a valid alternative to estimation approaches while overcoming some of their typical drawbacks. Research limitations/implications Bank mergers are interpreted as stochastic processes focusing on two main parameters, that is, number of banks and asset size. Future research could expand the model analyzing the micro-dynamic taking place behind bank mergers. Furthermore, bank demerging and partial bank merging could be considered in order to complete and strengthen the proposed approach. Practical implications The implementation of the proposed method assists managers in making informed decisions regarding future merging actions and marketing strategies so as to maximize the benefits of merging actions while reducing the associated potential risks from both a financial and marketing viewpoint. Originality/value To the best of the authors’ knowledge, this is the first study where bank merging is analyzed using a dynamic stochastic model and the merging probabilities are determined by a multi-variable matrix equation in place of an estimation procedure.

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