Parametric Method of Moments for Solving the Smoluchowski Coagulation Equation in the Theory of Accumulation of Dust Bodies in a Protoplanetary Disk

2020 ◽  
Vol 54 (3) ◽  
pp. 187-202
Author(s):  
A. V. Kolesnichenko
Keyword(s):  
Method Of Moments ◽  
Parametric Method ◽  
Protoplanetary Disk ◽  
Smoluchowski Coagulation Equation ◽  
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.

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