scholarly journals A note on mass-conserving solutions to the coagulation-fragmentation equation by using non-conservative approximation

2018 ◽  
Vol 11 (5) ◽  
pp. 1125-1138 ◽  
Author(s):  
Prasanta Kumar Barik ◽  
◽  
Ankik Kumar Giri
Keyword(s):  
Conservative Approximation ◽  
Fragmentation Equation

scholarly journals Limit theorems for some branching measure-valued processes

2017 ◽  
Vol 49 (2) ◽  
pp. 549-580 ◽  
Author(s):  
Bertrand Cloez
Keyword(s):  
Continuous Time ◽  
Limit Theorems ◽  
Particle System ◽  
Large Population ◽  
Empirical Measure ◽  
Spatial Motion ◽  
Auxiliary Process ◽  
Discrete Population ◽  
A Cell ◽  
Fragmentation Equation

AbstractWe consider a particle system in continuous time, a discrete population, with spatial motion, and nonlocal branching. The offspring's positions and their number may depend on the mother's position. Our setting captures, for instance, the processes indexed by a Galton–Watson tree. Using a size-biased auxiliary process for the empirical measure, we determine the asymptotic behaviour of the particle system. We also obtain a large population approximation as a weak solution of a growth-fragmentation equation. Several examples illustrate our results. The main one describes the behaviour of a mitosis model; the population is size structured. In this example, the sizes of the cells grow linearly and if a cell dies then it divides into two descendants.

A Practical Computing Method for Residual Area of Rebar Cross-Sections under Carbonation Induced Corrosion

2012 ◽  
Vol 166-169 ◽  
pp. 1895-1899
Author(s):  
Xiao Gang Wang ◽  
De Ming Zhong
Keyword(s):  
Cross Sections ◽  
Laser Scanning ◽  
Major Axis ◽  
Structural Deterioration ◽  
Minimum Residual ◽  
Degree Of Confidence ◽  
Conservative Approximation ◽  
Rc Slabs ◽  
Computing Method ◽  
Geometric Measurement

Area loss of severely weakened rebar cross sections is a crucial variable in assessment of structural deterioration for corroded concrete structures, which is hard to be measured or estimated precisely in conventional methods. In this paper, rebar samples were taken from naturally corroded RC slabs. Their virtual models were built using 3D laser scanning technique to facilitate geometric measurement. From these models seriously weakened sections were screened out as analyzing samples, and residual areas as well as profiles of the cross-sections were derived and investigated consequently. Shown by the results, corrosion was non-uniformly distributed on rebar surface, and profiles of the residual cross-sections can hardly be formulated efficiently. However, they can be simplified into ellipse with minor axis of minimum residual diameter and major axis of diameter in perpendicular direction. This model has been proved to give an conservative approximation of residual sectional area with 4.27% underestimation and 89.2% degree of confidence.

scholarly journals Law and aesthetics: critical note

2010 ◽  
Vol 6 (2) ◽  
pp. 631-640 ◽  
Author(s):  
Luis Satie
Keyword(s):  
Legal Philosophy ◽  
Philosophy Of Law ◽  
Legal Form ◽  
Critical Note ◽  
Art Form ◽  
Conservative Approximation ◽  
Conditions Of Possibility ◽  
The Relationship ◽  
The Way

It is thought in the theory and philosophy of law, aimed at discussing the conditions of possibility of rapprochement between the art form and legal form. The text investigates, dialectically, the implications for the legal philosophy of the impossibility of such approximation, and the problems in a conservative approximation. It follows that: 1) would be a loss for a reason and therefore to legal philosophy, not to communicate between art and law; 2) the relationship between legal and aesthetic standards should be guided by the critical, especially in terms of Adorno's thought. It is by overcoming the dichotomy between possibility and impossibility, opening on the idea of constellation of methodological categorical fields of law and aesthetics in their current forms, paving the way for understanding the legal form as a tragic way.

scholarly journals Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation

2021 ◽  
Vol 17 (9) ◽  
pp. e1008964
Author(s):  
Magali Tournus ◽  
Miguel Escobedo ◽  
Wei-Feng Xue ◽  
Marie Doumic
Keyword(s):  
Mathematical Theory ◽  
Length Distribution ◽  
Numerical Approach ◽  
Distribution Profile ◽  
Fragmentation Dynamics ◽  
Mathematical Equations ◽  
Fragmentation Reactions ◽  
The Stability ◽  
Fragmentation Equation ◽  
The Mathematical Model

The dynamics by which polymeric protein filaments divide in the presence of negligible growth, for example due to the depletion of free monomeric precursors, can be described by the universal mathematical equations of ‘pure fragmentation’. The rates of fragmentation reactions reflect the stability of the protein filaments towards breakage, which is of importance in biology and biomedicine for instance in governing the creation of amyloid seeds and the propagation of prions. Here, we devised from mathematical theory inversion formulae to recover the division rates and division kernel information from time dependent experimental measurements of filament size distribution. The numerical approach to systematically analyze the behaviour of pure fragmentation trajectories was also developed. We illustrate how these formulae can be used, provide some insights on their robustness, and show how they inform the design of experiments to measure fibril fragmentation dynamics. These advances are made possible by our central theoretical result on how the length distribution profile of the solution to the pure fragmentation equation aligns with a steady distribution profile for large times.

Fast Reaction Limit of the Discrete Diffusive Coagulation–Fragmentation Equation

2003 ◽  
Vol 28 (5-6) ◽  
pp. 1113-1133 ◽  
Author(s):  
Miguel Escobedo ◽  
Philippe Laurençot ◽  
Stéphane Mischler
Keyword(s):  
Fast Reaction ◽  
Fast Reaction Limit ◽  
Fragmentation Equation

Numerical solutions to the smoluchowski aggregation—fragmentation equation

1991 ◽  
Vol 144 (2) ◽  
pp. 315-323 ◽  
Author(s):  
Imam M. Elminyawi ◽  
S. Gangopadhyay ◽  
C.M. Sorensen
Keyword(s):  
Numerical Solutions ◽  
Fragmentation Equation

scholarly journals Branching processes for the fragmentation equation

2015 ◽  
Vol 125 (5) ◽  
pp. 1861-1885 ◽  
Author(s):  
Lucian Beznea ◽  
Madalina Deaconu ◽  
Oana Lupaşcu
Keyword(s):  
Branching Processes ◽  
Fragmentation Equation
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