Approximations of Markovian non linear partial differential equations by particle systems

2002 ◽  
pp. 55-63
Author(s):  
A. Guionnet
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Particle Systems ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Non Linear

ON TAYLOR'S SCRAPING PROBLEM AND FLOW OF A SISKO FLUID

2009 ◽  
Vol 14 (4) ◽  
pp. 515-529 ◽  
Author(s):  
Abdul M. Siddiqui ◽  
Ali R. Ansari ◽  
Ahmed Ahmad ◽  
N. Ahmad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Viscous Fluid ◽  
Normal Stress ◽  
Partial Differential ◽  
Sisko Fluid ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Special Case

The aim of the present investigation is to study the properties of a Sisko fluid flowing between two intersecting planes. The problem is similar to Taylor's scraping problem for a viscous fluid. We determine the solution of the complicated set of non‐linear partial differential equations describing the flow analytically. The analysis is carried out in detail reflecting the effects of varying the angle of the scraper on the flow. In addition, the tangential and normal stress are also computed. We also show the well known Taylor scraper problem as a special case.

Clumping in multitype-branching trees

1996 ◽  
Vol 28 (04) ◽  
pp. 1034-1050
Author(s):  
J. Alfredo López-Mimbela ◽  
Anton Wakolbinger
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Critical Dimension ◽  
Particle Systems ◽  
Partial Differential ◽  
Locally Finite ◽  
Linear Partial Differential Equations ◽  
Ergodic Properties ◽  
Branching Trees ◽  
The Individual

We investigate the ‘clumping versus local finiteness' behavior in the infinite backward tree for a class of branching particle systems in ℝd with symmetric stable migration and critical ‘genuine multitype' branching. Under mild assumptions on the branching we establish, by analysing certain ergodic properties of the individual ancestral process, a critical dimension d c such that the (measure-valued) tree-top is almost surely locally finite if and only if d > d c. This result is used to obtain L 1-norm asymptotics of a corresponding class of systems of non-linear partial differential equations.

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