scholarly journals Large-time asymptotics for the density of a branching Wiener process

2005 ◽  
Vol 42 (4) ◽  
pp. 1081-1094 ◽  
Author(s):  
Pál Révész ◽  
Jay Rosen ◽  
Zhan Shi
Keyword(s):  
Asymptotic Expansion ◽  
Wiener Process ◽  
Large Time ◽  
Large Time Asymptotics ◽  
Complete Asymptotic Expansion ◽  
Time Asymptotics ◽  
Number Of Particles

Given an ℝd-valued supercritical branching Wiener process, let ψ(A, T) be the number of particles in A ⊂ ℝd at time T (T = 0, 1, 2, …). We provide a complete asymptotic expansion of ψ(A, T) as T → ∞, generalizing the work of X. Chen.

scholarly journals Large-time asymptotics for the density of a branching Wiener process

2005 ◽  
Vol 42 (04) ◽  
pp. 1081-1094 ◽  
Author(s):  
Pál Révész ◽  
Jay Rosen ◽  
Zhan Shi
Keyword(s):  
Asymptotic Expansion ◽  
Wiener Process ◽  
Large Time ◽  
Large Time Asymptotics ◽  
Complete Asymptotic Expansion ◽  
Time Asymptotics ◽  
Number Of Particles

Given an ℝ d -valued supercritical branching Wiener process, let ψ(A, T) be the number of particles in A ⊂ ℝ d at time T (T = 0, 1, 2, …). We provide a complete asymptotic expansion of ψ(A, T) as T → ∞, generalizing the work of X. Chen.

scholarly journals Explicit Asymptotic Velocity of the Boundary between Particles and Antiparticles

2012 ◽  
Vol 2012 ◽  
pp. 1-32
Author(s):  
V. A. Malyshev ◽  
A. D. Manita ◽  
A. A. Zamyatin
Keyword(s):  
Infinite Number ◽  
Real Line ◽  
Large Time ◽  
Half Line ◽  
Large Time Asymptotics ◽  
Asymptotic Velocity ◽  
The Real ◽  
Time Asymptotics ◽  
Positive Half ◽  
Number Of Particles

On the real line initially there are infinite number of particles on the positive half line, each having one of -negative velocities . Similarly, there are infinite number of antiparticles on the negative half line, each having one of -positive velocities . Each particle moves with constant speed, initially prescribed to it. When particle and antiparticle collide, they both disappear. It is the only interaction in the system. We find explicitly the large time asymptotics of —the coordinate of the last collision before between particle and antiparticle.

SIMULATIONS OF THE LIFSHITZ–SLYOZOV EQUATIONS: THE ROLE OF COAGULATION TERMS IN THE ASYMPTOTIC BEHAVIOR

2013 ◽  
Vol 23 (07) ◽  
pp. 1177-1215 ◽  
Author(s):  
THIERRY GOUDON ◽  
FRÉDÉRIC LAGOUTIÈRE ◽  
LÉON MATAR TINE
Keyword(s):  
Asymptotic Behavior ◽  
Large Time ◽  
Finite Volume Schemes ◽  
Large Time Asymptotics ◽  
Asymptotic Profile ◽  
Time Asymptotics ◽  
Supersaturated Solid Solutions ◽  
Kinetics Of ◽  
Selection Of

We consider the Lifshitz–Slyozov system that describes the kinetics of precipitation from supersaturated solid solutions. We design specific Finite Volume schemes and we investigate numerically the behavior of the solutions, in particular the large time asymptotics. Our purpose is two-fold: first, we introduce an adapted scheme based on downwinding techniques in order to reduce the numerical diffusion; second, we discuss the influence of coagulation effects on the selection of the asymptotic profile.

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