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.

scholarly journals Role of antigen, CD8, and cytotoxic T lymphocyte (CTL) avidity in high dose antigen induction of apoptosis of effector CTL.

1996 ◽  
Vol 184 (2) ◽  
pp. 485-492 ◽  
Author(s):  
M A Alexander-Miller ◽  
G R Leggatt ◽  
A Sarin ◽  
J A Berzofsky
Keyword(s):  
T Lymphocytes ◽  
Cytotoxic T Lymphocyte ◽  
Target Cells ◽  
High Dose ◽  
High Avidity ◽  
Apoptotic Pathway ◽  
Peptide Antigen ◽  
Kinetics Of ◽  
Selection Of

Experimental data suggest that negative selection of thymocytes can occur as a result of supraoptimal antigenic stimulation. It is unknown, however, whether such mechanisms are at work in mature CD8+ T lymphocytes. Here, we show that CD8+ effector cytotoxic T lymphocytes (CTL) are susceptible to proliferative inhibition by high dose peptide antigen, leading to apoptotic death mediated by TNF-alpha release. Such inhibition is not reflected in the cytolytic potential of the CTL, since concentrations of antigen that are inhibitory for proliferation promote efficient lysis of target cells. Thus, although CTL have committed to the apoptotic pathway, the kinetics of this process are such that CTL function can occur before death of the CTL. The concentration of antigen required for inhibition is a function of the CTL avidity, in that concentrations of antigen capable of completely inhibiting high avidity CTL maximally stimulate low avidity CTL. Importantly, the inhibition can be detected in both activated and resting CTL. Blocking studies demonstrate that the CD8 molecule contributes significantly to the inhibitory signal as the addition of anti-CD8 antibody restores the proliferative response. Thus, our data support the model that mature CD8+ CTL can accommodate an activation signal of restricted intensity, which, if surpassed, results in deletion of that cell.

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.

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