scholarly journals Pointwise stability of reaction diffusion fronts

2019 ◽  
Vol 150 (5) ◽  
pp. 2216-2254
Author(s):  
Yingwei Li
Keyword(s):  
Spectral Decomposition ◽  
Exponential Convergence ◽  
Reaction Diffusion ◽  
Spatial Diffusion ◽  
Diffusion Front ◽  
Function Decomposition ◽  
Viscous Shock Waves ◽  
New Feature ◽  
Rates Of Decay ◽  
Short Time

AbstractUsing pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential convergence in weighted Lp and Sobolev norms, while capturing the new feature of spatial diffusion at Gaussian rate. Novel features of the argument are a pointwise Green function decomposition reconciling spectral decomposition and short-time Nash-Aronson estimates and an instantaneous tracking scheme similar to that used in the study of stability of viscous shock waves.

Destruction of Actin Filaments by Osmium Tetroxide

1977 ◽  
Vol 35 ◽  
pp. 466-467
Author(s):  
P. Maupin-Szamier ◽  
T. D. Pollard
Keyword(s):  
Actin Filaments ◽  
Time Course ◽  
Osmium Tetroxide ◽  
Rabbit Muscle ◽  
Muscle Actin ◽  
Sodium Phosphate Buffer ◽  
Transmission Electron ◽  
The Difference ◽  
Rates Of Decay ◽  
Short Time

We have studied the destruction of rabbit muscle actin filaments by osmium tetroxide (OSO4) to develop methods which will preserve the structure of actin filaments during preparation for transmission electron microscopy.Negatively stained F-actin, which appears as smooth, gently curved filaments in control samples (Fig. 1a), acquire an angular, distorted profile and break into progressively shorter pieces after exposure to OSO4 (Fig. 1b,c). We followed the time course of the reaction with viscometry since it is a simple, quantitative method to assess filament integrity. The difference in rates of decay in viscosity of polymerized actin solutions after the addition of four concentrations of OSO4 is illustrated in Fig. 2. Viscometry indicated that the rate of actin filament destruction is also dependent upon temperature, buffer type, buffer concentration, and pH, and requires the continued presence of OSO4. The conditions most favorable to filament preservation are fixation in a low concentration of OSO4 for a short time at 0°C in 100mM sodium phosphate buffer, pH 6.0.

scholarly journals Dynamic multiscaling of the reaction-diffusion front formA+nB→0

1995 ◽  
Vol 52 (4) ◽  
pp. 3500-3505 ◽  
Author(s):  
Stephen Cornell ◽  
Zbigniew Koza ◽  
Michel Droz
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Front

scholarly journals NEW EXACT SOLUTIONS OF SPATIALLY AND TEMPORALLY VARYING REACTION-DIFFUSION EQUATIONS

2008 ◽  
Vol 06 (04) ◽  
pp. 371-381 ◽  
Author(s):  
NALINI JOSHI ◽  
TEGAN MORRISON
Keyword(s):  
Reaction Diffusion ◽  
Elliptic Functions ◽  
Point Of View ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Source Terms ◽  
Symmetry Approach ◽  
New Exact Solutions ◽  
Special Cases ◽  
New Feature

This paper considers reaction-diffusion equations from a new point of view, by including spatiotemporal dependence in the source terms. We show for the first time that solutions are given in terms of the classical Painlevé transcendents. We consider reaction-diffusion equations with cubic and quadratic source terms. A new feature of our analysis is that the coefficient functions are also solutions of differential equations, including the Painlevé equations. Special cases arise with elliptic functions as solutions. Additional solutions given in terms of equations that are not integrable are also considered. Solutions are constructed using a Lie symmetry approach.

scholarly journals Coarsening of precipitation patterns in a moving reaction-diffusion front

2009 ◽  
Vol 80 (5) ◽  
Author(s):  
A. Volford ◽  
I. Lagzi ◽  
F. Molnár ◽  
Z. Rácz
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Front ◽  
Precipitation Patterns

The development of travelling waves in a simple isothermal chemical system II. Cubic autocatalysis with quadratic and linear decay

1990 ◽  
Vol 430 (1879) ◽  
pp. 315-345 ◽  
Keyword(s):  
Numerical Solutions ◽  
Travelling Waves ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
Chemical System ◽  
Necessary Condition ◽  
Travelling Wave Solution ◽  
Diffusion Front ◽  
Initial Value ◽  
Linear Decay

The possibility of travelling reaction-diffusion waves developing in the isothermal chemical system governed by the cubic autocatalytic reaction A + 2B → 3B (rate k 3 ab 2 ) coupled with either the linear decay step B → C (rate k 2 b ) or the quadratic decay step B + B → C (rate k 4 b 2 ) is examined. Two simple solutions are obtained,namely the well-stirred analogue of the spatially inhomogeneous problem and the solution for small input of the autocatalyst B. Both of these suggest that, for the quadratic decay case, a wave will develop only if the non-dimensional parameter k ═ k 4 / k 3 a 0 < 1 (where a 0 is the initial concentration of the reactant A), with there being no restriction on the initial input of the autocatalyst B. However, for the linear decay case the initiation of a travelling wave depends on the parameter v ═ k 2 / k 3 a 2 0 and that, in addition, there is an input threshold on B before the formation of a wave will occur. The equations governing the fully developed travelling waves are then considered and it is shown that for the quadratic decay case the situation is similar to previous work in quadratic autocatalysis with linear decay, with a necessary condition for the existence of a travelling-wave solution being that K < 1. However, the case of linear decay is quite different, with a necessary condition for the existence of a travelling wave solution now found to be v < 1/4 Numerical solutions of the equations governing this case reveal further that a solution exists only for v < v c , with v c ≈ 0.0465, and that there are two branches of solution for 0 < v < v c . The behaviour of these lower branch solutions as v → 0 is discussed. The initial-value problem is then considered. For the quadratic decay case it is shown that the uniform state a ═ a 0 , b ═ 0 is globally asymptotically stable (i. e. a → a 0 , b → 0 uniformly for large times) for all k > 1. For the linear decay case it is shown that the development of a travelling wave requires β 0 > v (where β 0 is a measure of the initial input of B) for v < v c . These theoretical results are then complemented by numerical solutions of the initial-value problem for both cases, which confirm the various predictions of the theory. The behaviour of the solution of the equations governing the travelling waves is then discussed in the limits K → 0, v → 0 and K → 1. In the first case the solution approaches the solution for K ═ 0 (or v =0) on the length scale of the reaction-diffusion front, with there being a long tail region of length scale O ( K -1 ) (or O ( v -1 )) in which the autocatalyst B decays to zero. In the latter case we find that the concentration of reactant A is 1 + O [(1 - k )] and autocatalyst B is O[(1 - k 2 ] with the thickness of the reaction-diffusion front becoming large, of thickness O [(1- k ) -3/2 ].

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