scholarly journals Scaling invariance of the diffusion coefficient in a family of two-dimensional Hamiltonian mappings

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
Juliano A. de Oliveira ◽  
Carl P. Dettmann ◽  
Diogo R. da Costa ◽  
Edson D. Leonel
Keyword(s):  
Diffusion Coefficient ◽  
Two Dimensional ◽  
Scaling Invariance

scholarly journals ONSHORE-OFFSHORE SEDIMENT MOVEMENT ON A BEACH

1978 ◽  
Vol 1 (16) ◽  
pp. 87 ◽  
Author(s):  
P. Nielsen ◽  
I.A. Svensen ◽  
C. Staub
Keyword(s):  
Experimental Data ◽  
Diffusion Coefficient ◽  
Oscillatory Flow ◽  
Sediment Flux ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Present Formulation ◽  
Exact Analytical Solutions ◽  
Net Flux ◽  
Loose Sediments

A theoretical model is developed for the movement of loose sediments in oscillatory flow with or without a net current. In the present formulation the model is two-dimensional, but may readily be extended to three dimensions. It is assumed that all movement of sediments occurs in suspension, and exact analytical solutions are given for the time variation of the concentration profile, the instantaneous sediment flux and the net flux of sediment over a wave period. The model requires as empirical input a diffusion coefficient e and pick-up function p(t), for which experimental data are presented. Two examples are discussed in detail, illustrating important aspects of the onshore-offshore sediment motion.

Stability of reaction-diffusion fronts

1994 ◽  
Vol 446 (1928) ◽  
pp. 517-528 ◽  
Keyword(s):  
Growth Rate ◽  
Diffusion Coefficient ◽  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Reaction Rate ◽  
Reaction Diffusion ◽  
Two Dimensional ◽  
Isothermal Reaction ◽  
Analytic Expression ◽  
Cubic Autocatalysis

Horvath, Petrov, Scott and Showalter (1993) have shown that isothermal reaction-diffusion fronts with cubic autocalysis are linearly unstable to two-dimensional disturbances if the ratio, δ , of the diffusion coefficient of the reactant to that of the autocatalyst, is sufficiently large. However, they were only able to obtain an analytic expression for the growth rate by assuming an infinitely thin reaction zone, which is a poor approximation for cubic autocatalysis. We have carried out a linear stability analysis of such fronts with a finite reaction rate, and find that the critical δ for instability is unchanged, but the range of unstable wavenumbers is larger and increases rather than decreases with δ .

The convergence of a branching Brownian motion used as a model describing the spread of an epidemic

1980 ◽  
Vol 17 (2) ◽  
pp. 301-312 ◽  
Author(s):  
Frank J. S. Wang
Keyword(s):  
Diffusion Coefficient ◽  
Brownian Motion ◽  
Unit Area ◽  
Transition Probability ◽  
Random Variable ◽  
Two Dimensional ◽  
Infection Period ◽  
Branching Brownian Motion ◽  
Almost Everywhere ◽  
Probability Rate

A spatial epidemic process where the individuals are located at positions in the Euclidean space R2 is considered. The infective individuals, with an infection period that is exponentially distributed with parameter µ, move in R2 according to a Brownian motion with a diffusion coefficient σ2. The susceptible individuals may also move. But we shall use the approximation that they remain unchanged in numbers and therefore assume that the averaged ‘density' of susceptibles per unit area is the same throughout space and time. The transition probability rate of infection of a susceptible in the infinitesimal element of area dy by an infective in dx is assumed to be a function h(x – y |) of the distance | x – y | between x and y. Then our process can be considered as a two-dimensional birth and death Brownian motion. Let be the number of infective individuals in the set D at time t and . The almost everywhere convergence of the random variables to a limit random variable W(D) is established.

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