Almost-Invariant and Finite-Time Coherent Sets: Directionality, Duration, and Diffusion

2014 ◽  
pp. 171-216 ◽  
Author(s):  
Gary Froyland ◽  
Kathrin Padberg-Gehle
Keyword(s):  
Finite Time ◽  
And Diffusion

scholarly journals Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients

2010 ◽  
Vol 467 (2130) ◽  
pp. 1563-1576 ◽  
Author(s):  
Martin Hutzenthaler ◽  
Arnulf Jentzen ◽  
Peter E. Kloeden
Keyword(s):  
Exact Solution ◽  
Finite Time ◽  
Weak Sense ◽  
Mean Square ◽  
Euler’S Method ◽  
Lipschitz Continuous ◽  
The Difference ◽  
And Diffusion ◽  
Weak Divergence ◽  
Time Point

The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation (SDE) with globally Lipschitz continuous drift and diffusion coefficients. Recent results extend this convergence to coefficients that grow, at most, linearly. For superlinearly growing coefficients, finite-time convergence in the strong mean-square sense remains. In this article, we answer this question to the negative and prove, for a large class of SDEs with non-globally Lipschitz continuous coefficients, that Euler’s approximation converges neither in the strong mean-square sense nor in the numerically weak sense to the exact solution at a finite time point. Even worse, the difference of the exact solution and of the numerical approximation at a finite time point diverges to infinity in the strong mean-square sense and in the numerically weak sense.

Meridional Circulation, Turbulence, and Diffusion Processes in Stars

1976 ◽  
Vol 32 ◽  
pp. 109-116 ◽  
Author(s):  
S. Vauclair
Keyword(s):  
Convection Zone ◽  
Diffusion Processes ◽  
Meridional Circulation ◽  
Diffusion Time ◽  
Work In Progress ◽  
First Results ◽  
Stellar Envelopes ◽  
And Diffusion ◽  
Turbulence And Diffusion ◽  
Hr Diagram

This paper gives the first results of a work in progress, in collaboration with G. Michaud and G. Vauclair. It is a first attempt to compute the effects of meridional circulation and turbulence on diffusion processes in stellar envelopes. Computations have been made for a 2 Mʘstar, which lies in the Am - δ Scuti region of the HR diagram.Let us recall that in Am stars diffusion cannot occur between the two outer convection zones, contrary to what was assumed by Watson (1970, 1971) and Smith (1971), since they are linked by overshooting (Latour, 1972; Toomre et al., 1975). But diffusion may occur at the bottom of the second convection zone. According to Vauclair et al. (1974), the second convection zone, due to He II ionization, disappears after a time equal to the helium diffusion time, and then diffusion may happen at the bottom of the first convection zone, so that the arguments by Watson and Smith are preserved.

Ordering and diffusion in II-VI/III-VI alloys with structural vacancies

1997 ◽  
Vol 101-103 (1-2) ◽  
pp. 479-487
Author(s):  
H v. Wensierski
Keyword(s):  
And Diffusion

The origins and diffusion of operational research in the UK

1998 ◽  
Vol 49 (4) ◽  
pp. 307-326
Author(s):  
M W Kirby ◽  
R Capey
Keyword(s):  
Operational Research ◽  
The Uk ◽  
And Diffusion

Velocity and diffusion coefficient of a random asymmetric one-dimensional hopping model

1989 ◽  
Vol 50 (8) ◽  
pp. 899-921 ◽  
Author(s):  
C. Aslangul ◽  
N. Pottier ◽  
D. Saint-James
Keyword(s):  
Diffusion Coefficient ◽  
One Dimensional ◽  
And Diffusion ◽  
Hopping Model
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