scholarly journals A problem in one-dimensional diffusion-limited aggregation (DLA) and positive recurrence of Markov chains

2008 ◽  
Vol 36 (5) ◽  
pp. 1838-1879 ◽  
Author(s):  
Harry Kesten ◽  
Vladas Sidoravicius
Keyword(s):  
Markov Chains ◽  
Diffusion Limited Aggregation ◽  
Positive Recurrence ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Dimensional Diffusion

Multifractal spectrum of off-lattice three-dimensional diffusion-limited aggregation

1992 ◽  
Vol 46 (6) ◽  
pp. R3016-R3019 ◽  
Author(s):  
Stefan Schwarzer ◽  
Marek Wolf ◽  
Shlomo Havlin ◽  
Paul Meakin ◽  
H. Eugene Stanley
Keyword(s):  
Three Dimensional ◽  
Multifractal Spectrum ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Dimensional Diffusion

Diffusion-Limited Cell Dehydration: Analytical and Numerical Solutions for a Planar Model

1999 ◽  
Author(s):  
Alexander V. Kasharin ◽  
Jens O. M. Karlsson
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Planar System ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Constant Diffusivity ◽  
A Cell ◽  
Cell Dehydration ◽  
The One

Abstract The process of diffusion-limited cell dehydration is modeled for a planar system by writing the one-dimensional diffusion-equation for a cell with moving, semipermeable boundaries. For the simplifying case of isothermal dehydration with constant diffusivity, an approximate analytical solution is obtained by linearizing the governing partial differential equations. The general problem must be solved numerically. The Forward Time Center Space (FTCS) and Crank-Nicholson differencing schemes are implemented, and evaluated by comparison with the analytical solution. Putative stability criteria for the two algorithms are proposed based on numerical experiments, and the Crank-Nicholson method is shown to be accurate for a mesh with as few as six nodes.

scholarly journals One-dimensional long-range diffusion-limited aggregation I

2016 ◽  
Vol 44 (5) ◽  
pp. 3546-3579 ◽  
Author(s):  
Gideon Amir ◽  
Omer Angel ◽  
Itai Benjamini ◽  
Gady Kozma
Keyword(s):  
Long Range ◽  
Diffusion Limited Aggregation ◽  
One Dimensional ◽  
Diffusion Limited

The Anomalous Diffusion-limited Reaction Kinetics of a Phototrapping Reaction

1996 ◽  
Vol 464 ◽  
Author(s):  
Eric Monson ◽  
Anna L. Lin ◽  
Raoul Kopelman
Keyword(s):  
Laser Beam ◽  
Two Dimensions ◽  
One Dimensional ◽  
Rate Laws ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Diffusion Controlled ◽  
Kinetics Of ◽  
Diffusion Limited Reaction ◽  
Classical Constant

AbstractA focused laser beam acts as both a “phototrap”, bleaching fluorophore molecules which diffuse into the beam path, and as a confocal probe, detecting the excited, unbleached fluorophore molecules still present in the trap. With this focused laser beam, we observe anomalous asymptotic rate laws similar to those predicted for a diffusion-controlled elementary trapping reaction, A + T → T, in one and two dimensions. One dimensional diffusion-limited trapping kinetics are approached in capillaries with 10 μm diameters while two dimensional diffusion limited trapping kinetics are observed with unstirred samples having a quasi 2-D geometry. In the presence of stirring, the 2-D samplesexhibit the classical, constant trapping rate over time.

Quasi-two-dimensional diffusion-limited aggregation

1990 ◽  
Vol 41 (16) ◽  
pp. 11591-11592 ◽  
Author(s):  
Bi Lingsong ◽  
Wu Ziqin
Keyword(s):  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Dimensional Diffusion
Sign in / Sign up

Export Citation Format

Share Document