scholarly journals Critical spreading dynamics of parity conserving annihilating random walks with power-law branching

2018 ◽  
Vol 505 ◽  
pp. 648-654 ◽  
Author(s):  
T. Laise ◽  
F.C. dos Anjos ◽  
C. Argolo ◽  
M.L. Lyra
Keyword(s):  
Random Walks ◽  
Power Law ◽  
Spreading Dynamics ◽  
Annihilating Random Walks

scholarly journals Clustered continuous-time random walks: diffusion and relaxation consequences

2012 ◽  
Vol 468 (2142) ◽  
pp. 1615-1628 ◽  
Author(s):  
Karina Weron ◽  
Aleksander Stanislavsky ◽  
Agnieszka Jurlewicz ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Walks ◽  
Power Law ◽  
Continuous Time ◽  
Waiting Times ◽  
Scaling Limit ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
The Novel ◽  
Fractional Diffusion Equations ◽  
Continuous Time Random Walks

We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observed two power-law relaxation patterns. The parameters of the scaling limit process determine the power-law exponents and loss peak frequencies.

scholarly journals Marangoni-driven spreading of miscible liquids in the binary pendant drop geometry

Soft Matter ◽  
2019 ◽  
Vol 15 (42) ◽  
pp. 8525-8531 ◽  
Author(s):  
Robin B. J. Koldeweij ◽  
Bram F. van Capelleveen ◽  
Detlef Lohse ◽  
Claas Willem Visser
Keyword(s):  
Power Law ◽  
Large Array ◽  
Pendant Drop ◽  
Binary Liquid ◽  
Spreading Dynamics ◽  
Liquid Systems ◽  
Miscible Liquids ◽  
Single Power

The Marangoni-driven spreading dynamics of binary pendant droplets show a remarkable consistency with other geometries. A single power law describes a large array of Marangoni-driven spreading in binary liquid systems.

Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing

2018 ◽  
Vol 20 (32) ◽  
pp. 20827-20848 ◽  
Author(s):  
Ru Hou ◽  
Andrey G. Cherstvy ◽  
Ralf Metzler ◽  
Takuma Akimoto
Keyword(s):  
Random Walks ◽  
Computer Simulations ◽  
Power Law ◽  
Waiting Time ◽  
Continuous Time ◽  
Zero Drift ◽  
Renewal Processes ◽  
Waiting Time Distributions ◽  
Continuous Time Random Walks ◽  
Ergodicity Breaking

We examine renewal processes with power-law waiting time distributions and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics.

scholarly journals Type Transition of Simple Random Walks on Randomly Directed Regular Lattices

2014 ◽  
Vol 51 (4) ◽  
pp. 1065-1080 ◽  
Author(s):  
Massimo Campanino ◽  
Dimitri Petritis
Keyword(s):  
Random Walk ◽  
Periodic Function ◽  
Random Walks ◽  
Power Law ◽  
Random Perturbation ◽  
Simple Random Walk ◽  
Critical Value ◽  
Absolute Value ◽  
Horizontal Orientation ◽  
Regular Lattices

Simple random walks on a partially directed version ofZ2are considered. More precisely, vertical edges between neighbouring vertices ofZ2can be traversed in both directions (they are undirected) while horizontal edges are one-way. The horizontal orientation is prescribed by a random perturbation of a periodic function; the perturbation probability decays according to a power law in the absolute value of the ordinate. We study the type of simple random walk that is recurrent or transient, and show that there exists a critical value of the decay power, above which it is almost surely recurrent and below which it is almost surely transient.

scholarly journals Annihilating random walks in one-dimensional disordered media

1998 ◽  
Vol 57 (3) ◽  
pp. 2563-2567 ◽  
Author(s):  
G. Schütz ◽  
K. Mussawisade
Keyword(s):  
Random Walks ◽  
Disordered Media ◽  
One Dimensional ◽  
Annihilating Random Walks

scholarly journals Annihilating random walks and perfect matchings of planar graphs

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Massimiliano Mattera
Keyword(s):  
Partition Function ◽  
Random Walks ◽  
Mechanical Model ◽  
Planar Graphs ◽  
Perfect Matchings ◽  
Statistical Mechanical Model ◽  
International Audience ◽  
Statistical Mechanical ◽  
Annihilating Random Walks

International audience We study annihilating random walks on $\mathbb{Z}$ using techniques of P.W. Kasteleyn and $R$. Kenyonon perfect matchings of planar graphs. We obtain the asymptotic of the density of remaining particles and the partition function of the underlying statistical mechanical model.

Sign in / Sign up

Export Citation Format

Share Document