Localization and Diffusion in Nonlinear One-Dimensional Lattices

2012 ◽  
pp. 165-190
Author(s):  
Tassos Bountis ◽  
Haris Skokos
Keyword(s):  
One Dimensional ◽  
And Diffusion

scholarly journals Ergodic control of diffusions with random intervention times

2021 ◽  
Vol 58 (1) ◽  
pp. 1-21
Author(s):  
Harto Saarinen ◽  
Jukka Lempa
Keyword(s):  
Optimal Solution ◽  
Singular Control ◽  
Control Policy ◽  
Control Problems ◽  
Ergodic Control ◽  
Linear Diffusion ◽  
One Dimensional ◽  
And Diffusion ◽  
Independent Poisson Process ◽  
Exact Amount

AbstractWe study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at the jump times of an independent Poisson process. Under relatively weak assumptions, we characterize the optimal solution as an impulse-type control policy, where it is optimal to exert the exact amount of control needed to push the process to a unique threshold. Moreover, we discuss the connection of the present problem to ergodic singular control problems, and illustrate the results with different well-known cost and diffusion structures.

scholarly journals LATTICE THREE-SPECIES MODELS OF THE SPATIAL SPREAD OF RABIES AMONG FOXES

1999 ◽  
Vol 10 (06) ◽  
pp. 1025-1038 ◽  
Author(s):  
A. BENYOUSSEF ◽  
N. BOCCARA ◽  
H. CHAKIB ◽  
H. EZ-ZAHRAOUY
Keyword(s):  
Carrying Capacity ◽  
Short Range ◽  
Lattice Models ◽  
Infection Process ◽  
Spatial Spread ◽  
One Dimensional ◽  
Sense Of Direction ◽  
Speed Of Propagation ◽  
Automata Network ◽  
And Diffusion

Lattice models describing the spatial spread of rabies among foxes are studied. In these models, the fox population is divided into three-species: susceptible (S), infected or incubating (I), and infectious or rabid (R). They are based on the fact that susceptible and incubating foxes are territorial while rabid foxes have lost their sense of direction and move erratically. Two different models are investigated: a one-dimensional coupled-map lattice model, and a two-dimensional automata network model. Both models take into account the short-range character of the infection process and the diffusive motion of rabid foxes. Numerical simulations show how the spatial distribution of rabies, and the speed of propagation of the epizootic front depend upon the carrying capacity of the environment and diffusion of rabid foxes out of their territory.

scholarly journals A simple moment model to study the effect of diffusion on the coagulation of nanoparticles due to Brownian motion in the free molecule regime

2012 ◽  
Vol 16 (5) ◽  
pp. 1331-1338 ◽  
Author(s):  
Wenxi Wang ◽  
Qing He ◽  
Nian Chen ◽  
Mingliang Xie
Keyword(s):  
Method Of Moments ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Particle Coagulation ◽  
Average Volume ◽  
One Dimensional ◽  
The One ◽  
And Diffusion ◽  
Dimensional Domain ◽  
Series Expansion Method

In the study a simple model of coagulation for nanoparticles is developed to study the effect of diffusion on the particle coagulation in the one-dimensional domain using the Taylor-series expansion method of moments. The distributions of number concentration, mass concentration, and particle average volume induced by coagulation and diffusion are obtained.

scholarly journals Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 881 ◽  
Author(s):  
Karl Hoffmann ◽  
Kathrin Kulmus ◽  
Christopher Essex ◽  
Janett Prehl
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Irreversible Processes ◽  
Entropy Production Rate ◽  
Continuous Space ◽  
One Dimensional ◽  
Fractional Diffusion Equations ◽  
And Diffusion

The entropy production rate is a well established measure for the extent of irreversibility in a process. For irreversible processes, one thus usually expects that the entropy production rate approaches zero in the reversible limit. Fractional diffusion equations provide a fascinating testbed for that intuition in that they build a bridge connecting the fully irreversible diffusion equation with the fully reversible wave equation by a one-parameter family of processes. The entropy production paradox describes the very non-intuitive increase of the entropy production rate as that bridge is passed from irreversible diffusion to reversible waves. This paradox has been established for time- and space-fractional diffusion equations on one-dimensional continuous space and for the Shannon, Tsallis and Renyi entropies. After a brief review of the known results, we generalize it to time-fractional diffusion on a finite chain of points described by a fractional master equation.

Adsorption, desorption, and diffusion ofk-mers on a one-dimensional lattice

2009 ◽  
Vol 80 (2) ◽  
Author(s):  
I. Lončarević ◽  
Lj. Budinski-Petković ◽  
S. B. Vrhovac ◽  
A. Belić
Keyword(s):  
Dimensional Lattice ◽  
One Dimensional ◽  
Adsorption Desorption ◽  
And Diffusion

Adsorption and diffusion in a one-dimensional potential well

2003 ◽  
Vol 68 (1) ◽  
Author(s):  
L. E. Helseth ◽  
H. Z. Wen ◽  
T. M. Fischer ◽  
T. H. Johansen
Keyword(s):  
Potential Well ◽  
One Dimensional ◽  
And Diffusion

Multi-phase Stefan problems for a non-linear one-dimensional model of cell-to-cell adhesion and diffusion

2010 ◽  
Vol 21 (2) ◽  
pp. 109-136 ◽  
Author(s):  
K. ANGUIGE
Keyword(s):  
Cell Adhesion ◽  
Existence Theory ◽  
Dimensional Model ◽  
One Dimensional ◽  
Stefan Problems ◽  
Non Linear ◽  
Long Time ◽  
Multi Phase ◽  
Cell To Cell Adhesion ◽  
And Diffusion

We consider a family of multi-phase Stefan problems for a certain one-dimensional model of cell-to-cell adhesion and diffusion, which takes the form of a non-linear forward–backward parabolic equation. In each material phase the cell density stays either high or low, and phases are connected by jumps across an ‘unstable’ interval. We develop an existence theory for such problems which allows for the annihilation of phases and the subsequent continuation of solutions. Stability results for the long-time behaviour of solutions are also obtained, and, where necessary, the analysis is complemented by numerical simulations.

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