Diffusion in the presence of scale-free absorbing boundaries.

@article{Alfasi2014DiffusionIT,
  title={Diffusion in the presence of scale-free absorbing boundaries.},
  author={Nir Alfasi and Yacov Kantor},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2014},
  volume={91 4},
  pages={
          042126
        }
}
  • N. AlfasiY. Kantor
  • Published 8 December 2014
  • Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
Scale-free surfaces, such as cones, remain unchanged under a simultaneous expansion of all coordinates by the same factor. Probability density of a particle diffusing near such absorbing surface at large time approaches a simple form that incorporates power-law dependencies on time and distance from a special point, such as apex of the cone, which are characterized by a single exponent η. The same exponent is used to describe the number of spatial conformations of long ideal polymer attached to… 

Figures from this paper

Localization of random walks to competing manifolds of distinct dimensions.

Extensive numerical analyses on two-dimensional RWs confined inside or outside a rectangular wedge confirm general features expected from a continuum theory, but also exhibit unexpected attributes, such as a reentrant localization to the corner while repelled by it.

Anomalous dimension in a two-species reaction–diffusion system

We study a two-species reaction–diffusion system with the reactions A+A→(0,A) and A+B→A, with general diffusion constants DA and DB. Previous studies showed that for dimensions d⩽2 the B particle

Quantum particle in a spherical well confined by a cone

We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone with an apex angle 2θ 0 emanating from the center of the sphere, with 0

References

SHOWING 1-10 OF 27 REFERENCES

Scaling and Renormalization in Statistical Physics

This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. Beginning with a brief review of phase transitions in simple systems and of mean field theory,

Scaling and Renormalization

We begin with the static scaling laws which have the objective of reducing the number of independent critical exponents to a couple, and the proposal is to achieve this by focussing on ever smaller

Random Walks in Biology

This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. It provides a sound basis

Scanning Force Microscopy

Scanning force microscopy (SFM) belongs to a class of real-space microscopic techniques, which combine high spatial resolution, 3-D imaging capabilities, and contrast mechanisms based on specific

First-passage phenomena and their applications

Arrival Statistics and Exploration Properties of Mortal Walkers (S B Yuste et al.) First-Passage of a Randomly Accelerated Particle (T Burkhardt) First-Passage Problems in Anomalous Diffusion (A

The Laplacian on a Riemannian Manifold: The Laplacian on a Riemannian Manifold

In this chapter we will generalize the Laplacian on Euclidean space to an operator on differential forms on a Riemannian manifold. By a Riemannian manifold, we roughly mean a manifold equipped with a

Phase transitions and critical phenomena

  • D. Landau
  • Physics
    Computing in Science & Engineering
  • 1999
The examination of phase transitions and critical phenomena has dominated statistical physics for the latter half of this century--there is a great theoretical challenge in solving special

Methods Of Theoretical Physics

The methods of theoretical physics is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.

Aspects and Applications of the Random Walk

Introductory comments the ubiquitous characteristic function asymptotic properties and the diffusion limit lattice walks boundaries and constraints multistate random walks selected applications.

Introduction to Polymer Physics