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Related Experiment Video

Updated: Jun 18, 2026

Spatial Separation of Molecular Conformers and Clusters

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Target annihilation by diffusing particles in inhomogeneous geometries.

¹Dipartimento di Fisica, Università di Parma, Viale Usberti 7/a, 43100 Parma, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2009

Summary

This summary is machine-generated.

The survival probability of random walkers on complex structures depends on the spectral dimension (d). For recurrent structures (d≤2), survival is site-independent, while for transient structures (d>2), it depends on the target

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Last Updated: Jun 18, 2026

Spatial Separation of Molecular Conformers and Clusters

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Published on: January 9, 2014

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Published on: December 4, 2017

Area of Science:

Physics
Materials Science
Statistical Mechanics

Background:

Random walks are fundamental models for diffusion and transport in disordered systems.
Understanding target annihilation dynamics is crucial for processes in complex materials.

Purpose of the Study:

To analytically investigate the survival probability of immobile targets in random walks on inhomogeneous discrete structures.
To establish a relationship between survival probability and the spectral dimension of these structures.

Main Methods:

Analytical investigation of random walker populations.
Focus on inhomogeneous discrete structures like disordered solids, glasses, fractals, polymer networks, and gels.
Derivation of asymptotic behavior for survival probability at large times.

Main Results:

Survival probability cannot generally be linked to distinct visited points on inhomogeneous structures.
Asymptotic survival probability is expressible using the spectral dimension (d) for bounded coordination numbers.
Site-independent survival for recurrent structures (d≤2), and position-dependent survival for transient structures (d>2).

Conclusions:

The spectral dimension (d) is a key parameter governing random walker survival probability on complex structures.
The derived analytical expressions provide insights into annihilation dynamics in disordered materials.
Explicit calculation of target position dependence on transient structures offers predictive capabilities.