A model of diffusion in a spatially disordered lattice

The present review focuses on the plane strain problem of high strain rate expansion of a cylindrical cavity within an infinite brittle material with random microstructure. The material is represented by an ensemble of "continuum particles" forming a two-dimensional geometrically and structurally disordered lattice. The proposed model includes the aleatory variability and epistemic uncertainty of the process. The dynamic particle simulations are performed at seven different cavity expansion rates. The resulting damage evolution process is non-stationary, non-local, and non-equilibrium. This problem, therefore, belongs to the class of phenomena for which the traditional continuum models are not well suited, and detailed experimental data are either difficult to get or not available at all. The present study explores the potential role of the particle dynamics in addressing these problems. .

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Electric Conductivity for Lloyd's Disordered Lattice Model

Progress of Theoretical Physics ◽

10.1143/ptp.45.746 ◽

1971 ◽

Vol 45 (3) ◽

pp. 746-755 ◽

Cited By ~ 7

Author(s):

Motohiko Saitoh

Keyword(s):

Electric Conductivity ◽

Lattice Model ◽

Disordered Lattice

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Ground state of one-dimension repulsing particles on disordered lattice

International Journal of Modern Physics C ◽

10.1142/s0129183114500284 ◽

2014 ◽

Vol 25 (08) ◽

pp. 1450028 ◽

Cited By ~ 2

Author(s):

L. A. Pastur ◽

V. V. Slavin ◽

A. A. Krivchikov

Keyword(s):

Ground State ◽

Domain Walls ◽

Host Lattice ◽

One Dimension ◽

Weak Disorder ◽

Interacting Particles ◽

One Dimensional ◽

Lattice Disorder ◽

Disordered Lattice ◽

The Mean

The ground state (GS) of interacting particles on a disordered one-dimensional (1D) host-lattice is studied by a new numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal (GWC), replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes.

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