scholarly journals PHASE TRANSITIONS IN TWO- AND THREE-DIMENSIONAL COMPOUND-LATTICE MODELS

1977 ◽  
Vol 38 (C4) ◽  
pp. C4-133-C4-140
Author(s):  
H. P. NEUMANN
Keyword(s):  
Phase Transitions ◽  
Three Dimensional ◽  
Lattice Models

scholarly journals Crystal–liquid phase transitions in three-dimensional complex plasma under microgravity conditions

2018 ◽  
Vol 946 ◽  
pp. 012144 ◽  
Author(s):  
V N Naumkin ◽  
A M Lipaev ◽  
V I Molotkov ◽  
D I Zhukhovitskii ◽  
A D Usachev ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Liquid Phase ◽  
Three Dimensional ◽  
Complex Plasma ◽  
Microgravity Conditions

scholarly journals Fractional Diffusion Equations for Lattice and Continuum: Grünwald-Letnikov Differences and Derivatives Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Fractional Derivatives ◽  
Three Dimensional ◽  
Lattice Models ◽  
Fractional Diffusion ◽  
Lattice Diffusion ◽  
Diffusion Equations ◽  
Difference Operators ◽  
Fractional Diffusion Equations ◽  
Nonlocal Media ◽  
Derivatives Of

Fractional diffusion equations for three-dimensional lattice models based on fractional-order differences of the Grünwald-Letnikov type are suggested. These lattice fractional diffusion equations contain difference operators that describe long-range jumps from one lattice site to another. In continuum limit, the suggested lattice diffusion equations with noninteger order differences give the diffusion equations with the Grünwald-Letnikov fractional derivatives for continuum. We propose a consistent derivation of the fractional diffusion equation with the fractional derivatives of Grünwald-Letnikov type. The suggested lattice diffusion equations can be considered as a new microstructural basis of space-fractional diffusion in nonlocal media.

Current-induced reordering phase transitions of vortex matter in 3D-layered superconductors

2018 ◽  
Vol 32 (25) ◽  
pp. 1850281 ◽  
Author(s):  
Qingmiao Nie ◽  
Haibin Li
Keyword(s):  
Phase Transitions ◽  
Thermal Noise ◽  
Vortex Lattice ◽  
Three Dimensional ◽  
Xy Model ◽  
Vortex Matter ◽  
Nonequilibrium Phase Transitions ◽  
External Current ◽  
Layered Superconductors ◽  
Pinning Potential

Nonequilibrium phase transitions of vortex matter with a strong random pinning potential in layered superconductors are investigated by the three-dimensional frustrated anisotropic XY model and resistively-shunted junction dynamics at low, middle and high-temperatures, respectively. It is found that a disorder to order phase transition driven by an external current can be obtained at a low-temperature, however, a reordering configuration does not occur at a high-temperature. With the competition between thermal noise, disorder pins and current, the vortex matter can even show the reordering process twice at an intermediate temperature, giving a clear evidence of dc driven vortex lattice reorganization.

scholarly journals A Novel (2, 3)-Threshold Reversible Secret Image Sharing Scheme Based on Optimized Crystal-Lattice Matrix

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2063
Author(s):  
Jiang-Yi Lin ◽  
Ji-Hwei Horng ◽  
Chin-Chen Chang
Keyword(s):  
Crystal Lattice ◽  
Three Dimensional ◽  
Lattice Models ◽  
Cover Image ◽  
Secret Image Sharing ◽  
Secret Data ◽  
Secret Image ◽  
Image Sharing ◽  
Sharing Scheme ◽  
Growth Phenomenon

The (k, n)-threshold reversible secret image sharing (RSIS) is technology that conceals the secret data in a cover image and produces n shadow versions. While k (kn) or more shadows are gathered, the embedded secret data and the cover image can be retrieved without any error. This article proposes an optimal (2, 3) RSIS algorithm based on a crystal-lattice matrix. Sized by the assigned embedding capacity, a crystal-lattice model is first generated by simulating the crystal growth phenomenon with a greedy algorithm. A three-dimensional (3D) reference matrix based on translationally symmetric alignment of crystal-lattice models is constructed to guide production of the three secret image shadows. Any two of the three different shares can cooperate to restore the secret data and the cover image. When all three image shares are available, the third share can be applied to authenticate the obtained image shares. Experimental results prove that the proposed scheme can produce secret image shares with a better visual quality than other related works.

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