Cell dynamical system study of phase separation dynamics

If spinodal decomposition is modeled by the Cahn-Hilliard (-Cook) equation, the effect of a uniform external force such as gravitation does not appear in the bulk phase kinetics. In contrast, in the Kawasaki exchange modeling of the local dynamics of binary alloys, this effect directly modifies the bulk phase kinetics. We resolve this paradox through the cell-dynamical-system modeling of the Kawasaki exchange dynamics. Its continuum version has turned out to be a modified Cahn-Hilliard equation already proposed by Langer et al. about ten years ago. We demonstrate some examples in which the correction to the Cahn-Hilliard equation is significant.

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Asymptotic Independence and Uniform Distribution of Quantization Errors for Spatially Discretized Dynamical Systems

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127498001133 ◽

1998 ◽

Vol 08 (07) ◽

pp. 1479-1490 ◽

Cited By ~ 3

Author(s):

P. Diamond ◽

I. Vladimirov

Keyword(s):

Dynamical System ◽

Computer Simulation ◽

Dynamical Systems ◽

Computer Arithmetic ◽

Original System ◽

Unit Interval ◽

Asymptotic Independence ◽

System Study ◽

Polynomial Mappings ◽

Finite Set

Computer simulation of dynamical systems involves a state space which is the finite set of computer arithmetic. Restricting state values to this grid produces roundoff effects which can be studied by replacing the original system with a spatially discretized dynamical system. Study of the deviation of the discretized trajectories from those of the original system reduces to that of appropriately defined quantization errors. As the grid is refined, the asymptotic behavior of these quantization errors follows probabilistic laws. These results are applied to discretized polynomial mappings of the unit interval.

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A dynamical system study of the inhomogeneous Λ-CDM model

Classical and Quantum Gravity ◽

10.1088/0264-9381/28/4/045006 ◽

2011 ◽

Vol 28 (4) ◽

pp. 045006 ◽

Cited By ~ 9

Author(s):

Roberto A Sussman ◽

Germán Izquierdo

Keyword(s):

Dynamical System ◽

System Study

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Dynamical System Study of Nonminimal Tachyon Field within Holographic Cosmology

Gravitation and Cosmology ◽

10.1134/s0202289320040039 ◽

2020 ◽

Vol 26 (4) ◽

pp. 379-386

Author(s):

Farida Bargach ◽

Aatifa Bargach ◽

Taoufik Ouali

Keyword(s):

Dynamical System ◽

System Study ◽

Tachyon Field

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A dynamical system study for the ecological development of mineral resources in minority areas

Discrete & Continuous Dynamical Systems - S ◽

10.3934/dcdss.2019074 ◽

2019 ◽

Vol 12 (4-5) ◽

pp. 1073-1089 ◽

Cited By ~ 1

Author(s):

Yuyan Luo ◽

◽

Yong Qin ◽

Zhong Wang ◽

Jun Wang ◽

...

Keyword(s):

Dynamical System ◽

Mineral Resources ◽

System Study ◽

Ecological Development

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Bulk standards for low-temperature biological x-ray microanalysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100111525 ◽

1984 ◽

Vol 42 ◽

pp. 282-283

Author(s):

P. Echlin ◽

M. McKoon ◽

E.S. Taylor ◽

C.E. Thomas ◽

K.L. Maloney ◽

...

Keyword(s):

Phase Separation ◽

Low Temperature ◽

Analytical Method ◽

Salt Solutions ◽

Absolute Concentration ◽

Cooling Process ◽

X Ray ◽

The Absolute ◽

Analytical Procedures ◽

Electrical Conductors

Although sections of frozen salt solutions have been used as standards for x-ray microanalysis, such solutions are less useful when analysed in the bulk form. They are poor thermal and electrical conductors and severe phase separation occurs during the cooling process. Following a suggestion by Whitecross et al we have made up a series of salt solutions containing a small amount of graphite to improve the sample conductivity. In addition, we have incorporated a polymer to ensure the formation of microcrystalline ice and a consequent homogenity of salt dispersion within the frozen matrix. The mixtures have been used to standardize the analytical procedures applied to frozen hydrated bulk specimens based on the peak/background analytical method and to measure the absolute concentration of elements in developing roots.

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Phase separation in sol gel-derived ceramic films of silica-zirconia, alumina-zirconia, and titania-zirconia system

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100170967 ◽

1994 ◽

Vol 52 ◽

pp. 646-647

Author(s):

J. Tong ◽

L. Eyring

Keyword(s):

Fracture Toughness ◽

Phase Separation ◽

Sol Gel ◽

Great Influence ◽

High Strength ◽

Chemical Durability ◽

Separation Method ◽

Toughening Mechanism ◽

Ceramic Films ◽

Zirconia Toughened Alumina

There is increasing interest in composites containing zirconia because of their high strength, fracture toughness, and its great influence on the chemical durability in glass. For the zirconia-silica system, monolithic glasses, fibers and coatings have been obtained. There is currently a great interest in designing zirconia-toughened alumina including exploration of the processing methods and the toughening mechanism.The possibility of forming nanocrystal composites by a phase separation method has been investigated in three systems: zirconia-alumina, zirconia-silica and zirconia-titania using HREM. The morphological observations initially suggest that the formation of nanocrystal composites by a phase separation method is possible in the zirconia-alumina and zirconia-silica systems, but impossible in the zirconia-titania system. The separation-produced grain size in silica-zirconia system is around 5 nm and is more uniform than that in the alumina-zirconia system in which the sizes of the small polyhedron grains are around 10 nm. In the titania-zirconia system, there is no obvious separation as was observed in die alumina-zirconia and silica-zirconia system.

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