Mathematical modeling phase transition in solids

The article deals with constructing and implementing mathematical models of non-isothermal moisture transfer during drying of anisotropic capillary-porous materials, in particular wood, taking into account the movement of the evaporation zone for non-steady drying schedules, as well as to the development of effective analytical and numerical methods for their implementation. An analytical-numerical method for the determination of non-isothermal moisture transfer under non-steady schedules of the drying process has been developed, taking into account the dynamics of the phase transition boundary change. Calculation relationships are established for determining the phase transition temperature taking into account transport gradients and time for which the relative saturation reaches the boundaries of the phase transition.

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Mathematical modeling of phase transition and separation in fluids: A unified approach

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2014.19.1889 ◽

2014 ◽

Vol 19 (7) ◽

pp. 1889-1909 ◽

Cited By ~ 2

Author(s):

Alessia Berti ◽

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Claudio Giorgi ◽

Angelo Morro ◽

◽

...

Keyword(s):

Mathematical Modeling ◽

Phase Transition ◽

Unified Approach

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Mathematical modeling of bulk and directional crystallization with the moving phase transition layer

10.22541/au.163250947.73804831/v1 ◽

2021 ◽

Author(s):

Liubov Toropova ◽

Danil Aseev ◽

Sergei Osipov ◽

Alexander Ivanov

Keyword(s):

Mathematical Modeling ◽

Phase Transition ◽

Transition Layer ◽

Solid Phase ◽

Phase Region ◽

Mushy Region ◽

Solidification Velocity ◽

Mushy Layer ◽

Two Phase ◽

Phase Layer

This paper is devoted to the mathematical modeling of a combined effect of directional and bulk crystallization in a phase transition layer with allowance for nucleation and evolution of newly born particles. We consider two models with and without fluctuations in crystal growth velocities, which are analytically solved using the saddle-point technique. The particle-size distribution function, solid-phase fraction in a supercooled two-phase layer, its thickness and permeability, solidification velocity, and desupercooling kinetics are defined. This solution enables us to characterize the mushy layer composition. We show that the region adjacent to the liquid phase is almost free of crystals and has a constant temperature gradient. Crystals undergo intense growth leading to fast mushy layer desupercooling in the middle of a two-phase region. The mushy region adjacent to the solid material is filled with the growing solid phase structures and is almost desupercooled.

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Mathematical modeling of polymer melt crystallization with the phase transition velocity taken into account

Journal of Engineering Physics ◽

10.1007/bf00870758 ◽

1987 ◽

Vol 52 (2) ◽

pp. 170-174

Author(s):

M. I. Il'in ◽

Yu. V. Sharikov ◽

A. A. Zhitinkin

Keyword(s):

Mathematical Modeling ◽

Phase Transition ◽

Polymer Melt ◽

Melt Crystallization ◽

Transition Velocity

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Microstructure of laser-irradiated, conducting Kapton polyimide

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100138889 ◽

1995 ◽

Vol 53 ◽

pp. 502-503

Author(s):

D. L. Callahan ◽

Z. Ball ◽

H. M. Phillips ◽

R. Sauerbrey

Keyword(s):

Electron Microscopy ◽

Phase Transition ◽

Transmission Electron Microscopy ◽

Cross Section ◽

Film Surface ◽

Cross Sectional ◽

General Utility ◽

Transmission Electron ◽

Considerable Debate ◽

Potential Applications

Ultraviolet laser-irradiation can be used to induce an insulator-to-conductor phase transition on the surface of Kapton polyimide. Such structures have potential applications as resistors or conductors for VLSI applications as well as general utility electrodes. Although the percolative nature of the phase transformation has been well-established, there has been little definitive work on the mechanism or extent of transformation. In particular, there has been considerable debate about whether or not the transition is primarily photothermal in nature, as we propose, or photochemical. In this study, cross-sectional optical microscopy and transmission electron microscopy are utilized to characterize the nature of microstructural changes associated with the laser-induced pyrolysis of polyimide.Laser-modified polyimide samples initially 12 μm thick were prepared in cross-section by standard ultramicrotomy. Resulting contraction in parallel to the film surface has led to distortions in apparent magnification. The scale bars shown are calibrated for the direction normal to the film surface only.

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The structure of membranes and membrane proteins embedded in amorphous ice

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100122563 ◽

1992 ◽

Vol 50 (1) ◽

pp. 432-433

Author(s):

Uwe Lücken ◽

Joachim Jäger

Keyword(s):

Phase Transition ◽

Transition Temperature ◽

Membrane Proteins ◽

Phase Transition Temperature ◽

Lipid Vesicles ◽

Freezing Stress ◽

Amorphous Ice ◽

Different Temperatures ◽

Band Pass ◽

Lipid Polymorphism

TEM imaging of frozen-hydrated lipid vesicles has been done by several groups Thermotrophic and lyotrophic polymorphism has been reported. By using image processing, computer simulation and tilt experiments, we tried to learn about the influence of freezing-stress and defocus artifacts on the lipid polymorphism and fine structure of the bilayer profile. We show integrated membrane proteins do modulate the bilayer structure and the morphology of the vesicles.Phase transitions of DMPC vesicles were visualized after freezing under equilibrium conditions at different temperatures in a controlled-environment vitrification system. Below the main phase transition temperature of 24°C (Fig. 1), vesicles show a facetted appearance due to the quasicrystalline areas. A gradual increase in temperature leads to melting processes with different morphology in the bilayer profile. Far above the phase transition temperature the bilayer profile is still present. In the band-pass-filtered images (Fig. 2) no significant change in the width of the bilayer profile is visible.

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Electron Microscope study of commensurate-incommensurate phase transition in BaZnGeO4

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173996 ◽

1990 ◽

Vol 48 (4) ◽

pp. 172-173

Author(s):

Naoki Yamamoto ◽

Makoto Kikuchi ◽

Tooru Atake ◽

Akihiro Hamano ◽

Yasutoshi Saito

Keyword(s):

Phase Transition ◽

Electron Microscope Study ◽

Room Temperature ◽

Hexagonal Lattice ◽

Ferroelectric Materials ◽

Temperature Phase ◽

X Ray Diffraction ◽

X Ray ◽

Periodic Arrays ◽

Modulation Wave Vector

BaZnGeO4 undergoes many phase transitions from I to V phase. The highest temperature phase I has a BaAl2O4 type structure with a hexagonal lattice. Recent X-ray diffraction study showed that the incommensurate (IC) lattice modulation appears along the c axis in the III and IV phases with a period of about 4c, and a commensurate (C) phase with a modulated period of 4c exists between the III and IV phases in the narrow temperature region (—58°C to —47°C on cooling), called the III' phase. The modulations in the IC phases are considered displacive type, but the detailed structures have not been studied. It is also not clear whether the modulation changes into periodic arrays of discommensurations (DC’s) near the III-III' and IV-V phase transition temperature as found in the ferroelectric materials such as Rb2ZnCl4.At room temperature (III phase) satellite reflections were seen around the fundamental reflections in a diffraction pattern (Fig.1) and they aligned along a certain direction deviated from the c* direction, which indicates that the modulation wave vector q tilts from the c* axis. The tilt angle is about 2 degree at room temperature and depends on temperature.

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