scholarly journals Some thermodynamic aspects of viscoplasticity of ferromagnetic

2002 ◽  
Vol 15 (2) ◽  
pp. 195-204
Author(s):  
Milan Micunovic
Keyword(s):  
Plastic Strain ◽  
Evolution Equations ◽  
Irreversible Thermodynamics ◽  
Ferromagnetic Materials ◽  
Residual Magnetization ◽  
Tensor Representation ◽  
Special Cases ◽  
Evolution Function ◽  
Elastic Strains ◽  
Small Plastic Strain

The paper deals with viscoplasticity of ferromagnetic materials. Tensor representation is applied to a set of evolution equations comprising the plastic stretching and residual magnetization tensors. Small magneto elastic strains of isotropic insulators are considered in detail in two special cases of finite as well as small plastic strain. A special emphasis is given to piezomagnetism effects in the case of uniaxial cycling strain. Vakulenko's irreversible thermodynamics is applied to irreversible magnetic phenomena by means of a hereditary evolution function. Purely mechanical as well as purely magnetic irreversible phenomena are considered in detail.

scholarly journals Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2023
Author(s):  
Christopher Nicholas Angstmann ◽  
Byron Alexander Jacobs ◽  
Bruce Ian Henry ◽  
Zhuang Xu
Keyword(s):  
Initial Value Problems ◽  
Fractional Derivatives ◽  
Evolution Equations ◽  
Integral Transform ◽  
Initial Value ◽  
Intrinsic Nature ◽  
Recent Interest ◽  
Special Cases ◽  
Singular Kernels

There has been considerable recent interest in certain integral transform operators with non-singular kernels and their ability to be considered as fractional derivatives. Two such operators are the Caputo–Fabrizio operator and the Atangana–Baleanu operator. Here we present solutions to simple initial value problems involving these two operators and show that, apart from some special cases, the solutions have an intrinsic discontinuity at the origin. The intrinsic nature of the discontinuity in the solution raises concerns about using such operators in modelling. Solutions to initial value problems involving the traditional Caputo operator, which has a singularity inits kernel, do not have these intrinsic discontinuities.

scholarly journals Measuring reaction rates at equilibrium with the isotope doping method

2019 ◽  
Vol 98 ◽  
pp. 13003
Author(s):  
Chen Zhu ◽  
Yilun Zhang ◽  
J Donald Rimstidt ◽  
Honglin Yuan
Keyword(s):  
Chemical Engineering ◽  
Experimental Testing ◽  
Detailed Balance ◽  
Reaction Rates ◽  
Irreversible Thermodynamics ◽  
Experimental Conditions ◽  
Special Cases ◽  
Wide Range ◽  
Long Time ◽  
Dissolution And Precipitation

Since the time of J. H. van’t Hoff [1], it has been known that chemical equilibrium is dynamic, meaning that at equilibrium, chemical reactions do not cease, but instead the forward and backward reaction rates are equal. The constant concentrations at equilibrium preclude the use of concentrations to measure reaction rates at equilibrium. Therefore, with the exception of a few special cases, no reaction rates at equilibrium have been published in the literature of chemistry, physics, or chemical engineering. Here we report dissolution and precipitation rates at equilibrium for quartz and barite with the isotope-doping method. Experimental data show that dissolution and precipitation rates are equal at equilibrium, indicating the principle of detailed balance (PDB) appear to be applicable at these experimental conditions. The PDB has been a cornerstone for irreversible thermodynamics and chemical kinetics for a long time, and its wide application in geochemistry has mostly been implicit and without experimental testing of its applicability. Nevertheless, many extrapolations based on PDB without experimental validation have far reaching impacts on society’s mega environmental enterprises. The isotope doping method appears to able to test its applicability for a variety of minerals at a wide range of conditions.

A round robin EBSD measurement for quantitative assessment of small plastic strain

2020 ◽  
Vol 170 ◽  
pp. 110662
Author(s):  
Masayuki Kamaya ◽  
Yohei Sakakibara ◽  
Rika Yoda ◽  
Seiichi Suzuki ◽  
Hirobumi Morita ◽  
...  
Keyword(s):  
Plastic Strain ◽  
Quantitative Assessment ◽  
Round Robin ◽  
Ebsd Measurement ◽  
Small Plastic ◽  
Small Plastic Strain

Exact solutions for scalar field cosmology in f(R) gravity

2017 ◽  
Vol 32 (30) ◽  
pp. 1750164 ◽  
Author(s):  
S. D. Maharaj ◽  
R. Goswami ◽  
S. V. Chervon ◽  
A. V. Nikolaev
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Scalar Curvature ◽  
Evolution Equations ◽  
Initial Conditions ◽  
De Sitter ◽  
Airy Functions ◽  
Special Cases ◽  
The Universe ◽  
Current Stage

We study scalar field FLRW cosmology in the content of f(R) gravity. Our consideration is restricted to the spatially flat Friedmann universe. We derived the general evolution equations of the model, and showed that the scalar field equation is automatically satisfied for any form of the f(R) function. We also derived representations for kinetic and potential energies, as well as for the acceleration in terms of the Hubble parameter and the form of the f(R) function. Next we found the exact cosmological solutions in modified gravity without specifying the f(R) function. With negligible acceleration of the scalar curvature, we found that the de Sitter inflationary solution is always attained. Also we obtained new solutions with special restrictions on the integration constants. These solutions contain oscillating, accelerating, decelerating and even contracting universes. For further investigation, we selected special cases which can be applied with early or late inflation. We also found exact solutions for the general case for the model with negligible acceleration of the scalar curvature in terms of special Airy functions. Using initial conditions which represent the universe at the present epoch, we determined the constants of integration. This allows for the comparison of the scale factor in the new solutions with that for current stage of the universe evolution in the [Formula: see text]CDM model.

On Gradient Nanomechanics: Plastic Flow in Nanopolycrystals

2010 ◽  
Vol 667-669 ◽  
pp. 991-996 ◽  
Author(s):  
Xu Zhang ◽  
A.E. Romanov ◽  
Elias C. Aifantis
Keyword(s):  
Grain Size ◽  
Plastic Strain ◽  
Continuum Mechanics ◽  
Evolution Equations ◽  
Surface Interactions ◽  
Structural Defects ◽  
Field Equations ◽  
Size Dependent ◽  
Bulk Surface ◽  
Generalized Continuum

Gradient nanomechanics is a generalized continuum mechanics framework accounting for “bulk-surface” interactions in the form of gradient terms that enter in the evolution equations of the relevant constitutive variables and/or in the governing field equations. This approach is discussed in the paper by developing appropriate differential equations for the plastic strain and/or the structural defects that bring this about. The effectiveness of the approach is illustrated by considering size-dependent stress-strain curves for nanopolycrystals with varying grain size.

Understanding the Biases of Generalised Recombination: Part II

2007 ◽  
Vol 15 (1) ◽  
pp. 95-131 ◽  
Author(s):  
Riccardo Poli ◽  
Christopher R. Stephens
Keyword(s):  
Population Model ◽  
Gene Deletion ◽  
Evolution Equations ◽  
Coarse Grained ◽  
General Notion ◽  
Schema Evolution ◽  
Infinite Population ◽  
Special Cases ◽  
Model Predictions ◽  
Hierarchical Nature

This is the second part of a two-part paper where we propose, model theoretically and study a general notion of recombination for fixed-length strings where homologous recombination, inversion, gene duplication, gene deletion, diploidy and more are just special cases. In Part I, we derived both microscopic and coarse-grained evolution equations for strings and schemata for a selecto-recombinative GA using generalised recombination, and we explained the hierarchical nature of the schema evolution equations. In this part, we provide a variety of fixed points for evolution in the case where recombination is used alone, thereby generalising Geiringer's theorem. In addition, we numerically integrate the infinite-population schema equations for some interesting problems, where selection and recombination are used together to illustrate how these operators interact. Finally, to assess by how much genetic drift can make a system deviate from the infinite-population-model predictions we discuss the results of real GA runs for the same model problems with generalised recombination, selection and finite populations of different sizes.

Inertial effects in time-dependent motion of thin films and drops

2002 ◽  
Vol 467 ◽  
pp. 1-17 ◽  
Author(s):  
L. M. HOCKING ◽  
S. H. DAVIS
Keyword(s):  
Thin Films ◽  
Contact Angle ◽  
Contact Line ◽  
Evolution Equations ◽  
Liquid Films ◽  
Contact Angles ◽  
Terminal State ◽  
Lubrication Theory ◽  
Plate Motion ◽  
Special Cases

Capillarity is an important feature in controlling the spreading of liquid drops and in the coating of substrates by liquid films. For thin films and small contact angles, lubrication theory enables the analysis of the motion to be reduced to single evolution equations for the heights of the drops or films, provided the inertia of the liquid can be neglected. In general, the presence of inertia destroys the major simplification provided by lubrication theory, but two special cases that can be treated are identified here. In the first example, the approach of a drop to its equilibrium position is studied. For sufficiently low Reynolds numbers, the rate of approach to the terminal state and the contact angle are slightly reduced by inertia, but, above a critical Reynolds number, the approach becomes oscillatory. In the latter case there is no simple relation connecting the dynamic contact angle and contact-line speed. In the second example, the spreading drop is supported by a plate that is forced to oscillate in its own plane. For the parameter range considered, the mean spreading is unaffected by inertia, but the oscillatory motion of the contact line is reduced in magnitude as inertia increases, and the drop lags behind the plate motion. The oscillatory contact angle increases with inertia, but is not in phase with the plate oscillation.

scholarly journals Phase Space Analysis and Thermodynamics of Interacting Umami Chaplygin Gas in FRW Universe

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Sujay Kr. Biswas ◽  
Atreyee Biswas
Keyword(s):  
Evolution Equations ◽  
Coupling Parameter ◽  
Irreversible Thermodynamics ◽  
Chaplygin Gas ◽  
Dynamical Behaviour ◽  
Late Time ◽  
Coincidence Problem ◽  
Frw Universe ◽  
Dynamical Systems Analysis ◽  
Accelerated Evolution

AbstractIn this work interacting Umami Chaplygin gas has been studied in flat FRW model of universe in context of it’s thermodynamic and dynamical behaviour. In particular, considering Umami fluid as dark energy interacting with dark matter, irreversible thermodynamics has been studied both for apparent and event horizon as bounding horizon in two separate cases. Also the model has been investigated in purview of dynamical systems analysis by converting the cosmological evolution equations to an autonomous system of ordinary differential equations. With some restrictions on model parameter $$\omega $$ ω and coupling parameter $$\lambda $$ λ , some cosmologically interesting critical points describing late time accelerated evolution of the universe attracted by cosmological constant and accelerated scaling attractor in quintessence era have been found to alleviate coincidence problem.

scholarly journals A Unified Extended Thermodynamic Description of Diffusion, Thermo-Diffusion, Suspensions, and Porous Media

2005 ◽  
Vol 73 (1) ◽  
pp. 16-20 ◽  
Author(s):  
Georgy Lebon ◽  
Thomas Desaive ◽  
Pierre Dauby
Keyword(s):  
Porous Media ◽  
Evolution Equations ◽  
Diffusion Flux ◽  
Thermodynamic Description ◽  
Fluid Flows ◽  
Irreversible Thermodynamics ◽  
Heat Fluxes ◽  
Flows In Porous Media ◽  
Extended Thermodynamic ◽  
Higher Order Terms

It is shown that extended irreversible thermodynamics (EIT) provides a unified description of a great variety of processes, including matter diffusion, thermo-diffusion, suspensions, and fluid flows in porous media. This is achieved by enlarging the set of classical variables, as mass, momentum and temperature by the corresponding fluxes of mass, momentum and heat. For simplicity, we consider only Newtonian fluids and restrict ourselves to a linear analysis: quadratic and higher order terms in the fluxes are neglected. In the case of diffusion in a binary mixture, the extra flux variable is the diffusion flux of one the constituents, say the solute. In thermo-diffusion, one adds the heat flux to the set of variables. The main result of the present approach is that the traditional equations of Fick, Fourier, Soret, and Dufour are replaced by time-evolution equations for the matter and heat fluxes, such generalizations are useful in high-frequency processes. It is also shown that the analysis can be easily extended to the study of particle suspensions in fluids and to flows in porous media, when such systems can be viewed as binary mixtures with a solid and a fluid component.

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