scholarly journals A new fractal viscoelastic element: Promise and applications to Maxwell-rheological model

2021 ◽  
pp. 15-15
Author(s):  
Yan-Hong Liang ◽  
Kang-Jia Wang
Keyword(s):  
Continuum Mechanics ◽  
Rheological Model ◽  
Bright Light ◽  
Elastic Model ◽  
Relaxation Equation ◽  
Creep Equation ◽  
Fractal Derivative ◽  
Special Cases ◽  
Viscoelastic Element ◽  
First Time

This paper proposes a fractal viscoelastic element via He?s fractal derivative, its properties are analyzed in details by the two-scale transform for the first time. The element is used to establish a fractal Maxwell-rheological model(FMRM), which unifies the fractal creep equation and relaxation equation, and includes the classic elastic model and the classical Maxwell-rheological model as two special cases. This paper sheds a bright light on viscoelasticity, and the model can find wide applications in rock mechanics, plastic mechanics, and non-continuum mechanics.

The Inverse Modeling Method of Rock Rheological Model

2011 ◽  
Vol 255-260 ◽  
pp. 3807-3811
Author(s):  
Xiang Dong Zhang ◽  
Jian Jian Ruan ◽  
Chang Yu Lan
Keyword(s):  
Inverse Modeling ◽  
Rheological Model ◽  
Inverse Method ◽  
Element Model ◽  
Relaxation Equation ◽  
Creep Equation ◽  
Rheological Models ◽  
Rock Creep ◽  
Simplified Method ◽  
Creep Constitutive Model

Along with the economical and the industrialization development, The development domain of rheology will be expanded. At present There are many researches about rock rheological, but the existing model Cannot completely, indication properties of rock, Especially the nonlinear rheological model and rock creep constitutive model of accelerating rheological phase of the study is scarce. After viewing a large number of the composition of rheological models and their laws in current papers, we find out what they are common and give the simplified method of creep equation and relaxation equation .Then we propose the inverse method to establish the new nonlinear rheological element model and the constitutive equation method. This paper focuses on establishing a new method of rheological model which provide technical support.

scholarly journals Fractal diffusion-reaction model for a porous electrode

2021 ◽  
pp. 26-26
Author(s):  
Ling Lin ◽  
Yun Qiao
Keyword(s):  
Surface Morphology ◽  
Porous Electrode ◽  
Enzymatic Reaction ◽  
Bright Light ◽  
Reaction Model ◽  
Solution Procedure ◽  
Diffusion Reaction ◽  
Fast Diffusion ◽  
Fractal Derivative ◽  
Intuitive Grasp

Fractal modifications of Fick?s laws are discussed by taking into account the electrode?s porous structure, and a fractal derivative model for diffusion-reaction process in a thin film of an amperometric enzymatic reaction is established. Particular attention is paid to giving an intuitive grasp for its fractal variational principle and its solution procedure. Extremely fast or extremely slow diffusion process can be achieved by suitable control of the electrode?s surface morphology, a sponge-like surface leads to an extremely fast diffusion, while a lotus-leaf-like uneven surface predicts an extremely slow process. This paper sheds a bright light on an optimal design of an electrode?s surface morphology.

Helium

2010 ◽  
Author(s):  
David Fisher
Keyword(s):  
Nineteenth Century ◽  
Emission Spectrum ◽  
Mass Spectrometer ◽  
Solar Eclipse ◽  
Atomic Structure ◽  
Chemical Elements ◽  
Bright Light ◽  
The Sun ◽  
The Moon ◽  
First Time

Today we learn at such a young age about the periodic properties of the elements and their atomic structure that it seems as if we grew up with the knowledge, and that everyone must always have known such basic, simple stuff. But till nearly the end of the nineteenth century no one even suspected that such things as the noble gases, with their filled electronic orbits, might exist. Helium was the first one we at Brookhaven looked for in our mass spectrometer, and the first one discovered. This was in 1868, but the discovery was ignored and the discoverer ridiculed. He didn’t care; he had other things on his mind. His name was Pierre Jules César Janssen, and he was a French astronomer who sailed to India that year in order to take advantage of a predicted solar eclipse. With the overwhelming brightness of the sun’s disk blocked by the moon, he hoped to observe the outer layers using the newly discovered technique of absorption spectroscopy. Nobody at the time understood why, but it had been observed that when a bright light shone through a gas, the chemical elements in the gas absorbed the light at specific wavelengths. The resulting dark lines in the emission spectrum of the light were like fingerprints, for it had been found in chemical laboratories that when an element was heated it emitted light at the same wavelengths it would absorb when light from an outside source was shined on it. So the way the technique worked, Janssen reasoned, was that he could measure the wavelengths of the solar absorbed lines and compare them with lines emitted in chemical laboratories where different elements were routinely studied, thus identifying the gases present in the sun. On August 18 of that year the moon moved properly into position, and Janssen’s spectroscope captured the dark absorption lines of the gases surrounding the sun. It was an exciting moment, as for the first time the old riddle could be answered: “Twinkle twinkle, little star, how I wonder what you are.” The answer now was clear: the sun, a typical star, was made overwhelmingly of hydrogen. But to Janssen’s surprise there was one additional and annoying line, with a wavelength of 587.49 nanometers.

scholarly journals Lévy Distributions for One-Dimensional Analysis of the Bose–Einstein Correlations

2017 ◽  
Vol 2017 ◽  
pp. 1-18 ◽  
Author(s):  
V. A. Okorokov
Keyword(s):  
Reasonable Agreement ◽  
Emission Region ◽  
General Study ◽  
Gaussian Distributions ◽  
One Dimensional ◽  
Interaction Processes ◽  
Special Cases ◽  
Centrally Symmetric ◽  
Bose Einstein ◽  
First Time

A general study of relations between the parameters of two centrally symmetric Lévy distributions, often used for one-dimensional investigation of Bose–Einstein correlations, is given for the first time. These relations of the strength of correlations and of the radius of the emission region take into account possible various finite ranges of the Lorentz invariant four-momentum difference for two centrally symmetric Lévy distributions. In particular, special cases of the relations are investigated for Cauchy and normal (Gaussian) distributions. The mathematical formalism is verified using the recent measurements given that a generalized centrally symmetric Lévy distribution is used. The reasonable agreement is observed between estimations and experimental results for all available types of strong interaction processes and collision energies.

scholarly journals NUTRITION OF THE HOST AND NATURAL RESISTANCE TO INFECTION

1949 ◽  
Vol 89 (5) ◽  
pp. 529-539 ◽  
Author(s):  
Howard A. Schneider
Keyword(s):  
Inbred Mouse ◽  
Natural Resistance ◽  
Single Infection ◽  
Mouse Strains ◽  
Time Interval ◽  
Special Cases ◽  
Resistance To Infection ◽  
Relationship Of ◽  
First Time ◽  
The Relationship

The double strain inoculation (DSI) method of testing for natural resistance to infection has been examined in the instance of mouse salmonellosis. The DSI method has been found capable of detecting differences in natural resistance due to genetic as well as nutritional causes. A difference in response to Salmonella infection was found for the first time between the two "susceptible" inbred mouse strains, BSVR and BSVS. Whereas BSVS mice for the most part survived an intraperitoneal injection of 103 "avirulent" S. typhimurium, BSVR mice all succumbed. The relationship of the DSI test to the usual single infection test has been discussed and it is suggested that such single infection tests are special cases of the DSI test, since they involve a heterogeneous bacterial population which can be considered as a mixture of cultures of differing virulence and in which, by a single injection, the usual time interval between the two injections of the DSI method has been reduced to 0.

scholarly journals Some Hermite-Hadamard type inequalities for (P;m)-function and quasi m-convex functions

2020 ◽  
Vol 10 (1) ◽  
pp. 78-84
Author(s):  
Mahir Kadakal
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
New Class ◽  
Special Cases ◽  
First Time ◽  
Class Of Functions

In this paper, we introduce a new class of functions called as (P;m)-function and quasi-m-convex function. Some inequalities of Hadamard's type for these functions are given. Some special cases are discussed. Results represent signicant renement and improvement of the previous results. We should especially mention that the denition of (P;m)-function and quasi-m-convexity are given for the first time in the literature and moreover, the results obtained in special cases coincide with thewell-known results in the literature.

scholarly journals Local fractional Euler’s method for the steady heat-conduction problem

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 735-738 ◽  
Author(s):  
Feng Gao ◽  
Xiao-Jun Yang
Keyword(s):  
Heat Conduction ◽  
Exact Solutions ◽  
Numerical Solution ◽  
Heat Conduction Problem ◽  
Relaxation Equation ◽  
Euler’S Method ◽  
Steady Heat Conduction ◽  
First Time ◽  
Steady Heat

In this paper, the local fractional Euler?s method is proposed to consider the steady heat-conduction problem for the first time. The numerical solution for the local fractional heat-relaxation equation is presented. The comparison between numerical and exact solutions is discussed.

scholarly journals Truth and Concept, or What a Concept in Philosophy of Henri Bergson Is, and What It Is Not. Afterword to the Ukrainian Translation of the Henri Bergson’s Letter to Richard Kroner

2020 ◽  
Vol 6 (2) ◽  
pp. 51-52
Author(s):  
Pavlo Bartusiak
Keyword(s):  
Bright Light ◽  
Henri Bergson ◽  
New Concepts ◽  
First Time

The Letter to Richard Kroner was written by Henri Bergson in the end of November 1910. It is translated into Ukrainian for the first time. In the letter, Bergson sheds a bright light on tiny and usually invisible but very important details of his doctrine about truth and concepts, in particular creating new concepts.

scholarly journals Application of Decomposable Semi-Regenerative Processes to the Study of k-out-of-n Systems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1933
Author(s):  
Vladimir Rykov ◽  
Nika Ivanova ◽  
Dmitry Kozyrev
Keyword(s):  
Closed Form ◽  
Time Dependent ◽  
System State ◽  
Regenerative Processes ◽  
Full System ◽  
Special Cases ◽  
Form Representation ◽  
History Of ◽  
First Time ◽  
Stationary Probabilities

This paper aimed to demonstrate the capabilities of decomposable semi-regenerative processes for the investigation of the k-out-of-n system. Proposed in 1955 by W. Smith, the regeneration idea has come a long way in terms of development and has found widespread applications. First, we briefly recall the history of the development of the regeneration idea and the main results of the theory of regenerative, semi-regenerative, and decomposable semi-regenerative processes. Then, the methods of the theory of decomposable semi-regenerative processes are used for the study of a k-out-of-n renewable system with exponentially distributed life and generally distributed repair times of its components. This system is very important for practice and its special cases have previously been considered (including by the authors); however, only special cases and using other methods are considered herein. In the current paper, two scenarios of system repair after its failure are considered for the first time: the partial and the full system repair scenarios. For both scenarios, the time-dependent system state probabilities are calculated in terms of their Laplace transforms. The closed form representation of the stationary probabilities for both scenarios are also presented. These latest results represent a new contribution to the study of this system.

scholarly journals Flow Properties Inferred from Generalized Maxwell Models

2009 ◽  
Vol 64 (1-2) ◽  
pp. 81-95 ◽  
Author(s):  
Siegfried Hess ◽  
Bastian Arlt ◽  
Sebastian eidenreich ◽  
Patrick Ilg ◽  
Chris Goddard ◽  
...  
Keyword(s):  
Stress Tensor ◽  
Maxwell Model ◽  
Stationary Solutions ◽  
Model Parameters ◽  
Relaxation Equation ◽  
Newtonian Viscosity ◽  
Stick Slip ◽  
First Case ◽  
Scalar Invariant ◽  
Special Cases

The generalized Maxwell model is formulated as a nonlinear relaxation equation for the symmetric traceless stress tensor. The relaxation term of the equation involves the derivative of a potential function with respect to the stress tensor. Two special cases for this potential referred to as “isotropic” and “anisotropic” are considered. In the first case, the potential solely depends on the second scalar invariant, viz. the norm of the tensor. In the second case, also a dependence on the third scalar invariant, essentially the determinant, is taken into account in analogy to the Landau-de Gennes potential of nematic liquid crystals. Rheological consequences of the model are presented for a plane Couette flow with an imposed shear rate. The non-Newtonian viscosity and the normal stress differences are analyzed for stationary solutions. The dependence on the model parameters is discussed in detail. In particular, the occurrence of a shear-thickening behaviour is studied. The possibility to describe substances with yield stress and the existence of non-stationary, stick-slip-like solutions are pointed out. The extension of the model to magneto-rheological fluids is indicated.

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