scholarly journals MATHEMATICAL MODEL OF THE DEVELOPMENT OF A SINGLE TWIN LAYER IN METAL CRYSTALS

2021 ◽  
pp. 3-9
Author(s):  
Mark Bosin ◽  
Yevgen Gomozov ◽  
Tetyana Drygach
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Phenomenological Model ◽  
Bauschinger Effect ◽  
Scientific Literature ◽  
Mathematical Approach ◽  
Quantitative Theory ◽  
Specific Effects ◽  
Experimental Works ◽  
Loading Modes

By analyzing the experimental data available in the scientific literature, a mathematical model of the development of a single twin layer in metal crystals has been obtained. The model has the form of a differential equation, the order of which is determined by the required accuracy of obtaining the results associated with the solution of this equation. Even in the linear approximation of one of the main parameters of the phenomenological model, the latter gives qualitatively the same dependences of the development of single twins under different loading conditions compared to the experiment. Despite a large number of experimental works devoted to twinning, there is still no rigorous quantitative theory of the development of twinning layers in different media and under different conditions. However, in these works, the mathematical approach was demonstrated only in relation to elastic twins. This work is an introduction to the creation of a quantitative theory of twinning in metal crystals. Comparisons with the experimental results of the proposed phenomenological model were limited in this work to the task of demonstrating the performance of the model in the sense of predicting the most specific effects of the development of twins under various conditions and loading modes. In particular, the model implies the effect of loss and subsequent restoration of hardening by twin boundaries during stress pulsations, the Bauschinger effect upon a change in the sign of the applied voltage, and a number of other effects observed experimentally on a number of different metal crystals.

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

A MATHEMATICAL MODEL OF ANEURYSM OF CIRCLE OF WILLIS

1995 ◽  
Vol 03 (03) ◽  
pp. 653-659 ◽  
Author(s):  
J. J. NIETO ◽  
A. TORRES
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Ordinary Differential Equation ◽  
Blood Flow ◽  
Nonlinear Analysis ◽  
Existence Of Solutions ◽  
Circle Of Willis ◽  
Second Order ◽  
Qualitative Properties

We introduce a new mathematical model of aneurysm of the circle of Willis. It is an ordinary differential equation of second order that regulates the velocity of blood flow inside the aneurysm. By using some recent methods of nonlinear analysis, we prove the existence of solutions with some qualitative properties that give information on the causes of rupture of the aneurysm.

scholarly journals Introducing a Conditional Ghost Correction Into the Vector Method

1984 ◽  
Vol 6 (2) ◽  
pp. 117-123 ◽  
Author(s):  
H. Schaeben
Keyword(s):  
Mathematical Model ◽  
Quadratic Programming ◽  
Optimization Problem ◽  
Linear Equations ◽  
Singular System ◽  
Orientation Distribution ◽  
Mathematical Approach ◽  
System Of Linear Equations ◽  
Vector Method ◽  
The Mathematical Model

The concept of conditional ghost correction is introduced into the vector method of quantitative texture analysis. The mathematical model actually chosen here reduces the texture problem to one of quadratic programming. Thus, a well defined optimization problem has to be solved, the singular system of linear equations governing the correspondence between pole and orientation distribution being reduced to a set of equality constraints of the restated texture problem. This new mathematical approach in terms of the vector method reveals the modeling character of the solution of the texture problem provided by the vector method completely.

Design of Control of DC Motor

2014 ◽  
Vol 611 ◽  
pp. 325-331
Author(s):  
Ľubica Miková ◽  
Michal Kelemen ◽  
Vladislav Maxim ◽  
Jaromír Jezný
Keyword(s):  
Mathematical Model ◽  
Virtual Environment ◽  
Computer Technology ◽  
Current Practice ◽  
Scientific Literature ◽  
Model Simulation ◽  
Graphical Interface ◽  
Dc Motors ◽  
Matlab Program ◽  
Simulation Results

In current practice the use of mathematical models is substantially widespread, reason being the recent increase in development of programs for this purpose, with the option of model simulation in a virtual environment, proportional to the evolving computer technology. The article contains a mathematical model created using Matlab program. The simulation results are compared with scientific literature that addresses DC motors and evaluated. For simplicity, a graphical interface was created.

scholarly journals Detection, not mortality, constrains the evolution of virulence

2021 ◽  
Author(s):  
David A Kennedy
Keyword(s):  
Mathematical Model ◽  
Disease Severity ◽  
Behavioral Change ◽  
Scientific Literature ◽  
Empirical Support ◽  
Infectious Period ◽  
Trade Off ◽  
Evolution Of Virulence ◽  
Host Mortality

Why would a pathogen evolve to kill its hosts when killing a host ends a pathogen's own opportunity for transmission? A vast body of scientific literature has attempted to answer this question using "trade-off theory," which posits that host mortality persists due to its cost being balanced by benefits of other traits that correlate with host mortality. The most commonly invoked trade-off is the mortality-transmission trade-off, where increasingly harmful pathogens are assumed to transmit at higher rates from hosts while the hosts are alive, but the pathogens truncate their infectious period by killing their hosts. Here I show that costs of mortality are too small to plausibly constrain the evolution of disease severity except in systems where survival is rare. I alternatively propose that disease severity can be much more readily constrained by a cost of behavioral change due to the detection of infection, whereby increasingly harmful pathogens have increasing likelihood of detection and behavioral change following detection, thereby limiting opportunities for transmission. Using a mathematical model, I show the conditions under which detection can limit disease severity. Ultimately, this argument may explain why empirical support for trade-off theory has been limited and mixed.

scholarly journals Bifurcation analysis of a mathematical model of atopic dermatitis to determine patient-specific effects of treatments on dynamic phenotypes

2018 ◽  
Vol 448 ◽  
pp. 66-79 ◽  
Author(s):  
Gouhei Tanaka ◽  
Elisa Domínguez-Hüttinger ◽  
Panayiotis Christodoulides ◽  
Kazuyuki Aihara ◽  
Reiko J. Tanaka
Keyword(s):  
Mathematical Model ◽  
Atopic Dermatitis ◽  
Bifurcation Analysis ◽  
Patient Specific ◽  
Specific Effects

Whole-Earth Decompression Dynamics: New Earth Formation Geoscience Paradigm Fundamental Basis of Geology and Geophysics

2021 ◽  
Vol 8 (2) ◽  
pp. 340-365
Author(s):  
J. Marvin Herndon
Keyword(s):  
Magnetic Field ◽  
Phenomenological Model ◽  
Scientific Literature ◽  
Geothermal Gradient ◽  
Government Funding ◽  
Energy Sources ◽  
Submarine Canyons ◽  
Mountain Ranges ◽  
Scientific Principles ◽  
Consensus View

Policymakers and educators depend upon the advice of scientists to warn of natural and anthropogenic dangers to the environment and to Earth’s biota. Decades of mal-administered government-funding have led to the corruption of science, however, and to the formation of unofficial cartels that promulgate a seriously flawed, consensus view of Earth’s origins, structure, and geodynamic behavior. Proponents of this “consensus” view, in contradiction to long-standing scientific principles, suppress or ignore concepts that better explain Earth’s fundamental behavior. Here I present, as published in the peer-reviewed scientific literature over a period of four decades, a fundamentally new, indivisible paradigm that posits Earth’s early formation as a Jupiter-like gas giant, which makes it possible to derive virtually all the geological and geodynamic behavior of our planet, including two previously unanticipated, powerful endogenous energy sources; the origin of mountain ranges characterized by folding; the origin and typography of ocean floors and continents; the origin of fjords and the primary initiation of submarine canyons; the origin of Earth’s magnetic field; the causes of geomagnetic disruptions; the source of the geothermal gradient; the origin of Earth’s petroleum and natural gas deposits; and more. The logical, causally related advances documented here stand as a reference by which to compare and evaluate the phenomenological model-nonsense that has been published for decades by government-funded scientists.

Mathematical Modeling of the λ Switch

2010 ◽  
pp. 573-603
Author(s):  
Dmitriy Laschov ◽  
Michael Margaliot
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Mathematical Model ◽  
Gene Regulation ◽  
Equilibrium Points ◽  
Domain Of Attraction ◽  
Verbal Description ◽  
Quantitative Understanding ◽  
Living Organisms ◽  
Scientific Challenge

Gene regulation plays a central role in the development and functioning of living organisms. Developing a deeper qualitative and quantitative understanding of gene regulation is an important scientific challenge. The Lambda switch is commonly used as a paradigm of gene regulation. Verbal descriptions of the structure and functioning of the Lambda switch have appeared in biological textbooks. We apply fuzzy modeling to transform one such verbal description into a well-defined mathematical model. The resulting model is a piecewise-quadratic, second-order differential equation. It demonstrates functional fidelity with known results while being simple enough to allow a rather detailed analysis. Properties such as the number, location, and domain of attraction of equilibrium points can be studied analytically. Furthermore, the model provides a rigorous explanation for the so-called stability puzzle of the Lambda switch.

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