Theory of Microstructure Evolution in Heterogeneous Materials

1993 ◽  
Vol 309 ◽  
Author(s):  
Sokrates T. Pantelides
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Constitutive Relations ◽  
Quantitative Description ◽  
Heterogeneous Materials ◽  
Dislocation Climb ◽  
Atomic Scale ◽  
Induced Stress ◽  
Growth Dislocation ◽  
Stress Induced Diffusion

AbstractThis paper summarizes the main ingredients of a general theory for a quantitative description of dynamical processes in heterogeneous materials under stresses, thermal cycling, or current. The theory is derived analytically from the atomic scale using the principles of quantum mechanics and statistical mechanics, without any empirical postulates. The equations describe the cross-coupled phenomena of stress-induced diffusion, diffusion-induced stress, electromigration, void growth, dislocation climb, and slip. The laws of continuum mechanics are recovered as a subset of the general equations. All constitutive relations can be constructed by a general and systematic procedure.

scholarly journals Experiments on the symmetry of length and time

2021 ◽  
Author(s):  
Li Chunhong
Keyword(s):  
Experimental Data ◽  
Quantum Mechanics ◽  
General Theory ◽  
Piezoelectric Sensor ◽  
Atomic Scale ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Speed Of Light ◽  
Time Coordinate ◽  
Time Position

Abstract The F - t curve obtained from the process of applying and releasing force to the piezoelectric sensor shows that in the atomic scale, the time coordinate is equivalent to the position coordinate. The time-position coordinate relationship calculated by the experimental data is consistent with the geometric unit obtained in the general theory of relativity, thus the experiment verifies the symmetry of length and time,and connection between the microscopic - quantum mechanics and the macroscopic - general theory of relativity, and a new method for calculating the speed of light is obtained.

Dualism QM and GR

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Noncommutative Geometry ◽  
Quantum Tunneling ◽  
Closed Surface ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Surface Integral ◽  
Definition Of

Quantum tunneling of noncommutative geometry gives the definition of time in the form of holography, that is, in the form of a closed surface integral. Ultimately, the holography of time shows the dualism between quantum mechanics and the general theory of relativity.

The Physical World

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Quantum Mechanics ◽  
Particle Physics ◽  
Variational Principles ◽  
Black Body ◽  
Black Body Radiation ◽  
Physical World ◽  
Atomic Scale ◽  
Solid State Physics ◽  
Least Action ◽  
Dimensional Spacetime

The book is an inspirational survey of fundamental physics, emphasizing the use of variational principles. Chapter 1 presents introductory ideas, including the principle of least action, vectors and partial differentiation. Chapter 2 covers Newtonian dynamics and the motion of mutually gravitating bodies. Chapter 3 is about electromagnetic fields as described by Maxwell’s equations. Chapter 4 is about special relativity, which unifies space and time into 4-dimensional spacetime. Chapter 5 introduces the mathematics of curved space, leading to Chapter 6 covering general relativity and its remarkable consequences, such as the existence of black holes. Chapters 7 and 8 present quantum mechanics, essential for understanding atomic-scale phenomena. Chapter 9 uses quantum mechanics to explain the fundamental principles of chemistry and solid state physics. Chapter 10 is about thermodynamics, which is built around the concepts of temperature and entropy. Various applications are discussed, including the analysis of black body radiation that led to the quantum revolution. Chapter 11 surveys the atomic nucleus, its properties and applications. Chapter 12 explores particle physics, the Standard Model and the Higgs mechanism, with a short introduction to quantum field theory. Chapter 13 is about the structure and evolution of stars and brings together material from many of the earlier chapters. Chapter 14 on cosmology describes the structure and evolution of the universe as a whole. Finally, Chapter 15 discusses remaining problems at the frontiers of physics, such as the interpretation of quantum mechanics, and the ultimate nature of particles. Some speculative ideas are explored, such as supersymmetry, solitons and string theory.

HYPER-SPHERICAL HARMONICS AND ANHARMONICS IN m-DIMENSIONAL SPACE

2008 ◽  
Vol 17 (06) ◽  
pp. 1125-1130
Author(s):  
M. R. SHOJAEI ◽  
A. A. RAJABI ◽  
H. HASANABADI
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Spherical Harmonics ◽  
Interaction Potential ◽  
Dimensional Space ◽  
Harmonic Polynomials ◽  
Central Importance ◽  
Computational Tools ◽  
Relative Coordinate

In quantum mechanics the hyper-spherical method is one of the most well-established and successful computational tools. The general theory of harmonic polynomials and hyper-spherical harmonics is of central importance in this paper. The interaction potential V is assumed to depend on the hyper-radius ρ only where ρ is the function of the Jacobi relative coordinate x1, x2,…, xn which are functions of the particles' relative positions.

On the error of approximations in quantum mechanics. I. General theory

1965 ◽  
Vol 257 (1081) ◽  
pp. 309-326 ◽  
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Computer Applications ◽  
Quantum Mechanical ◽  
Quantum Mechanical Calculations ◽  
Density Matrices ◽  
Single Error

General formulas for estimating the errors in quantum-mechanical calculations are given in the formalism of density matrices. Some properties of the traces of matrices are used to simplify the estimating and to indicate a way of obtaining a better approximation. It is shown that the simultaneous correction of all the equations to be fulfilled leads in most cases to a faster convergence than the exact fulfilment of some of the equations and approximating stepwise to some of the others. The corrective formulas contain only direct operations of the matrices occurring and so they are advantageous in computer applications. In the last section a ‘subjective error’ definition is given and by taking into account the weight of the errors of the several equations a faster convergence and a single error quantity is obtained. Some special applications of the method will be published later.

Atomistic Aspects of Fracture Modelling in the Framework of Continuum Mechanics

1998 ◽  
Vol 538 ◽  
Author(s):  
F. Cleri
Keyword(s):  
Continuum Mechanics ◽  
Constitutive Relations ◽  
Point Of View ◽  
Atomic Scale ◽  
Continuum Models ◽  
Cohesive Law ◽  
Macroscopic Models ◽  
Scale Models ◽  
Level Information ◽  
Set Up

AbstractThe validity and predictive capability of continuum models of fracture rests on basic informations whose origin lies at the atomic scale. Examples of such crucial informations are, e.g., the explicit form of the cohesive law in the Barenblatt model and the shear-displacement relation in the Rice-Peierls-Nabarro model. Modem approaches to incorporate atomic-level information into fracture modelling require to increase the size of atomic-scale models up to millions of atoms and more; or to connect directly atomistic and macroscopic, e.g. finite-elements, models; or to pass information from atomistic to continuum models in the form of constitutive relations. A main drawback of the atomistic methods is the complexity of the simulation results, which can be rather difficult to rationalize in the framework of classical, continuum fracture mechanics. We critically discuss the main issues in the atomistic simulation of fracture problems (and dislocations, to some extent); our objective is to indicate how to set up atomistic simulations which represent well-posed problems also from the point of view of continuum mechanics, so as to ease the connection between atomistic information and macroscopic models of fracture.

The “Fractional” Kinetic Equations and General Theory of Dielectric Relaxation

2005 ◽  
Author(s):  
Raoul R. Nigmatullin
Keyword(s):  
General Theory ◽  
Dielectric Relaxation ◽  
Collective Motion ◽  
Kinetic Equations ◽  
Heterogeneous Materials ◽  
Complex Conjugate ◽  
Electric Circuits ◽  
Self Similar ◽  
Fractional Kinetic Equations ◽  
Frequency Temperature

Based on the Mori-Zwanzig formalism it becomes possible to suggest a general decoupling procedure, which reduces a wide set of various micromotions distributed over a self-similar structure to a few collective/reduced motions describing the relaxation/exchange behavior of a complex system in the mesoscale region. The frequency dependence of the reduced collective motion contains real and pair of complex-conjugate power-law exponents in the frequency domain and explains naturally the “universal response” (UR) phenomenon discovered by A. Jonscher in a wide class of heterogeneous materials. This strict mathematical result allows in developing a consistent and general theory of dielectric relaxation that can describe wide set of dielectric spectroscopy (DS) data measured in some frequency/temperature range in many heterogeneous materials. Based on this result it becomes possible also to suggest a new set of two-pole elements, which generalizes the conventional RLC-elements and can constitute the basis of new theory of the linear electric circuits.

scholarly journals Mathematical analogies in physics. Thin-layer wave theory

2014 ◽  
Vol 57 (1) ◽  
Author(s):  
José M. Carcione ◽  
Vivian Grünhut ◽  
Ana Osella
Keyword(s):  
Quantum Mechanics ◽  
Thin Layer ◽  
Quantum Physics ◽  
Constitutive Relations ◽  
Normal Incidence ◽  
Wave Theory ◽  
Transverse Magnetic ◽  
Momentum Conservation ◽  
Tunnel Effect ◽  
Basic Equations

<p>Field theory applies to elastodynamics, electromagnetism, quantum mechanics, gravitation and other similar fields of physics, where the basic equations describing the phenomenon are based on constitutive relations and balance equations. For instance, in elastodynamics, these are the stress-strain relations and the equations of momentum conservation (Euler-Newton law). In these cases, the same mathematical theory can be used, by establishing appropriate mathematical equivalences (or analogies) between material properties and field variables. For instance, the wave equation and the related mathematical developments can be used to describe anelastic and electromagnetic wave propagation, and are extensively used in quantum mechanics. In this work, we obtain the mathematical analogy for the reflection/refraction (transmission) problem of a thin layer embedded between dissimilar media, considering the presence of anisotropy and attenuation/viscosity in the viscoelastic case, conductivity in the electromagnetic case and a potential barrier in quantum physics (the tunnel effect). The analogy is mainly illustrated with geophysical examples of propagation of S (shear), P (compressional), TM (transverse-magnetic) and TE (transverse-electric) waves. The tunnel effect is obtained as a special case of viscoelastic waves at normal incidence.</p>

On the general theory of damping in quantum mechanics

1951 ◽  
Vol 8 (11) ◽  
pp. 817-842 ◽  
Author(s):  
M. Schönberg
Keyword(s):  
Quantum Mechanics ◽  
General Theory
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