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Mathematical Foundations of Classical Statistical Mechanics
  • Language: en
  • Pages: 352

Mathematical Foundations of Classical Statistical Mechanics

  • Type: Book
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  • Published: 2002-04-11
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  • Publisher: CRC Press

This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov equations for the sequences of correlation functions in the thermodynamic limit. This is the first detailed investigation of the thermodynamic limit for non-equilibrium systems and of the states of infinite systems in the cases of both canonical and grand canonical ensembles, for which the thermodynamic equivalence is proved. A comprehensive survey...

Mathematical Foundations of Quantum Statistical Mechanics
  • Language: en
  • Pages: 460

Mathematical Foundations of Quantum Statistical Mechanics

This monograph is devoted to quantum statistical mechanics. It can be regarded as a continuation of the book "Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems" (Gordon & Breach SP, 1989) written together with my colleagues V. I. Gerasimenko and P. V. Malyshev. Taken together, these books give a complete pre sentation of the statistical mechanics of continuous systems, both quantum and classical, from the common point of view. Both books have similar contents. They deal with the investigation of states of in finite systems, which are described by infinite sequences of statistical operators (reduced density matrices) or Green's functions in the quantum case and b...

Many-Particle Dynamics and Kinetic Equations
  • Language: en
  • Pages: 252

Many-Particle Dynamics and Kinetic Equations

As our title suggests, there are two aspects in the subject of this book. The first is the mathematical investigation of the dynamics of infinite systems of in teracting particles and the description of the time evolution of their states. The second is the rigorous derivation of kinetic equations starting from the results of the aforementioned investigation. As is well known, statistical mechanics started in the last century with some papers written by Maxwell and Boltzmann. Although some of their statements seemed statistically obvious, we must prove that they do not contradict what me chanics predicts. In some cases, in particular for equilibrium states, it turns out that mechanics easily ...

Uncertainty Quantification for Hyperbolic and Kinetic Equations
  • Language: en
  • Pages: 277

Uncertainty Quantification for Hyperbolic and Kinetic Equations

  • Type: Book
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  • Published: 2018-03-20
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  • Publisher: Springer

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.

Stochastic Dynamics and Boltzmann Hierarchy
  • Language: en
  • Pages: 310

Stochastic Dynamics and Boltzmann Hierarchy

The monograph is devoted to one of the most important trends in contemporary mathematical physics, the investigation of evolution equations of many-particle systems of statistical mechanics. The book systematizes rigorous results obtained in this field in recent years, and it presents contemporary methods for the investigation of evolution equations of infinite-particle systems. The book is intended for experts in statistical physics, mathematical physics, and probability theory and for students of universities specialized in mathematics and physics.

Mathematical Modelling, Optimization, Analytic and Numerical Solutions
  • Language: en
  • Pages: 431

Mathematical Modelling, Optimization, Analytic and Numerical Solutions

This book discusses a variety of topics related to industrial and applied mathematics, focusing on wavelet theory, sampling theorems, inverse problems and their applications, partial differential equations as a model of real-world problems, computational linguistics, mathematical models and methods for meteorology, earth systems, environmental and medical science, and the oil industry. It features papers presented at the International Conference in Conjunction with 14th Biennial Conference of ISIAM, held at Guru Nanak Dev University, Amritsar, India, on 2–4 February 2018. The conference has emerged as an influential forum, bringing together prominent academic scientists, experts from industry, and researchers. The topics discussed include Schrodinger operators, quantum kinetic equations and their application, extensions of fractional integral transforms, electrical impedance tomography, diffuse optical tomography, Galerkin method by using wavelets, a Cauchy problem associated with Korteweg–de Vries equation, and entropy solution for scalar conservation laws. This book motivates and inspires young researchers in the fields of industrial and applied mathematics.

Operator Algebras and Quantum Statistical Mechanics
  • Language: en
  • Pages: 525

Operator Algebras and Quantum Statistical Mechanics

For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Operator Algebras and Quantum Statistical Mechanics II
  • Language: en
  • Pages: 508

Operator Algebras and Quantum Statistical Mechanics II

For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Love Lords and Lady-Birds
  • Language: en
  • Pages: 138

Love Lords and Lady-Birds

Running away from the school that she hates, headstrong and rebellious, beautiful young Petrina Lyndon clambers over a wall into a country road, flinging her bag over before her and narrowly missing a dashingly handsome young Earl, to whom she complains about the ‘horrible, beastly’ Guardian who placed her at the school and how he never listens to her. She is even more shocked when the Earl reveals that he himself is actually her Guardian, the Earl of Staverton. And although he is not the elderly ‘stuffed shirt’ she expected, he is cold and unfriendly and unimpressed by her stated desire to go to London and become one of the ‘Lady-Birds’ that she has heard so much about. She tells the Earl that she wants to enjoy herself and not get married to some boring and stuffy aristocrat. The Earl is horrified at this unseemly and ignorant revelation and tells her so in no uncertain terms. Determined to dissuade her from a path that would lead her into depravity and danger the Earl insists that she allows him to launch her into Society as a debutante in an effort to marry her off. But Petrina has very different ideas. And she resolves to somehow steal his Lordship’s heart!

Be Proud of Your Scars
  • Language: en
  • Pages: 352

Be Proud of Your Scars

Do you realise how beautiful your life truly is when you focus on your blessings and strengths with a positive mindset in facing the present pandemic? “ Be Proud of Your Scars “ is the perfect book to have and share during the time of bonding at home. This book is written as a legacy to take the younger generation to the next level to be worthy citizens:- - view the present situation in a more positive way,and, - make a difference in someone’s life. This book is not written in chronological order. The unique writing style gives readers the choice and freedom to begin reading from any page. It’s like someone choosing the first piece from a jigsaw puzzle to begin completing it. Written by a grounded optimist octogenarian with an infectious and selfless attitude towards other people ,her writing reflects her personality. Reading her book may inspire readers to write their story too. If you are inspired to write , then this is the book to have !