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The Self-Avoiding Walk
The self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple definition—a path on a lattice that does not visit the same site more than once—it is difficult to analyze mathematically. The Self-Avoiding Walk provides the first unified account of the known rigorous results for the self-avoiding walk, with particular emphasis on its critical behavior. Its goals are to give an account of the current mathematical understanding of the model, to indicate some of the applications of the concept in physics and in chemistry, and to give an introduction to some of the nonrigorous methods used in those fields. Top...
Mathematical Constants
Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
In Celebration of K.C. Hines
This book presents a comprehensive review of a diverse range of subjects in physics written by physicists who have all been taught by or are associated with K C Hines. Ken Hines was a great mentor with far-reaching influence on his students who later went on to make outstanding contributions to physics in their careers. The papers provide significant insights into statistical physics, plasma physics from fluorescent lighting to quantum pair plasmas, cosmic ray physics, nuclear reactions, and many other fields. Sample Chapter(s). Chapter 1: Concerning Ken Hines... (358 KB). Contents: Resonant X-Ray Scattering and X-Ray Absorption: Closing the Circle? (Z Barnea et al.); The Screened Field of a Test Particle (R L Dewar); Aspects of Plasma Physics (R J Hosking); The Boltzmann Equation in Fluorescent Lamp Theory (G Lister); Pair Modes in Relativistic Quantum Plasmas (D B Melrose & J McOrist); Neutrons from the Galactic Centre (R R Volkas); Quaternions and Octonions in Nature (G C Joshi); Accretion onto the Supermassive Black Hole at the Centre of Our Galaxy (F Melia); and other papers. Readership: Academics and graduate students interested in physics.
Differential Geometry and Physics
This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory.
Algorithmic Probability and Combinatorics
This volume contains the proceedings of the AMS Special Sessions on Algorithmic Probability and Combinatories held at DePaul University on October 5-6, 2007 and at the University of British Columbia on October 4-5, 2008. This volume collects cutting-edge research and expository on algorithmic probability and combinatories. It includes contributions by well-established experts and younger researchers who use generating functions, algebraic and probabilistic methods as well as asymptotic analysis on a daily basis. Walks in the quarter-plane and random walks (quantum, rotor and self-avoiding), permutation tableaux, and random permutations are considered. In addition, articles in the volume pres...
Polygons, Polyominoes and Polycubes
The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn’t been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many oth...
Confronting The Infinite - Proceedings Of A Conference In Celebration Of The Years Of H S Green And C A Hurst
In 1992, students of Bert Green and Angas Hurst conceived the idea of a meeting to commemorate their contributions to Mathematical Physics and to celebrate their passing the milestone of three score years and ten.In designing the scientific program there were two objectives. The first was to cover the full breadth of research in Mathematical Physics at Adelaide University since the founding of the Department of Mathematical Physics with the appointment of Professor Green in 1952. The second was to seek original contributions in areas of current interest and rapid development. The underlying theme was the interaction of mathematics and physics in the key areas of relativity, quantum field the...
The Seventh European Conference on Combinatorics, Graph Theory and Applications
In the tradition of EuroComb'01 (Barcelona), Eurocomb'03 (Prague), EuroComb'05 (Berlin), Eurocomb'07 (Seville), Eurocomb'09 (Bordeaux), and Eurocomb'11 (Budapest), this volume covers recent advances in combinatorics and graph theory including applications in other areas of mathematics, computer science and engineering. Topics include, but are not limited to: Algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, ordered sets, random methods, topological combinatorics.
Statistics of Linear Polymers in Disordered Media
With the mapping of the partition function graphs of the n-vector magnetic model in the n to 0 limit as the self-avoiding walks, the conformational statistics of linear polymers was clearly understood in early seventies. Various models of disordered solids, percolation model in particular, were also established by late seventies. Subsequently, investigations on the statistics of linear polymers or of self-avoiding walks in, say, porous medium or disordered lattices were started in early eighties. Inspite of the brilliant ideas forwarded and extensive studies made for the next two decades, the problem is not yet completely solved in its generality. This intriguing and important problem has re...
