Abelian Gauge Theories
in Quantum Field Theory and Critical Phenomena
June 2002; published online January 2010.
Chapter. Subjects: mathematical and statistical physics. 12905 words.
This chapter focuses on abelian gauge theory, whose physical realization is Quantum Electrodynamics (QED). The chapter is organized as follows. It begins with elementary considerations about the...
Accuracy of the multipole expansion applied to a sphere in a creeping flow parallel to a wall
in The Quarterly Journal of Mechanics and Applied Mathematics
November 2006; published online November 2006.
Journal Article. Subjects: applied mathematics; mathematical and statistical physics. 6446 words.
An example system is studied to discuss precision of the multipole expansion, applied to determine forces exerted on particles by a viscous low-Reynolds-number fluid flow. A single sphere in an...
Acoustic diffraction by a semi-infinite plane with different face impedances
in The Quarterly Journal of Mechanics and Applied Mathematics
September 1999; published online September 1999.
Journal Article. Subjects: applied mathematics; mathematical and statistical physics. 0 words.
The problem of plane wave scattering by a half-plane with different impedance boundary conditions on each face is examined using the Wiener-Hopf-Hilbert technique. For the special case where...
Acoustic quasi-modes in slowly varying cylindrical tubes
in The Quarterly Journal of Mechanics and Applied Mathematics
August 2005; published online August 2005.
Journal Article. Subjects: applied mathematics; mathematical and statistical physics. 0 words.
Guided wave propagation in slowly varying elastic bars is of increasing importance in the non-destructive evaluation of structures. This paper develops an asymptotic theory for the simpler...
Acoustic Radiation Properties of an Elastic Plate with an Infinite Baffle and Cavity
in The Quarterly Journal of Mechanics and Applied Mathematics
November 2002; published online November 2002.
Journal Article. Subjects: applied mathematics; mathematical and statistical physics. 0 words.
A cavity (0 < x < a, 0 < y < b, −d < z < 0) set in an otherwise rigid plane surface (z = 0) is covered by a rectangular elastic plate (of dimensions a × b) that is simply supported at its...
Acoustic scattering by a pair of poroelastic spheres
in The Quarterly Journal of Mechanics and Applied Mathematics
February 2004; published online February 2004.
Journal Article. Subjects: applied mathematics; mathematical and statistical physics. 0 words.
An exact analysis for sound scattering by two interacting fluid‐saturated porous‐elastic spheres that are insonified by plane waves at arbitrary angles of incidence is outlined. The novel...
Acoustic scattering from semi-infinite, rigid plates: a new technique
in The Quarterly Journal of Mechanics and Applied Mathematics
May 1999; published online May 1999.
Journal Article. Subjects: applied mathematics; mathematical and statistical physics. 0 words.
A plane sound wave is obliquely incident on a semi-infinite, rigid plate (which may or may not have finite thickness). This problem has been studied previously, but it is thought that the...
Activated switching in nonlinear micromechanical resonators
in Fluctuating Nonlinear Oscillators
July 2012; published online September 2012.
Chapter. Subjects: mathematical and statistical physics. 16526 words.
This chapter reviews a series of experiments on Gaussian noise-induced switching in nonlinear micromechanical torsional resonators that are periodically driven into multistability, a system that is...
Adaptive finite element methods, by W. Dörfler
in Numerical Methods for Nonlinear Elliptic Differential Equations
October 2010; published online January 2011.
Chapter. Subjects: mathematical and statistical physics. 18823 words.
Chapter 6 describes the idea of a posteriori error estimation and adaptive mesh refinement. The main points are the description of the adaptive finite element algorithm, its convergence and a sketch...
Advanced Statistical Mechanics
December 2009; published online February 2010.
Book. Subjects: mathematical and statistical physics. 640 pages.
This book begins where elementary books and courses leave off and covers the advances made in statistical mechanics in the past fifty years. The book is divided into three parts. The first part is on...