## Abelian Gauge Theories

in** Quantum Field Theory and Critical Phenomena**

June 2002; p ublished 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...

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## Absence of localisation in ocean wave interactions with a rough seabed in intermediate water depth

in** The Quarterly Journal of Mechanics and Applied Mathematics**

February 2015; p ublished online December 2014 .

Journal Article. Subjects: Applied Mathematics; Mathematical and Statistical Physics. 0 words.

The possibility of a rough seabed causing localisation of ocean waves in intermediate water depth is considered. A numerical and analytical study of the localisation phenomenon is conducted...

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** » ** abstract

## Abstract Hilbert Space

in** Mathematical Foundations of Quantum Mechanics**

February 2018; p ublished online September 2018 .

Chapter. Subjects: Mathematical and Statistical Physics. 55785 words.

This chapter defines Hilbert space, which furnishes the mathematical basis for the treatment of quantum mechanics. This is done within the context of an equation introduced in the previous...

## Acceleration and Force

in** The Elements of Relativity**

June 2018; p ublished online August 2018 .

Chapter. Subjects: Astronomy and Astrophysics; Mathematical and Statistical Physics. 4561 words.

This chapter develops crucial distinctions between constant‐velocity (also called inertial) frames of reference and accelerating ones. Inertial frames respect Newton’s first law—objects...

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** » ** abstract

## Acceleration Kernel

in** Nonlocal Gravity**

May 2017; p ublished online July 2017 .

Chapter. Subjects: Astronomy and Astrophysics; Mathematical and Statistical Physics. 14108 words.

The phenomenon of spin-rotation coupling provides the key to the determination of the kernel. Imagine an observer rotating in the positive sense about the direction of propagation of an...

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** » ** abstract

## Acceleration-Induced Nonlocality

in** Nonlocal Gravity**

May 2017; p ublished online July 2017 .

Chapter. Subjects: Astronomy and Astrophysics; Mathematical and Statistical Physics. 10600 words.

The locality postulate of the standard relativity theory is exact when dealing with phenomena involving classical point particles and rays of radiation, but breaks down for electromagnetic...

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** » ** abstract

## Accounting for all parts (subgraphs)

in** The Structure of Complex Networks**

October 2011; p ublished online December 2013 .

Chapter. Subjects: Mathematical and Statistical Physics. 7558 words.

This chapter examines the concept of invariants aimed at characterising the global subgraph structure of a network. The discussions cover functions of adjacency matrix, such as the Estrada...

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## 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; p ublished 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...

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** » ** abstract

## Acids, bases and buffer solutions

in** Modern Thermodynamics for Chemists and Biochemists**

June 2018; p ublished online August 2018 .

Chapter. Subjects: Mathematical and Statistical Physics. 18779 words.

Many reactions in solution involve acids and bases, and so this chapter examines these important reactions in detail. Topics covered include the ionisation of water, pH, pOH, acids and...

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** » ** abstract

## Acoustic diffraction by a semi-infinite plane with different face impedances

in** The Quarterly Journal of Mechanics and Applied Mathematics**

September 1999; p ublished 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...

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** » ** abstract

## Acoustic quasi-modes in slowly varying cylindrical tubes

in** The Quarterly Journal of Mechanics and Applied Mathematics**

August 2005; p ublished 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...

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## Acoustic Radiation Properties of an Elastic Plate with an Infinite Baffle and Cavity

in** The Quarterly Journal of Mechanics and Applied Mathematics**

November 2002; p ublished 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...

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** » ** abstract

## Acoustic scattering by a pair of poroelastic spheres

in** The Quarterly Journal of Mechanics and Applied Mathematics**

February 2004; p ublished 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...

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** » ** abstract

## Acoustic scattering from semi-infinite, rigid plates: a new technique

in** The Quarterly Journal of Mechanics and Applied Mathematics**

May 1999; p ublished 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...

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** » ** abstract

## Acoustic wave propagation through a triply periodic lattice of arbitrary shape scatterers

in** The Quarterly Journal of Mechanics and Applied Mathematics**

February 2015; p ublished online September 2014 .

Journal Article. Subjects: Applied Mathematics; Mathematical and Statistical Physics. 0 words.

Acoustic wave propagation through a triply periodic array of arbitrary shape scatterers is considered by the method of matched asymptotic expansions. It is assumed that the scatterer size...

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** » ** abstract

## Activated switching in nonlinear micromechanical resonators

in** Fluctuating Nonlinear Oscillators**

July 2012; p ublished online September 2012 .

Chapter. Subjects: Mathematical and Statistical Physics. 16508 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...

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** » ** abstract

## Active cloaking of inclusions for flexural waves in thin elastic plates

in** The Quarterly Journal of Mechanics and Applied Mathematics**

August 2015; p ublished online June 2015 .

Journal Article. Subjects: Applied Mathematics; Mathematical and Statistical Physics. 6500 words.

We present a new method to create an active cloak for a single clamped inclusion in a Kirchhoff plate in the presence of flexural waves. In order to cloak this inclusion, we place control...

## Active cloaking of resonant coated inclusions for waves in membranes and Kirchhoff plates

in** The Quarterly Journal of Mechanics and Applied Mathematics**

May 2016; p ublished online April 2016 .

Journal Article. Subjects: Applied Mathematics; Mathematical and Statistical Physics. 11280 words.

The dynamic response of a coated inclusion is considered in the context of active cloaking. The active cloak is achieved for a coated inclusion in the presence of flexural and membrane...

## Adaptive finite element methods, by W. Dörfler

in** Numerical Methods for Nonlinear Elliptic Differential Equations**

October 2010; p ublished online January 2011 .

Chapter. Subjects: Mathematical and Statistical Physics. 8839 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...

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## Additional fermionic fields onto parallelizable 7-spheres

in** Progress of Theoretical and Experimental Physics**

P ublished online June 2018 .

Journal Article. Subjects: Mathematical and Statistical Physics; Particles and Fields. 5428 words.

**Abstract**

The geometric Fierz identities are employed to generate new emergent fermionic fields on the parallelizable (curvatureless, torsionfull) 7-sphere...

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