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The simplest cases: Dirichlet and Neumann boundary conditions

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0001
Subject:
Mathematics, Applied Mathematics

After a short derivation of the Helmholtz equation in acoustics this chapter formulates the direct scattering problem and presents results on uniqueness and existence without proofs (but gives ... More


Time-harmonic fields

Mauro Fabrizio and Morro Angelo

in Electromagnetism of Continuous Media: Mathematical Modelling and Applications

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198527008
eISBN:
9780191713316
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527008.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter reviews balance laws and relevant solutions to Maxwell’s equations in connection with the time-harmonic dependence. The wave equation becomes the Helmholtz equation and, for it, Green’s ... More


The factorization method for other types of inverse obstacle scattering problems

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0002
Subject:
Mathematics, Applied Mathematics

This chapter studies some examples of inverse scattering problems in which the data operator fails to be normal. The impedance boundary condition, the reconstruction from limited-angle data, and the ... More


The MUSIC algorithm and scattering by an inhomogeneous medium

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter examines the case of a penetrable scatterer with an index of refraction that can be space-dependent and is assumed to be different from the constant background index. The inverse ... More


The mixed boundary value problem

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0003
Subject:
Mathematics, Applied Mathematics

For the mixed boundary value problem, the scattering domain D consists of several components with different types of boundary conditions. The chapter begins by reviewing results on uniqueness and ... More


Vorticity, Vortex Dynamics and Rotating Flows

Etienne Guyon, Jean-Pierre Hulin, Luc Petit, and Catalin.D. Mitescu

in Physical Hydrodynamics, 2nd Edn

Published in print:
2015
Published Online:
March 2015
ISBN:
9780198702443
eISBN:
9780191772153
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198702443.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Vorticity characterizes the local rotation within a fluid. It can be continuously distributed or nonzero only on singular lines: the study of such “vortex filaments” suggests an analogy with ... More


Electromagnetic Scattering: The Mie Solution

John A. Adam

in Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691148373
eISBN:
9781400885404
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691148373.003.0019
Subject:
Mathematics, Applied Mathematics

This chapter focuses on the mathematics underlying the scattering of electromagnetic waves. An electromagnetic wave is comprised of an electric field and a magnetic field, both of which are functions ... More


The 2nd Law, entropy, and the chemists

Robert T. Hanlon

in Block by Block: The Historical and Theoretical Foundations of Thermodynamics

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198851547
eISBN:
9780191886133
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198851547.003.0039
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The Thomsen–Berthelot principle together with the thermal theory of affinity theorized that the change in enthalpy of a reaction (dHrxn) is the sole determiner of reaction spontaneity. Exothermic ... More


Diffraction and Gaussian Beams

B. D. Guenther

in Modern Optics

Published in print:
2015
Published Online:
January 2016
ISBN:
9780198738770
eISBN:
9780191801983
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198738770.003.0009
Subject:
Physics, Atomic, Laser, and Optical Physics

A descriptive scalar theory, based on Huygens’ principle is used to derive an integral called the Huygens–Fresnel integral. Two more rigorous mathematical treatments of scalar diffraction theory: ... More


Wave Mechanics & Elements of Mathematical Physics

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents an in-depth look at classical wave mechanics and mathematical physics, containing key examples directly relevant to molecular physics. The separation of variables is used to ... More


Euler’s Equations

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0002
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Euler derived the fundamental equations of an ideal fluid, that is, in the absence of friction (viscosity). They describe the conservation of momentum. We can derive from it the equation for the ... More


Chemical equilibrium and chemical kinetics

Dennis Sherwood and Paul Dalby

in Modern Thermodynamics for Chemists and Biochemists

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198782957
eISBN:
9780191826177
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198782957.003.0014
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Building on the previous chapter, this chapter examines gas phase chemical equilibrium, and the equilibrium constant. This chapter takes a rigorous, yet very clear, ‘first principles’ approach, ... More


Scalar and Vector Fields

B. K. Ridley

in Hybrid Phonons in Nanostructures

Published in print:
2017
Published Online:
April 2017
ISBN:
9780198788362
eISBN:
9780191830280
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198788362.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

Those quantum structures describable in terms of Cartesian coordinates (e.g. the quantum well) can be treated with the minimum of formality. Turning to quantum structures describable in terms of ... More


Wave Theory

B. D. Guenther

in Modern Optics

Published in print:
2015
Published Online:
January 2016
ISBN:
9780198738770
eISBN:
9780191801983
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198738770.003.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

A traveling wave on a string is used to find the functional form of a one-dimensional wave. Following a discussion of the energy associated with the traveling wave, the one-dimensional model ... More


Waves

B. D. Guenther

in Modern Optics Simplified

Published in print:
2019
Published Online:
January 2020
ISBN:
9780198842859
eISBN:
9780191878770
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198842859.003.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

A description of the solution of the wace equation is described as a wave that propagates without change. The set of parameters needed to describe a wave are: period, frequency, wave number, ... More


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