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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

## An Introduction to Finite Differencing

*T. N. Krishnamurti, H. S. Bedi, and V. M. Hardiker*

### in An Introduction to Global Spectral Modeling

- Published in print:
- 1998
- Published Online:
- November 2020
- ISBN:
- 9780195094732
- eISBN:
- 9780197560761
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195094732.003.0004
- Subject:
- Earth Sciences and Geography, Meteorology and Climatology

This chapter on finite differencing appears oddly placed in the early part of a text on spectral modeling. Finite differences are still traditionally used for vertical differencing and for time ... 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

## 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

## 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

## 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

## Time-Differencing Schemes

*T. N. Krishnamurti, H. S. Bedi, and V. M. Hardiker*

### in An Introduction to Global Spectral Modeling

- Published in print:
- 1998
- Published Online:
- November 2020
- ISBN:
- 9780195094732
- eISBN:
- 9780197560761
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195094732.003.0005
- Subject:
- Earth Sciences and Geography, Meteorology and Climatology

Atmospheric models generally require the solutions of partial differential equations. In spectral models, the governing partial differential equations reduce to a set of coupled ordinary nonlinear ... 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

## Measurement of Scattering Coefficients

*Dale Chimenti, Stanislav Rokhlin, and Peter Nagy*

### in Physical Ultrasonics of Composites

- Published in print:
- 2011
- Published Online:
- November 2020
- ISBN:
- 9780195079609
- eISBN:
- 9780197560389
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195079609.003.0012
- Subject:
- Chemistry, Industrial Chemistry

In the previous chapters, we saw how waves in composites behaved under various circumstances, depending on material anisotropy and wave propagation direction. The most important function that ... More

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