*Daniel Thomas Gillespie and Effrosyni Seitaridou*

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199664504
- eISBN:
- 9780191748516
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199664504.001.0001
- Subject:
- Physics, Soft Matter / Biological Physics

Brownian diffusion is the motion of one or more solute molecules in a sea of very many, much smaller solvent molecules. Its importance today owes mainly to cellular chemistry, since Brownian ...
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Brownian diffusion is the motion of one or more solute molecules in a sea of very many, much smaller solvent molecules. Its importance today owes mainly to cellular chemistry, since Brownian diffusion is one of the ways in which key reactant molecules move about inside a living cell. This book focuses on the four simplest models of Brownian diffusion: the classical Fickian model, the Einstein model, the discrete-stochastic (cell-jumping) model, and the Langevin model. The book carefully develops the theories underlying these models, assess their relative advantages, and clarify their conditions of applicability. Special attention is given to the stochastic simulation of diffusion, and to showing how simulation can complement theory and experiment. Two self-contained tutorial chapters, one on the mathematics of random variables and the other on the mathematics of continuous Markov processes (stochastic differential equations), make the book accessible to researchers from a broad spectrum of technical backgrounds.Less

Brownian diffusion is the motion of one or more solute molecules in a sea of very many, much smaller solvent molecules. Its importance today owes mainly to cellular chemistry, since Brownian diffusion is one of the ways in which key reactant molecules move about inside a living cell. This book focuses on the four simplest models of Brownian diffusion: the classical Fickian model, the Einstein model, the discrete-stochastic (cell-jumping) model, and the Langevin model. The book carefully develops the theories underlying these models, assess their relative advantages, and clarify their conditions of applicability. Special attention is given to the stochastic simulation of diffusion, and to showing how simulation can complement theory and experiment. Two self-contained tutorial chapters, one on the mathematics of random variables and the other on the mathematics of continuous Markov processes (stochastic differential equations), make the book accessible to researchers from a broad spectrum of technical backgrounds.

*Stephen J. Blundell and Katherine M. Blundell*

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199562091
- eISBN:
- 9780191718236
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562091.003.0024
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

In a solid, energy can be stored in vibrations of the atoms which are arranged in a lattice. In the same way that photons are quantized electromagnetic waves that describe the elementary excitations ...
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In a solid, energy can be stored in vibrations of the atoms which are arranged in a lattice. In the same way that photons are quantized electromagnetic waves that describe the elementary excitations of the electromagnetic field, phonons are the quantized lattice waves that describe the elementary excitations of vibrations of the lattice. This chapter discusses the analogous behaviour of lattice vibrations, quantized as phonons. It introduces the Einstein model and Debye model of the thermal properties of solids.Less

In a solid, energy can be stored in vibrations of the atoms which are arranged in a lattice. In the same way that photons are quantized electromagnetic waves that describe the elementary excitations of the electromagnetic field, phonons are the quantized lattice waves that describe the elementary excitations of vibrations of the lattice. This chapter discusses the analogous behaviour of lattice vibrations, quantized as phonons. It introduces the Einstein model and Debye model of the thermal properties of solids.

*Nathalie Deruelle and Jean-Philippe Uzan*

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198786399
- eISBN:
- 9780191828669
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198786399.003.0058
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the laws governing the evolution of the scale factor as well as Hubble’s law, which is historically the first observational signature of cosmic expansion. Hubble’s law relates ...
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This chapter discusses the laws governing the evolution of the scale factor as well as Hubble’s law, which is historically the first observational signature of cosmic expansion. Hubble’s law relates two measurable quantities, the redshift and the luminosity distance of a galaxy. The chapter also introduces the Weyl postulate (1923), which stipulates that the ‘cosmological fluid’ consisting of galaxies, quasars, and so on, visible or invisible, follows such geodesics. It then presents the Friedmann–Lemaître equations. Finally, the chapter discusses the first models of the universe, from 1917–60: the static Einstein model and the de Sitter and steady state models.Less

This chapter discusses the laws governing the evolution of the scale factor as well as Hubble’s law, which is historically the first observational signature of cosmic expansion. Hubble’s law relates two measurable quantities, the redshift and the luminosity distance of a galaxy. The chapter also introduces the Weyl postulate (1923), which stipulates that the ‘cosmological fluid’ consisting of galaxies, quasars, and so on, visible or invisible, follows such geodesics. It then presents the Friedmann–Lemaître equations. Finally, the chapter discusses the first models of the universe, from 1917–60: the static Einstein model and the de Sitter and steady state models.

*Robert H. Swendsen*

- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199646944
- eISBN:
- 9780191775123
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199646944.003.0025
- Subject:
- Physics, Condensed Matter Physics / Materials

The harmonic solid is a model of vibrations in a crystal. It goes beyond the simpler Einstein model, which was discussed in Chapter 23. The low-temperature behaviour is shown to be extremely similar ...
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The harmonic solid is a model of vibrations in a crystal. It goes beyond the simpler Einstein model, which was discussed in Chapter 23. The low-temperature behaviour is shown to be extremely similar to that of black-body radiation, which was discussed in Chapter 24. The Debye approximation is introduced, and its advantages and disadvantages are discussed.Less

The harmonic solid is a model of vibrations in a crystal. It goes beyond the simpler Einstein model, which was discussed in Chapter 23. The low-temperature behaviour is shown to be extremely similar to that of black-body radiation, which was discussed in Chapter 24. The Debye approximation is introduced, and its advantages and disadvantages are discussed.