Nicolas Chopin and Pierre Jacob
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199694587
- eISBN:
- 9780191731921
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199694587.003.0003
- Subject:
- Mathematics, Probability / Statistics
We introduce a new class of Sequential Monte Carlo (SMC) methods, which we call free energy SMC. This class is inspired by free energy methods, which originate from physics, and where one samples ...
More
We introduce a new class of Sequential Monte Carlo (SMC) methods, which we call free energy SMC. This class is inspired by free energy methods, which originate from physics, and where one samples from a biased distribution such that a given function ξ(θ) of the state θ is forced to be uniformly distributed over a given interval. From an initial sequence of distributions (π t ) of interest, and a particular choice of ξ(θ), a free energy SMC sampler computes sequentially a sequence of biased distributions (π̃ t ) with the following properties: (a) the marginal distribution of ξ(θ) with respect to π̃ t is approximatively uniform over a specified interval, and (b) π̃ t and π t have the same conditional distribution with respect to ξ. We apply our methodology to mixture posterior distributions, which are highly multimodal. In the mixture context, forcing certain hyper‐parameters to higher values greatly facilitates mode swapping, and makes it possible to recover a symmetric output. We illustrate our approach with univariate and bivariate Gaussian mixtures and two real‐world datasets.Less
We introduce a new class of Sequential Monte Carlo (SMC) methods, which we call free energy SMC. This class is inspired by free energy methods, which originate from physics, and where one samples from a biased distribution such that a given function ξ(θ) of the state θ is forced to be uniformly distributed over a given interval. From an initial sequence of distributions (π t ) of interest, and a particular choice of ξ(θ), a free energy SMC sampler computes sequentially a sequence of biased distributions (π̃ t ) with the following properties: (a) the marginal distribution of ξ(θ) with respect to π̃ t is approximatively uniform over a specified interval, and (b) π̃ t and π t have the same conditional distribution with respect to ξ. We apply our methodology to mixture posterior distributions, which are highly multimodal. In the mixture context, forcing certain hyper‐parameters to higher values greatly facilitates mode swapping, and makes it possible to recover a symmetric output. We illustrate our approach with univariate and bivariate Gaussian mixtures and two real‐world datasets.
Helmut Hofmann
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0005
- Subject:
- Physics, Nuclear and Plasma Physics
In finite nuclei, the shell effects of the independent particle model are manifest for states in the neighborhood of the Fermi level. Guided by the Strutinsky energy theorem, this fact is exploited ...
More
In finite nuclei, the shell effects of the independent particle model are manifest for states in the neighborhood of the Fermi level. Guided by the Strutinsky energy theorem, this fact is exploited in the Strutinsky method by renormalizing the macroscopic liquid drop energy through a shell correction. This chapter presents details of this method in its various facets, discusses consequences for the deformation energy, and provides numerical examples. The relation of the fluctuating part of the level density to periodic orbit theory (POT) is explained. An extension to finite temperature is presented. For the model of a strictly harmonic variation of the level density with energy, useful analytic formulas for the temperature dependence of thermal quantities of interest are derived, such as free energy or entropy; comparisons with the general case are given, both analytically in the spirit of POT and numerically.Less
In finite nuclei, the shell effects of the independent particle model are manifest for states in the neighborhood of the Fermi level. Guided by the Strutinsky energy theorem, this fact is exploited in the Strutinsky method by renormalizing the macroscopic liquid drop energy through a shell correction. This chapter presents details of this method in its various facets, discusses consequences for the deformation energy, and provides numerical examples. The relation of the fluctuating part of the level density to periodic orbit theory (POT) is explained. An extension to finite temperature is presented. For the model of a strictly harmonic variation of the level density with energy, useful analytic formulas for the temperature dependence of thermal quantities of interest are derived, such as free energy or entropy; comparisons with the general case are given, both analytically in the spirit of POT and numerically.
David M. Wilkinson
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568469
- eISBN:
- 9780191717611
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568469.003.0002
- Subject:
- Biology, Ecology
The second law of thermodynamics is central to understanding ecology, although it is ignored by most ecology text books. It follows from the second law that all organisms must draw free energy from ...
More
The second law of thermodynamics is central to understanding ecology, although it is ignored by most ecology text books. It follows from the second law that all organisms must draw free energy from their environment and return waste products back to their environment. Microorganisms often play a central role in decomposition of these waste products, but in spite of their importance are ignored by most food web studies. The possible relevance of developing ideas on maximum entropy production (MEP) to global ecology is also discussed.Less
The second law of thermodynamics is central to understanding ecology, although it is ignored by most ecology text books. It follows from the second law that all organisms must draw free energy from their environment and return waste products back to their environment. Microorganisms often play a central role in decomposition of these waste products, but in spite of their importance are ignored by most food web studies. The possible relevance of developing ideas on maximum entropy production (MEP) to global ecology is also discussed.
M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199238743
- eISBN:
- 9780191716461
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199238743.003.0012
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics
Starting with this chapter, the book goes on to deal with the Casimir effect for real bodies made of various materials rather than idealized boundaries. It presents Lifshitz theory, which provides a ...
More
Starting with this chapter, the book goes on to deal with the Casimir effect for real bodies made of various materials rather than idealized boundaries. It presents Lifshitz theory, which provides a unified description of both the van der Waals and the Casimir interaction between planar dielectrics. The chapter contains various formulations of the Lifshitz theory as applied to planar, stratified dielectric media at both zero and nonzero temperatures. As an illustration, computational results for various dielectric materials are given. The consistency of the theory with the requirements of thermodynamics and its application region are discussed. The Lifshitz formula for anisotropic plates is presented as well as Lifshitz-type formulas for radiative heat transfer. Problems arising for polar dielectrics are considered.Less
Starting with this chapter, the book goes on to deal with the Casimir effect for real bodies made of various materials rather than idealized boundaries. It presents Lifshitz theory, which provides a unified description of both the van der Waals and the Casimir interaction between planar dielectrics. The chapter contains various formulations of the Lifshitz theory as applied to planar, stratified dielectric media at both zero and nonzero temperatures. As an illustration, computational results for various dielectric materials are given. The consistency of the theory with the requirements of thermodynamics and its application region are discussed. The Lifshitz formula for anisotropic plates is presented as well as Lifshitz-type formulas for radiative heat transfer. Problems arising for polar dielectrics are considered.
R. T. Deam and S. F. Edwards
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528531
- eISBN:
- 9780191713415
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528531.003.0018
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter reprints a paper which attempts to improve upon several weaknesses in the classical theories of rubber elasticity. It develops a formulation of the statistical thermodynamics of ...
More
This chapter reprints a paper which attempts to improve upon several weaknesses in the classical theories of rubber elasticity. It develops a formulation of the statistical thermodynamics of amorphous materials analogous to the Gibbs formalism for conventional statistical mechanics. This then permits the replacement of ‘phantom chains’, i.e., long polymer molecules with the fictitious property that they experience no forces except at cross link points and are transparent to one another, by realistic molecules which do experience forces and which can become entangled. The chapter is divided into four sections. The first section demonstrates that just as Gibbs's famous formula provides an abstract formula for the statistical mechanics of systems in which all states are accessible, the new formula extends to systems with frozen-in degrees of freedom. The second section shows how the formalism fits the problem of rubber elasticity. In the third section, the effect of excluded volume, i.e., of short-range forces, is included in the calculation of the free energy of a rubber, while in fourth section, the effects of entanglements are included to complete the kinds of force normally encountered.Less
This chapter reprints a paper which attempts to improve upon several weaknesses in the classical theories of rubber elasticity. It develops a formulation of the statistical thermodynamics of amorphous materials analogous to the Gibbs formalism for conventional statistical mechanics. This then permits the replacement of ‘phantom chains’, i.e., long polymer molecules with the fictitious property that they experience no forces except at cross link points and are transparent to one another, by realistic molecules which do experience forces and which can become entangled. The chapter is divided into four sections. The first section demonstrates that just as Gibbs's famous formula provides an abstract formula for the statistical mechanics of systems in which all states are accessible, the new formula extends to systems with frozen-in degrees of freedom. The second section shows how the formalism fits the problem of rubber elasticity. In the third section, the effect of excluded volume, i.e., of short-range forces, is included in the calculation of the free energy of a rubber, while in fourth section, the effects of entanglements are included to complete the kinds of force normally encountered.
ANGELO GAVEZZOTTI
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198570806
- eISBN:
- 9780191718779
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570806.003.0007
- Subject:
- Physics, Atomic, Laser, and Optical Physics
Spectroscopic and diffraction experiments can give a detailed picture of molecular objects. The dimensions of a water molecule are known with extreme reliability and accuracy. In real life, however, ...
More
Spectroscopic and diffraction experiments can give a detailed picture of molecular objects. The dimensions of a water molecule are known with extreme reliability and accuracy. In real life, however, one is never confronted with a single water molecule, but rather with bodies composed of a very large number of molecules. Chemical systems do not tend to equilibrium by minimising their internal energy. Another driving force is provided by spontaneous randomisation of the position of molecules in space and of the distribution of energies among available energy levels. This fundamental fact is embodied in the macroscopic property called entropy. Temperature, pressure, internal energy, and entropy are the basic functions of chemical thermodynamics. This chapter discusses calorimetry and thermodynamic measurements of the molecular structure and properties of macroscopic systems, partition function and calculation of molecular energies, measurement of heat capacity and entropy, calculation of entropy for chemical systems, free energy and chemical equilibrium, and thermodynamic measurements of melting enthalpies and sublimation enthalpies.Less
Spectroscopic and diffraction experiments can give a detailed picture of molecular objects. The dimensions of a water molecule are known with extreme reliability and accuracy. In real life, however, one is never confronted with a single water molecule, but rather with bodies composed of a very large number of molecules. Chemical systems do not tend to equilibrium by minimising their internal energy. Another driving force is provided by spontaneous randomisation of the position of molecules in space and of the distribution of energies among available energy levels. This fundamental fact is embodied in the macroscopic property called entropy. Temperature, pressure, internal energy, and entropy are the basic functions of chemical thermodynamics. This chapter discusses calorimetry and thermodynamic measurements of the molecular structure and properties of macroscopic systems, partition function and calculation of molecular energies, measurement of heat capacity and entropy, calculation of entropy for chemical systems, free energy and chemical equilibrium, and thermodynamic measurements of melting enthalpies and sublimation enthalpies.
M. E. LINES and A. M. GLASS
- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198507789
- eISBN:
- 9780191709944
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507789.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials
The theoretical foundations of the preceding chapters have dealt with uniform infinite ferroelectrics. In real crystals, important additional considerations arise owing to the presence of crystal ...
More
The theoretical foundations of the preceding chapters have dealt with uniform infinite ferroelectrics. In real crystals, important additional considerations arise owing to the presence of crystal surfaces and imperfections. The most fundamental consideration is the change of spontaneous polarization at inhomogeneities. In the linear relation between electric displacement, field, and polarization, the polarization arises from both the polarizability of the material in the presence of a field and from the spontaneous alignment of dipoles in the ferroelectric. This chapter discusses domains and imperfections, free energy of domains and its minimization, the effect of free carriers, polarization reversal, surfaces, the influence of defects, and Barkhausen pulses.Less
The theoretical foundations of the preceding chapters have dealt with uniform infinite ferroelectrics. In real crystals, important additional considerations arise owing to the presence of crystal surfaces and imperfections. The most fundamental consideration is the change of spontaneous polarization at inhomogeneities. In the linear relation between electric displacement, field, and polarization, the polarization arises from both the polarizability of the material in the presence of a field and from the spontaneous alignment of dipoles in the ferroelectric. This chapter discusses domains and imperfections, free energy of domains and its minimization, the effect of free carriers, polarization reversal, surfaces, the influence of defects, and Barkhausen pulses.
Ralph Skomski
- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780198570752
- eISBN:
- 9780191718816
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570752.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials
Hysteresis is a key feature of magnetic materials, and its prediction from atomic or intrinsic parameters is a major challenge in magnetism. The determination of hysteresis loops from local ...
More
Hysteresis is a key feature of magnetic materials, and its prediction from atomic or intrinsic parameters is a major challenge in magnetism. The determination of hysteresis loops from local quantities is the subject of a branch of magnetism known as micromagnetics. Its scope also includes phenomena such as magnetic domains and domain walls. As a complex nonlinear, nonequilibrium, and nonlocal phenomenon, hysteresis is caused by energy barriers associated with the magnetic anisotropy. In most cases, there is no simple relation between hysteretic properties and the anisotropy constants. The reason is the extrinsic dependence of the hysteresis on real-structure features such as metallurgical and chemical inhomogeneities, as contrasted to the atomic character of intrinsic properties. A well-known example is the low coercivity of as-cast permanent-magnet alloys. This chapter discusses micromagnetic models including the Stoner–Wohlfarth model, along with aligned Stoner-Wohlfarth particles, micromagnetic free energy, domains and domain walls, phenomenological coercivity modelling, and grain-boundary models.Less
Hysteresis is a key feature of magnetic materials, and its prediction from atomic or intrinsic parameters is a major challenge in magnetism. The determination of hysteresis loops from local quantities is the subject of a branch of magnetism known as micromagnetics. Its scope also includes phenomena such as magnetic domains and domain walls. As a complex nonlinear, nonequilibrium, and nonlocal phenomenon, hysteresis is caused by energy barriers associated with the magnetic anisotropy. In most cases, there is no simple relation between hysteretic properties and the anisotropy constants. The reason is the extrinsic dependence of the hysteresis on real-structure features such as metallurgical and chemical inhomogeneities, as contrasted to the atomic character of intrinsic properties. A well-known example is the low coercivity of as-cast permanent-magnet alloys. This chapter discusses micromagnetic models including the Stoner–Wohlfarth model, along with aligned Stoner-Wohlfarth particles, micromagnetic free energy, domains and domain walls, phenomenological coercivity modelling, and grain-boundary models.
M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199238743
- eISBN:
- 9780191716461
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199238743.003.0005
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics
This chapter considers Casimir energy not in the vacuum state of a quantum field in the presence of boundaries but in a state containing real particles in thermal equilibrium. In fact, an ensemble of ...
More
This chapter considers Casimir energy not in the vacuum state of a quantum field in the presence of boundaries but in a state containing real particles in thermal equilibrium. In fact, an ensemble of states characterized by a temperature T and a probability distribution is considered. In quantum field theory there exist several methods to treat a system at nonzero temperature. The easiest and most frequently used method is the imaginary-time Matsubara formalism. It is applied to find a general finite expression for Casimir free energy. Asymptotic expressions for the Casimir free energy are obtained in the cases of low and high temperature. The coefficients of the high-temperature expansion are expressed in terms of the heat kernel coefficients.Less
This chapter considers Casimir energy not in the vacuum state of a quantum field in the presence of boundaries but in a state containing real particles in thermal equilibrium. In fact, an ensemble of states characterized by a temperature T and a probability distribution is considered. In quantum field theory there exist several methods to treat a system at nonzero temperature. The easiest and most frequently used method is the imaginary-time Matsubara formalism. It is applied to find a general finite expression for Casimir free energy. Asymptotic expressions for the Casimir free energy are obtained in the cases of low and high temperature. The coefficients of the high-temperature expansion are expressed in terms of the heat kernel coefficients.
C. N. Hinshelwood
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198570257
- eISBN:
- 9780191717659
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570257.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter discusses thermodynamic principles. Topics covered include the laws of thermodynamics, the second law of thermodynamics, the principle of Caratheodory, a comparison of various methods of ...
More
This chapter discusses thermodynamic principles. Topics covered include the laws of thermodynamics, the second law of thermodynamics, the principle of Caratheodory, a comparison of various methods of the formulation of the second law, applications of the second law, free energy and related functions, entropy and volume, systems of several phases or components, entropy of gas mixtures, and forces and ordered structures.Less
This chapter discusses thermodynamic principles. Topics covered include the laws of thermodynamics, the second law of thermodynamics, the principle of Caratheodory, a comparison of various methods of the formulation of the second law, applications of the second law, free energy and related functions, entropy and volume, systems of several phases or components, entropy of gas mixtures, and forces and ordered structures.
Owe Philipsen
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199691609
- eISBN:
- 9780191731792
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691609.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter gives an introduction to lattice QCD at finite temperature and baryon density. After a discussion of some fundamental aspects and difficulties of quantum field theory at finite ...
More
This chapter gives an introduction to lattice QCD at finite temperature and baryon density. After a discussion of some fundamental aspects and difficulties of quantum field theory at finite temperature in the continuum, the lattice formulation of the partition function for the grand canonical ensbemble is introduced and its relation to the transfer matrix formalism is presented. As analytic tools for its evaluation, weak coupling perturbation theory on the lattice as well as the strong coupling expansion are discussed. Regarding Monte Carlo evaluations, similarities and differences to the situation in the vacuum are pointed out. All concepts are illustrated with various applications like the equation of state, screening masses, the free energy of static quark systems and phase transitions. In the second part, special emphasis is put on lattice QCD at finite baryon density. The sign problem is discussed and current techniques to deal with it at small baryon chemical potential are presented. The implications for the QCD phase diagram are summarized.Less
This chapter gives an introduction to lattice QCD at finite temperature and baryon density. After a discussion of some fundamental aspects and difficulties of quantum field theory at finite temperature in the continuum, the lattice formulation of the partition function for the grand canonical ensbemble is introduced and its relation to the transfer matrix formalism is presented. As analytic tools for its evaluation, weak coupling perturbation theory on the lattice as well as the strong coupling expansion are discussed. Regarding Monte Carlo evaluations, similarities and differences to the situation in the vacuum are pointed out. All concepts are illustrated with various applications like the equation of state, screening masses, the free energy of static quark systems and phase transitions. In the second part, special emphasis is put on lattice QCD at finite baryon density. The sign problem is discussed and current techniques to deal with it at small baryon chemical potential are presented. The implications for the QCD phase diagram are summarized.
ANGELO GAVEZZOTTI
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198570806
- eISBN:
- 9780191718779
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570806.003.0009
- Subject:
- Physics, Atomic, Laser, and Optical Physics
In the gaseous state, molecules are to a good approximation isolated entities traveling in space at high speed with sparse and near elastic collisions. At the other extreme, a perfect crystal has a ...
More
In the gaseous state, molecules are to a good approximation isolated entities traveling in space at high speed with sparse and near elastic collisions. At the other extreme, a perfect crystal has a periodic and symmetric intermolecular structure. The structure is dictated by intermolecular forces, and molecules can only perform small oscillations around their equilibrium positions. In between these two extremes, matter has many more ways of aggregation. This chapter deals with proper liquids and the liquid state. Molecular diffusion in liquids occurs approximately on the timescale of nanoseconds, to be compared with the timescale of molecular or lattice vibrations. This chapter also discusses molecular dynamics (MD), the Monte Carlo (MC) method, structural and dynamic descriptors for liquids, physicochemical properties of liquids from MD or MC simulations, simulations of enthalpy, heat capacity and density, crystal and liquid equations of state, polarisability and dielectric constants, free energy simulations, and simulation of water.Less
In the gaseous state, molecules are to a good approximation isolated entities traveling in space at high speed with sparse and near elastic collisions. At the other extreme, a perfect crystal has a periodic and symmetric intermolecular structure. The structure is dictated by intermolecular forces, and molecules can only perform small oscillations around their equilibrium positions. In between these two extremes, matter has many more ways of aggregation. This chapter deals with proper liquids and the liquid state. Molecular diffusion in liquids occurs approximately on the timescale of nanoseconds, to be compared with the timescale of molecular or lattice vibrations. This chapter also discusses molecular dynamics (MD), the Monte Carlo (MC) method, structural and dynamic descriptors for liquids, physicochemical properties of liquids from MD or MC simulations, simulations of enthalpy, heat capacity and density, crystal and liquid equations of state, polarisability and dielectric constants, free energy simulations, and simulation of water.
VOLOVIK GRIGORY E.
- Published in print:
- 2009
- Published Online:
- January 2010
- ISBN:
- 9780199564842
- eISBN:
- 9780191709906
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199564842.003.0010
- Subject:
- Physics, Condensed Matter Physics / Materials, Particle Physics / Astrophysics / Cosmology
There are three levels of phenomenology of 3He-A: the Ginzburg–Landau level in the vicinity of transition temperature, the London level which studies statics and dynamics of the soft variables ...
More
There are three levels of phenomenology of 3He-A: the Ginzburg–Landau level in the vicinity of transition temperature, the London level which studies statics and dynamics of the soft variables describing the ‘vacuum’ in the vicinity of a given vacuum manifold, and the analog of the relativistic quantum field theory that arises in 3He-A in the low temperature limit. This chapter examines these three levels in more detail and discusses different contributions to particle current including the fermionic charge, chemical potential for quasiparticles, Fermi surface emerging from the Fermi point, non-zero density of states in the presence of flow which leads to nonzero normal component at zero temperature, parameters of effective theory in London limit and fundamental constants, how to improve quantum liquid to make the closer connection to relativistic quantum fields, the universal temperature correction to Newton constant in general and in effective gravity emerging in 3He-A in particular, and the hierarchy of Planck scales as origin of precision of symmetries in effective theory.Less
There are three levels of phenomenology of 3He-A: the Ginzburg–Landau level in the vicinity of transition temperature, the London level which studies statics and dynamics of the soft variables describing the ‘vacuum’ in the vicinity of a given vacuum manifold, and the analog of the relativistic quantum field theory that arises in 3He-A in the low temperature limit. This chapter examines these three levels in more detail and discusses different contributions to particle current including the fermionic charge, chemical potential for quasiparticles, Fermi surface emerging from the Fermi point, non-zero density of states in the presence of flow which leads to nonzero normal component at zero temperature, parameters of effective theory in London limit and fundamental constants, how to improve quantum liquid to make the closer connection to relativistic quantum fields, the universal temperature correction to Newton constant in general and in effective gravity emerging in 3He-A in particular, and the hierarchy of Planck scales as origin of precision of symmetries in effective theory.
Brian G. Cox
- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199670512
- eISBN:
- 9780199670512
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670512.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials
The change in dissociation constant of an acid with solvent is directly and quantitatively related to the change in solvation energies of the species involved. The solvation of electrolytes and ...
More
The change in dissociation constant of an acid with solvent is directly and quantitatively related to the change in solvation energies of the species involved. The solvation of electrolytes and non-electrolytes across a wide range of solvents is reviewed. The transfer of simple anions from water to non-aqueous solvents is almost universally unfavourable because of the loss of important hydrogen-bond interactions with water. Cation solvation is strongly dependent upon the basicity of the solvent. It is highly favourable in solvents such as dimethylsulphoxide, which are strong Lewis bases, but much weaker than water in low-polarity and low-basicity solvents such as acetonitrile and tetrahydrofuran. Non-electrolytes, such as carboxylic acids and amines, are more stable in non-aqueous media, but the effects are generally much smaller than for ions. In mixed solvents, preferential solvation by the most favourable solvent component determines the dependence of solvation and dissociation constants upon solvent composition.Less
The change in dissociation constant of an acid with solvent is directly and quantitatively related to the change in solvation energies of the species involved. The solvation of electrolytes and non-electrolytes across a wide range of solvents is reviewed. The transfer of simple anions from water to non-aqueous solvents is almost universally unfavourable because of the loss of important hydrogen-bond interactions with water. Cation solvation is strongly dependent upon the basicity of the solvent. It is highly favourable in solvents such as dimethylsulphoxide, which are strong Lewis bases, but much weaker than water in low-polarity and low-basicity solvents such as acetonitrile and tetrahydrofuran. Non-electrolytes, such as carboxylic acids and amines, are more stable in non-aqueous media, but the effects are generally much smaller than for ions. In mixed solvents, preferential solvation by the most favourable solvent component determines the dependence of solvation and dissociation constants upon solvent composition.
Dennis Sherwood and Paul Dalby
- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198782957
- eISBN:
- 9780191826177
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198782957.003.0013
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
A critical chapter, explaining how the principles of thermodynamics can be applied to real systems. The central concept is the Gibbs free energy, which is explored in depth, with many examples. ...
More
A critical chapter, explaining how the principles of thermodynamics can be applied to real systems. The central concept is the Gibbs free energy, which is explored in depth, with many examples. Specific topics addressed are: Spontaneous changes in closed systems. Definitions and mathematical properties of Gibbs free energy and Helmholtz free energy. Enthalpy- and entropy-driven reactions. Maximum available work. Coupled reactions, and how to make non-spontaneous changes happen, with examples such as tidying a room, life, and global warming. Standard Gibbs free energies. Mixtures, partial molar quantities and the chemical potential.Less
A critical chapter, explaining how the principles of thermodynamics can be applied to real systems. The central concept is the Gibbs free energy, which is explored in depth, with many examples. Specific topics addressed are: Spontaneous changes in closed systems. Definitions and mathematical properties of Gibbs free energy and Helmholtz free energy. Enthalpy- and entropy-driven reactions. Maximum available work. Coupled reactions, and how to make non-spontaneous changes happen, with examples such as tidying a room, life, and global warming. Standard Gibbs free energies. Mixtures, partial molar quantities and the chemical potential.
E. R. DOBBS
- Published in print:
- 2001
- Published Online:
- January 2010
- ISBN:
- 9780198506409
- eISBN:
- 9780191709463
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506409.003.0022
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter examines the effects of applying a magnetic field to the A and B phases of superfluid 3He. The first section describes the distortions of the energy gap in the B phase, producing changes ...
More
This chapter examines the effects of applying a magnetic field to the A and B phases of superfluid 3He. The first section describes the distortions of the energy gap in the B phase, producing changes in the spin susceptibility and enabling transitions to the A phase to be measured as functions of field and pressure. The second section describes the discovery of the unique properties of the small A1 phase. Finally, modern measurements of the Ginzburg–Landau free energy β-parameters by several methods are compared, and conclusions are drawn.Less
This chapter examines the effects of applying a magnetic field to the A and B phases of superfluid 3He. The first section describes the distortions of the energy gap in the B phase, producing changes in the spin susceptibility and enabling transitions to the A phase to be measured as functions of field and pressure. The second section describes the discovery of the unique properties of the small A1 phase. Finally, modern measurements of the Ginzburg–Landau free energy β-parameters by several methods are compared, and conclusions are drawn.
Masao Doi
- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199652952
- eISBN:
- 9780191774942
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199652952.003.0002
- Subject:
- Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials
Soft matter solutions are made of large solute dissolved in small solvent. The contrast in the size of solute and solvent gives special features to soft matter solutions. This chapter discusses these ...
More
Soft matter solutions are made of large solute dissolved in small solvent. The contrast in the size of solute and solvent gives special features to soft matter solutions. This chapter discusses these special features from the general solution theory. It first explains general solution theory for incompressible solutions (an assumption generally made for soft matter) and then considers the relation between free energy of mixing, osmotic pressure, and chemical potentials, followed by a discussion of the conditions for having uniform solutions or phase separated solutions. A model free energy is derived for the lattice model of solutions. Next, two typical soft matter solutions – the polymer solutions and colloidal solutions – are explained. The effect of size difference on osmotic pressure and phase diagrams, and the reason why inter-surface potential is important in colloidal solutions are discussed.Less
Soft matter solutions are made of large solute dissolved in small solvent. The contrast in the size of solute and solvent gives special features to soft matter solutions. This chapter discusses these special features from the general solution theory. It first explains general solution theory for incompressible solutions (an assumption generally made for soft matter) and then considers the relation between free energy of mixing, osmotic pressure, and chemical potentials, followed by a discussion of the conditions for having uniform solutions or phase separated solutions. A model free energy is derived for the lattice model of solutions. Next, two typical soft matter solutions – the polymer solutions and colloidal solutions – are explained. The effect of size difference on osmotic pressure and phase diagrams, and the reason why inter-surface potential is important in colloidal solutions are discussed.
Yas̨ar Demirel
- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262201742
- eISBN:
- 9780262295246
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262201742.003.0003
- Subject:
- Philosophy, Philosophy of Science
This chapter describes and elaborates on the energy coupling processes of living systems. First, equilibrium and nonequilibrium systems are discussed, introducing living systems as open, ...
More
This chapter describes and elaborates on the energy coupling processes of living systems. First, equilibrium and nonequilibrium systems are discussed, introducing living systems as open, nonequilibrium, and dissipative structures continuously interacting with their surroundings. The roles of thermodynamics and Gibbs free energy as they apply to energy coupling phenomena are then summarized, followed by a discussion of protein structures as playing a crucial role in information processes and energy couplings. The “well-informed” character of living systems and the control of free energy, or exergy, by information are also briefly discussed. Finally, using the linear nonequilibrium thermodynamic approach, energy couplings in ATP production through oxidative phosphorylation and active transport of ions by chemical pumps are discussed as a part of bioenergetics.Less
This chapter describes and elaborates on the energy coupling processes of living systems. First, equilibrium and nonequilibrium systems are discussed, introducing living systems as open, nonequilibrium, and dissipative structures continuously interacting with their surroundings. The roles of thermodynamics and Gibbs free energy as they apply to energy coupling phenomena are then summarized, followed by a discussion of protein structures as playing a crucial role in information processes and energy couplings. The “well-informed” character of living systems and the control of free energy, or exergy, by information are also briefly discussed. Finally, using the linear nonequilibrium thermodynamic approach, energy couplings in ATP production through oxidative phosphorylation and active transport of ions by chemical pumps are discussed as a part of bioenergetics.
M. Kanduč, A. Schlaich, E. Schneck, and R. R. Netz
- Published in print:
- 2017
- Published Online:
- November 2017
- ISBN:
- 9780198789352
- eISBN:
- 9780191831201
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198789352.003.0012
- Subject:
- Physics, Soft Matter / Biological Physics
In this chapter we review the various types of generic (non-specific) forces acting between lipid membranes in an aqueous environment and discuss the underlying mechanisms, with particular focus on ...
More
In this chapter we review the various types of generic (non-specific) forces acting between lipid membranes in an aqueous environment and discuss the underlying mechanisms, with particular focus on the competing roles of enthalpic and entropic contributions. The interaction free energy (or interaction potential) is typically the result of a subtle interplay of several, often antagonistic contributions with comparable magnitude. First, we will briefly introduce the underlying physics of various kinds of surface–surface interactions, starting with theories of van der Waals and undulation interactions, covering electrostatics, depletion, and order–parameter fluctuation effects as well. We then turn our attention to a strong and universal repulsive force at small membrane–membrane separations, namely the hydration interaction. It has been under debate and investigation for decades and is not well captured by continuum approximations, thus here we will mainly rely on atomistic simulation techniques.Less
In this chapter we review the various types of generic (non-specific) forces acting between lipid membranes in an aqueous environment and discuss the underlying mechanisms, with particular focus on the competing roles of enthalpic and entropic contributions. The interaction free energy (or interaction potential) is typically the result of a subtle interplay of several, often antagonistic contributions with comparable magnitude. First, we will briefly introduce the underlying physics of various kinds of surface–surface interactions, starting with theories of van der Waals and undulation interactions, covering electrostatics, depletion, and order–parameter fluctuation effects as well. We then turn our attention to a strong and universal repulsive force at small membrane–membrane separations, namely the hydration interaction. It has been under debate and investigation for decades and is not well captured by continuum approximations, thus here we will mainly rely on atomistic simulation techniques.
Helmut Hofmann
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0019
- Subject:
- Physics, Nuclear and Plasma Physics
This chapter introduces density operators and matrices for many-body systems, and explains their reduction to one- and two-body densities. Starting from the Slater determinant, the latter are ...
More
This chapter introduces density operators and matrices for many-body systems, and explains their reduction to one- and two-body densities. Starting from the Slater determinant, the latter are explicitly calculated for independent fermions. For such systems, the classical limit is discussed and formulas for partition function, free energy, and entropy are derived by introducing and employing the concept of Wigner transformations. The propagation of wave packets is described in one dimension, a case for which correspondence rules are derived for various combinations of quantum operators. Finally, formulas are given for the equilibrium distribution of the quantal oscillator and the associated Wigner function.Less
This chapter introduces density operators and matrices for many-body systems, and explains their reduction to one- and two-body densities. Starting from the Slater determinant, the latter are explicitly calculated for independent fermions. For such systems, the classical limit is discussed and formulas for partition function, free energy, and entropy are derived by introducing and employing the concept of Wigner transformations. The propagation of wave packets is described in one dimension, a case for which correspondence rules are derived for various combinations of quantum operators. Finally, formulas are given for the equilibrium distribution of the quantal oscillator and the associated Wigner function.
