Systematic names for the tartaric acids

Baxter, J. N.

doi:10.1021/ed041p619

Cited by 6 publications

(7 citation statements)

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“…In bulk, the one-body direct correlation function becomes spatially constant and Equation (15) is equivalent to the first of Baxter's sum rules [11]:…”

Section: Integration Of the Direct Correlation Functionsmentioning

confidence: 99%

Free power dissipation from functional line integration

Brader

Schmidt

2015

Molecular Physics

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Power functional theory provides an exact generalisation of equilibrium density functional theory to non-equilibrium systems undergoing Brownian many-body dynamics. Practical implementation of this variational approach demands knowledge of an excess (over ideal gas) dissipation functional. Using functional line integration (i.e. the operation inverse to functional differentiation), we obtain an exact expression for the excess free power dissipation, which involves the pair interaction potential and the two-body, equal-time density correlator. This provides a basis for the development of approximation schemes.

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“…In bulk, the one-body direct correlation function becomes spatially constant and Equation (15) is equivalent to the first of Baxter's sum rules [11]:…”

Section: Integration Of the Direct Correlation Functionsmentioning

confidence: 99%

Free power dissipation from functional line integration

Brader

Schmidt

2015

Molecular Physics

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“…The particle densities n k depend on the temperature T and on the number density n of the system. In 1964, Baxter [1] proved an elegant hierarchy relating the derivative of n k with respect to density with an integral of n k+1 , namely…”

Section: Multi-particle Correlation Functionsmentioning

confidence: 99%

“…In order to study this question we use the infinite hierarchy of equations derived by Baxter [1]. The hierarchy relates the spatial integrals of (k + 1)-particle correlation functions to k-particle correlations and their derivatives with respect to the density, for k = 2, 3, .…”

Section: Introductionmentioning

confidence: 99%

Multi-particle critical correlations

Santos

Piasecki

2015

Molecular Physics

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We study the role of multi-particle spatial correlations in the appearance of a liquid-vapour critical point. Our analysis is based on the exact infinite hierarchy of equations relating spatial integrals of $(k+1)$-particle correlations to the $k$-particle ones and their derivatives with respect to the density. Critical exponents corresponding to generalized compressibility equations resulting from the hierarchy are shown to grow linearly with the order of correlations. We prove that the critical behaviour requires taking into account correlation functions of arbitrary order. It is however only a necessary condition. Indeed, approximate closures of the hierarchy obtained by expressing higher order correlations in terms of lower order ones (Kirkwood's superposition approximation and its generalizations) turn out to be inconsistent with the critical behaviour.Comment: 14 pages, 1 figure; v2: minor change

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“…Thus the entropy of a free spin with average magnetisation m i is simply the Gibbs mixing entropy of two ideal gases with mole fractions (1 + m i )/2 and (1 − m i )/2, per particle. Now, the excess term includes all other contributions to the free energy and is difficult to write down except in a few cases [26,77]. We will content ourselves with a mean-field approximation, which becomes exact when each spin interacts infinitely weakly with an infinite number of other spins.…”

Section: Placing the Glass Transition On The Map Thermodynamics-wise:...mentioning

confidence: 99%

“…One can now use Eqs. ( 73), (77), and (54) to determine the Helmholtz free energy F of the solid as a function of the density-which is specified automatically given a lattice-and the effective spring constant α. This free energy is further optimised with respect to α thus giving an approximation for the free energy of the solid as a function of the density, thus allowing one to compute the pressure.…”

Section: B Emergence Of the Molecular Fieldmentioning

confidence: 99%

Theory of the Structural Glass Transition: A Pedagogical Review

Lubchenko

2015

Preprint

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The random first-order transition (RFOT) theory of the structural glass transition is reviewed in a pedagogical fashion. The rigidity that emerges in crystals and glassy liquids is of the same fundamental origin. In both cases, it corresponds with a breaking of the translational symmetry; analogies with freezing transitions in spin systems can also be made. The common aspect of these seemingly distinct phenomena is a spontaneous emergence of the molecular field, a venerable and well-understood concept. In crucial distinction from periodic crystallisation, the free energy landscape of a glassy liquid is vastly degenerate, which gives rise to new length and time scales while rendering the emergence of rigidity gradual. We obviate the standard notion that to be mechanically stable a structure must be essentially unique; instead, we show that bulk degeneracy is perfectly allowed but should not exceed a certain value. The present microscopic description thus explains both crystallisation and the emergence of the landscape regime followed by vitrification in a unified, thermodynamics-rooted fashion. The article contains a self-contained exposition of the basics of the classical density functional theory and liquid theory, which are subsequently used to quantitatively estimate, without using adjustable parameters, the key attributes of glassy liquids, viz., the relaxation barriers, glass transition temperature, and cooperativity size. These results are then used to quantitatively discuss many diverse glassy phenomena, including: the intrinsic connection between the excess liquid entropy and relaxation rates, the non-Arrhenius temperature dependence of α-relaxation, the dynamic heterogeneity, violations of the fluctuation-dissipation theorem, glass ageing and rejuvenation, rheological and mechanical anomalies, super-stable glasses, enhanced crystallisation near the glass transition, the excess heat capacity and phonon scattering at cryogenic temperatures, the Boson peak and plateau in thermal conductivity, and the puzzling midgap electronic states in amorphous chalcogenides.

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Systematic names for the tartaric acids

Cited by 6 publications

References 0 publications

Free power dissipation from functional line integration

Free power dissipation from functional line integration

Multi-particle critical correlations

Theory of the Structural Glass Transition: A Pedagogical Review

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