Laboring in the Vineyard of Physical Chemistry

Widom, B.

doi:10.1146/annurev-physchem-032210-103501

Cited by 5 publications

(6 citation statements)

References 76 publications

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“…To answer this, we should recall how it was that critical phenomena came to be understood, and what were the crucial steps. The complex history of this problem has been extensively reviewed by the active participants [45,90,25,46,87,61] (see also [11] for historical context and the relationship to renormalization in field theory), but the key steps can be seen by going backwards in time. The breakthrough in the problem is the 1971 article by Wilson [89], whose very title ("Renormalization Group and the Kadanoff Scaling Picture" -a rare instance of a Physical Review editor allowing a title to refer to an individual) indicates that the renormalization group emerged from the key insights of Kadanoff's 1966 paper on the Ising model [44].…”

Section: Friction Factor Of Turbulent Flow In Rough Pipesmentioning

confidence: 99%

Turbulence as a Problem in Non-equilibrium Statistical Mechanics

Goldenfeld

Shih

2016

J Stat Phys

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The transitional and well-developed regimes of turbulent shear flows exhibit a variety of remarkable scaling laws that are only now beginning to be systematically studied and understood. In the first part of this article, we summarize recent progress in understanding the friction factor of turbulent flows in rough pipes and quasi-two-dimensional soap films, showing how the data obey a two-parameter scaling law known as roughness-induced criticality, and exhibit power-law scaling of friction factor with Reynolds number that depends on the precise form of the nature of the turbulent cascade. These results hint at a nonequilibrium fluctuation-dissipation relation that applies to turbulent flows. The second part of this article concerns the lifetime statistics in smooth pipes around the transition, showing how the remarkable super-exponential scaling with Reynolds number reflects deep connections between large deviation theory, extreme value statistics, directed percolation and the onset of coexistence in predator-prey ecosystems. Both these phenomena reflect the way in which turbulence can be fruitfully approached as a problem in non-equilibrium statistical mechanics.

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Section: Friction Factor Of Turbulent Flow In Rough Pipesmentioning

confidence: 99%

Turbulence as a Problem in Non-equilibrium Statistical Mechanics

Goldenfeld

Shih

2016

J Stat Phys

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“…where the contibutions U A 1 B , U A 2 B , etc, to U AB from molecules A 1 , A 2 , etc, in the average (29) have been assumed uncorrelated due to the assumption of far-apart A-molecules; in the pairwise additive vacuum potential model these contributions are given explicitly by…”

Section: Introduction Of the Pmf'smentioning

confidence: 99%

“…A 1 fixed at position r 1 , averaged over the solvent configurations. For N A identical solute molecules in a uniform solvent the effective one-body potentials v A (r i ) are all equal and independent of position, so that the last expression in (29) is the product of N A identical constant factors. The total one-body PMF term in (28),…”

Section: Introduction Of the Pmf'smentioning

confidence: 99%

“…1 is very hard to read and this is likely the main reason for the relative neglect of MM theory compared to KB theory. Indeed, as another leading practitioner29 has put it "...somewhere, hidden in an impenetrable jungle of notation in the 1945 paper of McMillan and Mayer, must be the potential distribution theorem!" As it turns out the Widom potential distribution theorem 30 (also called the particle insertion theorem) is not explicitly written down by MM(Hill 15 comes close in his reformulation of MM theory using the semi-grand canonical ensemble-see remarks following).…”

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confidence: 99%

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McMillan-Mayer theory of solutions revisited: Simplifications and extensions

Vafaei

Tomberli

Gray

2014

The Journal of Chemical Physics

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McMillan and Mayer (MM) proved two remarkable theorems in their paper on the equilibrium statistical mechanics of liquid solutions. They first showed that the grand canonical partition function for a solution can be reduced to one with an effectively solute-only form, by integrating out the solvent degrees of freedom. The total effective solute potential in the effective solute grand partition function can be decomposed into components which are potentials of mean force for isolated groups of one, two, three, etc., solute molecules. Second, from the first result, now assuming low solute concentration, MM derived an expansion for the osmotic pressure in powers of the solute concentration, in complete analogy with the virial expansion of gas pressure in powers of the density at low density. The molecular expressions found for the osmotic virial coefficients have exactly the same form as the corresponding gas virial coefficients, with potentials of mean force replacing vacuum potentials. In this paper, we restrict ourselves to binary liquid solutions with solute species A and solvent species B and do three things: (a) By working with a semi-grand canonical ensemble (grand with respect to solvent only) instead of the grand canonical ensemble used by MM, and avoiding graphical methods, we have greatly simplified the derivation of the first MM result, (b) by using a simple nongraphical method developed by van Kampen for gases, we have greatly simplified the derivation of the second MM result, i.e., the osmotic pressure virial expansion; as a by-product, we show the precise relation between MM theory and Widom potential distribution theory, and (c) we have extended MM theory by deriving virial expansions for other solution properties such as the enthalpy of mixing. The latter expansion is proving useful in analyzing ongoing isothermal titration calorimetry experiments with which we are involved. For the enthalpy virial expansion, we have also changed independent variables from semi-grand canonical, i.e., fixed {N(A), μ(B), V, T}, to those relevant to the experiment, i.e., fixed {N(A), N(B), p, T}, where μ denotes chemical potential, N the number of molecules, V the volume, p the pressure, and T the temperature.

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“…The dynamics at the surface of the DPPC bilayer are decoupled from the bulk dynamics but by no means immobilized; water at the surface only moves at ∼20% of the typical diffusion rate and exhibits insensitivity to changes in the bulk viscosity. Interestingly, the same 1 nm length scale that the ODNP approach probes corresponds to the correlation length of water, which determines the length scale of structural and dynamic changes of the fluid. , This suggests that the DPPC surface itself controls the dynamics of local water molecules within 1 nm of the lipid vesicle surface, while Ficoll or sucrose controls the dynamics of water molecules located a few nm away from the DPPC surface, in the bulk solvent.…”

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confidence: 99%

Nonlinear Scaling of Surface Water Diffusion with Bulk Water Viscosity of Crowded Solutions

2013

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The translational hydration dynamics within 0.5-1.5 nanometers (nm) of the surface of a DPPC liposome – a model biomacromolecular surface – is analyzed by the recently developed Overhauser dynamic nuclear polarization (ODNP) technique. We find that dramatic changes to the bulk solvent cause only weak changes in the surface hydration dynamics. Specifically, both a >10-fold increase in bulk viscosity and the restriction of diffusion by confinement on a multiple-nm length-scale change the local translational diffusion coefficient of the surface water surrounding the lipid bilayer by less than 2.5-fold. By contrast, previous ODNP studies have shown that changes to the biomacromolecular surface induced by folding, binding, or aggregation can cause local hydration dynamics to vary by factors of up to 30.1,2 We suggest that the surface topology and chemistry at the ≤ 1.5 nm scale, rather than the characteristics of the bulk fluid, nearly exclusively determine the surface hydration dynamics of aqueous macromolecular solutes.

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Laboring in the Vineyard of Physical Chemistry

Cited by 5 publications

References 76 publications

Turbulence as a Problem in Non-equilibrium Statistical Mechanics

Turbulence as a Problem in Non-equilibrium Statistical Mechanics

McMillan-Mayer theory of solutions revisited: Simplifications and extensions

Nonlinear Scaling of Surface Water Diffusion with Bulk Water Viscosity of Crowded Solutions

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