Lars Onsager, a giant of the twentieth-century science and the 1968 Nobel Laureate in Chemistry, made deep contributions to several areas of physics and chemistry. Perhaps less well known is ground-breaking work and lifelong interest in the subject of hydrodynamic turbulence. He wrote two papers on the subject in the 1940s, one of them just a short abstract. Unbeknownst to Onsager, one of his major results was derived a few years earlier by A. N. Kolmogorov, but Onsager’s work contains many gems and shows characteristic originality and deep understanding. His only full-length article on the subject in 1949 introduced two novel ideas negative-temperature equilibria for two-dimensional ideal fluids and energy dissipation anomaly for singular Euler solutions that stimulated much later work. However, a study of Onsager’s letters to his peers around that time, as well as his private papers of that period and the early 1970s, shows that he had much more to say about the problem than he published. Reamarkably, his private notes of the 1940s contain the essential elements of at least four major results that appeared decades later in the literature: a mean-field equation, Poisson-Boltzmann equation and other thermodynamic relations for point vortices; a relation similar to Kolmogorov’s 4/5 law connecting singularities and dissipation and so on. The goal of this seminar is a summary of Onsager’s published and unpublished contributions to hydrodynamic turbulence and an account of their place in the field as the subject has evolved through the years.

Condensation potentials and corresponding electrical currents are observed during the isothermal growth of amorphous, cubic, and hexagonal ice from the vapor phase. Upon heating of the condensate a thermally stimulated current (TSC) spectrum is observed with the application of any external electric field. Current peaks in the TSC spectrum are shown to be of two types: depolarization currents related to dipolar relaxation processes in the condensate and peaks due to phase transitions. Nearly all depolarization (∼90%) occurs in the amorphous phase via relaxation processes. Shifts in the maximum temperature of the peaks are observed for deuterated water for both types of peaks, and are on the order of 5–10 K. Models are proposed for the electrical effects observed during condensation, phase change, and depolarization.

The prediction and experimental confirmation of a previously unsuspected kinetic effect occurring in electrolyte solutions are presented herein. Kinetic polarization deficiency may be described as a reduction, with respect to the pure solvent, in the static permittivity of the solution; the decrement in epsilon0 is shown to be proportional to the product of the dielectric relaxation time of the solvent and the low frequency conductivity of the solution. The kinetic ion-solvent interaction affects the capacitive admittance in two closely related ways: as an ion migrates, the surrounding volume elements of the liquid tend to rotate according to the laws of hydrodynamics, and although dielectric relaxation tends to restore an equilibrium polarization appropriate to the local electric field, this adjustment is not instantaneous; rather it lags behind by the dielectric relaxation time. Conversely, the force that an external field exerts on an ion does not develop its full strength instantly because the ion is driven partly by the external field and partly by the polarization that develops in response to the applied field, the polarization field evolving with a time constant that is the relaxation time for the orientation of solvent dipoles.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTThe generalized conductance equationMou-Shan Chen and Lars OnsagerCite this: J. Phys. Chem. 1977, 81, 21, 2017–2021Publication Date (Print):October 1, 1977Publication History Published online1 May 2002Published inissue 1 October 1977https://pubs.acs.org/doi/10.1021/j100536a013https://doi.org/10.1021/j100536a013research-articleACS PublicationsRequest reuse permissionsArticle Views281Altmetric-Citations33LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTThe integral representation of the relaxation effects in mixed strong electrolytes in the limiting law regionShoon K. Kim and Lars OnsagerCite this: J. Phys. Chem. 1977, 81, 12, 1211–1212Publication Date (Print):June 1, 1977Publication History Published online1 May 2002Published inissue 1 June 1977https://pubs.acs.org/doi/10.1021/j100527a019https://doi.org/10.1021/j100527a019research-articleACS PublicationsRequest reuse permissionsArticle Views94Altmetric-Citations7LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

A self-consistent, kinetic theory of ion–solvent interactions is developed within the framework of continuum mechanics. It is shown that the hydrodynamic coupling between viscous momentum transport and dielectric relaxation leads not only to a theory of ion mobility but also to a description of the dielectric properties of electrolyte solutions. The concept of kinetic polarization deficiency is introduced, whereby the static permittivity of a solution is reduced from that of the pure solvent by an amount proportional to the product of solvent dielectric relaxation time and low frequency conductivity of the solution. Furthermore, if the viscous and dielectric relaxation times are assumed to be comparable it is demonstrated that ’’deformation inertia’’ should make a significant contribution to the decrement Δε0. Ion mobility is calculated to first order in a coupling parameter which is inversely proportional to the fourth power of the ion radius, the limiting case of zero ion size is analyzed, and general aspects of ion migration are investigated with the aid of the principle of minimum dissipation. Given that the pure solvent has a dispersion characterized by a single Debye relaxation time τD, it is asserted that the solution will, as a consequence of dielectric friction, possess an infinite number of relaxation times extending from τD down to the longitudinal time τL=τD(ε∞/ε0).

The effects of intermolecular tunneling by protons in ice and other protonic semiconductors on thermodynamic and transport properties are estimated on the basis of an idealized model. The model involves a simple tight-binding Hamiltonian on the infinite-dimensional set of molecular configurations in the generally proton-bonded but otherwise disordered structure. The cycle-poor topology of the state set is approximated by that of a cycle-free Bethe lattice, i.e., an infinite, homogeneous Cayley tree. For coordination q and hopping matrix element V the distribution of energy levels is given by the function g(u) = g(E/V) = q[4(q − 1) − u2]1/2/2π(q2 − u2), where q = 3 for the set of hopping options available to an ion in ice. The thermal average of the group velocity v = [4(q − 1) − u2]1/2 V d / ℏ on the Bethe lattice with lattice spacings d determines a finite coefficient of diffusion in real three-dimensional space, where paths on the Bethe lattice are represented by random walks in 3 space with only a finite measure of correlation between the directions of successive steps. These results agree with recent computations by Minagawa and with the results of various parallel efforts in the theory of electron tunneling. Some questions of principle are resolved by an analysis of the corresponding eigenvalue problem for a symmetrically constructed finite Cayley tree, and an effective upper bound for the error incurred by disregarding cycles is obtained from a computation for a periodic graph in three dimensions. While the ionic mobilities in ice are not yet well known, even the greatest claimed values of about 0.075 cm2/V · sec are compatible with matrix elements somewhat smaller than 1 mV, which would entail tunneling corrections to the partition function for a hydrogen ion of less than 2% near the freezing point.

The decay of luminescent intensity due to pairs of donors and acceptors present in unequal concentrations is described by a simple asymptotic formula, which becomes accurate as soon as the closest pairs have decayed completely. For shorter times a known power series is serviceable but corrections for various more or less specific interactions are particularly pertinent to the earliest stages of decay. In dealing with Cu-activated ZnS, Hagston's idea of preferential pairing applies in modified form. The expected early decay rates of green and blue emissions differ and both vary with the ratio of their intensities.

Angewandte ChemieVolume 81, Issue 24 p. 1009-1016 Article Die Bewegung von Ionen: Prinzipien und Vorstellungen (Nobel-Vortrag)† Prof. Dr. L. Onsager, Prof. Dr. L. Onsager Sterling Chemistry Laboratory Yale University New Haven, Conn. 06 520 (USA)Search for more papers by this authorDr. F. Sauer, Dr. F. Sauer Sterling Chemistry Laboratory Yale University New Haven, Conn. 06 520 (USA)Search for more papers by this author Prof. Dr. L. Onsager, Prof. Dr. L. Onsager Sterling Chemistry Laboratory Yale University New Haven, Conn. 06 520 (USA)Search for more papers by this authorDr. F. Sauer, Dr. F. Sauer Sterling Chemistry Laboratory Yale University New Haven, Conn. 06 520 (USA)Search for more papers by this author First published: Dezember 1969 https://doi.org/10.1002/ange.19690812402 † Copyright © The Nobel Foundation 1969. – Wir danken der Nobel-Stiftung, Stockholm, für die Genehmigung zum Abdruck dieses Textes. AboutPDF ToolsRequest permissionAdd to favorites ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume81, Issue24Dezember 1969Pages 1009-1016 This article also appears in:Nobel-Aufsätze This is the German version of Angewandte Chemie. Note for articles published since 1962: Do not cite this version alone. Take me to the International Edition version with citable page numbers, DOI, and citation export. We apologize for the inconvenience. RelatedInformation

The underlying mechanisms of several rate processes in ice are examined through cross comparisons of the processes with each other and with experimental observations. The assumption that the migration of orientational defects (Bjerrum faults) is the common origin of dielectric and elastic relaxation leads to a predicted ratio of dielectric-to-elastic relaxation time of 32, in close agreement with experiment. The conclusion that a separate process is responsible for diffusion is based on a comparison of diffusion and dielectric relaxation data. The faster diffusive motion controls the thermal equilibration of the proton spins as well as the magnetic resonance linewidths; an interstitial migration appears to be the mostlikely diffusion mechanism.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTThe Conductance of Symmetrical Electrolytes. V. The Conductance Equation1,2Raymond M. Fuoss, Lars Onsager, and James F. SkinnerCite this: J. Phys. Chem. 1965, 69, 8, 2581–2594Publication Date (Print):August 1, 1965Publication History Published online1 May 2002Published inissue 1 August 1965https://doi.org/10.1021/j100892a017Request reuse permissionsArticle Views380Altmetric-Citations95LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEArticleNEXTThe Conductance of Symmetrical Electrolytes.1a IV. Hydrodynamic and Osmotic Terms in the Relaxation FieldRaymond M. Fuoss and Lars OnsagerCite this: J. Phys. Chem. 1964, 68, 1, 1–8Publication Date (Print):January 1, 1964Publication History Published online1 May 2002Published inissue 1 January 1964https://pubs.acs.org/doi/10.1021/j100783a001https://doi.org/10.1021/j100783a001research-articleACS PublicationsRequest reuse permissionsArticle Views162Altmetric-Citations31LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTA Correction to the Poisson-Boltzmann Equation for Unsymmetrical ElectrolytesLars. OnsagerCite this: J. Am. Chem. Soc. 1964, 86, 17, 3421–3423Publication Date (Print):September 1, 1964Publication History Published online1 May 2002Published inissue 1 September 1964https://doi.org/10.1021/ja01071a004RIGHTS & PERMISSIONSArticle Views205Altmetric-Citations18LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (317 KB) Get e-Alertsclose Get e-Alerts

Understanding a visual scene is an unsolved and daunting task, since scenes can contain a large number of objects, their properties, and interrelations. Extracting the full scene structure is therefore infeasible, but often unnecessary, since ...In modeling vision, there has been a remarkable progress in recognizing a range of scene components, but the problem of analyzing full scenes, an ultimate goal of visual perception, is still largely open. To deal with complete scenes, recent work focused ...