Phase diagram of hard colloidal platelets: a theoretical account

We construct the complete liquid crystal phase diagram of hard plate-like cylinders for variable aspect ratio using Onsager's second virial theory and employing the Parsons–Lee decoupling approximation to account for higher-body interactions in the isotropic and nematic fluid phases. The stability of the solid (columnar) state at high packing fraction is included by invoking a simple equation of state based on a Lennard–Jones–Devonshire cell model which has proven to be quantitatively reliable over a large range of packing fractions. By employing an asymptotic analysis based on the Gaussian approximation we are able to show that the nematic–columnar transition is universal and independent of particle shape. The predicted phase diagram is in qualitative agreement with simulation results.     

Lars, the Oracle

Lars Onsager was known for his obscure but correct predictions in several fields of science. Some scientific events, particularly in the field of superfluidity, are recollected here by one of his old friends.     

The BEH mechanism and its scalar boson

The theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles was recently confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN's Large Hadron Collider. In his Nobel lecture, F. Englert gives an overview of this research which has led to the Nobel Prize in Physics in 2013 which he shared with Peter W. Higgs. 1     

Theory of quantum fluctuations and the Onsager relations

A microscopic model is constructed within the theory of normal fluctuations for quantum systems, yielding an irreversible dynamics satisfying the Onsager relations. The property of return to equilibrium and the principle of minimal entropy production are proved.     

Higher Order Quantum Onsager Coefficients from Dynamical Invariants

Functionals representing dynamical invariants under unitary quantum dynamics of open systems are used to derive Onsager coefficients for entropy production in irreversible processes if the nonunitary time evolution is determined by quantum dynamical semigroups. The procedure allows a derivation from first principles of the quantum analogue to the classical case.     

Derivation of Two-Fluid Model Based on Onsager Principle

Using the Onsager variational principle, we study the dynamic coupling between the stress and the composition in a polymer solution. In the original derivation of the two-fluid model of Doi and Onuki the polymer stress was introduced a priori; therefore, a constitutive equation is required to close the equations. Based on our previous study of viscoelastic fluids with homogeneous composition, we start with a dumbbell model for the polymer, and derive all dynamic equations using the Onsager variational principle.     

Relaxation theory of spin-3/2 Ising system near phase transition temperatures

<正>Dynamics of a spin-3/2 Ising system Hamiltonian with bilinear and biquadratic nearest-neighbour exchange interactions is studied by a simple method in which the statistical equilibrium theory is combined with the Onsager's theory of irreversible thermodynamics.First,the equilibrium behaviour of the model in the molecular-field approximation is given briefly in order to obtain the phase transition temperatures,i.e.the first- and second-order and the tricritical points.Then,the Onsager theory is applied to the model and the kinetic or rate equations are obtained.By solving these equations three relaxation times are calculated and their behaviours are examined for temperatures near the phase transition points.Moreover,the z dynamic critical exponent is calculated and compared with the z values obtained for different systems experimentally and theoretically,and they are found to be in good agrement.     

On the Onsager Variation Principle and its Generalization for Nonlinear Irreversible Thermodynamics

The Onsager variation principle is examined from the viewpoint of the thermodynamic analogue of the D'Alembert principle in mechanics when the irreversible processes are linear and thus the system is near equilibrium. The thermodynamic D'Alembert principle is shown to be a precursor to the Onsager variation principle. The thermodynamic D'Alembert principle is then generalised to the cases of nonlinear irreversible processes occurring removed from equilibrium and a generalised form of the Onsager variation principle is obtained under some restricting conditions. The restricted variation principle so deduced has an accompanying exact differential form generalising the Clausius entropy differential (equilibrium Gibbs relations) and contains in it the essence of the thermodynamics of irreversible processes in systems where non-linear transport processes occur. An example is given for the nonlinear dissipation function in the variation functional. The evolution equations for fluxes are shown to yield those known in the literature.     

Heike Kamerlingh Onnes and the Nobel Prize in Physics for 1913: The Highest Honor for the Lowest Temperatures

One century ago this year the Dutch experimental physicist Heike Kamerlingh Onnes (1853–1926) was awarded the Nobel Prize in Physics for his work in low-temperature physics, in particular for his production of liquid helium. I trace the route to his Nobel Prize within the context of his and his colleagues’ research in his laboratory at the University of Leiden, and in light of his nominators and the nominations he received in the five years 1909–1913.     

Onsager and Kaufman’s Calculation of the Spontaneous Magnetization of the Ising Model

Lars Onsager announced in 1949 that he and Bruria Kaufman had proved a simple formula for the spontaneous magnetization of the square-lattice Ising model, but did not publish their derivation. It was three years later when C.N. Yang published a derivation in Physical Review. In 1971 Onsager gave some clues to his and Kaufman’s method, and there are copies of their correspondence in 1950 now available on the Web and elsewhere. Here we review how the calculation appears to have developed, and add a copy of a draft paper, almost certainly by Onsager and Kaufman, that obtains the result.     

Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem

It is shown that the chaoticity hypothesis recently introduced in statistical mechanics, which is analogous to Ruelle's principle for turbulence, implies the Onsager reciprocity and the fluctuation-dissipation theorem in various reversible models for coexisting transport phenomena.This paper is dedicated to David Ruelle on the occasion of his 60th birthday.     

In Appreciation Julian Schwinger: From Nuclear Physics and Quantum Electrodynamics to Source Theory and Beyond

Julian Schwinger’s influence on twentieth-century science is profound and pervasive. He is most famous for his renormalization theory of quantum electrodynamics, for which he shared the Nobel Prize in Physics for 1965 with Richard Feynman and Sin-itiro Tomonaga. This triumph undoubtedly was his most heroic work, but his legacy lives on chiefly through subtle and elegant work in classical electrodynamics, quantum variational principles, proper-time methods, quantum anomalies, dynamical mass generation, partial symmetry, and much more. Starting as just a boy, he rapidly became one of the preeminent nuclear physicists in the world in the late 1930s, led the theoretical development of radar technology at the Massachusetts Institute of Technology during World War II, and soon after the war conquered quantum electrodynamics, becoming the leading quantum-field theorist for two decades, before taking a more iconoclastic route during the last quarter century of his life.     

Linear and Nonlinear Generalizations of Onsager's Reciprocity Relations. Treatment of an Example of Chemical Reaction Kinetics

Linear and nonlinear generalizations of Onsager's reciprocity relations are derived from the fact that the time derivatives and time integrals of state quantities calculated by the help of the kinetic equations are state quantities again. Maxwell's reciprocity relations of thermostatics appear as special cases. The formalism is applied to a system of three linear dependent chemical elementary reactions. Onsager's relations and their generalizations are phenomenologically derived without the aid of the fluctuation theory.     

Onsager relations for transport in inhomogeneous media

The nonlinear equations that describe transport in inhomogeneous media cannot be obtained by a straightforward extension of the known phenomenological equations for homogeneous media. One cannot therefore asserta priori that the Onsager reciprocity relations remain valid. Previously the correct equations have been obtained for three special models using kinetic theory. It is here shown that in these models the Onsager relations do indeed hold, provided that they are formulated with care.     

A Conversation with William A. Fowler – Part I

Nobel laureate William A. Fowler recalls his early education in physics; his part in the history of nuclear physics at the California Institute of Technology in the 1930s; parallel efforts elsewhere, particularly at Berkeley and the Department of Terrestrial Magnetism in Washington,D.C.; his contacts with J. Robert Oppenheimer; and his work with Charles C. Lauritsen and Tommy Lauritsen before and after World War II.John Greenberg received his Ph.D. degree from the University of Wisconsin and was Caltech research fellow in history from 1980–1984. The Editors were saddened to learn that he died while this interview was in press. Requests for reprints may be directed to Judith R. Goodstein, Institute Archives 015A-74, Caltech, Pasadena, CA 91125 USA; e-mail: jrg@caltech.edu.     

The Onsager reciprocity relation and generalized efficiency of a thermal Brownian motor

Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper.     

Influence of random electric fields on luminescence yield and kinetics of insulators

In the present work we investigate theoretically the influence of random electric fields on electron-hole recombination in wide bandgap crystals. Effective Onsager radius and, therefore, electron-hole recombination rate are significantly modified by external electric fields. Electric field distribution functions for point defects and charged dislocations are evaluated analytically. Electron-hole recombination rate decreases with concentration of point defects and dislocations. In simple case of random fields created by charge carriers in highly excited regions the recombination rate is proportional to n 2/3 rather than n , where n is the concentration of excitations. Therefore modification of luminescence kinetics is most pronounced at initial stages of relaxation of highly excited regions.     

The excluded volume of hard sphero-zonotopes

Excluded volume effects can account for most ordering transitions in simple liquids and liquid crystals. Starting with the work of Onsager, this has been demonstrated in the case of liquid crystals for a number of simple convex bodies, e.g. sphero-cylinders, for which the orientation-dependent pair-excluded volume could be written down analytically. However, in recent years, experiments and simulations have been reported on ordering transitions in suspensions of more complex convex colloids. For these systems, theoretical understanding is hampered by the fact that no analytical expressions for the pair-excluded volume were available. Here we show that it is possible to obtain explicit expressions for the pair-excluded volume of a much larger class of convex bodies: the so-called sphero-zonotopes. These bodies are obtained by ‘padding’ a special class of convex polytopes with a blanket of uniform thickness. The resultant family of particles encompasses a wide range of shapes that have been considered as models for fluid and liquid crystalline behaviour e.g. spheres, cubes, sphero-cylinders, sphero-platelets. We discuss two explicit examples: sphero-cuboids, the 3D core generalization of the sphero-cylinder and the sphero-platelet, and hexagonal prisms that are models for the recently synthesized colloidal gibbsite platelets. Employing the fact that a cylinder is a zonoid, i.e. the limit of a sequence of right regular prisms, we are able to compute the excluded volume of the ‘true’ sphero-cylinder, a uniformly padded cylinder, of which the oblate-spherocylinder is a known example. Our approach en passant provides a relatively elementary rederivation of Onsager's classical result on cylinders.