Joseph E. Mayer

Bio: Joseph E. Mayer is an academic researcher from University of Baltimore. The author has contributed to research in topics: Distribution function & Halide. The author has an hindex of 26, co-authored 58 publications receiving 6747 citations.

On the Quantum Correction for Thermodynamic Equilibrium

Abstract: The behavior of any system at high enough temperatures approaches that of its classical counterpart. The probability of any configurational position is then proportional to exp—U/kT, with U the potential energy. Wigner has shown that quantum‐mechanical deviations, as the temperature is lowered, may be approximated by multiplication of this with 1–f, where f is a function proportional to h2 and having terms in T−2 and terms in T−3. This type of approximation is unsatisfactory for a system of many degrees of freedom, that is, one of many dependent molecules. For such a system it is shown that instead of Wigner's approximation we may replace the classical potential U in the exponent by U—kTf, where f is the same as Wigner's function.

The Statistical Thermodynamics of Multicomponent Systems

Abstract: Distribution functions, Fn(z, {n}), for multicomponent systems are defined proportional to the probability density that n molecules in an infinite isothermal system of fugacity set z will occupy the configurational coordinates symbolized by {n}. All thermodynamic functions may be obtained as certain sums of integrals of these distribution functions. These sums are always convergent, but impractically slow in convergence for numerical use without further transformation. In particular, the grand‐partition function, exp [VP(z)/kT], may be expanded in a power series in the fugacities z with coefficients given by integrals of the distribution functions Fn(0, {n}) at the fugacity set 0. As has been previously demonstrated for one component systems, this is shown to be a special case of a more general relation permitting the calculation of the distribution functions (and therefore the thermodynamic functions) for one fugacity set from those at another set. The function —kT ln Fn(z, {n}) is the potential of avera...

Zur Gittertheorie der Ionenkristalle

Abstract: Die Gittertheorie der Ionenkristalle wird durch drei Anderungen des Energieansatzes verscharft: Das Abstosungspotential wird nicht als Potenz des Gitterabstandes, sondern als Exponentialfunktion angenommen. Dabei wird das Gesetz der Additivitat der Ionenradien berucksichtigt. Endlich werden die van der Waalsschen Kohasionskrafte mit in Rechnung gesetzt. Es wird gezeigt, das hierdurch die verschiedene Stabilitat der Gittertypen NaCl und CsCl verstandlich gemacht werden kann.

Dispersion and Polarizability and the van der Waals Potential in the Alkali Halides

Abstract: It is shown that the ultraviolet absorption of NaCl, KCl and KI, which one may estimate from recent experimental work, is in agreement with the dispersion of these salts. With these assumed absorption curves, the dipole‐dipole potential constant for the van der Waals attraction between negative ions can be calculated with considerable accuracy. The constants can be estimated for the other alkali halides. The quadrupole‐dipole constant is also approximated for all alkali halides. The resulting van der Waals potential is much greater than that previously calculated and accounts for the stability of CsCl type lattice for CsCl, CsBr and CsI. The polarizability of a given ion depends on the crystal. It is here assumed that the polarizability varies inversely as the ``main frequency'' in the crystal. This is shown to be in approximate agreement with experiment.

The Theory of Ionic Solutions

Abstract: The virial development for the osmotic pressure of a solution may be used, if the potentials of average force of the solute molecules at infinite dilution are known, to compute the deviations from perfect solution behavior. The expression for the logarithm of the activity coefficient can thus be obtained as a sum of coefficients multiplied by powers of the concentration. For an ionic solution, with 1/R2 forces, the series is only conditionally convergent. By summing certain additive terms occurring in the coefficients over all powers of concentration convergence can be attained.The integrations necessary to obtain terms correct up to and including c32 are performed. The results are given in terms of certain functions which can readily be computed.

A wavelet tour of signal processing

Abstract: Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

New method for calculating the one-particle green's function with application to the electron-gas problem

Abstract: A set of successively more accurate self-consistent equations for the one-electron Green's function have been derived. They correspond to an expansion in a screened potential rather than the bare Coulomb potential. The first equation is adequate for many purposes. Each equation follows from the demand that a corresponding expression for the total energy be stationary with respect to variations in the Green's function. The main information to be obtained, besides the total energy, is one-particle-like excitation spectra, i.e., spectra characterized by the quantum numbers of a single particle. This includes the low-excitation spectra in metals as well as configurations in atoms, molecules, and solids with one electron outside or one electron missing from a closed-shell structure. In the latter cases we obtain an approximate description by a modified Hartree-Fock equation involving a "Coulomb hole" and a static screened potential in the exchange term. As an example, spectra of some atoms are discussed. To investigate the convergence of successive approximations for the Green's function, extensive calculations have been made for the electron gas at a range of metallic densities. The results are expressed in terms of quasiparticle energies E(k) and quasiparticle interactions f(k, k′). The very first approximation gives a good value for the magnitude of E(k). To estimate the derivative of E(k) we need both the first- and the second-order terms. The derivative, and thus the specific heat, is found to differ from the free-particle value by only a few percent. Our correction to the specific heat keeps the same sign down to the lowest alkali-metal densities, and is smaller than those obtained recently by Silverstein and by Rice. Our results for the paramagnetic susceptibility are unreliable in the alkali-metal-density region owing to poor convergence of the expansion for f. Besides the proof of a modified Luttinger-Ward-Klein variational principle and a related self-consistency idea, there is not much new in principle in this paper. The emphasis is on the development of a numerically manageable approximation scheme. (Less)

Time-frequency distributions-a review

Abstract: A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented. The objective of the field is to describe how the spectral content of a signal changes in time and to develop the physical and mathematical ideas needed to understand what a time-varying spectrum is. The basic gal is to devise a distribution that represents the energy or intensity of a signal simultaneously in time and frequency. Although the basic notions have been developing steadily over the last 40 years, there have recently been significant advances. This review is intended to be understandable to the nonspecialist with emphasis on the diversity of concepts and motivations that have gone into the formation of the field. >

A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions

Abstract: On the basis of the model of the water molecule derived from spectral and x-ray data and a proposed internal structure for water, the following properties of water and ionic solutions have been deduced quantitatively in good agreement with experiment. (1) The crystal structure of ice. (2) The x-ray diffraction curve for water. (3) The total energy of water and ice. (4) The degree of hydration of positive and negative ions in water. (5) The heat of solutions of ions. (6) The mobility of hydrogen and hydroxyl ions in water. And the following inferred in a qualitative way. (7) The density and density changes of water. (8) The explanation of the unique position of water among molecular liquids. (9) The dielectric properties of water and ice. (10) The viscosities of dilute ionic solutions. (11) The viscosities of concentrated acids.

Conformation of Polypeptides and Proteins

Abstract: Publisher Summary This chapter deals with the recent developments regarding the description and nature of the conformation of proteins and polypeptides with special reference to the stereochemical aspects of the problem. This chapter considers the parameters that are required for an adequate description of a polypeptide chain. This chapter focuses the attention on what may be called “internal parameters”—that is, those which can be defined in terms of the relationships among atoms or units that form the building blocks of the polypeptide chains. This chapter also provides an account of the mathematical method of utilizing these parameters for calculating the coordinates of all the atoms in a suitable frame of reference, so that all the interatomic distances, and bond angles, can be calculated and their consequences worked out. This chapter observes conformations in amino acids, peptides, polypeptides, and proteins.