Molecular dynamics of 16000 Lennard-Jones particles

We report a molecular-dynamics simulation of very large two-dimensional Lennard-Jones systems (up to 16383 particles). The simulation was carried out on a special-purpose processor built by Bakker. The processor's principal features and possibilities are described. Preliminary results of measurements along the isochore $\text{?}{}^1\text{= 0.94}$ are presented.     

A general method to describe forgetting effect of memristors

Building suitable memristor models is essential when memristors are attractive to researchers and play a vital role in fields such as neuromorphic computing. The forgetting effect, which is usually used to mimic forgetting process of biological synapses, should be considered during the modeling process. Several models have been proposed to describe forgetting effect. However, they have some deficiencies in describing forgetting effect, such as boundary problems. In this paper, a general method is presented to resolve these problems. The method is suitable for models that employ an inner state to describe the change of resistance and use a window function to constrain the inner state (e.g., Chang's model, Chen's model, and Berdan's model). When the reason of forgetting effect is considered as dopant diffusion in previous models, the method determines the value of window function and the change rate of inner state according to the integrated result of dopant drift and dopant diffusion. Simulation results indicate that the issues of previous models are solved when the proposed method is applied in these models.     

Separation of variables in the two-point BBGKY equations

Under two particular closure conditions, the two-point BBGKY equation is shown to be separable into equations for one- point turbulent fluctuations, yielding, respectively, a linear equation anda nonlinear integro-differential equation of convolution type. Analogy with Schrödinger's equation is discussed.     

Time evolution and spectral concentration in quantum systems

Time dependence and spectral concentration in quantum systems are reviewed. A partitioning technique is presented based on retarded and advanced propagators. The associated fundamental time symmetry is conveniently formulated in correspondence with the classical notion of reversal of time and momenta. Symmetry breakings occur when a particular convolution product is broken up into past and future times.The separation of the time variable into two scales is discussed. Comparison with the wave and reaction operator formulation gives a reciprocal relationship between these times together with an emphasis of the role played by the associated spectral density. Examples are given from applications of Weyl's complex eigenvalue theory.     

Observation of selection rules and restricted valence band self convolution for the KVV Auger transition of alkali graphite intercalation compounds

The Auger spectrum of the KVV transition in alkali graphite intercalation compounds (AGIC's) gives unambiguous evidence that the electron states from the alkali metals in the valence band of the compound form a narrow structure in the KVV Auger spectrum which corresponds to the self convolution of these states and that they are not convoluted with the whole valence band. This observation shows that strong matrix element effects or selection rules for KVV Auger transitions have to be taken into account.     

Electron momentum distributions and binding energies for the valence orbitals of hydrogen bromide and hydrogen iodide

Electron binding energy spectra and momentum distributions have been obtained for the valence orbitals of HBr and HI using noncoplanar symmetric electron coincidence spectroscopy at 1200 eV. The weakly bonding inner valence ns orbitals, which have not been observed previously, have their spectroscopic (pole) strength severely split among a number of ion states. For HBr the strength of the “main” inner valence (ns) transition is 0.42±0.03 whereas for HI it is 0.37±0.04, in close agreement with the value observed for the valence s orbitals of the corresponding isoelectronic inert-gas atoms. The spectroscopic strength for the two outermost orbitals is found to be close to unity, in agreement with many-body Green's function calculations. The measured momentum distributions are compared with several spherically averaged MO momentum distributions, as well as (for HBr) with a Green's function calculation of the generalized overlap amplitude (GOA). The GOA momentum distributions are in excellent agreement with the HBr data, both in shape and relative magnitude. Not all of the MO momentum distributions are in reasonable agreement with the data. Comparison is also made with the calculated momentum distributions for Kr, Br, Xe and I.     

Slavnov-Taylor identities in Weinberg's renormalization scheme

Weinberg's renormalization scheme, although more cumbersome from the computational point of view, has a more immediate physical interpretation than 't Hooft's minimal renormalization scheme. It is expected to lead to smaller higher-order coefficients in a perturbative approach to QCD. However, it a priori violates the Slavnov-Taylor identities. A complete study of this problem is performed, both theoretically and for the practitioner's sake. The ambiguities in the choice of the tensorial basis of some of the QCD vertices, as well as the dependence in the gauge parameter are used for substantiating, eventually, the Slavnov-Taylor identities in this renormalization scheme.     

Layer iteration calculation of low-energy electron-diffraction by Beeby's multiple scattering method

The interlayer structural propagator in Beeby's multiple scattering method is transformed into a reciprocal space representation. Interlayer multiple scattering events can then be summed to convergence in a layer iteration scheme. LEED spectra calculations for general angles of Ni (001) using 8 phase shifts and up to 49 Bloch waves are reported. A 3–5 eV shift in peak positions is found between calculations using 5 and 8 phase shifts, resolving a recent controversy over different inner potential values used for Ni (001).     

Valence band state densities of tetrahedrally coordinated amorphous semiconductors

A novel technique, for obtaining the valence band state densities (VBSD's) of tetrahedrally coordinated amorphous semiconductors from normal incidence reflectance data, is applied to Si and Ge and GaP, GaAs and GaSb. The VBSD's of Si and Ge are similar to other published results, obtained by conventional techniques, and cannot be described by broadened crystalline VBSD's. On the other hand, the VBSD's of the 3–5's contain many of the crystalline features. The relation of these results to the structure of the amorphous phase is discussed.     

Relativistic Boltzmann theory for a plasma: II. Reciprocal relations

The linear or phenomenological laws such as Ohm's law, Fourier's law and Fick's law are derived for a relativistic plasma in an electromagnetic field. It is shown that the choice of a reference frame as proposed by Landau and Lifshitz entails-in contrast to, for instance, the choice of Eckart-the validity of Onsager's reciprocity relations.     

Field-theoretic approach to the properties of the solid state

The techniques of quantum field theory are used to investigate the thermodynamic ion displacement correlation function—or Green's function of the phonon field—in a crystal and especially in a metal. The structure of thermodynamic Green's functions is outlined and the method for solving for them at finite temperature is fully discussed.The analytic structure of the phonon Green's function is then considered. This function is shown to be bounded and invertible everywhere off the real axis; a spectral form is derived for its inverse. The symmetries imposed by the point group of the crystal are then discussed.Assuming small ionic oscillations, we find the inverse of the phonon Green's function as a linear function of the electronic contribution to the dielectric response function of the metal. This dielectric function is shown to be simply related to the longitudinal part of the conductivity tensor that gives the response of the electrons to the effective electric field in the metal. The assumption of translational invariance then leads to an explicit expression for the phonon Green's function in terms of this conductivity.The deformations in the lattice induced by an arbitrarily time varying external force are calculated in terms of the retarded phonon Green's function. In the static long wavelength limit the phonon Green's function yields the macroscopic elastic constants of the crystal. Their relation to the conductivity is exhibited, and several elastic constants are estimated. We also see that the complete phonon spectrum and the lifetimes of the phonon states may be calculated from this Green's function. A relation between the long wavelength acoustic attenuation in metals and the de conductivity is derived, which is in good agreement with recent experiments. Furthermore, the ions in a metal are shown to have a high-frequency oscillation along with the electrons, at essentially the electron plasma frequency.     

Adjustability as a requirement of ideal clocks

A coordinate frame is considered as an arrangement of clocks that meet certain criteria of synchronization. Einstein's ideal clock is compared with the behavior required for clocks to maintain synchrony in the group of coordinate frames that leaves Maxwell's equations invariant. The required clock rates differ from the rate of Einstein's clock. An ideal adjustable clock is defined as an Einstein clock augmented by variable “gearing” that can offset its rate. Ongoing adjustment of these clocks enables them to meet all synchronization criteria in the group of coordinate frames. The need for adjustment is due to the well known invariance of Maxwell's equations under a group of coordinate transformations larger than the Lorentz group, and has nothing to do with imperfections in clocks. It is shown that the adjustments needed by ideal adjustable clocks to maintain synchrony can be measurably separated from additional adjustments that may be needed to compensate for random imperfections. The necessity for adjustment brings with it the necessity for ongoing measurement of the light signals whose exchange defines synchronization. Implications are discussed, both for the interpretation of Maxwell's equations and for the role of measuring instruments.     

Canonical forms for quadratic Hamiltonians

Our analysis of the applicable representations of the group of Bogoliubov transformations shows that the diagonalization of a quadratic fermion Hamiltonian with arbitrary complex coefficients is equivalent to the reduction of a skew symmetric matrix to secondary diagonal form by an orthogonal transformation, which we construct explicitly.Similarly, the diagonalization of a positive definite boson Hamiltonian with complex coefficients is equivalent to Whittaker's diagonalization of a symmetric matrix by a symplectic transformatio. Both results are shown to follow from a general spectral theorem for indefinite inner product space, a recent extension of which allows us to block diagonalize a positive definite quadratic boson Hamiltonian with complex coefficients and infinite degrees of freedom and thereby provide a counterpart to Araki's result for Fermi fields.     

Green's functions for gravitational multi-instantons

The Green's functions for scalar fields propagating on the self-dual gravitational multi-instantons and multi-Taub-NUT metrics are given explicitly in closed form. The special cases for flat space, Taub-NUT and the Eguchi-Hanson instanton are listed. A construction is described for obtaining the Green's functions for fields of arbitrary spin.     

Ultrasonic waves in porous ceramics with non-spherical holes

Formulae describing the effective elastic moduli of a porous ceramic medium are derived using Eshelby's solution and Maxwell's approximation. The ceramic medium is considered as an infinite matrix, which has uniform elastic properties and encloses non-spherical pores. A numerical evaluation of the velocity of an ultrasonic wave in the ceramic, as function of the porosity and pore shape, is presented. The theoretical results were combined with those obtained experimentally for different firing temperatures of the ceramic.     

A sector finite element for dynamic analysis of thick plates

A 24 degree of freedom sector finite element is developed for the static and dynamic analysis of thick circular plates. The element formulation is based on Reissner's thick plate theory. The convergence characteristic of the elements is first studied in a static example of an unsymmetrically loaded annular plate. The obvious advantageous effect of including the twist derivatives of deflection as degrees of freedom is shown. The elements are then used to analyze the natural frequencies of an annular plate with various ratios of inner to outer radius. The results are in good agreement with an alternative solution in which thick plate theory is used. The versatility of this finite element is finally demonstrated by performing free vibration analysis of an example of clamped sector plates with various thicknesses and different sectorial angles.     

Calculation of the vertical ionization potentials of HCNO,HNCO, HOCN,and HN3 by perturbation corrections to Koopmans'Theorem

Vertical ionization potentials (VIP's) have been calculated for HCNO, HNCO, HOCN, and HN₃, using Rayleigh—Schrödinger perturbation theory (RSPT) to determine corrections to Koopmans' Theorem. The calculated VIP's are used to resolve discordances between previous assignments of the PE spectra of HCNO, HNCO, and HN₃. Very little is known about HOCN. The present work contains predicted VIP's for this molecule, which it is hoped will aid in its identification in the laboratory. A diagram is presented correlating the VIP's of the isoelectronic series N₂O, HN₃, HOCN, HNCO, HCNO, and CO₂. It is shown that the variation in the magnitudes of the VIP's associated with the ionization of π electrons, and in the splittings induced in these VIP's by deviations from a linear geometry, can be accounted for qualitatively using a simple Hückel model.     

Electronic spectra of carotenoids. Schiff's bases of carotenal and carotenones

Visible absorption bands of β-apo-8′-carotenal, citranaxanthin, and reticulataxanthin Schiff's bases are measured and analyzed in relation to the visual chromophore, retinal Schiff's base. The former shows a strong red shift of the absorption maxima upon protonation in ethanol, and the magnitude of the band shift is comparable to that of retinal Schiff's base. Molecular orbital analysis of the ground and excited state electronic structures of both types of Schiff's bases suggests the usefulness of carotenal Schiff's bases as a model for comparative studies with visual chromophore.     

Simulation of pressure pulsations in the breathing circuit of a deep-sea diving system by using the four-pole method

A method for calculating pressure pulsations in compressor and engine manifolds known as the “four-pole method” is applied to the breathing circuit of a deep-sea diving system. The response of the diver's helmet to the input of two banks of compressors is formulated. A computer is used to solve the response equation and generate the sound pressure level spectrum in the helmet. Results are shown to be in good agreement with experimental data. The computer simulation is used to examine the effects of such parameters as diver's depth, breathing gas flow rate, cylinder bank phasing and system geometry.