First principles study on the charge density and the bulk modulus of the transition metals and their carbides and nitrides

A first principles study of the electronic properties and bulk modulus （B0） of the fcc and bcc transition metals, transition metal carbides and nitrides is presented. The calculations were performed by plane-wave pseudopotential method in the framework of the density functional theory with local density approximation. The density of states and the valence charge densities of these solids are plotted. The results show that B0 does not vary monotonically when the number of the valence d electrons increases. B0 reaches a maximum and then decreases for each of the four sorts of solids. It is related to the occupation of the bonding and anti-bonding states in the solid. The value of the valence charge density at the midpoint between the two nearest metal atoms tends to be proportional to B0.     

Λ and the Heisenberg Principle

A time dependent “cosmological constant” Λ(t) is conjectured, in terms of the Gaussian curvature of the causal horizon. It is nonvanishing even in Minkowski space because of the lack of informations beyond the light cone. Using the Heisenberg Principle, the corresponding energy of the quantum fluctuations localized on the past or future null horizons is proportional to Λ^1/2. We compute Λ(t) for the (Lorenzian version) of the (conformally flat) Hawking wormhole geometry (written in static spherical Rindler coordinates) and for the de Sitter spacetime. A possible explanation of the Hawking temperature is proposed, in terms of a constant Λ.     

Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox

The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of the so-called “quantum liar paradox,” an experimental set-up alleged to be problematic for a spacetime conception of reality, and conclude by speculating on RBW’s implications for quantum gravity.     

The relation between the generalised Eshelby integral and the generalised BCS and DB models

The generalised BCS dislocation group model and the generalised DB atomic cohesive force zone model have obtained the same results on nonlinear fracture study of some one-,two-and three-dimensional quasicrystals.This work reveals some inherent connection between the two models,and finds that their common basis is the generalised Eshelby integral based on the generalised Eshelby energy-momentum tensor for quasicrystals.Further applications of the theory in solving nonlinear fracture problems of the materials are also discussed.     

On the Scattering of the Electron off the Hydrogen Atom and the Helium Ion Below and Above the Ionization Threshold: Temkin–Poet Model

We generalize here the splitting approach to the long range (Coulomb) interaction for the three body scattering problem. With this approach, the exterior complex rotation technique can be applied for systems with asymptotic Coulomb interaction. We illustrate the method with calculations of the electron scattering on the hydrogen atom and positive helium ion in the frame of the Temkin–Poet model.     

Effect of the free surface and the rigid plane on structural vibration and acoustic radiation

The coupled fluid-structure interaction equation is estabhshed for bodies in the half-space fluid domain, especially sitting on the infinite plane, based on the BEM (Boundary Element Method) theory. Then, the natural frequencies, vibration responses and the acoustic radiation for a box are calculated, and the effect of the free surface and the rigid plane is discussed. Finally, several relative factors including the plate thickness, the structure damping and the distance between the body and the infinite plane are studied. The results show that the effect of the free surface and the rigid plane on the structural natural frequencies, vibration responses and the acoustic radiation cannot be ignored.     

Hyperbolic Structures and the Stickiness Effect

The stickiness effect of invariant tori in the phase space is widely studied,and extended to the slow-down of orbital diffusion due to some other invariant sets,such as Cantori,island-chains and hyperbolic periodic orbits.We report on two models in which hyperbolic periodic orbits show the stickiness effect.We discuss the generalized stickiness effects caused by different invariant sets.We believe that the main cause of the generalized stickiness effects is the hyperbolic structures in the phase space of the dynamical systems.     

Correlation Between the IR Transmission Spectra and the CdZnTe Qualities

Tens of Cd0.9Zn0.1Te wafers from three ingots grown by the vertical Bridgman method (VBM) are characterized by infrared (IR) transmission. Four types of distinct IR transmission spectra are found for these wafers. Each of them corresponds to one kind of wafers with specified quaJities. At the same time, approximate mathematical relations exist between the wafer dislocation density and their IR transmissions at the wavenumber 4000cm^-1, as well as between the resistivity and the IR transmissions at the wavenumber 500cm^-1. The reasons of the above results are attempted to be given.     

The triple-α process and the origin of the elements

The triple-α process is the nuclear fusion of helium to carbon. Two ⁴He nuclei collide and form an unstable state of ⁸Be. Before this can decay back a third α-particle collides with it to form a ¹²C nucleus. The reaction rate is probably the most temperature sensitive known to physics because there is a resonant state of the ¹²C nucleus at just the energy of the ⁸Be? and the ⁴He that have the greatest chance of penetrating the Coulomb barrier. The reaction takes place in stars that have exhausted their central hydrogen fuel. Most interesting are the asymptotic giants that can dredge the carbon produced to the surface and return it, perhaps first processing it to nitrogen, to the interstellar medium. The fortuitous energy of the resonant state of ¹²C and its consequences are crucial to the way stars evolve and the abundance of carbon on the Earth.     

Shock wave polarizations and optical metrics in the Born and the Born–Infeld electrodynamics

We analyze the behavior of shock waves in nonlinear theories of electrodynamics. For this, by use of generalized Hadamard step functions of increasing order, the electromagnetic potential is developed in a series expansion near the shock wave front. This brings about a corresponding expansion of the respective electromagnetic field equations which allows for deriving relations that determine the jump coefficients in the expansion series of the potential. We compute the components of a suitable gauge-normalized version of the jump coefficients given for a prescribed tetrad compatible with the shock front foliation. The solution of the first-order jump relations shows that, in contrast to linear Maxwell’s electrodynamics, in general the propagation of shock waves in nonlinear theories is governed by optical metrics and polarization conditions describing the propagation of two differently polarized waves (leading to a possible appearance of birefringence). In detail, shock waves are analyzed in the Born and Born–Infeld theories verifying that the Born–Infeld model exhibits no birefringence and the Born model does. The obtained results are compared to those ones found in literature. New results for the polarization of the two different waves are derived for Born-type electrodynamics.     

Effective action and vacuum instability in the chiral σ-model and the standard electroweak model

We develop a partial expansion of the effective action from fermion integration relevant for spatially small configurations of the meson fields in the chiral σ-model. It is shown that this leads (in this semiclassical approximation) to a vacuum instability. For weak Yukawa coupling, when the semiclassical calculation is valid, this would indicate an instability of the Weinberg-Salam model, implying that the latter is only an effective theory. We give an estimate of the approximate length scale at which this occurs.     

On the Schrödinger equation and the eigenvalue problem

If _k is thek ^th eigenvalue for the Dirichlet boundary problem on a bounded domain in ⁿ , H. Weyl's asymptotic formula asserts that , hence . We prove that for any domain and for all . A simple proof for the upper bound of the number of eigenvalues less than or equal to - for the operator –V(x) defined on ⁿ (n3) in terms of is also provided.Research partially supported by a Sloan Fellowship and NSF Grant No. 81-07911-A1     

On the polynomial τ-functions for the KP hierarchy and the bispectral property

We show that the -functions obtained from Schur polynomials lead to wave functions w(x ₁, x ₂, ... ; k) that possess the following bispectral property: There exists a differential operator B{k,_k}, independent of x ₁ , such that B{k,_k}w = {x ₁}w, where {x ₁} is independent of k. This extends for the KP hierarchy some earlier results of J. J. Duistermaat and F. A. Grünbaum for the rational solutions of KdV and of P. Wright for certain rational solutions of the generalized KdV equations.     

Vibrations of Au?? and FeAu?? nanoparticles and the limits of the Debye temperature concept

We present first-principles calculations of the vibrational density of states (VDOS), the specific heat and the mean-squared displacement of the five lowest-energy isomers of Au(13) and of two low-energy FeAu(12) nanoparticles. We find that the vibrational contributions to the Helmholtz energy do not affect the energy ordering of the isomers. As expected, for nanoparticles the vibrational density of states differs dramatically from the function proposed by the Debye model. We demonstrate that, for the nanoclusters we studied, the alternative calculations of the 'Debye temperature' yield significantly inconsistent results. We conclude that T(D) obtained from a particular thermodynamic property is neither applicable for deriving conclusions about other thermodynamic properties nor correlated with atomic bond strengths. Instead, in order to describe the temperature dependence of a nanoparticle's mean-squared displacement and its specific-heat capacity, what is necessary is its discrete phonon spectrum.     

Design and Construction of a Three-Color Gold–Copper-Vapor Laser and the Output-Power Dependence on the Frequency and Buffer-gas Pressure

We design and construct a three-color gold–copper-vapor laser emitting green (510.6 nm), yellow (578.2 nm), and red (627.8 nm) light. The maximum measured total average output power is 12 W under sealed-off conditions. We divide the active medium into three zones (two at both ends for copper and the central zone for gold) in order to vaporize both gold and copper simultaneously. For this purpose, we use a single type of thermal insulator to change the temperature along the medium by varying its thickness, which is the main point in our design. In addition, we carry out some experiments to distinguish the dependence of the output power on the frequency and buffer-gas pressure; the measured ratio of these three wavelengths, green : yellow: red, is 22 : 10 : 7.     

Weak Ferromagnetism along the Triad Axis and the Basal Anisotropy Caused by the Dzyaloshinskii–Moriya Interaction and the Cubic Electric Field of the FeBO3 Crystal

Journal of Experimental and Theoretical Physics - Based on the spin Hamiltonian and taking into account the cubic invariant of the crystal field and the Dzyaloshinskii–Moriya interaction, the...     

The conversion width of the σ- and ξ-hyperons in nuclei and the one-meson exchange

The conversion width in nuclear matter for and is estimated in the frame of one-mesonexchange model (OMEM). There is a considerable reduction of the width for if additional mesons besides are taken into account. The expected width for is about 3 MeV.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.