Higher-order <Emphasis Type="Bold">?</Emphasis> corrections in the semiclassical quantization of chaotic billiards

In the periodic orbit quantization of physical systems, usually only the leading-order ? contribution to the density of states is considered. Therefore, by construction, the eigenvalues following from semiclassical trace formulae generally agree with the exact quantum ones only to lowest order of ?. In different theoretical work the trace formulae have been extended to higher orders of ?. The problem remains, however, how to actually calculate eigenvalues from the extended trace formulae since, even with ? corrections included, the periodic orbit sums still do not converge in the physical domain. For lowest-order semiclassical trace formulae the convergence problem can be elegantly, and universally, circumvented by application of the technique of harmonic inversion. In this paper we show how, for general scaling chaotic systems, also higher-order ? corrections to the Gutzwiller formula can be included in the harmonic inversion scheme, and demonstrate that corrected semiclassical eigenvalues can be calculated despite the convergence problem. The method is applied to the open three-disk scattering system, as a prototype of a chaotic system. Received 10 September 2001 and Received in final form 3 January 2002     

Prospects for new physics observations in diffractive processes at the LHC and Tevatron

We study the double-diffractive production of various heavy systems (e.g. Higgs, dijet, and SUSY particles) at LHC and Tevatron collider energies. In each case we compute the probability that the rapidity gaps, which occur on either side of the produced system, survive the effects of soft rescattering and QCD bremsstrahlung effects. We calculate both the luminosity for different production mechanisms, and a wide variety of subprocess cross sections. The results allow numerical predictions to be readily made for the cross sections of all these processes at the LHC and the Tevatron collider. For example, we predict that the cross section for the exclusive double-diffractive production of a 120 GeV Higgs boson at the LHC is about 3 fb, and that the QCD background in the decay mode is about 4 times smaller than the Higgs signal if the experimental missing-mass resolution is 1 GeV. For completeness we also discuss production via or WW fusion. Received: 7 November 2001 / Revised version: 11 December 2001 / Published online: 25 January 2002     

Diffractive heavy vector meson production from the BFKL equation

Diffractive heavy vector meson photoproduction accompanied by proton dissociation is studied for arbitrary momentum transfer. The process is described by the non-forward BFKL equation, for which a complete analytical solution is found, giving the scattering amplitude. The impact of non-leading corrections to the BFKL equation is also analysed. Results are compared to the HERA data on production. Received: 2 July 2002 / Revised version: 29 August 2002 / Published online: 18 October 2002     

Effect of amorphization on the electronic and lattice specific heat of an Ni2B alloy

The specific heats of the Ni₂B amorphous system and of its crystal analog were studied in the temperature range 3–270 K. The data obtained permitted us to isolate the contribution due to atomic vibrations from the experimentally measured specific heat, determine the electronic density of states at the Fermi level and the temperature dependence of the characteristic Debye parameter Θ, and to calculate some average frequencies (moments) of the vibrational spectrum. The electronic density of states at the Fermi level increases under amorphization. An analysis of the temperature dependence of the lattice specific heat showed that amorphization brings about a substantial growth in the density of vibrational states at low frequencies, whereas the spectrum-averaged and rms frequencies change very little, which is in good agreement with neutron diffraction measurements.     

Study of the Surface Processes in Vapor-Phase Epitaxial GaAs: Asymmetric Trapping of Atoms at the Step

Experimental proofs of asymmetric trapping of atoms at the growth step in vapor-phase epitaxy of gallium arsenide in the GaAs–AsCl₃–H₂ system are given. The data obtained confirm the important role of the surface diffusion mass transfer in the growth of epitaxial GaAs layers on vicinals in the neighborhood of (111)A. The effective diffusion length is estimated.     

Development of high-speed video cameras for Dynamic PIV

The most promising next generation Image Velocimtry (IV) is the high-speed Dynamic PIV. It requires the development of innovative high-speed video camera sensors. We started by specifying the required performance of these new sensors, for measurements in air and water flows. These criteria founded on the most recent developments in PIV algorithms and incorporate results from a large questionnaire survey of users of high-speed video cameras in Japan. The results suggest that the followings are required: (1) frame rate of 1,000,000 fps, (2) pixel count of 1,000,000 pixels, (3) frame storage capacity of 100–200 frames for tracing a single event and 10,000 frames for turbulent measurements, (4) gray levels of 4–8 bits for PTV; 12 bits for observation. Finally, we reviewed the state of the art of high-speed video-image sensors. Currently the standard parallel-readout sensors can operate at 1 Kfps with a pixel count of approximately 1 Kpixels. The In-situ Storage Image Sensor (ISIS) developed by the authors has recently achieved frame rates of 1 Mfps.     

Estimation of the parameters of a bivariate distribution of Gaussian random variables that cannot be observed simultaneously

A point estimator is proposed for certain numerical characteristics of a bivariate normal distribution with parameters that cannot be observed simultaneously. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 21–28, Perm, 1990.     

Fractional programming and characterization of some vertices of the feasible region

This paper considers a problem of nonlinear programming in which the objective function is the ratio of two linear functions and the constraints define a bounded and connected feasible region. Using a coordinate transformation, this problem is transformed into a simpler one, whose geometric interpretation is of particular significance. The transformation leads to a characterization of some special vertices of the feasible region from both the theoretical and operational points of view.     

Dirac-Hestenes spinor fields on Riemann-Cartan manifolds

In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the RCST), thereby being certain particular sections of a new bundle named the spin-Clifford bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to Geroch's theorem concerning the existence of spinor structures in a Lorentzian spacetime. We introduce also the covariant and algebraic Dirac spinor fields and compare these with DHSF, showing that all three kinds of spinor fields contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-Kähler spinor fields are of this type), showing that they cannot be used to describe fermionic fields. We develop a rigorous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle, CB) and of Dirac-Hestenes spinor fields. We show how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.     

A method of computing the gradient and the Hessian of the quality criterion in parametric optimization of continuous-discrete stochastic systems

We propose an effective method of numerical determination of the gradient vector and the Hessian matrix of a quadratic quality criterion in parametric optimization of continuous-discrete stochastic dynamic control systems based on the application of adjoint equations. Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 20–25.