Fractional Pais–Uhlenbeck Oscillator

In this paper we study the fractional Lagrangian of Pais–Uhlenbeck oscillator. We obtained the fractional Euler–Lagrangian equation of the system and then we studied the obtained Euler–Lagrangian equation numerically. The numerical study is based on the so-called Grünwald–Letnikov approach, which is power series expansion of the generating function (backward and forward difference) and it can be easy derived from the Grünwald–Letnikov definition of the fractional derivative. This approach is based on the fact, that Riemman–Liouville fractional derivative is equivalent to the Grünwald–Letnikov derivative for a wide class of the functions.     

An analytic perturbation approach for classical spinning particle dynamics

A perturbation method to analytically describe the dynamics of a classical spinning particle, based on the Mathisson–Papapetrou–Dixon (MPD) equations of motion, is presented. By a power series expansion with respect to the particle’s spin magnitude, it is shown how to obtain in general form an analytic representation of the particle’s kinematic and dynamical degrees of freedom that is formally applicable to infinite order in the expansion. Within this formalism, it is possible to identify a classical analogue of radiative corrections to the particle’s mass and spin due to spin–gravity interaction. The robustness of this approach is demonstrated by showing how to explicitly compute the first-order momentum and spin tensor components for arbitrary particle motion in a general space–time background. Potentially interesting applications based on this perturbation approach are outlined.     

Monochromatic,Cicularly Polarized Resonant Radiation in the Investigation of Magnetic Materials

Monochromatic, circularly polarized radiation brings useful information on orientations of hyperfine fields in investigation of magnetic materials. This information can be extracted even from poorly resolved spectra by a model free method. In particular, the z-component of the average hyperfine magnetic field is given simply by a “center of gravity” of the difference between the spectra measured with two opposite polarizations. The efficiency of such an approach is demonstrated on the example of the ⁵⁷Fe h.m.f. in bcc Cr–Fe–Mn alloys. This revised version was published online in September 2006 with corrections to the Cover Date.     

Effect of the Nucleon-Density Distribution on the Description of Nuclear Decay

It is proposed to test the parameters used in a self-consistent analysis of the nucleon distribution in nuclei via the calculation of the nucleus–nucleus potential, which is necessary for describing nuclear decays. The nucleon distribution is shown to correlate with the parameters of the nucleon–nucleon interaction. A unified approach to calculating characteristic alpha-decay and spontaneous-fission times is developed on the basis of the dinuclear-system model.     

Unrestricted symmetry-projected Hartree-Fock-Bogoliubov calculations for some PF-shell nuclei

Total binding energies and yrast energy spectra of three selected 1p0f–nuclei have been calculated using an unrestricted Hartree–Fock–Bogoliubov approach with symmetry–projection before the variation. The full 1p0f–shell has been used as single–particle basis and the semi–empirical FPD6 interaction as effective Hamiltonian. The results are compared to those of truncated shell–model calculations performed with the OXBASH code. In the middle of the 1p0f–shell the variational method yields energy gains up to 4.5 MeV and thus proves to be far superior than the conventional truncation methods at least if in the latter only up to about 13000 configurations for each spin–isospin combination are admitted. Received: 15 September 1999     

Calculation of open p-shell atoms in the algebraic approach of the Hartree–Fock method

Highly precise calculations of analytical Hartree–Fock orbitals and energies have been performed within the limits of the Roothaan–Hartree–Fock atomic theory (Roothaan–Bagus method) for all open p-shell atoms of the Periodic Table. They were calculated in an algebraic approach using Slater-type atomic orbitals (AOs) as basis functions. Nonlinear parameters (orbital exponents) of AOs were optimized with exceptional accuracy by second-order methods. As a result, it was possible to satisfy exactly the virial relation (10^–14–10^–17) with calculated atomic term energies being close to the Hartree–Fock limit.     

Existence of Static BPS Monopoles and Dyons in Arbitrary (4p – 1)-Dimensional Spaces

We prove the existence and uniqueness of a static and radially symmetric BPS monopole of unit topological charge in an arbitrary (4p – 1)-dimensional space descended from the generalized Yang–Mills theory in 4p dimensions and formulated and presented in a recent study of Radu and Tchrakian. This monopole solution also gives rise to an electrically and magnetically charged soliton, called dyon, in the same spacetime setting through the well-known Julia–Zee correspondence. Our method is based on a dynamical shooting approach depending on two shooting parameters which provides an effective framework for constructing the BPS monopole and dyon solutions in general dimensions.     

Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations

There are two distinct approaches to the study of initial value problem of the periodic box-ball systems. One way is the rigged configuration approach due to Kuniba–Takagi–Takenouchi and another way is the 10-elimination approach due to Mada–Idzumi–Tokihiro. In this paper, we describe precisely interrelations between these two approaches.      

Self-association of the molecules of alcohols in a condensed phase at different temperatures

Using a probability approach, we investigate the process of self-association of the molecules of alcohols in a condensed phase. We obtained data on the nature of association, in particular, on the association degree distribution of molecules and concerning the dependence of the form of this distribution on temperature. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 4, pp. 497–503, July–August, 1998.     

Using the coordinates of the mass centers of atomic groups in analyzing vibrations of large molecules

We show that in describing the vibrations of molecules it is worthwhile to use coordinates that include the mass centers of atomic groups. We note special features of the program implementation of the approach in application to the earlier devised set of “Spectrum-structure” and LEV programs. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 1, pp. 42–47, January–February, 2000.     

An alternative to the horizontality condition in the superfield approach to BRST symmetries

We provide an alternative to the gauge covariant horizontality condition, which is responsible for the derivation of the nilpotent (anti-) BRST symmetry transformations for the gauge and (anti-) ghost fields of a (3+1)-dimensional (4D) interacting 1-form non-Abelian gauge theory in the framework of the usual superfield approach to the Becchi–Rouet–Stora–Tyutin (BRST) formalism. The above covariant horizontality condition is replaced by a gauge invariant restriction on the (4,2)-dimensional supermanifold, parameterised by a set of four spacetime coordinates, x^μ(μ=0,1,2,3), and a pair of Grassmannian variables, θ and θ̄. The latter condition enables us to derive the nilpotent (anti-) BRST symmetry transformations for all the fields of an interacting 1-form 4D non-Abelian gauge theory in which there is an explicit coupling between the gauge field and the Dirac fields. The key differences and the striking similarities between the above two conditions are pointed out clearly. PACS 11.15.-q; 12.20.-m; 03.70.+k     

Calculation of the IR spectrum of (22S,23S)-24-epicastasterone

Normal vibrational frequencies and absolute IR band intensities for the biologically active steroidal phytohormone (22S,23S)-24-epicastasterone have been calculated within the framework of an original combined approach that uses classical normal coordinate analysis by means of the molecular mechanics method coupled with the quantum-chemical estimation of absolute intensities. Absorption bands in the IR spectrum of this molecule in the region 1500-900 cm⁻¹ were first interpreted based on a comparison of the experimental IR spectrum with the calculated optical-density spectral curve. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 6, pp. 768–775, November–December, 2008.     

On the current-voltage characteristic of a tunnel metal-semiconductor Schottky-Barrier contact

A possibility of a more simple and exact representation of the current-voltage (I–V) characteristic of a tunnel metal-semiconductor contact is investigated. Analysis is made on the basis of the approach proposed earlier, according to which the behaviour of the (I–V) characteristics of the Schottky-barrier contacts at low temperatures depends on the nonlinear dependence of the true (or effective for a tunnel contact) barrier height on the bias voltage. A simple equation for the (I–V) characteristic of the tunnel contact is theoretically substantiated using measurable parameters-the ideality factor n and barrier height ϕ_bm where the quantity ϕ_bn ≡ nϕ_bm plays the role of a barrier height. The calculation shows that this quantity is very close to the true barrier height of the tunnel contact (with allowance for the effect of image force) in wide current, temperature, and impurity-concentration ranges. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 18–25, March, 2006.     

Boundary term in metric <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) gravity: field equations in the metric formalism

The main goal of this paper is to get in a straightforward form the field equations in metric f (R) gravity, using elementary variational principles and adding a boundary term in the action, instead of the usual treatment in an equivalent scalar–tensor approach. We start with a brief review of the Einstein–Hilbert action, together with the Gibbons–York–Hawking boundary term, which is mentioned in some literature, but is generally missing. Next we present in detail the field equations in metric f (R) gravity, including the discussion about boundaries, and we compare with the Gibbons–York–Hawking term in General Relativity. We notice that this boundary term is necessary in order to have a well defined extremal action principle under metric variation.     

Assessment of nanoparticle surface area by measuring unattached fraction of radon progeny

A number of studies on the exposure of nanometer aerosols have indicated that health effects associated with low-solubility inhaled particles in the range of 1–100 nm may be more appropriately associated with particulate surface area than mass concentration. Such data on correlation between number, surface area and mass concentration are needed for exposure investigations, but the means for measuring aerosol surface area are not readily available. In this paper we propose a method for particle surface area assessment based on a new approach, deposition of the “unattached fraction of radon progeny” onto nanometer aerosols. The proposed approach represents a synthesis of: (1) Derived direct analytical correlation between the “unattached fraction” of radon progeny and surface area particle concentration in the range of 1–100 nm particle diameter; (2) Experimental data on correlation between the unattached fraction of radon progeny and particle surface area for particles with diameter in the range of 44 nm–2.1 μm.     

IR spectroscopic study of the effect of polymer nanofilm thickness on its surface density

The effect of the thickness (in the range 50–10,000 nm) of free-standing (separated from substrate) polystyrene (PS) films on their surface density was investigated by FTIR spectroscopy. For this, an approach has been employed for the first time than consists of analyzing the distortions of the IR band shape caused by anomalous dispersion of the refractive index in the vicinities of these bands. It was found that the surface density of PS films is halved as the film thickness changes from 1500 to 150 nm. The fact that the density starts to decrease in the micron range of film thickness rather than in the submicron range may suggest that there are important factors not taken into account by existing theoretical models for thin and ultrathin polymer films. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 1, pp. 63–67, January–February, 2008.     

On the Unification of Geometric and Random Structures through Torsion Fields: Brownian Motions,Viscous and Magneto-fluid-dynamics

We present the unification of Riemann–Cartan–Weyl (RCW) space-time geometries and random generalized Brownian motions. These are metric compatible connections (albeit the metric can be trivially euclidean) which have a propagating trace-torsion 1-form, whose metric conjugate describes the average motion interaction term. Thus, the universality of torsion fields is proved through the universality of Brownian motions. We extend this approach to give a random symplectic theory on phase-space. We present as a case study of this approach, the invariant Navier–Stokes equations for viscous fluids, and the kinematic dynamo equation of magnetohydrodynamics. We give analytical random representations for these equations. We discuss briefly the relation between them and the Reynolds approach to turbulence. We discuss the role of the Cartan classical development method and the random extension of it as the method to generate these generalized Brownian motions, as well as the key to construct finite-dimensional almost everywhere smooth approximations of the random representations of these equations, the random symplectic theory, and the random Poincaré–Cartan invariants associated to it. We discuss the role of autoparallels of the RCW connections as providing polygonal smooth almost everywhere realizations of the random representations.     

A Monte Carlo and continuum study of mechanical properties of nanoparticle based films

A combination Monte Carlo and equivalent-continuum simulation approach was used to investigate the structure-mechanical property relationships of titania nanoparticle deposits. Films of titania composed of nanoparticle aggregates were simulated using a Monte Carlo approach with diffusion-limited aggregation. Each aggregate in the simulation is fractal-like and random in structure. In the film structure, it is assumed that bond strength is a function of distance with two limiting values for the bond strengths: one representing the strong chemical bond between the particles at closest proximity in the aggregate and the other representing the weak van der Waals bond between particles from different aggregates. The Young’s modulus of the film is estimated using an equivalent-continuum modeling approach, and the influences of particle diameter (5–100 nm) and aggregate size (3–400 particles per aggregate) on predicted Young’s modulus are investigated. The Young’s modulus is observed to increase with a decrease in primary particle size and is independent of the size of the aggregates deposited. Decreasing porosity resulted in an increase in Young’s modulus as expected from results reported previously in the literature.     

A Mathematical Theory for Vibrational Levels Associated with Hydrogen Bonds I: The Symmetric Case

We propose an alternative to the usual time–independentBorn–Oppenheimer approximation that is specifically designed todescribe molecules with symmetrical Hydrogen bonds. In our approach,the masses of the Hydrogen nuclei are scaled differently from thoseof the heavier nuclei, and we employ a specialized form for theelectron energy level surface. Consequently, anharmonic effects playa role in the leading order calculations of vibrational levels. Although we develop a general theory, our analysis is motivated byan examination of symmetric bihalide ions, such as FHF ⁻ orClHCl ⁻. We describe our approach for the FHF ⁻ ion in detail. Partially Supported by National Science Foundation Grants DMS–0303586 andDMS–0600944.