Band 8, Heft 4

Analytic wave functions and the corresponding energies for a class of the $$ \mathcal{P}\mathcal{T} $$-symmetric two-dimensional quartic potentials are found. The general form of the solutions is discussed.

In this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential andWeierstrass functions.

A simple modification of the definition of the S-matrix is proposed. It is expected that the divergences related to nonzero self-energies are considerably milder with the modified definition than with the usual one. This conjecture is verified in a few examples using perturbation theory. The proposed formula is written in terms of the total Hamiltonian operator and a free Hamiltonian operator and is therefore applicable in any case when these Hamiltonian operators are known.

New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.

The aim of this paper is to analyze the asymptotic behavior of the solution of a nonlinear problem arising in the modelling of thermal diffusion in a two-component composite material. We consider, at the microscale, a periodic structure formed by two materials with different thermal properties. We assume that we have nonlinear sources and that at the interface between the two materials the flux is continuous and depends in a dynamical nonlinear way on the jump of the temperature field. We shall be interested in describing the asymptotic behavior of the temperature field in the periodic composite as the small parameter which characterizes the sizes of our two regions tends to zero. We prove that the effective behavior of the solution of this system is governed by a new system, similar to Barenblatt’s model, with additional terms capturing the effect of the interfacial barrier, of the dynamical boundary condition, and of the nonlinear sources.

The one-dimensional path decomposition expression for the step potential and mass is formulated. The propagator is analytically determined and the limiting case m 1; m 2 → m is exactly obtained.

The continuous states of the l-wave Schrödinger equation for the diatomic molecule represented by the hyperbolical function potential are carried out by a proper approximation scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Schrödinger equation for the hyperbolical function potential are presented and the corresponding calculation formula of phase shifts is derived. Also, we interestingly obtain the corresponding bound state energy levels by analyzing analytical properties of scattering amplitude.

The two-photon decay widths of scalar mesons σ(600), f 0(980) and a 0(980) as well a 0 → ju(ω)γ and f 0 → ju(ω)γ are calculated in the framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/N c-approximation where N c is the number of colors) are taken into account. The values of these contributions, as we show, are of the same order of magnitude. For the f 0 decay the K-loop contribution plays the dominant role. The results for two-gamma decays are in satisfactory agreement with modern experimental data. The predictions for a 0 → ju(ω)γ and f 0 → ju(ω)γ widths are given.

A Variational Monte Carlo (VMC) method is employed to investigate the properties of symmetric and asymmetric nuclear matter. The realistic Urbana V 14 twonucleon interaction potential of Lagaris and Pandharipande was used to describe the microscopic interactions. Also, many body interactions are included as a density dependent term in the potential. Total kinetic and potential energies per particle are calculated for asymmetric nuclear matter by VMC method at various densities and isospin asymmetry parameters. The results are compared with data found in literature, and it was observed that the results obtained in this study reasonably agree with the results found in the literature. Also, the symmetry energy and incompressibility factor of the nuclear matter were obtained. The results obtained are in good agreement with those obtained by various authors with different methods and techniques.

For the first time discrete gamma-rays following the nuclear reaction 170Er(p,n)170Tm with enriched target were measured with a high resolution GeHP spectrometer. Protons delivered by the Bucharest FN Tandem Van de Graaff accelerator bombarded a thin self-supporting film of enriched erbium. Measured γ-ray energies (Eγ), their relative intensities (Iγ) and corresponding excitation functions for the beam energy range 2.0–3.6 MeV are reported in the present work. The measured excitation functions were fairly well reproduced by compound nucleus calculations based on the Hauser-Feshbach formalism.

A three-dimensional Lattice Boltzmann flow and scour model is developed to simulate time-dependent scour below a submarine pipeline. The proposed model presented in this paper is able to predict streamwise and spanwise propagations of scour with respect to lattice unit of time. It is evident from this study that the existence of a spiral vortex in the proximity of the span shoulder is quite noteworthy. It is revealed that the critical regime of the 2-D scour process is found to be up to one pipe diameter away in both directions from the middle of the unsupported length of pipelines. The equilibrium maximum scour depth and the shape of streamwise equilibrium scour hole compare well with the available experimental data. The speed of propagation of scour along the pipeline length maintains an almost constant rate, which is consistent with the experimental observations found in literature. In addition, it is seen that the scour slope at the shoulder region remains fairly constant throughout the whole scour process.

X-ray Diffraction (XRD), X-ray Photoelectron Spectroscopy (XPS), Transmission Electron Microscopy (TEM) and magnetic measurements as a function of applied magnetic field and temperature for In1−x MnxSb (0.05≤x≤0.2) system are reported. Magnetic measurements performed at high and small magnetic field in ZFC and FC indicate the coexistence of ferromagnetic In1−x MnxSb solid solution and two types of magnetic cluster: ferromagnetic MnSb and ferrimagnetic Mn2Sb. XPS valence band and Mn 2p core level spectra have confirmed the presence of MnSb and Mn2Sb phases. TEM images show some manganese antimonide phase microinclusions with dimension between (30–40) nm.

The structural, electronic and elastic properties of the cubic boron nitride (BN) compound are investigated by a first-principle pseudopotential method. The calculations show that the structural phase transition from the zinc-blende(ZB) structure to the rocksalt (RS) structure occurs at a transition pressure of 1088 GPa and with a volume reduction of 3.1%. Both the ZB and RS structures of BN have indirect gaps, with energy gaps of 4.80 eV and 2.11 eV, respectively. The positive pressure derivative of the indirect band gap (Γ-X) energy for the the ZB phase and the predicted ultrahigh metallization pressure are attributed to the absence of d occupations in the valence bands. The increase of the shear modulus with increasing pressure implies that the lattice stability becomes higher when BN is compressed.

We show that the front photoacoustic signal due to a sample consisting of a glass plate with a metal coated surface, at which thermal waves are generated by periodical light absorption, enhances for certain modulation frequencies when the other glass surface is covered with a liquid sample. This contradicts the intuitive expectation based on the assumption that the liquid provides a new channel for heat conduction thereby decreasing the substrate temperature. Experimental results are shown and the described effect is explained using a thermal wave interference model.

A polycrystalline sample, Ba3Sr2DyTi3V7O30, with tungsten bronze structure was prepared by a mixed-oxide method at high temperature (950°C). Preliminary structural analysis of the compound showed an orthorhombic crystal structure at room temperature. Surface morphology of the compound was studied by scanning electron microscopy. The dielectric anomaly at 321°C may be attributed to the ferro-paraelectric phase transitions. This was also confirmed from the appearance of a hysteresis loop. The nature of variation of the ac conductivity and value of activation energy at different temperature regions, suggest that the conduction process is of mixed-type (i.e., ionic-polaronic and space charge generated from the oxygen ion vacancies).

A new analytical, independent-particle model potential with four shell-independent parameters is proposed, which is suitable for high, medium, and low Z atoms. The four parameters are determined for 101 atoms from Li to Lr by fitting the results of the X a method found in the literature. The average fitting error 0.675% of the new potential for the 101 atoms is far better than 3.92% of the widely used Green’s potential. The radial Schrödinger equation with the new potential is solved by using Numerov’s numerical method for 7 typical atoms: Ne, Ca, Zn, Zr, Sn, Yb, and Th. The energy eigenvalues, radial wave functions, and atomic ground-state energy are in good agreement with the results of the X a method. The new potential here shows greater flexibility and better accuracy compared with the Green’s potential.

We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. We apply the Nikiforov-Uvarov method (which solves a second-order linear differential equation by reducing it to a generalized hypergeometric form) to spin- and pseudospin-symmetry to obtain, in closed form, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of two Dirac particles. The special cases κ = ±1 (s = $$ \tilde l $$ = 0, s-wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. We compare the non-relativistic results with those obtained by others.

The effects of ultralow-frequency or static magnetic and electric fields on biological processes is of huge interest for researchers due to the resonant change of the intensity of biochemical reactions, despite the energy in such fields being small in comparison with the characteristic energy k B T of the chemical reactions. In the present work, a simplified model to study the effects of weak static magnetic fields on fluctuations of the random ionic currents in blood is presented with a view to solving the k B T problem in magnetobiology. An analytic expression for the kinetic energy of the molecules dissolved in certain liquid media is obtained. The values of the magnetic field leading to resonant effects in capillaries are then estimated. The numerical estimates show that the resonant values of the energy of molecules in capillaries and the aorta are different. These estimates prove that under identical conditions, a molecule in the aorta gets 10−9 times less energy than the molecules in blood capillaries. Therefore, the capillaries are very sensitive to the resonant effect. As the magnetic field approaches the resonant value, the average energy of a molecule localized in a capillary is increased by several orders of magnitude as compared to its thermal energy. This amount of energy is sufficient to cause deterioration of certain chemical bonds.

Predicting genes likely to be involved in human diseases is an important task in bioinformatics field. Nowadays, the accumulation of human protein-protein interactions (PPIs) data provides us an unprecedented opportunity to gain insight into human diseases. In this paper, we adopt the topological similarity in human protein-protein interaction network to predict disease-related genes. As a computational algorithm to speed up the identification of disease-related genes, the topological similarity has substantial advantages over previous topology-based algorithms. First of all, it provides a global measurement of similarity between two vertices. Secondly, quantity which can measure new topological feature has been integrated into the notion of topological similarity. Our method is specially designed for predicting disease-related genes of single disease-gene family. The proposed method is applied to human protein-protein interaction and hepatocellular carcinoma (HCC) data. The results show a significant enrichment of disease-related genes that are characterized by higher topological similarity than other genes.

A ridge carbon beam filter for Spreading Out the Bragg Peak (SOBP) up to 20 mm in the targeted area has been designed and experimentally tested. The instrument was constructed of Plexiglas with a density of 1.165 g/cm3 and has a “teeth” structure with a period of 2.5 mm. The design is based on a simple analytical model and detailed GEANT4 Monte Carlo simulations. In-beam test measurements were performed with a 500-MeV/u 12C beam at the Nuclotron facility of the Joint Institute for Nuclear Research (JINR) in Dubna. The filter can be used as a static device positioned in front of patients undergoing carbon therapy.