International Journal of Modern Physics B

It is proposed to create materials with a desired refraction coefficient in a bounded domain D ⊂ ℝ³ by embedding many small balls with constant refraction coefficients into a given material. The number of small balls per unit volume around every point x ∈ D, i.e., their density distribution, is calculated, as well as the constant refraction coefficients in these balls. Embedding into D small balls with these refraction coefficients according to the calculated density distribution creates in D a material with a desired refraction coefficient.

This paper studies a type of single scroll attractor chaos system. Based on the research of Jiang et al. the global synchronization method is designed, and moreover, the author uses a combined synchronization of linear and nonlinear feedback, active control, single vector and unidirectional coupling synchronization three methods else, the problem of synchronization between same and different chaotic systems are realized by the four methods, respectively. The range of control function parameter is discussed according to the Routh–Hurwitz criterion and numerical simulations show the effectiveness of them.

Evolutionary graph theory (EGT) is recently proposed by Lieberman et al. in 2005. EGT is successful for explaining biological evolution and some social phenomena. It is extremely important to consider the time of fixation for EGT in many practical problems, including evolutionary theory and the evolution of cooperation. This study characterizes the time to asymptotically reach fixation.

The flows around a typical open cavity with a store are numerically simulated in this paper. A fully implicit unfactored method is employed in the solver of RANS equations, where the S-A turbulent model is implemented to calculate the turbulent eddy viscosity. The flow-induced oscillation of the free shear layer around the cavity lip is captured and analyzed. Comparisons for the different cases of the cavity flow are made. The calculated results show that the pressure fluctuation is pertinent to the different positions of the store inside the cavity. The power spectral density (PSD) of the pressure by fast Fourier transformations (FFT) is also displayed in the paper. For the Rossiter's oscillatory mode, the numerical results compare well with the experimental data.

For the quantized LC electric circuit, when taking the Joule thermal effect into account, we think that physical observables should be evaluated in the context of ensemble average. We then use the generalized Feynman–Hellmann theorem for ensemble average to calculate them, which seems convenient. Fluctuation of observables in various LC electric circuits in the presence of thermo bath growing with temperature is exhibited.

Considering the inhomogeneous exchange anisotropy, the nonlinear surface spin waves in a dipole-exchange ferromagnetic media will be investigated. The total free energy of a dipole-exchange ferromagnet (FM) is given, and then the Landau–Lifshitz equation and the boundary conditions for a weakly nonlinear case are derived. The linear and nonlinear dispersion relations for dipole-exchange spin waves are given in a weak nonlinear approximation. The nonlinear Schrödinger equation, for the spin-wave envelope amplitude, is derived and its solitonic solution is discussed.

The Bogolyubov model of liquid helium is considered. The validity of substituting a c-number for the k = 0 mode operator â₀ is established rigorously. The domain of stability of the Bogolyubov's Hamiltonian is found. We derive sufficient conditions which ensure an appearance of the Bose condensate in the model. For some temperatures and some positive values of the chemical potential, there is the gapless Bogolyubov spectrum of elementary excitations, leading to the proper microscopic interpretation of the superfluidity.

The properties of long wavelength optical phonons in mixed crystals AB_1-xC_x is discussed by a model similar to Modified Random Element Isodisplacement (MREI). Using this method we investigate the frequencies, the dielectric functions, and the reflectivity of several mixed crystals. It is found that this model can be applied to the one-mode behavior, the two-mode behavior, and that of the third category. So the model provides a possible way to understand the optical character of the ternary mixed crystal. Based on it, we can discuss other problems similar to electron–phonon interaction and so on.

This work analyzes the Abrikosov's idea that high temperature conductivity is based on resonant tunneling. A rectangular rod was considered and it was shown that high values of transparency coefficient can be produced in it. It is the consequence of the fact that electrons as well as phonons have energy gap within a rectangular rod.

With the help of symbolic computation, a generalized (2+1)-dimensional variable-coefficient Korteweg–de Vries equation is studied for its Painlevé integrability. Then, Hirota bilinear form is derived, from which the one- and two-solitary-wave solutions with the corresponding graphic illustration are presented. Furthermore, a bilinear auto-Bäcklund transformation is constructed and the nonlinear superposition formula and Lax pair are also obtained. Finally, the analytic solution in the Wronskian form is constructed and proved by direct substitution into the bilinear equation.

Current conduction mechanisms of atomic-layer deposited Al₂O₃ (13 nm) stacked on different thermal nitrided SiO₂ thicknesses (2, 4, and 6 nm) on n-type 4H-SiC have been systematically analyzed. It has been observed that the oxides were thermally stable at the investigated temperature range (25–140^°C). By using different conduction process models, such as Schottky emission, direct tunneling, Fowler–Nordheim tunneling, Poole–Frenkel emission, and space-charge limited conduction, which consists of three limited conduction processes, namely, Ohm's law, Child's law, and trap-filled limit, the conduction mechanisms of charge through the oxides have been evaluated. It has been found that the conduction mechanisms were not affected by the investigated temperature range. A relationship plot has been proposed among nitrided SiO₂ thickness, electric field, and conduction mechanisms.

Laser ablation has attracted special interest for the formation of thin films compared with other formation technique. A distinctive feature of laser ablation is that it allows high quality and stoichiometry of films of even very complex element material. In this presentation, laser ablation of AgInSe₂ chalcopyrite semiconductor will be discussed in which it is difficult to maintain stoichiometry by conventional method. High Quality AgInSe₂ (AIS) films were grown on Glass substrates by the ultra-high-vacuum pulsed laser deposition technique from the AIS target synthesized from high-purity materials. The X-ray diffraction studies of the films show that films are textured in (112) direction. The substrate temperature appears to influence the properties of films. Increase in substrate temperature results in a more ordered structure. Compositional analysis has been carried out by EDAX. It is observed that compositional stoichiometry is maintained to a greater extent by PLD technique than other traditional methods like thermal evaporation. The optical studies of the films show that the optical band gap is about 1.20 eV.

This article deals with the connection between a.m. the hydrogenic radial integrals in the theory of atomic spectra and new properties of Appell's function F₂(x, y) to the vicinity of the singular point (1, 1) and to the domain |x|+|y| < 1. In Tables 1–7 exact numerical values of these integrals are first given, i.e., actually for all Mendeleev's table. (Author has all values these of integrals for arbitrary nl-states of H-like atoms, k ≥ 0 and Z ≤ 137).

Nanocrystalline spinel Zn–Cu–Cr ferrites with Gd substitution were prepared by a rheological phase reaction method. By means of the Fourier transform infrared (FTIR) spectra, Raman spectra, and X-ray diffraction (XRD), the cubic spinel structure of samples had been confirmed. The magnetic parameters such as saturation magnetization, remanent magnetization and coercivity can be tailored by controlling the content of substituting Gd ions.

We have calculated the electrical resistivity of amorphous transition metals Fe and Ni by using the Diffraction model as proposed by Ziman. The electron–ion interaction is described by a local model pseudopotential, and the static structure factors are taken from the experiment. The d-band effect, a characteristic of the transition metals, is accounted for through the sp–d hybridization effect. Agreement of the calculated results with the available experimental data is found to be remarkably good for both systems.

In this paper, hierarchies of multi-component AKNS–Kaup–Newell equations are derived, including positive nonisospectral AKNS–Kaup–Newell hierarchy and negative nonisospectral AKNS–Kaup–Newell hierarchy. Moreover, new integrable couplings of the resulting AKNS–Kaup–Newell soliton hierarchies are constructed by enlarging the associated matrix spectral problem.

Using the effective-mass Hamiltonian for an arbitrary direction wurtzite semiconductor on the basis of k⋅p theory, we investigate the strain effects on the optical anisotropy in semi-polar and nonpolar GaN planes. The optical matrix elements are formulated for an arbitrary direction and calculated for the A- and R-planes. It is found that giant optical anisotropy appears in the A- and R-planes and the biaxial strain significantly changes the polarization properties.

Ag-doped La_0.7Ca_0.3MnO₃ (LCMO) films were prepared on silicon substrate by RF magnetron sputtering. The dependences of transport properties on annealing temperature were explored. It is shown that the resistivity of the samples decreases and the metal–insulator transition temperature shifts to higher temperature with the increase in annealing temperature. Two metal–insulator transition temperatures are presented in the R – T plots of Ag-doped LCMO films, which can be explained by the Ag¹⁺ substitution of La³⁺ to form La_1-xAg_xMnO₃ compound. Compared with LCMO thin films, Ag-doping can observably improve the T_M-I and decrease the resistivity of the samples.

In this work we present a semi-classical transfer matrix method to study one-dimensional modified quantum transverse-field Ising model. Both average magnetization per spin along the z-direction 〈σ^z〉 and along the x-direction 〈σ^x〉 are calculated in this picture. It is predicted that the t > 1 case is the corresponding effective ferromagnetic phase at sufficiently high H_z whereas t < 1 case is an effective paramagnetic phase . Consequently, it is concluded that t = H_z/K = 1, here H_z is the transverse field along the z-axis and K is the coupling strength, which corresponds to quantum ferromagnetic-paramagnetic phase transition. In other words, the same result of the sophisticated quantum field theoretical calculation is predicted unexpectedly in the naive semiclassical picture.

In the current stage, left-handed material (LHM) has aroused wide interest based on several basic prototypes such as metamaterials. In this work, we have theoretically investigated the possible existence of granular LHM by using the Bruggeman formalism. The Wiener bounds and the Hashin–Shtrikman bounds were invoked and some examples were represented. We had found that when the dissipations are increased adequately, the estimates of the Bruggeman formalism will lie within the two bounds rigorously, even if the two permittivities have real parts of opposite signs. Thus, one particulate LHM may be achieved by choosing the two component mediums with negative permittivity and negative permeability, respectively.