International Journal of Modern Physics B

The polaron model in ionic crystal is studied in the N. Bogolubov representation using a special RPA-approximation. A new exactly solvable approximated polaron model is derived and described in detail. Its free energy at finite temperature is calculated analytically. The polaron free energy in the constant magnetic field at finite temperature is also discussed.

An isospectral problem is introduced, a spectral radius of the corresponding spectral matrix is obtained, which enlightens us to set up an isospectral problem whose compatibility condition gives rise to a zero curvature equation in formalism, from which a Lax integrable soliton equation hierarchy with constraints of potential functions is generated along with 5 parameters, whose reduced cases present three integrable systems, i.e., AKNS hierarchy, Levi hierarchy and D-AKNS hierarchy. Enlarging the above Lie algebra into two bigger ones, the two integrable couplings of the hierarchy are derived, one of them has Hamiltonian structure by employing the quadratic-form identity or variational identity. The corresponding integrable couplings of the reduced systems are obtained, respectively. Finally, as comparing study for generating expanding integrable systems, a Lie algebra of antisymmetric matrices and its corresponding loop algebra are constructed, from which a great number of enlarging integrable systems could be generated, especially their Hamiltonian structure could be computed by the trace identity.

Compositions with x=0.1, 0.2, 0.4, and 0.5 in the system (Pb_0.95Sr_0.05)·(Zr_0.53Ti_0.47)O₃+xwt%Cr₂O₃ (PSZTC) were synthesized using conventional ceramic method. Addition of Cr₂O₃ stabilized the tetragonal phase against the rhombohedral one. Scanning electron microscopy (SEM) showed a decrease of the mean grain size when increasing the doping level. The permittivity and electrical conductivities of the PSZTC compounds have been investigated and the activation energies were calculated.

We have investigated magnetization, magneto-transport, and complex impedance spectroscopy of structurally characterized multiferroic composites xLa_0.7Sr_0.3MnO₃ (LSMO)–(1-x)ErMnO₃ (EMO) (0≤x≤1). Para- to ferromagnetic Curie temperatures for this series of composites indicate almost complete immiscibility within the mixture of those two compounds of LSMO and EMO having nearly identical chemical formula. Magnetization as a function of magnetic field curves at T=300 K exhibit an appreciable enhancement of coercive field of LSMO in the composites with increase in EMO content. This feature has been attributed to the increasing grain boundary pinning center of LSMO grains at their interfaces in the composites. Magneto-transport measurements reveal a considerable decrease in spin polarized tunneling transport with increase in EMO content in the composites. This feature is understood as a consequence of increasing grain boundary pinning centers of magnetic domains of LSMO grains in the composites. Room temperature complex impedance spectroscopy studies, i.e., -Z^′′ versus Z′ curves (Nyquist plots) for EMO, x=0.1, x=0.2, and LSMO samples reveal that relaxation time of both bulk and grain boundary increases with increase in EMO content in the composites. Slow relaxation processes of conduction electrons at both bulk and grain boundary occurs due to the proximity of highly resistive insulating EMO in the composites.

In this paper, the lattice Boltzmann method is employed to simulate buoyancy-driven motion of a single bubble. First, an axisymmetric bubble motion under buoyancy force in an enclosed duct is investigated for some range of Eötvös number and a wide range of Archimedes and Morton numbers. Numerical results are compared with experimental data and theoretical predictions, and satisfactory agreement is shown. It is seen that increase of Eötvös or Archimedes number increases the rate of deformation of the bubble. At a high enough Archimedes value and low Morton numbers breakup of the bubble is observed. Then, a bubble rising and finally bursting at a free surface is simulated. It is seen that at higher Archimedes numbers the rise velocity of the bubble is greater and the center of the free interface rises further. On the other hand, at high Eötvös values the bubble deforms more and becomes more stretched in the radial direction, which in turn results in lower rise velocity and, hence, lower elevations for the center of the free surface.

To develop high-quality film device with good reliability, it is often essential to be able to evaluate the parameters such as stress, the biaxial elastic modulus, and coefficient of thermal expansion (CTE) of film. Based on the stress measurement in situ during the thermal cycle by laser scanning method, two techniques were used to measure the biaxial elastic modulus and CTE of BaTiO₃ films deposited on substrate. The value of the biaxial elastic modulus and CTE for BaTiO₃ films determined from two methods is close, in which the biaxial elastic modulus of BaTiO₃ films is higher than that of corresponding bulk while the CTE of BaTiO₃ films is a little smaller than that of bulk material.

We consider two types of motion, one with particle occupying only the sites on a given regular lattice and another when the bonds between neighboring lattice sites are displaced to the positions of the neighboring bonds. We refer to these models as site- and bond-diffusion. The latter is equivalent to site-diffusion on a lattice constructed from the middle points on each bond of the original lattice. The transition probability is assumed equal to all neighboring positions. The diffusion constant is obtained by periodic orbit theory for all Archimedean lattices, as well as some three-dimensional lattices (cubic, diamond, body centered cubic and face centered cubic lattice). Every single step of bond-motion is expressed through two site-motion steps. Analytic results for the diffusion constant for bond-diffusion for square, triangular and Kagomé lattice are also obtained. Kurtosis is calculated for site-diffusion on square and (4, 8²)-lattice, to estimate the deviation of the distribution of displacements from the Gaussian. All theoretical results are verified with numerical simulation.

Generally, fuzzy approximation models require some human knowledge and experience. Operator's experience is involved in the mathematics of fuzzy theory as a collection of heuristic rules. The main goal of this paper is to present a new method for identifying unknown nonlinear dynamics such as Rössler system without any human knowledge. Instead of heuristic rules, the presented method uses the input-output data pairs to identify the Rössler chaotic system. The training algorithm is a modified Levenberg-Marquardt (L-M) method, which can adjust the parameters of each linear polynomial and fuzzy membership functions on line, and do not rely on experts' experience excessively. Finally, it is applied to training Rössler chaotic system fuzzy identification. Comparing this method with the standard L-M method, the convergence speed is accelerated. The simulation results demonstrate the effectiveness of the proposed method.

A mean-field approximation is developed for a decorated ferrimagnetic Ising model, in which the two magnetic atoms A and B have spins σ=1/2 and S=1, respectively. In this system, the exchange interaction between nearest-neighbors of atom B is taken into account. Some interesting phenomena, such as the appearance of three types of phase diagrams and the existence of one and two compensation points are found. Phase diagrams and temperature dependence of the magnetizations of the system are investigated in detail.

We show that the electron–positron annihilation process ending with the creation of two gamma photons (with right- and left-hand circular helicity) can be explained in terms of the current loop model. We first show that both electron and positron (which are spin 1/2 particles) carry an intrinsic flux quantum of ±Φ₀/2 even in the absence of an external magnetic field. By using the conservation of the magnetic flux quanta for collisions, we then argue that photon also carries a magnetic flux quantum of ±Φ₀ = ±(hc/e) with itself along the propagation direction, where the (+) sign corresponds to the right-hand helicity and (-) one to the left-hand one.