International Journal of Modern Physics B

A system of coupled nonlinear Schrödinger (CNLS) equations is derived, starting with a model for an electric LC transmission line, in which nonlinear capacitance C is approximated, as a function of voltage V, by a general truncated expansion, C(V) = C₀(1 - αV + βV² + ⋯). Within the framework of the CNLS equations, we obtain exact solutions for solitary-wave and kink-anti-kink complexes, at specific relations between the XPM and SPM coefficients. The modulational stability of uniform states with constant amplitudes in the framework of the pair of CNLS equations is analyzed too.

In this paper, we are planning to consider the fluctuations of two nonlinear equations which govern the dynamics of water waves named Camassa–Holm and KdV. We consider the total number of positive slopes produced when the fluctuations of the wave velocity u(x) of a surface wave of a fluid, for example water, is crossed by the level in the Camassa–Holm and KdV equations. Here, we just concentrate on the high Reynolds number limit and do the level crossing analysis where υ → 0. In our desired limit, the dissipative term becomes absent or very weak compared to the nonlinear term which is responsible for increasing the amplitude and creating wave steepening, which results in the appearance of shocks. Thus, our analysis works at the times before the appearance of shocks. Our aim in this paper is to show how the quantity, , counts the fluctuations of the wave velocity in the surface water wave fluctuations which are governed by the KdV and Camassa–Holm (CH) equations.

We evaluated the magnetic alignment and superconducting magnetic anisotropies of high-T_c superconductor Yb₁Ba₂Cu₃O_7-δ by both X-ray diffraction and magnetization measurements. The sample was grain aligned under a high magnetic field of 6 T. X-ray diffraction pattern revealed normal alignment in Yb-123 by showing the c axis aligned perpendicular to the magnetic field. At low temperatures, magnetic hysteresis ΔM with magnetic field perpendicular to a–b plane is larger than magnetic hysteresis parallel to a–b plane. A crossover was observed at higher temperature in magnetic hystereses, i.e., ΔM_⊥a - b < ΔM_‖a - b at certain applied field. This crossover can be explained due to difference in vortex structure along both field directions.

Within the framework of Biham–Middleton–Levine traffic model with origin–destination trips, we study the evacuation processes of cars in cities. Cars move from the origin to the destination points. A driver which reaches its destination disappears with rate β. It is found that the evacuation processes are greatly influenced by the origin–destination distance probability distribution. We also find that the evacuation time of drivers diverges in the form of a power law τ ∝ β^-ν, with ν = 1.

We explore electron transport properties in molecular wires made of heterocyclic molecules (pyrrole, furan and thiophene) by using the Green's function technique. Parametric calculations are given based on the tight-binding model to describe the electron transport in these wires. It is observed that the transport properties are significantly influenced by (a) the heteroatoms in the heterocyclic molecules and (b) the molecule-to-electrodes coupling strength. Conductance (g) shows sharp resonance peaks associated with the molecular energy levels in the limit of weak molecular coupling, while they get broadened in the strong molecular coupling limit. These resonances get shifted with the change of the heteroatoms in these heterocyclic molecules. All the essential features of the electron transfer through these molecular wires become much more clearly visible from the study of our current-voltage (I-V) characteristics, and they provide several key information in the study of molecular transport.

Stochastic resonance in a chain of coupled threshold elements driven by a spatiotemporal periodic signal and noise is studied. It is shown that stochastic resonance can be enhanced for a fixed coupling strength by introducing proper time delays in the coupling terms which balance the effect of the phase difference between the periodic signals at the input of the interacting elements. Hence, in spatially extended systems driven by spatiotemporal periodic signals, stochastic resonance can be controlled by a delayed coupling. This method of controlling stochastic resonance is robust against random perturbations of the periodicity of the input signal and of the individual time delays.

The upper bound U_B(t) of the time derivative of entropy for a dynamical system driven by both additive colored noise and multiplicative colored noise with colored cross-correlation is investigated. Based on the Fokker–Planck equation, the effects of the parameters on U_B(t) are analyzed. The results show that: (i) α (the multiplicative noise intensity), D (the additive noise intensity) and τ₂ (the correlation time of the additive noise) always enhance U_B (t) monotonically; (ii) λ (the intensity of the cross-correlation between the multiplicative noise and the additive noise), τ₁ (the correlation time of the multiplicative noise), τ₃ (the correlation time of the cross-correlation) and γ (the dissipative constant) all possess a minimum, i.e., U_B (t) decreases for small values and increases for large values.

Most engineering problems, especially heat transfer equations are mostly nonlinear. Variational iteration method (VIM) and homotopy perturbation method (HPM) are useful numerical and analytical methods for solving nonlinear heat transfer equations. Perturbation methods depend on a small parameter, which is difficult to be found for real-life nonlinear problems. To overcome this shortcoming, two newly powerful analytical methods are introduced to solve nonlinear heat transfer problems in our work; one is the VIM and the other one is the HPM. The VIM is to construct correction functionals using general Lagrange multipliers identified optimally via the variational theory, and the initial approximations can be freely chosen with unknown constants. The HPM makes a difficult problem much easier to be evaluated. In this research, these methods are used to solve nonlinear ordinary differential system for melting of a finite slab.

A series of Fe_2-xAl_xCoO₄ ferrite nanoparticles have been synthesized by sol-gel method. Powder X-ray diffraction (XRD), thermo gravimetric (TG) and differential thermal analysis (DTA), transmission electron microscopy (TEM) and IR spectroscopy analysis were employed to study structural and morphological characterization of these ferrite nanoparticles. The effect of substitution of Fe³⁺ by Al³⁺ ions on the structural properties of cobalt ferrite nanoparticles was investigated. The crystallite (D) is found in the range 39 nm to 6 nm, which decreases with increasing aluminum content. The values of lattice parameters (a), X-ray density (d_x), hopping length (L_A, L_B) decreases with aluminum content. The tetrahedral bond (d_AX), octahedral bond (d_BX), tetra edge (d_AXE) and octa edge (d_BXE) (shared and unshared) showed the linear decrease with the increasing aluminum content x. IR spectroscopy analysis revealed the chemical and structural changes taking place in the combustion reaction.

It is known from the early work of May in 1964 that ideal Bose gas do not exhibit condensation phenomenon in two dimensions. On the other hand, it is also known that the thermostatistics arising from q-deformed oscillator algebra has no connection with the spatial dimensions of the system. Our recent work concerns the study of important thermodynamic functions such as the entropy, occupation number, internal energy and specific heat in ordinary three spatial dimensions, where we established that such thermostatistics is developed by consistently replacing the ordinary thermodynamic derivatives by the Jackson derivatives. The thermostatistics of q-deformed bosons and fermions in two spatial dimensions is an unresolved question that is the subject of this investigation. We study the principal thermodynamic functions of both bosons and fermions in the two-dimensional q-deformed formalism and we find that, different from the standard case, the specific heat of q-boson and q-fermion ideal gas, at fixed temperature and number of particles, are no longer identical.

In this paper, we investigate the magnetic properties of double-layer thin film using Monte Carlo technique, in anisotropic Heisenberg model. The magnetization, out-of-plane and in-plane magnetic susceptibilities, and also the specific heat behaviors according to temperature are investigated in order to find out the contingent magnetic ordering phases and the critical temperatures values, for two easy-axis anisotropy parameters settings. We also calculate the relative variation rate of the critical temperature along with the easy-plane anisotropy interaction parameter distribution, and we comparatively appraise the numerical obtained results, in order to get quantitative response on the physical model parameters changes. Finally, we present a finite size effect study on magnetic susceptibility, respecting the two settings physical parameters we assumed in the paper.

Mössbauer spectroscopic measurements have been carried out for CeSn₃ and CeSn_3.1 single crystals in the temperature range 1.5 K to 300 K under applied magnetic field, with an aim to look into the local surroundings of the Sn site and the possibility of magnetization at low temperatures. The spectra indicate a paramagnetic ground state throughout the temperature range with two different doublets associated with two sites S₁ and S₂. This indicates two crystallographic sites of Sn with the presence of a distortion in the cubic crystal. However, the contribution of S₂ site is very small (only 3% for the CeSn₃ but slightly higher, i.e., 4.3% for the CeSn_3.1) at room temperature. Upon cooling (below 4 K), the S₂ contribution disappears for the stoichiometric sample (CeSn₃) but continues to stay for the slightly nonstoichiometric compound (CeSn_3.1). The isomer shift reveals a Sn²⁺ valence state throughout. A weak hyperfine field has been observed only at low temperatures (4.2 and 1.5 K spectra) for both the compounds, but not for the 300 K spectra. This is indicative of some magnetization, i.e., an increase in magnetic moments of Ce atoms, that is felt by the neighbor Sn atoms through RKKY interactions. However, upon cooling the samples from 4.2 K to 1.5 K, no further enhancement in magnetization is observed. The magnetic field was also applied for the CeSn₃ sample at low temperatures to check if there is any enhancement in the magnetic properties that yielded negative results, i.e., the applied field is equal to the hyperfine field, indicating no enhancement of magnetic moment.