Volume 64, Issue 3-4

The dispersion relation for the inverse hyperbolic potential is calculated in the classical limit. This is shown for both the low amplitude phonon branch and the high amplitude soliton branch. It is shown that these results qualitatively follow the previously found ones for the inverse squared potential where explicit analytic solutions are known

We apply a relatively new technique which is called the homotopy perturbation method (HPM) for solving linear and nonlinear partial differential equations. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the HPM solves nonlinear problems without using Adomian’s polynomials can be considered as a clear advantage of this technique over the decomposition method

We consider equations in the modified Korteweg-de Vries (mKdV) hierarchy and make use of the Miura transformation to construct expressions for their Lax pair. We derive a Lagrangian-based approach to study the bi-Hamiltonian structure of the mKdV equations. We also show that the complex modified KdV (cmKdV) equation follows from the action principle to have a Lagrangian representation. This representation not only provides a basis to write the cmKdV equation in the canonical form endowed with an appropriate Poisson structure but also help to construct a semianalytical solution of it. The solution obtained by us may serve as a useful guide for purely numerical routines which are currently being used to solve the cmKdV equation

We consider a coupled system of nonlinear viscoelastic equations with linear damping and source terms. Under suitable conditions of the initial data and the relaxation functions, we prove a finitetime blow-up result with vanishing initial energy by using the modified energy method and a crucial lemma on differential inequality

We study, within a mean-field approach, the stationary states of the kinetic metamagnetic spin −3/2 Blume-Emery-Griffiths model under the presence of a time-varying (sinusoidal) magnetic field.We use the Glauber-type stochastic dynamics to describe the time evolution of the system. The behaviour of the time dependence of the average order parameters in a period, which are also called the dynamic order parameters, as functions of the reduced temperature are investigated. The natures (continuous or discontinuous) of the transitions are characterized by investigating the behaviours of the thermal variations of the dynamic order parameters. The dynamic phase transition points are obtained and the phase diagrams are constructed in the plane of the reduced temperature (T) and the amplitude of the magnetic field (h), and sixteen fundamental types of phase diagrams are found. The phase diagrams exhibit one, two, three or four dynamic tricritical points and a dynamic double-critical end point, and, besides a disordered and three ordered phases, seven coexistence regions or mixed phases depending on the interaction parameters. We also investigate the influence of the reduced biquadratic exchange parameter (k) and obtain nine different phase diagram topologies in the (k,T) plane

The Lennard-Jones(12-6) and the Exponential-6 potential functions are commonly used in computational softwares for describing the van der Waals interaction energy. Some softwares allow switching between these two potentials under prescribed condition(s) that attempt to connect the parameter relationship between the two functions. Here we propose a technique by which the parameter relationship between both potentials is extracted by simultaneously imposing an equal force constant at the well depth’s minimum and an equal mean interatomic energy from the point of equilibrium to the point of total separation. The former imposition induces good agreement for the interatomic compression and a small change in the interatomic distance near the equilibrium while the latter enables good agreement for large interatomic separation. The excellent agreement exhibited by the plots validates the technique of combined criteria proposed herein

Analytical approximations of the Lyapunov exponent are derived for a random displacement model with equal potential barriers and random positions of the scatterers. Two asymptotic regions are considered corresponding to high and low reflectivity of the single scattering potential. The analytical results are in terms of a distribution function W for certain phases of the transfer matrices. A functional equation for W is derived and numerically solved. This serves to validate the analytical asymptotic formulas which turn out to be accurate in the high and low reflectivity regions with dimensionless wave number K < 2 and K > 6, respectively. The high wave number asymptotics allows for an analytical examination of the sufficient conditions for Anderson localization

The variable-coefficient two-dimensional Korteweg-de Vries (KdV) model is of considerable significance in describing many physical situations such as in canonical and cylindrical cases, and in the propagation of surface waves in large channels of varying width and depth with nonvanishing vorticity. Under investigation hereby is a generalized variable-coefficient two-dimensional KdV model with various external-force terms. With the extended bilinear method, this model is transformed into a variable-coefficient bilinear form, and then a Bäcklund transformation is constructed in bilinear form. Via symbolic computation, the associated inverse scattering scheme is simultaneously derived on the basis of the aforementioned bilinear Bäcklund transformation. Certain constraints on coefficient functions are also analyzed and finally some possible cases of the external-force terms are discussed

The grain size effects on the bremsstrahlung emission spectrum due to nonrelativisitc electrondust grain collisions are investigated in dusty plasmas. Using the Born approximation for the initial and final states of the projectile electron, the bremsstranhlung radiation cross section is obtained as a function of the grain size, dust charge, Debye radius, collision energy, and radiation photon energy. It is found that the effects of the grain size enhance the bremsstrahlung radiation cross section, especially for soft-photon radiations. The effect of the Debye radius on the bremsstrahlung cross section is found to be increased with an increase of the magnitude of the charge number of the dust grain. In addition, the grain size effect on the bremsstrahlung spectrum is found to be more significant for highly charged dusty grains

The effects of neutral particle collisions on the quantum interference in electron-electron collisions are investigated in collisional plasmas. The effective potential model taking into account the electronneutral particle collision effects is employed in order to obtain the electron-electron collision cross section including the total spin states of the collision system. It is found that the collision effects significantly enhance the cross section. In addition, the collision-induced quantum interference effects are found to be significant in the singlet spin state. It is shown that the quantum interference effects decrease with increasing the thermal energy of the plasma. It is also shown that the quantum interference effects increase with an increase of the collision energy

The oscillatory screening effects on elastic electron-ion collisions are investigated in dense quantum plasmas. The eikonal method with the modified Debye-Hückel potential is employed to obtain the scattering phase shift and scattering amplitude. In addition, the total elastic collision cross section is obtained by the optical theorem with the forward scattering amplitude in quantum plasmas. It is shown that the modified Debye-Hückel screening in quantum plasmas produces the oscillatory behaviour of the scattering phase shift. In addition, the minimum position of the phase shift is receded from the target ion with decreasing the quantum wave number. It is also found that the oscillatory screening effect suppresses the differential cross section. The total cross section is also found to be decreased due to the oscillatory screening effect. In addition, it is shown that the total cross section decreases with an increase of the quantum wave number

In ultra-low-temperature experiments at 4.7 K the luminescence of Eu(III) bound to different hydroxy- and methoxybenzoic acids and to humic substances (HS) was investigated. The benzoic acid derivatives were used as simple model compounds for common metal-binding structures in HS. The Eu(III) luminescence was directly excited by means of a pulsed dye laser, scanning through the 5 D 0 ← 7 F 0 transition of Eu(III) and subsequently high-resolution total luminescence spectra (TLS) were recorded. Based on the thorough analysis of the high-resolution TLS conclusions were drawn with respect to the number of different complexes formed and to the symmetry of the complexes. The crystal-field strength parameter Nν (B 2q ) was dependent on the electrostatic forces induced by the ligands as well as on the symmetry of the complexes. The formation of thermodynamically stable complexes was found to be slow even for small model ligands such as 2-hydroxybenzoic acid. Comparison between the model compounds and HS clearly revealed that the carboxylate group is the dominant binding site in HS. Indices for the formation of chelates, e. g. similar to 2-hydroxybenzoic acid, were not found for HS

A density functional theory (DFT) study is performed to investigate the influence of structural defects on the electronic structure properties of perfect boron nitride nanotubes (BNNTs). To this aim, as representative models, the single-walled (6,0) BNNT consisting of 36 boron, 36 nitrogen, and 12 hydrogen atoms and the single-walled (4,4) BNNT consisting of 36 boron, 36 nitrogen, and 16 hydrogen atoms are considered. The nuclear quadrupole resonance (NQR) parameters are calculated and compared in two perfect and defective models of the considered BNNTs. The results indicate that due to formation of non-hexagonal rings in the defective model because of removing a B-N bond, the NQR parameters at the sites of first neighbouring nuclei are significantly influenced by imposed perturbation, however, the sites of other nuclei, farther from perturbation, remain almost unchanged. The calculations are performed at the level of the BLYP method and 6-31G* standard basis set using the GAUSSIAN 98 package

A relationship between diffusivity and mobility in degenerate semiconductors is presented. The relationship is general enough to be applicable to both non-degenerate and degenerate semiconductors. It is suitable for the investigation of the electrical transport in heavily doped semiconductors

Electrocapillary curves (surface tension γ as a function of the electrode potential E) for a series of room-temperature ionic liquids (RTILs) were measured using a mercury dropping electrode with the drop-weight (drop-volume) technique. The curves γ = f (E) for the Hg/RTIL interface have one maximum and may be approximated with a polynomial of sixth-order. There are no ‘humps’ in the curves. The interfacial tension of the Hg/RTIL system changes with potential E in a monotonic way. The second derivative of γ = f (E) leads to a polynomial of fourth order, indicating the capacitance of the Hg/RTIL interface. The potential of zero charge is within a relatively narrow range. The specific capacitance at the minimum is of the order 10 μF/cm 2

Attempts have been made to prepare some novel copper(I) nitrate, sulfate, and perchlorate complexes. Molar conductances of these complexes have been measured in organic solvents like acetonitrile (AN), acetone (AC), methanol (MeOH), N,N -dimethylformamide (DMF), N,N dimethylacetamide (DMA), and dimethylsulfoxide (DMSO) at 298 K. The molar conductance data have been analyzed to obtain limiting molar conductances (λ 0 ) and ion association constants (K A ) of the electrolytes. The results showed that all these complexes are strong electrolytes in all organic solvents. The limiting ionic molar conductances (λ o ± ) for various ions have been calculated using Bu 4 NBPh 4 as reference electrolyte. The actual radii for copper(I) complex ions are very large and different in different solvents and indicate some solvation effects in each solvent system