• Volume 83, Issue 4

October 2014,   pages  457-632

• Solitary wave solutions to nonlinear evolution equations in mathematical physics

This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.

• Inclined periodic homoclinic breather and rogue waves for the (1+1)-dimensional Boussinesq equation

A new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed. (1+1)-dimensional Boussinesq equation is used as an example to illustrate the effectiveness of the suggested method. Rational homoclinic wave solution, a new family of two-wave solution, is obtained by inclined periodic homoclinic breather wave solution and is just a rogue wave solution. This result shows that rogue wave originates by the extreme behaviour of homoclinic breather wave in (1+1)-dimensional nonlinear wave fields.

• Biased trapping issue on weighted hierarchical networks

In this paper, we present trapping issues of weight-dependent walks on weighted hierarchical networks which are based on the classic scale-free hierarchical networks. Assuming that edge’s weight is used as local information by a random walker, we introduce a biased walk. The biased walk is that a walker, at each step, chooses one of its neighbours with a probability proportional to the weight of the edge. We focus on a particular case with the immobile trap positioned at the hub node which has the largest degree in the weighted hierarchical networks. Using a method based on generating functions, we determine explicitly the mean first-passage time (MFPT) for the trapping issue. Let parameter $a (0 &lt; a &lt; 1)$ be the weight factor. We show that the efficiency of the trapping process depends on the parameter a; the smaller the value of a, the more efficient is the trapping process.

• Enriched vibrational resonance in certain discrete systems

We wish to report the occurrence of vibrational resonance in certain discrete systems like sine square map and sine circle map, in a unique fashion, comprising of multiple resonant peaks which pave the way for enrichment. As the systems of our choice are capable of exhibiting vibrational resonance behaviour unlike the earlier reports, they are taken for investigation and the necessary numerical and analytical results are presented. Further, we study the effect of external forcing on various attractors of these systems with appropriate bifurcation and Lyapunov exponent diagrams.

• Dynamics of coupled field solitons: A collective coordinate approach

In this paper we consider a class of systems of two coupled real scalar fields in bidimensional space-time, with the main motivation of studying classical stability of soliton solutions using collective coordinate approach. First, we present the class of systems of the collective coordinate equations which are derived using the presented method. After that, we follow the dynamics of the coupled fields with local inhomogeneity like a delta function potential wall as well as a delta function potential well. The results of the investigation of the two coupled fields are compared to each other and the differences are discussed. The method can predict most of the characters of the interaction.

• Emergence of new magic numbers, $N = 16$ and 32 by tensor interaction in Skyrme–Hartree–Fock theory

Melting of $N = 20$ shell and development of $N = 16$ and 32 shells for neutronrich nuclei have been studied extensively by including tensor interaction in Skyrme–Hartree–Fock theory optimized to reproduce the splitting $\Delta 1 f$ shells of 40,48Ca and 56Ni nuclei. Evolution of gap generated by the energy difference of single-particle levels $v2s_{1/2}$ and $v1d_{3/2}$ has been found to be responsible for shell closure at $N = 16$. The splitting pattern of spin–orbit partners $2p$ shell model state in Ca, Ti, Cr, Fe and Ni isotopes indicates the formation of a new shell at $N = 32$ region.

• Capture cross-section and rate of the 14C($n, \gamma$)15C reaction from the Coulomb dissociation of 15C

We calculate the Coulomb dissociation of 15C on a Pb target at 68 MeV/u incident beam energy within the fully quantum mechanical distorted wave Born approximation formalism of breakup reactions. The capture cross-section and the subsequent rate of the 14C($n, \gamma$)15C reaction are calculated from the photodisintegration of 15C, using the principle of detailed balance. Our theoretical model is free from the uncertainties associated with the multipole strength distributions of the projectile.

• Calculation of excitation functions of the 54,56,57,58Fe($p, n$) reaction from threshold to 30 MeV

The cross-sections for the formation of 54,56,57,58Co in the 54,56,57,58Fe($p, n$) reaction from threshold to 30 MeV protons have been theoretically calculated using the TALYS-1.4 nuclear model code, whereby we have studied major nuclear reaction mechanisms, including direct, preequilibrium and compound nuclear reaction. Subsequently, the level density and shell damping parameters have been adjusted and at the same time, the odd–even effects are well comprehended. The excitation functions have been compared with experimental nuclear data. It is observed that the theoretical cross-sections match fairly well. Proton-induced reaction cross-sections provide clues to understand the nuclear structure and offers a good testing ground for ideas about nuclear forces. In addition, complete information in this field is very much required for application in accelerator-driven subcritical system.

• Immiscible multicomponent lattice Boltzmann model for fluids with high relaxation time ratio

An immiscible multicomponent lattice Boltzmann model is developed for fluids with high relaxation time ratios, which is based on the model proposed by Shan and Chen (SC). In the SC model, an interaction potential between particles is incorporated into the discrete lattice Boltzmann equation through the equilibrium velocity. Compared to the SC model, external forces in our model are discretized directly into the discrete lattice Boltzmann equation, as proposed by Guo et al. We develop it into a new multicomponent lattice Boltzmann (LB) model which has the ability to simulate immiscible multicomponent fluids with relaxation time ratio as large as 29.0 and to reduce `spurious velocity’. In this work, the improved model is validated and studied using the central bubble case and the rising bubble case. It finds good applications in both static and dynamic cases for multicomponent simulations with different relaxation time ratios.

• Molecular and impedance spectroscopy of Na2Mo2O7 ceramics

The fine (i.e. 38 nm) powder of polycrystalline Na2Mo2O7 was prepared by the hightemperature solid-state reaction technique. The formation of the compound in orthorhombic system is confirmed by preliminary structural analysis using X-ray diffraction (XRD) data. Spectroscopic studies of the compound have been carried out by vibration spectroscopy (Raman/FTIR) to understand its molecular structure at microscopic level. The complex impedance spectroscopy (CIS) technique has been used to study the electrical properties of the material as a function of frequency (102–10$^6$ Hz) at different temperatures (23–450°C), and also to investigate the fundamental mechanism involved in the material. Impedance analysis also indicates that below 300°C, the electrical conduction in the material is due to grain interior only. At and above 325°C, the contribution of grain boundary is clearly evident. The electrical processes in the material are found to be temperature-dependent and are due to the relaxation phenomena in it. A frequency-dependent maximum of the imaginary electrical impedance is found to obey the Vogel–Fulcher law.

• Dielectric relaxation of ethanol and 𝑁-methyl acetamide polar mixture in C6H6 at 9.90 GHz

Debye relaxation times $(\tau_{jk})$ and dipole moments $(\mu_{jk})$ of binary ($jk$) polar mixtures of ethanol (EtOH) and 𝑁-methyl acetamide (NMA) dissolved in benzene(i) are studied by studying conductivity of solution at 9.90 GHz for different temperatures, different mole fractions ($x_j$) of ethanol and different weight fractions $(w_{jk})$ of the mixtures, respectively. The variation of $\tau_{jk}−x_j$ from linear slope of imaginary ($\sigma''_{ijk}$) against real ($\sigma'_{ijk}$) part of total conductivity ($\sigma^{\ast}_{ijk}$) curve reveals solute–solute (dimer) or solute–solvent (monomer) molecular associations up to $x_j$ = 0.0−0.3 and thereafter, solute–solvent molecular associations. $\tau_{jk}$s from the ratio of slopes of $\sigma''_{ijk}$−w_{jk}$and$\sigma'_{ijk}$−w_{jk}$ curves exhibit solute–solvent molecular association for all $x_j$s which are consistent with the $\mu_{jk}−x_j$ curves at all temperatures except at 35°C. This signifies the validity of both the proposed methods in estimating 𝜏 and 𝜇. The molecular dynamics of the polar mixture are ascertained from Eyring rate theory. Theoretical dipole moments from bond angles and bond moments ($\mu_{\text{theo}}$) are also calculated to predict associational aspects.

• Coherent nonlinear electromagnetic response in twisted bilayer and few-layer graphene

The phenomenon of Rabi oscillations far from resonance is described in bilayer and few-layer graphene. These oscillations in the population and polarization at the Dirac point in 𝑛-layer graphene are seen in the nth harmonic termin the external driving frequency. The underlying reason behind these oscillations is attributable to the pseudospin degree of freedom possessed by all these systems. Conventional Rabi oscillations, which occur only near resonance, are seen in multiple harmonics in multilayer graphene. However, the experimentally measurable current density exhibits anomalous behaviour only in the first harmonic in all the graphene systems. A fully numerical solution of the optical Bloch equations is in complete agreement with the analytical results, thereby justifying the approximation schemes used in the latter. The same phenomena are also described in twisted bilayer graphene with and without an electric potential difference between the layers. It is found that the anomalous Rabi frequency is strongly dependent on twist angle for weak applied fields – a feature absent in single-layer graphene, whereas the conventional Rabi frequency is relatively independent of the twist angle.

• Quark matter coupled to domain walls in Bianchi types II, VIII and IX Universes

In this study of Bianchi types II, VIII and IX Universes, quark matter coupled to domain walls in the context of general relativity are explored. To obtain deterministic solution of the Einstein’s field equations, various techniques are adopted. The features of the obtained solution are discussed.

• Erratum to: An integral transform of Green’s function, off-shell Jost solution and T-matrix for Coulomb–Yamaguchi potential in coordinate representation

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Posted on July 25, 2019