• Volume 85, Issue 4

October 2015,   pages  567-747

• On the analytical solution of Fornberg–Whitham equation with the new fractional derivative

Motivated by the simplicity, natural and efficient nature of the new fractional derivative introduced by R Khalil et al in J. Comput. Appl. Math. 264, 65 (2014), analytical solution of space-time fractional Fornberg–Whitham equation is obtained in series form using the relatively new method called q-homotopy analysis method (q-HAM). The new fractional derivative makes it possible to introduce fractional order in space to the Fornberg–Whitham equation and be able to obtain its solution. This work displays the elegant nature of the application of q-HAM to solve strongly nonlinear fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for nonlinear differential equations. Comparisons are made on the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.

• Blow-up of solutions for the sixth-order thin film equation with positive initial energy

In this paper, a sixth-order parabolic thin film equation with the initial boundary condition is considered. By using the improved energy estimate method and by constructing second-order elliptic problem, a blow-up result for certain solution with positive initial energy is established, which is an improve over the previous result of Li and Liu.

• The functional variable method for solving the fractional Korteweg–de Vries equations and the coupled Korteweg–de Vries equations

This paper presents the exact solutions for the fractional Korteweg–de Vries equations and the coupled Korteweg–de Vries equations with time-fractional derivatives using the functional variable method. The fractional derivatives are described in the modified Riemann–Liouville derivative sense. It is demonstrated that the calculations involved in the functional variable method are extremely simple and straightforward and this method is very effective for handling nonlinear fractional equations.

• The first integral method to study the (2+1)-dimensional Jaulent–Miodek equations

In this paper, we have presented the applicability of the first integral method for constructing exact solutions of (2+1)-dimensional Jaulent–Miodek equations. The first integral method is a powerful and effective method for solving nonlinear partial differential equations which can be applied to nonintegrable as well as integrable equations. The present paper confirms the significant features of the method employed and exact kink and soliton solutions are constructed through the established first integrals.

• Spectral intensity distribution of trapped fermions

To calculate static response properties of a many-body system, local density approximation (LDA) can be safely applied. But, to obtain dynamical response functions, the applicability of LDA is limited bacause dynamics of the system needs to be considered as well. To examine this in the context of cold atoms, we consider a system of non-interacting spin-$\frac{1}{2}$ fermions confined by a harmonic trapping potential. We have calculated a very important response function, the spectral intensity distribution function (SIDF), both exactly and using LDA at zero temperature and compared with each other for different dimensions, trap frequencies and momenta. The behaviour of the SIDF at a particular momentum can be explained by noting the behaviour of the density of states (DoS) of the free system (without trap) in that particular dimension. The agreement between exact and LDA SIDFs becomes better with increase in dimensions and number of particles.

• An efficient parallel pseudorandom bit generator based on an asymmetric coupled chaotic map lattice

In this paper, an asymmetric coupled map lattice (CML) combining sawtooth map as a local map is presented and its chaotic behaviours are analysed. Based on this asymmetric CML, a pseudorandom bit generator (PRBG) is proposed. The specific parameters of the system that make complicated floating-point computation and multiplication computation transform into simple shift bit operations are adopted, that not only ensures the nonlinear operations, but also increases the performance efficiency. The PRBG is implemented in software and hardware. The parallel output bit sequences pass all of the NIST SP800-22 statistical tests.

• Regge-like initial input and evolution of non-singlet structure functions from DGLAP equation up to next-next-to-leading order at low 𝑥 and low $Q^{2}$

This is an attempt to study how the features of Regge theory, along with QCD predictions, lead towards the understanding of unpolarized non-singlet structure functions $F_{2}^{\text{NS}}$ $(x, Q^{2})$ and 𝑥 𝐹3 $(x, Q^{2})$ at low 𝑥 and low $Q^{2}$ . Combining the features of perturbative quantum chromodynamics (pQCD) and Regge theory, an ansatz for $F_{2}^{\text{NS}}$ $(x, Q^{2})$ and 𝑥 𝐹3 $(x, Q^{2})$ structure functions at small 𝑥 was obtained, which when used as the initial input to Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) equation, gives the $Q^{2}$ evolution of the non-singlet structure functions. The non-singlet structure functions, evolved in accordance with DGLAP evolution equations up to next-next-to-leading order are studied phenomenologically in comparison with the available experimental and parametrization results taken from NMC, CCFR, NuTeV, CORUS, CDHSW, NNPDF and MSTW Collaborations and a very good agreement is observed in this regard.

• On the role of deformed Coulomb potential in fusion using energy density formalism

Using the Skyrme energy density formalism, the effect of deformed Coulomb potential on fusion barriers and fusion cross-sections is studied. Our detailed study reveals that the fusion barriers as well as fusion probabilities depend on the shape deformation (due to deformed Coulomb potential) of the colliding nuclei. However, this dependence due to deformed Coulomb potential is found to be very weak.

• Oscillations of the fusion cross-sections in the 16O + 16O reaction

Evolution of the fusion cross-section in the 16O + 16O reaction has been analysed. It is shown, both analytically and numerically, that in this excitation function some oscillations can be observed. These oscillations are related to the quantum character of the orbital angular momentum increase as well as to the distinct features of the 16O + 16O reaction. In order to perform the numerical calculations, the fluctuation–dissipation model and the single barrier penetration model are used. It turns out that the experimental data available in the literature do not have any definite proof about the presence or absence of the oscillations. We stress, that the question still remains unanswered for more than three decades whereas during this time lapse the experimental errors for other reactions are reduced to 1–2%.

• Multiple recycling of fuel in prototype fast breeder reactor in a closed fuel cycle with pressurized heavy-water reactor external feed

A fast breeder reactor (FBR) closed fuel cycle involves recycling of the discharged fuel, after reprocessing and refabrication, in order to utilize the unburnt fuel and the bred fissile material. Our previous study in this regard for the prototype fast breeder reactor (PFBR) indicated the possibility of multiple recycling with self-sufficiency. It was found that the change in Pu composition becomes negligible (less than 1%) after a few cycles. The core-1 Pu increases by 3% from the beginning of cycle-0 to that of recycle-1, the Pu increase from the beginning of the 9th cycle to that of the 10th by only 0.3%. In this work, the possibility of multiple recycling of PFBR fuel with external plutonium feed from pressurized heavy-water reactor (PHWR) is examined. Modified in-core cooling and reprocessing periods are considered. The impact of multiple recycling on PFBR core physics parameters due to the changes in the fuel composition has been brought out. Instead of separate recovery considered for the core and axial blankets in the earlier studies, combined fuel recovery is considered in this study. With these modifications and also with PHWR Pu as external feed, the study on PFBR fuel recycling is repeated. It is observed that the core-1 initial Pu inventory increases by 3.5% from cycle-0 to that of recycle-1, the Pu increase from the beginning of the 9th cycle to that of the 10th is only 0.35%. A comparison of the studies done with different external plutonium options viz., PHWR and PFBR radial blanket has also been made.

• An alternative method for the measurement of neutron flux

A simple and easy method for measuring the neutron flux is presented. This paper deals with the experimental verification of neutron dose rate–flux relationship for a non-dissipative medium. Though the neutron flux cannot be obtained from the dose rate in a dissipative medium, experimental result shows that for non-dissipative medium one can obtain the neutron flux from dose rate. We have used a 241 AmBe neutron source for neutron irradiation, and the neutron dose rate and count rate were measured using a NM2B neutron monitor and R-12 superheated droplet detector (SDD), respectively. Here, the neutron flux inferred from the neutron count rate obtained with R-12 SDD shows an excellent agreement with the flux inferred from the neutron dose rate in a non-dissipative medium.

• 𝑀1 and 𝐸2 transitions in the ground-state configuration of atomic manganese

Using the multiconfiguration Hartree–Fock approximation within the framework of the Breit–Pauli Hamiltonian (MCHF+BP) and the relativistic Hartree–Fock (HFR) approximation, we have calculated the forbidden transition (𝑀1 and 𝐸2) parameters such as transition energies, logarithmic weighted oscillator strengths and transition probabilities between the fine-structure levels in the ground-state configuration of 3d5 4s2 for atomic manganese (Mn I, Z =25). A discussion of these calculations for manganese using MCHF+BP and HFR methods is given here.

• A computational method for the solution of one-dimensional nonlinear thermoelasticity

In this paper, one of the newest analytical methods, new homotopy perturbation method (NHPM), is considered to solve thermoelasticity equations. Results obtained by NHPM, which does not need small parameters, are compared with the numerical results and a very good agreement is found. This method provides a convenient way to control the convergence of approximation series and adjust convergence regions when necessary. The results reveal that the proposed method is explicit, effective and easy to use.

• Second-harmonic ion cyclotron resonance heating scenarios of Aditya tokamak plasma

Plasma heating with the fast magnetosonic waves in the ion cyclotron range of frequencies (ICRF) is one of the auxiliary heating schemes of Aditya tokamak. Numerical simulation of second-harmonic resonance heating scenarios in low-temperature, low-density Aditya plasma has been carried out for fast magnetosonic wave absorption in ICRF range, using full-wave ion cyclotron heating code TORIC combined with Fokker–Planck quasilinear solver SSFPQL and the results are explained. In such low-temperature, low-density plasma, ion absorption for second-harmonic resonance heating is less but significant amount of direct electron heating is observed.

• Application of Tietz potential to study optical properties of spherical quantum dots

In this work, we study the optical properties of spherical quantum dots by using Tietz potential. In this regard, we have applied Nikiforov–Uvarov (NU) technique and numerically solved the Schrödinger equation to obtain energy levels and wave functions. Then, by using the density matrix method, we have derived expressions for the changes in linear and third-order nonlinear absorption coefficients and refractive index. According to the results obtained from this work, it is deduced that: (i) the total refractive index and the absorption coefficients increase and shift towards higher energies as $v_{0}$ increases; (ii) the total absorption coefficient and refractive index decrease and also shift towards lower energies as $r_{0}$ increases.

• Soliton solutions of the generalized sinh-Gordon equation by the binary $(G'/G)$-expansion method

The aim of this paper is to extend the applications of $(G'/G)$-expansion method to solve a generalized sinh-Gordon equation. In fact, the binary $(G'/G)$-expansion method is introduced for finding different new exact solutions. It is shown that this method is a powerful mathematical tool for solving nonlinear evolution equations with time-dependent coefficients in mathematical physics.

• A computational method for the solution of one-dimensional nonlinear thermoelasticity

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