• Volume 81, Issue 6

December 2013,   pages  893-1067

• Direct approach for solving nonlinear evolution and two-point boundary value problems

Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples including time-delayed nonlinear Burgers equation to illustrate the validity and the great potential of the differential transform method. Numerical experiments demonstrate the use and computational efﬁciency of the method. This method can easily be applied to many nonlinear problems and is capable of reducing the size of computational work.

• Exact solutions for nonlinear variants of Kadomtsev–Petviashvili ($n, n$) equation using functional variable method

Studying compactons, solitons, solitary patterns and periodic solutions is important in nonlinear phenomena. In this paper we study nonlinear variants of the Kadomtsev–Petviashvili (KP) and the Korteweg–de Vries (KdV) equations with positive and negative exponents. The functional variable method is used to establish compactons, solitons, solitary patterns and periodic solutions for these variants. This method is a powerful tool for searching exact travelling solutions in closed form.

• The classification of the single travelling wave solutions to the generalized Pochhammer–Chree equation

By the complete discrimination system for the polynomial, we invest the classifications of single travelling wave solutions to the generalized Pochhammer–Chree (PC) equation with $p = 1/2$ and $p = 3/2$.

• Pitchfork bifurcation and vibrational resonance in a fractional-order Duffing oscillator

The pitchfork bifurcation and vibrational resonance are studied in a fractional-order Duffing oscillator with delayed feedback and excited by two harmonic signals. Using an approximation method, the bifurcation behaviours and resonance patterns are predicted. Supercritical and subcritical pitchfork bifurcations can be induced by the fractional-order damping, the exciting highfrequency signal and the delayed time. The fractional-order damping mainly determines the pattern of the vibrational resonance. There is a bifurcation point of the fractional order which, in the case of double-well potential, transforms vibrational resonance pattern from a single resonance to a double resonance, while in the case of single-well potential, transforms vibrational resonance from no resonance to a single resonance. The delayed time influences the location of the vibrational resonance and the bifurcation point of the fractional order. Pitchfork bifurcation is the necessary condition for the double resonance. The theoretical predictions are in good agreement with the numerical simulations.

• On the nucleon–nucleon scattering phase shifts through supersymmetry and factorization

By exploiting the supersymmetry-inspired factorization method through a judicious use of deuteron ground state wave function, higher partial wave nucleon–nucleon potentials, both energy independent and energy dependent, are generated. We adopt the phase function method to deal with the scattering phase shifts and demonstrate the usefulness of our constructed potentials by means of model calculation.

• A clean signal for a top-like isosinglet fermion at the Large Hadron Collider

We predict a clean signal at the Large Hadron Collider ($\sqrt{s} = 14$ TeV) for a scenario where there is a top-like, charge +2/3 vector-like isosinglet fermion. Such a quark, via mixing with the standard model top, can undergo decays via both flavour-changing Z-boson coupling and flavour-changing Yukawa interactions. We concentrate on the latter channel, and study the situation where, following its pair production, the heavy quark pair gives rise to two tops and two Higgs bosons. We show that when each Higgs decays in the $b\bar{b}$ channel, there can be a rather distinct and background-free signal that can unveil the existence of the vector-like isosinglet quark of this kind.

• Monitoring foam coarsening using a computer optical mouse as a dynamic laser speckle measurement sensor

In this paper, we present an experimental approach to track coarsening process of foam using a computer optical mouse as a dynamic laser speckle measurement sensor. The dynamics of foam coarsening and rearrangement events cause changes in the intensity of laser speckle backscattered from the foam. A strong negative correlation between the average speed of the cursor and the evolution of bubble diameter was found. We used microscopic images to demonstrate that decrease in speed is related to increase in bubble size. The proposed set-up is not very expensive, is highly portable and can be used in laboratory measurements of dynamics in other kinds of opaque materials.

• High harmonic generation in H$_2^+$ and HD$^+$ by two-colour femtosecond laser pulses

We have theoretically investigated the high harmonic generation (HHG) spectra of H$_2^+$ and HD$^+$ using a time-dependent wave packet approach for the nuclear motion with combined twocolour (1$\omega_L$–3$\omega_L$) pulsed lasers for ωL corresponding to wavelengths 1064 nm and 800 nm. The 1$\omega_L$ and 3$\omega_L$ lasers have peak intensities of $I_1^0 = 5.0 \times 10^{13}$ W/cm$^2$ and $I_2^0 = 2.0 \times 10^{14}$ W/cm$^2$, respectively. We have taken the pulse duration of $T = 50$ fs for both the fields, and the molecular initial vibrational level $v_0 = 0$. We have argued that for these combinations, the harmonic generation due to transitions in the electronic continuum by tunnelling or multiphoton ionization may be neglected and only the electronic transitions within the two lowest electronic states would be important. Thus, the characteristic features of HHG spectra in the two-colour field are determined, in our model, by the nuclear motions on the two lowest field-coupled electronic states between which interelectronic and intraelectronic (due to the intrinsic dipole moments in case of HD$^+$) radiative transitions can take place. We have studied the role of relative phase ($\varphi$) of the two fields on the HHG spectra of the molecular ions. In case of HD$^+$, the effect of nonadiabatic (NA) nonradiative interaction between the two lowest Born–Oppenheimer (BO) electronic states (1$s\sigma_g$, 2$p\sigma_u$) has been taken into account. Our calculations give realistic HHG spectra which are reasonably efficient and extended for both H$_2^+$ and HD$^+$ in the mixed two-colour field without involving the electronic continuum. The use of two-colour (1$\omega_L$–3$\omega_L$) field enables us to generate high harmonics beyond that achievable with a single 1$\omega_L$ or 3$\omega_L$ field of the corresponding intensity, frequency and pulse time.

• Statistical model of stress corrosion cracking based on extended form of Dirichlet energy

The mechanism of stress corrosion cracking (SCC) has been discussed for decades. Here I propose a model of SCC reflecting the feature of fracture in brittle manner based on the variational principle under approximately supposed thermal equilibrium. In that model the functionals are expressed with extended forms of Dirichlet energy, and Dirichlet principle is applied to them to solve the variational problem that represents SCC and normal extension on pipe surface. Based on the model and the maximum entropy principle, the statistical nature of SCC colony is discussed and it is indicated that the crack has discrete energy and length under ideal isotropy of materials and thermal equilibrium.

• Phonon dispersions in graphene sheet and single-walled carbon nanotubes

In the present research paper, phonons in graphene sheet have been calculated by constructing a dynamical matrix using the force constants derived from the second-generation reactive empirical bond order potential by Brenner and co-workers. Our results are comparable to inelastic X-ray scattering as well as first principle calculations. At $\Gamma$ point, for graphene, the optical modes (degenerate) lie near 1685 cm$^{−1}$. The frequency regimes are easily distinguishable. The lowfrequency ($\omega \to 0$) modes are derived from acoustic branches of the sheet. The radial modes can be identified with $\omega \to 584$ cm$^{−1}$. High-frequency regime is above 1200 cm$^{−1}$ (i.e. ZO mode) and consists of TO and LO modes. The phonons in a nanotube can be derived from zone folding method using phonons of a single layer of the hexagonal sheet. The present work aims to explore the agreement between theory and experiment. A better knowledge of the phonon dispersion of graphene is highly desirable to model and understand the properties of carbon nanotubes. The development and production of carbon nanotubes (CNTs) for possible applications need reliable and quick analytical characterization. Our results may serve as an accurate tool for the spectroscopic determination of the tube radii and chiralities.

• Dynamo in protostars

In this paper, we estimate the magnetic Reynolds number of a typical protostar before and after deuterium burning, and claim for the existence of dynamo process in both the phases, because the magnetic Reynolds number of the protostar far exceeds the critical magnetic Reynolds number for dynamo action. Using the equipartition of kinetic and magnetic energies, we estimate the steady-state magnetic field of the protostar to be of the order of kilogauss, which is in good agreement with observations.

• Shape transition of state density for bosonic systems

For a finite $m$ boson system, the ensemble-averaged state density has been computed with respect to the body interaction rank $k$. The shape of such a state density changes from Gaussian to semicircle as the body rank of the interaction increases. This state density is expressed as a linear superposition of Gaussian and semicircular states. The nearest-neighbour spacing distribution (NNSD), which is one of the most important spectral properties of a system, is studied. The NNSDs are rather independent of body rank $k$ and show a Wigner distribution throughout.

• Antisynchronization of a novel hyperchaotic system with parameter mismatch and external disturbances

In our recent publication (Pramana – J. Phys. 79, 81 (2012), DOI: 10.1007/s12043-012-0285-6), our statement on adaptive antisynchronization (AS) controller design is incorrect. In this erratum we propose a correct control law. The corresponding proof is also given to demonstrate the effectiveness of the proposed control strategy.

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• # Pramana – Journal of Physics

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• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019