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      Volume 88, Issue 4

      April 2017

    • Dynamics of rogue waves on multisoliton background in the Benjamin Ono equation


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      For the Benjamin Ono equation, the Hirota bilinear method and long wave limit method are applied to obtain the breathers and the rogue wave solutions. Bright and dark rogue waves exist in the Benjamin Ono equation, and their typical dynamics are analysed and illustrated. The semirational solutions possessing rogue waves and solitons are also obtained, and demonstrated by the three-dimensional figures. Furthermore, the hybrid of rogue wave and breather solutions are also found in the Benjamin Ono equation.

    • Recessed insulator and barrier AlGaN/GaN HEMT: A novel structure for improving DC and RF characteristics


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      In this study, a gallium nitride (GaN) high electron mobility transistor (HEMT) with recessed insulator and barrier is reported. In the proposed structure, insulator is recessed into the barrier at the drain side and barrier is recessed into the buffer layer at the source side. We study important device characteristics such as electric field, breakdown voltage, drain current, maximum output power density, gate-drain capacitance, short channel effects and DC transconductance using two-dimensional and two-carrier device simulator. Recessed insulator in the drain side of the proposed structure reduces maximum electric field in the channel and therefore increases the breakdown voltage and maximum output power density compared to the conventional counterpart. Also, gate-drain capacitance value in the proposed structure is less than that of the conventional structure. Overall, the proposed structure reduces short channel effects. Because of the recessed regions at both the source and the drain sides, the average barrier thickness of the proposed structure is not changed. Thus, the drain current of the proposed structure is almost equivalent to that of the conventional transistor. In this work, length (Lr) and thickness (Tr) of the recessed region of the barrier at the source side are the same as those of the insulator at the drain side.

    • Dependence of $\it{in-situ}$ Bose condensate size on final frequency of RF-field in evaporative cooling


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      We report the results of $\it{in-situ}$ characterization of $^{87}$Rb atom cloud in a quadrupole Ioffe configuration (QUIC) magnetic trap after a radio-frequency (RF) evaporative cooling of the trapped atom cloud. The $\it{in-situ}$ absorption images of the atom cloud have shown clear bimodal optical density (OD) profiles which indicate the Bose–Einstein condensation (BEC) phase transition in the trapped gas. Also, we report here, for the first time, the measured variation in the sizes of the condensate and thermal clouds with the final frequency selected in the frequency scan of the RF-field for evaporative cooling. These results on frequency-dependent sizes of the clouds are consistent with the theoretical understanding of the BEC phenomenon in the trap.

    • Corrigendum: ‘Anomalous Kolar events revisited: Dark matter?’


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      Some unusual and unexplained events (the so-called Kolar events) were interpreted in $\it{Pramana – J. Phys}$. $\bf{82}$, 609 (2014). This article is a corrigendum to it.

    • The general class of Bianchi cosmological models with dark energy and variable $\Lambda$ and $G$ in viscous cosmology


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      The general class of Bianchi cosmological models with dark energy in the form of modified Chaplygin gas with variable $\Lambda$ and $G$ and bulk viscosity have been considered. We discuss three types of average scalefactor by using a special law for deceleration parameter which is linear in time with negative slope. The exact solutions to the corresponding field equations are obtained. We obtain the solution of bulk viscosity ($\xi$ ), cosmologicalconstant ($\Lambda$), gravitational parameter ($G$) and deceleration parameter ($q$) for different equations of state. The model describes an accelerating Universe for large value of time $t$ , wherein the effective negative pressure induced by Chaplygin gas and bulk viscous pressure are driving the acceleration.

    • Hidden attractors without equilibrium and adaptive reduced-order function projective synchronization from hyperchaotic Rikitake system


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      By introducing an additional state feedback into classic Rikitake system, a new hyperchaotic system without equilibrium is derived. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, and Poincaré maps. Based on adaptive control and Lyapunov stability theory, we design a reduced-order projective synchronization scheme for synchronizing the hyperchaotic Rikitake system coexisting without equilibria and the original classic Rikitake system coexisting with two non-hyperbolic equilibria. Finally, numerical simulations are given to illustrate the effectiveness of the proposedsynchronization scheme.

    • The hydrodynamic description of pseudorapidity distributions at lower energies at BNL-RHIC


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      The hot and dense matter produced in nucleus–nucleus collisions is supposed to expand accordingto unified hydrodynamics, one of the few theoretical models that can be worked out exactly. The solutionis then used to formulate the rapidity distribution of charged particles frozen out from the fluid on thespace-like hypersurface with a fixed temperature, $T_{FO}$. A comparison is made between the theoretical predictions and the experimental measurements carried out by PHOBOS Collaboration in the Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Laboratory (BNL) in different centrality Au–Au and Cu–Cu collisions at $\sqrt{s_{NN}}$=19.6 and 22.4 GeV, respectively. The theoretical results are in good accordance with experimental data.

    • Kac’s ring: The case of four colours


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      We present an instance from nonequilibrium statistical mechanics which combines increase in entropy and finite Poincaré recurrence time. The model we consider is a variation of the well-known Kac’s ring where we consider balls of four colours. As is known, Kac introduced this model where balls arranged between lattice sites, in each time step, move one step clockwise. The colour of the balls change as they cross marked sites. This very simple example rationalize the increase in entropy and recurrence. In our variation, the interesting quantity which counts the difference in the number of balls of different colours is shown to reduce to a set of linear equations if the probability of change of colour is symmetric among a pair of colours. The transfer matrix turns out to be non-Hermitian with real eigenvalues, leading to all colours being equally likely for long times, and a monotonically varying entropy. The new features appearing due to four colours is very instructive.

    • The anisotropic cosmological models in $f (R, T)$ gravity with $\Lambda (T)$


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      The general class of anisotropic Bianchi cosmological models in $f(R, T)$ modified theories of gravity with $\Lambda (T)$ has been considered. This paper deals with $f(R, T)$ modified theories of gravity, where the gravitational Lagrangian is given by an arbitrary function of Ricci scalar $R$ and the trace of the stress-energy tensor $T$ has been investigated for a specific choice of $f (R,T )$ = $f_{1}(R) + f_{2}(T)$. The exact solutions to the corresponding field equations are obtained in quadrature form. We have discussed three types of solutions of the average scale factor for the general class of Bianchi cosmological models by using a special law for deceleration parameter which is linear in time with a negative slope. The solutions to the Einstein field equations are obtained for three differentphysical viable cosmologies. All physical parameters are calculated and discussed in each model.

    • Energy distributions of Bianchi type-$VI_{h}$ Universe in general relativity and teleparallel gravity


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      In this paper, we have investigated the energy and momentum density distributions for the inhomogeneous generalizations of homogeneous Bianchi type-$VI_{h}$ metric with Einstein, Bergmann–Thomson, Landau–Lifshitz,Papapetrou, Tolman and M$\phi$ller prescriptions in general relativity (GR) and teleparallel gravity (TG). We have found exactly the same results for Einstein, Bergmann–Thomson and Landau–Lifshitz energy–momentum distributions in Bianchi type-$VI_{h}$ metric for different gravitation theories. The energy–momentum distributions of the Bianchi type-$VI_{h}$ metric are found to be zero for $h$ = −1 in GR and TG. However, our results agree with Tripathy et al, Tryon, Rosen and Aygün et al.

    • Multiwave solutions of time-fractional (2 + 1)-dimensional Nizhnik–Novikov–Veselov equations

      M S OSMAN

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      In this paper, we present a generalized unified method for finding multiwave solutions of the timefractional (2+1)-dimensional Nizhnik–Novikov–Veselov equations. The fractional derivatives are described in the modified Riemann–Liouville sense. The fractional complex transform has been suggested to convert fractional order differential equations with modified Riemann–Liouville derivatives into integer-order differential equations, and the reduced equations can be solved by symbolic computation. Multiauxiliary equations have been introduced in this method to obtain not only multisoliton solutions but also multiperiodic or multielliptic solutions. It is shown that the considered method is very effective and convenient for solving wide classes of nonlinear partial differential equations of fractional order.

    • A new approach for cluster structures in $^{16}$O and $^{20}Ne$


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      In this article, the cluster–cluster interaction between $\alpha$-clusters in $^{16}$O and $^{20}$Ne is studied theoretically. Using the generalized Nikiforov–Uvarov (NU) technique, the clusterization energy for these nuclei is calculated. Based on the obtained results, one can find out that the clustering phenomenon does not take place neither at the ground state, nor at the excited states of these nuclei and it is more probable at energies among excited levels. It is shown that the formulation presented for the clustering phenomenon reproduces the results obtained in previous experimental and theoretical attempts. It is worth mentioning that the consistency of the results with the previous experimental and theoretical predictions for clustering phenomenon in $^{16}$O and $^{20}$Ne indicates the reliability of this formulation for various types of light $\alpha$-conjugate nuclei, such as $^{8}$Be, $^{12}$C, $^{24}$Mg and so on.

    • Solitary wave solution to a singularly perturbed generalized Gardner equation with nonlinear terms of any order


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      This paper is concerned with the existence of travelling wave solutions to a singularly perturbed generalized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of solitary wave solutions of this equation is proved when the perturbation parameter is sufficiently small. The numerical simulations verify our theoretical analysis.

    • A study of fractional Schrödinger equation composed of Jumarie fractional derivative


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      In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag–Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the fractional Schrödinger equation are then described for the case of particles in one-dimensional infinite potential well. One of the motivations for using fractional calculus in physical systems is that the space and time variables, which we often deal with, exhibit coarse-grained phenomena. This means infinite simal quantities cannot be arbitrarily taken to zero – rather they are non-zero with a minimum spread. This type of non-zero spread arises in the microscopic to mesoscopic levels of system dynamics, which means that, if we denote x as the point in space and t as the point in time, then limit of the differentials dx (and dt ) cannot be taken as zero. To take the concept of coarse graining into account, use the infinite simal quantities as $(\Delta x)^\alpha$ (and $(\Delta t)^\alpha$) with 0 < $\alpha$ < 1; called as ‘fractional differentials’. For arbitrarily small $\Delta x$ and $\Delta t$ (tending towards zero), these ‘fractional’ differentials are greaterthan $\Delta x$ (and $\Delta t$), i.e. $(\Delta x)^\alpha$ > $\Delta x$ and $(\Delta t)^\alpha$ > $\Delta t$. This way of defining the fractional differentials helps us to use fractional derivatives in the study of dynamic systems.

    • Terahertz radiation source using a high-power industrial electron linear accelerator


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      High-power $(\sim 100 kW)$ industrial electron linear accelerators (linacs) are used for irradiations, e.g., for pasteurization of food products, disinfection of medical waste, etc.We propose that high-power electron beam from such an industrial linac can first pass through an undulator to generate useful terahertz (THz) radiation, and the spent electron beam coming out of the undulator can still be used for the intended industrial applications. This will enhance the utilization of a high-power industrial linac. We have performed calculation of spontaneous emission in the undulator to show that for typical parameters, continuous terahertz radiation having power of the order of $\mu$W can be produced, which may be useful for many scientific applications such as multispectral imaging of biological samples, chemical samples etc.

    • A new source of radiation in single-bubble sonoluminescence


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      An unsolved challenge of sonoluminescence phenomenon is the mechanism of light emission at the moment of collapse. In this article, by considering single-bubble sonoluminescence and based on the hydrochemical model and thermal bremsstrahlung approach, for the first time two different origins of light havenumerically been studied to describe the Ar bubble radiation in water at the moment of collapse: (a) radiation from the Ar gas inside the bubble and (b) radiation from the thin layer of the surrounding fluid. The results indicatethat, contrary to the previous studies, the radiation from the water shell is dominant, and it is about one order of magnitude stronger than the radiation from the gas inside the bubble. This result can decrease the differencebetween the theoretical results and the previous experimental data. In addition, based on the role of acoustic pressure amplitude on the characteristics of single-bubble sonoluminescence, various parameters such as degree of ionization, gas pressure, temperature and power were calculated. The results are in excellent agreement with the reported experimental measurements.

    • The relativistic bound states of a non-central potential


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      We investigate the relativistic effects of a moving particle in the field of a pseudoharmonic oscillatory ring-shaped potential under the spin and pseudospin symmetric Dirac wave equation. We obtain the bound-state energy eigenvalue equation and the corresponding two-components spinor wave functions by using the formalism of supersymmetric quantum mechanics (SUSYQM). Furthermore, the non-relativistic limits are obtained by simply making a proper replacement of parameters. The thermodynamic properties are also studied. Our numerical results for the energy eigenvalues are also presented.

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