Showing papers in "Pramana in 2013"

The functional variable method for finding exact solutions of some nonlinear time-fractional differential equations

Abstract: In this paper, we implemented the functional variable method and the modified Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled KdV system. This method is extremely simple but effective for handling nonlinear time-fractional differential equations.

Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations

Abstract: Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Benard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 10243, 20483, and 40963 grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good ‘weak’ and ‘strong’ scaling for Tarang on these systems.

A class of exact strange quark star model

Abstract: Static spherically symmetric space-time is studied to describe dense compact star with quark matter within the framework of MIT Bag Model. The system of Einstein’s field equations for anisotropic matter is expressed as a new system of differential equations using transformations and it is solved for a particular general form of gravitational potential with parameters. For a particular parameter, as an example, it is shown that the model satisfies all major physical features expected in a realistic star. The generated model also smoothly matches with the Schwarzschild exterior metric at the boundary of the star. It is shown that the generated solutions are useful to model strange quark stars.

Effect of Al doping on microstructure and optical band gap of ZnO thin film synthesized by successive ion layer adsorption and reaction

Abstract: Thin films of pure and aluminum-doped zinc oxide (AZO) were deposited on glass substrates from ammonium zincate bath following a chemical dipping technique called successive ion layer adsorption and reaction (SILAR). Characterization techniques such as X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy-dispersive X-rays (EDX) were used to investigate the effect of Al doping on the microstructure of AZO films. Particle size analysis using X-ray line broadening shows marginally increasing trend with increasing Al impurity. The average particle size for pure ZnO is 22.75 nm. It increases to 24.26 nm for 1% AZO film and 25.13 nm for 2% AZO film. Incorporation of Al was confirmed from elemental analysis using EDX. SEM micrograph shows that pure ZnO particles are spherical shaped. However, AZO films show particles with off-spherical shape with compact interconnected grains. The value of band gap for pure ZnO is 3.229 eV and it increases to 3.29 eV for 1% AZO indicating a blue-shift for 1% AZO film. However, for 2% AZO film, a decrease in band gap compared to pure ZnO is observed indicating a red-shift of fundamental absorption edge. Electrical resistance shows an initial decrease with increasing Al content. With further enhancement of Al incorporation, the resistance increases.

Solutions and conservation laws of Benjamin–Bona–Mahony–Peregrine equation with power-law and dual power-law nonlinearities

Abstract: In this paper, exact solutions of Benjamin–Bona–Mahony–Peregrine equation are obtained with power-law and dual power-law nonlinearities. The Lie group analysis as well as the simplest equation method are used to carry out the integration of these equations. The solutions obtained are cnoidal waves, periodic solutions and soliton solutions. Subsequently, the conservation laws are derived for the underlying equations.

Exact solutions of some nonlinear partial differential equations using functional variable method

Abstract: The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm Kadomtsev–Petviashvili equation and the higher-order nonlinear Schrodinger equation. By using this useful method, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. It is shown that the proposed method is effective and general.

Energy-dispersive X-ray diffraction beamline at Indus-2 synchrotron source

Abstract: An energy-dispersive X-ray diffraction beamline has been designed, developed and commissioned at BL-11 bending magnet port of the Indian synchrotron source, Indus-2. The performance of this beamline has been benchmarked by measuring diffraction patterns from various elemental metals and standard inorganic powdered samples. A few recent high-pressure investigations are presented to demonstrate the capabilities of the beamline.

Real gauge singlet scalar extension of the Standard Model: A possible candidate for cold dark matter

Abstract: The simplest extension of Standard Model (SM) is considered in which a real SM gauge singlet scalar with an additional discrete symmetry Z 2 is introduced to SM. This additional scalar can be a viable candidate of cold dark matter (CDM) since the stability of S is achieved by the application of Z 2 symmetry on S. Considering S as a possible candidate of CDM, Boltzmann’s equation is solved to find the freeze-out temperature and relic density of S for Higgs mass 120 GeV in the scalar mass range 5 GeV to 1 TeV. As HHSS coupling δ 2 appearing in Lagrangian depends upon the value of scalar mass m S and Higgs mass m h, the m S − δ 2 parameter space has been constrained by using the Wilkinson microwave anisotropy probe (WMAP) limit on the relic density of DM in the Universe and the results of recent ongoing DM direct search experiments, namely CDMS-II, CoGeNT, DAMA, EDELWEISS-II, XENON-10 and XENON-100. From such analyses, two distinct mass regions are found (a lower and higher mass domain) for such a DM candidate that satisfy both the WMAP limit and the experimental results considered here. The possible differential direct detection rates and annual variation of total detection rates have been estimated for this scalar DM candidate S for two detector materials, namely Ge and Xe. Finally, the γ-ray flux has been calculated from the galactic centre due to annihilation of two 130 GeV scalar DM into two monoenergetic γ-rays.

Exact travelling wave solutions for some important nonlinear physical models

Abstract: The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrodinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.

Numerical solution of the one-dimensional Burgers’ equation: Implicit and fully implicit exponential finite difference methods

Abstract: This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.

Bifurcation analysis and the travelling wave solutions of the Klein–Gordon–Zakharov equations

Abstract: In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by using the bifurcation method (Feng et al, Appl. Math. Comput. 189, 271 (2007); Li et al, Appl. Math. Comput. 175, 61 (2006)).

Adaptive control and synchronization of a fractional-order chaotic system

Abstract: In this paper, the chaotic dynamics of a three-dimensional fractional-order chaotic system is investigated The lowest order for exhibiting chaos in the fractional-order system is obtained Adaptive schemes are proposed for control and synchronization of the fractional-order chaotic system based on the stability theory of fractional-order dynamic systems The presented schemes, which contain only a single-state variable, are simple and flexible Numerical simulations are used to demonstrate the feasibility of the presented methods

Complete switched modified function projective synchronization of a five-term chaotic system with uncertain parameters and disturbances

Abstract: A five-term three-dimensional (3D) autonomous chaotic system with an exponential nonlinear term is reported in this paper. Basic dynamical behaviours of the chaotic system are further investigated. Then a new synchronization phenomenon, complete switched modified function projective synchronization (CSMFPS), for this novel five-term chaotic system with uncertain parameters and disturbances is investigated. This paper extends previous work, where CSMFPS of chaotic systems means that all the state variables of the drive system synchronize with different state variables of the response system. As the synchronization scheme has many combined forms, it is a promising type of synchronization and can provide greater security in secure communication. Based on Lyapunov stability theory, a robust adaptive controller is contrived to acquire CSMFPS, parameter identification and suppress disturbances simultaneously. Finally, the Lorenz system and the new five-term chaotic system are taken as examples and the corresponding numerical simulations are presented to verify the effectiveness and feasibility of the proposed control scheme.

Stability analysis of a class of fractional delay differential equations

Abstract: In this paper we analyse stability of nonlinear fractional order delay differential equations of the form $D^{\alpha} y(t) = a f\left(y(t-\tau)\right) - b y(t)$ , where D α is a Caputo fractional derivative of order 0 < α ≤ 1. We describe stability regions using critical curves. To explain the proposed theory, we discuss fractional order logistic equation with delay.

Bright and dark soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili equation and generalized Benjamin equation

Abstract: In this paper, we obtain the 1-soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and the generalized Benjamin equation. By using two solitary wave ansatz in terms of sech p and $\tanh^{p}$ functions, we obtain exact analytical bright and dark soliton solutions for the considered model. These solutions may be useful and desirable for explaining some nonlinear physical phenomena in genuinely nonlinear dynamical systems.

Comparison of backstepping and modified active control in projective synchronization of chaos in an extended Bonhöffer–van der Pol oscillator

Abstract: In this article, projective synchronization of double–scroll attractor of an extended Bonoffer–van der Pol oscillator (BVPO) is considered via the backstepping and active control techniques. In each synchronization scheme, a single control function is designed to achieve projective synchronization between two Bonhoffer–van der Pol oscillator evolving from different initial conditions. To obtain a single control function via the active control, the coefficient of the error dynamics is chosen such that the number of control functions is reduced from three to one, thereby, reducing control function complexity in design. The results show that the transient error dynamics convergence and synchronization time are achieved faster via the backstepping than that of the active control technique. However, the control function obtained via the active control is simpler with a more stable synchronization time and hence, it is more suitable for practical implementation. Numerical simulations are presented to confirm the effectiveness of the analytical results.

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

Abstract: 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.

Effect of doping and annealing on the physical properties of ZnO:Mg nanoparticles

Abstract: Well-dispersed undoped and Mg-doped ZnO nanoparticles with different doping concentrations at various annealing temperatures are synthesized using basic chemical solution method without any capping agent. To understand the effect of Mg doping and heat treatment on the structure and optical response of the prepared nanoparticles, the samples are characterized using X-ray diffraction (XRD), energy-dispersive X-ray (EDX), UV–Vis optical absorption, photoluminescence (PL), scanning electron microscopy (SEM) and transmission electron microscopy (TEM) measurements. The UV–Vis absorbance and PL emission show a blue shift with increasing Mg doping concentration with respect to bulk value. UV–Vis spectroscopy is also used to calculate the band-gap energy of nanoparticles. X-ray diffraction results clearly show that the Mg-doped nanoparticles have hexagonal phase similar to ZnO nanoparticles. TEM image as well as XRD study confirm the estimated average size of the samples to be between 6 and 12 nm. Furthermore, it is seen that there was an increase in the grain size of the particles when the annealing temperature is increased.

Soliton solutions of some nonlinear evolution equations with time-dependent coefficients

Abstract: In this paper, we obtain exact soliton solutions of the modified KdV equation, inhomogeneous nonlinear Schrodinger equation and G(m, n) equation with variable-coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.

Generation of uniform atmospheric pressure argon glow plasma by dielectric barrier discharge

Abstract: In this paper, atmospheric pressure glow discharges (APGD) in argon generated in parallel plate dielectric barrier discharge system is investigated by means of electrical and optical measurements. Using a high voltage (0–20 kV) power supply operating at 10–30 kHz, homogeneous and steady APGD has been observed between the electrodes with gap spacing from 0.5 mm to 2 mm and with a dielectric barrier of thickness 2 mm while argon gas is fed at a controlled flow rate of 1 l/min. The electron temperature and electron density of the plasma are determined by means of optical emission spectroscopy. Our results show that the electron density of the discharge obtained is of the order of 1016 cm − 3 while the electron temperature is estimated to be 0.65 eV. The important result is that electron density determined from the line intensity ratio method and stark broadening method are in very good agreement. The Lissajous figure is used to estimate the energy deposited to the glow discharge. It is found that the energy deposited to the discharge is in the range of 20 to 25 μJ with a discharge voltage of 1.85 kV. The energy deposited to the discharge is observed to be higher at smaller gas spacing. The glow discharge plasma is tested to be effective in reducing the hydrophobicity of polyethylene film significantly.

The Standard Model with one universal extra dimension

Abstract: Effects of universal extra dimensions on Standard Model observables first arise at the one-loop level The quantization of this class of theories is therefore essential in order to perform predictions A comprehensive study of the SU C(3) × SU L(2) × U Y(1) Standard Model defined in a space-time manifold with one universal extra dimension, compactified on the oribifold $S^1/Z_2$ , is presented The fact that the four-dimensional Kaluza–Klein theory is subjected to two types of gauge transformations is stressed and its quantization under the basis of the BRST symmetry discussed A SU C(3) × SU L(2) × U Y(1)-covariant gauge-fixing procedure for the Kaluza–Klein excitations is introduced The connection between gauge and mass eigenstate fields is established in an exact way An exhaustive list of the explicit expressions for all physical couplings induced by the Yang–Mills, Currents, Higgs, and Yukawa sectors is presented The one-loop renormalizability of the standard Green’s functions, which implies that the Standard Model observables do not depend on a cut-off scale, is stressed

Vibrational resonance in the Morse oscillator

Abstract: The occurrence of vibrational resonance is investigated in both classical and quantum mechanical Morse oscillators driven by a biharmonic force. The biharmonic force consists of two forces of widely different frequencies ω and Ω with Ω ≫ ω. In the damped and biharmonically driven classical Morse oscillator, by applying a theoretical approach, an analytical expression is obtained for the response amplitude at the low-frequency ω. Conditions are identified on the parameters for the occurrence of resonance. The system shows only one resonance and moreover at resonance the response amplitude is 1/dω where d is the coefficient of linear damping. When the amplitude of the high-frequency force is varied after resonance the response amplitude does not decay to zero but approaches a nonzero limiting value. It is observed that vibrational resonance occurs when the sinusoidal force is replaced by a square-wave force. The occurrence of resonance and antiresonance of transition probability of quantum mechanical Morse oscillator is also reported in the presence of the biharmonic external field.

The Kepler problem in the Snyder space

Abstract: In this paper the Kepler problem in the non-commutative Snyder scenario was studied. The deformations were characterized in the Poisson bracket algebra under a mimic procedure from quantum standard formulations by taking into account a general recipe to build the non-commutative phase space coordinates (in the sense of Poisson brackets). An expression for the deformed potential was obtained, and then the consequences in the precession of the orbit of Mercury were calculated. The result could be used for finding an estimated value for the non-commutative deformation parameter.

Space-time algebra for the generalization of gravitational field equations

Abstract: The Maxwell–Proca-like field equations of gravitolectromagnetism are formulated using space-time algebra (STA). The gravitational wave equation with massive gravitons and gravitomagnetic monopoles has been derived in terms of this algebra. Using space-time algebra, the most generalized form of gravitoelectromagnetic Klein–Gordon equation has been obtained. Finally, the analogy in formulation between massive gravitational theory and electromagnetism has been discussed.

Quantum capacitance of the armchair-edge graphene nanoribbon

Abstract: The quantum capacitance, an important parameter in the design of nanoscale devices, is derived for armchair-edge single-layer graphene nanoribbon with semiconducting property. The quantum capacitance oscillations are found and these capacitance oscillations originate from the lateral quantum confinement in graphene nanoribbon. Detailed studies of the capacitance oscillations demonstrate that the local channel electrostatic potential at the capacitance peak, the height and the number of the capacitance peak strongly depend on the width, especially a few nanometres, of the armchair-edge graphene nanoribbon. It implies that the capacitance oscillations observed in the experiments can be utilized to measure the width of graphene nanoribbon. The results also show that the capacitance oscillations are not seen when the width is larger than 30 nm.

Novel experimentally observed phenomena in soft matter

Abstract: Soft materials such as colloidal suspensions, polymer solutions and liquid crystals are constituted by mesoscopic entities held together by weak forces. Their mechanical moduli are several orders of magnitude lower than those of atomic solids. The application of small to moderate stresses to these materials results in the disruption of their microstructures. The resulting flow is non-Newtonian and is characterized by features such as shear rate-dependent viscosities and non-zero normal stresses. This article begins with an introduction to some unusual flow properties displayed by soft matter. Experiments that report a spectrum of novel phenomena exhibited by these materials, such as turbulent drag reduction, elastic turbulence, the formation of shear bands and the existence of rheological chaos, flow-induced birefringence and the unusual rheology of soft glassy materials, are reviewed. The focus then shifts to observations of the liquid-like response of granular media that have been subjected to external forces. The article concludes with examples of the patterns that emerge when certain soft materials are vibrated, or when they are displaced with Newtonian fluids of lower viscosities.

Adaptive projective synchronization between different chaotic systems with parametric uncertainties and external disturbances

Abstract: The article deals with adaptive projective synchronization between two different chaotic systems with parametric uncertainties and external disturbances. Based on Lyapunov stability theory, the projective synchronization between a pair of different chaotic systems with fully unknown parameters are derived. An adaptive control law and a parameter update rule for uncertain parameters are designed such that the chaotic response system controls the chaotic drive system. Numerical simulation results are performed to explain the effectiveness and feasibility of the techniques.

Anisotropic cosmological models in $f$(R, T) theory of gravitation

Abstract: A class of non-singular bouncing cosmological models of a general class of Bianchi models filled with perfect fluid in the framework of f(R,T) gravity is presented. The model initially accelerates for a certain period of time and decelerates thereafter. The physical behaviour of the model is also studied.

Investigation of the zenith angle dependence of cosmic-ray muons at sea level

Abstract: Angular distribution of cosmic-ray muons at sea level has been investigated using the Geant4 simulation package. The model used in the simulations was tested by comparing the simulation results with the measurements made using the Berkeley Lab cosmic ray detector. Primary particles’ energy and fluxes were obtained from the experimental measurements. Simulations were run at each zenith angle starting from θ = 0° up to θ = 70° with 5° increment. The angular distribution of muons at sea level has been estimated to be in the form I(θ) = I(0°) cos n (θ), where I(0°) is the muon intensity at 0° and n is a function of the muon momentum. The exponent n = 1.95±0.08 for muons with energies above 1 GeV is in good agreement, within error, with the values reported in the literature.

Q-S synchronization of the fractional-order unified system

Abstract: Concept of Q-S synchronization for fractional-order systems is introduced and Q-S synchronization of the fractional-order unified system is investigated in this paper. On the basis of the stability theory of the fractional-order system, two suitable control schemes are designed to achieve Q-S synchronization of the fractional-order unified systems under the given observable variables of drive system and the response system. Theoretical analysis and numerical simulations are shown to demonstrate the validity and feasibility of the proposed method.