Sultan Z. Alamri

Reconnection of superfluid vortex bundles.

Using the vortex filament model and the Gross-Pitaevskii nonlinear Schroedinger equation, we show that bundles of quantized vortex lines in He II are structurally robust and can reconnect with each other maintaining their identity. We discuss vortex stretching in superfluid turbulence and show that, during the bundle reconnection process, kelvin waves of large amplitude are generated, in agreement with the finding that helicity is produced by nearly singular vortex interactions in classical Euler flows.

Velocity, energy, and helicity of vortex knots and unknots.

In this paper we determine the velocity, the energy, and estimate writhe and twist helicity contributions of vortex filaments in the shape of torus knots and unknots (as toroidal and poloidal coils) in a perfect fluid. Calculations are performed by numerical integration of the Biot-Savart law. Vortex complexity is parametrized by the winding number w given by the ratio of the number of meridian wraps to that of longitudinal wraps. We find that for w<1 vortex knots and toroidal coils move faster and carry more energy than a reference vortex ring of same size and circulation, whereas for w>1 knots and poloidal coils have approximately same speed and energy of the reference vortex ring. Helicity is dominated by writhe contributions. Finally, we confirm the stabilizing effect of the Biot-Savart law for all knots and unknots tested, found to be structurally stable over a distance of several diameters. Our results also apply to quantized vortices in superfluid 4He .

Heat transfer analysis in ferromagnetic viscoelastic fluid flow over a stretching sheet with suction

In this article, an investigation has been performed to explore the two-dimensional boundary layer flow problem and heat transfer characteristic of ferromagnetic viscoelastic fluid flow over a stretching surface with a linear velocity under the impact of magnetic dipole and suction. The governing PDEs are converted into a system of nonlinear ODEs by applying appropriate similarity approach. The modelled equations are then solved numerically by utilizing efficient Runge–Kutta–Fehlberg procedure based on shooting algorithm. Influence of pertinent flow parameter involved, such as ferromagnetic interaction parameter, suction parameter, viscoelastic parameter, Prandtl number on dimensionless velocity, temperature, skin friction, and Nusselt inside the boundary layer, are portrayed graphically and discussed. The results show that pressure profile and skin friction coefficient increase with the variation of ferromagnetic interaction parameter and opposite behaviour is noted for local Nusselt number.

Convective Poiseuille flow of Al2O3-EG nanofluid in a porous wavy channel with thermal radiation

Abstract In current article, convective Poiseuille boundary layer flow of ethylene glycol (C2H6O2)-based nanofluid with suspended aluminum oxide (Al2O3) nanoparticles through a porous wavy channel has been examined. The impact of thermal radiation, Ohmic dissipation, electric field, and magnetic fields are also considered. The flow is due to constant pressure gradient in a wavy frame of reference. The governed momentum and thermal boundary layer equations is system of PDE’s, which are converted to system of ODE’s via suitable similarity transformations. The homotopy analysis method is applied to solve the governed flow problem. Convergence of series solutions is inspected through h-curves and residual errors norm, whereas the optimal value of convergence control parameter is obtained by means of genetic algorithm Nelder–Mead approach. The influence of numerous involving parameters like Hartmann number, Grashof number, Eckert number, electric parameter, radiation parameter, and porosity parameter on flow, heat transfer, skin friction coefficient and Nusselt number are illustrated through graphs and discussed briefly.

Kinetic energy of vortex knots and unknots

New results on the kinetic energy of ideal vortex filaments in the shape of torus knots and unknots are presented. These knots are given by small-amplitude torus knot solutions (Ricca, 1993) to the Localized Induction Approximation (LIA) law. The kinetic energy of different knot and unknot types is calculated and presented for comparison. These results provide new information on relationships between geometry, topology and dynamics of complex vortex systems and help to establish possible connections between aspects of structural complexity of dynamical systems and vortical flows.

Effects of MHD and slip on heat transfer boundary layer flow over a moving plate based on specific entropy generation

ABSTRACT In this article, combined effects of magnetohydrodynamics (MHD) heat transfer flow under the influence of slip over a moving flat plate are investigated. Effects of entropy generation are also examined. A set of non-dimensional resulting equations are solved by means of Bvp4c Matlab package. The role of flow parameters like magnetic parameter and slip parameter on flow velocity profile and temperature profile are presented and elaborated through graphs. The expressions for entropy generation and flow against Bejan number are also examined. The obtained results reveal that for various values of slip parameter, the Bejan number (Be) decreases for , whereas opposite behaviour is noted for .

A stable flat universe with variable cosmological constant in f(R, T) gravity

In this paper, a general FRW cosmological model has been constructed in f(R,T) gravity reconstruction with variable cosmological constant. A number of solutions to the field equations has been generated by utilizing a form for the Hubble parameter that leads to Berman’s law of constant deceleration parameter q = m − 1. The possible decelerating and accelerating solutions have been investigated. For (q > 0) we get a stable flat decelerating radiation-dominated universe at q = 1. For (q < 0) we get a stable accelerating solution describing a flat universe with positive energy density and negative cosmological constant. Nonconventional mechanisms that are expected to address the late-time acceleration with negative cosmological constant have been discussed.

The collinear equilibrium points in the restricted three body problem with triaxial primaries

Abstract The perturbed restricted three body problem has been reviewed. The mass of the primaries are assumed as triaxial. The locations of the collinear points have been computed. Series forms of these locations are obtained as new analytical results. In order to introduce a semi-analytical view, a Mathematica program has been constructed to graph the locations of collinear points versus the whole range of the mass ratio μ taking into account the triaxiality. The resultant figures have been analyzed

V cosmological models in f(R,T) modified gravity with Λ(T) by using generation technique

Abstract A new class of cosmological models in modified theories of gravity proposed by Harko et al. (2011), 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 by generation of new solutions. Motivated by recent work of Pradhan et al. (2015) we have revisited the recent work of Ahmed and Pradhan (2014) by using a generation technique, it is shown that modified field equations are solvable for any arbitrary cosmic scale function. A class of new solutions for particular forms of cosmic scale functions have been investigated. In the present study we consider the cosmological constant as a function of the trace of the stress energy-momentum-tensor, and dub such a model “ gravity” where we specified a certain form of . Such models may exhibit better equability with the cosmological observations. The cosmological constant is found to be a positive decreasing function of time which is supported by results from recent supernovae Ia observations. Expressions for Hubble’s parameter in terms of redshift, luminosity distance redshift, distance modulus redshift and jerk parameter are derived and their significances are described in detail. The physical and geometric properties of the cosmological models are also discussed.

Reconnection of vortex bundles

Recent experimental and theoretical studies have shown striking similarities between ordinary turbulence and quantum turbulence[1, 2]. Quantum turbulence is the turbulence of a superfluid, such as liquid helium (both 4He and 3He) and atomic Bose–Einstein condensates. Particularly interesting is the case in which the superfluid’s temperature is small enough that thermal excitations can be neglected. In this case, the superfluid almost becomes the physical realization of the textbooks’ concept of perfect (inviscid) Euler fluid, from which it differs in only two respects: firstly, superfluid vorticity is concentrated to thin filaments of fixed circulation k and fixed core size ξ secondly, these vortex filaments can reconnect [4] even if the viscosity is zero In superfluid 4He we have k ≈ 10-3 cm3/s and ξ ≈ 10-8 cm.