Angular Velocity Omega Research Articles

Exploration of the effects of Coriolis force and thermal radiation on water-based hybrid nanofluid flow over an exponentially stretching plate

Hybrid nanofluids’ enhanced thermophysical properties make them applicable in a plethora of mechanical and engineering applications requiring augmented heat transfer. The present study focuses on a three-dimensional Copper-Aluminium Oxide left( Cutext{- }Al_{2}O_{3}right)-water based hybrid nanofluid flow within the boundary layer with heat transfer over a rotating exponentially stretching plate, subjected to an inclined magnetic field. The sheet rotates at an angular velocity Omega and the angle of inclination of the magnetic field is gamma. Employing a set of appropriate similarity transformation reduces the governing PDEs to ODEs. The resulting ODEs are solved with the finite difference code with Shooting Technique. Primary velocity increases at large rotation but the secondary velocity reduces as the rotation increases. In addition, the magnetic field is found to oppose the flow and thereby causing a reduction in both the primary and secondary velocities. Increasing the volume fraction reduces the skin friction coefficient and enhances the heat transfer rate.

On the Dynamics of a Heavy Symmetric Ball that Rolls Without Sliding on a Uniformly Rotating Surface of Revolution

We study the class of nonholonomic mechanical systems formed by a heavy symmetric ball that rolls without sliding on a surface of revolution, which is either at rest or rotates about its (vertical) figure axis with uniform angular velocity Omega . The first studies of these systems go back over a century, but a comprehensive understanding of their dynamics is still missing. The system has an mathrm {SO(3)}times mathrm {SO(2)} symmetry and reduces to four dimensions. We extend in various directions, particularly from the case Omega =0 to the case Omega not =0, a number of previous results and give new results. In particular, we prove that the reduced system is Hamiltonizable even if Omega not =0 and, exploiting the recently introduced “moving energy,” we give sufficient conditions on the profile of the surface that ensure the periodicity of the reduced dynamics and hence the quasiperiodicity of the unreduced dynamics on tori of dimension up to three. Furthermore, we determine all the equilibria of the reduced system, which are classified in three distinct families, and determine their stability properties. In addition to this, we give a new form of the equations of motion of nonholonomic systems in quasi-velocities which, at variance from the well-known Hamel equations, use any set of quasi-velocities and explicitly contain the reaction forces.

Periodic Solutions and KAM Tori for the Spatial Maxwell Restricted N+1-Body Problem with Manev Potential

We consider the motion of an infinitesimal mass under the Newtonian attraction of N point masses forming a ring plus a central body where a Manev potential (-1/r + e/r^2, e in {mathbb {R}}), is applied to the central body. More precisely, the bodies are arranged in a planar ring configuration. This configuration consists of N-1 primaries of equal mass m located at the vertices of a regular polygon that is rotating on its own plane about its center of mass with a constant angular velocity omega . Another primary of mass m_0=beta m (beta >0 parameter) is placed at the center of the ring. Moreover, we assume that the central body may be an ellipsoid, or a radiation source, which introduces a new parameter e. The existence and stability of periodic solutions of the spatial Maxwell restricted N+1-body problem is obtained using averaging theory. The determination of KAM 3-tori encasing some of the linearly stable periodic solutions is proved. The planar case is moreover considered.

Mechanical factors contributing to the Venus flytrap\u2019s rate-dependent response to stimuli

The sensory hairs of the Venus flytrap (Dionaea muscipula Ellis) detect mechanical stimuli imparted by their prey and fire bursts of electrical signals called action potentials (APs). APs are elicited when the hairs are sufficiently stimulated and two consecutive APs can trigger closure of the trap. Earlier experiments have identified thresholds for the relevant stimulus parameters, namely the angular displacement theta and angular velocity omega . However, these experiments could not trace the deformation of the trigger hair’s sensory cells, which are known to transduce the mechanical stimulus. To understand the kinematics at the cellular level, we investigate the role of two relevant mechanical phenomena: viscoelasticity and intercellular fluid transport using a multi-scale numerical model of the sensory hair. We hypothesize that the combined influence of these two phenomena and omega contribute to the flytrap’s rate-dependent response to stimuli. In this study, we firstly perform sustained deflection tests on the hair to estimate the viscoelastic material properties of the tissue. Thereafter, through simulations of hair deflection tests at different loading rates, we were able to establish a multi-scale kinematic link between omega and the cell wall stretch delta . Furthermore, we find that the rate at which delta evolves during a stimulus is also proportional to omega . This suggests that mechanosensitive ion channels, expected to be stretch-activated and localized in the plasma membrane of the sensory cells, could be additionally sensitive to the rate at which stretch is applied.

Remarks on Stationary and Uniformly-rotating Vortex Sheets: Rigidity Results

In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity Omega , such that it has positive vorticity and is concentrated in a finite disjoint union of smooth curves with finite length is the trivial one: constant vorticity amplitude supported on a union of nested, concentric circles. The proof follows a desingularization argument and a calculus of variations flavor.

Holographic energy loss in non-relativistic backgrounds

In this paper, we study some aspects of energy loss in non-relativistic theories from holography. We analyze the energy lost by a rotating heavy point particle along a circle of radius l with angular velocity omega in theories with general dynamical exponent z and hyperscaling violation exponent theta . It is shown that this problem provides a novel perspective on the energy loss in such theories. A general computation at zero and finite temperature is done and it is shown how the total energy loss rate depends non-trivially on two characteristic exponents (z,theta ). We find that at zero temperature there is a special radius l_c where the energy loss is independent of different values of (theta ,z). Also at zero temperature, there is a crossover between a regime in which the energy loss is dominated by the linear drag force and by the radiation because of the acceleration of the rotating particle. We find that the energy loss of the particle decreases by increasing theta and z. We note that, unlike in the zero temperature, there is no special radius l_c at finite temperature case.

BLACK HOLE MAGNETOSPHERES

We investigate the structure of the steady-state force-free magnetosphere around a Kerr black hole in various astrophysical settings. The solution Psi(r,theta) depends on the distributions of the magnetic field line angular velocity omega(Psi) and the poloidal electric current I(Psi). These are obtained self-consistently as eigenfunctions that allow the solution to smoothly cross the two singular surfaces of the problem, the Inner Light Surface (ILS) inside the ergosphere, and the Outer Light Surface (OLS), which is the generalization of the pulsar light cylinder. Magnetic field configurations that cross both singular surfaces (e.g. monopole, paraboloidal) are uniquely determined. Configurations that cross only one light surface e.g. the artificial case of a rotating black hole embedded in a vertical magnetic field) are degenerate. We show that, similarly to pulsars, black hole magnetospheres naturally develop an electric current sheet that potentially plays a very important role in the dissipation of black hole rotational energy and in the emission of high-energy radiation.

THE FORCE-FREE MAGNETOSPHERE OF A ROTATING BLACK HOLE

We revisit the Blandford & Znajek (1977) process and solve the fundamental equation that governs the structure of the steady-state force-free magnetosphere around a Kerr black hole. The solution depends on the distributions of the magnetic field angular velocity omega and the poloidal electric current I. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem, the inner `light surface' located inside the ergosphere, and the outer `light surface' which is the generalization of the pulsar light cylinder. We find the solution for the simplest possible magnetic field configuration, the split monopole, through a numerical iterative relaxation method analogous to the one that yields the structure of the steady-state axisymmetric force-free pulsar magnetosphere (Contopoulos, Kazanas & Fendt 1999). We obtain the rate of electromagnetic extraction of energy and confirm the results of Blandford and Znajek and of previous time dependent simulations. Furthermore, we discuss the physical applicability of magnetic field configurations that do not cross both `light surfaces'.

Chirality of SuperfluidHe3-A

We have used torsional oscillators, containing disk-shaped slabs of superfluid 3He-A, to probe the chiral orbital textures created by cooling into the superfluid state while continuously rotating. Comparing the observed flow-driven textural transitions with numerical simulations of possible textures shows that an oriented monodomain texture with l antiparallel to the angular velocity Omega_0 is left behind after stopping rotation. The bias towards a particular chirality, while in the vortex state, is due to the inequivalence of energies of vortices of opposite circulation. When spun-up from rest, the critical velocity for vortex nucleation depends on the sense of rotation, Omega, relative to that of l. A different type of vorticity, apparently linked to the slab's rim by a domain wall, appears when Omega is parallel to l.

Energy momentum tensor, and theD-term ofQ-balls

We study the energy-momentum tensor of stable, meta-stable and unstable Q-balls in scalar field theories with U(1) symmetry. We calculate properties such as charge, mass, mean square radii and the constant d1 ("D-term") as functions of the phase space angular velocity omega. We discuss the limits when omega approaches the boundaries of the region in which solutions exist, and derive analytical results for the quantities in these limits. The central result of this work is the rigorous proof that d1 is strictly negative for all finite energy solutions in the Q-ball system. We also show that for Q-balls stability is a sufficient, but not necessary, condition for d1 to be negative.

Alpha effect due to buoyancy instability of a magnetic layer

A strong toroidal field can exist in form of a magnetic layer in the overshoot region below the solar convection zone. This motivates a more detailed study of the magnetic buoyancy instability with rotation. We calculate the alpha effect due to helical motions caused by a disintegrating magnetic layer in a rotating density-stratified system with angular velocity Omega making an angle theta with the vertical. We also study the dependence of the alpha effect on theta and the strength of the initial magnetic field. We carry out three-dimensional hydromagnetic simulations in Cartesian geometry. A turbulent EMF due to the correlations of the small scale velocity and magnetic field is generated. We use the test-field method to calculate the transport coefficients of the inhomogeneous turbulence produced by the layer. We show that the growth rate of the instability and the twist of the magnetic field vary monotonically with the ratio of thermal conductivity to magnetic diffusivity. The resulting alpha effect is inhomogeneous and increases with the strength of the initial magnetic field. It is thus an example of an "anti-quenched" alpha effect. The alpha effect is nonlocal, requiring around 8--16 Fourier modes to reconstruct the actual EMF based on the actual mean field.

EQUILIBRIUM CONFIGURATIONS OF SYNCHRONOUS BINARIES: NUMERICAL SOLUTIONS AND APPLICATION TO KUIPER BELT BINARY 2001 QG298

We present numerical computations of the equilibrium configurations of tidally-locked homogeneous binaries, rotating in circular orbits. Unlike the classical Roche approximations, we self-consistently account for the tidal and rotational deformations of both components, and relax the assumptions of ellipsoidal configurations and Keplerian rotation. We find numerical solutions for mass ratios q between 1e-3 and 1, starting at a small angular velocity for which tidal and rotational deformations are small, and following a sequence of increasing angular velocities. Each series terminates at an appropriate ``Roche limit'', above which no equilibrium solution can be found. Even though the Roche limit is crossed before the ``Roche lobe'' is filled, any further increase in the angular velocity will result in mass-loss. For close, comparable-mass binaries, we find that local deviations from ellipsoidal forms may be as large as 10-20%, and departures from Keplerian rotation are significant. We compute the light curves that arise from our equilibrium configurations, assuming their distance is >>1 AU (e.g. in the Kuiper Belt). We consider both backscatter (proportional to the projected area) and diffuse (Lambert) reflections. Backscatter reflection always yields two minima of equal depths. Diffuse reflection, which is sensitive to the surface curvature, generally gives rise to unequal minima. We find detectable intensity differences of up to 10% between our light curves and those arising from the Roche approximations. Finally, we apply our models to Kuiper Belt binary 2001 QG298, and find a nearly edge-on binary with a mass ratio q = 0.93 ^{+0.07}_{-0.03}, angular velocity Omega^2/G rho = 0.333+/-0.001 (statistical errors only), and pure diffuse reflection. For the observed period of 2001 QG298, these parameters imply a bulk density, rho = 0.72 +/- 0.04 g cm^-3.

Chiral sedimentation of extended objects in viscous media

We study theoretically the chirality of a generic rigid object's sedimentation in a fluid under gravity in the low Reynolds number regime. We represent the object as a collection of small Stokes spheres or stokeslets and the gravitational force as a constant point force applied at an arbitrary point of the object. For a generic configuration of stokeslets and forcing point, the motion takes a simple form in the nearly free draining limit where the stokeslet radius is arbitrarily small. In this case, the internal hydrodynamic interactions between stokeslets are weak, and the object follows a helical path while rotating at a constant angular velocity omega about a fixed axis. This omega is independent of initial orientation and thus constitutes a chiral response for the object. Even though there can be no such chiral response in the absence of hydrodynamic interactions between the stokeslets, the angular velocity obtains a fixed nonzero limit as the stokeslet radius approaches zero. We characterize empirically how omega depends on the placement of the stokeslets, concentrating on three-stokeslet objects with the external force applied far from the stokeslets. Objects with the largest omega are aligned along the forcing direction. In this case, the limiting omega varies as the inverse square of the minimum distance between stokeslets. We illustrate the prevalence of this robust chiral motion with experiments on small macroscopic objects of arbitrary shape.

Precessing rotating flows with additional shear: Stability analysis

We consider unbounded precessing rotating flows in which vertical or horizontal shear is induced by the interaction between the solid-body rotation (with angular velocity Omega(0)) and the additional "precessing" Coriolis force (with angular velocity -epsilonOmega(0)), normal to it. A "weak" shear flow, with rate 2epsilon of the same order of the Poincaré "small" ratio epsilon , is needed for balancing the gyroscopic torque, so that the whole flow satisfies Euler's equations in the precessing frame (the so-called admissibility conditions). The base flow case with vertical shear (its cross-gradient direction is aligned with the main angular velocity) corresponds to Mahalov's [Phys. Fluids A 5, 891 (1993)] precessing infinite cylinder base flow (ignoring boundary conditions), while the base flow case with horizontal shear (its cross-gradient direction is normal to both main and precessing angular velocities) corresponds to the unbounded precessing rotating shear flow considered by Kerswell [Geophys. Astrophys. Fluid Dyn. 72, 107 (1993)]. We show that both these base flows satisfy the admissibility conditions and can support disturbances in terms of advected Fourier modes. Because the admissibility conditions cannot select one case with respect to the other, a more physical derivation is sought: Both flows are deduced from Poincaré's [Bull. Astron. 27, 321 (1910)] basic state of a precessing spheroidal container, in the limit of small epsilon . A Rapid distortion theory (RDT) type of stability analysis is then performed for the previously mentioned disturbances, for both base flows. The stability analysis of the Kerswell base flow, using Floquet's theory, is recovered, and its counterpart for the Mahalov base flow is presented. Typical growth rates are found to be the same for both flows at very small epsilon , but significant differences are obtained regarding growth rates and widths of instability bands, if larger epsilon values, up to 0.2, are considered. Finally, both flow cases are briefly discussed in view of a subsequent nonlinear study using pseudospectral direct numerical simulations, which is a natural continuation of RDT.

Decay of Turbulence Generated by Spin-Down to Rest in Superfluid 4He

We report on the extension of the experiments (P. M. Walmsley et al., Phys. Rev. Lett. 99, 265302 (2007)) on the decay of quasiclassical turbulence generated by an impulsive spin-down from angular velocity Omega to rest of superfluid 4He in a cubic container at temperatures 0.15 K - 1.6 K. The density of quantized vortex lines L is measured by scattering negative ions. Following the spin-down, the maximal density of vortices is observed after time t ~ 10 Omega^-1. By observing the propagation of ions along the axis of the initial rotation, the transient dynamics of the turbulence spreading from the perimeter of the container into its central region is investigated. Nearly homogeneous turbulence develops after time t ~ 100 Omega^-1 and decays as L proportional to t^(-3/2). The effective kinematic viscosity in T=0 limit is nu = 0.003 kappa, where kappa=10^-3 cm^2 / s is the circulation quantum.

High spin baryon in hot strongly coupled plasma

We consider a strings-junction holographic model of a probe baryon in the finite-temperature supersymmetric Yang-Mills dual of the AdS-Schwarzschild black hole background. In particular, we investigate the screening length for a high spin baryon composed of rotating N-c heavy quarks. To rotate quarks by finite force, we put a hard infrared cutoff in the bulk and give quarks a finite mass. We find that N-c microscopic strings are embedded reasonably in the bulk geometry when they have finite angular velocity omega, similar to the meson case. By defining the screening length as the critical separation of quarks, we compute the omega dependence of the baryon screening length numerically and obtain a reasonable result which shows that baryons with high spin dissociate more easily. Finally, we discuss the relation between J and E-2 for baryons.

10.1007/s11490-008-1001-6

After reviewing the ideal Bose-Einstein gas in a box and in a harmonic trap, I discuss the effect of interactions on the formation of a Bose-Einstein condensate (BEC), along with the dynamics of small-amplitude perturbations (the Bogoliubov equations). When the condensate rotates with angular velocity Omega, one or several vortices nucleate, with many observable consequences. With more rapid rotation, the vortices form a dense triangular array, and the collective behavior of these vortices has additional experimental implications. For Omega near the radial trap frequency omega_perp, the lowest-Landau-level approximation becomes applicable, providing a simple picture of such rapidly rotating condensates. Eventually, as Omega approaches omega_perp, the rotating dilute gas is expected to undergo a quantum phase transition from a superfluid to various highly correlated (nonsuperfluid) states analogous to those familiar from the fractional quantum Hall effect for electrons in a strong perpendicular magnetic field.

Dissipation of Quantum Turbulence in the Zero Temperature Limit

Turbulence, produced by an impulsive spin down from angular velocity Omega to rest of a cube-shaped container, is investigated in superfluid 4He at temperatures 0.08 K-1.6 K. The density of quantized vortex lines L is measured by scattering negative ions. Homogeneous turbulence develops after time t approximately 20/Omega and decays as L proportional, t-3/2. The corresponding energy flux =nu'(kappaL)2 proportional, t-3 is characteristic of quasiclassical turbulence at high Re with a saturated energy-containing length. The effective kinematic viscosity in T=0 limit is nu'=0.003kappa, where kappa=10(-3) cm2 s(-1) is the circulation quantum.

Behavior of flowing granular materials under variableg

We consider the impact of the effective gravitational acceleration g{eff} on gravity-driven granular shear flow utilizing a tumbler of radius R rotating at angular velocity omega when g{eff} is varied up to 25 times the gravitational level on Earth in a large centrifuge. The Froude number Fr=omega{2}R/g{eff} is shown to be the proper scaling to characterize the effect of gravity on the angle of repose of the flowing layer. Likewise, transitions between flow regimes depend on Fr. Furthermore, the thickness of the flowing layer is independent of the g level. These results provide a starting point for understanding granular flows on planetary bodies with g{eff} different than on Earth for application to planetary exploration and formation of geologic features.

Derivation of the Spiral Motion of an Eruptive Prominence and Its Explanation

A 2D velocity field of the eruptive prominence (EP) of 1991 March 5 is obtained from its spectral data observed at the Yunnan Observatory and the velocity distributions along the entrance slit are derived for different observing frames. Under the assumption that matter in the EP undergoes axial, radial and possible rotational motions, we construct a theoretical velocity distribution of the EP along the entrance slit, to derive, by fitting, the angular velocity of rotation w and the other three parameters (axial velocity v(o), radial velocity v(r) and the angle between the EP plane and the line of sight phi). We found: an averaged angular velocity omega of 3.0 X 10(-3) arc s(-1) and the variation of omega with the height above the solar limb. As the EP rises, the matter within it in fact moves along a spiral path around its axis. The spiral motion may be explained by the theory of plasma 'double pole diffusion' (DPD) caused by a sharp density gradient between the eruptive prominence and the surrounding corona. A theoretical angular velocity omega' is estimated based on the DPD and basically coincides with U) obtained from the optimal velocity fitting.