Effect of Rossby and Alfv\'{e}n waves on the dynamics of the tachocline

To understand magnetic diffusion, momentum transport, and mixing in the interior of the sun, we consider an idealized model of the tachocline, namely magnetohydrodynamics (MHD) turbulence on a $\beta$ plane subject to a large scale shear (provided by the latitudinal differential rotation). This model enables us to self-consistently derive the influence of shear, Rossby and Alfv\'{e}n waves on the transport properties of turbulence. In the strong magnetic field regime, we find that the turbulent viscosity and diffusivity are reduced by magnetic fields only, similarly to the two-dimensional MHD case (without Rossby waves). In the weak magnetic field regime, we find a crossover scale ($L\_R$) from a Alfv\'{e}n dominated regime (on small scales) to a Rossby dominated regime (on large scales). For parameter values typical of the tachocline, $L\_R$ is larger that the solar radius so that Rossby waves are unlikely to play an important role in the transport of magnetic field and angular momentum. This is mainly due to the enhancement of magnetic back-reaction by shearing which efficiently generates small scales, thus strong currents

Choreographic Three Bodies on the Lemniscate

We show that choreographic three bodies {x(t), x(t+T/3), x(t-T/3)} of period T on the lemniscate, x(t) = (x-hat+y-hat cn(t))sn(t)/(1+cn^2(t)) parameterized by the Jacobi's elliptic functions sn and cn with modulus k^2 = (2+sqrt{3})/4, conserve the center of mass and the angular momentum, where x-hat and y-hat are the orthogonal unit vectors defining the plane of the motion. They also conserve the moment of inertia, the kinetic energy, the sum of square of the curvature, the product of distance and the sum of square of distance between bodies. We find that they satisfy the equation of motion under the potential energy sum_{i<j}(1/2 ln r_{ij} -sqrt{3}/24 r_{ij}^2) or sum_{i<j}1/2 ln r_{ij} -sum_{i}sqrt{3}/8 r_{i}^2, where r_{ij} the distance between the body i and j, and r_{i} the distance from the origin. The first term of the potential energies is the Newton's gravity in two dimensions but the second term is the mutual repulsive force or a repulsive force from the origin, respectively. Then, geometric construction methods for the positions of the choreographic three bodies are given

Sleeping more as a way to lose weight

Caloric consumption in a society with readily available food is likely to be approximately proportional to the number of hours of being awake. Thus, replacing 1 h of inactive wakefulness (e.g. watching TV), with sleeping is likely to result in a substantial reduction in caloric intake. Calculations are presented to illustrate the possible benefits of such a switch on weight reduction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75728/1/j.1467-789X.2006.00262.x.pd

The Renormalized Stress Tensor in Kerr Space-Time: Numerical Results for the Hartle-Hawking Vacuum

We show that the pathology which afflicts the Hartle-Hawking vacuum on the Kerr black hole space-time can be regarded as due to rigid rotation of the state with the horizon in the sense that when the region outside the speed-of-light surface is removed by introducing a mirror, there is a state with the defining features of the Hartle-Hawking vacuum. In addition, we show that when the field is in this state, the expectation value of the energy-momentum stress tensor measured by an observer close to the horizon and rigidly rotating with it corresponds to that of a thermal distribution at the Hawking temperature rigidly rotating with the horizon.Comment: 17 pages, 7 figure

Bound States of the Klein-Gordon Equation for Woods-Saxon Potential With Position Dependent Mass

The effective mass Klein-Gordon equation in one dimension for the Woods-Saxon potential is solved by using the Nikiforov-Uvarov method. Energy eigenvalues and the corresponding eigenfunctions are computed. Results are also given for the constant mass case.Comment: 13 page

Promoting kangaroo as a sustainable option for meat production on the rangelands of Australia

Implications •As kangaroo meat is sourced from native wildlife, conservation of the species is important in developing sustainable meat harvesting. Landholders, conservationists, and commercial meat producers need to work together to achieve this goal. •The production of high quality meat products from field-harvested carcasses can be augmented through a better understanding of the impact that field conditions and carcass handling have on final meat eating quality. •Food safety is also paramount, with measures taken to minimize the impacts of parasitism and microbial contamination. Any breaches of inspection protocols can only serve to undermine consumer confidence and viability of the industry

Exact Spin and Pseudo-Spin Symmetric Solutions of the Dirac-Kratzer Problem with a tensor potential via Laplace Transform Approach

Exact bound state solutions of the Dirac equation for the Kratzer potential in the presence of a tensor potential are studied by using the Laplace transform approach for the cases of spin- and pseudo-spin symmetry. The energy spectra is obtained in the closed form for the relativistic as well as non-relativistic cases including the Coulomb potential. It is seen that our analytical results are in agrement with the ones given in literature. The numerical results are also given in a table for different parameter values.Comment: 8 page

Self-force on a scalar charge in radial infall from rest using the Hadamard-WKB expansion

We present an analytic method based on the Hadamard-WKB expansion to calculate the self-force for a particle with scalar charge that undergoes radial infall in a Schwarzschild spacetime after being held at rest until a time t = 0. Our result is valid in the case of short duration from the start. It is possible to use the Hadamard-WKB expansion in this case because the value of the integral of the retarded Green's function over the particle's entire past trajectory can be expressed in terms of two integrals over the time period that the particle has been falling. This analytic result is expected to be useful as a check for numerical prescriptions including those involving mode sum regularization and for any other analytical approximations to self-force calculations.Comment: 22 pages, 2 figures, Physical Review D version along with the corrections given in the erratu