Using Perron-Frobenius theorem, we prove that the results by Wilkin, Gunn and Smith [1] for the ground states of rotating N Bose atoms in a harmonic atomic trap with frequency ω interacting via attractive δ2(r) forces, are valid for a broad class of predominantly attractive interactions V (r), not necessarily attractive for any r. The sufficient condition for the interaction is that all the two...

Abstract. We study the mean capture time of an unbiased random walker by multiple absorbing mobile traps in bounded domains of one and two spatial dimensions. In one dimension, we consider multiple traps undergoing prescribed oscillatory motion on an interval with reflecting or absorbing boundary conditions. We develop trap co-operation strategies which optimize the mean capture time. We find t...

The 2-point angular correlation function of galaxies, ω(θ) , has been computed on equatorial fields observed with the CTIO 4m prime focus, within a total area of 2.31 deg. In the magnitude range 19 ≤ mR ≤ 21.5, corresponding to < z >≈ 0.35, we find an excess of power in ω(θ) at scales 2 ≤ θ ≤ 6 over what would be expected from an extrapolation of ω(θ) measured at larger θ. The significance of t...

Transport of angular momentum is one of the thrust areas of astrophysical flows. Instabilities and hence the turbulence generated by it has been invoked to understand its role in angular momentum transport in hydrodynamic and magnetohydrodynamic regime. Investigation of an unexplored region described by the parameter space Ω e < 0, Ωe being the epicyclic frequency, resulted in a powerful magnet...

A mechanism is proposed and evaluated for driving rotation in tokamak plasmas by minority ioncyclotron heating, even though this process introduces negligible angular momentum. The mechanism has two elements: First, angular momentum transport is governed by a diffusion equation with a non-slip boundary condition at the separatrix. Second, Monte-Carlo calculations show that energized particles w...

There are many different methods to obtain an orthogonal matrix. Householder discovered an orthogonal matrix, and it can be applied to solve physical problems of reflection. In this classroom note, we can obtain an orthogonal matrix group eAt, where A is antisymmetric with angular vector ω. When t is setting to be t=π/|ω|, eAt is equivalent to a Householder matrix of a reflecting plane with nor...

Linear stability analysis is used to investigate instability mechanisms for a horizontally oriented hyperbolic tangent mixing layer with uniform stable stratification and coordinate system rotation about the vertical axis. The important parameters governing inviscid dynamics are maximum shear S, buoyancy frequency N, angular velocity of rotation Ω and characteristic shear thickness L. Growth ra...

We present accurate analytic fitting formulae which summarize the results of the recent calculation by Nozawa, Itoh & Kohyama on the relativistic thermal bremsstrahlung Gaunt factor for the intracluster plasma. The fitting is carried out for 1≤ Zj ≤ 28, 6.0 ≤ log10 T [K] ≤ 8.5,−4.0 ≤ log10(h̄ω/kBT ) ≤ 1.0, where Zj is the charge number of the ion, T is the temperature, and ω is the angular frequ...

seismic waves travelling through inelastic media are attenuated by the conversion of elastic energy into heat. upon being attenuated, the travelling wave changes: amplitude is reduced, travelling waveform is modified due to high-frequency content absorption, and phase is delayed. attenuation is usually quantified through the quality factor q: the ratio between the energy stored and lost in each...

Many engineering and natural systems are dynamical systems. For example a pendulum is a dynamical system. l mg 2 Figure 1. Simple pendulum. State The state of the dynamical system specifies it conditions. For a pendulum in the absence of external excitation shown in the figure, the angle and the angular velocity uniquely define the state of the dynamical system. Plots of the state variables aga...