Oscillation of higher order difference equations via comparison

In this paper we shall present some new oscillation criteria for difference equations of the form x(n) + q(n)f(x[n - ]) = 0 and x(n) = q(t)f(x[n - ]) + p(n)F(x[n + ]) via comparison with some difference equations of lower order whose oscillatory behavior are known

Non-radial oscillations of the rapidly rotating Be star HD 163868

We study the pulsational stability of the rapidly rotating Be star HD 163868 using a newly developed 2D oscillation code which takes the Coriolis force fully into account and compare our results with observations (MOST) and recent other stability analyses of this ~ 6 Msun star. We find both prograde and retrograde overstable modes (although more prograde than retrograde modes) and confirm the existence of low degree odd r-modes destabilised by the kappa-mechanism. The ultra-low frequency modes that could not be explained in a previous analysis are interpreted as high degree, retrograde m=1 modes. A reasonably good fit to the observed oscillation spectrum is possible if we assume that only even modes are observed. This requires a nearly equator-on view of the observed star, consistent with the measured high v sin i value of 250 km/s.Comment: 7 pages, 7 figures; accepted by A&

Augmenting Numerical Stability of the Galerkin Finite Element Formulation for Electromagnetic Flowmeter Analysis

The magnetic flow meter is one of the best possible choice for the measurement of flow rate of liquid metals in fast breeder reactors. Due to the associated complexities in the measuring environment, theoretical evaluation of their sensitivity is always preferred. In order to consider the 3D nature of the problem and the general flow patterns, numerical field computational approach is inevitable. When classical Galerkin's finite element formulation is employed for the solution, it is known to introduce numerical oscillations at high flow rates. The magnetic field produced by the flow induced currents circulate within the fluid and forms the source of this numerical problem. To overcome this, modified methods like stream-line upwind Petrov-Galerkin schemes are generally suggested in the allied areas like fluid dynamics, in which a similar dominance of advective (curl or circulation) component occurs over diffusion (divergence) component. After a careful analysis of the numerical instability through a reduced one dimensional problem, an elegant stable approach is devised. In this scheme, a pole-zero cancellation approach is adopted. The proposed scheme is shown to be absolutely stable. However, at lower flow rates numerical results exhibits small oscillation, which can be controlled by reducing the element size. The source of stability at higher flow rates, as well as, oscillations at lower flow rates are analysed using analytical solution of the associated difference equation. Finally the proposed approach is applied to the original flow meter problem and the solution is shown to be stable.Comment: IET Science, Measurement & Technology, 201

The Frequency Dependence of Critical-velocity Behavior in Oscillatory Flow of Superfluid Helium-4 Through a 2-micrometer by 2-micrometer Aperture in a Thin Foil

The critical-velocity behavior of oscillatory superfluid Helium-4 flow through a 2-micrometer by 2-micrometer aperture in a 0.1-micrometer-thick foil has been studied from 0.36 K to 2.10 K at frequencies from less than 50 Hz up to above 1880 Hz. The pressure remained less than 0.5 bar. In early runs during which the frequency remained below 400 Hz, the critical velocity was a nearly-linearly decreasing function of increasing temperature throughout the region of temperature studied. In runs at the lowest frequencies, isolated 2 Pi phase slips could be observed at the onset of dissipation. In runs with frequencies higher than 400 Hz, downward curvature was observed in the decrease of critical velocity with increasing temperature. In addition, above 500 Hz an alteration in supercritical behavior was seen at the lower temperatures, involving the appearance of large energy-loss events. These irregular events typically lasted a few tens of half-cycles of oscillation and could involve hundreds of times more energy loss than would have occurred in a single complete 2 Pi phase slip at maximum flow. The temperatures at which this altered behavior was observed rose with frequency, from ~ 0.6 K and below, at 500 Hz, to ~ 1.0 K and below, at 1880 Hz.Comment: 35 pages, 13 figures, prequel to cond-mat/050203

Oscillation-free method for semilinear diffusion equations under noisy initial conditions

Noise in initial conditions from measurement errors can create unwanted oscillations which propagate in numerical solutions. We present a technique of prohibiting such oscillation errors when solving initial-boundary-value problems of semilinear diffusion equations. Symmetric Strang splitting is applied to the equation for solving the linear diffusion and nonlinear remainder separately. An oscillation-free scheme is developed for overcoming any oscillatory behavior when numerically solving the linear diffusion portion. To demonstrate the ills of stable oscillations, we compare our method using a weighted implicit Euler scheme to the Crank-Nicolson method. The oscillation-free feature and stability of our method are analyzed through a local linearization. The accuracy of our oscillation-free method is proved and its usefulness is further verified through solving a Fisher-type equation where oscillation-free solutions are successfully produced in spite of random errors in the initial conditions.Comment: 19 pages, 9 figure

Fundamental properties of solar-like oscillating stars from frequencies of minimum Δν\Delta \nu : II. Model computations for different chemical compositions and mass

The large separations between the oscillation frequencies of solar-like stars are measures of stellar mean density. The separations have been thought to be mostly constant in the observed range of frequencies. However, detailed investigation shows that they are not constant, and their variations are not random but have very strong diagnostic potential for our understanding of stellar structure and evolution. In this regard, frequencies of the minimum large separation are very useful tools. From these frequencies, in addition to the large separation and frequency of maximum amplitude, Y\i ld\i z et al. recently have developed new methods to find almost all the fundamental stellar properties. In the present study, we aim to find metallicity and helium abundances from the frequencies, and generalize the relations given by Y\i ld\i z et al. for a wider stellar mass range and arbitrary metallicity ($Z$) and helium abundance ($Y$). We show that the effect of metallicity is { significant} for most of the fundamental parameters. For stellar mass, for example, the expression must be multiplied by (Z/Z_{\sun})^{0.12}. For arbitrary helium abundance, M \propto (Y/Y_{\sun})^{0.25} . Methods for determination of $Z$ and $Y$ from pure asteroseismic quantities are based on amplitudes (differences between maximum and minimum values of \Dnu) in the oscillatory component in the spacing of oscillation frequencies. Additionally, we demonstrate that the difference between the first maximum and the second minimum is very sensitive to $Z$. It also depends on $\nu_{\rm min1}/\nu_{\rm max}$ and small separation between the frequencies. Such a dependence leads us to develop a method to find $Z$ (and $Y$) from oscillation frequencies. The maximum difference between the estimated and model $Z$ values is about 14 per cent. It is 10 per cent for $Y$.Comment: 8 pages, 13 figures; published in MNRAS (2015

Electron-nuclear correlations for photo-induced dynamics in molecular dimers

Ultrafast photoinduced dynamics of electronic excitation in molecular dimers is drastically affected by the dynamic reorganization of inter- and intra- molecular nuclear configuration modeled by a quantized nuclear degree of freedom [Cina et. al, J. Chem Phys. {118}, 46 (2003)]. The dynamics of the electronic population and nuclear coherence is analyzed by solving the chain of coupled differential equations for %mean coordinate, population inversion, electron-vibrational correlation, etc. [Prezhdo, Pereverzev, J. Chem. Phys. {113} 6557 (2000)]. Intriguing results are obtained in the approximation of a small change of the nuclear equilibrium upon photoexcitation. In the limiting case of resonance between the electronic energy gap and the frequency of the nuclear mode these results are justified by comparison to the exactly solvable Jaynes-Cummings model. It is found that the photoinduced processes in the model dimer are arranged according to their time scales: (i) fast scale of nuclear motion, (ii) intermediate scale of dynamical redistribution of electronic population between excited states as well as growth and dynamics of electron-nuclear correlation, (iii) slow scale of electronic population approach to the quasi-equilibrium distribution, decay of electron-nuclear correlation, and decrease of the amplitude of mean coordinate oscillation. The latter processes are accompanied by a noticeable growth of the nuclear coordinate dispersion associated with the overall nuclear wavepacket width. The demonstrated quantum relaxation features of the photoinduced vibronic dynamics in molecular dimers are obtained by a simple method, applicable to systems with many degrees of freedom