Selfdecomposability of Weak Variance Generalised Gamma Convolutions

Weak variance generalised gamma convolution processes are multivariate Brownian motions weakly subordinated by multivariate Thorin subordinators. Within this class, we extend a result from strong to weak subordination that a driftless Brownian motion gives rise to a self-decomposable process. Under moment conditions on the underlying Thorin measure, we show that this condition is also necessary. We apply our results to some prominent processes such as the weak variance alpha-gamma process, and illustrate the necessity of our moment conditions in some cases

Domain wall switching: optimizing the energy landscape

It has recently been suggested that exchange spring media offer a way to increase media density without causing thermal instability (superparamagnetism), by using a hard and a soft layer coupled by exchange. Victora has suggested a figure of merit xi = 2 E_b/mu_0 m_s H_sw, the ratio of the energy barrier to that of a Stoner-Wohlfarth system with the same switching field, which is 1 for a Stoner-Wohlfarth (coherently switching) particle and 2 for an optimal two-layer composite medium. A number of theoretical approaches have been used for this problem (e.g., various numbers of coupled Stoner-Wohlfarth layers and continuum micromagnetics). In this paper we show that many of these approaches can be regarded as special cases or approximations to a variational formulation of the problem, in which the energy is minimized for fixed magnetization. The results can be easily visualized in terms of a plot of the energy as a function of magnetic moment m_z, in which both the switching field [the maximum slope of E(m_z)] and the stability (determined by the energy barrier E_b) are geometrically visible. In this formulation we can prove a rigorous limit on the figure of merit xi, which can be no higher than 4. We also show that a quadratic anistropy suggested by Suess et al comes very close to this limit.Comment: Acccepted for proceedings of Jan. 2007 MMM Meeting, paper BE-0

The breakage prediction for hydromechanical deep drawing based on local bifurcation theory

A criterion of sheet metal localized necking under plane stress was established based on the bifurcation theory and the characteristics theory of differential equation. In order to be capable to incorporate the directional dependence of the plastic strain rate on stress rate, Ito-Goya’s constitutive equation which gave a one to one relationship between stress rate component and plastic strain rate component was employed. The hydromechanical deep drawing process of a cylindrical cup part was simulated using the commercial software ABAQUS IMPLICIT. The onset of breakage of the part during the forming process was predicted by combining the simulation results with the local necking criterion. The proposed method is applied to the hydro-mechanical deep drawing process for A2219 aluminum alloy sheet metal to predict the breakage of the cylindrical cup part. The proposed method can be applied to the prediction of breakage in the forming of the automotive bodies

Spectrums of Black Hole in de Sitter Spacetime with Highly Damped Quasinormal Modes: High Overtone Case

Motivated by recent physical interpretation on quasinormal modes presented by Maggiore, the adiabatic quantity method given by Kunstatter is used to calculate the spectrums of a non-extremal Schwarzschild de Sitter black hole in this paper, as well as electrically charged case. According to highly damped Konoplya and Zhidenko's numerical observational results for high overtone modes\cite{Konoplya}, we found that the asymptotic non-flat spacetime structure leads two interesting facts as followings: (i) near inner event horizon, the area and entropy spectrums, which are given by $A_{en} = 8 n_1 \pi \hbar$, $S_{en} = 2\pi n_1\hbar$, are equally spaced accurately. (ii) However, near outer cosmological horizon the spectrums, which are in the form of $A_{cn} = 16 n_2 \pi \hbar - \sqrt{\frac{48\pi}{\Lambda}A_{cn} - 3 A_{cn}^2}$, $S_{cn} = 4 \pi n_2 \hbar - \sqrt{\frac{3\pi}{\Lambda}A_{cn} - 3/16 A_{cn}^2}$, are not markedly equidistant. Finally, we also discuss the electrically charged case and find the black holes in de Sitter spacetime have similar quantization behavior no matter with or without charge.Comment: 12 pages, 2 firures, published versio

Relationship between the gamma-ray burst pulse width and energy due to the Doppler effect of fireballs

We study in details how the pulse width of gamma-ray bursts is related with energy under the assumption that the sources concerned are in the stage of fireballs. Due to the Doppler effect of fireballs, there exists a power law relationship between the two quantities within a limited range of frequency. The power law range and the power law index depend strongly on the observed peak energy $E_p$ as well as the rest frame radiation form, and the upper and lower limits of the power law range can be determined by $E_p$. It is found that, within the same power law range, the ratio of the $FWHM$ of the rising portion to that of the decaying phase of the pulses is also related with energy in the form of power laws. A platform-power-law-platform feature could be observed in the two relationships. In the case of an obvious softening of the rest frame spectrum, the two power law relationships also exist, but the feature would evolve to a peaked one. Predictions on the relationships in the energy range covering both the BATSE and Swift bands for a typical hard burst and a typical soft one are made. A sample of FRED (fast rise and exponential decay) pulse bursts shows that 27 out of the 28 sources belong to either the platform-power-law-platform feature class or the peaked feature group, suggesting that the effect concerned is indeed important for most of the sources of the sample. Among these bursts, many might undergo an obvious softening evolution of the rest frame spectrum.Comment: Accepted for publication in The Astrophysical Journa