The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadr
upolar field as a model for the current-carrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions.
Giant flares on soft gamma-ray repeaters that are thought to take place on magnetars release enormous energy in a short time interval. Their power can be explained by catastrophic instabilities occurring in the magnetic field configuration and the su
bsequent magnetic reconnection. By analogy with the coronal mass ejection (CME) events on the Sun, we develop a theoretical model via an analytic approach for magnetar giant flares. In this model, the rotation and/or displacement of the crust causes the field to twist and deform, leading to flux rope formation in the magnetosphere and energy accumulation in the related configuration. When the energy and helicity stored in the configuration reach a threshold, the system loses its equilibrium, the flux rope is ejected outward in a catastrophic way, and magnetic reconnection helps the catastrophe develop to a plausible eruption. By taking SGR 1806 - 20 as an example, we calculate the free magnetic energy released in such an eruptive process and find that it is more than $10^{47}$ ergs, which is enough to power a giant flare. The released free magnetic energy is converted into radiative energy, kinetic energy and gravitational energy of the flux rope. We calculated the light curves of the eruptive processes for the giant flares of SGR 1806 - 20, SGR 0526-66 and SGR 1900+14, and compared them with the observational data. The calculated light curves are in good agreement with the observed light curves of giant flares.
We report that the finite thickness of three-dimensional topological insulator (TI) thin films produces an observable magnetoresistance (MR) in phase coherent transport in parallel magnetic fields. The MR data of Bi2Se3 and (Bi,Sb)2Te3 thin films are
compared with existing theoretical models of parallel field magnetotransport. We conclude that the TI thin films bring parallel field transport into a unique regime in which the coupling of surface states to bulk and to opposite surfaces is indispensable for understanding the observed MR. The {beta} parameter extracted from parallel field MR can in principle provide a figure of merit for searching TI compounds with more insulating bulk than existing materials.
A series of high quality NaFe$_{1-x}$Cu$_x$As single crystals has been grown by a self-flux technique, which were systematically characterized via structural, transport, thermodynamic, and high pressure measurements. Both the structural and magnetic
transitions are suppressed by Cu doping, and bulk superconductivity is induced by Cu doping. Superconducting transition temperature ($T_c$) is initially enhanced from 9.6 to 11.5 K by Cu doping, and then suppressed with further doping. A phase diagram similar to NaFe$_{1-x}$Co$_x$As is obtained except that insulating instead of metallic behavior is observed in extremely overdoped samples. $T_c$s of underdoped, optimally doped, and overdoped samples are all notably enhanced by applying pressure. Although a universal maximum transition temperature ($T_c^{max}$) of about 31 K under external pressure is observed in underdoped and optimally doped NaFe$_{1-x}$Co$_x$As, $T_c^{max}$ of NaFe$_{1-x}$Cu$_x$As is monotonously suppressed by Cu doping, suggesting that impurity potential of Cu is stronger than Co in NaFeAs. The comparison between Cu and Co doping effect in NaFeAs indicates that Cu serves as an effective electron dopant with strong impurity potential, but part of the doped electrons are localized and do not fill the energy bands as predicted by the rigid-band model.
The minimum aberration criterion has been frequently used in the selection of fractional factorial designs with nominal factors. For designs with quantitative factors, however, level permutation of factors could alter their geometrical structures and
statistical properties. In this paper uniformity is used to further distinguish fractional factorial designs, besides the minimum aberration criterion. We show that minimum aberration designs have low discrepancies on average. An efficient method for constructing uniform minimum aberration designs is proposed and optimal designs with 27 and 81 runs are obtained for practical use. These designs have good uniformity and are effective for studying quantitative factors.
Classical statistical process control often relies on univariate characteristics. In many contemporary applications, however, the quality of products must be characterized by some functional relation between a response variable and its explanatory va
riables. Monitoring such functional profiles has been a rapidly growing field due to increasing demands. This paper develops a novel nonparametric $L$-1 location-scale model to screen the shapes of profiles. The model is built on three basic elements: location shifts, local shape distortions, and overall shape deviations, which are quantified by three individual metrics. The proposed approach is applied to the previously analyzed vertical density profile data, leading to some interesting insights.
Supersaturated design (SSD) has received much recent interest because of its potential in factor screening experiments. In this paper, we provide equivalent conditions for two columns to be fully aliased and consequently propose methods for construct
ing $E(f_{mathrm{NOD}})$- and $chi^2$-optimal mixed-level SSDs without fully aliased columns, via equidistant designs and difference matrices. The methods can be easily performed and many new optimal mixed-level SSDs have been obtained. Furthermore, it is proved that the nonorthogonality between columns of the resulting design is well controlled by the source designs. A rather complete list of newly generated optimal mixed-level SSDs are tabulated for practical use.
The fusion excitation functions have been measured with rather good accuracy for 32S+90Zr and 32S+96Zr near and below the Coulomb barrier. The sub-barrier cross sections for 32S+96Zr are much larger compared with 32S+90Zr. Semi-classical coupled-chan
nels calculations including two-phonon excitations are capable to describe sub-barrier enhancement only for 32S+90Zr. The remaining disagreement for 32S+96Zr comes from the positive Q-value intermediate neutron transfers in this system. The comparison with 40Ca+96Zr suggests that couplings to the positive Q-value neutron transfer channels may play a role in the sub-barrier fusion enhancement. A rather simple model calculation taking neutron transfers into account is proposed to overcome the discrepancies of 32S+96Zr.
The angular distributions of fission fragments for the $^{32}$S+$^{184}$W reaction at center-of-mass energies of 118.8, 123.1, 127.3, 131.5, 135.8, 141.1 and 144.4 MeV were measured. The experimental fission excitation function is obtained. The fragm
ent angular anisotropy ($mathcal{A}_{rm exp}$) is found by extrapolating the each fission angular distributions. The measured fission cross sections of the $^{32}$S+$^{182,184}$W reaction are decomposed into fusion-fission, quasifission and fast fission contributions by the dinuclear system model. The total evaporation residue excitation function for the $^{32}$S+$^{184}$W reaction calculated in the framework of the advanced statistical model is in good agreement with the available experimental data up to about $E_{rm c.m.}approx 160$ MeV. The theoretical descriptions of the experimental capture excitation functions for both reactions and quantities $K_0^2$, $<ell^2>$ and $mathcal{A}_{rm exp}$ which characterize angular distributions of the fission products were performed by the same partial capture cross sections at the considered range of beam energy.
We use a two-photon dressing field to create an effective vector gauge potential for Bose-condensed Rb atoms in the F=1 hyperfine ground state. The dressed states in this Raman field are spin and momentum superpositions, and we adiabatically load the
atoms into the lowest energy dressed state. The effective Hamiltonian of these neutral atoms is like that of charged particles in a uniform magnetic vector potential, whose magnitude is set by the strength and detuning of Raman coupling. The spin and momentum decomposition of the dressed states reveals the strength of the effective vector potential, and our measurements agree quantitatively with a simple single-particle model. While the uniform effective vector potential described here corresponds to zero magnetic field, our technique can be extended to non-uniform vector potentials, giving non-zero effective magnetic fields.
