Heisenberg equation for a nonrelativistic particle on a hypersurface: from the centripetal force to a curvature induced force

In classical mechanics, a nonrelativistic particle constrained on an $N-1$ curved hypersurface embedded in $N$ flat space experiences the centripetal force only. In quantum mechanics, the situation is totally different for the presence of the geometric potential. We demonstrate that the motion of the quantum particle is "driven" by not only the the centripetal force, but also a curvature induced force proportional to the Laplacian of the mean curvature, which is fundamental in the interface physics, causing curvature driven interface evolution.Comment: 4 page

The centripetal force law and the equation of motion for a particle on a curved hypersurface

It is pointed out that the current form of extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once the fact be taken into consideration, the equation takes that same form as that for centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is favorable.Comment: 5 pages, major revisio

The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies

We develop an approach of Grad-Shafranov (GS) reconstruction for toroidal structures in space plasmas, based on in-situ spacecraft measurements. The underlying theory is the GS equation that describes two-dimensional magnetohydrostatic equilibrium as widely applied in fusion plasmas. The geometry is such that the arbitrary cross section of the torus has rotational symmetry about the rotation axis $Z$, with a major radius $r_0$. The magnetic field configuration is thus determined by a scalar flux function $\Psi$ and a functional $F$ that is a single-variable function of $\Psi$. The algorithm is implemented through a two-step approach: i) a trial-and-error process by minimizing the residue of the functional $F(\Psi)$ to determine an optimal $Z$ axis orientation, and ii) for the chosen $Z$, a $\chi^2$ minimization process resulting in the range of $r_0$. Benchmark studies of known analytic solutions to the toroidal GS equation with noise additions are presented to illustrate the two-step procedures and to demonstrate the performance of the numerical GS solver, separately. For the cases presented, the errors in $Z$ and $r_0$ are 9$^\circ$ and 22\%, respectively, and the relative percent error in the numerical GS solutions is less than 10\%. We also make public the computer codes for these implementations and benchmark studies.Comment: submitted to Sol. Phys. late Dec 2016; under review; code will be made public once review is ove

Catastrophic eruption of magnetic flux rope in the corona and solar wind with and without magnetic reconnection

It is generally believed that the magnetic free energy accumulated in the corona serves as a main energy source for solar explosions such as coronal mass ejections (CMEs). In the framework of the flux rope catastrophe model for CMEs, the energy may be abruptly released either by an ideal magnetohydrodynamic (MHD) catastrophe, which belongs to a global magnetic topological instability of the system, or by a fast magnetic reconnection across preexisting or rapidly-developing electric current sheets. Both ways of magnetic energy release are thought to be important to CME dynamics. To disentangle their contributions, we construct a flux rope catastrophe model in the corona and solar wind and compare different cases in which we either prohibit or allow magnetic reconnection to take place across rapidly-growing current sheets during the eruption. It is demonstrated that CMEs, even fast ones, can be produced taking the ideal MHD catastrophe as the only process of magnetic energy release. Nevertheless, the eruptive speed can be significantly enhanced after magnetic reconnection sets in. In addition, a smooth transition from slow to fast eruptions is observed when increasing the strength of the background magnetic field, simply because in a stronger field there is more free magnetic energy at the catastrophic point available to be released during an eruption. This suggests that fast and slow CMEs may have an identical driving mechanism.Comment: 7 pages, 4 figures, ApJ, in press (vol. 666, Sept. 2007

EFFECTS OF TEMPERATURE ANOMALIES ON THE PALMER DROUGHT SEVERITY INDEX IN THE CENTRAL UNITED STATES

The purpose of this study is to improve our understanding of temperature and precipitation effects on the Palmer Drought Severity Index (PDSI). Both theoretical and observational analyses were applied to separate and compare temperature and precipitation effects on PDSI. The results showed that because of the dependence of PDSI on the ‘climatologically appropriate rainfall’, which is a function of time and varies with surface air temperature, the PDSI can be equally affected by temperature and precipitation, when both have similar magnitudes of anomalies. Calculations using observational data further illustrated the temperature influence on PDSI in different climate regions in the central United States. The temperature effect on PDSI complicates the usage of the index in interpreting precipitation anomalies and its application in inferring precipitation variations, particularly from reconstructed PDSI

Dynamics of glass phases in the two-dimensional gauge glass model

Large-scale simulations have been performed on the current-driven two-dimensional XY gauge glass model with resistively-shunted-junction dynamics. It is observed that the linear resistivity at low temperatures tends to zero, providing strong evidence of glass transition at finite temperature. Dynamic scaling analysis demonstrates that perfect collapses of current-voltage data can be achieved with the glass transition temperature $T_{g}=0.22$, the correlation length critical exponent $\nu =1.8$, and the dynamic critical exponent $z=2.0$. A genuine continuous depinning transition is found at zero temperature. For creeping at low temperatures, critical exponents are evaluated and a non-Arrhenius creep motion is observed in the glass phase.Comment: 10 pages, 6 figure