Fourth Order Gradient Symplectic Integrator Methods for Solving the Time-Dependent Schr\"odinger Equation

We show that the method of splitting the operator ${\rm e}^{\epsilon(T+V)}$ to fourth order with purely positive coefficients produces excellent algorithms for solving the time-dependent Schr\"odinger equation. These algorithms require knowing the potential and the gradient of the potential. One 4th order algorithm only requires four Fast Fourier Transformations per iteration. In a one dimensional scattering problem, the 4th order error coefficients of these new algorithms are roughly 500 times smaller than fourth order algorithms with negative coefficient, such as those based on the traditional Ruth-Forest symplectic integrator. These algorithms can produce converged results of conventional second or fourth order algorithms using time steps 5 to 10 times as large. Iterating these positive coefficient algorithms to 6th order also produced better converged algorithms than iterating the Ruth-Forest algorithm to 6th order or using Yoshida's 6th order algorithm A directly.Comment: 11 pages, 2 figures, submitted to J. Chem. Phy

Nonlinear analysis of an axisymmetric structure subjected to non-axisymmetric loading

The development of the SHELPC finite element computer program is detailed. This program is specialized to simulate the nonlinear material behavior which results from combustor liner hot streaks. This problem produces a nonlinear Fourier Series type loading on an axisymmetric structure. Example cases are presented

Dense crystalline dimer packings of regular tetrahedra

We present the densest known packing of regular tetrahedra with density phi = 4000/4671 = 0.856347... Like the recently discovered packings of Kallus et al. [arXiv:0910.5226] and Torquato-Jiao [arXiv:0912.4210], our packing is crystalline with a unit cell of four tetrahedra forming two triangular dipyramids (dimer clusters). We show that our packing has maximal density within a three-parameter family of dimer packings. Numerical compressions starting from random configurations suggest that the packing may be optimal at least for small cells with up to 16 tetrahedra and periodic boundaries.Comment: 43 pages, revision of the proofs and the appendices, data for small unit cell packings in appendix

The role of gravity on macrosegregation in alloys

During dendritic solidification liquid flow is induced both by buoyancy forces and solidification shrinkage. There is strong evidence that the major reason for the liquid flow is the former, i.e., thermosolutal convection. In the microgravity environment, it is thought that the thermosolutal convection will be greatly diminished so that convection will be confined mainly to the flow of interdendritic liquid required to satisfy the solidification shrinkage. An attempt is made to provide improved models of dendritic solidification with emphasis on convection and macrosegregation. Macrosegregation is an extremely important subject to the commercial casting community. The simulation of thermosolutal convection in directionally solidified (DS) alloys is described. A linear stability analysis was used to predict marginal stability curves for a system that comprises a mushy zone underlying an all-liquid zone. The supercritical thermosolutal convection in directionally solidified dendritic alloys was also modeled. The model assumes a nonconvective initial state with planar and horizontal isotherms and isoconcentration that move upward at a constant solidification velocity. Results are presented for systems involving lead-tin alloys and show significant differences with results of plane-front solidification

Eternally accelerating spacelike braneworld cosmologies

We construct an eternally inflating spacelike brane world model. If the space dimension of the brane is three (SM2) or six (SM5) for M theory or four (SD3) for superstring theory, a time-dependent $n$-form field would supply a constant energy density and cause exponentially expansion of the spacelike brane. In these cases, the hyperbolic space perpendicular to the brane would not vary in size. In the other cases, however, the extra space would vary in size.Comment: 8 pages, Mod. Phys. Lett. A Vol.21, No.40(2006) 2989-299

Are Giant Planets Forming Around HR 4796A?

We have obtained FUSE and HST STIS spectra of HR 4796A, a nearby 8 Myr old main sequence star that possesses a dusty circumstellar disk whose inclination has been constrained from high resolution near-infrared observations to be ~17 deg from edge-on. We searched for circumstellar absorption in the ground states of C II at 1036.3 A, O I at 1039.2 A, Zn II at 2026.1 A, Lyman series H2, and CO (A-X) and failed to detect any of these species. We place upper limits on the column densities and infer upper limits on the gas masses assuming that the gas is in hydrostatic equilibrium, is well-mixed, and has a temperature, Tgas ~ 65 K. Our measurements suggest that this system possesses very little molecular gas. Therefore, we infer an upper limit for the gas:dust ratio (<4.0) assuming that the gas is atomic. We measure less gas in this system than is required to form the envelope of Jupiter.Comment: 10 pages, 3 figures (including 1 color figure), accepted for publication in Ap