Building elderly friendly community - service learning in Yaumatei

Other Versio

Supercomputer optimizations for stochastic optimal control applications

Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations

Gradient Symplectic Algorithms for Solving the Radial Schrodinger Equation

The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators are well known for their excellent conservation properties. The class of {\it gradient} symplectic algorithms is particularly suited for solving harmonic oscillator dynamics. By use of Suzuki's rule for decomposing time-ordered operators, these algorithms can be easily applied to the Schrodinger equation. We demonstrate the power of this class of gradient algorithms by solving the spectrum of highly singular radial potentials using Killingbeck's method of backward Newton-Ralphson iterations.Comment: 19 pages, 10 figure

Higher-order splitting algorithms for solving the nonlinear Schr\"odinger equation and their instabilities

Since the kinetic and the potential energy term of the real time nonlinear Schr\"odinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even when the total energy is very well conserved. A detail error analysis reveals that the noise, or elementary excitations of the nonlinear Schr\"odinger, obeys the Bogoliubov spectrum and the instability is due to the exponential growth of high wave number noises caused by the splitting process. For a continuum wave function, this instability is unavoidable no matter how small the time step. For a discrete wave function, the instability can be avoided only for \dt k_{max}^2{<\atop\sim}2 \pi, where $k_{max}=\pi/\Delta x$.Comment: 10 pages, 8 figures, submitted to Phys. Rev.

Human face recognition using a spatially weighted Hausdorff distance

Version of RecordPublishe