Tsung Min Hwang

Jacobi-Davidson methods for cubic eigenvalue problems

This study investigates the isothermal crystallization behaviors of polypropylene-polyethylene-(1-butene) terpolymer and the adiabatically expanded polyolefin structured foams. For this purpose, butane gas was used as a physical blowing agent. Avrami equation has been used to interpret theoretically the experimental results obtained by either DSC or polarized optical microscope. It is believed that elongation induced crystallization occurring during the adiabatic expansion process has resulted in an increase in crystallization rate, eventually leading to a faster growth rate of spherulites and an increase in the nucleation density. An analysis of the foam by SEM images showed that the structure of foam is uniform (below diameter 30 m closed cell) In addition, the thermal conductivity and the compressive strength of the polyolefin structured foams was measured. The thermal conductivity of foamed resin with excellent insulation characteristics is reduced compared with unfoamed resin. The compressive strength is decreased with increase in the expansion ratio.

Numerical methods for semiconductor heterostructures with band nonparabolicity

This article presents numerical methods for computing bound state energies and associated wave functions of three-dimensional semiconductor heterostructures with special interest in the numerical treatment of the effect of band nonparabolicity. A nonuniform finite difference method is presented to approximate a model of a cylindrical-shaped semiconductor quantum dot embedded in another semiconductor matrix. A matrix reduction method is then proposed to dramatically reduce huge eigenvalue systems to relatively very small subsystems. Moreover, the nonparabolic band structure results in a cubic type of nonlinear eigenvalue problems for which a cubic Jacobi-Davidson method with an explicit nonequivalence deflation method are proposed to compute all the desired eigenpairs. Numerical results are given to illustrate the spectrum of energy levels and the corresponding wave functions in rather detail.

Numerical Solution of Quadratic Eigenvalue Problems with Structure-Preserving Methods

Numerical methods for the solution of large scale structured quadratic eigenvalue problems are discussed. We describe a new extraction procedure for the computation of eigenvectors and invariant subspaces of skew-Hamiltonian/Hamiltonian pencils using the recently proposed skew-Hamiltonian isotropic implicitly restarted Arnoldi method (SHIRA). As an application we discuss damped gyroscopic systems. For this problem we first solve the eigenvalue problem for the undamped system using the structure-preserving method and then use the quadratic Jacobi--Davidson method as correction procedure. We also illustrate the properties of the new approach for several other application problems.

A synchronization scheme using self-pulsating laser diodes in optical chaotic communication

A synchronization scheme using self-pulsating laser diodes in optical chaotic communication is proposed. Optical chaotic light can be obtained by injecting a sinusoidal electronic signal into a self-pulsating laser diode. To synchronize between two identical chaotic systems with different initial conditions, a drive and response system model is constructed according to Pecora and Carrolls theory. Synchronization can be achieved for optical simplex and duplex transmissions provided that the conditional Lyapunov exponents for the drive and response systems are all negative. This approach offers a key step toward realizing optical chaotic modulation and demodulation.

Rank revealing LU factorizations

Abstract We consider permutations of any given squared matrix and the generalized LU ( r ) factorization of the permuted matrix that reveals the rank deficiency of the matrix. Chan has considered the case with nearly rank deficiency equal to one. This paper extends his results to the case with nearly rank deficiency greater than one. Two applications in constrained optimization are given. We are primarily interested in the existence of such factorizations. In addition to the theories, we also present an efficient two-pass rank revealing LU ( r ) algorithm.

Improved bound for rank revealing LU factorizations

Abstract In many applications it is necessary to determine the rank (or numerical rank) of a matrix. Many of these situations involve matrices that are very large order or that are sparse or that may undergo some form of modification (rank- k update, row or column appended or removed). In these cases the singular value decompositions cost may be prohibitively high or the decomposition may not be computationally feasible (especially for large sparse problems). We thus examine the theoretical merits of rank revealing LU (RRLU) factorizations. We find that in those cases where the nullity is small and the gap is well defined, an RRLU factorization could be a very useful tool.

A generalized structure-preserving doubling algorithm for generalized discrete-time algebraic Riccati equations

In Chu et al. (2004), an efficient structure-preserving doubling algorithm (SDA) was proposed for the solution of discrete-time algebraic Riccati equations (DAREs). In this paper, we generalize the SDA to the G-SDA, for the generalized DARE: E T XE = A T XA − (A T XB…+C TS )(R + B T XB)−1(B T XA + S TC ) + C T QC. Using Cayley transformation twice, we transform the generalized DARE to a DARE in a standard symplectic form without any explicit inversions of (possibly ill-conditioned) R and E. The SDA can then be applied. Selected numerical examples illustrate that the G-SDA is efficient, out-performing other algorithms.

Numerical schemes for three-dimensional irregular shape quantum dots over curvilinear coordinate systems

In this article, we present efficient and stable numerical schemes to simulate three-dimensional quantum dot with irreg- ular shape, so that we can compute all the bound state energies and associated wave functions. A curvilinear coordinate system that fits the target quantum dot shape is first determined. Three finite difference discretizations of the Schrodinger equation are then developed on the original and the skewed curvilinear coordinate system. The resulting large-scale gen- eralized eigenvalue systems are solved by a modified Jacobi-Davidson method. Intensive numerical experiments show that the scheme using both grid points on the original and skewed curvilinear coordinate system can converge to the eigenpairs quickly and stably with second-order accuracy.

A second-order finite volume scheme for three dimensional truncated pyramidal quantum dot

Abstract Three dimensional truncated pyramidal quantum dots are simulated numerically to compute the energy states and the wave functions. The simulation of the hetero-structures is realized by using a novel finite volume scheme to solve the Schrodinger equation. The simulation benefits greatly from the finite volume scheme in threefold. Firstly, the BenDaniel–Duke hetero-junction interface condition is ingeniously embedded into the scheme. Secondly, the scheme uses uniform meshes in discretization and leads to simple computer implementation. Thirdly, the scheme is efficient as it achieves second-order convergence rates over varied mesh sizes. The scheme has successfully computed all the confined energy states and visualized the corresponding wave functions. The results further predict the relation of the energy states and wave functions versus the height of the truncated pyramidal quantum dots.

Subcarrier multiplexing by chaotic multitone modulation

Subcarrier multiplexing by chaotic multitone modulation is investigated. Optical chaotic light can be achieved by injecting multiple subcarriers into a self-pulsating laser diode. Synchronization between two identical chaotic systems (drive and response) can be implemented provided that the conditional Lyapunov exponents are all negative. By adding amplitude modulation (AM) signals to each subcarrier, the two systems become asymptotically synchronized. The AM signals in each subcarrier can be recovered by the introduction of a filtering process where the Lyapunov exponent of the synchronized error function matches the cutoff frequency of a first order low pass filter.