Continuation and stability analysis for Bloch waves of the Gross-Pitaevskii equation

We describe a two-parameter continuation algorithm for computing Bloch waves of Bose-Einstein condensates (BEC) in optical lattices which is governed by the Gross-Pitaevskii equation (GPE). The Fourier collocation method and fourth-order Adini’s elements with penalty are used to discretize the GPE. We propose two different approaches so that the two-parameter continuation algorithm can be modified to compute closed tubes at the four corners of the Bloch band. We also study linear stability analysis for the GPE. We show that all the discrete steady-state solutions are numerically neutrally stable. Numerical results show that the four edges of the Bloch waves are surrounded by closed loops if the coefficient of the cubic nonlinear term is greater than that of the periodic potential. Moreover, closed tubes at the four corners of the Bloch band are obtained. The numerical results display superfluidity of BEC.     

Numerical simulation of Taylor Couette flow of Bingham fluids

The Bingham fluid flow between two concentric cylinders is studied using numerical simulation. The cylinders are assumed to rotate independently, and with an imposed axial sliding. The flow field is decomposed with linearity arguments of the base circular Couette shear flow and corresponding deviation field. The numerical methods are based on the expression of the deviation field in terms of complete sets of orthogonal functions and Chebyshev series. The Galerkin projection method is used with the pressure term being eliminated. The Adams Bashforth scheme is adopted for time marching. The results show that the vortices are squeezed toward the inner cylinder due to the effect of yield stress. When the outer cylinder is held stationary, the yield stress plays a role in weakening the vortex flow. However, for the co-rotation situation, the vortex flow is initially strengthened with an increase of yield stress, and then weakened as the yield stress is raised large enough. The annular unyielded regions emerge and stick to the outer cylinder. In case of Taylor Couette flow with an imposed axial sliding, a spiral vortex flow is visible with spiral unyielded region being obtained.     

Electrospray ionization from a droplet deposited on a surface-modified glass rod

This paper reports development of a non-mechanical electrospray ionization (ESI) method to generate electrospray from a droplet deposited on an optical fiber coated with a thin gold or Nafion film. Modification of the surface of the optical fiber in this manner increases its wettability, such that a droplet of the aqueous sample solution can adhere sufficiently strongly to the tip of the fiber. The aqueous sample solution was deposited near the tip of the fiber with a micropipette. When a high voltage (2,000 V) was applied to the fiber by electrical connection through the gold film, the sample solution moved and hung at the tip of the fiber. Simultaneously, ESI was generated from the sample droplet. Multiply charged peptide and protein ions were detected by connecting the ESI source to a quadrupole mass analyzer.     

A continuation–domain decomposition algorithm for bifurcation problems

We study numerical solution branches of certain parameter-dependent problems defined on compact domains with various boundary conditions. The finite differences combined with the domain decomposition method are exploited to discretize the partial differential equations. We propose efficient numerical algorithms for solving the associated linear systems and for the detection of bifurcation points. Sample numerical results are reported. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fast fractal image compression using spatial correlation

Fractal image compression is time consuming in the encoding process. The time is essentially spent on the search for the best-match block in a large domain pool. In this paper, the spatial correlations in both the domain pool and the range pool are utilized to reduce the searching space. With this technique, the encoding speed is 2.6 times faster than that of the full search method while the quality of the retrieved image is almost the same. Moreover, since the searching space is limited to the matched blocks of the previous range blocks, fewer bits are required to represent the transform. The bit rate is thus improved by about 20%.     

Nonisothermal crystallization behavior of syndiotactic polystyrene/montmorillonite nanocomposites

X‐ray diffraction methods and differential scanning calorimetry were used to investigate the crystalline structure and crystallization kinetics of syndiotactic polystyrene (sPS)/clay nanocomposites. X‐ray diffraction data showed the presence of polymorphism in sPS/montmorillonite (MMT) nanocomposites, which was strongly dependent on the processing conditions (premelting temperature and cooling rate) of the sPS/MMT nanocomposites and on the content of MMT in the sPS/MMT nanocomposites. The α‐crystalline form could be transformed into β‐crystalline forms at higher premelting temperatures. The nonisothermal melt‐crystallization kinetics and melting behavior of the sPS/MMT nanocomposites were also studied at various cooling rates. The correlation of the crystallization kinetics, melting behavior, and crystalline structure of the sPS/MMT nanocomposites was examined. The results indicated that the addition of a small amount of MMT to sPS caused a change in the mechanism of nucleation and the crystal growth of the sPS crystallite. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 560–570, 2003     

A 2.5-D dynamic model for a saturated porous medium: Part I. Green’s function

Based on Biot’s theory, the dynamic 2.5-D Green’s function for a saturated porous medium is obtained using the Fourier transform and the potential decomposition methods. The 2.5-D Green’s function corresponds to the solutions for the following two problems: the point force applied to the solid skeleton, and the dilatation source applied within the pore fluid. By performing the Fourier transform on the governing equations for the 3-D Green’s function, the governing differential equations for the two parts of the 2.5-D Green’s function are established and then solved to obtain the dynamic 2.5-D Green’s function. The derived 2.5-D Green’s function for saturated porous media is verified through comparison with the existing solution for 2.5-D Green’s function for the elastodynamic case and the closed-form 3-D Green’s function for saturated porous media. It is further demonstrated that a simple form 2-D Green’s function for saturated porous media can be been obtained using the potential decomposition method.