Kernel Free Boundary Integral Method for 3D Stokes and Navier Equations on Irregular Domains

A second-order accurate kernel-free boundary integral method is presented for Stokes and Navier boundary value problems on three-dimensional irregular domains. It solves equations in the framework of boundary integral equations, whose corresponding discrete forms are well-conditioned and solved by the GMRES method. A notable feature of this approach is that the boundary or volume integrals encountered in BIEs are indirectly evaluated by a Cartesian grid-based method, which includes discretizing corresponding simple interface problems with a MAC scheme, correcting discrete linear systems to reduce large local truncation errors near the interface, solving the modified system by a CG method together with an FFT-based Poisson solver. No extra work or special quadratures are required to deal with singular or hyper-singular boundary integrals and the dependence on the analytical expressions of Green's functions for the integral kernels is completely eliminated. Numerical results are given to demonstrate the efficiency and accuracy of the Cartesian grid-based method

Peakon, Cuspon, Compacton, and Loop Solutions of a Three-Dimensional 3DKP(3, 2) Equation with Nonlinear Dispersion

We study peakon, cuspon, compacton, and loop solutions for the three-dimensional Kadomtsev-Petviashvili equation (3DKP(3,2) equation) with nonlinear dispersion. Based on the method of dynamical systems, the 3DKP(3,2) equation is shown to have the parametric representations of the solitary wave solutions such as peakon, cuspon, compacton, and loop solutions. As a result, the conditions under which peakon, cuspon, compacton, and loop solutions appear are also given

Kernel-free boundary integral method for two-phase Stokes equations with discontinuous viscosity on staggered grids

A discontinuous viscosity coefficient makes the jump conditions of the velocity and normal stress coupled together, which brings great challenges to some commonly used numerical methods to obtain accurate solutions. To overcome the difficulties, a kernel free boundary integral (KFBI) method combined with a modified marker-and-cell (MAC) scheme is developed to solve the two-phase Stokes problems with discontinuous viscosity. The main idea is to reformulate the two-phase Stokes problem into a single-fluid Stokes problem by using boundary integral equations and then evaluate the boundary integrals indirectly through a Cartesian grid-based method. Since the jump conditions of the single-fluid Stokes problems can be easily decoupled, the modified MAC scheme is adopted here and the existing fast solver can be applicable for the resulting linear saddle system. The computed numerical solutions are second order accurate in discrete $\ell^2$-norm for velocity and pressure as well as the gradient of velocity, and also second order accurate in maximum norm for both velocity and its gradient, even in the case of high contrast viscosity coefficient, which is demonstrated in numerical tests

Combustion Catalyst: Nano‐Fe2O3 and Nano‐Thermite Al/ Fe2O3 with Different Shapes

In order to enable the energetic materials to possess a more powerful performance, adding combustion catalysts is a quite effective method. Granular, oval, and polyhedral Fe2O3 particles have been prepared by the hydrothermal method and used to fabricate Al/Fe2O3 thermites. All the Fe2O3 and Al/Fe2O3 thermite samples were characterized using a combination of experimental techniques including scanning electron microscopy (SEM), energy dispersive spectrometer (EDS), X‐ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), transmission electron microscope (TEM), and high‐resolution TEM (HRTEM). The non‐isothermal decomposition kinetics of the composites and nitrocellulose (NC) can be modeled by the Avrami‐Erofeev equation f(α)=3(1–α)[–ln(1–α)]1/3/2 in differential form. Through the thermogravimetric analysis infrared (TG‐IR) analysis of decomposition processes and products, it is speculated that Fe2O3 and Al/Fe2O3 can effectively accelerate the thermal decomposition reaction rate of NC by promoting the O‐NO2 bond cleavage. Adding oxides or thermites can distinctly increase the burning rate, decrease the burning rate pressure exponent, increase the flame temperature, and improve the combustion wave structures of the ammonium perchlorate/hydroxyl‐terminated polybutadiene (AP/HTPB) propellants. Among the three studied, different shapes of Fe2O3, the granular Fe2O3, and its corresponding thermites (Al/Fe2O3(H)) exhibit the highest burning rate due to larger surface area associated with smaller particle size. Moreover, Al/Fe2O3(H) thermites have more effective combustion‐supporting ability for AP/HTPB propellants than Fe2O3 structures and the other two as‐prepared Al/Fe2O3 thermites

A Genetic Transformation Method for Cadmium Hyperaccumulator Sedum plumbizincicola and Non-hyperaccumulating Ecotype of Sedum alfredii

The present study demonstrates the development of an Agrobacterium-mediated genetic transformation method for species of the Sedum genus, which includes the Cd/Zn hyperaccumulator Sedum plumbizincicola and the non-hyperaccumulating ecotype of S. alfredii. Multiple shoots were induced from stem nodes of two Sedum plants using Murashige and Skoog (MS) medium containing 0.1 mg/L cytokinin 6-benzyladenine (6-BA) and 1.0 mg/L auxin 1-naphthaleneacetic acid (NAA). The shoot primordia were used as direct targets for Agrobacterium infection. Selection on hygromycin was highly effective in generating Agrobacterium-transformed explants. This callus-free procedure allowed us to obtain transgenic plantlets after rooting hygromycin-resistant shoots on phytohormone-free MS medium containing the antibiotic. The presence and expression of the reporter genes gusA and GFP in transgenic plants were confirmed by a real-time polymerase chain reaction, histochemical GUS assays, and confocal microscopy. This reliable method for genetic transformation of Sedum plants will help us to understand gene functions and the molecular mechanisms underlying Cd hypertolerance and hyperaccumulation in these species

Image-based highly interactive Web mapping for geo-referenced data publishing

This paper describes an image-based technique that enables highly interactive Web choropleth maps for geo-referenced data publishing and visual exploration. Geographic knowledge is encoded into raster images and delivered to the client, instead of in vector formats. Differing from traditional raster-image-based approaches that are static and allow very little user interaction, it allows varieties of sub-second fine-grained interface controls such as dynamic query, dynamic classification, geographic object data identification, user setting adjusting, as well as turning on/off layers, panning and zooming, with no or minimum server support. Compared to Web GIS approaches that are based on vector geographic data, this technique has the features of short initial download time, near-constant performance scalability for larger numbers of geographic objects, and download-map-segment-only-when-necessary which potentially reduces the overall data transfer over the network. As a result, it accommodates general public users with slow modem network connections and low-end machines, as well as users with fast T-1 connections and fast machines. The client-side (browser) is implemented as light-weight Java applets. YMap, an easy-to-use, user-task-oriented highly interactive mapping tool prototype for visual geo-referenced data exploration is implemented using this technique. (UMIACS-TR-2003-02) (HCIL-TR-2002-26

Image-Based Highly Interactive Web Mapping for Geo-Referenced Data Publishing (2002)

This paper describes an image-based technique that enables highly interactive Web choropleth maps for geo-referenced data publishing and visual exploration. Geographic knowledge is encoded into raster images and delivered to the client, instead of in vector formats. Differing from traditional raster-imagebased approaches that are static and allow very little user interaction, it allows varieties of sub-second fine-grained interface controls such as dynamic query, dynamic classification, geographic object data identification, user setting adjusting, as well as turning on/off layers, panning and zooming, with no or minimum server support. Compared to Web GIS approaches that are based on vector geographic data, this technique has the features of short initial download time, near-constant performance scalability for larger numbers of geographic objects, and download-map-segment-only-when-necessary which potentially reduces the overall data transfer over the network. As a result, it accommodates general public users with slow modem network connections and low-end machines, as well as users with fast T-1 connections and fast machines. The client-side (browser) is implemented as light-weight Java applets. YMap, an easy-to-use, user-task-oriented highly interactive mapping tool prototype for visual georeferenced data exploration is implemented using this technique