A Comparison of Splittings and Integral Equation Solvers for a Nonseparable Elliptic Equation

Iterative numerical schemes for solving the electrostatic partial differential equation with variable conductivity, using fast and high-order accurate direct methods for preconditioning, are compared. Two integral method schemes of this type, based on previously suggested splittings of the equation, are proposed, analyzed, and implemented. The schemes are tested for large problems on a square. Particular emphasis is paid to convergence as a function of geometric complexity in the conductivity. Differences in performance of the schemes are predicted and observed in a striking manner. AMS subject classification (2000) 31A10, 35C15, 65R20.Received May 2004. Accepted September 2004. Communicated by Anders Szepessy.Johan Helsing: This work was supported by the Swedish Science Research Council under contract 621-2001-2799.     

Some Notes on Reaction Diffusion Systems with Nonlinear Boundary Conditions

This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions.For the heat diffusion case,the necessary and sufficient conditions on the global existence of all positive solutions are obtained.For the general fast diffusion case,we get some conditions on the global existence and nonexistence of positive solutions.The results of this paper fill the some gaps which were left in this field.     

On a Construction of Fast Direct Solvers

Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped and a fast direct solver is used there. All extendable domains are found. Eigenproblems are also considered.     

Fast MAS total through-bond correlation spectroscopy

Mixing sequences for total through-bond correlation spectroscopy in solids (TOBSY) were developed. The motivation is the design of broadband, effective, and robust sequences adapted for "fast" MAS. Possible sequences with the desired Hamiltonian (the homonuclear isotropic J interaction) were identified using lowest order average Hamiltonian theory. Numerical simulations as a function of the MAS frequency were then employed to further characterize the performance. An experimental TOBSY spectrum of a uniformly (13)C-labeled decapeptide at 20 kHz MAS was obtained using one of the new sequences. The spectrum allows us to assign the (13)C resonances to the respective spin systems.     

A conceptual high flux reactor design with scope for use in ADS applications

A 100 MWt reactor design has been conceived to support flux level of the order of 10¹⁵ n/cm²/s in selected flux trap zones. The physics design considers high enriched metallic alloy fuel in the form of annular plates placed in a D₂O moderator tank in a hexagonal lattice arrangement. By choosing a tight lattice pitch in the central region and double the lattice pitch in the outer region, it is possible to have both high fast flux and thermal flux trap zones. By design the flux level in the seed fuel has been kept lower than in the high flux trap zones so that the burning rate of the seed is reduced. Another important objective of the design is to maximize the time interval of refueling. As against a typical refueling interval of a few weeks in such high flux reactor cores, it is desired to maximize this period to as much as six months or even one year. This is possible to achieve by eliminating the conventional control absorbers and replacing them with a suitable amount of fertile material loading in the reactor. Requisite number of seedless thorium-aluminum alloy plates are placed at regular lattice locations vacated by seed fuel in alternate fuel layers. It is seen that these thorium plates are capable of acquiring asymptotic fissile content of 14 g/kg in about 100 days of irradiation at a flux level of 8 × 10¹⁴ n/cm²/s. In summary, the core has a relatively higher fast flux in the central region and high thermal flux in the outer region. The present physics design envisages a flat core excess reactivity for the longest possible cycle length of 6 months to one year. It is also possible to modify the design for constant subcriticality for about the same period or longer duration by considering neutron spallation source at the centre and curtailing the power density in the inner core region by shielding it with a layer of thoria fuel loading.      

基于傅里叶变换的高精度条纹细分方法

针对传统傅里叶变换法在提取条纹图相位中存在的能量泄漏问题,提出了条纹图整周期裁剪的方法,可有效抑制能量泄漏对检相精度的影响,提高傅里叶变换法相位计算的精度。在此基础上,提出了一种基于傅里叶变换时移特性的叠栅条纹细分新方法。与传统傅里叶变换法相比,该方法求取相邻两帧条纹图间的相移,只需经过两次傅里叶变换,不需要截取条纹图的基频再逆变换回空域,因此计算量至少减少了一倍,计算速度大大提高。数值计算结果表明,对两束单色平面波形成的条纹,理想条件下细分精度高达10-12量级;对高斯包络调制的条纹,细分精度至少可达10-3量级。     

Simultaneous determination of β2‐agonists in human urine by fast‐gas chromatography/mass spectrometry: method validation and clinical application

A fast screening protocol was developed and validated for the simultaneous determination of 15 β₂‐agonists in human urine (bambuterol, cimbuterol, clenbuterol, fenoterol, formoterol, isoproterenol, mapenterol, metaproterenol, procaterol, ractopamine, ritodrine, salbutamol, salmeterol, terbutaline, tulobuterol). The overall sample processing includes deconjugation with enzyme hydrolysis, liquid–liquid extraction, followed by derivatization of the extract and detection of β₂‐agonists trimethylsilyl‐derivatives by fast‐gas chromatography/electron impact–mass spectrometry (fast‐GC/EI‐MS). Sample extraction and derivatization were optimized with the purpose of improving recoveries and reaction yields for a variety of analytes with different structures simultaneously, while keeping the procedure simple and reliable. Validation parameters were determined for each analyte under investigation, including selectivity, linearity, intra‐ and inter‐assay precision, extraction recoveries and signal to noise ratio (S/N) at the lowest calibration level. Fast‐GC/MS sequences, based on the use of short columns, high carrier‐gas velocity and fast temperature ramping, allow considerable reduction of the analysis time (7 min), while maintaining adequate chromatographic resolution. The overall GC cycle time was less than 9 min, allowing a processing rate of 6 samples/h. High MS‐sampling rate, using a benchtop quadrupole mass analyzer, resulted in accurate peak shape definition under both scan and selected ion monitoring modes, and high sensitivity in the latter mode. The method was successfully tested on real samples arising from clinical treatments. Copyright © 2009 John Wiley & Sons, Ltd.     

Optimal superconvergent one step quadratic spline collocation methods

We formulate new optimal quadratic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the collocation equations can be solved using a matrix decomposition algorithm. The results of numerical experiments exhibit the expected optimal global accuracy as well as superconvergence phenomena. AMS subject classification (2000)  65N35, 65N22     

A hybrid vortex method for the simulation of three‐dimensional flows

This paper presents an integral vorticity method for solving three‐dimensional Navier–Stokes equations. A finite volume scheme is implemented to solve the vorticity transport equation, which is discretized on a structured hexahedral mesh. A vortex sheet algorithm is used to enforce the no‐slip boundary condition through a vorticity flux at the boundary. The Biot–Savart integral is evaluated to compute the velocity field, in conjunction with a fast algorithm based on multipole expansion. This method is applied to the simulation of uniform flow past a sphere. Copyright © 2007 John Wiley & Sons, Ltd.     

The thorium cycle for fast breeder reactors

The role that could be played by liquid metal-cooled fast breeder reactors (LMFBRs) in the utilization of India’s considerable thorium resources is reviewed in this article. Distinct advantages of thorium-based fuels over plutonium-uranium fuels in LMFBRs pertain to a more favourable coolant voiding reactivity coefficient and better fuel element irradiation stability. The poorer breeding capability of thorium-fuelled fast reactors can in principle be overcome by improved core design and development of advanced fuel concepts. The technical feasibility of such advanced thorium fuels and core designs must be established by sustained research and development. It is also necessary to efficiently close the thorium fuel cycle of fast breeder reactors by appropriate development of the fuel reprocessing and refabrication stages. The Fast Breeder Test Reactor (FBTR) at Kalpakkam is expected to be an important tool for development of thorium fuel and fuel cycle technology. A quick look at the economics of the thorium cycle for fast reactors, vis-a-vis the more conventional uranium cycle indicates only a small and acceptable cost disadvantage on account of the need for remote fabrication of recycled thorium fuel. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.