Interpolation with circular basis functions

In this paper we consider basis function methods for solving the problem of interpolating data over distinct points on the unit circle. In the special case where the points are equally spaced we can appeal to the theory of circulant matrices which enables an investigation into the stability and accuracy of the method. This work is a further extension and application of the research of Cheney, Light and Xu ([W.A. Light and E.W. Cheney, J. Math. Anal. Appl., 168:110–130, 1992] and [Y. Xu and E.W. Cheney, Computers Math. Applic., 24:201–215, 1992]) from the early nineties

Lurasidone is not associated with risk of QTc prolongation

A critical appraisal and clinical application of Meltzer HY, Cucchiaro J, Silva R, Ogasa M, Phillips D, Xu J, Kalali AH, Scheizer E, Pikalov A, Loebel A. Lurasidone in the treatment of schizophrenia: a randomized, double-blind, placebo- and olanzapine-controlled study. Am J Psychiatry. 2011 Sep;168(9):957-67. doi: https://doi.org/10.1176/appi.ajp.2011.10060907

On the convergence of feasibility based bounds tightening

Global Optimization and Mixed-Integer Nonlinear Programming problems such as min{f(x) | gL ≤ g(x) ≤ gU ∧ xL ≤ x ≤ xU ∧ ∀j ∈ Z (xj ∈ Z)}, where f : Rn → R, g : Rn → Rm, gL, gU ∈ Rm, xL, x, xU ∈ Rn and Z ⊆ {1, . . . , n},are usually solved to "-guaranteed approximation by the spatial Branch-and-Bound (sBB) algorithm [2], a variant of the usual Branch-and-Bound for dealing with nonlinear, possibly nonconvex f, g. Since the gap between the original problem P and its convex relaxation ¯ P is due both to integral variable restrictions being lifted as well as nonconvex functions being replaced by a convex relaxation, sBB is able to branch at continuous variables as well as integer ones. If ¯x solves ¯ P, the standard disjunction used at a node in the sBB search tree is xj ≤ ¯xj ∨xj ≥ ¯xj , the more usual one xj ≤ ⌊¯xj⌋∨xj ≥ ⌈¯xj⌉ being used only if j ∈ Z

Multi-scale simulation of gas solid fluidization based on EMMS- DPM

This presentation will discuss some efforts to improve the speed and accuracy of discrete particle method from physical models to computational methods. For physical model, the multiscale method is used. At global scale, the particles are distributed according to global distribution predicted by the Energy Minimization Multi-Scale (EMMS) model, so that the computation domain can be decomposed non-uniformly for load balance. At grid scale, to improve accuracy, the structure dependent drag coefficient based on the EMMS is used. At particle scale, the coarse grained method is used. The size and solids concentration of the coarse-grained particles (CGP) are determined by the cluster properties which can be predicted by the EMMS model. The coefficient of restitution is modified according to the kinetic theory of granular flows (KTGF). The method thus established in called EMMS-DPM(Lu, Xu et al. 2014). As for computation, using system shared memory, the CFD computation on CPU is fully overlapped with particle computation on GPU. Also, the computation program is coupled with parallel visualization and control program, forming an online interactive simulation platform(Ge, Lu et al. 2015). This method is verified by the simulation of two different CFB risers and several orders of speedup can be achieved. A methanol to orifin (MTO) process is simulated for more than 6800s. We also simulated a CFB with 30kg 0.082mm particles in 3D full loop. Furthermore, the interactive simulation platform can also be used for education and training purpose since it allows virtual experiment on computers. REFERENCES 1.Ge, W., L. Lu, S. Liu, J. Xu, F. Chen and J. Li (2015). Multiscale Discrete Supercomputing - A Game Changer for Process Simulation? Chemical Engineering & Technology 38(4): 575-584. 2.Lu, L., J. Xu, W. Ge, Y. Yue, X. Liu and J. Li (2014). EMMS-based discrete particle method (EMMS–DPM) for simulation of gas–solid flows. Chemical Engineering Science 120(0): 67-87