Global Convergence of a Nonlinear Programming Method Using Convex Approximations

The method of moving asymptotes (MMA) and its globally convergent extension SCP (sequential convex programming) are known to work well for certain problems arising in structural optimization. In this paper, the methods are extended for a general mathematical programming framework and a new scheme to update certain penalty parameters is defined, which leads to a considerable improvement in the performance. Properties of the approximation functions are outlined in detail. All convergence results of the traditional methods are preserved.     

不同翅片单元外颗粒流换热特性的数值研究

由于成本低,运行稳定,重力驱动移动床在高温固体散料余热回收领域应用潜力较大。然而,相关强化传热技术目前仍待完善。本文基于离散单元法,对颗粒流外掠翅片单元的流动换热特性进行了数值研究。研究表明:通过翅片增加换热面,可以显著提高传热量,但不同翅片单元外颗粒流传热特性不同。颗粒流与不同表面的换热,由颗粒更新、颗粒接触、颗粒竞争掺混以及表面面积共同决定。总体来说,在迎流区,倾斜平表面能扩大面积并确保颗粒更新,更有利于换热增强。而对于背流区,竞争掺混与颗粒接触的影响更大,采用圆弧表面更有优势。     

A numerical study of the motion of a wave running up a beach

The main difficulty for the numerical calculation of the wave running up a beach is the treatment of its moving water boundary. In this paper a scheme of turning the free boundary problem into a fixed boundary problem is designed. The calculated run-up height is consistent with the experiments. Some interesting wave phenomena are also found.     

Intermittent simulated moving bed chromatography: 2. Separation of Tröger’s base enantiomers

The intermittent simulated moving bed (I-SMB) process is a modification of the conventional SMB process that has been recently analyzed theoretically [1]. Here, we present a comparative analysis of the two processes, each operated in a six column 1-2-2-1 configuration (one column in sections 1 and 4 and two columns in sections 2 and 3) and in a four-column 1-1-1-1 configuration. Experiments are carried out on a properly modified laboratory unit to separate racemic mixtures of the enantiomers of Tröger’s base in ethanol on ChiralPak AD at a total feed concentration of 1 g/L. Simulations are carried out for the same system using the equilibrium dispersive model and a bi-Langmuir isotherm, whose parameters have been preliminarily estimated from pulse and breakthrough experiments. Experiments and simulations are fully consistent and demonstrate that the four-column I-SMB process (but not the four-column SMB process) can separate the two enantiomers at very high purity and achieve a productivity twice as large as that of the six-column I-SMB and conventional SMB processes with the same solvent consumption.     

Optimization of simulated moving bed chromatography with fractionation and feedback: Part II. Fractionation of both outlets

A new improvement based on outlet fractionation and feedback has been developed for simulated moving bed (SMB) chromatography. In this contribution, this fractionation and feedback SMB (FF-SMB) concept is extended to the general scenario which integrates a simultaneous fractionation of both outlet streams. A model-based optimization approach, previously adopted to investigate single fractionation, is extended to consider this flexible fractionation policy. Quantitative optimization studies based on a specific separation problem reveal that the double fractionation is the most efficient operating scheme in terms of maximum feed throughput, while the two existing single fractionation modes discussed in our previous study are also significantly superior to the conventional SMB operation. The advantages of the double fractionation extension are further demonstrated in terms of several more detailed performance criteria. In order to evaluate the applicability of the fractionation and feedback modification, the effect of product purity, adsorption selectivity, column efficiency and column number on the relative potential of FF-SMB over SMB is examined.     

Streamlined,two-column,simulated countercurrent chromatography for binary separation

We report on a numerical and experimental study of two-column versions of streamlined, multicolumn, semi-continuous chromatography for binary separation. The systems combine a flexible node design, cyclic flow-rate modulation, and relayed operation of the inlet/outlet ports to extend the mass-transfer zone over the largest possible length, while keeping it inside the system at all times. One advantage of these streamlined designs is the simplicity of their physical realization: regardless of the number of columns, they only require two pumps to supply feed and desorbent into the system, while the flow rates of liquid withdrawn from the system are controlled by material balance using simple two-way valves. In one case, an extra pump is needed to recirculate the fluid in closed-loop. A rigorous model-based optimization approach is employed in the optimal design of the cycles to generate solutions that are physically realizable in the experimental set-ups. The optimized schemes for two-column operation supply fresh feed into the middle of the system where the composition of the circulating fluid is closest to that of the feedstock fluid, and recover the purified products, extract and raffinate, alternately at the downstream end of the unit, while desorbent is continuously supplied into the upstream end of the system. By internally recycling part of the non-pure cut fraction, the scheme with a step of closed-loop recycling significantly reduces its solvent consumption. The feasibility and effectiveness of the reported two-column processes have been verified experimentally on the linear separation of nucleosides by reversed phase subject to 99% purity constraints on both products. It is shown that our processes compare favorably against single-column batch chromatography, steady-state recycling, and four-column, open-loop SMB, for the same amount of adsorbent; they are also better than the four-column, closed-loop SMB at high feed throughputs.     

多重调和Dirichlet问题奇异正解的对称性

我们在穿孔单位球上研究下面多重调和Dirichlet问题{(-Δ)ku=f(u),在B\{0)内,u＞0,在B\{0)内,u=(e)u/(e)v=…=(e)k-1u/(e)vk-1=0,在(e)B上,其中,B是RN中的单位球,v是(e)B的单位外法向量,N＞2k,k≥2.在f满足适当假设条件下,如果0是不可去奇点,我们...     

Weak type heterodimensional cycle bifurcation with orbit-flip

In this paper, we study the weak type heterodimensional cycle with orbit-flip in its non-transversal orbit by using the local moving frame approach. For the first two subcases, we present the sufficient conditions for the existence, uniqueness and non-coexistence of the homoclinic orbit, heteroclinic orbit and periodic orbit. Based on the bifurcation analysis, the bifurcation surfaces and the existence regions are located. And for the third subcase, we theoretically established both the coexistence conditio...     

带插值的自适应网格重构算法求解带移动热源的反应扩散方程的理论分析

本文研究一个带插值的网格重构算法求解一类带移动热源的反应扩散方程. 算法包括两步: 第一步是用旧时间网层上的计算解计算新时间层上的空间网格; 第二步是使用有限差分方法在新时间层 空间网格上离散方程, 并且将旧时间层上计算解的插值作为初始值. 对于时间, 我们获得了一阶收敛结果. 对于空间, 我们证明了使用线性插值算法的一阶收敛性和使用二次插值算法的二阶收敛性. 数值例子肯定了本文的理论结果.