Macromodeling of high-speed interconnects by positive interpolation of vertical segments

In this paper a novel macromodeling scheme is presented to model the per unit of length (p.u.l.) parameters of uniform transmission lines. In particular, it is focused on single on-chip interconnects, because their p.u.l. parameters are influenced by the presence of semiconductor (s) and as such exhibit a strong frequency-dependency, making the modeling process harder. Starting from a set of very accurate tabulated data samples, obtained by two-dimensional electromagnetic modeling, rational models for the four p.u.l. parameters are constructed. The novelty of the approach lies in the fact that the rational models are positive by construction and that a controllable accuracy is obtained. These models can then further be used to construct multivariate models, e.g., for variability analysis. Here, the novel scheme is applied to an on-chip inverted embedded microstrip line, of which the signal integrity behavior is assessed in both the frequency and the time domain, demonstrating the applicability of the macromodels.     

Properties of updating methods for the multipliers in augmented Lagrangians

The convergence properties of different updating methods for the multipliers in augmented Lagrangians are considered. It is assumed that the updating of the multipliers takes place after each line search of a quasi-Newton method. Two of the updating methods are shown to be linearly convergent locally, while a third method has superlinear convergence locally. Modifications of the algorithms to ensure global convergence are considered. The results of a computational comparison with other methods are presented.This work was supported by the Swedish Institute of Applied Mathematics.     

A multiplier method with automatic limitation of penalty growth

This paper presents a multiplier method for solving optimization problems with equality and inequality constraints. The method realizes all the good features that were foreseen by R. Fletcher for this type of algorithm in the past, but which suffers from none of the drawbacks of the earlier attempts.Research sponsored by the National Science Foundation (RANN) Grant ENV76-04264 the National Science Foundation Grant ENG73-08214-A01 and the Sweden-American Foundation.     

Multi-objective Geometry Optimization of a Gas Cyclone Using Triple-Fidelity Co-Kriging Surrogate Models

Cyclone separators are widely used in a variety of industrial applications. A low-mass loading gas cyclone is characterized by two performance parameters, namely the Euler and Stokes numbers. These parameters are highly sensitive to the geometrical design parameters defining the cyclone. Optimizing the cyclone geometry therefore is a complex problem. Testing a large number of cyclone geometries is impractical due to time constraints. Experimental data and even computational fluid dynamics simulations are time-consuming to perform, with a single simulation or experiment taking several weeks. Simpler analytical models are therefore often used to expedite the design process. However, this comes at the cost of model accuracy. Existing techniques used for cyclone shape optimization in literature do not take multiple fidelities into account. This work combines cheap-to-evaluate well-known mathematical models of cyclones, available data from computational fluid dynamics simulations and experimental data to build a triple-fidelity recursive co-Kriging model. This model can be used as a surrogate with a multi-objective optimization algorithm to identify a Pareto set of a finite number of solutions. The proposed scheme is applied to optimize the cyclone geometry, parametrized by seven design variables.     

Optimization of functions whose values are subject to small errors

In this paper we consider the minimization of a function whose values can only be obtained with an error. For the case when the error has certain statistical properties this problem has been investigated by Kiefer and Wolfowitz (1) and Kushner (2, 3). Kushner has shown that a certain class of algorithms converge to a stationary point with probability one. Here a different approach is used. The error is assumed to have an upper bound and it is shown that a stationary point can be obtained to within a certain accuracy, dependent on the magnitude of the error. Our results are related to works concerning roundoff errors for one dimensional optimization (4) and solution of nonlinear equations (5). The algorithm we use can be regarded as an extension of the methods used in (6), (8) and (9).Supported by: Institutet för tillämpad matematik (Sweden) and the National Science Foundation (USA) under grant MPS 72-04787-a02.     

Immunocapillarymigration

The method is based upon the attachment of antibodies to a porous insoluble support and the subsequent capillary migration of the antigen-containing solution in the support. The antigen-covered area thereby obtained was visualized with fluoresceinor horseradish peroxidase-labeled antibodies. The height of this area increased with increasing antigen concentration. The method was used to quantitate C-reactive protein.     

A combination of penalty function and multiplier methods for solving optimal control problems

The properties of combined multiplier and penalty function methods are investigated using a second-order expansion and results known for the Riccati equation. It is shown that the lower bound of the values of the penalty constant necessary to obtain a minimum is given by a certain Riccati equation. The convergence rate of a common updating rule for the multipliers is shown to be linear.This work has been supported by the Swedish Institute of Applied Mathematics.     

Application of fuzzy decision making to the fuzzy finite element method

In this paper we present a new approach to handle uncertainty in the Finite Element Method. As this technique is widely used to tackle real-life design problems, it is also very prone to parameter-uncertainty. It is hard to make a good decision regarding design optimization if no claim can be made with respect to the outcome of the simulation. We propose an approach that combines several techniques in order to offer a total order on the possible design choices, taking the inherent fuzziness into account. Additionally we propose a more efficient ordering procedure to build a total order on fuzzy numbers.     

Preparation and characterization of prototypes for multi-modal separation aimed for capture of positively charged biomolecules at high-salt conditions

Several prototypes of aromatic (Ar) and non-aromatic (NoAr) cation-exchange ligands suitable for capture of proteins from high conductivity (ca. 30 mS/cm) mobile phases were coupled to Sepharose 6 Fast Flow. These new prototypes of multi-modal cation-exchangers were found by screening a diverse library of multi-modal ligands and selecting cation-exchangers resulting in elution of test proteins at high ionic-strength. Candidates were then tested with respect to breakthrough capacity of bovine serum albumin (BSA), human IgG and lysozyme in buffers adjusted to a high conductivity. By applying a salt-step or a pH-step the recoveries were also tested. We have found that aromatic multi-modal cation-exchanger ligands based on carboxylic acids seem to be optimal for the capture of proteins at high-salt conditions. Experimental evidence on the importance of the relative position of the aromatic group in order to improve the breakthrough capacity at high-salt conditions has been found. It was also found that an amide group on the alpha-carbon was essential for capture of proteins at high-salt conditions. Compared to a strong cation-exchanger such as SP Sepharose Fast Flow the best new multi-modal weak cation-exchangers have breakthrough capacities of BSA, human IgG and lysozyme that are 10-30 times higher at high-salt conditions. The new multi-modal cation-exchangers can also be used at normal cation-exchange conditions and with either a salt-step or a pH-step (to pH-values where the proteins are negatively charged) to accomplish elution of proteins. In addition, the functional performance of the new cation-exchangers was found to be intact after treatment in 1.0 M sodium hydroxide solution for 10 days. For BSA it was also possible to design cation-exchangers based on non-aromatic carboxyl acid ligands with high capacities at high-salt conditions. A common feature of these ligands is that they contain hydrogen acceptor groups close to the carboxylic group. Furthermore, it was also possible to obtain high breakthrough capacities for lysozyme and BSA of a strong cation-exchanger (SP Sepharose Fast Flow) if phenyl groups were attached to the beads. Varying the ligand ratio (SP/Phenyl) could be used for optimizing the function of mixed-ligand ion-exchange media.