Luke E.K. Achenie

Designing environmentally safe refrigerants using mathematical programming

Computer-aided molecular design is a strategy in which a set of structural groups are systematically combined to form molecules with desired properties. In this paper, a mathematical programming-based approach to computer-aided molecular design is presented. Using a set of structural groups, the problem is formulated as a mixed integer nonlinear program in which discrete variables represent the number of each type of structural groups present in the candidate compound. The augmented-penalty/outer-approximation algorithm is used to solve the MINLP to obtain compound(s) with an optimum value of an appropriate performance index such that molecular structural constraints, physical property constraints and process design limitations are met. With the current renewed interest in the environment, the suggested approach is applied to refrigerant design with an environmental constraint. The results indicate the viability of this approach.

Genetic signatures of High- and Low-Risk Aberrant Crypt Foci in a Mouse Model of Sporadic Colon Cancer

To determine whether cancer risk is related to histopathological features of preneoplastic aberrant crypt foci (ACF), gene expression analysis was performed on ACF from two mouse strains with differing tumor sensitivity to the colonotropic carcinogen, azoxymethane. ACF from sensitive A/J mice were considered at high risk, whereas ACF from resistant AKR/J mice were considered at low risk for tumorigenesis. A/J and AKR/J mice received weekly injections of azoxymethane (10 mg/kg body weight), and frozen colon sections were prepared 6 weeks later. Immunohistochemistry was performed using biomarkers associated with colon cancer, including adenomatous polyposis coli, β-catenin, p53, c-myc, cyclin D1, and proliferating cell nuclear antigen. Hyperplastic ACF, dysplastic ACF, microadenomas, adjacent normal-appearing epithelium, and vehicle-treated colons were laser captured, and RNA was linearly amplified (LCM-LA) and subjected to cDNA microarray-based expression analysis. Patterns of gene expression were identified using adaptive centroid algorithm. ACF from low- and high-risk colons were not discriminated by immunohistochemistry, with the exception of membrane staining of β-catenin. To develop genetic signatures that predict cancer risk, LCM-LA RNA from ACF was hybridized to cDNA arrays. Of 4896 interrogated genes, 220 clustered into six broad clusters. A total of 226 and 202 genes was consistently altered in lesions from A/J and AKR/J mice, respectively. Although many alterations were common to both strains, expression profiles stratified high- and low- risk lesions. These data demonstrate that ACF with distinct tumorigenic potential have distinguishing molecular features. In addition to providing insight into colon cancer promotion, our data identify potential biomarkers for determining colon cancer risk in humans.

Environmentally benign solvent design by global optimization

Abstract Changes in environmental regulations have often resulted in the need to replace existing solvents with more environmentally benign substitutes. For example, solvents such as 1,1,1, trichloroethane are being phased out within the next few years. In general, ‘designer’ compounds, which have desired properties, can be obtained with the help of computer-aided molecular design (CAMD) approaches. In recent years, the above product design problem has often been posed as a mathematical programming problem. In this framework, the desired attributes of the compound are posed as performance objective and constraint functions. Nonlinear functions, such as those associated with solubility parameter models seen in solvent design, can lead to multiple local solutions (i.e. optimization minima). For these cases, the failure to design the globally optimal compound (using a local optimization approach) can introduce a source of uncertainty. Thus, there is a need for global optimization techniques in product design. To address this need, we have developed a new global optimization algorithm that exploits the structure of the CAMD formulation. We have used this algorithm to study the design of environmentally benign solvents for surface cleaning applications in the printing industry.

Computer aided solvent design for extractive fermentation

This paper presents a systematic computer aided molecular design (CAMD) framework for designing solvents for a reaction system. One of the functions of such solvents is to enhance the yield by product extraction. A number of solvent characteristics including biocompatibility, inertness, and ability to cause phase splitting, are considered for the reaction system. We employ the group contribution method to quantitatively represent the relationship between the structure and properties of the solvent molecule. The framework is modeled as a mixed integer nonlinear programming (MINLP) problem and the outer-approximation method with equality relaxation and augmented penalty (OA/ER/AP) is employed to solve it. We present two case studies on ethanol extractive fermentation to illustrate the proposed methodology.

Robust H ∞ control for linear discrete-time systems with norm-bounded time-varying uncertainty

The problem of robust H∞ analysis and synthesis for linear discrete-time systems with norm-bounded time-varying uncertainty is studied in this paper. It will be shown that this problem is equivalent to the problem of H∞ analysis and synthesis of an auxiliary system. The necessary and sufficient conditions for the equivalency are proved. Thus the original problem can be solved by existing H∞ control methods.

On the design of environmentally benign refrigerant mixtures: a mathematical programming approach

Abstract Chlorofluorocarbon (CFC)-based refrigerants (such as CFC12) have found widespread uses in home refrigerators and automotive air conditioners primarily due to their non-toxic, non-flammable nature and their high overall thermodynamic efficiency. However, CFC and hydrochlorofluorocarbon (HCFC) refrigerants with intermediate to high ozone depletion potentials (ODPs) will be banned during the next two decades. The outcome of replacing CFCs in the vapor recompression cycle and various other processes is vital to several industries. Feasible solutions appear to include mixtures of hydrofluorocarbons (HFCs) which have the potential for matching thermodynamic properties of current working fluids while meeting several criteria for ozone depletion potential, flammability, toxicity, materials compatibility and cost. In this paper, a proof-of-concept study is made to show that mathematical programming can be used effectively to identify a small set of alternative refrigerant mixtures which then can be evaluated experimentally. In the mathematical programming model, binary variables specify the type and number of single component refrigerants that exist in a mixture and continuous variables specify the mixture properties, in addition to the proportion in which the single component refrigerants are blended to form the mixture. The environmental issue has been addressed partially by incorporating the ODP, a quantitative measure of the ozone depleting capability of a compound, into the mathematical programming framework. The results indicate the viability of the approach.

Machine-Learning-Augmented Chemisorption Model for CO2 Electroreduction Catalyst Screening

We present a machine-learning-augmented chemisorption model that enables fast and accurate prediction of the surface reactivity of metal alloys within a broad chemical space. Specifically, we show that artificial neural networks, a family of biologically inspired learning algorithms, trained with a set of ab initio adsorption energies and electronic fingerprints of idealized bimetallic surfaces, can capture complex, nonlinear interactions of adsorbates (e.g., *CO) on multimetallics with ∼0.1 eV error, outperforming the two-level interaction model in prediction. By leveraging scaling relations between adsorption energies of similar adsorbates, we illustrate that this integrated approach greatly facilitates high-throughput catalyst screening and, as a specific case, suggests promising {100}-terminated multimetallic alloys with improved efficiency and selectivity for CO2 electrochemical reduction to C2 species. Statistical analysis of the network response to perturbations of input features underpins our fundamental understanding of chemical bonding on metal surfaces.

The optimal design of refrigerant mixtures for a two-evaporator refrigeration system

Abstract The use of liquid-phase mixtures is common in a number of industrial applications. Mixtures have certain advantages over individual components, and these have been exploited advantageously. For the case of refrigerants, a number of azeotropic mixtures are used in practise. The use of non-azeotropic refrigerant mixtures, however, is not as common. This paper looks at the design of refrigerant mixtures for a refrigeration cycle consisting of two evaporators operating at two different temperatures. Such a cycle has been proposed for use in, for example, a commercial refrigerator having a separate freezer section. Compared to the single evaporator cycle operating at the freezer temperature and circulating the cold air from the freezer to the rest of the refrigerator, the double-evaporator cycle can give higher efficiencies since cooling is not done at a lower temperature than what is required. Also, the use of nonazeotropic mixtures has a number of advantages over single component refrigerants and azeotropic mixtures. A mathematical programming approach developed earlier is applied to the double-evaporator cycle to obtain refrigerant mixtures that maximize cooling.

A hybrid global optimization approach for solvent design

This paper presents a hybrid global optimization approach for solving solvent design problems modeled by mixed integer nonlinear programming (MINLP). The strategy incorporates a variant of the outer approximation mathematical programming algorithm and a soft computing global optimization approach, namely simulated annealing. The suggested approach is not provably globally optimal. However, computational experience with benchmark examples and solvent design MINLP models indicate strongly that the approach gives near globally optimal solutions.

On the solution of mixed-integer nonlinear programming models for computer aided molecular design

This paper addresses the efficient solution of computer aided molecular design (CAMD) problems, which have been posed as mixed-integer nonlinear programming models. The models of interest are those in which the number of linear constraints far exceeds the number of nonlinear constraints, and with most variables participating in the nonconvex terms. As a result global optimization methods are needed. A branch-and-bound algorithm (BB) is proposed that is specifically tailored to solving such problems. In a conventional BB algorithm, branching is performed on all the search variables that appear in the nonlinear terms. This translates to a large number of node traversals. To overcome this problem, we have proposed a new strategy for branching on a set of linear branchingfunctions, which depend linearly on the search variables. This leads to a significant reduction in the dimensionality of the search space. The construction of linear underestimators for a class of functions is also presented. The CAMD problem that is considered is the design of optimal solvents to be used as cleaning agents in lithographic printing.