A new method preserving the positive definiteness of a second order tensor variable in flow simulations with application to viscoelastic turbulence

We present a new numerical method for the simulation of the flow of complex fluids with internal microstructure that is described by a second order, positive definite, internal structural parameter, so that its positive definiteness is preserved in the simulations. An example of such an internal structural parameter is the conformation tensor, used in the modeling of viscoelastic flows, which characterizes the flow-induced molecular deformation. Numerical methods that guarantee the preservation of the positive definiteness of the conformation tensor help both the physical interpretation of the results and the numerical stability of the simulations. The new method presented here is based on the log-conformation representation of a second order tensor. It is implemented through the application of the Cayley-Hamilton theorem for second order tensors. When necessary, we also use an additional mapping that ensures the boundness of the conformation tensor. This approach has been applied in Direct Numerical Simulations (DNS) of viscoelastic turbulent channel flow, which has received great attention since the mid 1990s with ultimate goal to understand the phenomenon of maximum drag reduction. The algorithm uses a full 3D spectral representation of the spatial dependence for the flow and conformation variables and a second order accurate backward differentiation formula for the integration of the governing equations in time. The key issue for the successful implementation of the proposed scheme is a second order finite difference multigrid diffusion applied to the conformation field. Numerical diffusion has been always added to the hyperbolic evolution equations for the conformation tensor in spectral DNS of viscoelastic turbulent flows in order to remove a-physical high wavenumber instabilities induced due to the chaotic nature of the flow. The main advantage of the finite-difference implementation (as opposed to a spectral implementation as done before) is that it allows for the preservation of the positive definiteness of the conformation tensor.     

A genetic algorithm for solving the fixed-charge transportation model: Two-stage problem

Transportation of goods in a supply chain from plants to customers through distribution centers (DCs) is modeled as a two-stage distribution problem in the literature. In this paper we propose genetic algorithms to solve a two-stage transportation problem with two different scenarios. The first scenario considers the per-unit transportation cost and the fixed cost associated with a route, coupled with unlimited capacity at every DC. The second scenario considers the opening cost of a distribution center, per-unit transportation cost from a given plant to a given DC and the per-unit transportation cost from the DC to a customer. Subsequently, an attempt is made to represent the two-stage fixed-charge transportation problem (Scenario-1) as a single-stage fixed-charge transportation problem and solve the resulting problem using our genetic algorithm. Many benchmark problem instances are solved using the proposed genetic algorithms and performances of these algorithms are compared with the respective best existing algorithms for the two scenarios. The results from computational experiments show that the proposed algorithms yield better solutions than the respective best existing algorithms for the two scenarios under consideration.     

Recombinant antibody fragments that detect enoyl acyl carrier protein reductase in Brassica napus

Purified Brassica napus enoyl acyl carrier protein reductase (ENR) was used to select specific antibodies from a library of antibody fragments, single-chain F_v (scF_v), displayed on filamentous phage. Analysis of the selected clones by BstNl fingerprinting and nucleotide sequencing showed that the scF_v were derived from three different human V_H germline genes. The binding specificities were confirmed by Western blots and ELISA. The scF_v preparations reacted with B. napus ENR, but not with β-keto reductase, nor enoyl reductase from Escherichia coli. Analysis of fragments generated by CNBr treatment indicates that the scF_v 3.13 recognizes an epitope located within the n-terminal 80 amino acids of the enzyme molecule. The scF_v were used to detect ENR directly in extracts of B. napus seeds.     

An insight into spray pulsed reactor through mathematical modeling of catalytic dehydrogenation of cyclohexane

A mathematical model has been developed to study the impact of nozzle-catalyst distance and bulk gas temperature on the conversion and hydrogen evolution rate in a spray pulse reactor. The effects of reactor configuration and operating parameters on conversion and evolution rate were predicted with more than 90% accuracy. Reactor optimization and sensitivity analysis were carried out and an optimal design of nozzle-catalyst distance 5 cm and bulk gas temperature of 50 °C were proposed. The optimized design was predicted to increase the conversion from approximately 32–74%. The model could be in general used for designing any endothermic heterogeneous catalytic reaction in a spray pulse reactor.     

A Monotone Iterative Technique for Nonlinear Fourth Order Elliptic Equations with Nonlocal Boundary Conditions

This paper proposes an accelerated iterative procedure for a nonlinear fourth order elliptic equation with nonlocal boundary conditions. First, an existence and uniqueness theorem is proved for the fourth order elliptic equation via the accelerated iterative procedure. To solve this problem numerically, a finite difference based numerical scheme is also developed in view of the main theorem. Theoretically, the monotone property as well as the convergence analysis are proved for both the continuous and discretized cases. The main result also supplements several algorithms for computing the solution of the fourth order elliptic integro-partial differential equation. The proposed scheme not only accelerates the scheme in the literature but also provides a greater flexibility in choosing the initial guess. The efficacy of the proposed scheme is demonstrated through a comparative numerical study with the recent literature. The numerical simulation confirms the theoretical claims too.     

Optimization of multiple responses using a fuzzy-rule based inference system

The optimization of multiple responses (or performance characteristics) has received increasing attention over the last few years in many manufacturing organizations. Many Taguchi practitioners have employed past experience and engineering knowledge or judgement when dealing with multiple responses. This approach brings an element of uncertainty to the decision-making process and therefore is not recommended for optimization of multiple responses. The approach presented in this paper takes advantage of both the Taguchi method and a fuzzy-rule based inference system, which forms a robust and practical methodology in tackling multiple response optimization problems. The paper also presents a case study to illustrate the potential of this powerful integrated approach for tackling multiple response optimization problems. The variance analysis is also an integral part of the study, which identifies the most critical and statistically significant parameters.     

Modified analytic hierarchy process to incorporate uncertainty and managerial aspects

The analytic hierarchy process (AHP) is a powerful multiple-criteria decision analysis technique for dealing with complex problems. Traditional AHP forces decision-makers to converge vague judgements to single numeric preferences in order to estimate the pairwise comparisons of all pairs of objectives and decision alternatives required in the AHP. The resultant rankings of alternatives cannot be tested for statistical significance and it lacks a systematic approach that addresses managerial/soft aspects. To overcome the above limitations, the present paper presents a modified analytic hierarchy process, which incorporates probabilistic distributions to include uncertainty in the judgements. The vector of priorities is calculated using Monte Carlo simulation. The final rankings are analysed for rank reversal using analysis of variance, and managerial aspects (stake holder analysis, soft system methods, etc.) are introduced systematically. The focus is on the actual methodology of the modified analytic hierarchy process, which is illustrated by a brief account of a case study.     

Amphiphilic drug interactions with model cellular membranes are influenced by lipid chain-melting temperature

Small-molecule amphiphilic species such as many drug molecules frequently exhibit low-to-negligible aqueous solubility, and generally have no identified transport proteins assisting their distribution, yet are able to rapidly penetrate significant distances into patient tissue and even cross the blood–brain barrier. Previous work has identified a mechanism of translocation driven by acid-catalysed lipid hydrolysis of biological membranes, a process which is catalysed by the presence of cationic amphiphilic drug molecules. In this study, the interactions of raclopride, a model amphiphilic drug, were investigated with mixtures of biologically relevant lipids across a range of compositions, revealing the influence of the chain-melting temperature of the lipids upon the rate of acyl hydrolysis.