Numerical solution of minimax problems of optimal control,part 1

This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

Discontinuous Galerkin methods on graphics processing units for nonlinear hyperbolic conservation laws

We present a novel implementation of the modal DG method for hyperbolic conservation laws in two dimensions on graphics processing units (GPUs) using NVIDIA's Compute Unified Device Architecture. Both flexible and highly accurate, DG methods accommodate parallel architectures well as their discontinuous nature produces element‐local approximations. High‐performance scientific computing suits GPUs well, as these powerful, massively parallel, cost‐effective devices have recently included support for double‐precision floating‐point numbers. Computed examples for Euler equations over unstructured triangle meshes demonstrate the effectiveness of our implementation on an NVIDIA GTX 580 device. Profiling of our method reveals performance comparable with an existing nodal DG‐GPU implementation for linear problems. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of PCBs in Biotic Matrices by Two-Dimensional GC-ECD

Abstract

The suitability of three GC-ECD systems for the separation of a model mixture containing various congeners of PCBs together with persistent chlorinated aromatics (pesticides and their metabolites, industrial chemicals) was tested. Analyses were performed on two parallel capillaries, the stationary phase of one of them was always in routine practice very common 5% phenyl-methylpolysiloxane, the second one was either 50% phenylmethylpolysiloxane or 7% phenyl-7% cyanopropyl-methylpolysiloxane. The number of unresolved (coeluted) analytes was significantly reduced in these systems and thus unbiased quantitation of PCBs and other components used for regulation was possible. The utilization of this type of multidimensional chromatography for rapid and reliable analysis of real samples (fish oil, human fat) was documented.     

Effect of gap and flow orientation on two-phase flow in an oil-wet gap: Relative permeability curves and flow structures

Naturally fractured reservoirs contain about 25–30% of the world supply of oil. In these reservoirs, fractures are the dominant flow path. Therefore, a good understanding of transfer parameters such as relative permeability as well as flow regimes occurring in a fracture plays an important role in developing and improving oil production from such complex systems. However, in contrast with gas–liquid flow in a single fracture, the flow of heavy oil and water has received less attention. In this research, a Hele-Shaw apparatus was built to study the flow of water in presence of heavy oil and display different flow patterns under different flow rates and analyze the effect of fracture orientations on relative permeability curves as well as flow regimes. The phase flow rates versus phase saturation results were converted to experimental relative permeability curves. The results of the experiments demonstrate that, depending on fracture and flow orientation, there could be a significant interference between the phases flowing through the fracture. The results also reveal that both phases can flow in both continuous and discontinuous forms. The relative permeability curves show that the oil–water relative permeability not only depends on fluid saturations and flow patterns but also fracture orientation.     

Poisson–Boltzmann for oppositely charged bodies: an explicit derivation

The interaction between two parallel charged plates in ionic solution is a general starting point for studying colloidal complexes. An intuitive expression of the pressure exerted on the plates is usually proposed, which includes an electrostatic plus an osmotic contribution. We present here an explicit and self-consistent derivation of this formula in the only framework of the Poisson–Boltzmann (PB) theory. We also show that, depending on external constraints, the correct thermodynamic potential can differ from the usual PB free energy. For asymmetric, oppositely charged plates, the resulting expression predicts a non-trivial equilibrium position with the plates separated by a finite distance. The depth of this energy minimum is decisive for the stability of the complex. It is therefore crucial to obtain its explicit dependence on the charge densities of the plates and on the ion concentration. Analytic expressions for the position and depth of the energy minimum were derived in 1975 by Ohshima [Colloid Polym. Sci. 253, 150 (1975)] but, surprisingly, these important results seem to have been overlooked. We retrieve these expressions in a simpler formalism, more familiar to the physics community, and give a physical interpretation of the observed behavior.     

The Construction of DNA Logic Gates Restricted to Certain Live Cells Based on the Structure Programmability and Aptamer-Cell Affinity of G-Quadruplexes

DNA computation is considered a fascinating alternative to silicon-based computers; it has evoked substantial attention and made rapid advances. Besides realizing versatile functions, implementing spatiotemporal control of logic operations, especially at the cellular level, is also of great significance to the development of DNA computation. However, developing simple and efficient methods to restrict DNA logic gates performing in live cells is still a challenge. In this work, a series of DNA logic gates was designed by taking full advantage of the diversity and programmability of the G-quadruplex (G4) structure. More importantly, by further using the high affinity and specific endocytosis of cells to aptamer G4, an INHIBIT logic gate has been realized whose operational site is precisely restricted to specific live cells. The design strategy might have great potential in the field of molecular computation and smart bio-applications.     

Lattice Boltzmann simulation of two-sided lid-driven flow in a staggered cavity

In this article, the lattice Boltzmann method is employed in order to explore incompressible fluid flow inside a two-sided lid-driven staggered cavity. Results of the lattice Boltzmann simulation for antiparallel motion of lids are compared with the data from existing literature. For parallel motion of lids, the characteristics of flow pattern for a variety of Re numbers (50–3200) are presented. An asymmetric steady-state flow pattern for parallel motion of lids is obtained.     

Flexible composition and execution of large scale applications on distributed e-infrastructures

Computer simulation is finding a role in an increasing number of scientific disciplines, concomitant with the rise in available computing power. Marshalling this power facilitates new, more effective and different research than has been hitherto possible. Realizing this inevitably requires access to computational power beyond the desktop, making use of clusters, supercomputers, data repositories, networks and distributed aggregations of these resources. The use of diverse e-infrastructure brings with it the ability to perform distributed multiscale simulations. Accessing one such resource entails a number of usability and security problems; when multiple geographically distributed resources are involved, the difficulty is compounded. In this paper we present a solution, the Application Hosting Environment,³ which provides a Software as a Service layer on top of distributed e-infrastructure resources. We describe the performance and usability enhancements present in AHE version 3, and show how these have led to a high performance, easy to use gateway for computational scientists working in diverse application domains, from computational physics and chemistry, materials science to biology and biomedicine.