Optimal Control of Nonlocal Thermistor Equations

We are concerned with the optimal control problem of the well known nonlocal thermistor problem, i.e., in studying the heat transfer in the resistor device whose electrical conductivity is strongly dependent on the temperature. Existence of an optimal control is proved. The optimality system consisting of the state system coupled with adjoint equations is derived, together with a characterization of the optimal control. Uniqueness of solution to the optimality system, and therefore the uniqueness of the optimal control, is established. The last part is devoted to numerical simulations.Comment: Submitted 21-March-2012; revised 11-June-2012; accepted 13-June-2012; for publication in the International Journal of Contro

Optimal Control of the Thermistor Problem in Three Spatial Dimensions

This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system are derived by employing maximal parabolic regularity in the fundamental theorem of Pr\"uss. Global solutions are addressed, which includes analysis of the linearized state system via maximal parabolic regularity, and existence of optimal controls is shown if the temperature gradient is under control. The adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem in form of a qualified optimality system. The theoretical findings are illustrated by numerical results

Necessary Optimality Conditions for a Dead Oil Isotherm Optimal Control Problem

We study a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of the mechanics of a continuous medium. Recent results on the problem provide existence, uniqueness and regularity of the optimal solution. Here we obtain the first necessary optimality conditions.Comment: 9 page

Upsilon Dissociation in Quark-Gluon Plasma

I consider the dissociation of the upsilon meson due to absorption of a thermal gluon. I discuss the dissociation rate in terms of the energy density, the number density, and the temperature of the quark-gluon plasma. I compare this to the effect due to screening.Comment: 5 pages, added calculations on screening; added figur

Aspek Ekologi Ikan Kancera (Tor Soro) Kuningan Dan Pematangan Gonad Melalui Implantasi Hormon Gonadotropin (HCG)

Ecological Aspect and Gonadal Maturation of Tor soro by HCG peletted Implantation. Theexperiment was conducted to determine optimal dosage of Gnrh-a hormon at gonadal maturationof mahseer from Kuningan (Tor soro). The fish was reared in concrete tanks (60m2). Thehormon was used for implantation is HCG (pregnyl). The different dosage of hormon are 250Iu/Kg-1 ; 500 Iu/Kg-1 ; 750 Iu/Kg-1 . The result of this reaserch showed that egg development isMei-Juni (average of egg diameter is 1,4 mm) and Januari (average of egg diameter is 1,35 mm),Other month, the egg diameter was not develop or atresia. Treatment with 500 Iu/Kg-1 dossageshowed the best effect on oosit diameter was at 21 day and 63 day from first oosit diameter of0,9 mm to 1,4 mm

Editorial for the special issue of axioms “Calculus of variations, optimal control and mathematical biology: a themed issue dedicated to professor Delfim F. M. Torres on the occasion of his 50th birthday”

No abstract available.publishe

Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction

The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for dealing with divergent series must be used. Among these, the Distributional Borel Sum appears to be the most well suited tool to give answers and to describe the spectral properties of the system. A detailed investigation is made in one and in three space dimensions with a central potential. We present numerical results for the Dirac equation in one space dimension: these are obtained by determining the perturbation expansion and using the Pad\'e approximants for calculating the distributional Borel transform. A complete agreement is found with previous non-perturbative results obtained by the numerical solution of the singular boundary value problem and the determination of the density of the states from the continuous spectrum.Comment: 10 pages, 1 figur

Commissioning of the Liquid Nitrogen Thermo-Siphon System for NASA-JSC Chamber-A

NASA's Space Environment Simulation Laboratory's (SESL) Chamber A, located at the Johnson Space Center in Houston Texas has recently implemented major enhancements of its cryogenic and vacuum systems. The new liquid nitrogen (LN2) thermo-siphon system was successfully commissioned in August of 2012. Chamber A, which has 20 K helium cryo-panels (or shrouds ) which are shielded by 80 K nitrogen shrouds, is capable of simulating a deep space environment necessary to perform ground testing of NASA s James Webb Space Telescope (JWST). Chamber A s previous system used forced flow LN2 cooling with centrifugal pumps, requiring 200,000 liters of LN2 to cool-down and consuming 180,000 liters per day of LN2 in steady operation. The LN2 system did not have the reliability required to meet the long duration test of the JWST, and the cost estimate provided in the initial approach to NASA-JSC by the sub-contractor for refurbishment of the system to meet the reliability goals was prohibitive. At NASA-JSC's request, the JLab Cryogenics Group provided alternative options in 2007, including a thermo-siphon, or natural flow system. This system, eliminated the need for pumps and used one tenth of the original control valves, relief valves, and burst disks. After the thermo-siphon approach was selected, JLab provided technical assistance in the process design, mechanical design, component specification development and commissioning oversight, while the installation and commissioning operations of the system was overseen by the Jacobs Technology/ESC group at JSC. The preliminary commissioning data indicate lower shroud temperatures, 70,000 liters to cool-down and less than 90,000 liters per day consumed in steady operation. All of the performance capabilities have exceeded the design goals. This paper will outline the comparison between the original system and the predicted results of the selected design option, and the commissioning results of thermo-siphon system