Contraction and observer design on cones

We consider the problem of positive observer design for positive systems defined on solid cones in Banach spaces. The design is based on the Hilbert metric and convergence properties are analyzed in the light of the Birkhoff theorem. Two main applications are discussed: positive observers for systems defined in the positive orthant, and positive observers on the cone of positive semi-definite matrices with a view on quantum systems. © 2011 IEEE.

Consensus in non-commutative spaces

Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. The Lyapunov function used in the early analysis by Tsitsiklis is shown to be the Hilbert distance to consensus in log coordinates. Birkhoff theorem, which proves contraction of the Hilbert metric for any positive homogeneous monotone map, provides an early yet general convergence result for consensus algorithms. Because Birkhoff theorem holds in arbitrary cones, we extend consensus algorithms to the cone of positive definite matrices. The proposed generalization finds applications in the convergence analysis of quantum stochastic maps, which are a generalization of stochastic maps to non-commutative probability spaces. ©2010 IEEE.

Low-rank optimization on the cone of positive semidefinite matrices

We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = Y Y T leads to a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second-order optimization method with guaranteed quadratic convergence. It furthermore provides some conditions on the rank of the factorization to ensure equivalence with the original problem. In contrast to existing methods, the proposed algorithm converges monotonically to the sought solution. Its numerical efficiency is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis. © 2010 Society for Industrial and Applied Mathematics.

Recycle of transuranium elements in light water reactors for reduction of geological storage requirements

This paper presents results of a feasibility study aimed at developing a zero-transuranic-discharge fuel cycle based on the U-Th-TRU ternary cycle. The design objective is to find a fuel composition (mixture of thorium, enriched uranium, and recycled transuranic components) and fuel management strategy resulting in an equilibrium charge-discharge mass flow. In such a fuel cycle scheme, the quantity and isotopic vector of the transuranium (TRU) component is identical at the charge and discharge time points, thus allowing the whole amount of the TRU at the end of the fuel irradiation period to be separated and reloaded into the following cycle. The TRU reprocessing activity losses are the only waste stream that will require permanent geological storage, virtually eliminating the long-term radiological waste of the commercial nuclear fuel cycle. A detailed three-dimensional full pressurized water reactor (PWR) core model was used to analyze the proposed fuel composition and management strategy. The results demonstrate the neutronic feasibility of the fuel cycle with zero-TRU discharge. The amount of TRU and enriched uranium loaded reach equilibrium after about four TRU recycles. The reactivity coefficients were found to be within a range typical for a reference PWR core. The soluble boron worth is reduced by a factor of ∼2 from a typical PWR value. Nevertheless, the results indicate the feasibility of an 18-month fuel cycle design with an acceptable beginning-of-cycle soluble boron concentration even without application of burnable poisons.

Light water breeding with nitride fuel

This scoping study proposes using mixed nitride fuel in Pu-based high conversion LWR designs in order to increase the breeding ratio. The higher density fuel reduces the hydrogen-to-heavy metal ratio in the reactor which results in a harder spectrum in which breeding is more effective. A Resource-renewable Boiling Water Reactor (RBWR) assembly was modeled in MCNP to demonstrate this effect in a typical high conversion LWR design. It was determined that changing the fuel from (U,TRU)O2 to (U,TRU)N in the assembly can increase its fissile inventory ratio (fissile Pu mass divided by initial fissile Pu mass) from 1.04 to up to 1.17. © 2011 Elsevier Ltd. All rights reserved.

Thorium fuel cycles for light water reactors: homogeneous design

The proliferation potential of the present light water reactor (LWR) fuel cycle is related primarily to the quantity and the quality of the residual Pu contained in the spent-fuel stockpile, although other potentially “weapons usable” materials are also a concern. Thorium-based nuclear fuel produces much smaller amounts of Pu in comparison with standard LWR fuel, and consequently, it is more proliferation resistant than conventional slightly enriched all-U fuel; the long-term toxicity of the spent-fuel stockpile is also reduced

Fluid-structure interaction simulations of a tension-cone inflatable aerodynamic decelerator

A series of fluid-structure interaction simulations of an aerodynamic tension-cone supersonic decelerator prototype intended for large mass payload deployment in planetary explorations are discussed. The fluid-structure interaction computations combine large deformation analysis of thin shells with large-eddy simulation of compressible turbulent flows using a loosely coupled approach to enable quantification of the dynamics of the vehicle. The simulation results are compared with experiments carried out at the NASA Glenn Research Center. Reasonably good agreement between the simulations and the experiment is observed throughout a deflation cycle. The simulations help to illuminate the details of the dynamic progressive buckling of the tension-cone decelerator that ultimately results in the collapse of the structure as the inflation pressure is decreased. Furthermore, the tension-cone decelerator exhibits a transient oscillatory behavior under impulsive loading that ultimately dies out. The frequency of these oscillations was determined to be related to the acoustic time scale in the compressed subsonic region between the bow shock and the structure. As shown, when the natural frequency of the structure and the frequency of the compressed subsonic region approximately match, the decelerator exhibits relatively large nonaxisymetric oscillations. The observed response appears to be a fluid-structure interaction resonance resulting from an acoustic chamber (pistonlike) mode exciting the structure. Copyright © 2013 by Christopher Porter, R. Mark Rennie, Eric J. Jumper.

Aberration correction in Spatial Light Modulator based mode multiplexers

The Spatial Light Modulator in a mode demultiplexer is used to measure the aberrations of the system in which it is installed before applying aberration correction to improve the insertion loss and modal extinction ratios. © 2013 OSA.

Electroluminescence analysis and simulation of the effects of injection and temperature on carrier distribution in InGaN-based light-emitting diodes with color-coded quantum wells

This paper reports on an extensive analysis of the electroluminescence characteristics of InGaN-based LEDs with color-coded structure, i.e., with a triple quantum well structure in which each quantum well has a different indium content. The analysis is based on combined electroluminescence measurements and two-dimensional simulations, carried out at different current and temperature levels. Results indicate that (i) the efficiency of each of the quantum wells strongly depends on device operating conditions (current and temperature); (ii) at low current and temperature levels, only the quantum well closer to the p-side has a significant emission; (iii) emission from the other quantum wells is favored at high current levels. The role of carrier injection, hole mobility, carrier density and non-radiative recombination in determining the relative intensity of the quantum wells is discussed in the text. © 2013 The Japan Society of Applied Physics.

A computational fluid-structure interaction study of inflation cycles of a tension cone decelerator

Inflatable aerodynamic decelerators present potential advantages for planetary entry in missions of robotic and human exploration. The design of these structures face many engineering challenges, including complex deformable geometries, anisotropic material response, and coupled shockturbulence interactions. In this paper, we describe a comprehensive computational fluid-structure interaction study of an inflation cycle of a tension cone decelerator in supersonic flow and compare the simulations with earlier published experimental results. The aeroshell design and flow conditions closely match recent experiments conducted at Mach 2.5. The structural model is a 16-sided polygonal tension cone with seams between each segment. The computational model utilizes adaptive mesh refinement, large-eddy simulation, and shell mechanics with self-contact modeling to represent the flow and structure interaction. This study focuses on the dynamics of the structure as the inflation pressure varies gradually, and the behavior of forces experienced by the flexible and rigid (the payload capsule) structures. © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Aberration correction in spatial light modulator based mode multiplexers

The Spatial Light Modulator in a mode demultiplexer is used to measure the aberrations of the system in which it is installed before applying aberration correction to improve the insertion loss and modal extinction ratios. © 2013 OSA.