Energy functional depending on elastic strain and chemical composition

In this paper we deal with energy functionals depending on elastic strain and chemical composition and we obtain lower semicontinuity results, existence theorems and relaxation in the spacesH ^1,p(; ⁿ)×L ^q (; ^d) with respect to weak convergence. Our proofs use parametrized measures associated with weakly converging sequences.The research was partially supported by the National Science Foundation under Grants No. DMS-9000133 and DMS-9201215 and also by the Army Research Office and the National Science Foundation through the Center for Nonlinear Analysis.The research was partially supported by the National Science Foundation uncer Grants No. DMs 911572, the AFOSR 91 0301, the ARO DAAL03 92 G 003 and also by the ARO and the NSF through the Center for Nonlinear Analysis.The research was supported by DGICYT (Spain) through Programa de Perfeccionamiento y Movilidad del Personal Investigador and through grant PB90-0245, by the Army Research Office and the National Science Foundation through the Center for Nonlinear Analysis and also by the project EurHomogenization SC1-CT91-0732 of the European Comunity.     

Gradient Young measures generated by sequences in Sobolev spaces

Oscillatory properties of a weak convergent sequence of functions bounded inL ^p , 1 ≤p ≤ ∞, may be summarized by the parametrized measure it generates. When such a measure is generated by the gradients of a sequence of functions bounded inH ^1,p , it must have special properties. The purpose of this paper is to characterize such parametrized measures as the ones that obey Jensen’s inequality for all quasiconvex functions with the appropriate growth at infinity. We have found subtle differences between the casesp < ∞ andp = ∞. A consequence is that any measure determined by biting convergence is in fact generated by a sequence convergent in a stronger sense. We also give a few applications. Research groupTransitions and Defects in Ordered Materials, funded by the NSF, the AFOSR, and the ARO. The work of the second author is also supported by DGICYT (Spain) through “Programa de Perfeccionamiento y Movilidad del Personal Investigador” and through Grant PB90-0245.     

Multi-objective Bayesian Artificial Immune System: Empirical Evaluation and Comparative Analyses

Recently, we have proposed a Multi-Objective Bayesian Artificial Immune System (MOBAIS) to deal effectively with building blocks (high-quality partial solutions coded in the solution vector) in combinatorial multi-objective problems. By replacing the mutation and cloning operators with a probabilistic model, more specifically a Bayesian network representing the joint distribution of promising solutions, MOBAIS takes into account the relationships among the variables of the problem, avoiding the disruption of already obtained high-quality partial solutions. The preliminary results have indicated that our proposal is able to properly build the Pareto front. Motivated by this scenario, this paper better formalizes the proposal and investigates its usefulness on more challenging problems. In addition, an important enhancement regarding the Bayesian network learning was incorporated into the algorithm in order to speed up its execution. To conclude, we compare MOBAIS with state-of-the-art algorithms taking into account quantitative aspects of the Pareto front found by the algorithms. MOBAIS outperforms the contenders in terms of the quality of the obtained solutions and requires an amount of computational resource inferior or compatible with the contenders.     

Mach–Zehnder interferometers in photonic crystals

Photonic crystal technology allows the creation of optical waveguides with low sharp-bending losses as well as ultra-low group velocity. This last property is particularly interesting to develop highly-compact optical devices based on the controlled modification of the optical phase of the signals traveling through the waveguides. Among these devices, the Mach–Zehnder interferometer acquires fundamental importance because it can be used as a building block of more complex optical devices and functionalities such as optical filters, wavelength demultiplexers, channels interleavers, intensity modulators, switches and optical gates. In this paper, the performance of a Mach–Zehnder interferometer consisting of two coupled-cavity waveguides with different lengths created in a two-dimensional photonic crystal is theoretically analyzed. We also provide simulation results using a finite-difference time-domain code that confirm the theoretical analysis. The main limitations in the performance of the structure are addressed and discussed.     

Spin Label Studies of the Hemoglobin–Membrane Interaction During Sickle Hemoglobin Polymerization

An enhanced hemoglobin–membrane association has been previously documented in sickle cell anemia. However, it is not known how this interaction is modified during the hemoglobin S polymerization process. In this work, we use a model of reconstituted erythrocytes from ghost membranes whose cytoskeleton proteins had been previously labeled with the 4-maleimido Tempo spin label, and that were subsequently resealed with hemoglobin S or A solutions. Using electron paramagnetic resonance spectroscopy, we studied the time dependence of the spectral W/S parameter, indicative of the conformational state of cytoskeleton proteins (mainly spectrin) under spontaneous deoxygenation, with the aim of detecting the eventual effects due to hemoglobin S polymerization. The differences observed in the temporal behavior of W/S in erythrocytes reconstituted with both hemoglobins were considered as experimental evidence of an increment in hemoglobin S–membrane interaction as a result of the polymerization process of hemoglobin S under spontaneous deoxygenation.     

A factored variant of the Newton iteration for the solution of algebraic Riccati equations via the matrix sign function

In this paper we introduce a variant of the Newton iteration for the matrix sign function that results in an efficient numerical solver for a certain class of algebraic Riccati equations (AREs). In particular, when the Hamiltonian matrix associated with the ARE can be composed as \(\left [\begin {array}{llll}{A}&{BB^{T}}\\{C^{T}C}&{-A^{T}}\end {array}\right ]\) , with B and \(C^{T}\) having a much larger number of rows than columns, the new algorithm exploits the special structure of the off-diagonal blocks to yield an alternative factored Newton iteration which reduces the cost per iteration by a factor of up to 8 (16 in case A is symmetric negative definite) w.r.t. the conventional iterative scheme. Experiments with a large collection of benchmark examples show that the factored iteration attains numerical accuracy similar to that of the conventional Newton iteration as well as the structure-preserving doubling algorithm. High-performance implementations of these methods, making heavy use of LAPACK linked to a multi-threaded implementation of BLAS, demonstrate the clear advantage of the new iteration on a 48-core AMD-based platform.     

Extended formulations in mixed integer conic quadratic programming

In this paper we consider the use of extended formulations in LP-based algorithms for mixed integer conic quadratic programming (MICQP). Extended formulations have been used by Vielma et al. (INFORMS J Comput 20: 438–450, 2008) and Hijazi et al. (Comput Optim Appl 52: 537–558, 2012) to construct algorithms for MICQP that can provide a significant computational advantage. The first approach is based on an extended or lifted polyhedral relaxation of the Lorentz cone by Ben-Tal and Nemirovski (Math Oper Res 26(2): 193–205 2001) that is extremely economical, but whose approximation quality cannot be iteratively improved. The second is based on a lifted polyhedral relaxation of the euclidean ball that can be constructed using techniques introduced by Tawarmalani and Sahinidis (Math Programm 103(2): 225–249, 2005). This relaxation is less economical, but its approximation quality can be iteratively improved. Unfortunately, while the approach of Vielma, Ahmed and Nemhauser is applicable for general MICQP problems, the approach of Hijazi, Bonami and Ouorou can only be used for MICQP problems with convex quadratic constraints. In this paper we show how a homogenization procedure can be combined with the technique by Tawarmalani and Sahinidis to adapt the extended formulation used by Hijazi, Bonami and Ouorou to a class of conic mixed integer programming problems that include general MICQP problems. We then compare the effectiveness of this new extended formulation against traditional and extended formulation-based algorithms for MICQP. We find that this new formulation can be used to improve various LP-based algorithms. In particular, the formulation provides an easy-to-implement procedure that, in our benchmarks, significantly improved the performance of commercial MICQP solvers.     

Tetranuclear and Octanuclear Manganese Carboxylate Clusters: Preparation and Reactivity of (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(9)(H(2)O)] and Synthesis of (NBu(n)(4))(2)[Mn(8)O(4)(O(2)CPh)(12)(Et(2)mal)(2)(H(2)O)(2)] with a "Linked-Butterfly" Structure

The reaction of Mn(O(2)CPh)(2).2H(2)O and PhCO(2)H in EtOH/MeCN with NBu(n)(4)MnO(4) gives (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(9)(H(2)O)] (4) in high yield (85-95%). Complex 4 crystallizes in monoclinic space group P2(1)/c with the following unit cell parameters at -129 degrees C: a = 17.394(3) ?, b = 19.040(3) ?, c = 25.660(5) ?, beta = 103.51(1) degrees, V = 8262.7 ?(3), Z = 4; the structure was refined on F to R (R(w)) = 9.11% (9.26%) using 4590 unique reflections with F > 2.33sigma(F). The anion of 4 consists of a [Mn(4)(&mgr;(3)-O)(2)](8+) core with a "butterfly" disposition of four Mn(III) atoms. In addition to seven bridging PhCO(2)(-) groups, there is a chelating PhCO(2)(-) group at one "wingtip" Mn atom and terminal PhCO(2)(-) and H(2)O groups at the other. Complex 4 is an excellent steppingstone to other [Mn(4)O(2)]-containing species. Treatment of 4 with 2,2-diethylmalonate (2 equiv) leads to isolation of (NBu(n)(4))(2)[Mn(8)O(4)(O(2)CPh)(12)(Et(2)mal)(2)(H(2)O)(2)] (5) in 45% yield after recrystallization. Complex 5 is mixed-valent (2Mn(II),6Mn(III)) and contains an [Mn(8)O(4)](14+) core that consists of two [Mn(4)O(2)](7+) (Mn(II),3Mn(III)) butterfly units linked together by one of the &mgr;(3)-O(2)(-) ions in each unit bridging to one of the body Mn atoms in the other unit, and thus converting to &mgr;(4)-O(2)(-) modes. The Mn(II) ions are in wingtip positions. The Et(2)mal(2)(-) groups each bridge two wingtip Mn atoms from different butterfly units, providing additional linkage between the halves of the molecule. Complex 5.4CH(2)Cl(2) crystallizes in monoclinic space group P2(1)/c with the following unit cell parameters at -165 degrees C: a = 16.247(5) ?, b = 27.190(8) ?, c = 17.715(5) ?, beta = 113.95(1) degrees, V = 7152.0 ?(3), Z = 4; the structure was refined on F to R (R(w)) = 8.36 (8.61%) using 4133 unique reflections with F > 3sigma(F). The reaction of 4 with 2 equiv of bpy or picolinic acid (picH) yields the known complex Mn(4)O(2)(O(2)CPh)(7)(bpy)(2) (2), containing Mn(II),3Mn(III), or (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(7)(pic)(2)] (6), containing 4Mn(III). Treatment of 4 with dibenzoylmethane (dbmH, 2 equiv) gives the mono-chelate product (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(8)(dbm)] (7); ligation of a second chelate group requires treatment of 7 with Na(dbm), which yields (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(7)(dbm)(2)] (8). Complexes 7 and 8 both contain a [Mn(4)O(2)](8+) (4Mn(III)) butterfly unit. Complex 7 contains chelating dbm(-) and chelating PhCO(2)(-) at the two wingtip positions, whereas 8 contains two chelating dbm(-) groups at these positions, as in 2 and 6. Complex 7.2CH(2)Cl(2) crystallizes in monoclinic space group P2(1) with the following unit cell parameters at -170 degrees C: a = 18.169(3) ?, b = 19.678(4) ?, c = 25.036(4) ?, beta = 101.49(1) degrees, V = 8771.7 ?(3), Z = 4; the structure was refined on F to R (R(w)) = 7.36% (7.59%) using 10 782 unique reflections with F > 3sigma(F). Variable-temperature magnetic susceptibility studies have been carried out on powdered samples of complexes 2 and 5 in a 10.0 kG field in the 5.0-320.0 K range. The effective magnetic moment (&mgr;(eff)) for 2 gradually decreases from 8.61 &mgr;(B) per molecule at 320.0 K to 5.71 &mgr;(B) at 13.0 K and then increases slightly to 5.91 &mgr;(B) at 5.0 K. For 5, &mgr;(eff) gradually decreases from 10.54 &mgr;(B) per molecule at 320.0 K to 8.42 &mgr;(B) at 40.0 K, followed by a more rapid decrease to 6.02 &mgr;(B) at 5.0 K. On the basis of the crystal structure of 5 showing the single Mn(II) ion in each [Mn(4)O(2)](7+) subcore to be at a wingtip position, the Mn(II) ion in 2 was concluded to be at a wingtip position also. Employing the reasonable approximation that J(w)(b)(Mn(II)/Mn(III)) = J(w)(b)(Mn(III)/M(III)), where J(w)(b) is the magnetic exchange interaction between wingtip (w) and body (b) Mn ions of the indicated oxidation state, a theoretical chi(M) vs T expression was derived and used to fit the experimental molar magnetic susceptibility (chi(M)) vs T data. The obtained fitting parameters were J(w)(b) = -3.9 cm(-)(1), J(b)(b) = -9.2 cm(-)(1), and g = 1.80. These values suggest a S(T) = (5)/(2) ground state spin for 2, which was confirmed by magnetization vs field measurements in the 0.5-50.0 kG magnetic field range and 2.0-30.0 K temperature range. For complex 5, since the two bonds connecting the two [Mn(4)O(2)](7+) units are Jahn-Teller elongated and weak, it was assumed that complex 5 could be treated, to a first approximation, as consisting of weakly-interacting halves; the magnetic susceptibility data for 5 at temperatures >/=40 K were therefore fit to the same theoretical expression as used for 2, and the fitting parameters were J(w)(b) = -14.0 cm(-)(1) and J(b)(b) = -30.5 cm(-)(1), with g = 1.93 (held constant). These values suggest an S(T) = (5)/(2) ground state spin for each [Mn(4)O(2)](7+) unit of 5, as found for 2. The interactions between the subunits are difficult to incorporate into this model, and the true ground state spin value of the entire Mn(8) anion was therefore determined by magnetization vs field studies, which showed the ground state of 5 to be S(T) = 3. The results of the studies on 2 and 5 are considered with respect to spin frustration effects within the [Mn(4)O(2)](7+) units. Complexes 2 and 5 are EPR-active and -silent, respectively, consistent with their S(T) = (5)/(2) and S(T) = 3 ground states, respectively.