Lateral Metallation and Redistribution Reactions of Sodium Ferrates Containing Bulky 2,6-Diisopropyl-N-(trimethylsilyl)anilide Ligands

Alkali-metal ferrates containing amide groups have emerged as regioselective bases capable of promoting Fe−H exchanges of aromatic substrates. Advancing this area of heterobimetallic chemistry, a new series of sodium ferrates is introduced incorporating the bulky arylsilyl amido ligand N(SiMe₃)(Dipp) (Dipp=2,6-iPr₂-C₆H₃). Influenced by the large steric demands imposed by this amide, transamination of [NaFe(HMDS)₃] (HMDS=N(SiMe₃)₂) with an excess of HN(SiMe₃)(Dipp) led to the isolation of heteroleptic [Na(HMDS)₂Fe{N(SiMe₃)Dipp}]_∞ ( 1 ) resulting from the exchange of just one HMDS group. An alternative co-complexation approach, combining the homometallic metal amides [NaN(SiMe₃)Dipp] and [Fe{N(SiMe₃)Dipp}₂] induces lateral metallation of one Me arm from the SiMe₃ group in the iron amide furnishing tetrameric [NaFe{N(SiCH₂Me₂)Dipp}{N(SiMe₃)Dipp}]₄ ( 2 ). Reactivity studies support that this deprotonation is driven by the steric incompatibility of the single metal amides rather than the basic capability of the sodium reagent. Displaying synergistic reactivity, heteroleptic sodium ferrate 1 can selectively promote ferration of pentafluorobenzene using one of its HMDS arms to give heterotrileptic [Na{N(SiMe₃)Dipp}(HMDS)Fe(C₆F₅)]_∞ ( 4 ). Attempts to deprotonate less activated pyridine led to the isolation of NaHMDS and heteroleptic Fe(II) amide [(py)Fe{N(SiMe₃)Dipp}(HMDS)] ( 5 ), resulting from an alternative redistribution process which is favoured by the Lewis donor ability of this substrate.     

Light charged particle emission and fission in238U+238U collisions at 1,740 MeV

Inclusive⁴He and⁴H energy spectra and heavy fragment coincidence correlations have been measured for reactions of 7.31 MeV/u²³⁸U with²³⁸U and^?197Au targets. The H/He production cross sections are in the range 15–26 mb, and their emission spectra are very similar for the two systems. The observed strong kinematic shifts with angle are reproduced in shape and magnitude by Monte Carlo simulations of particle evaporation from projectile-like and target-like fragments, indicating competition between charged particle emission and sequential fission. No evidence is found for high energy charged particle emission associated with ultra-highZ composite systems. Heavy fragment measurements indicate an abundance of quasielastic and deeply inelastic reaction fragments, as well as sequential fission of target and projectile nuclei. For²³⁸U nuclei, the fission occurs predominantly in an asymmetric mode, reminiscent of fission at low excitation energy. For²³⁸+²³⁸U reactions in the vicinity of the grazing angle, the frequency of single sequential fission (with survival of the partner fragment) is twice as large as double sequential fission in which both the target and projectile undergo fission. In²³⁸U+¹⁹⁷Au reactions, the survival probability of the heavy fragments is even greater. The surprisingly high survival probabilities of high-Z fragments imply a preponderance of very soft collisions in these very-heavy-ion reactions, at least at energies not very far over the Coulomb barrier.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

Assessing solution quality in stochastic programs

Determining whether a solution is of high quality (optimal or near optimal) is fundamental in optimization theory and algorithms. In this paper, we develop Monte Carlo sampling-based procedures for assessing solution quality in stochastic programs. Quality is defined via the optimality gap and our procedures' output is a confidence interval on this gap. We review a multiple-replications procedure that requires solution of, say, 30 optimization problems and then, we present a result that justifies a computationally simplified single-replication procedure that only requires solving one optimization problem. Even though the single replication procedure is computationally significantly less demanding, the resulting confidence interval might have low coverage probability for small sample sizes for some problems. We provide variants of this procedure that require two replications instead of one and that perform better empirically. We present computational results for a newsvendor problem and for two-stage stochastic linear programs from the literature. We also discuss when the procedures perform well and when they fail, and we propose using ɛ-optimal solutions to strengthen the performance of our procedures.     

OPTIMAL FISH HARVESTING FOR A POPULATION MODELED BY A NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no‐take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.     

The Berkeley Center for Structural Biology at the Advanced Light Source

The Berkeley Center for Structural Biology (BCSB) operates and develops a suite of protein crystallography beamlines at the Advanced Light Source (ALS) located at Lawrence Berkeley National Laboratory (LBNL). Although the ALS was conceived as a low-energy (1.9-GeV), third-generation synchrotron source of vacuum ultraviolet (VUV) and soft X-ray radiation, it was realized during the development of the facility in the mid-1990s that a multipole wiggler coupled with brightness-preserving optics would result in a beamline whose performance in the energy range of 5 to 15 keV would be sufficient for most protein crystallographic experiments. Later, the hard X-ray capabilities of the ALS were expanded by the addition of three superconducting bending magnets, resulting in additional protein crystallography facilities at the ALS [1 A.A. MacDowell, J Synchrotron Radiation 11(6), 447–55 (2004).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]].     

Cut sharing for multistage stochastic linear programs with interstage dependency

Multistage stochastic programs with interstage independent random parameters have recourse functions that do not depend on the state of the system. Decomposition-based algorithms can exploit this structure by sharing cuts (outer-linearizations of the recourse function) among different scenario subproblems at the same stage. The ability to share cuts is necessary in practical implementations of algorithms that incorporate Monte Carlo sampling within the decomposition scheme. In this paper, we provide methodology for sharing cuts in decomposition algorithms for stochastic programs that satisfy certain interstage dependency models. These techniques enable sampling-based algorithms to handle a richer class of multistage problems, and may also be used to accelerate the convergence of exact decomposition algorithms. Research leading to this work was partially supported by the Department of Energy Contract DE-FG03-92ER25116-A002; the Office of Naval Research Contract N00014-89-J-1659; the National Science Foundation Grants ECS-8906260, DMS-8913089; and the Electric Power Research Institute Contract RP 8010-09, CSA-4O05335. This author's work was supported in part by the National Research Council under a Research Associateship at the Naval Postgraduate School, Monterey, California.     

Evolution Galerkin methods for hyperbolic systems in two space dimensions

The subject of the paper is the analysis of three new evolution Galerkin schemes for a system of hyperbolic equations, and particularly for the wave equation system. The aim is to construct methods which take into account all of the infinitely many directions of propagation of bicharacteristics. The main idea of the evolution Galerkin methods is the following: the initial function is evolved using the characteristic cone and then projected onto a finite element space. A numerical comparison is given of the new methods with already existing methods, both those based on the use of bicharacteristics as well as commonly used finite difference and finite volume methods. We discuss the stability properties of the schemes and derive error estimates.