Reparameterization for statistical state estimation applied to differential equations

The ensemble Kalman filter is a widely applied data assimilation technique useful for improving the forecast of computational models. The main computational cost of the ensemble Kalman filter comes from the numerical integration of each ensemble member forward in time. When the computational model involves a partial differential equation, the degrees of freedom of the solution in the discretization of the spatial domain are oftentimes used for the representation of the state of the system, and the filter is applied to this state vector. We propose a method of approximating the state of a partial differential equation in a representation space developed separately from the numerical method. This representation space represents a reparameterization of the state vector and can be chosen to retain desirable physical features of the solutions. We apply the ensemble Kalman filter to this representation of the state, and numerically demonstrate that acceptable results are obtained with substantially smaller ensemble sizes.     

Photoreactivity of iron(III)-aerobactin: photoproduct structure and iron(III) coordination

UV photolysis of the ferric aerobactin complex results in decarboxylation of the alpha-hydroxy carboxylic acid group of the central citrate moiety of aerobactin. The structure determination of the photooxidized ligand shows that decarboxylation occurs at the citrate moiety forming a 3-ketoglutarate moiety. Proton and carbon-13 NMR establish the presence of keto and enol tautomers of the apo-photoproduct, with the enol form prevailing in water. The photoproduct retains the ability to coordinate iron(III). The values of the ligand protonation constants, the pKa of the Fe(III)-ligand complex, and the Fe(III) stability constant of the photoproduct of aerobactin are all close to those of aerobactin. CD spectroscopy suggests that the chirality of the ferric complexes of aerobactin and its photoproduct are similar. Like aerobactin, the photoproduct promotes iron acquisition by the source bacterium, Vibrio sp. DS40M5.     

Reactions of alkynes with bis(triphenylphosphine)platinum-ethylene: A 31P-{1H} NMR study

Internally consistent assignments of the ³¹P-{¹H} NMR parameters of the complexes [Pt(RCCR′)(PPh₃)₂] are proposed, based on the premise that the magnitude of ¹J(PtP) depends mainly on the nature of the moiety CR trans to P. For a given R, ²J(PP) correlates with ¹J(PtP) for thebond trans to CR. The alkynes PhCCSnEt₃, PhCCSnPh₃, Me₃SiCCCl, Me₃SiCCBr, Et₃SiCCI and MeCCI undergo oxidative addition reactions with [Pt(C₂H₄)(PPh₃)₂]; the intermediate alkyne complex was detected for PhCCSnEt₃, Me₃SiCCCl and Me₃CCBr. The triyne Me(CC)₃Me forms platinum(0) complexes by coordination with the central or terminal CC bond and appears also to give a platinum(II) complex by oxidative addition.     

Enantioselective total synthesis of (-)-kibdelone C

The kibdelones are aromatic polyketide natural products featuring isoquinolinone and tetrahydroxanthone ring systems. They display potent cytotoxicity toward a range of human cancer cell lines. Here, we present an enantioselective total synthesis of kibdelone C that utilizes a Shi epoxidation to establish the absolute and relative stereochemistry, an acid-catalyzed cyclization to form the tetrahydroxanthone, and a C-H arylation to complete the hexacyclic skeleton.     

The Crystal and Molecular Structure of Bis(cyclopentadienyldicarbonylchromium) (CrCr)

The crystal structure of bis(cyclopentadienyldicarbonyl-chromium) has been determined by x-ray diffraction. The compound crystalizes in the triclinic system, space group P1¯(C¹_i, No. 2) with unit cell parameters: a, 7.829(3); b, 14.543(6); c, 6.588(2)Å; α, 94.67(3), β, 110.70(3); γ, 104.04°(3); V, 699.1(4)ų; z=2. There are two independent molecules per unit cell located at the inversion centers at O,O,O and O, 1/2, O. The CrCr bond distances are, respectively 2.200(3) and 2.230(3), thus supporting their formulation as triple bonds. The CpCrCr angles in the two molecules are 165.0° and 158.7°, respectively. The structural features are compared with those of Cp₂Mo₂(CO)₄, which has a linear CpMoMoCp axis; and the differences rationalized in terms of electronic interactions of the Cp-ligand with the orbitals of the M₂ unit. The differences observed in the structures of the two independent molecules are also related to the proposed bonding model and to packing considerations.     

Anionic-initiated polymerization of β-nitrostyrenes

β-Nitrostyrene and many of its derivatives have been shown to yield high polymers via anionic initiation with alkoxide ions in protic solvents, e.g., alcohols. A study was conducted to determine the effect of certain substituents on the polymerization characteristics of representative monomers of this series and the properties of their polymers. A kinetic study was conducted and the relative rates of propagation were unexpectedly found to correlate well with brown's σ⁺ values. The rates of initiation of two representative monomers, β-nitrostyrene and p-methoxy-β-nitrostyrene, with sodium ethoxide were found to be 3.51 and 2.86 liter/mole sec, respectively. The rate of chain transfer in ethanol was studied qualitatively by using gel-permeation chromatography (GPC) to obtain molecular weight distribution (MWD) curves. The low values of the M _w/M _n ratios indicated little chain transfer in the protic solvent.     

Synthesis and Characterization of Water-Soluble Starch-Acrylamide Graft Copolymers

A series of water-soluble starch-polyacrylamide graft copolymers (ST-g-PAM) were prepared by Ce⁴⁺-initiated graft copolym-erizations of acrylamide (AM) onto starch (ST) dissolved in water at 30°C. The copolymers were found to contain 3-33% (wt) of ST. The structure of the copolymers, including the average number of grafts per chain and the efficiency of the initiator, was determined by acid-catalyzed degradation of the ST followed by size exclusion chromatography (SEC) analysis of the PAM chains and was found to be consistent with the presence or absence of free ST in the polymerization product prior to hydrolysis. The average number of grafts per starch molecule was found to be three or less, depending on conditions. The initiator efficiency (6–43%) was shown to decrease with increasing [Ce⁴⁺] and decreasing [AM], and this was found to be qualitatively in accord with the proposed mechanism of initiation and polymerization. The low efficiency was shown to be due, in part, to the low rate of reaction of Ce⁴⁺ compared to the polymerization rate. The copolymers were characterized by ultra-centrifugation, SEC, and viscometry.     

Isoindole Cycloadditions. Part III: The Synthesis of "Windscreen Wiper" and Other N-Bridged Cavity Systems

The thermal addition of N-carbobenzyloxyisoindole (N-Z isoindole) 11a, generated by the reaction of 3,6-di(2-pyridyl)-s-tetrazine 9 with N-Z 7-azabenzonorbornadiene 8a, onto dimethyl tricyclo[4.2.1.0^2.5]nona-3,7-diene-3,4-dicarboxylate 17 occurred site selectively at the cyclobutene -bond to form a stereoisomeric mixture of 1 : 1-adducts 18 and 19, in which the bent-frame isomer 19 was dominant (ratio 5 : 1). In contrast, N-benzyl tetrafluoroisoindole 11c reacted with 17 only under high-pressure conditions (14 kbar, RT, 4 days) to afford 1 : 1-adducts at the cyclobutene site, in which the extended-frame isomer 18c was dominant and the accompanying bent-frame product 19c reverted to starting materials soon after isolation. These same stereoselectivities were used to prepare "windscreen wiper" compound 28c having two mobile N-benzyl substituents attached to a rigid scaffold by the reaction of N-benzyl tetrafluoroisoindole 11c with tetramethyl tetracyclo[4.4.1.0.^2,5.0^7.10]undeca-3,8-diene-3,4,7,8-tetracarboxylate 23. Cavity bis-(cyclobutene-1,2-diester) 6 reacted with N-benzyl tetrafluoroisoindole 11c twice over to produce cavity structure 36 with two O- and two N-benzyl bridges on the inner face, whereas the narrower cavity bis-alkene 32 stopped at the 1 : 1-addition stage. The dynamics of the Z-group in the dual adducts 26a–28a are discussed briefly and key adducts and cavity systems have been structurally evaluated by X-ray crystallography, VT NMR, and molecular modeling.     

Oligomeric phthalonitriles and tetrakis(phenylethynyl)benzene blends with improved processing and thermal properties

Blended resins were prepared from the resorcinol-based PEEK-like oligomeric phthalonitrile resin (RES) and tetrakis(phenylethynyl)benzene (TPEB), a high char yield arylacetylene resin. Initial probing of curing properties using differential scanning calorimetry, indicated that TPEB and RES co-cure when heated. Characterization of thermal properties using thermogravimetric analysis indicated that a 1:1 TPEB-RES blend (by weight) exhibited a char yield of 80% which was 6% larger compared to pure RES (74%). According to FTIR characterization, the enhanced thermal properties of TPEB-RES were the result of increased crosslinking density. Rheological studies of TPEB, RES, and TPEB-RES blends indicated that blended systems exhibit similar processing characteristics as RES resin. For example, resins display ideal viscosities and relatively large processing windows when cured at 175 °C. Alternatively, pure TPEB resin exhibits low viscosities when melted, which are not suitable for preparing composite materials. This study indicates that preparing TPEB-RES blends is an effect strategy for improving thermal performance of potential RES composites while still maintaining the required processability for fabrication of dense polymer composites. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2630–2640     

Rhodium(I) catalyst supported on polymer crystal surfaces: Further hydrogenation studies

Catalysts bound to polymers in the form of crosslinked beads have been demonstrated to have a number of advantages over homogeneous catalysts. However, there are several problems that exist due to the polymer support being in the form of a bead. The rate of reaction depends on the presence of solvents that adequately swell the bead in order to allow access to the catalytic sites. Differences in polarity and reactant size can inhibit diffusion into the bead. Recently a new system has been developed whereby tris(triphenyl phosphine) chlororhodium (I) (Wilkinson's catalyst) is bound to the surface of polyethylene single crystals. Polyethylene single crystals have a very high surface to volume ratio allowing for greater ease of reaction compared to a bead system. In a previous paper we showed that there is a dramatic increase in catalytic activity and that the reaction rate increased as the polarity of solvent was increased, even in ethanol where the homogeneous catalyst is not soluble and the polystyrene bead support would not swell. In this letter we are describing the activity of hydrogenation of olefins contained in both large and/or polar molecules. The results demonstrate the advantages of supported catalysts on polyethylene single crystals rather than on polymer beads.