The finite element method with non-uniform mesh sizes applied to the exterior Helmholtz problem

Summary The finite element method with non-uniform mesh sizes is employed to approximately solve Helmholtz type equations in unbounded domains. The given problem on an unbounded domain is replaced by an approximate problem on a bounded domain with the radiation condition replaced by an approximate radiation boundary condition on the artificial boundary. This approximate problem is then solved using the finite element method with the mesh graded systematically in such a way that the element mesh sizes are increased as the distance from the origin increases. This results in a great reduction in the number of equations to be solved. It is proved that optimal error estimates hold inL ²,H ¹ andL , provided that certain relationships hold between the frequency, mesh size and outer radius.     

Ergodic properties of a system in contact with a heat bath: A one dimensional model

We consider a one-dimensional model of a system in contact with a heat bath: A particle (the system ormolecule) of massM, confined to the unit interval [0, 1], is surrounded by an infinite ideal gas (thebath of atoms) of point particles of massm with which it interacts via elastic collisions. The atoms are not affected by the walls at 0 and at 1. We obtain convergence to equilibrium for the molecule, from essentially any initial distribution on its position and velocity. The infinite composite system of molecule and bath has very good ergodic properties: it is a Bernoulli system.Supported in part by NSF Grants PHY 78-03816 and PHY 78-15920     

Uranyl coordination environment in hydrophobic ionic liquids: an in situ investigation

Different inner-sphere coordination environments are observed for the uranyl nitrate complexes formed with octyl-phenyl-N,N-diisobutylcarbamoylmethylphosphine oxide and tributyl phosphate in dodecane and in the hydrophobic ionic liquids (ILs) [C(4)mim][PF(6)] and [C(8)mim][N(SO(2)CF(3))(2)]. Qualitative differences in the coordination environment of the extracted uranyl species are implied by changes in peak intensity patterns and locations for uranyl UV-visible spectral bands when the solvent is changed. EXAFS data for uranyl complexes in dodecane solutions is consistent with hexagonal bipyramidal coordination and the existence of UO(2)(NO(3))(2)(CMPO)(2). In contrast, the complexes formed when uranyl is transferred from aqueous nitric acid solutions into the ILs exhibit an average equatorial coordination number of approximately 4.5. Liquid/liquid extraction results for uranyl in both ILs indicate a net stoichiometry of UO(2)(NO(3))(CMPO)(+). The concentration of the IL cation in the aqueous phase increases in proportion to the amount of UO(2)(NO(3))(CMPO)(+) in the IL phase, supporting a predominantly cation exchange mechanism for partitioning in the IL systems.     

Research applications of the Cambridge Structural Database (CSD)

Crystal structure data are of fundamental importance in a wide spectrum of scientific activities. This tutorial review summarises the principal application areas, so far, for the data from more than 300,000 crystal structures of small organic and metal-organic compounds that are stored in the Cambridge Structural Database (CSD). Direct use of the accumulated data is valuable in establishing standard molecular dimensions, determining conformational preferences and in the study of intermolecular interactions, all of which are crucial in structural chemistry and rational drug design. More recently, information derived from the CSD has been used to construct two dynamic libraries of structural knowledge: Mogul, which stores intramolecular information, and IsoStar, which stores information about intermolecular interactions. These electronic libraries provide information "at the touch of a button". In their turn, the libraries also serve as sources of structural knowledge for applications software that address specific problems in small-molecule and biological chemistry.     

Proteomic analysis of the endoplasmic reticulum from developing and germinating seed of castor (Ricinus communis)

Endoplasmic reticulum (ER) has been prepared and analysed from germinating and developing castor bean endosperm. A combination of one- and two-dimensional (1-D and 2-D) gel electrophoresis was used to study the complexity of sample and protein differences between the two stages. The ER of the developing oilseed is central to the synthesis, sorting and storage of protein and lipid reserves while the germinating seed is concerned with their degradation. Sample complexity has been reduced by separation of ER proteins into lumenal, peripheral membrane and integral membrane subfractions. Membrane proteins pose specific problems in aggregation and binding to passive surfaces. We have overcome this by collection of membranes at density gradient interfaces and by silanization of plastic ware. Several major components have been identified from 1-D gels by N-terminal sequencing and matrix-assisted laser desorption/ionization (MALDI) peptide mass fingerprints. These include protein disulphide isomerase (PDI), calreticulin and developing-ER-specific oleate-12-hydroxylase involved in the biosynthesis of ricinoleic acid. In excess of 300 spots are detectable in each developmental fraction by high sensitivity 2-D gels. This is the first 2-D electrophoretic analysis of plant ER. These gels reveal significant differences between germinating and developing ER. Preparative loading 2-D gels of germinating ER have been run and 14 selected spots characterized by quadrupole time of flight tandem mass spectrometry (Q-TOF MS/MS). Ten of these proteins were assigned function on the basis of identity with existing castor database entries, or by homology with other species. Two proteins, aspartate proteinase precursor and N-carbamyl-L-aminohydrolase-like protein, appear to be absent from developing profiles. Most of the proteins identified are concerned with roles in protein processing and storage, and lipid metabolism which occur in the ER. Data from three of the assigned spots included unidentified peptides indicating the presence of more than one protein in these spots following 2-D electrophoresis. More extensive analysis will have to await developments in genomics but the basic separation technologies to simplify sample identity for a plant ER preparation have been established.     

Organometallic reagents in organic synthesis—V: An organocuprate conjugate addition—Aldol condensation synthetic procedure for sequential formation of two carbon-carbon bonds

The enolates produced from the conjugate addition reaction of lithium dialkylcuprates with α,β- unsaturated ketones react with aldehydes in the presence of zinc chloride to give overall β-alkyl α-hydroxyalkyl addition to the original alkene. Reaction of these enolates with carbon dioxide and ethyl formate is also reported.     

DEPENDENCE OF THE TRIPLET YIELD ON EXCITATION ENERGY IN ALL-TRANS AND 11-CIS RETINAL*

Abstract. The triplet-triplet absorption of all-trans and 11- cis retinal was measured as a function of the exciting radiation from 423 nm to 365 nm in a glass of 3-methylpentane at 77 K. This experiment was also accomplished with all-trans retinal in hexane at ambient temperature. The relative triplet formation quantum yields of all-trans and 11-cis retinal at 77 K were found to be independent (±10%) of the frequency of the exciting radiation. At room temperature we measured an increase in this relative quantum yield for all- trans retinal from 1.0 at 365 nm to 1.82 at 423 nm [Bensasson et al. (1975) measured an absolute quantum yield of 0.45 at 353 nm]. These results are used to evaluate previous interpretations for photophysical decay processes in all-trans retinal, and previous suggestions for wavelength dependent radiationless transitions are shown to be unacceptable. High energy excitation of 300 K solutions of all- trans retinal produce excited states that result in less efficient intersystem crossing. These states appear to be inaccessible in the 77 K matrices. We suggest that steric restrictions introduced by the retinal matrix interaction at 77 K are able to block this new internal conversion pathway back to the ground state.     

f-Element/crown ether complexes: 21. Conformational changes in metal complexed versus hydrogen bonded benzo-15-crown-5 in the structure of [Y(OH2)3(NCMe)-(benzo-15-crown-5)][ClO4]3·benzo-15-crown-5·CH3CN

Crystalline [Y(OH₂)₃(NCMe)(benzo-15-crown-5)][ClO₄]₃·benzo-15-crown-5-CH₃CN can be obtained by slowly cooling a reaction mixture of Y(ClO₄)₃·n H₂O with benzo-15-crown-5 in a solution of acetonitrile and methanol (3 : 1) from 60°C to room temperature. The crystal structure of this complex has been determined at –150 and 20°C. The complex is triclinic,P . At –150°C the cell parameters area = 11.986(4),b = 12.071(7),c = 16.364(5) Å, = 93.56(3), = 98.68(3), = 109.68(4)°, vol = 2187 ų, andD _calc = 1.61 g cm^–3 forZ = 2 formula units. 3633 independently observed [F _o 5(F _o)] reflections were used in the final least-squares refinement leading to an agreement index ofR = 0.048. The Y(III) ion coordination geometry approximates a tricapped trigonal prism with three water molecules and three benzo-15-crown-5 oxygen atoms forming the prism, with the two remaining benzo-15-crown-5 oxygen atoms and the acetonitrile molecule completing the coordination as capping atoms. The three water molecules hydrogen bond a second crown ether molecule and two of the perchlorate anions. The two acetonitrile molecules have contacts with perchlorate oxygen atoms close enough for some weak interaction. One perchlorate is ordered, one is partially disordered as is the coordinated solvent molecule, and the third anion is totally disordered. The two unique crown ether molecules have distinctively different conformations.For Part 20, see reference [1].