Synthesis and X-ray analysis of 1-((1S)-phenylethyl)-azetidine-(2R)-piperidinamide

The crystal and molecular structure of a new azetidine-2-carboxylic amide derivative is described. The structure was solved by direct methods and refined by least squares methods toR1=0.0393 for 4264 reflections (withI>2(I)) The structure consists of two independent molecules which are chemically the same with slight differences in geometry. Crystal data: C₁₇H₂₄N₂O, monoclinic, space groupP2₁,a=8.3782(4),b=20.0342(13),c=9.7769(8) Å, =109.687(6)°,V=1545.1(2)ų,Z=4.     

Hydraulic conductivity of rock fractures

The flow of a single-phase fluid through a rough-walled rock fracture is discussed within the context of fluid mechanics. The derivation of the cubic law is given as the solution to the Navier-Stokes equations for flow between smooth, parallel plates - the only fracture geometry that is amenable to exact treatment. The various geometric and kinematic conditions that are necessary in order for the Navier-Stokes equations to be replaced by the more tractable lubrication or Hele-Shaw equations are studied and quantified. In general, this requires a sufficiently low flow rate, and some restrictions on the spatial rate of change of the aperture profile. Various analytical and numerical results are reviewed pertaining to the problem of relating the effective hydraulic aperture to the statistics of the aperture distribution. These studies all lead to the conclusion that the effective hydraulic aperture is less than the mean aperture, by a factor that depends on the ratio of the mean value of the aperture to its standard deviation. The tortuosity effect caused by regions where the rock walls are in contact with each other is studied using the Hele-Shaw equations, leading to a simple correction factor that depends on the area fraction occupied by the contact regions. Finally, the predicted hydraulic apertures are compared to measured values for eight data sets from the literature for which aperture and conductivity data were available on the same fracture. It is found that reasonably accurate predictions of hydraulic conductivity can be made based solely on the first two moments of the aperture distribution function, and the proportion of contact area.     

A Product Formed from Glycylglycine in the Presence of Vanadate and Hydrogen Peroxide: The (Glycylde-N-hydroglycinato-kappa(3)N(2),N(N)(),O(1))oxoperoxovanadate(V) Anion

A crystalline glycylglycine complex of monoperoxovanadate has been obtained and its X-ray structure determined. The coordination is pentagonal bipyramidal with the peroxo group and a tridentate glycylglycine occupying the equatorial positions. The axial positions of the anion are occupied by the oxo ligand and by one oxygen of the peroxo group of the adjacent anion. The latter interaction establishes the seventh bond and produces a dimeric structure in the crystalline material. NMR studies of its dissolution in water combined with previously reported results from equilibrium measurements show that the dimer dissociates in water to the monomeric precursor. It is proposed that this monomer corresponds to the complex responsible for the inhibition of the vanadium-catalyzed decomposition of hydrogen peroxide by glycylglycine. Crystal structure of [NEt(4)][VO(O(2))(GlyGly)].1.58H(2)O: monoclinic, space group P2(1); Z = 4; a = 10.618(2) ?; b = 14.803(2) ?; c = 11.809(2) ?; beta = 101.37(2) degrees; V = 1819.7 ?(3); T = 198 K; R(F)() = 0.029 for 2664 data (I(o) >/= 2.5sigma(I(o))) and 431 variables.     

Conformations of 1,3,3,5,7,7-Hexamethyl-1,5-diazacyclooctane and Its Bis-BH(3) Adduct. Mono- and Bis-BH(3) Adducts of Di-Tertiary Amines

A variable-temperature (1)H- and (13)C-NMR study revealed a conformational equilibrium for 1,3,3,5,7,7-hexamethyl-1,5-diazacyclooctane (4) having DeltaG() = 8.8 +/- 0.6 kcal/mol at 184 K. This activation barrier connects a major and a minor form of 4. Molecular mechanics calculations on 4 led to the conclusion that the major form is a set of twist-chair-chairs interconverting rapidly via the chair-chair and that the minor form is most likely a set of twist-boat-boats interconverting rapidly via the boat-boat. The proximity of the two nitrogen lone pairs in the major form of 4 made plausible the expectation that 4, as well as a related diamine with apposed nitrogens, 3,7-dimethyl-3,7-diazabicyclo[3.3.1]nonane (3), might bind a Lewis acid, namely BH(3), using both lone pairs simultaneously and equally. This proved not to be the case: for 3 only the bis-BH(3) adduct was found and for 4 the mono-BH(3) adduct utilized only one nitrogen lone pair. The structure of the bis-BH(3) adduct of 4 (12) was determined by X-ray crystallography to be a twist-boat-boat with BH(3)s cis. Molecular mechanics calculations on 12 were consistent with the solid state conformation found.     

Complete separability of time-dependent second-order ordinary differential equations

Extending previous work on the geometric characterization of separability in the autonomous case, necessary and sufficient conditions are established for the complete separability of a system of time-dependent second-order ordinary differential equations. In deriving this result, extensive use is made of the theory of derivations of scalar and vector-valued forms along the projection :J ¹ EE of the first jet bundle of a fibre bundleE . Two illustrative examples are discussed, which fully demonstrate all aspects of the constructive nature of the theory.     

Necessary conditions for optimality in the identification of elliptic systems with parameter constraints

We consider the problems of dientifying the parametersa _ij (x), b _i (x), c(x) in a 2nd order, linear, uniformly elliptic equation, $$\begin{gathered} - \partial _i (a_{ij} (x)\partial _j u) + b_i (x)\partial _i u + c(x)u = f(x),in\Omega , \hfill \\ \partial _v u|_{\partial \Omega } = \phi (s),s \in \partial \Omega , \hfill \\ \end{gathered} $$ on the basis of measurement data $$u(s) = z(s),s \in B \subset \partial \Omega ,$$ with an equality constraint and inequality constraints on the parameters. The cost functionals are one-sided Gâteaux differentiable with respect to the state variables and the parameters. Using the Duboviskii-Milyutin lemma, we get maximum principles for the identification problems, which are necessary conditions for the existence of optimal parameters.     

Systematic analysis of the PSI experiment to directly measure the sticking probabilityω s in dt fusion

Starting in 1989 an experiment was run at PSI to directly measure the final sticking probability in muon catalyzed dt fusion. This experiment was based on an active-target ionization chamber (IC) built at Gatchina, Russia, and an array of plastic neutron counters. In three runs approximately 5×10⁶ isolated alpha signals were recorded with around one half of these occurring in the inner chamber region where we have more complete understanding of the systematic errors. Particularly from a long run in 1992 we were able to obtain a very clean sticking peak of some 5000 events. However, to reach an accurate value of sticking, all systematic effects and several major backgrounds had to be understood in detail. To this end a Monte Carlo code was written to simulate the full electrostatic environment of the IC and to recreate completely each signal type including the actual tritium decay noise from the live experiment. A slightly model dependent value of approx. 0.56±0.04% is obtained for final sticking.     

Feasibility of an experiment to determine the branching ratio for the emission of a heavy neutrino after muon capture in3He

The triton energy of the muon capture reaction ³He t+v, where ³ He is the ground state of muonic³He, has been measured in order to investigate a possible heavy v admixture into the flavour with high sensitivity. ³ He has been formed via the pd fusion reaction by stopping ^– in an ionization chamber (IC) filled with an H/D gas mixture of 3% D concentration at a pressure of 161 bar. In a first short experiment 650 triton events were observed yielding an upper limit for the -heavy v mixing strength of 2.3×10^–3 atE _0v=60 MeV.     

Pulsed NMRON oscillatory free induction decay signals in the angular distribution of gamma radiation from plated60CoFe

Results for an inhomogeneously broadened⁶⁰CoFe NMRON sample have been obtained for gamma detected single pulse (nutation) and two pulse (free induction decay) experiments in the region of intermediate-to-lowR(=₁/). Here ₁ is the angular frequency measure of the strength of the ferromagnetically enhanced RF field at the nucleus and is the HWHM of the inhomogeneously broadened line. Comparisons of the oscillatory FID signals obtained are made with the theoretical predictions of the following paper [6].