An adaptive continuation-multigrid method for the balanced vortex model

Obtaining solutions of the Eliassen balanced vortex model requires solving an invertibility relation, which is a nonlinear elliptic problem of the Monge-Ampere type. Multigrid techniques for this problem are investigated. An adaptive algorithm which combines the full multigrid method with continuation in a parameter related to the strength of the forcing is developed. Numerical results demonstrate the efficiency and robustness of this algorithm.     

When is a nanoparticle a cluster? An operando EXAFS study of amine borane dehydrocoupling by Rh(4-6) clusters

X-ray absorption fine structure (XAFS) is used to determine the structure of the rhodium cluster present during the catalyzed dehydrocoupling of amine boranes under operando conditions. We show how a variety of XAFS strategies can be used in combination with other analytical methods to differentiate homogeneous from heterogeneous systems. Analysis of the in situ XAFS spectra using a series of amine boranes (NH3BH3, R2NHBH3, and RNH2BH3 where R = methyl, isopropyl, tert-butyl, and cyclohexyl) and rhodium catalyst precursor compounds (including chloro-(1,5-cyclooctadiene)rhodium (I) dimer, bis(1,5-cyclooctadiene)rhodium (I) trifluoromethanesulfonate, chlorodicarbonylrhodium (I) dimer, dichloro(pentamethylcylcopentadienyl)rhodium (III) dimer, hexarhodium hexadecacarbonyl, and tetrarhodium dodecacarbonyl) strongly suggest that the active catalyst species for this reaction is a homogeneous rhodium complex. Rhodium clusters containing four or six rhodium atoms (Rh(4-6)) bound to amine boranes are observed as the major (>99%) rhodium containing species during and after the catalyzed anaerobic dehydrocoupling. During the later stages of the reaction a nonmetallic rhodium complex precipitates in which individual Rh(4-6) clusters likely form polymer chains ligated by the reaction products that have two or more ligating sites. The best fits of the XAFS data, using ab initio calculations of FEFF theory, show that the major rhodium species (80%) has each rhodium atom directly bound to three rhodium atoms with an observed bond distance of 2.73 A and to two boron atoms at 2.10 A. A minor (20%) rhodium species has each rhodium atom bound to four rhodium atoms with a bond distance of about 2.73 A and a single rhodium atom at a nonbonding distance of 3.88 A. No metallic rhodium was observed at any time during the anaerobic reaction.     

Nd3+ and Am3+ ion interactions with sulfate ion and their influence on NdPO4(c) solubility

The effects of Nd(III)/Am(III) complexation with sulfate were studied by 1) re-examining existing data for the Am–SO₄ system using more, advanced aqueous electrolyte models valid to high concentration to obtain reliable thermodynamic data for SO ₄ ^2– complexes or ion interactions with Nd³⁺ and Am³⁺ and 2) conducting experimental solubility studies of NdPO₄(c), an analog phase of AmPO ₄ (c), a possibly important phase in high level nuclear wastes, in the presence of SO ₄ ^2– to test the newly developed thermodynamic model and show the possible influence of sulfate in a repository environment. The data showed that the increase in the solubility of NdPO ₄ (c) resulted primarily from the increase in ionic strength. Slightly higher observed Nd concentrations in the presence of sulfate, as compared with concentrations predicted at the experimental ionic strengths, resulted from the weak complexes or ion interactions involving Nd ³⁺ –SO ₄ ^2– . The Pitzer ion interaction parameters, applicable to 0.5m sulfate, were obtained for Am ³⁺ –SO ₄ ^2– from a reinterpretation of known solvent extraction data. These parameters are also consistent with literature data for Am ³⁺ /Na⁺ exchange and solvent extraction in the presence of sulfate. When used for the analogous Nd ³⁺ –SO ₄ ^2– system to predict NdPO ₄ (c) solubility in the presence of sulfate, they provided excellent agreement between the predicted and the observed solubilities, indicating that they can be reliably used to determine Nd ³⁺ or Am ³⁺ ion interactions with SO ₄ ^2– in all ground waters where SO ₄ ^2– is less than 0.5m     

Spin measurements and reaction mechanism in the inelastic scattering of 18O on 12C

The alpha-decay of states in ¹⁸O have been studied in the inelastic scattering reaction ${}^{12}\text{C}\text{(}{}^{18}\text{O}\text{,}{}^{18}\text{O}{}^1\text{→}{}^{14}\text{C}\text{-α)}$ at 82 MeV. The double differential cross sections have been analysed with a strong absorption model. A systematic dependence of emission angle on spin is observed, allowing the determination of the transferred angular momentum.     

Direct and iterative solution of the generalized Dirichlet–Neumann map for elliptic PDEs on square domains

In this work we derive the structural properties of the Collocation coefficient matrix associated with the Dirichlet–Neumann map for Laplace’s equation on a square domain. The analysis is independent of the choice of basis functions and includes the case involving the same type of boundary conditions on all sides, as well as the case where different boundary conditions are used on each side of the square domain. Taking advantage of said properties, we present efficient implementations of direct factorization and iterative methods, including classical SOR-type and Krylov subspace (Bi-CGSTAB and GMRES) methods appropriately preconditioned, for both Sine and Chebyshev basis functions. Numerical experimentation, to verify our results, is also included.     

Polarization fluctuations in regions bounded by equi-potentials

It is shown that the integral of <{P(rτ), P(r')}>· n? as a function of r over a volume V_e bounded by an equi-potential is independent of r' and of V_e and is determined solely by [?(ω)?1] · n? provided the dielectric constant is local and that V_e is of macroscopic dimensions.     

A search for resonant two-step α-exchange in 6Li + 12C scattering

Excitation functions for ¹²C(⁶Li, ⁶Li)¹²C (gs, 4.43 MeV) have been measured at 10 angles (40° ? θ_cm ? 160°) over the energy range 20 MeV < E_lab < 36 MeV. A single anomaly of width Γ ≈ 800 keV is observed at E_lab = 22.8 MeV. The results casts doubts on the resonant two-step α-exchange mechanism suggested to occur in this system.