An iterative semi-implicit scheme with robust damping

An efficient, iterative semi-implicit (SI) numerical method for the time integration of stiff wave systems is presented. Physics-based assumptions are used to derive a convergent iterative formulation of the SI scheme which enables the monitoring and control of the error introduced by the SI operator. This iteration essentially turns a semi-implicit method into a fully implicit method. Accuracy, rather than stability, determines the timestep. The scheme is second-order accurate and shown to be equivalent to a simple preconditioning method. We show how the diffusion operators can be handled so as to yield the property of robust damping, i.e., dissipating the solution at all values of the parameter \mathcal D\dt, where $\mathcal D$ is a diffusion operator and \dt the timestep. The overall scheme remains second-order accurate even if the advection and diffusion operators do not commute. In the limit of no physical dissipation, and for a linear test wave problem, the method is shown to be symplectic. The method is tested on the problem of Kinetic Alfv\'en wave mediated magnetic reconnection. A Fourier (pseudo-spectral) representation is used. A 2-field gyrofluid model is used and an efficacious k-space SI operator for this problem is demonstrated. CPU speed-up factors over a CFL-limited explicit algorithm ranging from $\sim20$ to several hundreds are obtained, while accurately capturing the results of an explicit integration. Possible extension of these results to a real-space (grid) discretization is discussed.Comment: Submitted to the Journal of Computational Physics. Clarifications and caveats in response to referees, numerical demonstration of convergence rate, generalized symplectic proo

Development of a catalytic enantioselective synthesis of the guanacastepene and heptemerone tricyclic core

For nearly two decades, synthetic chemists have been fascinated by the structural complexity and synthetic challenges afforded by the guanacastepene and heptemerone diterpenoids. Numerous synthetic approaches to these compounds have been reported, but to date the application of enantioselective catalysis to this problem has not been realized. Herein we report an enantioselective synthesis of an advanced intermediate corresponding to the tricyclic core common to the guanacastepenes and heptemerones. Highlights of this work include sequential Pd-catalyzed decarboxylative allylic alkylation reactions to generate the two all carbon quaternary stereocenters, the use of ring-closing metathesis to close the A ring in the presence of a distal allyl sidechain, and a regio- and diastereoselective oxidation of a trienol ether to introduce oxygenation on the A ring

Inelastic Dark Matter at DAMA, CDMS and Future Experiments

The DAMA annual modulation signature, interpreted as evidence for a spin-independent WIMP coupling, seems in conflict with null results from CDMS. However, in models of ``inelastic dark matter'', the experiments are compatible. Inelastic dark matter can arise in supersymmetric theories as the real component of a sneutrino mixed with a singlet scalar. In contrast with ordinary sneutrino dark matter, such particles can satisfy all experimental constraints while giving the appropriate relic abundance. We discuss the modifications to the signal seen at DAMA, in particular noting the strong suppression of low energy events in both modulated and unmodulated components. We discuss future experiments, with emphasis on distinguishing inelastic dark matter from ordinary dark matter, and stressing the significance of experiments with heavy target nuclei, such as xenon and tungsten.Comment: 4 pages; to appear in the proceedings of 5th International UCLA Symposium on Sources and Detection of Dark Matter and Dark Energy in the Universe (DM 2002), Marina del Rey, California, 20-22 Feb 200

A semi-implicit Hall-MHD solver using whistler wave preconditioning

The dispersive character of the Hall-MHD solutions, in particular the whistler waves, is a strong restriction to numerical treatments of this system. Numerical stability demands a time step dependence of the form $\Delta t\propto (\Delta x)^2$ for explicit calculations. A new semi--implicit scheme for integrating the induction equation is proposed and applied to a reconnection problem. It it based on a fix point iteration with a physically motivated preconditioning. Due to its convergence properties, short wavelengths converge faster than long ones, thus it can be used as a smoother in a nonlinear multigrid method

Synthesis of enantioenriched γ-quaternary cycloheptenones using a combined allylic alkylation/Stork–Danheiser approach: preparation of mono-, bi-, and tricyclic systems

A general method for the synthesis of β-substituted and unsubstituted cycloheptenones bearing enantioenriched all-carbon γ-quaternary stereocenters is reported. Hydride or organometallic addition to a seven-membered ring vinylogous ester followed by finely tuned quenching parameters achieves elimination to the corresponding cycloheptenone. The resulting enones are elaborated to bi- and tricyclic compounds with potential for the preparation of non-natural analogs and whose structures are embedded in a number of cycloheptanoid natural products

Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system

This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and ions, through a set of scaling limits. We also propose a kinetic formulation for the Hall-MHD equations which contains as fluid closure different variants of the Hall-MHD model. Then, we prove the existence of global weak solutions for the incompressible viscous resistive Hall-MHD model. We use the particular structure of the Hall term which has zero contribution to the energy identity. Finally, we discuss particular solutions in the form of axisymmetric purely swirling magnetic fields and propose some regularization of the Hall equation

Ring-Contraction Strategy for the Practical, Scalable, Catalytic Asymmetric Synthesis of Versatile γ-Quaternary Acylcyclopentenes

Contraction action! A simple protocol for the catalytic asymmetric synthesis of highly functionalized γ-quaternary acylcyclopentenes (see schematic) in up to 91 % overall yield and 92 % ee has been developed. The reaction sequence employs a palladium-catalyzed enantioselective alkylation reaction and exploits the unusual stability of β-hydroxy cycloheptanones to achieve a general and robust method for performing two-carbon ring contractions

Electroviscous effects of simple electrolytes under shear

On the basis of a hydrodynamical model analogous to that in critical fluids, we investigate the influences of shear flow upon the electrostatic contribution to the viscosity of binary electrolyte solutions in the Debye-H\"{u}ckel approximation. Within the linear-response theory, we reproduce the classical limiting law that the excess viscosity is proportional to the square root of the concentration of the electrolyte. We also extend this result for finite shear. An analytic expression of the anisotropic structure factor of the charge density under shear is obtained, and its deformation at large shear rates is discussed. A non-Newtonian effect caused by deformations of the ionic atmosphere is also elucidated for $\tau_D\dot{\gamma}>1$. This finding concludes that the maximum shear stress that the ionic atmosphere can support is proportional to $\lambda_D^{-3}$, where $\dot{\gamma}$, $\lambda_D$ and $\tau_D=\lambda_D^2/D$ are, respectively, the shear rate, the Debye screening length and the Debye relaxation time with $D$ being the relative diffusivity at the infinite dilution limit of the electrolyte.Comment: 13pages, 2figure