Some monotonicity properties of symmetric pólya densities and their exponential families

Summary In this note we observe that for independent symmetric random variables X and Y, when the pdf of X is PF, the conditional distributions of ¦Y¦ given S = X + Y form a MLR family. We then show that for a function : R ⁿR that is symmetric in each coordinate and increasing on (0, )ⁿ, E((S₁,...,S_n)¦S_n = s) is even and increasing in ¦s¦. Here S₁,...,S_n are partial sums with independent symmetric PF summands. Application is made to sequential tests that minimize the maximum expected sample size when the model is a one-parameter exponential family generated by a symmetric PF density.Work supported by NSF grants MPS 72-05082 AO2 and MCS 75-23344     

Lattice-Boltzmann simulations of the dynamics of polymer solutions in periodic and confined geometries

A numerical method to simulate the dynamics of polymer solutions in confined geometries has been implemented and tested. The method combines a fluctuating lattice-Boltzmann model of the solvent [Ladd, Phys. Rev. Lett. 70, 1339 (1993)] with a point-particle model of the polymer chains. A friction term couples the monomers to the fluid [Ahlrichs and Dunweg, J. Chem. Phys. 111, 8225 (1999)], providing both the hydrodynamic interactions between the monomers and the correlated random forces. The coupled equations for particles and fluid are solved on an inertial time scale, which proves to be surprisingly simple and efficient, avoiding the costly linear algebra associated with Brownian dynamics. Complex confined geometries can be represented by a straightforward mapping of the boundary surfaces onto a regular three-dimensional grid. The hydrodynamic interactions between monomers are shown to compare well with solutions of the Stokes equations down to distances of the order of the grid spacing. Numerical results are presented for the radius of gyration, end-to-end distance, and diffusion coefficient of an isolated polymer chain, ranging from 16 to 1024 monomers in length. The simulations are in excellent agreement with renormalization group calculations for an excluded volume chain. We show that hydrodynamic interactions in large polymers can be systematically coarse-grained to substantially reduce the computational cost of the simulation. Finally, we examine the effects of confinement and flow on the polymer distribution and diffusion constant in a narrow channel. Our results support the qualitative conclusions of recent Brownian dynamics simulations of confined polymers [Jendrejack et al., J. Chem. Phys. 119, 1165 (2003) and Jendrejack et al., J. Chem. Phys. 120, 2513 (2004)].     

GROMACS: fast, flexible, and free

This article describes the software suite GROMACS (Groningen MAchine for Chemical Simulation) that was developed at the University of Groningen, The Netherlands, in the early 1990s. The software, written in ANSI C, originates from a parallel hardware project, and is well suited for parallelization on processor clusters. By careful optimization of neighbor searching and of inner loop performance, GROMACS is a very fast program for molecular dynamics simulation. It does not have a force field of its own, but is compatible with GROMOS, OPLS, AMBER, and ENCAD force fields. In addition, it can handle polarizable shell models and flexible constraints. The program is versatile, as force routines can be added by the user, tabulated functions can be specified, and analyses can be easily customized. Nonequilibrium dynamics and free energy determinations are incorporated. Interfaces with popular quantum-chemical packages (MOPAC, GAMES-UK, GAUSSIAN) are provided to perform mixed MM/QM simulations. The package includes about 100 utility and analysis programs. GROMACS is in the public domain and distributed (with source code and documentation) under the GNU General Public License. It is maintained by a group of developers from the Universities of Groningen, Uppsala, and Stockholm, and the Max Planck Institute for Polymer Research in Mainz. Its Web site is http://www.gromacs.org.     

Enamines of 1,3-dimethylbarbiturates and their symmetrical palladium(II) complexes: synthesis,characterization and biological activity

Transition Metal Chemistry - Three 1,3-dimethylbarbiturate-enamine derivatives and their symmetrical palladium(II) complexes were prepared and characterized by spectroscopic methods. In addition,...     

Model for spontaneous frequency sweeping of an Alfvén wave in a toroidal plasma

We study the frequency chirping signals arising from spontaneously excited toroidial Alfvén eigenmode (TAE) waves that are being driven by an inverted energetic particle distribution whose free energy is tapped from the generic particle/wave resonance interaction. Initially a wave is excited inside the Alfvén gap with a frequency determined from the linear tip model of Rosenbluth, Berk and Van dam (RBV) [1]. Hole/clumps structures are formed and are observed to chirp towards lower energy states. We find that the chirping signals from clump enter the Alfvén continuum which eventually produce more rapid chirping signals. The accuracy of the adiabatic approximation for the mode evolution is tested and verified by demonstrating that a WKB-like decomposition of the time response for the field phase and amplitude agree with the data. Plots of the phase space structure correlate well with the chirping dependent shape of the separatrix structure. A novel aspect of the simulation is that it performed close to the wave frame of the phase space structure, which enables the numerical time step to remain the same during the simulation, independent of the rest frame frequency.     

Librations of mercury in longitude based on the data of ground-based radar observations

The amplitude, phase, and period of free liberation and the amplitudes of five fundamental harmonics of forced (annual, semi-annual, …) librations of Mercury in longitude are determined based on the analytical theory of Mercury’s liberation (on an elliptical orbit) in longitude using a high-accuracy complex method for ground-based radar tracking.     

On the oxidation of malonic acid by ceric ions

The oxidation of malonic acid by ceric ions has been investigated in sulfuric acid solution under a variety of conditions. The initial rate at low ceric ion concentrations is first order in each of the two reactants and has an activation energy of 11.6 kcal/mol; the instantaneous rate constant increases somewhat with time during a single run. At higher concentrations of ceric ion, semilogarithmic plots are sigmoid with a reduced rate constant at long times. The rate decreases slightly with increasing sulfuric acid concentration. Rates of carbon dioxide evolution may be much less than rates of ceric ion reduction because of supersaturation effects. The observations can be explained if dissolved oxygen reacts with organic radicals to catalyze the rate of initial attack on malonic acid, but oxygen must also be consumed irreversibly during these reactions. Computations with plausible rate constants have simulated the experimental observations. These oxygen effects can rationalize peculiar almost discontinuous changes in rate when bromomalonic acid is oxidized by ceric ion. These effects may also explain the previously puzzling observation that some Belousov–Zhabotinsky solutions are oscillatory in bulk but become quiescent but excitable when spread in a thin film in contact with air.     

Supplier diversification under binomial yield

We consider supplier diversification in an EOQ type inventory setting with multiple suppliers and binomial yields. We characterize the optimal policy for the model and show that, in this case, it does not pay to diversify, in contrast to previous results in the random yield literature.