Lattice-BGK approach to simulating granular flows

Many continuum theories for granular flow produce an equation of motion for the fluctuating kinetic energy density (granular temperature) that accounts for the energy lost in inelastic collisions. Apart from the presence of an extra dissipative term, this equation is very similar in form to the usual temperature equation in hydrodynamics. It is shown how a lattice-kinetic model based on the Bhatnagar-Gross-Krook (BGK) equation that was previously derived for a miscible two-component fluid may be modified to model the continuum equations for granular flow. This is done by noting that the variable corresponding to the concentration of one species follows an equation that is essentially analogous to the granular temperature equation. A simulation of an unforced granular fluid using the modified model reproduces the phenomenon of clustering instability, namely the spontaneous agglomeration of particles into dense clusters, which occurs generically in all granular flows. The success of the continuum theory in capturing the gross features of this basic phenomenon is discussed. Some shear flow simulations are also presented.     

Variable-Energy Photoelectron Spectroscopy of (eta(5)-C(5)H(5))NiNO: Molecular Orbital Assignment and Xalpha-SW Calculations

Variable-energy valence and inner-valence photoelectron spectra have been recorded for the CpNiNO complex (Cp = eta(5)-C(5)H(5)) between 21.2 and 100 eV, using He I radiation and synchrotron radiation. The ground state electronic structure has been calculated by using the Xalpha-SW method. Photoionization cross sections (sigma) have also been calculated for the valence ionizations using the Xalpha-SW method. The theoretical branching ratios (sigma(i)/ summation operatorsigma) have been compared with the observed branching ratios (A(i)()/ summation operatorA) between 21.2 and 100 eV. The assignment of the photoelectron spectrum based on the analysis of intensity variations and width of vibrational peaks is consistent with the ion state orbital ordering 5e(1)(1) < 7a(1)(2) < 3e(2)(3) < 4e(1)(4) (band numbers are in parentheses) and is inconsistent with another recently proposed ordering 5e(1)(1), 5e(1)(2) < 7a(1), 3e(2)(3) < 4e(1)(4), which takes the 5e(1) vibronic effects into consideration. The experimental branching ratio results indicate a Ni 3p resonance effect around 75 eV in the photoionization process. The inner-valence spectrum has also been assigned with the aid of the Xalpha-SW calculations.     

Self-intersections of curves on surfaces

Let M be a compact orientable surface with nonempty boundary (x(M)<0) and fundamental group . Let be a geodesic on M (with a fixed hyperbolic structure), and let W be a (cyclically reduced) word in a fixed set of generators of which represents . In this paper, we give an algorithm to count the number of self-intersections of in terms of W, generalizing a result of Birman and Series, where an algorithm was given to decide if was simple. Some applications of the algorithm to surfaces with one boundary and the Markoff spectrum are also given.