SIAC Filtering for Nonlinear Hyperbolic Equations

We present the results of the symmetric and one-sided Smoothness-Increasing Accuracy-Conserving (SIAC) filter applied to a discontinuous Galerkin (DG) approximation for two examples of nonlinear hyperbolic conservation laws. The traditional symmetric SIAC filter relies on having a translation invariant mesh, periodic boundary conditions and linear equations. However, for practical applications that are modelled by nonlinear hyperbolic equations, this is not feasible. Instead we must concentrate on a filter that allows error reduction for nonuniform/unstructured meshes and non-periodic boundary conditions for nonlinear hyperbolic equations. This proceedings is an introductory exploration into the feasibility of these requirements for efficient filtering of nonlinear equations

The (m,n)(m,n)-rational q,tq, t-Catalan polynomials for m=3m=3 and their q,tq,t-symmetry

We introduce a new statistic, skip, on rational $(3,n)$-Dyck paths and define a marked rank word for each path when $n$ is not a multiple of 3. If a triple of valid statistics (area,skip,dinv) are given, we have an algorithm to construct the marked rank word corresponding to the triple. By considering all valid triples we give an explicit formula for the $(m,n)$-rational $q,t$-Catalan polynomials when $m=3$. Then there is a natural bijection on the triples of statistics (area,skips,dinv) which exchanges the statistics area and dinv while fixing the skip. Thus we prove the $q,t$-symmetry of $(m,n)$-rational $q, t$-Catalan polynomials for $m=3$.Comment: 11 pages, 4 figure

Far-infrared spectroelectrochemistry: a study of linear molybdenum/iron/sulfur clusters

The far-infrared spectroelectrochemistry of linear M/Fe/S (M=Mo, W) complexes was investigated in methylene chloride and dichloroethane. With CsI as spectral windows, bands above 200 cm−1 can be observed in methylene chloride, except for a weak methylene chloride band at 450 cm−1. Substitution of dichloroethane for methylene chloride, solvents of nearly identical electrochemical properties, allows one to observe solute bands in the 450-cm−1 region. The far-infrared spectroelectrochemistry of [MoFe2S4Cl4]2− and its tungsten analogue was investigated. The disappearance of the oxidation bands and the appearance of bands due to the reduced product could be clearly observed. The origin of the vibrational bands could be clearly identified using 34S-substituted complexes. In addition to the far-infrared bands, the resonance Raman spectroelectrochemistry of the oxidized and reduced complex, along with the 34S-substituted complexes was obtained. Far-infrared and resonance Raman spectroelectrochemistry can be combined to understand the electrochemical mechanism of transition metal complexes. The far-infrared spectroelectrochemistry of [MoFe2S4Cl4]2− and its tungsten analogue was investigated. The disappearance of the initial bands and the appearance of bands due to the reduced product could be clearly observed. Resonance Raman spectroscopy and the use of 34S-substituted complexes were used for characterization of the reactant and products

Dual-Topology Hamiltonian-Replica-Exchange Overlap Histogramming Method to Calculate Relative Free Energy Difference in Rough Energy Landscape

A novel overlap histogramming method based on Dual-Topology Hamiltonian-Replica-Exchange simulation technique is presented to efficiently calculate relative free energy difference in rough energy landscape, in which multiple conformers coexist and are separated by large energy barriers. The proposed method is based on the realization that both DT-HERM exchange efficiency and confidence of free energy determination in overlap histogramming method depend on the same criteria: neighboring states' energy derivative distribution overlap. In this paper, we demonstrate this new methodology by calculating free energy difference between amino acids: Leucine and Asparagine, which is an identified chanllenging system for free energy simulations.Comment: 14 pages with 4 figure