Conditional Source-term Estimation using dynamic ensemble selection and parallel iterative solution

A modified version of the Least-Square QR-factorisation (LSQR) algorithm has been implemented in conjunction with Conditional Source-term Estimation (CSE) for lean, turbulent premixed methane–air combustion via Large Eddy Simulation (LES). The iterative solver can reduce computational times by an order of magnitude during the inversion phase of CSE in comparison with the conventional LU-decomposition method. The advantages of iterative and parallel iterative solvers become more prominent as the size of the system increases. The ensemble selection procedure for computing averages within localised regions of the simulation domain has also been updated to a dynamic routine. This allows for more flexible and efficient allocation of computational resources along with reduced input from the user, especially for complex geometries. Preliminary LES calculations have shown that the implementation of an iterative solver and a dynamic ensemble selection algorithm will reduce computational times significantly with negligible error contribution for one-condition CSE, which is applicable to purely premixed or non-premixed turbulent combustion problems. In addition, these algorithms provide the foundation for exceptional computational cost savings for the inversion in two-condition CSE, or Doubly Conditional Source-term Estimation (DCSE), which has shown promise for predicting partially-premixed combustion. Parallel computation of the inverse solution is particularly beneficial to DCSE as the computational cost of the inversion process is considerably larger than in one-condition CSE.     

Polymerization and photochromism of ammonium molybdate in porous glass

Modification of porous glass (PG) plates is carried out by impregnation with aqueous solutions of ammonium molybdate (NH₄)₂MoO₄ with subsequent removal of water at 120°C. A long-wavelength shift of absorption spectra upon accumulation of the salt in PG indicates polymerization of MoO₄^2- anions at low concentrations of the encapsulated salt. Photochromism manifests itself as the anionic forms in PG become larger. UV irradiation of the modified plates causes enhancement of continuous absorption in the visible range. The proposed mechanism of photoreduction of the polianions in PG involves the removal of oxygen atoms from the bridging–Mo–O–Mo–bonds and stabilization of the colored forms by means of conjugation of the electrons released from the 4d-levels of pentavalent molybdenum.     

Distribution of luminescence excitation energy between Eu<Superscript>3+</Superscript> and Tb<Superscript>3+</Superscript> ions fixed in a perfluorosulfonic membrane

Ion-exchange modification of MF-4SK perfluorosulfonic membranes with Eu³⁺ and Tb³⁺ cations was realized. The state of cations in the membrane was studied by X-ray photoelectron spectroscopy. Special features of the luminescence of the resulting systems point to preferential excitation energy transfer from europium to terbium.     

Modeling positrons in molecular electronic structure calculations with the nuclear-electronic orbital method

The nuclear-electronic orbital (NEO) method was modified and extended to positron systems for studying mixed positronic-electronic wavefunctions, replacing the mass of the proton with the mass of the positron. Within the modified NEO framework, the NEO-HF (Hartree-Fock) method provides the energy corresponding to the single-configuration mixed positronic-electronic wavefunction, minimized with respect to the molecular orbitals expressed as linear combinations of Gaussian basis functions. The electron-electron and electron-positron correlation can be treated in the NEO framework with second-order perturbation theory (NEO-MP2) or multiconfigurational methods such as the full configuration interaction (NEO-FCI) and complete active space self-consistent-field (NEO-CASSCF) methods. In addition to implementing these methods for positronic systems, strategies for calculating electron-positron annihilation rates using NEO-HF, NEO-MP2, and NEO-FCI wavefunctions were also developed. To apply the NEO method to the positronium hydride (PsH) system, positronic and electronic basis sets were optimized at the NEO-FCI level and used to compute NEO-MP2 and NEO-FCI energies and annihilation rates. The effects of basis set size on NEO-MP2 and NEO-FCI correlation energies and annihilation rates were compared. Even-tempered electronic and positronic basis sets were also optimized for the e+LiH molecule at the NEO-MP2 level and used to compute the equilibrium bond length and vibrational energy.     

Metric Combinatorics of Convex Polyhedra: Cut Loci and Nonoverlapping Unfoldings

Let S be the boundary of a convex polytope of dimension d+1, or more generally let S be a convex polyhedral pseudomanifold. We prove that S has a polyhedral nonoverlapping unfolding into , so the metric space S is obtained from a closed (usually nonconvex) polyhedral ball in by identifying pairs of boundary faces isometrically. Our existence proof exploits geodesic flow away from a source point v∈S, which is the exponential map to S from the tangent space at v. We characterize the cut locus (the closure of the set of points in S with more than one shortest path to v) as a polyhedral complex in terms of Voronoi diagrams on facets. Analyzing infinitesimal expansion of the wavefront consisting of points at constant distance from v on S produces an algorithmic method for constructing Voronoi diagrams in each facet, and hence the unfolding of S. The algorithm, for which we provide pseudocode, solves the discrete geodesic problem. Its main construction generalizes the source unfolding for boundaries of three-polytopes into . We present conjectures concerning the number of shortest paths on the boundaries of convex polyhedra, and concerning continuous unfolding of convex polyhedra. We also comment on the intrinsic nonpolynomial complexity of nonconvex manifolds. The first author was partially supported by the National Science Foundation, and he acknowledges the Mathematisches Forschungsinstitut Oberwolfach for a stimulating research environment during the week-long program on Topological and Geometric Combinatorics (April, 2003). Most of this work was completed while the first author was at the Massachusetts Institute of Technology (Cambridge, MA) and the Mathematical Sciences Research Institute (Berkeley, CA). The second author was partially supported by the National Security Agency and the National Science Foundation. He thanks the organizers of the “Second Geometry Meeting dedicated to A.D. Aleksandrov” held at the Euler International Mathematical Institute in St. Petersburg (June, 2002), where these results were originally presented.     

A model of the multiple adsorption of hydrogen atoms on the surface of carbon nanotubes

A model of the multiple adsorption of atomic hydrogen on the surface of single-walled carbon nanotubes of the zigzag and arm-chair types was constructed. The adsorption model is based on the Anderson periodic model. An analytic equation for the band structure of carbon nanotubes with adsorbed hydrogen atoms was obtained, and the special features of this structure were studied. The dependence of the band structure of carbon nanotubes on the concentration of adsorbed hydrogen atoms was analyzed. The model constructed can be used to study adsorption of other univalent atoms on the surface of carbon particles.     

Electrochemical Oxidation of Catechols (=Benzene‐1,2‐diols) in the Presence of Benzoylacetonitrile: Synthesis of New Derivatives of 5,6‐Dihydroxybenzofuran

The electrochemical oxidation of catechol (=benzene‐1,2‐diol; 1a ) and some of its derivatives in H₂O/MeCN 1 : 1 containing benzoylacetonitrile (=β‐oxobenzenepropanenitrile; 3 ) as a nucleophile was studied by cyclic voltammetry and controlled‐potential coulometry. The voltammetric data showed that electrochemically generated o‐benzoquinones (=cyclohexa‐3,5‐diene‐1,2‐diones) from catechol ( 1a ) and 3‐methylcatechol ( 1b ) participate in a Michael‐addition reaction with 3 to form the corresponding 5,6‐dihydroxybenzofuran‐3‐carbonitrile 8 (Scheme 1). In this work, we report an efficient one‐pot method with high atom economy for the synthesis of new substituted 5,6‐dihydroxybenzofuran‐3‐carbonitriles in an undivided cell under ambient conditions.     

Acute triangulations of polyhedra and ℝ N

We study the problem of acute triangulations of convex polyhedra and the space ? ⁿ . Here an acute triangulation is a triangulation into simplices whose dihedral angles are acute. We prove that acute triangulations of the n-cube do not exist for n≥4. Further, we prove that acute triangulations of the space ? ⁿ do not exist for n≥5. In the opposite direction, in ?³, we present a construction of an acute triangulation of the cube, the regular octahedron and a non-trivial acute triangulation of the regular tetrahedron. We also prove nonexistence of an acute triangulation of ?⁴ if all dihedral angles are bounded away from π/2.     

Energy dependence of directed flow over a wide range of pseudorapidity in Au + Au collisions at the BNL Relativistic Heavy Ion Collider

We report on measurements of directed flow as a function of pseudorapidity in Au + Au collisions at energies of square root of SNN = 19.6, 62.4, 130 and 200 GeV as measured by the PHOBOS detector at the BNL Relativistic Heavy Ion Collider. These results are particularly valuable because of the extensive, continuous pseudorapidity coverage of the PHOBOS detector. There is no significant indication of structure near midrapidity and the data surprisingly exhibit extended longitudinal scaling similar to that seen for elliptic flow and charged particle pseudorapidity density.