Picard iteration-based variable-order integrator with dense output employing algorithmic differentiation

Numerical Algorithms - Motivated by the high accuracy requirements and the huge ratio of the largest to smallest time scales of Coulomb collision simulations of a considerable number of charges, we...     

Conformational and thermodynamic analysis of the COXIB scaffold using quantum chemical calculations

Selective cyclo‐oxygenase‐2 inhibitors (COXIBs) are prominent members of the nonsteroidal anti‐inflammatory drugs. The neutral and protonated COXIB scaffold has been subjected to molecular computations in the gas phase and implicit solvent to measure the relative changes in the thermodynamic functions, enthalpy (H_rel), potential energy (U_rel), Gibbs free energy (G_rel) and entropy (S_rel) induced by selected substituents. Conformational analysis of the COXIB scaffold indentified four pairs of atropisomeric conformers (from I, I′ to IV, IV′) associated with a molecular structure containing a double rotor system. All conformers had similar stability. Para‐substitution with substituents that cover a wide range of Hammett sigma values did not alter the geometries of the neutral COXIB conformers; however, the protonated COXIB scaffold was showed an increase in structural and thermodynamic perturbations due to inductive effects. Flexibility and structural resilience of the COXIB scaffold under the conditions studied herein could be an important feature of the COXIBs, especially considering the previously proposed flexibility of the cyclo‐oxygenase binding site. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Geometrization of Monte-Carlo numerical analysis of an elliptic operator: strong approximation

A one-step scheme is constructed, which, as the Milstein scheme, has the strong approximation property of order 1; in contrast to the Milstein scheme, our scheme does not involve the simulation of iterated Itô integrals of second order. To cite this article: A.B. Cruzeiro et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Fragmentation Reactions of Bridged Heterocyclic Phosphorus Compounds as a Source of Low-Coordination Species

Abstract

Several types of unsaturated, bridged structures have been prepared that can undergo retro-cycloaddition with the extrusion of phosphorus species having low coordination. By this technique, the species RO-PO₂, R-PO₂, R₂N-P=S, RO-P=S, and R-P=CH₂ have been generated and detected by trapping experiments.     

A general synthesis of 2,5-diaryl-4-chloro (or bromo)oxazoles

Reaction between acyleyanides (ArCOCN) and aldehydes (ArCHO) in the presence of ether and hydrogen chloride (or hydrogen bromide) gives good yields of 2,5-diaryl-4-chloro (or bromo)oxazoles ( 2 ).     

Construction of spherical t-designs

Spherical t-designs are Chebyshev-type averaging sets on the d-dimensional unit sphere S ^d–1, that are exact for polynomials of degree at most t. The concept of such designs was introduced by Delsarte, Goethals and Seidel in 1977. The existence of spherical t-designs for every t and d was proved by Seymour and Zaslavsky in 1984. Although some sporadic examples are known, no general construction has been given. In this paper we give an explicit construction of spherical t-designs on S ^d–1 containing N points, for every t,d and N,NN ₀, where N ₀ = C(d)t ^{O(d 3}).     

Cubatic phase for tetrapods

We investigate the phase behavior of tetrapods, hard nonconvex bodies formed by four rods connected under tetrahedral angles. We predict that, depending on the relative lengths of the rods these particles can form a uniaxial nematic phase, and more surprisingly they can exhibit a cubatic phase, a special case of the biaxial nematic phase. These predictions may be experimentally testable, as experimental realizations of tetrapods have recently become available.     

Local Search Methods for the Optimal Winner Determination Problem in Combinatorial Auctions

In this paper, both stochastic local search (SLS) and tabu search (TS) are studied for the optimal winner determination problem (WDP) in combinatorial auctions. The proposed methods are evaluated on various benchmark problems, and compared with the hybrid simulated annealing (SAGII), the memetic algorithms (MA) and Casanova. The computational experiments show that the SLS provides competitive results and finds solutions of a higher quality than TS and Casanova methods.     

Hybrid finite element/volume method for 3D incompressible flows with heat transfer

An implicit hybrid finite element (FE)/volume solver has been extended to incompressible flows coupled with the energy equation. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centred finite volume (FV) method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centres and the auxiliary variable at vertices. The Generalized Minimal Residual (GMRES) matrix-free strategy is adapted to solve the governing equations in both FE and FV methods. The presented 2D and 3D numerical examples show the robustness and accuracy of the numerical method.