Integration of large chemical kinetic mechanisms via exponential methods with Krylov approximations to Jacobian matrix functions

Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane–air and iso-octane–air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components.     

Effects of the commensurability and disorder on friction for the system Xe/Cu

We present molecular dynamics simulations of static friction for a monolayer of Xe deposited on a thick slab of Cu for two different geometries. The interaction potential between Xe and Cu has been derived from DFT calculations. The first geometry is the commensurate adsorption geometry (√3 × √3 suggested by LEED, corresponding to a coverage 1/3, where all Xe atoms are on top positions. The second one corresponds to a coverage 0.36 and is characterized by a large surface unit cell, containing 9 Xe atoms in different disordered positions. This large unit cell mimics an incommensurate case. Our analysis points out the effect of the order/disorder in tribological properties of a realistic three-dimensional system.     

Pyroxene inclusions in paleo-Christian mosaic tesserae: a new tool for constraining the glass manufacturing temperature

The mineral inclusions of two orange glass tesserae from paleo-Christian mosaics were investigated in order to derive the melting temperature reached during their production (sourced from Padua and Vicenza, Veneto region, Italy). In particular, clinopyroxene crystals were studied by single-crystal X-ray diffraction and electron microprobe WDS analysis. The crystals show C2/c symmetry, typical of disordered Ca/Na and Mg/Al distributions indicating high-temperature of formation (>700°C). The cation site populations were obtained by combining results from the two experimental techniques enabled us to derive the following stoichiometric formula:

Localization of Bose-Einstein condensates in optical lattices

The dynamics of repulsive bosons condensed in an optical lattice is effectively described by the Bose-Hubbard model. The classical limit of this model, reproduces the dynamics of Bose-Einstein condensates, in a periodic potential, and in the superfluid regime. Such dynamics is governed by a discrete nonlinear Schrödinger equation. Several papers, addressing the study of the discrete nonlinear Schrödinger dynamics, have predicted the spontaneous generation of (classical) breathers in coupled condensates. In the present contribute, we shall focus on localized solutions (quantum breathers) of the full Bose-Hubbard model. We will show that solutions exponentially localized in space and periodic in time exist also in absence of randomness. Thus, this kind of states, reproduce a novel quantum localization phenomenon due to the interplay between bounded energy spectrum and non-linearity.     

Scalar Quantum Electrodynamics on the lattice as classical statistical mechanics

Wilson's lattice approximation allows us to apply classical statistical mechanics ideas to the study of Scalar Quantum Electrodynamics. Our main tools are Griffiths-Kelly-Sherman inequalities, the transfer matrix formalism and exponential bounds. Our main result is the existence of the infinite volume limit for every value of the coupling parameters.     

Rapid detection and identification of liquid crystal states by light scattering

Thermotropic mesophases can be detected by the light scattering properties of these phases. This article deals with a rapid scan technique for the detection and characterization of these mesophases by measuring light scattering as a function of temperature. From the number of compounds studied it is apparent that the method allows for a rapid and reasonably precise determination of transition temperatures. In addition, the method is found to be useful in the characterization of mesophases, in particular the nematic phase.