General tooth boundary conditions for equation free modelling

We are developing a framework for multiscale computation which enables models at a ``microscopic'' level of description, for example Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators, to perform modelling tasks at ``macroscopic'' length scales of interest. The plan is to use the microscopic rules restricted to small "patches" of the domain, the "teeth'', using interpolation to bridge the "gaps". Here we explore general boundary conditions coupling the widely separated ``teeth'' of the microscopic simulation that achieve high order accuracy over the macroscale. We present the simplest case when the microscopic simulator is the quintessential example of a partial differential equation. We argue that classic high-order interpolation of the macroscopic field provides the correct forcing in whatever boundary condition is required by the microsimulator. Such interpolation leads to Tooth Boundary Conditions which achieve arbitrarily high-order consistency. The high-order consistency is demonstrated on a class of linear partial differential equations in two ways: firstly through the eigenvalues of the scheme for selected numerical problems; and secondly using the dynamical systems approach of holistic discretisation on a general class of linear \textsc{pde}s. Analytic modelling shows that, for a wide class of microscopic systems, the subgrid fields and the effective macroscopic model are largely independent of the tooth size and the particular tooth boundary conditions. When applied to patches of microscopic simulations these tooth boundary conditions promise efficient macroscale simulation. We expect the same approach will also accurately couple patch simulations in higher spatial dimensions.Comment: 22 page

Mock Catalogs for UHECR Studies

We provide realistic mock-catalogs of cosmic rays above 40 EeV, for a pure proton composition, assuming their sources are a random subset of ordinary galaxies in a simulated, volume-limited survey, for various choices of source density: 10^-3.5 Mpc^-3, 10^-4.0 Mpc^-3 and 10^-4.5 Mpc^-3. The spectrum at the source is taken to be E^-2.3 and the effects of cosmological redshifting as well as photo-pion and e^+ e^- energy losses are included.Comment: 7 pages, 4 figure

Fluctuation-induced interactions between dielectrics in general geometries

We study thermal Casimir and quantum non-retarded Lifshitz interactions between dielectrics in general geometries. We map the calculation of the classical partition function onto a determinant which we discretize and evaluate with the help of Cholesky factorization. The quantum partition function is treated by path integral quantization of a set of interacting dipoles and reduces to a product of determinants. We compare the approximations of pairwise additivity and proximity force with our numerical methods. We propose a ``factorization approximation'' which gives rather good numerical results in the geometries that we study

CLTs and asymptotic variance of time-sampled Markov chains

For a Markov transition kernel P and a probability distribution μ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel Pμ = Σkμ(k)Pk. In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker's and Metropolis algorithms in terms of asymptotic variance

Low-speed flowfield characterization by infrared measurements of surface temperatures

An experimental program was aimed at identifying areas in low speed aerodynamic research where infrared imaging systems can make significant contributions. Implementing a new technique, a long electrically heated wire was placed across a laminar jet. By measuring the temperature distribution along the wire with the IR imaging camera, the flow behavior was identified. Furthermore, using Nusselt number correlations, the velocity distribution could be deduced. The same approach was used to survey wakes behind cylinders in a wind-tunnel. This method is suited to investigate flows with position dependent velocities, e.g., boundary layers, confined flows, jets, wakes, and shear layers. It was found that the IR imaging camera cannot accurately track high gradient temperature fields. A correlation procedure was devised to account for this limitation. Other wind-tunnel experiments included tracking the development of the laminar boundary layer over a warmed flat plate by measuring the chordwise temperature distribution. This technique was applied also to the flow downstream from a rearward facing step. Finally, the IR imaging system was used to study boundary layer behavior over an airfoil at angles of attack from zero up to separation. The results were confirmed with tufts observable both visually and with the IR imaging camera

Time-resolved velocity map imaging of methyl elimination from photoexcited anisole

To date, H-atom elimination from heteroaromatic molecules following UV excitation has been extensively studied, with the focus on key biological molecules such as chromophores of DNA bases and amino acids. Extending these studies to look at elimination of other non-hydride photoproducts is essential in creating a more complete picture of the photochemistry of these biomolecules in the gas-phase. To this effect, CH3 elimination in anisole has been studied using time resolved velocity map imaging (TR-VMI) for the first time, providing both time and energy information on the dynamics following photoexcitation at 200 nm. The extra dimension of energy afforded by these measurements has enabled us to address the role of πσ* states in the excited state dynamics of anisole as compared to the hydride counterpart (phenol), providing strong evidence to suggest that only CH3 fragments eliminated with high kinetic energy are due to direct dissociation involving a 1πσ* state. These measurements also suggest that indirect mechanisms such as statistical unimolecular decay could be contributing to the dynamics at much longer times