Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations

Collocation is based on the discretization of the strong form of the underlying partial differential equations, which requires basis functions of sufficient order and smoothness. Consequently, the use of isogeometric analysis (IGA) for collocation suggests itself, since splines can be readily adjusted to any order in polynomial degree and continuity required by the differential operators. In addition, they can be generated for domains of arbitrary geometric and topological complexity, directly linked to and fully supported by CAD technology. The major advantage of isogeometric collocation over Galerkin type IGA is the minimization of the computational effort for numerical quadrature. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An MPI parallel level-set algorithm for propagating front curvature dependent detonation shock fronts in complex geometries

We present a parallel, two-dimensional, grid-based algorithm for solving a level-set function PDE that arises in Detonation Shock Dynamics (DSD). In the DSD limit, the detonation shock propagates at a speed that is a function of the curvature of the shock surface, subject to a set of boundary conditions applied along the boundaries of the detonating explosive. Our method solves for the full level-set function field, φ(x, y, t), that locates the detonation shock with a modified level-set function PDE that continuously renormalises the level-set function to a distance function based off of the locus of the shock surface, φ(x, y, t)=0. The boundary conditions are applied with ghost nodes that are sorted according to their connectivity to the interior explosive nodes. This allows the boundary conditions to be applied via a local, direct evaluation procedure. We give an extension of this boundary condition application method to three dimensions. Our parallel algorithm is based on a domain-decomposition model which uses the Message-Passing Interface (MPI) paradigm. The computational order of the full level-set algorithm, which is O(N ⁴), where N is the number of grid points along a coordinate line, makes an MPI-based algorithm an attractive alternative. This parallel model partitions the overall explosive domain into smaller sub-domains which in turn get mapped onto processors that are topologically arranged into a two-dimensional rectangular grid. A comparison of our numerical solution with an exact solution to the problem of a detonation rate stick shows that our numerical solution converges at better than first-order accuracy as measured by an L1-norm. This represents an improvement over the convergence properties of narrow-band level-set function solvers, whose convergence is limited to a floor set by the width of the narrow band. The efficiency of the narrow-band method is recovered by using our parallel model.     

Third-order statistics and the dynamics of strongly anisotropic turbulent flows

Anisotropy is induced by body forces and/or mean large-scale gradients in turbulent flows. For flows without energy production, the dynamics of second-order velocity or second-order vorticity statistics are essentially governed by triple correlations, which are at the origin of the anisotropy that penetrates towards the inertial range, deeply altering the cascade and the eventual dissipation process, with a series of consequences on the evolution of homogeneous turbulence statistics: in the case of rotating turbulence, the anisotropic spectral transfer slaves the multiscale anisotropic energy distribution; nonlinear dynamics are responsible for the linear growth in terms of Ωt of axial integral length-scales; third-order structure functions, derived from velocity triple correlations, exhibit a significant departure from the 4/5 Kolmogorov law. We describe all these implications in detail, starting from the dynamical equations of velocity statistics in Fourier space, which yield third-order correlations at three points (triads) and allow the explicit removal of pressure fluctuations. We first extend the formalism to anisotropic rotating turbulence with ‘production’, in the presence of mean velocity gradients in the rotating frame. Second, we compare the spectral approach at three points to the two-point approach directly performed in physical space, in which we consider the transport of the scalar second-order structure function ?(δq)²?. This calls into play componental third-order correlations ?(δq)²δu?(r) in axisymmetric turbulence. This permits to discuss inhomogeneous anisotropic effects from spatial decay, shear, or production, as in the central region of a rotating round jet. We show that the above-mentioned important statistical quantities can be estimated from experimental planar particle image velocimetry, and that explicit passage relations systematically exist between one- and two-point statistics in physical and spectral space for second-order tensors, but also sometimes for third-order tensors that are involved in the dynamics.     

New results from the T2K neutrino oscillation experiment

The T2K experiment searches for the appearance of electron neutrinos in a muon neutrino beam. The rate of this process is sensitive to the neutrino mixing parameter θ ₁₃. Recent measurements that $\theta_{13} \ne 0$ imply that ν _μ → ν _e oscillations should be observable. Using all data through May 15, 2012 the T2K experiment has detected 10 candidate ν _e events, with an expected background for θ ₁₃?=?0 of 2.73±0.37 events. This 3.2σ excess of ν _e events is the strongest indication to date for appearance of electron neutrinos in a neutrino oscillation experiment, and for normal mass hierarchy and δ _CP ?=?0 yields $0.059 < \sin^2 2\theta_{13} < 0.164$ at the 68 % C.L.     

Direct Form I Realization of Active Photonic Filters

Abstract

An integrated photonic architecture is introduced and used to realize an optical filter with direct form I realization. The architecture offers gain from semiconductor optical amplifiers, and this gain results in an active optical filter whose filter response depends on the individual gains. The presence of gain provides advantages in filter performance, and tunable and adaptive functionality. The optical filter is modeled as a discrete time system and the z-transform is used in its analysis and design. A low-pass filter design example is presented and the filter coefficients are derived in terms of gains and coupler splitting ratios. The region of stable operations is derived by applying the Schur-Cohn stability test.     

Evaluation of critical exponents from raman intensities

Theory and experiment are compared for Raman intensities near continuous structural phase transitions. Situations in which the order parameter couples linearly to light or quadratically are considered. Both cases are easily analyzed for the soft modes in ferroelastic LnP₅O₁₄ (Ln = La, Pr, Nd, Tb). The trace polarizability tensor yields β = 0.49 ± 0.02; off-diagonal terms give γ’ = 1.16 ± 0.15 and γ = 1.07 ± 0.10. Mean field results are also obtained for barium sodium niobate near T (incommensurate) = 582 K and for tris-sarcosine calcium chloride near T _c = 128 K.     

Hysteresis behavior in Raman intensities in YBa2Cu3O7-y -family superconductors between T c and T o = 234 K

The intensity of the 646 cm^-1 Raman line in YBa₂Cu_3-x V _x O_7-y has been measured for cooling and heating from 77 K to 234 K. The intensity exhibits intensity hysteresis of order 20% in the cooling versus heating values between T _c = 89 K and T _o = 234 K. This effect is unexplained but is extremely similar to that reported by Ledbetter et al. for the bulk modulus and C ₁₁ elastic coefficient. In each case the hysteresis vanishes below T _c , independent of the value of T _c , which may be adjusted from 60 K to 94 K by changing oxygen concentration y. Qualitative interpretation requires that the structural phase transition near 234 K be intimately related to the superconducting transition at T _c presumably through partial ordering of oxygens.     

Using the Viable System Model (VSM) to structure information processing complexity in disaster response

Earthquakes, hurricanes, flooding and terrorist attacks continue to threaten our society and, when the worst happens, lives depend on different agencies to manage the response. The literature shows that there is significant potential for operational research (OR) to aid disaster management and that, whilst some of this potential has been delivered, there is more that OR can contribute. In particular, OR can provide detailed support to analysing the complexity of information processing – an essential topic as failure could cause response agencies to act on low quality information or act too slowly – putting responders and victims at risk. However, there is a gap in methods for analysing information processing whilst delivering rapid response. This paper explores how OR can fill this gap through taking a Viable System Model (VSM) approach to analyse information processing. It contributes to the OR literature by showing how VSM can support the analysis of information processing as well as how the OR modelling technique can be further strengthened to facilitate the task.     

Representations of Parabolic and Borel Subgroups

We demonstrate a relationships between the representation theory of Borel subgroups and parabolic subgroups of general linear groups. In particular, we show that the representations of Borel subgroups could be computed from representations of certain maximal parabolic subgroups.