Non-symmetric Jacobi and Wilson type polynomials

Consider a root system of type $BC_1$ on the real line $\mathbb R$ with general positive multiplicities. The Cherednik-Opdam transform defines a unitary operator from an $L^2$-space on $\mathbb R$ to a $L^2$-space of $\mathbb C^2$-valued functions on $\mathbb R^+$ with the Harish-Chandra measure |c(\lam)|^{-2}d\lam. By introducing a weight function of the form \cosh^{-\sig}(t)\tanh^{2k} t on $\mathbb R$ we find an orthogonal basis for the $L^2$-space on $\mathbb R$ consisting of even and odd functions expressed in terms of the Jacobi polynomials (for each fixed \sig and $k$). We find a Rodrigues type formula for the functions in terms of the Cherednik operator. We compute explicitly their Cherednik-Opdam transforms. We discover thus a new family of $\mathbb C^2$-valued orthogonal polynomials. In the special case when $k=0$ the even polynomials become Wilson polynomials, and the corresponding result was proved earlier by Koornwinder

BBR-induced Stark shifts and level broadening in helium atom

The precise calculations of blackbody radiation (BBR)-induced Stark shifts and depopulation rates for low-lying states of helium atom with the use of variational approach are presented. An effect of the BBR-induced induced Stark-mixing of energy levels is considered. It is shown that this effect leads to a significant reduction of lifetimes of helium excited states. As a consequence the influence of Stark-mixing effect on the decay rates of metastable states in helium is discussed in context of formation processes of the cosmic microwave background

Implementing real-time reactive systems from object-oriented design specifications

Real-time reactive systems are among the most difficult systems to design and implement because of their size and complex functional and timing requirements. TROMLAB is a framework for a rigorous development of consistent design that satisfy an authoritative specification of requirements, validate the design through simulation, and verify the design for safety properties through a formal verifier. This thesis adds one more significant component to TROMLAB by providing a methodology for automatic generation of code in real-time Java for reactive systems designed in TROMLAB framework. The correctness and efficiency of the implementation are illustrated on the implementation of the design for a generalized rail-road crossing problem, a bench-mark case study in the real-time systems community

3D elastoplastic model for fine-grained gassy soil considering the gas-dependent yield surface shape and stress-dilatancy

Fine-grained sediments containing large discrete gas bubbles are widely distributed in the five continents throughout the world. The presence of gas bubbles could either degrade or enhance the hardening behavior and undrained shear strength (su) of the soil, depending on the initial pore water pressure (uw0) and initial gas volume fraction (ψ0). The existing constitutive models, however, can solely capture either detrimental or beneficial effect owing to the presence of gas. This study presents a new three-dimensional (3D) elastoplastic constitutive model that describes both the damaging and beneficial effects of gas bubbles on the stress–strain behavior of fine-grained gassy soil in a unified manner. This was achieved by incorporating (1) a versatile expression of yield function that simulates a wide range of yield curve shapes in a unified context, and (2) a dilatancy function capturing the distinct stress–dilatancy behavior of fine-grained gassy soil. Given the lack of direct experimental evidence on the shape of the yield curve of fine-grained gassy soil, new experiments were performed. This has led to the identification of three distinct shapes of yield curve—bullet, ellipse, and teardrop—as well as the formulation of the yield function considering the dependency of yield curve shapes on uw0 and ψ0. The new model was shown to reasonably capture both the damaging and beneficial effects of gas on the compression and shear behavior of three types of fine-grained gassy soils with a broad range of uw0 and ψ0 by using a unified set of parameters

Spatiotemporal seismic hazard and risk assessment of M9.0 megathrust earthquake sequences of wood-frame houses in Victoria, British Columbia, Canada

Megathrust earthquake sequences, comprising mainshocks and triggered aftershocks along the subduction interface and in the overriding crust, can impact multiple buildings and infrastructure in a city. The time between the mainshocks and aftershocks usually is too short to retrofit the structures; therefore, moderate‐size aftershocks can cause additional damage. To have a better understanding of the impact of aftershocks on city‐wide seismic risk assessment, a new simulation framework of spatiotemporal seismic hazard and risk assessment of future M9.0 sequences in the Cascadia subduction zone is developed. The simulation framework consists of an epidemic‐type aftershock sequence (ETAS) model, ground‐motion model, and state‐dependent seismic fragility model. The spatiotemporal ETAS model is modified to characterise aftershocks of large and anisotropic M9.0 mainshock ruptures. To account for damage accumulation of wood‐frame houses due to aftershocks in Victoria, British Columbia, Canada, state‐dependent fragility curves are implemented. The new simulation framework can be used for quasi‐real‐time aftershock hazard and risk assessments and city‐wide post‐event risk management.For this work, K.G. received funding from the Canada Research Chair program (950-232015) and the NSERC Discovery Grant (RGPIN-2019-05898), and M.J.W. received funding from the European Union's Horizon 2020 research and innovation program (No 821115, RISE: Real-Time Earthquake Risk Reduction for a Resilient Europe). L.Z. and M.J.W. appreciate the support from the London Mathematical Laboratory (http://lml.org.uk/). M.J.W. was also supported by the Southern California Earthquake Center (No. 10013); SCEC is funded by NSF Cooperative Agreement EAR-1600087 & USGS Cooperative Agreement G17AC00047

Dynamical Effects of Magnetic Opacity in Neutron Star Accretion Columns

We present relativistic, radiation magnetohydrodynamic simulations of supercritical neutron star accretion columns in Cartesian geometry, including temperature-dependent, polarization-averaged Rosseland mean opacities accounting for classical electron scattering in a magnetic field. Just as in our previous pure Thomson scattering simulations, vertical oscillations of the accretion shock and horizontally propagating entropy waves (photon bubbles) are present in all our simulations. However, at high magnetic fields $\gtrsim10^{12}$~G, the magnetic opacities produce significant differences in the overall structure and dynamics of the column. At fixed accretion rate, increasing the magnetic field strength results in a shorter accretion column, despite the fact that the overall opacity within the column is larger. Moreover, the vertical oscillation amplitude of the column is reduced. Increasing the accretion rate at high magnetic fields restores the height of the column. However, a new, slower instability takes place at these field strengths because they are in a regime where the opacity increases with temperature. This instability causes both the average height of the column and the oscillation amplitude to substantially increase on a time scale of $\sim10$~ms. We provide physical explanations for these results, and discuss their implications for the observed properties of these columns, including mixed fan-beam/pencil-beam emission patterns caused by the oscillations.Comment: Accepted for publication in MNRA