Coherent states for a system of an electron moving in a plane: case of discrete spectrum

In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], of an electron moving in a plane in uniform external magnetic and electric fields which possesses both discrete and continuous spectra. The eigenfunctions are realized as an orthonormal basis of a suitable Hilbert space appropriate for building the related coherent states. These latter are achieved in the context where we consider both spectra purely discrete obeying the criteria that a family of coherent states must satisfies.

Comparison of Metallization Schemes on Glass Dielectrics for X-Band Glass Antennas and Energy Harvesting

We prepare and test four types of glass antennas for X-band applications and energy harvesting. These antennas are made of three different glass metallization schemes, including conductive copper foil (CCF), conductive silver paste (CSP) and indium tin oxide (ITO) thin film. Compared with conventional microstrip patch antennas, the dielectric substrate materials of these designs are replaced with silicon-boron glass (εr = 6, tangent δ = 0.002). The antenna with CCF as a radiator and ground plane (case one) is compared with the antenna with ITO replacing the radiator (case two) and ground plane (case three), respectively, and the glass antenna made of CSP (case four) is also presented. In this paper, these four types of glass antennas are measured and analyzed, and a comparison of the fabrication process and performance of these antennas is demonstrated. This study could contribute to the development of human-machine interactivity (HMI) systems with glass dielectric substrates.

Scale sensitivity of the Gill circulation, Part II: Off-equatorial case

We investigate the steady dynamical response of the atmosphere on the equatorial β-plane to a steady, localized, mid-tropospheric heating source. Following Part I which investigates the case of an equatorial diabatic heating, we explore the sensitivity of the Gill circulation to the latitudinal location of the heating, together with the sensitivity to its horizontal scale. Again, we focus on characteristics of the response which would be particularly important if the circulation interacted with the hydrologic and energy cycles: overturning circulation and low-level wind. In the off-equatorial case, the intensity of the overturning circulation has the same limit as in the equatorial case for small horizontal extent of the diabatic heating, which is also the limit in the f-plane case. The decrease in this intensity with increasing horizontal scale of the diabatic heating is slightly faster in the off-equatorial case than in the equatorial case, which is due to the increase of rotational winds at the expense of divergent winds. The low-level westerly jet is more intense than in the equatorial case, with larger maximum wind and eastward mass transport that tend to infinity for small horizontal extent of the diabatic heating. In terms of spatial characteristics, this jet has a similar latitudinal extent as in the equatorial case but, unlike in the equatorial case, it extends further equatorward than poleward of the diabatic-heating center. It also extends further eastward than in the equatorial case.

Numerical investigation and application of 3D multi-phase non-Newtonian rheology model for debris flow

A 3D multiphase debris flow model – DebrisInterMixingFoam was studied. An improvement to include the VOF field updating in the iteration of updating the flow field variables was proposed. The improved model was first validated by a debris flow deposition on slope plane case. Then the model was applied to two benchmark debris flow cases and a real debris flow event. In all cases, the model results were favorably compared with the experimental data or field investigation data. As there were only two key parameters to be calibrated in DebrisInterMixingFoam, it was easy to be used to model debris flow. The numerical results showed that this model can achieve good accuracy for debris flow simulation after calibrations of these two key parameters.

Conceptual model of software to develop acoustic emission diagnostic system

A generalized diagram of an acoustic emission diagnostic system is presented and a set of programs for its design is proposed. The propagation of an acoustic wave simulation is carried out by COMSOL Multiphysics in plane case under various conditions and the coincidence of the results with the COSMOS / M modelling system results is shown.

Higher Order Polars of Quasi-Ordinary Singularities

A quasi-ordinary polynomial is a monic polynomial with coefficients in the power series ring such that its discriminant equals a monomial up to unit. In this paper, we study higher derivatives of quasi-ordinary polynomials, also called higher order polars. We find factorizations of these polars. Our research in this paper goes in two directions. We generalize the results of Casas–Alvero and our previous results on higher order polars in the plane to irreducible quasi-ordinary polynomials. We also generalize the factorization of the first polar of a quasi-ordinary polynomial (not necessarily irreducible) given by the first-named author and González-Pérez to higher order polars. This is a new result even in the plane case. Our results remain true when we replace quasi-ordinary polynomials by quasi-ordinary power series.

Natural Spring Cell Substitutes of Simplex Finite Elements

Spring cell models are presented which derive from the natural description of simplex finite elements, that is in conformity with the geometry of the triangle in the plane and of the tetrahedron in space. Thereby, the spring cells are interpreted as part of the finite elements. The deduction of two spring cells as defective substitutes is demonstrated for the triangular element. One approximates the flexibility matrix of the element, the other approximates the stiffness matrix. The performance with respect to the finite element is analyzed, the issue of elastic anisotropy is discussed. In space, the spring cell substitute of the tetrahedral element is derived from the flexibility matrix, an inherent difference to the plane case is pointed out. Remarks on the implication of plasticity are added. The account gives a brief summary of recent work on the subject.

In-Plane and Out-of Plane Failure of an Ice Sheet using Peridynamics

ABSTRACTWhen dealing with ice structure interaction modeling, such as designs for offshore structures/icebreakers or predicting ice cover’s bearing capacity for transportation, it is essential to determine the most important failure modes of ice. Structural properties, ice material properties, ice-structure interaction processes, and ice sheet geometries have significant effect on failure modes. In this paper two most frequently observed failure modes are studied; splitting failure mode for in-plane failure of finite ice sheet and out-of-plane failure of semi-infinite ice sheet. Peridynamic theory was used to determine the load necessary for inplane failure of a finite ice sheet. Moreover, the relationship between radial crack initiation load and measured out-of-plane failure load for a semi-infinite ice sheet is established. To achieve this, two peridynamic models are developed. First model is a 2 dimensional bond based peridynamic model of a plate with initial crack used for the in-plane case. Second model is based on a Mindlin plate resting on a Winkler elastic foundation formulation for out-of-plane case. Numerical results obtained using peridynamics are compared against experimental results and a good agreement between the two approaches is obtained confirming capability of peridynamics for predicting in-plane and out-of-plane failure of ice sheets.