Vanishing viscosity limits for the degenerate lake equations with Navier boundary conditions

The paper is concerned with the vanishing viscosity limit of the two-dimensional degenerate viscous lake equations when the Navier slip conditions are prescribed on the impermeable boundary of a simply connected bounded regular domain. When the initial vorticity is in the Lebesgue space $L^q$ with $2<q\le\infty$, we show the degenerate viscous lake equations possess a unique global solution and the solution converges to a corresponding weak solution of the inviscid lake equations. In the special case when the vorticity is in $L^\infty$, an explicit convergence rate is obtained

Analytical studies on transient groundwater flow induced by land reclamation

In many coastal areas, land has been reclaimed by dumping fill materials into the sea. Land reclamation may have a significant effect on groundwater regimes, especially when the reclamation is at large scale. Analytical studies on the impact of land reclamation on steady-state ground water flow conditions were conducted previously, but transient analytical solutions are not yet available. Transient analytical solutions are derived to illustrate the temporal change of groundwater systems in response to land reclamation using two hypothetical models: a hillside aquifer and an oceanic elongated island. The analytical solutions show that when time is short, the water level in the reclaimed area increases significantly after reclamation while that in the original aquifer remains almost unchanged. When time is great, the change of water level in the reclaimed site becomes small but the increase of water level propagates into the original aquifer. For the specific parameters and aquifer geometry used in the examples, it takes at least over 100 years for the whole system to approach a new equilibrium. The island example demonstrates that land reclamation on one side of the island will eventually modify the groundwater regimes over the entire island, including the water level, water divide, and submarine groundwater discharge. The degree of the modification of the groundwater system and the time required for the system to approach a new equilibrium depend mainly on the hydraulic conductivity and storativity of the fill materials and the reclamation length. It is suggested that for a large reclamation project, the response of the groundwater regime to reclamation should be studied in detail to evaluate the long-term change of the flow system and the consequent environmental and engineering impacts. Copyright 2008 by the American Geophysical Union.published_or_final_versio

Markov Chains and Dynamic Geometry of Polygons

In this paper we construct sequences of polygons from a given n-sided cyclic polygon by iterated procedures and study the limiting behaviors of these sequences in terms of non-negative matrices and Markov chains. (C) 2003 Elsevier Science Inc. All rights reserved

Porosity-enhanced solar powered hydrogen generation in GaN photoelectrodes

Two types of GaN based photoelectrodes using either horizontally aligned or vertically aligned nanopores have been fabricated by means of using an electrochemical etching approach. The photoelectrodes based on such nanostructures have demonstrated an up to 5-fold enhancement in applied bias photon-to-current efficiency and incident photon-to-current efficiency in comparison with their planar counterpart, leading to a high Faradaic conversion efficiency which approaches 1. The GaN photoelectrodes with these nanopores also show excellent chemical stability in HBr solution as an electrolyte. The results presented reveal that the gas diffusion in the nanopores plays an important role in water splitting processes, which should be taken into account when designing a GaN photoelectrode with a nanopore structur

Continuous extremal optimization for Lennard-Jones Clusters

In this paper, we explore a general-purpose heuristic algorithm for finding high-quality solutions to continuous optimization problems. The method, called continuous extremal optimization(CEO), can be considered as an extension of extremal optimization(EO) and is consisted of two components, one is with responsibility for global searching and the other is with responsibility for local searching. With only one adjustable parameter, the CEO's performance proves competitive with more elaborate stochastic optimization procedures. We demonstrate it on a well known continuous optimization problem: the Lennerd-Jones clusters optimization problem.Comment: 5 pages and 3 figure

Rotational Symmetry of Classical Orbits, Arbitrary Quantization of Angular Momentum and the Role of Gauge Field in Two-Dimensional Space

We study the quantum-classical correspondence in terms of coherent wave functions of a charged particle in two-dimensional central-scalar-potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level-space of angular momentum being greater or less than $\hbar$ is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily $2\pi$-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The quantum mechanical model of anyon proposed by Wilczek (Phys. Rev. Lette. 48, 1144) becomes a special case of the arbitrary-quantization.Comment: 6 pages, 5 figure

Semi-polar (11-22) AlGaN on overgrown GaN on micro-rod templates: Simultaneous management of crystal quality improvement and cracking issue

© 2017 Author(s).Thick and crack-free semi-polar (11-22) AlGaN layers with various high Al compositions have been achieved by means of growth on the top of nearly but not yet fully coalesced GaN overgrown on micro-rod templates. The range of the Al composition of up to 55.7% was achieved, corresponding to an emission wavelength of up to 270 nm characterised by photoluminescence at room temperature. X-ray diffraction (XRD) measurements show greatly improved crystal quality as a result of lateral overgrowth compared to the AlGaN counterparts on standard planar substrates. The full width at half maximums of the XRD rocking curves measured along the [1-100]/[11-2-3] directions (the two typical orientations for characterizing the crystal quality of (11-22) AlGaN) are 0.2923°/0.2006° for 37.8% Al and 0.3825°/0.2064° for 55.7% Al, respectively, which have never been achieved previously. Our calculation based on reciprocal space mapping measurements has demonstrated significant strain relaxation in the AlGaN as a result of utilising the non-coalesced GaN underneath, contributing to the elimination of any cracks. The results presented have demonstrated that our overgrowth technique can effectively manage strain and improve crystal quality simultaneously

Stimulated emission from semi-polar (11-22) GaN overgrown on sapphire

(11-22) semi-polar GaN is expected to exhibit major advantages compared with current c-plane polar GaN in the fabrication of long wavelength such as green and yellow emitters. However, all the III-nitride based semi-/non- polar laser diodes (LDs) reported so far have been achieved exclusively based on homo-epitaxial growth on extremely expensive free-standing GaN substrates with a very limited size. In this paper, we have observed a stimulated emission at room temperature achieved on our semi-polar (11-22) GaN overgrown on a micro-rod arrayed template with an optimized design on m-plane sapphire. This has never been achieved previously on any semi-polar GaN grown on sapphire. Furthermore, an optical gain of 130cm−1 has been measured by means of performing a standard laser stripe-length dependent optical measurement. The values of the threshold and the optical gain obtained are comparable to those of the c-plane GaN reported so far, further validating the satisfactory crystal quality of our overgrown semi-polar (11-22) GaN on sapphire. This represents a major step towards the development of III-nitride semi-polar based LDs on sapphire, especially in the long wavelength regime

Overgrowth and strain investigation of (11-20) non-polar GaN on patterned templates on sapphire

Non-polar (11–20) GaN with signifcantly improved crystal quality has been achieved by means of overgrowth on regularly arrayed micro-rod templates on sapphire in comparison with standard non-polar GaN grown without any patterning processes on sapphire. Our overgrown GaN shows massively reduced linewidth of X-ray rocking curves with typical values of 270arcsec along the [0001] direction and 380arcsec along the [1–100] direction, which are among the best reports. Detailed X-ray measurements have been performed in order to investigate strain relaxation and in-plane strain distribution. The study has been compared with the standard non-polar GaN grown without any patterning processes and an extra non-polar GaN sample overgrown on a standard stripe-patterned template. The standard non-polar GaN grown without involving any patterning processes typically exhibits highly anisotropic in-plane strain distribution, while the overgrown GaN on our regularly arrayed micro-rod templates shows a highly isotropic in-plane strain distribution. Between them is the overgrown non-polar GaN on the stripe-patterned template. The results presented demonstrate the major advantages of using our regularly arrayed micro-rod templates for the overgrowth of non-polar GaN, leading to both high crystal quality and isotropic in-plane strain distribution, which is important for the further growth of any device structures