On the discrete spectrum of quantum layers

Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, $\mathcal C^2$ smooth surface embedded in $\mathbb{R}^3$. We assume that the surface is asymptotically flat in the sense that the second fundamental form vanishes at infinity, and that the surface is not totally geodesic. This geometric setting is known as a quantum layer. We consider the quantum particle to be governed by the Dirichlet Laplacian as Hamiltonian. Our work concerns the existence of bound states with energy beneath the essential spectrum, which implies the existence of discrete spectrum. We first prove that if the Gauss curvature is integrable, and the surface is weakly $\kappa$-parabolic, then the discrete spectrum is non-empty. This result implies that if the total Gauss curvature is non-positive, then the discrete spectrum is non-empty. We next prove that if the Gauss curvature is non-negative, then the discrete spectrum is non-empty. Finally, we prove that if the surface is parabolic, then the discrete spectrum is non-empty if the layer is sufficiently thin.Comment: Clarifications and corrections to previous version, conjecture from previous version is proven here (Theorem 1.5), additional references include

Rule Managed Reporting in Energy Controlled Wireless Sensor Networks

This paper proposes a technique to extend the network lifetime of a wireless sensor network, whereby each sensor node decides its network involvement, based on energy resources and the information in each message (ascertained through a system of rules). Results obtained from the simulation of an industrial monitoring scenario have shown that a considerable increase in the lifetime and connectivity can be obtained

The impact of prior information on estimates of disease transmissibility using Bayesian tools

The basic reproductive number (R₀) and the distribution of the serial interval (SI) are often used to quantify transmission during an infectious disease outbreak. In this paper, we present estimates of R₀ and SI from the 2003 SARS outbreak in Hong Kong and Singapore, and the 2009 pandemic influenza A(H1N1) outbreak in South Africa using methods that expand upon an existing Bayesian framework. This expanded framework allows for the incorporation of additional information, such as contact tracing or household data, through prior distributions. The results for the R₀ and the SI from the influenza outbreak in South Africa were similar regardless of the prior information (R0 = 1.36-1.46, μ = 2.0-2.7, μ = mean of the SI). The estimates of R₀ and μ for the SARS outbreak ranged from 2.0-4.4 and 7.4-11.3, respectively, and were shown to vary depending on the use of contact tracing data. The impact of the contact tracing data was likely due to the small number of SARS cases relative to the size of the contact tracing sample

Quantum Layers over Surfaces Ruled Outside a Compact Set

In this paper, we proved the quantum layer over a surface which is ruled outside a compact set, asymptotically flat but not totally geodesic admits ground states

Wind tunnel studies of Martian aeolian processes

Preliminary results are reported of an investigation which involves wind tunnel simulations, geologic field studies, theoretical model studies, and analyses of Mariner 9 imagery. Threshold speed experiments were conducted for particles ranging in specific gravity from 1.3 to 11.35 and diameter from 10.2 micron to 1290 micron to verify and better define Bagnold's (1941) expressions for grain movement, particularly for low particle Reynolds numbers and to study the effects of aerodynamic lift and surface roughness. Wind tunnel simulations were conducted to determine the flow field over raised rim craters and associated zones of deposition and erosion. A horseshoe vortex forms around the crater, resulting in two axial velocity maxima in the lee of the crater which cause a zone of preferential erosion in the wake of the crater. Reverse flow direction occurs on the floor of the crater. The result is a distinct pattern of erosion and deposition which is similar to some martian craters and which indicates that some dark zones around Martian craters are erosional and some light zones are depositional

Metallic Triple Beam Resonator with Thick-film Printed Drive and Pickup

A triple beam resonator fabricated in 430S17 stainless steel with thick-film piezoelectric elements to drive and detect the vibrations is presented. The resonator substrate was fabricated by a simultaneous, double-sided photochemical etching technique and the thick-film piezoelectric elements were deposited by a standard screen-printing process. The combination of these two batch-fabrication processes provides the opportunity for mass production of the device at low cost. The resonator, a dynamically balanced triple beam tuning fork (TBTF) structure 23.5 mm long and 6.5 mm wide, has a favoured mode at 4.96 kHz with a Q-factor of 3630 operating in air

Dust storms on Mars: Considerations and simulations

Aeolian processes are important in modifying the surface of Mars at present, and appear to have been significant in the geological past. Aeolian activity includes local and global dust storms, the formation of erosional features such as yardangs and depositional features such as sand dunes, and the erosion of rock and soil. As a means of understanding aeolian processes on Mars, an investigation is in progress that includes laboratory simulations, field studies of earth analogs, and interpretation of spacecraft data. This report describes the Martian Surface Wind Tunnel, an experimental facility established at NASA-Ames Research Center, and presents some results of the general investigation. Experiments dealing with wind speeds and other conditions required for the initiation of particle movement on Mars are described and considerations are given to the resulting effectiveness of aeolian erosion

CO and CI maps of the starburst galaxy M82

The first map of an external galaxy in the 3P₁ - 3P0 fine-structure line of atomic carbon (CI) is presented towards the nucleus of the starbuster M82, and compared with the distinction of the CO J = 4 - 3 molecular emission. The CI traces features that are seen in lower transition CO maps, and shows that CI and the CO are well mixed and have similar spatial distributions. There are small differences between the CO J = 4 - 3 line and lower transition CO data towards the NE part of the molecular ring, where the emission is less prominent. The abundance ratio [CI]/[CO] across M82 is very high, with an average value ~ 0.5 across most of the nucleus, a factor at least 5 times that which is typical of dense molecular cloud cores seen in our own Galaxy. This means that on average, CI is overabundant towards M82. This result can be explained using models which provide enhancements to the CI abundance above normal Interstellar Medium values, a result of a greater cosmic ray flux in M82, or where there is substantial mixing of the gas

Aeolian processes aboard a space station: Saltation and particle trajectory analysis

The Carousel wind tunnel (CWT) proposed to study aeolian processes aboard a space station consists of two concentric rotating drums. The space between the two drums comprises the wind tunnel test section. Differential rates of rotation of the two drums would provide a wind velocity with respect to either drum surface. Preliminary results of measured velocity profiles made in a CWT prototype indicate that the wall bounded boundary layer profiles are suitable to simulate flat plate turbulent boundary layer flow. The two dimensional flat plate Cartesian coordinate equations of motion of a particle moving through the air are explained. In order to assess the suitability of CWT in the analysis of the trajectories of windblown particles, a series of calculations were conducted comparing cases for gravity with those of zero gravity. Results from the calculations demonstrate that a wind tunnel of the carousel design could be fabricted to operate in a space station environment and that experiments could be conducted which would yield significant results contributing to the understanding of the physics of particle dynamics