Position Estimating in Peer-to-Peer Networks

We present two algorithms for indoor positioning estimation in peer-to-peer networks. The setup is a network of two types of devices: reference devices with a known location and blindfolded devices that can determine distances to reference devices and each other. From this information the blindfolded devices try to estimate their positions. A typical scenario is navigation inside a shopping mall where devices in the parking lot can make contact with GPS satellites, whereas devices inside the building make contact with each other, devices on the parking lot, and devices fixed to the building. The devices can measure their in-between distances, with some measurement error, and exchange positioning information. However, other devices might only know their position with some error

Acoustic liner - mean flow interaction

Since the introduction in the 1950’s of the jet engine in civil aviation, its noise has been a stringent problem. National laws and international regulations forbid selling noisy aircraft and limit the total yearly noise load of airports, this noise load depending on both the number of flight motions (starts and landings), and the noise emitted per aircraft. Since the number of flight motions increases in direct proportion to economic growth, the noise per aircraft has to decrease in compensation. As a result, year by year a world wide effort in aeroacoustic research remains necessary. From elementary dimensional arguments, scaling is hardly possible, while full scale experiments are very expensive, thus making almost any mathematical model cheaper and better. We study in this thesis aspects of parts of the mathematical model used in duct acoustics, and focus on the interaction of acoustic liners with the mean flow, discussing reliability and accuracy in this context. A more than 50 years old modeling problem was the correctness of a vanishing boundary layer along an acoustic liner. Arguing classically, the acoustic effects of a boundary layer that is much thinner than any characteristic wave length is the same as of a vanishing boundary layer. So for a numerically e??cient and thrifty model without unnecessary parameters, it is reasonable to apply this limit yielding the so-called Ingard-Myers condition. This works well in frequency domain. Our research showed that in time domain, on the other hand, a boundary layer less than a certain (very small, but non-zero) thickness is absolutely unstable. This makes the model useless for any industrially relevant configuration. We propose here a corrected version of the limit that retains the stability properties of the finite boundary layer. In addition to this, we give an estimate for the critical boundary layer thickness, beyond which the flow is absolutely unstable. The last part of the thesis discusses the critical layer singularity arising in the mathematical model due to the inviscid assumption. Common treatment is to by-pass its contribution assuming it is negligible, without fully understanding its subtleties. We study this problem for linear-shear boundary layers over acoustic linings. We show that if the source is located in the boundary layer, neglecting the critical layer means neglecting also the trailing vorticity produced by source, which introduces significant errors. Moreover, extra care is needed for high frequencies, due to an existing leaking mode

A benzene interference single-electron transistor

Interference effects strongly affect the transport characteristics of a benzene single-electron transistor (SET) and for this reason we call it interference SET (I-SET). We focus on the effects of degeneracies between many-body states of the isolated benzene. We show that the particular current blocking and selective conductance suppression occurring in the benzene I-SET are due to interference effects between the orbitally degenerate states. Further we study the impact of reduced symmetry due to anchor groups or potential drop over the molecule. We identify in the quasi-degeneracy of the involved molecular states the necessary condition for the robustness of the results.Comment: 17pages, 9 figures, revised versio

Position estimating in peer-to-peer networks

We present two algorithms for indoor positioning estimation in peer-to-peer networks. The setup is a network of two types of devices: reference devices with a known location and blindfolded devices that can determine distances to reference devices and each other. From this information the blindfolded devices try to estimate their positions. A typical scenario is navigation inside a shopping mall where devices in the parking lot can make contact with GPS satellites, whereas devices inside the building make contact with each other, devices on the parking lot, and devices fixed to the building. The devices can measure their in-between distances, with some measurement error, and exchange positioning information. However, other devices might only know their position with some error. We present two algorithms for positioning estimation in such a peer-to-peer network. The first one is purely geometric and is based on Euclidean geometry and intersecting spheres. We rewrite the information to a linear system, which is typically overdetermined. We use least squares to ??nd the best estimate for a device its position. The second approach can be considered as a probabilistic version of the geometric approach. We estimate the probability density function that a device is located at a position given a probability density function for the positions of the other devices in the network, and a probability density function of the measured distances. First we study the case with a distance measurement to a single other user, then we focus on multiple other users. We give an approximation algorithm that is the probabilistic analogue of the intersecting spheres method. We show some simulated results where ambiguous data lead to well defined probability distributions for the position of a device. We conclude with some open questions

All-electric-spin control in interference single electron transistors

Single particle interference lies at the heart of quantum mechanics. The archetypal double-slit experiment has been repeated with electrons in vacuum up to the more massive $C_{60}$ molecules. Mesoscopic rings threaded by a magnetic flux provide the solid-state analogous. Intra-molecular interference has been recently discussed in molecular junctions. Here we propose to exploit interference to achieve all-electrical control of a single electron spin in quantum dots, a highly desirable property for spintronics and spin-qubit applications. The device consists of an interference single electron transistor (ISET), where destructive interference between orbitally degenerate electronic states produces current blocking at specific bias voltages. We show that in the presence of parallel polarized ferromagnetic leads the interplay between interference and the exchange coupling on the system generates an effective energy renormalization yielding different blocking biases for majority and minority spins. Hence, by tuning the bias voltage full control over the spin of the trapped electron is achieved.Comment: 9 pages, 5 figure

Mean flow boundary layer effects of hydrodynamic instability of impedance wall

The Ingard-Myers condition, modelling the effect of an impedance wall under a mean flow by assuming a vanishing boundary layer, is known to lead to an ill-posed problem in time-domain. By analysing the stability of a mean flow, uniform except for a linear boundary layer of thickness h, in the incompressible limit, we show that the flow is absolutely unstable for h smaller than a critical hc and convectively unstable or stable otherwise. This critical hc is by nature independent of wave length or frequency and is a property of liner and mean flow only. An analytical approximation of hc is given for a mass-spring-damper liner. For an aeronautically relevant example, hc is shown to be extremely small, which explains why this instability has never been observed in industrial practice. A systematically regularised boundary condition, to replace the Ingard-Myers condition, is proposed that retains the effects of a finite h, such that the stability of the approximate problem correctly follows the stability of the real problem

Reprint of: Mean flow boundary layer effects of hydrodynamic instability of impedance wall

The Ingard-Myers condition, modelling the effect of an impedance wall under a mean flow by assuming a vanishing boundary layer, is known to lead to an ill-posed problem in time-domain. By analysing the stability of a mean flow, uniform except for a linear boundary layer of thickness h, in the incompressible limit, we show that the flow is absolutely unstable for h smaller than a critical hc and convectively unstable or stable otherwise. This critical hc is by nature independent of wave length or frequency and is a property of liner and mean flow only. An analytical approximation of hc is given for a mass-spring-damper liner. For an aeronautically relevant example, hc is shown to be extremely small, which explains why this instability has never been observed in industrial practice. A systematically regularised boundary condition, to replace the Ingard-Myers condition, is proposed that retains the effects of a finite h, such that the stability of the approximate problem correctly follows the stability of the real problem

The critical layer in linear-shear boundary layers over acoustic linings

Acoustics within mean flows are governed by the linearized Euler equations, which possess a singularity wherever the local mean flow velocity is equal to the phase speed of the disturbance. Such locations are termed critical layers, and are usually ignored when estimating the sound field, with their contribution assumed to be negligible. This paper studies fully both numerically and analytically a simple yet typical sheared ducted flow in order to investigate the influence of the critical layer, and shows that the neglect of critical layers is sometimes, but certainly not always, justified. The model is that of a linear-then-constant velocity profile with uniform density in a cylindrical duct, allowing exact Green’s function solutions in terms of Bessel functions and Frobenius expansions. For sources outside the sheared flow, the contribution of the critical layer is found to decay algebraically along the duct as O(1/x^4), where x is the distance downstream of the source. For sources within the sheared ¿ow, the contribution from the critical layer is found to consist of a nonmodal disturbance of constant amplitude representing the hydrodynamic trailing vorticity of the source, and a disturbance decaying algebraically as O(1/x^5). For thin boundary layers, these disturbances trigger the inherent convective instability of the flow. Extra care is required for high frequencies as the critical layer can be neglected only in combination with a particular downstream pole. The advantages of Frobenius expansions over direct numerical calculation are also demonstrated, especially with regard to spurious modes around the critical layer

Boundary layer thickness effects of the hydrodynamic instability along an impedance wall

Abstract: The Ingard-Myers condition, modelling the effect of an impedance wall under a mean fl ow by assuming a vanishingly thin boundary layer, is known to lead to an ill-posed problem in time-domain. By analysing the stability of a linear-then-constant mean flow over a mass-spring-damper liner in a 2D incompressible limit, we show that the fl ow is absolutely unstable for h smaller than a critical hc and convectively unstable or stable otherwise. This critical hc is by nature independent of wave length or frequency and is a property of liner and mean flow only. An analytical approximation of hc is given, which is complemented by a contourplot covering all parameter values. For an aeronautically relevant example, hc is shown to be extremely small, which explains why this instability has never been observed in industrial practice. A systematically regularised boundary condition, to replace the Ingard-Myers condition, is proposed that retains the effects of a finite h, such that the stability of the approximate problem correctly follows the stability of the real problem. Keywords: Aeroacoustics, Boundary layer stability, Impedance wall

The trailing vorticity field behind a line source in two-dimensional incompressible linear shear flow

The explicit exact analytic solution for harmonic perturbations from a line mass source in an incompressible inviscid two-dimensional linear shear is derived using a Fourier transform method. The two cases of an infinite shear flow and a semi-infinite shear flow over an impedance boundary are considered. For the free-field and hard-wall configurations, the pressure field is (in general) logarithmically diverging and its Fourier representation involves a diverging integral that is interpreted as an integral of generalized functions; this divergent behaviour is not present for a finite impedance boundary or if the frequency equals the mean flow shear rate. The dominant feature of the solution is the hydrodynamic wake caused by the shed vorticity of the source. For linear shear over an impedance boundary, in addition to the wake, (at most) two surface modes along the wall are excited. The implications for duct acoustics with flow over an impedance wall are discussed. Keywords: aeroacoustics, general fluid mechanics, vortex sheddin