Existence and conditional energetic stability of solitary gravity-capillary water waves with constant vorticity

We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove the existence of a minimiser of the wave energy $\mathcal H$ subject to the constraint $\mathcal I=2\mu$, where $\mathcal I$ is the wave momentum and $0< \mu \ll 1$. Since $\mathcal H$ and $\mathcal I$ are both conserved quantities a standard argument asserts the stability of the set $D_\mu$ of minimisers: solutions starting near $D_\mu$ remain close to $D_\mu$ in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are described by solutions of a Korteweg-deVries equation (for strong surface tension) or a nonlinear Schr\"{o}dinger equation (for weak surface tension). We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of the appropriate model equation as $\mu \downarrow 0$Comment: Corrected version. To appear in Proceedings of the Royal Society of Edinburgh: Section

Periodic solitons for the elliptic-elliptic focussing Davey-Stewartson equations

We consider the elliptic-elliptic, focussing Davey-Stewartson equations, which have an explicit bright line soliton solution. The existence of a family of periodic solitons, which have the profile of the line soliton in the longitudinal spatial direction and are periodic in the transverse spatial direction, is established using dynamical systems arguments. We also show that the line soliton is linearly unstable with respect to perturbations in the transverse direction.Comment: arXiv admin note: text overlap with arXiv:1411.247

A dimension-breaking phenomenon for water waves with weak surface tension

It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence theory for three-dimensional periodically modulated solitary-wave solutions which have a solitary-wave profile in the direction of propagation and are periodic in the transverse direction; they emanate from the line solitary waves in a dimension-breaking bifurcation. In addition, it is shown that the line solitary waves are linearly unstable to long-wavelength transverse perturbations. The key to these results is a formulation of the water wave problem as an evolutionary system in which the transverse horizontal variable plays the role of time, a careful study of the purely imaginary spectrum of the operator obtained by linearising the evolutionary system at a line solitary wave, and an application of an infinite-dimensional version of the classical Lyapunov centre theorem.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0941-

Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

GNSS signals can be blocked and reflected by nearby objects, such as buildings, walls, and vehicles. They can also be reflected by the ground and by water. These effects are the dominant source of GNSS positioning errors in dense urban environments, though they can have an impact almost anywhere. Non- line-of-sight (NLOS) reception occurs when the direct path from the transmitter to the receiver is blocked and signals are received only via a reflected path. Multipath interference occurs, as the name suggests, when a signal is received via multiple paths. This can be via the direct path and one or more reflected paths, or it can be via multiple reflected paths. As their error characteristics are different, NLOS and multipath interference typically require different mitigation techniques, though some techniques are applicable to both. Antenna design and advanced receiver signal processing techniques can substantially reduce multipath errors. Unless an antenna array is used, NLOS reception has to be detected using the receiver's ranging and carrier-power-to-noise-density ratio (C/N0) measurements and mitigated within the positioning algorithm. Some NLOS mitigation techniques can also be used to combat severe multipath interference. Multipath interference, but not NLOS reception, can also be mitigated by comparing or combining code and carrier measurements, comparing ranging and C/N0 measurements from signals on different frequencies, and analyzing the time evolution of the ranging and C/N0 measurements

Environmental Context Detection for Adaptive Navigation using GNSS Measurements from a Smartphone

The signals available for navigation depend on the environment. To operate reliably in a wide range of different environments, a navigation system is required to adopt different techniques based on the environmental contexts. In this paper, an environmental context detection framework is proposed, building the foundation of a context adaptive navigation system. Different land environments are categorized into indoor, urban, and open-sky environments based on how Global Navigation Satellite System (GNSS) positioning performs in these environments. Indoor and outdoor environments are first detected based on the availability and strength of GNSS signals using a hidden Markov model. Then the further classification of outdoor environments into urban and open-sky is investigated. Pseudorange residuals are extracted from raw GNSS measurements in a smartphone and used for classification in a fuzzy inference system alongside the signal strength data. Practical test results under different kinds of environments demonstrate an overall 88.2 percent detection accuracy

Word Adjacency Graph Modeling: Separating Signal From Noise in Big Data

There is a need to develop methods to analyze Big Data to inform patient-centered interventions for better health outcomes. The purpose of this study was to develop and test a method to explore Big Data to describe salient health concerns of people with epilepsy. Specifically, we used Word Adjacency Graph modeling to explore a data set containing 1.9 billion anonymous text queries submitted to the ChaCha question and answer service to (a) detect clusters of epilepsy-related topics, and (b) visualize the range of epilepsy-related topics and their mutual proximity to uncover the breadth and depth of particular topics and groups of users. Applied to a large, complex data set, this method successfully identified clusters of epilepsy-related topics while allowing for separation of potentially non-relevant topics. The method can be used to identify patient-driven research questions from large social media data sets and results can inform the development of patient-centered interventions

Toward a unified PNT, Part 1: Complexity and context: Key challenges of multisensor positioning

The next generation of navigation and positioning systems must provide greater accuracy and reliability in a range of challenging environments to meet the needs of a variety of mission-critical applications. No single navigation technology is robust enough to meet these requirements on its own, so a multisensor solution is required. Known environmental features, such as signs, buildings, terrain height variation, and magnetic anomalies, may or may not be available for positioning. The system could be stationary, carried by a pedestrian, or on any type of land, sea, or air vehicle. Furthermore, for many applications, the environment and host behavior are subject to change. A multi-sensor solution is thus required. The expert knowledge problem is compounded by the fact that different modules in an integrated navigation system are often supplied by different organizations, who may be reluctant to share necessary design information if this is considered to be intellectual property that must be protected

An In vitro Simulation Method for the Tribological Assessment of Complete Natural Hip Joints

The use of hip joint simulators to evaluate the tribological performance of total hip replacements is widely reported in the literature, however, in vitro simulation studies investigating the tribology of the natural hip joint are limited with heterogeneous methodologies reported. An in vitro simulation system for the complete natural hip joint, enabling the acetabulum and femoral head to be positioned with different orientations whilst maintaining the correct joint centre of rotation, was successfully developed for this study. The efficacy of the simulation system was assessed by testing complete, matched natural porcine hip joints and porcine hip hemiarthroplasty joints in a pendulum friction simulator. The results showed evidence of biphasic lubrication, with a non-linear increase in friction being observed in both groups. Lower overall mean friction factor values in the complete natural joint group that increased at a lower rate over time, suggest that the exudation of fluid and transition to solid phase lubrication occurred more slowly in the complete natural hip joint compared to the hip hemiarthroplasty joint. It is envisaged that this methodology will be used to investigate morphological risk factors for developing hip osteoarthritis, as well as the effectiveness of early interventional treatments for degenerative hip disease

A physically-based model of the ionizing radiation from active galaxies for photoionization modeling

We present a simplified model of Active Galactic Nucleus (AGN) continuum emission designed for photoionization modeling. The new model {\sc oxaf} reproduces the diversity of spectral shapes that arise in physically-based models. We identify and explain degeneracies in the effects of AGN parameters on model spectral shapes, with a focus on the complete degeneracy between the black hole mass and AGN luminosity. Our re-parametrized model {\sc oxaf} removes these degeneracies and accepts three parameters which directly describe the output spectral shape: the energy of the peak of the accretion disk emission $E_\mathrm{peak}$, the photon power-law index of the non-thermal emission $\Gamma$, and the proportion of the total flux which is emitted in the non-thermal component $p_\mathrm{NT}$. The parameter $E_\mathrm{peak}$ is presented as a function of the black hole mass, AGN luminosity, and `coronal radius' of the {\sc optxagnf} model upon which {\sc oxaf} is based. We show that the soft X-ray excess does not significantly affect photoionization modeling predictions of strong emission lines in Seyfert narrow-line regions. Despite its simplicity, {\sc oxaf} accounts for opacity effects where the accretion disk is ionized because it inherits the `color correction' of {\sc optxagnf}. We use a grid of {\sc mappings} photoionization models with {\sc oxaf} ionizing spectra to demonstrate how predicted emission-line ratios on standard optical diagnostic diagrams are sensitive to each of the three {\sc oxaf} parameters. The {\sc oxaf} code is publicly available in the Astrophysics Source Code Library.Comment: 14 pages, 9 figures, 1 table. Accepted for publication in Ap

Toward a unified PNT, Part 2: Ambiguity and environmental data: Two further key challenges of multisensor positioning

The coming requirements of greater accuracy and reliability in a range of challenging environments for a multitude of missioncritical applications require a multisensor approach and an over-arching methodology that does not yet exist. The likelihood depends on both the positioning method and the context, both environmental and behavioral. Urban and indoor positioning techniques that do not require dedicated infrastructure are particularly vulnerable to ambiguity. Even where a signal of opportunity is identifiable, the transmission site may change without warning. For example, Wi-Fi access points are sometimes moved and mobile phone networks are periodically refigured. Thus, there is a risk of false landmark identification. The pattern-matching positioning method maintains a database of measurable parameters that vary with position. Examples include terrain height, magnetic field variations, Wi-Fi signal strengths, and GNSS signal availability information