Angle-Displacement Rigidity Theory with Application to Distributed Network Localization

This paper investigates the localization problem of a network in 2-D and 3-D spaces given the positions of anchor nodes in a global frame and inter-node relative measurements in local coordinate frames. It is assumed that the local frames of different nodes have different unknown orientations. First, an angle-displacement rigidity theory is developed, which can be used to localize all the free nodes by the known positions of the anchor nodes and local relative measurements (local relative position, distance, local relative bearing, angle, or ratio-of-distance measurements). Then, necessary and sufficient conditions for network localizability are given. Finally, a distributed network localization protocol is proposed, which can globally estimate the locations of all the free nodes of a network if the network is infinitesimally angle-displacement rigid. The proposed method unifies local-relative-position-based, distance-based, local-relative-bearing-based, angle-based, and ratio-of-distance-based distributed network localization approaches. The novelty of this work is that the proposed method can be applied in both generic and non-generic configurations with an unknown global coordinate frame in both 2-D and 3-D spaces

Stable Camera Motion Estimation Using Convex Programming

We study the inverse problem of estimating n locations $t_1, ..., t_n$ (up to global scale, translation and negation) in $R^d$ from noisy measurements of a subset of the (unsigned) pairwise lines that connect them, that is, from noisy measurements of $\pm (t_i - t_j)/\|t_i - t_j\|$ for some pairs (i,j) (where the signs are unknown). This problem is at the core of the structure from motion (SfM) problem in computer vision, where the $t_i$'s represent camera locations in $R^3$. The noiseless version of the problem, with exact line measurements, has been considered previously under the general title of parallel rigidity theory, mainly in order to characterize the conditions for unique realization of locations. For noisy pairwise line measurements, current methods tend to produce spurious solutions that are clustered around a few locations. This sensitivity of the location estimates is a well-known problem in SfM, especially for large, irregular collections of images. In this paper we introduce a semidefinite programming (SDP) formulation, specially tailored to overcome the clustering phenomenon. We further identify the implications of parallel rigidity theory for the location estimation problem to be well-posed, and prove exact (in the noiseless case) and stable location recovery results. We also formulate an alternating direction method to solve the resulting semidefinite program, and provide a distributed version of our formulation for large numbers of locations. Specifically for the camera location estimation problem, we formulate a pairwise line estimation method based on robust camera orientation and subspace estimation. Lastly, we demonstrate the utility of our algorithm through experiments on real images.Comment: 40 pages, 12 figures, 6 tables; notation and some unclear parts updated, some typos correcte

Potential effects of pneumatic fracturing on existing structures and utilities

This thesis develops a mathematical design model for predicting ground deformations resulting from pneumatic fracturing. Pneumatic fracturing is a patented process developed for the purpose of enhancing the in situ treatment and removal of hazardous contaminants from geologic formations. During pneumatic injections, measurable ground deformations are experienced both during and after the process. Safe application of pneumatic fracturing to contaminated plumes occurring beneath existing structures and utilities requires that the elastic deformation behavior of the geologic formation and overlying structures be quantified. Data from five pneumatic fracturing sites were regressed to establish the characteristic polynomial describing the curvature of ground deformation. A model was then developed using theories of elastic plate bending and ground deformations by igneous laccolith intrusions. The deformed geologic formation is modeled as a circular plate subjected to a linear tapering pressure distribution. Comparison of the model results with actual field data displayed reasonable agreement. An instrumented field test was performed beneath an actual contaminated industrial facility to obtain data on the dynamic response of the structure. Based on the field test results, as well as experience from over 40 additional pneumatic fracturing sites, a systematic design guideline was developed. The guideline classifies structures as either flexible or rigid, and then categorizes them into one of three characteristic design cases

Self-assembly mechanism of pH-responsive glycolipids : micelles, fibers, vesicles, and bilayers

A set of four structurally related glycolipids are described: two of them have one glucose unit connected to either stearic or oleic acid, and two other ones have a diglucose headgroup (sophorose) similarly connected to either stearic or oleic acid. The self-assembly properties of these compounds, poorly known, are important to know due to their use in various fields of application from cleaning to cosmetics to medical. At basic pH, they all form mainly small micellar aggregates. At acidic pH, the oleic and stearic derivatives of the monoglucose form, respectively, vesicles and bilayer, while the same derivatives of the sophorose headgroup form micelles and twisted ribbons. We use pH-resolved in situ small angle X-ray scattering (SAXS) under synchrotron radiation to characterize the pH-dependent mechanism of evolution from micelles to the more complex aggregates at acidic pH. By pointing out the importance of the COO-/COOH ratio, the melting temperature, T-m, of the lipid moieties, hydration of the glycosidic headgroup, the packing parameter, membrane rigidity, and edge stabilization, we are now able to draw a precise picture of the full self-assembly mechanism. This work is a didactical illustration of the complexity of the self-assembly process of a stimuli-responsive amphiphile during which many concomitant parameters play a key role at different stages of the process

Bearing-Based Network Localization Under Gossip Protocol

This paper proposes a bearing-based network localization algorithm with a randomized gossip protocol. Each sensor node is assumed to be able to obtain the bearing vectors and communicate its position estimates with several neighboring agents. Each update involves two agents, and the update sequence follows a stochastic process. Under the assumption that the network is infinitesimally bearing rigid and contains at least two beacon nodes, we show that the proposed algorithm could successfully estimate the actual positions of the network in probability. The randomized update protocol provides a simple, distributed, and reduces the communication cost of the network. The theoretical result is then supported by a simulation of a 1089-node sensor network.Comment: preprint, 7 pages, 2 figure

Flexibility in metal–organic frameworks : a basic understanding

Much has been written about the fundamental aspects of the metal-organic frameworks (MOFs). Still, details concerning the MOFs with structural flexibility are not comprehensively understood. However, a dramatic increase in research activities concerning rigid MOFs over the years has brought deeper levels of understanding for their properties and applications. Nonetheless, robustness and flexibility of such smart frameworks are intriguing for different research areas such as catalysis, adsorption, etc. This manuscript overviews the different aspects of framework flexibility. The review has touched lightly on several ideas and proposals, which have been demonstrated within the selected examples to provide a logical basis to obtain a fundamental understanding of their synthesis and behavior to external stimuli