Roundness: A closed form upper bound for the centroid to minimum zone center distance by worst-case analysis

The minimum zone tolerance (MZT) meets the ISO 1101 definition of roundness error: it determines two concentric circles that contain the roundness profile and such that the difference in radii is the least possible value. This article provides theoretical evidence that the minimum size of the neighborhood of the centroid containing the minimum zone center is pi E-1(C), where E-C is the roundness error related to the centroid, which can be evaluated in closed form. The implications of such linear estimating are twofold: (i) locating the part center with a given tolerance, e.g. for manufacturing tasks, such as handling (peg-hole) or machining (centering) and (ii) providing a search area for minimum zone center-based algorithms, such as metaheuristics (GA, PSO, etc.)

Dynamical response of the "GGG" rotor to test the Equivalence Principle: theory, simulation and experiment. Part I: the normal modes

Recent theoretical work suggests that violation of the Equivalence Principle might be revealed in a measurement of the fractional differential acceleration $\eta$ between two test bodies -of different composition, falling in the gravitational field of a source mass- if the measurement is made to the level of $\eta\simeq 10^{-13}$ or better. This being within the reach of ground based experiments, gives them a new impetus. However, while slowly rotating torsion balances in ground laboratories are close to reaching this level, only an experiment performed in low orbit around the Earth is likely to provide a much better accuracy. We report on the progress made with the "Galileo Galilei on the Ground" (GGG) experiment, which aims to compete with torsion balances using an instrument design also capable of being converted into a much higher sensitivity space test. In the present and following paper (Part I and Part II), we demonstrate that the dynamical response of the GGG differential accelerometer set into supercritical rotation -in particular its normal modes (Part I) and rejection of common mode effects (Part II)- can be predicted by means of a simple but effective model that embodies all the relevant physics. Analytical solutions are obtained under special limits, which provide the theoretical understanding. A simulation environment is set up, obtaining quantitative agreement with the available experimental data on the frequencies of the normal modes, and on the whirling behavior. This is a needed and reliable tool for controlling and separating perturbative effects from the expected signal, as well as for planning the optimization of the apparatus.Comment: Accepted for publication by "Review of Scientific Instruments" on Jan 16, 2006. 16 2-column pages, 9 figure

Deformable orthogonal grids: lemniscates

AbstractIn this paper we describe a technique, based on complex polynomials, for creating plane regions with a hole and propose a new method to produce an orthogonal grid on it. The thickness of the grid can be easily controlled and the sizes of the cells can be automatically estimated. The grid is automatically adapted to the boundary of the region. We offer parameters for the control of the geometric shape of the region, which depend on the roots of the polynomial and its derivative

Mechanics of the giant circle on high bar

In Men's Artistic Gymnastics the accelerated backward giant circle on high bar is used to generate the rotation required for the subsequent skill. When used prior to a dismount at the end of a high bar routine the gymnast performs a number of backward giant circles in order to generate sufficient rotation to perform the dismount. The most common dismounts from high bar require the gymnast to perform two backward somersaults in the layout position. Of all the dismounts performed by elite male gymnasts it is the double layout somersault dismount which requires the most rotation. Observations of elite gymnasts have shown that two different techniques may be adopted in the accelerated giant circle performed before release. Since gymnasts are able to perform the dismount from both types the question arises: What is the best technique for increasing rotation using accelerated backward giant circles? [Continues.

Kinematics of the local universe IX. The Perseus-Pisces supercluster and the Tolman-Bondi model

We study the mass distribution and the infall pattern of the Perseus-Pisces (PP) supercluster. First we calculate the mass of the central part of PP, a sphere with a radius of 15/h Mpc centered at (l,b)=(140.2\deg ,-22.0\deg), d=50/h Mpc, using the virial and other estimators. We get M_{PP} = 4 -- 7 /h 10^{15} M_{sun}, giving mass-to-light ratio 200 -- 600 h M_{sun} / L_{sun}, and overdensity \delta \approx 4. The radially averaged smoothed density distribution around the PP is inputted to the Tolman-Bondi (TB) equations, calculated for different cosmologies: \Omega_0 = [0.1,1], \Omega_{\Lambda} = 1-\Omega_0 or 0. As a result we get the infall velocities towards the PP center. Comparing the TB results to the peculiar velocities measured for the Kinematics of the Local Universe (KLUN) Tully-Fisher data set we get the best fit for the conditions \Omega_0 = 0.2 -- 0.4 and v_{inf} < 100 km/s for the Local Group infall towards the center of PP. The applicability of the TB method in a complex environment, such as PP, is tested on an N-body simulation.Comment: in press (A&A

Egocentric online social networks: Analysis of key features and prediction of tie strength in Facebook

The widespread use of online social networks, such as Facebook and Twitter, is generating a growing amount of accessible data concerning social relationships. The aim of this work is twofold. First, we present a detailed analysis of a real Facebook data set aimed at characterising the properties of human social relationships in online environments. We find that certain properties of online social networks appear to be similar to those found ?offline? (i.e., on human social networks maintained without the use of social networking sites). Our experimental results indicate that on Facebook there is a limited number of social relationships an individual can actively maintain and this number is close to the well-known Dunbar?s number (150) found in offline social networks. Second, we also present a number of linear models that predict tie strength (the key figure to quantitatively represent the importance of social relationships) from a reduced set of observable Facebook variables. Specifically, we are able to predict with good accuracy (i.e., higher than 80%) the strength of social ties by exploiting only four variables describing different aspects of users interaction on Facebook. We find that the recency of contact between individuals ? used in other studies as the unique estimator of tie strength ? has the highest relevance in the prediction of tie strength. Nevertheless, using it in combination with other observable quantities, such as indices about the social similarity between people, can lead to more accurate prediction

Stochastic Parameter Estimation of Poroelastic Processes Using Geomechanical Measurements

Understanding the structure and material properties of hydrologic systems is important for a number of applications, including carbon dioxide injection for geological carbon storage or enhanced oil recovery, monitoring of hydraulic fracturing projects, mine dewatering, environmental remediation and managing geothermal reservoirs. These applications require a detailed knowledge of the geologic systems being impacted, in order to optimize their operation and safety. In order to evaluate, monitor and manage such hydrologic systems, a stochastic estimation framework was developed which is capable of characterizing the structure and physical parameters of the subsurface. This software framework uses a set of stochastic optimization algorithms to calibrate a heterogeneous subsurface flow model to available field data, and to construct an ensemble of models which represent the range of system states that would explain this data. Many of these systems, such as oil reservoirs, are deep and hydraulically isolted from the shallow subsurface making near-surface fluid pressure measurements uninformative. Near-surface strainmeter, tiltmeter and extensometer signals were therefore evaluated in terms of their potential information content for calibrating poroelastic flow models. Such geomechanical signals are caused by mechanical deformation, and therefore travel through hydraulically impermeable rock much more quickly. A numerical geomechanics model was therefore developed using Geocentric, which couples subsurface flow and elastic deformation equations to simulate geomechanical signals (e.g. pressure, strain, tilt and displacement) given a set of model parameters. A high-performance cluster computer performs this computationally expensive simulation for each set of parameters, and compares the simulation results to measured data in order to evaluate the likelihood of each model. The set of data-model comparisons are then used to estimate each unknown parameter, as well as the uncertainty of each parameter estimate. This uncertainty can be inuenced by limitations in the measured dataset such as random noise, instrument drift, and the number and location of sensors, as well as by conceptual model errors and false underlying assumptions. In this study we find that strain measurements taken from the shallow subsurface can be used to estimate the structure and material parameters of geologic layers much deeper in the subsurface. This can signicantly mitigate drilling and installation costs of monitoring wells, as well as reduce the risk of puncturing or fracturing a target reservoir. These parameter estimates were also used to develop an ensemble of calibrated hydromechanical models which can predict the range of system behavior and inform decision-making on the management of an aquifer or reservoir