Constant Eccentricity Research Articles

Biologically-inspired heuristics for human-like walking trajectories toward targets and around obstacles

We describe simple heuristics, based on perceptual variables, that produce human-like trajectories towards moving and stationary targets, and around moving and stationary obstacles. Interception of moving and stationary objects can be achieved through regulation of self-movement to maintain a target at a constant eccentricity, or by cancelling the change (drift) in the eccentricity of the target. We first show how a constant eccentricity strategy can be extended to home in on optimal paths and avoid obstacles. We then identify a simple visual speed ratio that signals a future collision, and the change in path needed for avoidance. The combination of heuristics based on eccentricity and the speed-ratio produces human-like behaviour. The heuristics can be used to animate avatars in virtual environments or to guide mobile robots. Combined with higher-level goal setting and way-finding behaviours, such navigation heuristics could provide the foundation for generative models of natural human locomotion.

Behaviour of short polymer-high strength concrete columns under eccentric compression

Engineers have been looking for ways to combine two or more materials in order to take advantage of their strong features. This is how the hybrid materials were born. A very common type of such a construction material is the reinforced concrete. The present paper presents the results of the experimental and numerical investigations of the behaviour of short hybrid concrete columns subjected to short-time eccentric compression. The columns are made of high strength concrete, in the compression part, and polymer concrete located in the tensioned part. At the age of 28 days the columns were subjected to eccentric compression, with constant eccentricity. The influence of the second order effects, such as creep, was neglected. From the experimental results it can be concluded that the type of reinforcement can have a significant effect on the ultimate carrying capacity of the hybrid columns. The numerical simulations by means of non-linear finite element analysis are in good agreement with the experimental results.

Öpik-type collision probability for high-inclination orbits

The classical Öpik theory provides an estimate of the collision probability between two bodies on bound, heliocentric or planetocentric orbits under restrictive assumptions of: (i) constant eccentricity and inclination, and (ii) uniform circulation of the longitude of node and argument of pericenter. These assumptions are violated whenever either of the orbits has a large inclination with respect to the local Laplace plane or large eccentricity, and their motion is perturbed by an exterior (tidal) gravitational field of a planet or the Sun. In this situation, known as the Lidov–Kozai regime, the eccentricity and inclination values exhibit large and correlated oscillations. At the same time, the longitude of node and the argument of pericenter may have strongly nonlinear time evolution, with the latter being even bound to a small interval of values. Here we develop a new Öpik-type collision probability theory which is valid even for highly inclined and/or eccentric orbits of the projectile. We assume that the orbit of the target is circular and in the local Laplace plane. Such a generalized setting is necessary, as an example, to correctly estimate the terrestrial impact fluxes of sporadic micrometeoroids on high-inclination orbits (notably those from the toroidal source and the associated helion and anti-helion arcs).

Chemical analysis of ancient relicts in the Milky Way disk

We present detailed analysis of two groups of F- and G- type stars originally found to have similarities in their orbital parameters. The distinct kinematic properties suggest that they might originate from ancient accretion events in the Milky Way. From high resolution spectra taken with the spectrograph FIES at the Nordic Optical Telescope, La Palma, we determined abundances of oxygen, alpha- and r-process elements. Our results indicate that the sample of investigated stars is chemically homogeneous and the abundances of oxygen, alpha and r-process elements are overabundant in comparison with Galactic disk dwarfs. This provides the additional evidence that those stellar groups had the common formation and possible origin from disrupted satellites. 1. KINEMATIC SUBSTRUCTURES IN THE SOLAR NEIGHBORHOOD Observations and theoretical simulations have made much progress and provided us with tools to search for past accretion events in the Milky Way and beyond. The current events are the Sagittarius and Canis Major dwarf spheroidal galaxies, merging into the Galaxy. Traces of such mergers are visible in stellar trails revealed in the Galactic halo by large surveys (e.g. (9)). Can we also find such traces of ancient merger events in the solar neighborhood? Such events are much harder to discern among the stars of the disk. Combining kinematic and chemical analyses we could answer this question. Helmi et al. (2006), using Nordstrom et al. (2004) catalog, from correlations between the apocentre (A), pericentre (P) and z-angular momentum (Lz) - the so called APL space of orbital parameters - identified three new coherent groups of stars and suggested that those might correspond to remains of disrupted satellites. Stars in those groups cluster around regions of roughly constant eccentricity, they have the distinct distribution of kinematics, metallicity (Fe/H) and age, providing evidences of their extragalactic origin. In our high resolution spectroscopic study we aim to investigate the Milky Way disc. F - and G type dwarf stars are very useful in studing the ancient history of our Galaxy since they are long-lived, and their atmospheres reflect their initial chemical composition. In this study, we measured abundances of oxygen, - and r-process elements and here we discuss our results. The method of detailed chemical analysis, that we used in this study, can be found in our previous paper (8).

Enhanced reduced model for elastic earthquake response analysis of a class of mono-symmetric shear building structures with constant eccentricity

An enhanced reduced model is proposed for elastic earthquake response analysis of a class of mono-symmetric shear building structures with constant eccentricity. The proposed reduction method consists of two parts. The first stage is the construction of a reduced structural model with the degrees of freedom at representative floor levels only. In this stage, an inverse eigenmode-problem formulation is used to guarantee the limited equivalence between the original model and the reduced model. The reduced model is constructed so as to have the same fundamental natural frequency and the same lowest-mode component ratios at the representative floor levels as those of the original model. The second stage is the transformation of earthquake input forces into a set of reduced input forces. This transformation utilizes the static equivalence of lateral-torsional stiffness between these two models and is introduced to enhance the accuracy level of the reduced model. Several examples of a three-dimensional mono-symmetric ten-story shear building model with constant eccentricity are presented to demonstrate the validity and accuracy of the proposed reduction method for earthquake response analysis.

Simultaneous polarization monitoring of supernovae SN 2008D/XT 080109 and SN 2007uy: isolating geometry from dust

The possible existence of a continuum encompassing the diversity of explosive stellar deaths,ranging from ordinary SNe to relativistic hypernovae associated with long duration GRBs, is under intense debate. In this context, SN2008D associated with XT080109 could represent a paradigmatic case, since it might exemplify a potential borderline event. The main aim is to infer geometric information of SN2008D through the evolution of its linear optical polarization. We also report the polarization evolution of SN2007uy, and discuss the properties of the host ISM towards the XT. The final goal is to compare the polarization properties, and hence the geometries of both SNe, which shone contemporaneously in NGC2770. This fortunate coincidence brought us the opportunity to observe both SNe simultaneously, and most importantly, with identical instrumental setups. The observations span 74.9 days, starting 3.6 days after the XT and are distributed in 11 visits. In addition we performed observations in the mm range in order to identify the dominant polarization. We report positive linear polarization detections at several epochs for SN2008D at a level of ~1% and at ~1.5% for SN2007uy. SN2007uy shows constant polarization, which could be described by the host interstellar polarization plus a constant eccentricity expansion on the sky plane. A statistical analysis of the distribution of the SN2008D Stokes parametres suggests that it could show an intrinsic variable polarization component. Assuming the SN2007uy polarization is constant, we find that the evolution of the intrinsic SN2008D polarization could be explained by an aspherical axisymmetric expansion with variable eccentricity. We come to the same result even if we make no assumption on SN2007uy, although at a lower significance level. We suggest that at least the projected, if not the intrinsic, geometries of both SNe could differ.

Dissociating Eye Movements and Workload on Lateral Lane Position Variability

Recent research suggests that performing a secondary, non-visual task while driving may lead to a reduction in lateral vehicle movement. A plausible explanation for this counterintuitive pattern involves the joint findings that (1) increased cognitive load disrupts eye movements, and (2) eye movements often precipitate steering input. However, a partial dissociation of these factors by Cooper et al. (2009) found that increases in workload and eye movements (at a constant eccentricity) both reduce lateral lane variability. This follow-up study examines the contribution of eye movement eccentricity, under varying workload, on lateral lane position variability. Thirty-two participants drove nine, five minute scenarios in a fixed based driving simulator under varying eye movement and workload conditions. Consistent with previous finding, increased workload led to a decrease in lateral vehicle movement. Interestingly, an effect of visual eccentricity on eye movements was only observed in one of the driving measures. This research suggests that the impact of eye movements on lateral vehicle movement is much smaller than previously hypothesized and that impact of workload is much greater even after accounting for lateral shifts in eye movements.

Behavior of Fiber-Reinforced Concrete Columns under Axially and Eccentrically Compressive Loads

Fiber-reinforced concrete increasingly is being used for structural members. This study investigates the compressive behavior of reinforced concrete columns with and without steel fibers under axial and eccentric loads. The 16 confined columns had a concrete core 165 x 165 mm (6.49 x 6.49 in.) at the midsection and were hunched at the ends to apply eccentric loading and prevent boundary effects. The specimens were tested to failure at different strain rates under two loading schemes: concentric compression and eccentric compression with a constant eccentricity. The axial load and axial strains were obtained to evaluate the effects of the presence of steel fibers, the thickness of the cover concrete, and the eccentricity of the applied axial load. A comparative analysis of the experimental results showed that the presence of steel fibers delayed the spalling of concrete cover and increased the strain capacity and ductility. The eccentricity of the applied axial load caused substantial variation in the peak load, ultimate strength, and failure modes. The structural response of cross sections of normal concrete and steel fiber-reinforced concrete columns subjected to compressive concentric and eccentric loading was numerically modeled to compare the experimental results. Adequate reproduction of experimental results was obtained using a suitable choice of constitutive laws for concrete and reinforcing steel bars and a reasonable calibration criterion of the model. Directions for future research are discussed.

Parameter identification of torsionally coupled shear buildings from earthquake response records

AbstractThis paper presents an efficient procedure to determine the natural frequencies, modal damping ratios and mode shapes for torsionally coupled shear buildings using earthquake response records. It is shown that the responses recorded at the top and first floor levels are sufficient to identify the dominant modal properties of a multistoried torsionally coupled shear building with uniform mass and constant eccentricity even when the input excitation is not known. The procedure applies eigenrealization algorithm to generate the state‐space model of the structure using the cross‐correlations among the measured responses. The dynamic characteristics of the structure are determined from the state‐space realization matrices. Since the mode shapes are obtained only at the instrumented floor (top and first floors) levels, a new mode shape interpolation technique has been proposed to estimate the mode shape coefficients at the remaining floor levels. The application of the procedure has been demonstrated through a numerical experiment on an eight‐storied torsionally coupled shear building subjected to earthquake base excitation. The results show that the proposed parameter identification technique is capable of identifying dominant modal parameters and responses even with significant noise contamination of the response records. Copyright © 2008 John Wiley & Sons, Ltd.

Free vibration of rotating ring stiffened cylindrical shells with non-uniform stiffener distribution

In this research, the free vibration analysis of simply supported rotating cylindrical shells with circumferential stiffeners, i.e. rings with non-uniform stiffeners eccentricity and non-uniform stiffeners spacing distribution is investigated. Ritz method is applied while stiffeners are treated as discrete elements. In strain energy formulation, by adopting Sander's theorem, stretching and bending characteristics of shells are considered. Also stretching, bending and wrapping effects of stiffeners are investigated. The translational inertia in three directions for shell and stiffeners, and rotary inertia for stiffeners are considered. The effects of initial hoop tension, centrifugal and Coriolis forces due to the rotation of shell are studied. The polynomial functions are used for Ritz functions. Natural frequency results for rings with uniform spacing and constant eccentricity have been compared with analytical and experimental results of other researchers, which showed good agreement. Fortunately, the agreements of the presented analytical results with the experimental values are better than the analytical values. At constant total mass of stiffeners, the effects of non-uniform eccentricity distribution and non-uniform rings spacing distribution (separately and simultaneously) on natural frequencies are investigated. Moreover, the influence of rotating speed on natural frequencies for the so-called non-uniform stiffeners distribution is studied.

Pieces of the puzzle: ancient substructure in the Galactic disc

We search for signatures of past accretion events in the Milky Way in the recently published catalogue by Nordstrom et al., containing accurate spatial and kinematic information as well as metallicities for 13 240 nearby stars. To optimize our strategy, we use numerical simulations and characterize the properties of the debris from disrupted satellites. We find that stars with a common progenitor should show distinct correlations between their orbital parameters; in particular, between the apocentre (A) and pericentre (P), as well as their z-angular momentum (L-z). In the APL space, such stars are expected to cluster around regions of roughly constant eccentricity. The APL space for the Nordstrom catalogue exhibits a wealth of substructure, much of which can be linked to dynamical perturbations induced by spiral arms and the Galactic bar. However, our analysis also reveals a statistically significant excess of stars on orbits of common ( moderate) eccentricity, analogous to the pattern expected for merger debris. Besides being dynamically peculiar, the 274 stars in these substructures have very distinct metallicity and age distributions, providing further evidence of their extragalactic provenance. It is possible to identify three coherent groups among these stars, that, in all likelihood, correspond to the remains of disrupted satellites. The most metal-rich group ([Fe/H] >= -0.45 dex) has 120 stars distributed into two stellar populations of similar to 8 Gyr (33 per cent) and similar to 12 Gyr (67 per cent) of age. The second group with similar to -0.6 dex has 86 stars and shows evidence of three populations of 8 Gyr ( 15 per cent), 12 Gyr (36 per cent) and 16 Gyr (49 per cent) of age. Finally, the third group has 68 stars, with typical metallicity around -0.8 dex and a single age of similar to 14 Gyr. The identification of substantial amounts of debris in the Galactic disc whose origin can be traced back to more than one satellite galaxy, provides evidence of the hierarchical formation of the Milky Way. (Less)

Free vibration of non-uniformly ring stiffened cylindrical shells using analytical, experimental and numerical methods

In this research, the free vibration analysis of cylindrical shells with circumferential stiffeners, i.e. rings with non-uniform stiffeners eccentricity and unequal stiffeners spacing is investigated using analytical, experimental and finite elements (FE) methods. Ritz method is applied in analytical solution while stiffeners treated as discrete elements. The polynomial functions are used for Ritz functions and natural frequency results for simply supported stiffened cylindrical shell with equal rings spacing and constant eccentricity is compared with other's analytical and experimental results, which showed good agreement. Also, a stiffened shell with unequal rings spacing and non-uniform eccentricity with free–free boundary condition is considered using analytical, experimental and FE methods. In experimental method, modal testing is performed to obtain modal parameters, including natural frequencies, mode shapes and damping in each mode. In FE method, two types of modeling, including shell and beam elements and solid element are used, applying ANSYS software. The analytical and the FE results are compared with the experimental one, showing good agreements. Because of insufficient experimental modal data for non-uniformly stiffeners distribution, the results of modal testing obtained in this study could be as useful reference for validating the accuracy of other analytical and numerical methods for free vibration analysis.

Tests of Unstiffened Plate Elements Under Combined Compression and Bending

Details of a dual-actuator rig developed for testing rectangular plates simply supported on three sides, with the remaining (longitudinal) edge free, under combined uniaxial compression and in-plane bending are presented. Particular attention is given to ensuring a constant strain eccentricity to the loaded ends, as opposed to a constant load eccentricity, in order to determine the postbuckling behavior and ultimate load and moment capacities of unstiffened thin-walled elements. Strain gradients varying from pure compression to pure bending are facilitated.

Experimental techniques for testing unstiffened plates in compression and bending

We present details of a dual-actuator rig developed for testing rectangular plates supported on three sides, with the remaining (longitudinal) edge free, under combined uniaxial compression and in-plane bending. Particular attention is given to ensuring a constant strain gradient at the loaded ends, as opposed to a constant load eccentricity, in order to determine the post-buckling behavior and ultimate load and moment capacities of unstiffened thin-walled elements. Strain gradients varying from pure compression to pure bending are facilitated. Attention is also given to ensuring simply supported boundary conditions, and the methods used for anchoring the tensile stresses that develop at the loaded edges as a result of large plate deflections. Details of the methods for controlling the applied displacements are given, for which a system of four laser displacement devices was employed in order to achieve the required strain gradient. The operation of the rig is verified against established theoretical solutions.

Simulation of growth kinetics of octahedral and platelike oxygen precipitates in silicon

A model describing the growth kinetics of the characteristic size of octahedral and platelike oxygen precipitates in silicon is suggested. It is shown that the experimental data of various authors on the growth kinetics of precipitates are adequately described by the assumption that their growth is limited by diffusion, while the geometry of precipitates is characterized by constant eccentricity.

Slow growth of an isolated disk-shaped bubble of constant eccentricity in the presence of a distributed gas source

In this paper we consider the diffusion-controlled (small Péclet number) growth of an isolated, oblate-spheroidal (disk-shaped) bubble of constant eccentricity (aspect ratio) in a medium that actively produces the volatile substance via a distributed source, but does not itself offer significant resistance to growth. Oblate spheroidal bubbles are predicted to grow faster than spherical ones, due to the higher surface area to volume ratio; yet, bubbles of all eccentricities grow proportionally to the square root of time, as expected for a diffusive process. In the presence of a distributed source, however, the growth time becomes dependent on the square-root of the source strength, in the limit as the boundary forcing, i.e., the degree of super-saturation, becomes negligible. Furthermore, we demonstrate that the previously known spherical solution is contained within the more general spheroidal solution. In addition, we produced new expression to describe the growth of a disk in terms of the evolution of the radius of a volume-equivalent sphere and another simple expression relating the growth time of a disk to that of a sphere.

Growth of disk-shaped bubbles in sediments

Disc-shaped methane bubbles, often observed in marine sediments, result from growth in a medium that elastically resists expansion of the bubbles and yields by fracture. We have modeled this process to obtain estimates of growth times by using a reaction-diffusion model coupled to a linear elastic fracture mechanics (LEFM). For comparison, we also modeled the growth of a constant eccentricity bubble in a nonresistant medium. Discoidal bubbles that grow in sediments that obey LEFM grow much faster than spherical bubbles (two- to fourfold faster for the times and conditions tested here) and become more eccentric with time (aspect ratios falling from 0.3 to 0.03 over 8 d of growth). In addition, their growth is not continuous but punctuated by fracture events. Furthermore, under some conditions, LEFM predicts that bubble growth can become arrested, which is not possible for a bubble in a nonresistant medium, even for nonspherical bubbles. Cessation of growth occurs when the dissolved gas concentration gradient near the bubble surface disappears as a result of the increase in bubble gas pressure needed to overcome sediment elasticity.

Long-Term Third-Body Effects via Double Averaging

Westudy thelong-term effects of a third body on a satelliteof negligiblemass. Wehavein mind to study thelunisolar effects on an Earth satellite but many other applications can be imagined. We begin with the representation of the disturbing function in an ine nite series in Legendre polynomials but we truncate it at the second-degree terms. Our approach consists of a double analytic averaging: with the period of the satellite and with the period of the third body. We concentrate on using the two important integrals (energy and angular momentum ) to discuss and classify properties of the perturbed orbits of the satellite. For inclinations below 39 deg, the perigee of the orbits always circulates. There are circular and elliptic orbits but the eccentricity does not vary much. For the inclinations above 39 deg, the circular orbits are unstable and the eccentricities can increase rapidly but we have the appearance of new stableorbits: two ellipticfrozen orbits with constant eccentricity and e xed perigee location, at either 90 or 270 deg.

A Simple Family of Models for Eccentric Keplerian Fluid Disks

To be in a long-lived configuration, the density in a fluid disk should be constant along streamlines to prevent compressional (PdV) work from being done cyclically around every orbit. In a pure Kepler potential, flow along aligned elliptical streamlines of constant eccentricity will satisfy this condition. For most density profiles, differential precession driven by the pressure gradient will destroy the alignment; however, in the razor-thin approximation there is a family of simple equilibria in which the precession frequency is the same at all radii. These disks may therefore be long-lived at significant eccentricities. The density can be made axisymmetric as r → 0 while maintaining the precession rate by relaxing the requirement of constancy along streamlines in an arbitrarily small transition region near the center. In the limit of small eccentricity, the models can be seen as acoustically perturbed axisymmetric disks, and the precession rate is shown to agree with linear theory. The perturbation is a traveling wave similar to an ocean wave, with the fluid rising and falling epicyclically in the gravitational field of the central mass. The expected emission-line profiles from the eccentric disks are shown to be strongly asymmetric in general and, in extreme cases, prone to misinterpretation as single narrow lines with significant velocity offsets.

Minimal Surfaces in a Sphere and the Ricci Condition

In this paper we deal with minimal surfaces in a sphere which are locally isometric to a minimal surface in S3. We prove that a minimal surface in a sphere is locally isometric to a minimal surface in S3 if the curvature ellipse has constant and positive eccentricity. Moreover, we prove the following rigidity result: a compact minimal surface M in Sm, m ≤ 6, cannot be locally isometric to a minimal surface in S3 unless M already lies in S3 or M is flat and lies in S5.