The Relationship between Focal Surfaces and Surfaces at a Constant Distance from the Edge of Regression on a Surface

We investigate the relationship between focal surfaces and surfaces at a constant distance from the edge of regression on a surface. We show that focal surfaces F1 and F2 of the surface M can be obtained by means of some special surfaces at a constant distance from the edge of regression on the surface M

Accuracy of Surface Plate Measurements - General Purpose Software for Flatness Measurement

Flatness departures of surface plates are generally obtained from straightness measurements of lines on the surface. A computer program has been developed for on-line measurement and evaluation, based on the simultaneous coupling of measurements in all grid points. Statistical methods are used to determine the accuracy of the measurements. The program runs on standard personal computers and supports different types of measuring instruments like electronic levels, autocollimators, laser interferometers or straight edge based instruments. Apart from the given height map, some meaningful characteristic parameters: sphericity, torsion and waviness are obtained. They have been proven very valuable to record long term effects of surface plates. Reliable measurements with an accuracy of 0.1 μm/m demonstrate the capabilities of the method

Bayesian mapping of brain regions using compound Markov random field priors

Human brain mapping, i.e. the detection of functional regions and their connections, has experienced enormous progress through the use of functional magnetic resonance imaging (fMRI). The massive spatio-temporal data sets generated by this imaging technique impose challenging problems for statistical analysis. Many approaches focus on adequate modeling of the temporal component. Spatial aspects are often considered only in a separate postprocessing step, if at all, or modeling is based on Gaussian random fields. A weakness of Gaussian spatial smoothing is possible underestimation of activation peaks or blurring of sharp transitions between activated and non-activated regions. In this paper we suggest Bayesian spatio-temporal models, where spatial adaptivity is improved through inhomogeneous or compound Markov random field priors. Inference is based on an approximate MCMC technique. Performance of our approach is investigated through a simulation study, including a comparison to models based on Gaussian as well as more robust spatial priors in terms of pixelwise and global MSEs. Finally we demonstrate its use by an application to fMRI data from a visual stimulation experiment for assessing activation in visual cortical areas

Physics of puffing and microexplosion of emulsion fuel droplets

The physics of water-in-oil emulsion droplet microexplosion/puffing has been investigated using high-fidelity interface-capturing simulation. Varying the dispersed-phase (water) sub-droplet size/location and the initiation location of explosive boiling (bubble formation), the droplet breakup processes have been well revealed. The bubble growth leads to local and partial breakup of the parent oil droplet, i.e., puffing. The water sub-droplet size and location determine the after-puffing dynamics. The boiling surface of the water sub-droplet is unstable and evolves further. Finally, the sub-droplet is wrapped by boiled water vapor and detaches itself from the parent oil droplet. When the water sub-droplet is small, the detachment is quick, and the oil droplet breakup is limited. When it is large and initially located toward the parent droplet center, the droplet breakup is more extensive. For microexplosion triggered by the simultaneous growth of multiple separate bubbles, each explosion is local and independent initially, but their mutual interactions occur at a later stage. The degree of breakup can be larger due to interactions among multiple explosions. These findings suggest that controlling microexplosion/puffing is possible in a fuel spray, if the emulsion-fuel blend and the ambient flow conditions such as heating are properly designed. The current study also gives us an insight into modeling the puffing and microexplosion of emulsion droplets and sprays.This article has been made available through the Brunel Open Access Publishing Fund

A probabilistic data-driven model for planar pushing

This paper presents a data-driven approach to model planar pushing interaction to predict both the most likely outcome of a push and its expected variability. The learned models rely on a variation of Gaussian processes with input-dependent noise called Variational Heteroscedastic Gaussian processes (VHGP) that capture the mean and variance of a stochastic function. We show that we can learn accurate models that outperform analytical models after less than 100 samples and saturate in performance with less than 1000 samples. We validate the results against a collected dataset of repeated trajectories, and use the learned models to study questions such as the nature of the variability in pushing, and the validity of the quasi-static assumption.Comment: 8 pages, 11 figures, ICRA 201

Equilibrium Shapes with Stress Localisation for Inextensible Elastic Mobius and Other Strips

We formulate the problem of finding equilibrium shapes of a thin inextensible elastic strip, developing further our previous work on the Möbius strip. By using the isometric nature of the deformation we reduce the variational problem to a second-order one-dimensional problem posed on the centreline of the strip. We derive Euler–Lagrange equations for this problem in Euler–Poincaré form and formulate boundary-value problems for closed symmetric one- and two-sided strips. Numerical solutions for the Möbius strip show a singular point of stress localisation on the edge of the strip, a generic response of inextensible elastic sheets under torsional strain. By cutting and pasting operations on the Möbius strip solution, followed by parameter continuation, we construct equilibrium solutions for strips with different linking numbers and with multiple points of stress localisation. Solutions reveal how strips fold into planar or self-contacting shapes as the length-to-width ratio of the strip is decreased. Our results may be relevant for curvature effects on physical properties of extremely thin two-dimensional structures as for instance produced in nanostructured origami

Localized Regression on Principal Manifolds

No abstract available