Nonsmooth geometry and collapse of flexible structures under smooth loads

While static equilibria of flexible strings subject to various load types (gravity, hydrostatic pressure, Newtonian wind) is well understood textbook material, the combinations of the very same loads can give rise to complex spatial behaviour at the core of which is the unilateral material constraint prohibiting compressive loads. While the effects of such constraints have been explored in optimisation problems involving straight cables, the geometric complexity of physical configurations has not yet been addressed. Here we show that flexible strings subject to combined smooth loads may not have smooth solutions in certain ranges of the load ratios. This non-smooth phenomenon is closely related to the collapse geometry of inflated tents. After proving the nonexistence of smooth solutions for a broad family of loadings we identify two alternative, critical geometries immediately preceding the collapse. We verify these analytical results by dynamical simulation of flexible chains as well as with simple table-top experiments with an inflated membrane.

The geometry and the number of contacts of monodisperse sphere packs using X-ray tomography

The three-dimensional structure of very large samples of monodisperse bead packs is studied by means of X-Ray Computed Tomography. We retrieve the coordinatesofeach bead inthe pack and wecalculate the average coordination number by using the tomographic images to single out the neighbors in contact. The results are compared with the average coordination number obtained in Aste et al. (2005) by using a deconvolution technique. We show that the coordination number increases with the packing fraction, varying between 6.9 and 8.2 for packing fractions between 0.59 and 0.64. © 2005 Taylor & Francis Group.

Differential Dynamic Microscopy: a High-Throughput Method for Characterizing the Motility of Microorganism

We present a fast, high-throughput method for characterizing the motility of microorganisms in 3D based on standard imaging microscopy. Instead of tracking individual cells, we analyse the spatio-temporal fluctuations of the intensity in the sample from time-lapse images and obtain the intermediate scattering function (ISF) of the system. We demonstrate our method on two different types of microorganisms: bacteria, both smooth swimming (run only) and wild type (run and tumble) Escherichia coli, and the bi-flagellate alga Chlamydomonas reinhardtii. We validate the methodology using computer simulations and particle tracking. From the ISF, we are able to extract (i) for E. coli: the swimming speed distribution, the fraction of motile cells and the diffusivity, and (ii) for C. reinhardtii: the swimming speed distribution, the amplitude and frequency of the oscillatory dynamics. In both cases, the motility parameters are averaged over \approx 10^4 cells and obtained in a few minutes.

Geometry and interaction of structures in homogeneous isotropic turbulence

A strategy to extract turbulence structures from direct numerical simulation (DNS) data is described along with a systematic analysis of geometry and spatial distribution of the educed structures. A DNS dataset of decaying homogeneous isotropic turbulence at Reynolds number Reλ = 141 is considered. A bandpass filtering procedure is shown to be effective in extracting enstrophy and dissipation structures with their smallest scales matching the filter width, L. The geometry of these educed structures is characterized and classified through the use of two non-dimensional quantities, planarity' and filamentarity', obtained using the Minkowski functionals. The planarity increases gradually by a small amount as L is decreased, and its narrow variation suggests a nearly circular cross-section for the educed structures. The filamentarity increases significantly as L decreases demonstrating that the educed structures become progressively more tubular. An analysis of the preferential alignment between the filtered strain and vorticity fields reveals that vortical structures of a given scale L are most likely to align with the largest extensional strain at a scale 3-5 times larger than L. This is consistent with the classical energy cascade picture, in which vortices of a given scale are stretched by and absorb energy from structures of a somewhat larger scale. The spatial distribution of the educed structures shows that the enstrophy structures at the 5η scale (where η is the Kolmogorov scale) are more concentrated near the ones that are 3-5 times larger, which gives further support to the classical picture. Finally, it is shown by analysing the volume fraction of the educed enstrophy structures that there is a tendency for them to cluster around a larger structure or clusters of larger structures. Copyright © 2012 Cambridge University Press.

Transient flows in enclosures: A generalised approach for modelling the effects of geometry, heat gains and wind

Transient flows in a confined ventilated space induced by a buoyancy source of time-varying strength and an external wind are examined. The space considered has varying cross-sectional area with height. A generalised theoretical model is proposed to investigate the flow dynamics following the activation of an external wind and an internal source of buoyancy. To investigate the effect of geometry, we vary the angle of the wall inclination of a particular geometry in which a point source of constant buoyancy is activated in the absence of wind. Counter-intuitively the ventilation is worse and lower airflow rates are established for geometries of increasing cross-sectional areas with height. We investigate the effect of the source buoyancy strength by comparing two cases: (1) when the buoyancy input is constant and (2) when the buoyancy input gradually increases over time so that after a finite time the total buoyancy inputs for (1) and (2) are identical. The rate at which the source heat gains are introduced has a significant role on the flow behaviour as we find that, in case (2), a warmer layer and a more pronounced overshoot are obtained than in case (1). The effect of assisting and opposing wind on the transient ventilation of an enclosure of constant cross-sectional area with height and constant heat gains is examined. A Froude number Fr is used to define the relative strengths of the buoyancy-induced and wind-induced velocities and five different transient states and their associated critical Fr are identified. © 2010 Elsevier Ltd.

SOI membrane-based pressure sensor in stress sensitive differential amplifier configuration

This paper introduces a pressure sensing structure configured as a stress sensitive differential amplifier (SSDA), built on a Silicon-on-Insulator (SOI) membrane. Theoretical calculation show the significant increase in sensitivity which is expected from the pressure sensors in SSDA configuration compared to the traditional Wheatstone bridge circuit. Preliminary experimental measurements, performed on individual transistors placed on the membrane, exhibit state-the-art sensitivity values (1.45mV/mbar). © 2012 IEEE.

The influence of geometry on jet plume development

Our recent efforts of using large-eddy simulation (LES) type methods to study complex and realistic geometry single stream and co-flow nozzle jets and acoustics are summarized in this paper. For the LES, since the solver being used tends towards having dissipative qualities, the subgrid scale (SGS) model is omitted, giving a numerical type LES (NLES). To overcome near wall streak resolution problems a near wall RANS (Reynolds averaged Navier-Stokes) model is smoothly blended in the LES making a hybrid RANS-NLES approach. Several complex nozzle geometries including the serrated (chevron) nozzle, realistic co-axial nozzles with eccentricity, pylon and wing-flap are discussed. The hybrid RANS-NLES simulations show encouraging predictions for the chevron jets. The chevrons are known to increase the high frequency noise at high polar angles, but decrease the low frequency noise at lower angles. The deflection effect of the potential core has an important mechanism of noise reduction. As for co-axial nozzles, the eccentricity, the pylon and the deployed wing-flap are shown to influence the flow development, especially the former to the length of potential core and the latter two having a significant impact on peak turbulence levels and spreading rates. The studies suggest that complex and real geometry effects are influential and should be taken into count when moving towards real engine simulations. © 2012 Elsevier Ltd. All rights reserved.

Geometry of Miura-folded metamaterials.

This paper describes two folded metamaterials based on the Miura-ori fold pattern. The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which only depends on the geometry and therefore is scale-independent. First, a folded shell structure is introduced, where the fold pattern provides a negative Poisson's ratio for in-plane deformations and a positive Poisson's ratio for out-of-plane bending. Second, a cellular metamaterial is described based on a stacking of individual folded layers, where the folding kinematics are compatible between layers. Additional freedom in the design of the metamaterial can be achieved by varying the fold pattern within each layer.

Magnetic shielding with YBCO coated conductors: Influence of the geometry on its performances

A superconducting magnetic shield can be built as a stack of several sections of milled 2G coated conductors. Each section consists of a closed loop where persistent currents can flow and provide a strong attenuation of external dc magnetic fields. The purpose of the present work is to study experimentally several geometries of such magnetic shields made out of YBa2Cu 3O7 (YBCO) coated conductors from SuperPower. Our aim is to investigate in detail the influence of the aspect ratio and the number of layers of the assembly on the magnetic shielding properties. In order to do so, the magnetic shield is subjected to an axial quasi-static ('dc') magnetic field ramped slowly at a fixed sweep rate. A Hall probe is used to measure the local magnetic induction inside the assembly as a function of the applied magnetic induction. Results show that the shielding factor, SF, (defined as the ratio between the applied magnetic induction and the magnetic induction measured inside the shield) is improved for increasing aspect ratios of the global coated conductor assembly and that the threshold magnetic induction (defined for SF = 10) increases with the number of layers. Using a double layer of 18 sections at T = 77K , dc magnetic fields up to 56 mT can be shielded by a factor larger than 10. Finally, the effect of an air gap of constant width between coated conductor sections is also characterized. © 2002-2011 IEEE.

Differential encoding of losses and gains in the human striatum.

Studies on human monetary prediction and decision making emphasize the role of the striatum in encoding prediction errors for financial reward. However, less is known about how the brain encodes financial loss. Using Pavlovian conditioning of visual cues to outcomes that simultaneously incorporate the chance of financial reward and loss, we show that striatal activation reflects positively signed prediction errors for both. Furthermore, we show functional segregation within the striatum, with more anterior regions showing relative selectivity for rewards and more posterior regions for losses. These findings mirror the anteroposterior valence-specific gradient reported in rodents and endorse the role of the striatum in aversive motivational learning about financial losses, illustrating functional and anatomical consistencies with primary aversive outcomes such as pain.