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.

From subspace learning to distance learning: A geometrical optimization approach

In this paper, we adopt a differential-geometry viewpoint to tackle the problem of learning a distance online. As this problem can be cast into the estimation of a fixed-rank positive semidefinite (PSD) matrix, we develop algorithms that exploits the rich geometry structure of the set of fixed-rank PSD matrices. We propose a method which separately updates the subspace of the matrix and its projection onto that subspace. A proper weighting of the two iterations enables to continuously interpolate between the problem of learning a subspace and learning a distance when the subspace is fixed. © 2009 IEEE.

Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in ℝn. In these formulas, p-planes are represented as the column space of n × p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out.

Guidance of collective cell migration by substrate geometry.

Collective behavior refers to the emergence of complex migration patterns over scales larger than those of the individual elements constituting a system. It plays a pivotal role in biological systems in regulating various processes such as gastrulation, morphogenesis and tissue organization. Here, by combining experimental approaches and numerical modeling, we explore the role of cell density ('crowding'), strength of intercellular adhesion ('cohesion') and boundary conditions imposed by extracellular matrix (ECM) proteins ('constraints') in regulating the emergence of collective behavior within epithelial cell sheets. Our results show that the geometrical confinement of cells into well-defined circles induces a persistent, coordinated and synchronized rotation of cells that depends on cell density. The speed of such rotating large-scale movements slows down as the density increases. Furthermore, such collective rotation behavior depends on the size of the micropatterned circles: we observe a rotating motion of the overall cell population in the same direction for sizes of up to 200 μm. The rotating cells move as a solid body, with a uniform angular velocity. Interestingly, this upper limit leads to length scales that are similar to the natural correlation length observed for unconfined epithelial cell sheets. This behavior is strongly altered in cells that present a downregulation of adherens junctions and in cancerous cell types. We anticipate that our system provides a simple and easy approach to investigate collective cell behavior in a well-controlled and systematic manner.