Homogeneity and isotropy in a laboratory turbulent flow

We present a new design for a stirred tank that is forced by two parallel planar arrays of randomly actuated synthetic jets. This arrangement creates turbulence at high Reynolds number with low mean flow. Most importantly, it exhibits a region of 3D homogeneous isotropic turbulence that is significantly larger than the integral lengthscale. These features are essential for enabling laboratory measurements of turbulent suspensions. We use quantitative imaging to confirm isotropy at large, small, and intermediate scales by examining one-- and two--point statistics at the tank center. We then repeat these same measurements to confirm that the values measured at the tank center are constant over a large homogeneous region. In the direction normal to the symmetry plane, our measurements demonstrate that the homogeneous region extends for at least twice the integral length scale $L=9.5$ cm. In the directions parallel to the symmetry plane, the region is at least four times the integral lengthscale, and the extent in this direction is limited only by the size of the tank. Within the homogeneous isotropic region, we measure a turbulent kinetic energy of $6.07 \times 10^{-4}$m$^2$s$^{-2}$, a dissipation rate of $4.65 \times 10^{-5}$m$^2$s$^{-3}$, and a Taylor--scale Reynolds number of $R_\lambda=334$. The tank's large homogeneous region, combined with its high Reynolds number and its very low mean flow, provides the best approximation of homogeneous isotropic turbulence realized in a laboratory flow to date. These characteristics make the stirred tank an optimal facility for studying the fundamental dynamics of turbulence and turbulent suspensions.Comment: 18 pages, 9 figure

An improved synthesis of (2E,4Z)-6-(benzyloxy)-4-bromohexa-2,4-dien-1-ol

An improved synthesis of (2E,4Z)-6-(benzyloxy)-4-bromohexa-2,4-dien-1-ol has been devised. This new route increases the throughput and yield of the diene product by circumventing a low yielding preparation of boronic acid intermediate as well as removing the need to use multi-gram quantities of highly toxic thallium salts. In the process of developing this new route, a higher yielding preparation of ( E)-3-hydroxyprop-1-enylboronic acid was also achieved. (c) 2007 Elsevier Ltd. All rights reserved

Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

The Langevin dynamics of a self - interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one - loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval the disorder drives the center of mass of the chain to a trap or frozen state provided that the Harris parameter, $(\Delta/b^d) N^{2 - \nu d} \ge 1$, where $\Delta$ is a disorder strength, $b$ is a Kuhnian segment length, $N$ is a chain length and $\nu$ is the Flory exponent. We have derived the general equation for the non - ergodicity function $f(p)$ which characterizes the amplitude of frozen Rouse modes with an index $p = 2\pi j/N$. The numerical solution of this equation has been implemented and shown that the different Rouse modes freeze up at the same critical disorder strength $\Delta_c \sim N^{-\gamma}$ where the exponent $\gamma \approx 0.25$ and does not depend from the solvent quality.Comment: 17 pages, 6 figures, submitted to EPJB (condensed matter

The invariants of the Clifford groups

The automorphism group of the Barnes-Wall lattice L_m in dimension 2^m (m not 3) is a subgroup of index 2 in a certain ``Clifford group'' C_m (an extraspecial group of order 2^(1+2m) extended by an orthogonal group). This group and its complex analogue CC_m have arisen in recent years in connection with the construction of orthogonal spreads, Kerdock sets, packings in Grassmannian spaces, quantum codes, Siegel modular forms and spherical designs. In this paper we give a simpler proof of Runge's 1996 result that the space of invariants for C_m of degree 2k is spanned by the complete weight enumerators of the codes obtained by tensoring binary self-dual codes of length 2k with the field GF(2^m); these are a basis if m >= k-1. We also give new constructions for L_m and C_m: let M be the Z[sqrt(2)]-lattice with Gram matrix [2, sqrt(2); sqrt(2), 2]. Then L_m is the rational part of the mth tensor power of M, and C_m is the automorphism group of this tensor power. Also, if C is a binary self-dual code not generated by vectors of weight 2, then C_m is precisely the automorphism group of the complete weight enumerator of the tensor product of C and GF(2^m). There are analogues of all these results for the complex group CC_m, with ``doubly-even self-dual code'' instead of ``self-dual code''.Comment: Latex, 24 pages. Many small improvement

J-MOD2^{2}: Joint Monocular Obstacle Detection and Depth Estimation

In this work, we propose an end-to-end deep architecture that jointly learns to detect obstacles and estimate their depth for MAV flight applications. Most of the existing approaches either rely on Visual SLAM systems or on depth estimation models to build 3D maps and detect obstacles. However, for the task of avoiding obstacles this level of complexity is not required. Recent works have proposed multi task architectures to both perform scene understanding and depth estimation. We follow their track and propose a specific architecture to jointly estimate depth and obstacles, without the need to compute a global map, but maintaining compatibility with a global SLAM system if needed. The network architecture is devised to exploit the joint information of the obstacle detection task, that produces more reliable bounding boxes, with the depth estimation one, increasing the robustness of both to scenario changes. We call this architecture J-MOD$^{2}$. We test the effectiveness of our approach with experiments on sequences with different appearance and focal lengths and compare it to SotA multi task methods that jointly perform semantic segmentation and depth estimation. In addition, we show the integration in a full system using a set of simulated navigation experiments where a MAV explores an unknown scenario and plans safe trajectories by using our detection model

Starspot induced effects in microlensing events with rotating source star

We consider the effects induced by the presence of hot and cold spots on the source star in the light curves of simulated microlensing events due to either single or binary lenses taking into account the rotation of the source star and the orbital motion of the lens system. Our goal is to study the anomalies induced by these effects on simulated microlensing light curves.Comment: 5 pages, 2 figures, accepted for publication in MNRA