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

Nonlinear dynamics in superlattices driven by high frequency ac-fields

We investigate the dynamical processes taking place in nanodevices driven by high-frequency electromagnetic fields. We want to elucidate the role of different mechanisms that could lead to loss of quantum coherence. Our results show how the dephasing effects of disorder that destroy after some periods coherent oscillations, such as Rabi oscillations, can be overestimated if we do not consider the electron-electron interactions that can reduce dramatically the decoherence effects of the structural imperfections. Experimental conditions for the observation of the predicted effects are discussed.Comment: REVTEX (8 pages) and 4 figures (Postscript

On the (2,3)-generation of the finite symplectic groups

This paper is a new important step towards the complete classification of the finite simple groups which are $(2,3)$-generated. In fact, we prove that the symplectic groups $Sp_{2n}(q)$ are $(2,3)$-generated for all $n\geq 4$. Because of the existing literature, this result implies that the groups $PSp_{2n}(q)$ are $(2,3)$-generated for all $n\geq 2$, with the exception of $PSp_4(2^f)$ and $PSp_4(3^f)$

The simple classical groups of dimension less than 6 which are (2,3)-generated

In this paper we determine the classical simple groups of dimension r=3,5 which are (2,3)-generated (the cases r = 2, 4 are known). If r = 3, they are PSL_3(q), q 4, and PSU_3(q^2), q^2 9, 25. If r = 5 they are PSL_5(q), for all q, and PSU_5(q^2), q^2 >= 9. Also, the soluble group PSU_3(4) is not (2,3)-generated. We give explicit (2,3)-generators of the linear preimages, in the special linear groups, of the (2,3)-generated simple groups.Comment: 12 page

The (2,3)(2,3)-generation of the finite unitary groups

In this paper we prove that the unitary groups $SU_n(q^2)$ are $(2,3)$-generated for any prime power $q$ and any integer $n\geq 8$. By previous results this implies that, if $n\geq 3$, the groups $SU_n(q^2)$ and $PSU_n(q^2)$ are $(2,3)$-generated, except when $(n,q)\in\{(3,2),(3,3),(3,5),(4,2), (4,3),(5,2)\}$.Comment: In this version, we obtained a complete classification of the finite simple unitary groups which are (2,3)-generated; some proofs have been semplifie

Scott's formula and Hurwitz groups

This paper continues previous work, based on systematic use of a formula of L. Scott, to detect Hurwitz groups. It closes the problem of determining the finite simple groups contained in $PGL_n(F)$ for $n\leq 7$ which are Hurwitz, where $F$ is an algebraically closed field. For the groups $G_2(q)$, $q\geq 5$, and the Janko groups $J_1$ and $J_2$ it provides explicit $(2,3,7)$-generators

More on regular subgroups of the affine group

This paper is a new contribution to the study of regular subgroups of the affine group $AGL_n(F)$, for any field $F$. In particular we associate to any partition $\lambda\neq (1^{n+1})$ of $n+1$ abelian regular subgroups in such a way that different partitions define non-conjugate subgroups. Moreover, we classify the regular subgroups of certain natural types for $n\leq 4$. Our classification is equivalent to the classification of split local algebras of dimension $n+1$ over $F$. Our methods, based on classical results of linear algebra, are computer free

Slip-velocity of large neutrally-buoyant particles in turbulent flows

We discuss possible definitions for a stochastic slip velocity that describes the relative motion between large particles and a turbulent flow. This definition is necessary because the slip velocity used in the standard drag model fails when particle size falls within the inertial subrange of ambient turbulence. We propose two definitions, selected in part due to their simplicity: they do not require filtration of the fluid phase velocity field, nor do they require the construction of conditional averages on particle locations. A key benefit of this simplicity is that the stochastic slip velocity proposed here can be calculated equally well for laboratory, field, and numerical experiments. The stochastic slip velocity allows the definition of a Reynolds number that should indicate whether large particles in turbulent flow behave (a) as passive tracers; (b) as a linear filter of the velocity field; or (c) as a nonlinear filter to the velocity field. We calculate the value of stochastic slip for ellipsoidal and spherical particles (the size of the Taylor microscale) measured in laboratory homogeneous isotropic turbulence. The resulting Reynolds number is significantly higher than 1 for both particle shapes, and velocity statistics show that particle motion is a complex non-linear function of the fluid velocity. We further investigate the nonlinear relationship by comparing the probability distribution of fluctuating velocities for particle and fluid phases