T-duality acts on circle bundles by exchanging the first Chern class with the fiberwise integral of the H-flux, as we motivate using E 8 and also using S-duality. We present known and new examples including NS5-branes, nilmanifolds, Lens spaces, both circle bundles over RP n , and the AdS 5 × S 5 to AdS 5 × CP 2 × S 1 with background H-flux of Duff, Lü and Pope. When T-duality leads to M-theory on a non-spin manifold the gravitino partition function continues to exist due to the background flux, however the known quantization condition for G 4 receives a correction. In a more general context, we use correspondence spaces to implement isomorphisms on the twisted K-theories and twisted cohomology theories and to study the corresponding Grothendieck-Riemann-Roch theorem. Interestingly, in the case of decomposable twists, both twisted theories admit fusion products and so are naturally rings. * 1 However there are torii that do not lift to F-theory on which we may T-dualize, for example, a 2-torus that supports G3 flux. S-dualizing, the obstruction to T-duality on a torus with H-flux is the controversial obstruction to S-duality in the presence of G1 flux.2 Strictly speaking, the various forms entering (1.1) are the pull-backs of forms to the correspondence space3 To simplify the notations we will use the same notation for a cohomology class [H], or for a representative H, throughout this paper. It should be clear which is meant from the context. 4 Throughout this paper the notationÊ will refer to the T-dual of the bundle E, and not to the dual bundle in the usual sense.

Abstract. In this note we propose that D-brane charges, in the presence of a topologically non-trivial B-field, are classified by the K-theory of an infinite dimensional C * -algebra. In the case of B-fields whose curvature is pure torsion our description is shown to coincide with that of Witten.

The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962)PFLDAS0031-917110.1063/1.1706533]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-Bénard turbulence covering six decades in Rayleigh number Ra up to 10^{14} for Prandtl number Pr=1, for the first time in numerical simulations we find the transition to the ultimate regime, namely, at Ra^{*}=10^{13}. We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling Nu∼Ra^{1/3} [Proc. R. Soc. A 225, 196 (1954)PRLAAZ1364-502110.1098/rspa.1954.0197]. Beyond the transition, the mean velocity profiles are logarithmic throughout, indicating turbulent boundary layers. In contrast, the temperature profiles are only locally logarithmic, namely, within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling Nu∼Ra^{0.38}, corresponding to the effective scaling in the ultimate regime.

arXiv:2005.13774v1 [physics.flu-dyn] 28 May 2020

Heavy particles sink straight in water, while buoyant bubbles and spheres may zigzag or spiral as they rise. The precise conditions that trigger such path-instabilities are still not completely understood. For a buoyant rising sphere, two parameters are believed to govern the development of unsteady dynamics: the particle’s density relative to the fluid, and its Galileo number. Consequently, with these parameters specified, the opportunities for variation in particle dynamics appear limited. In contrast to this picture, here we demonstrate that vigorous path-oscillations can be triggered by modulating a spherical particle’s moment of inertia (MoI). For a buoyant sphere rising in a turbulent flow, MoI reduction triggers a tumble–flutter transition, while in quiescent liquid, it induces a modification of the sphere wake resulting in large-amplitude path-oscillations. The present finding opens the door for control of particle path- and wake-instabilities, with potential for enhanced mixing and heat transfer in particle-laden and dispersed multiphase environments.

This work reports an experimental characterisation of the flow properties in a homogeneous bubble swarm rising at high Reynolds numbers within a homogeneous and isotropic turbulent flow. Both the gas volume fraction alpha and the velocity fluctuations u '(0) of the carrier flow before bubble injection are varied, respectively, in the ranges 0% < alpha < 0.93% and 2.3 cm s(-1) < u '(0) < 5.5 cm s(-1). The so-called bubblance parameter (b = V-r(2)alpha/u '(2)(0) 0, where V-r is the bubble relative rise velocity) is used to compare the ratio of the kinetic energy generated by the bubbles to the one produced by the incident turbulence, and is varied from 0 to 1.3. Conditional measurements of the velocity field downstream of the bubbles in the vertical direction allow us to disentangle three regions that have specific statistical properties, namely the primary wake, the secondary wake and the far field. While the fluctuations in the primary wake are similar to that of a single bubble rising in a liquid at rest, the statistics of the velocity fluctuations in the far field follow a Gaussian distribution, similar to that produced by the homogenous and isotropic turbulence at the largest scales. In the secondary wake region, the conditional probability density function of the velocity fluctuations is asymmetric and shows an exponential tail for the positive fluctuations and a Gaussian one for the negative fluctuations. The overall agitation thus results from the combination of these three contributions and depends mainly on the bubblance parameter. For 0 < b < 0 : 7, the overall velocity fluctuations in the vertical direction evolve as b(0.4) and are mostly driven by the far-field agitation, whereas the fluctuations increase as b(1.3) for larger values of the bubblance parameter (b > 0.7), in which the significant contributions come both from the secondary wake and the far field. Thus, the bubblance parameter is a suitable parameter to characterise the evolution of liquid agitation in bubbly turbulent flows

No abstract

Transmission of highly infectious respiratory diseases, including SARS-CoV-2, is facilitated by the transport of exhaled droplets and aerosols that can remain suspended in air for extended periods of time. A passenger car cabin represents one such situation with an elevated risk of pathogen transmission. Here, we present results from numerical simulations to assess how the in-cabin microclimate of a car can potentially spread pathogenic species between occupants for a variety of open and closed window configurations. We estimate relative concentrations and residence times of a noninteracting, passive scalar—a proxy for infectious particles—being advected and diffused by turbulent airflows inside the cabin. An airflow pattern that travels across the cabin, farthest from the occupants, can potentially reduce the transmission risk. Our findings reveal the complex fluid dynamics during everyday commutes and nonintuitive ways in which open windows can either increase or suppress airborne transmission.