1,720,990 research outputs found
On master test plans for the space of BV functions
No full textNobili F, Pasqualetto E, Schultz T. On master test plans for the space of BV functions. Advances in Calculus of Variations . 2022.We prove that on an arbitrary metric measure space a countable collection of test plans is sufficient to recover all BV functions and their total variation measures. In the setting of non-branching CD(K, N) spaces (with finite reference measure), we can additionally require these test plans to be concentrated on geodesics
Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces
Full text linkWe prove that for a suitable class of metric measure spaces the abstract notion of tangent module as defined by the first author can be isometrically identified with the space of L2-sections of the ‘Gromov-Hausdorff tangent bundle’. The key assumption that we make is a form of rectifiability for which the space is ‘almost isometrically’ rectifiable (up to m-null sets) via maps that keep under control the reference measure. We point out that RCD∗(K, N) spaces fit in our framework
Differential of metric valued Sobolev maps
Full text linkWe introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces, developed by the first author. We prove that our notion is consistent with Kirchheim's metric differential when the source is a Euclidean space, and with the abstract differential provided by the first author when the target is R. We also show compatibility with the concept of co-local weak differential introduced by Convent and Van Schaftingen
Representation theorems for normed modules
No full textIn this paper we study the structure theory of normed modules, which have been introduced by Gigli. The aim is twofold: to extend von Neumann's theory of liftings to the framework of normed modules, thus providing a notion of precise representative of their elements; to prove that each separable normed module can be represented as the space of sections of a measurable Banach bundle. By combining our representation result with Gigli's differential structure, we eventually show that every metric measure space (whose Sobolev space is separable) is associated with a cotangent bundle in a canonical way
On the notion of parallel transport on RCD spaces
No full textWe propose a general notion of parallel transport on RCD spaces, prove an unconditioned uniqueness result and existence under suitable assumptions on the space.peerReviewe
Differential structure associated to axiomatic Sobolev spaces
Full text linkThe aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol’dshtein–Troyanov) induces – under suitable locality assumptions – a first-order differential structure.peerReviewe
Fra, A.M., Mastroianni, N., Mancini, M., Pasqualetto, E., Sitia, R., Human caveolin-1 and caveolin-2 are closely linked genes colocalized with WI-5336 in a region of 7q31 frequently deleted in tumors
No full textImpact of spanwise extent of transverse grooves on drag reduction in boat-tailed bluff bodies: an experimental study
No full textThe paper describes the first experimental study on the application of small contoured grooves in boat-tailed bodies characterized by vortex shedding. In particular, we experimentally investigate the flow-separation delay and drag-reducing performance of spanwise-extruded and spanwise-discontinuous grooves. For this purpose, we consider groove geometries similar to those proposed and numerically investigated by Mariotti et al. (Eur J Mech B/Fluids 74:351–362, 2019) and Pasqualetto et al. (Fluids 7:121, 2022a). The Reynolds number, based on the freestream velocity and the model crossflow dimension, is Re=9.6·104. In addition to serving as an experimental confirmation of previous numerical studies, an important difference is that the present experiments were conducted with a freestream turbulence intensity of 0.9%, whereas the simulations were carried out with a freestream without turbulence. This extends the applicability of this flow control device to a situation closer to real-world or industrial applications. In the experiments, we measure pressure-drag variations for different configurations and flow correlations in the spanwise direction through pressure and hot-wire measurements. The results confirm the good performance of the grooves as passive flow-control devices and the capability of grooves to delay flow separation even in a turbulent freestream. The experiments elucidate the physical mechanism leading to the enhanced performance, specifically the reduction of friction losses due to the local recirculation embedded in the groove region. However, the experiments reveal a different behavior in terms of vortex shedding correlation in the spanwise direction with the introduction of grooves of different spanwise extents. Interestingly, the spanwise-extruded grooves exhibit a weaker increase in spanwise correlation of vortex shedding in experiments compared to simulations. This difference is likely due to the presence of freestream turbulence in the wind tunnel, which is absent in simulations. As expected, the introduction of the spanwise-discontinuous groove reduces vortex shedding correlation. Consequently, in experiments the adoption of spanwise-discontinuous grooves yields fewer benefits than those previously found numerically
Human caveolin-1 and caveolin-2 are closely linked genes colocalized with WI-5336 in a region of 7q31 frequently deleted in tumors
No full textEffect of the Lateral Mean Recirculation Characteristics on Near-Wake and Bulk Quantities of a 5:1 Rectangular Cylinder
No full textA database of several LES carried out for the high-Reynolds number flow around a 5:1 rectangular cylinder is analyzed to highlight the effects of the characteristics of the mean flow over the cylinder side on the near-wake features and on some bulk quantities. Different simulation set-ups are considered by varying the grid refinement in the spanwise direction and the amount of SGS dissipation for sharp upstream edges and with different values of the upstream-edge rounding. These simulations may be considered as possible instances of this kind of flow with different mean flow features on the cylinder side. Among the different characteristic lengths defining the mean recirculation, the streamwise length is the most important parameter. The wake width increases linearly with this parameter, while the vortex-shedding non-dimensional frequency shows a linear decrease. The drag coefficient also linearly decreases with increasing the recirculation length and this is due to a reduction of the suctions on the cylinder base. However, the overall variation of CD is small. Finally, a significant, and once again linear, increase of the fluctuations of the lift coefficient is found for increasing the mean recirculation streamwise length
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