The Kraichnan-Kazantsev dynamo

The problem of the dynamo effect for a Kraichnan incompressible helicity-free velocity field is considered. Exploiting a quantum formalism first introduced by Kazantsev (A.P. Kazantsev, Sov. Phys. JETP 26, 1031-1034 (1968)), we show that a critical magnetic Reynolds number exists for the presence of dynamo. The value of the Prandtl number influences the spatial distribution of the magnetic field and its growth in time. The magnetic field correlation length is always the largest between the diffusive scale and the viscous scale of the flow. In the same way the field growth is characterized by a time scale that corresponds to the largest between the diffusive and the viscous characteristic time.Comment: 16 pages, 6 figure

Deformation of a flexible polymer in a random flow with long correlation time

The effects induced by long temporal correlations of the velocity gradients on the dynamics of a flexible polymer are investigated by means of theoretical and numerical analysis of the Hookean and FENE dumbbell models in a random renewing flow. For Hookean dumbbells, we show that long temporal correlations strongly suppress the Weissenberg-number dependence of the power-law tail characterising the probability density function (PDF) of the elongation. For the FENE model, the PDF becomes bimodal, and the coil-stretch transition occurs through the simultaneous drop and rise of the two peaks associated with the coiled and stretched configurations, respectively.Comment: 10 page

Effect of polymer-stress diffusion in the numerical simulation of elastic turbulence

Elastic turbulence is a chaotic regime that emerges in polymer solutions at low Reynolds numbers. A common way to ensure stability in numerical simulations of polymer solutions is to add artificially large polymer-stress diffusion. In order to assess the accuracy of this approach in the elastic-turbulence regime, we compare numerical simulations of the two-dimensional Oldroyd-B and FENE-P models sustained by a cellular force with and without artificial diffusion. We find that artificial diffusion can have a dramatic effect even on the large-scale properties of the flow and we show some of the spurious phenomena that may arise when artificial diffusion is used.Comment: 17 page

The Engel elements in generalized FC-groups

We generalize to FC*, the class of generalized FC-groups introduced in [F. de Giovanni, A. Russo, G. Vincenzi, Groups with restricted conjugacy classes, Serdica Math. J. 28 (2002), 241-254], a result of Baer on Engel elements. More precisely, we prove that the sets of left Engel elements and bounded left Engel elements of an FC*-group G coincide with the Fitting subgroup; whereas the sets of right Engel elements and bounded right Engel elements of G are subgroups and the former coincides with the hypercentre. We also give an example of an FC*-group for which the set of right Engel elements contains properly the set of bounded right Engel elements.Comment: to appear in "Illinois Journal of Mathematics

Analysis and Architecture Design of DSPACE, a Digital Signal Processor for space applications

The request of digital signal processing performed on satellites or spacecraft is greatly increased in past years, however the European Space Agency (ESA) has not got a suitable device for these applications made in Europe area. ESA is currently forced to address to United States (US) made alternatives but the exportation of those devices is restricted by the International Traffic in Arms Regulations (ITAR) and this places ESA in a dependent position. The DSPACE project aim to solve this lack providing a new Digital Signal Processor (DSP), as an intellectual property, and a software tool-chain to exploit its features. The first part of this thesis work regarded an analysis of the state-of-the-art and the practical solutions in order to identify a target technology and a reference architecture. The second part of this work concerned a detailed definitions of the DSPACE core architecture and features. Moreover a complete decode & dispatch VHDL model, with a formal functional verification, was realized. The third part of this work regarded two caches modelling, the instruction and the data cache, that are two essential components of the DSPACE core. This thesis work was concluded with the first functional simulations coming from the DSPACE model and considerations about the resource occupation of the core

Telegram from Robert W. Vincenzi, Business Agent for the National Association of Letter Carriers, to Geraldine Ferraro

Congratulatory telegram from Robert W. Vincenzi, national business agent for the National Association of Letter Carriers, to Geraldine Ferraro. Includes standard response letter from Ferraro and a data entry sheet.https://ir.lawnet.fordham.edu/vice_presidential_campaign_correspondence_1984_new_york/1288/thumbnail.jp

Nonlinear elastic polymers in random flow

Polymer stretching in random smooth flows is investigated within the framework of the FENE dumbbell model. The advecting flow is Gaussian and short-correlated in time. The stationary probability density function of polymer extension is derived exactly. The characteristic time needed for the system to attain the stationary regime is computed as a function of the Weissenberg number and the maximum length of polymers. The transient relaxation to the stationary regime is predicted to be exceptionally slow in the proximity of the coil-stretch transition.Comment: 10 pages, to be published in J. Fluid Mec

Droplets in isotropic turbulence: deformation and breakup statistics

The statistics of the deformation and breakup of neutrally buoyant sub-Kolmogorov ellipsoidal drops is investigated via Lagrangian simulations of homogeneous isotropic turbulence. The mean lifetime of a drop is also studied as a function of the initial drop size and the capillary number. A vector model of drop previously introduced by Olbricht, Rallison and Leal [J. Non-Newtonian Fluid Mech. $\mathbf{10}$, 291 (1982)] is used to predict the behaviour of the above quantities analytically.Comment: 16 pages, 16 figure

Elastic turbulence in a shell model of polymer solution

We show that, at low inertia and large elasticity, shell models of viscoelastic fluids develop a chaotic behaviour with properties similar to those of elastic turbulence. The low dimensionality of shell models allows us to explore a wide range both in polymer concentration and in Weissenberg number. Our results demonstrate that the physical mechanisms at the origin of elastic turbulence do not rely on the boundary conditions or on the geometry of the mean flow.Comment: 6 pages; 8 figure