Volume di Comics&Science dedicato alle donne in matematica

Albo di Comics&Science dedicato alla fisica delle particelle in collaborazione con ISM e una storia di Zerocalcare

The dynamic behaviour of rigid blocks subjected to support excitation is represented by discontinuous differential equations with state jumps, which are not known in advance. In the numerical simulation of these systems, the jump times corresponding to the numerical trajectory do not coincide with the ones of the given problem. When multiple state jumps occur, this approximation may affect the accuracy of the solution and even cause an order reduction in the method. Focus here is on the stability and convergence properties of the numerical dynamic. The basic idea is to investigate how the error propagates in successive impacts by decomposing the numerical integration process of the overall system into a sequence of discretized perturbed problems.

We present an extension of recent relativistic Lattice Boltzmann methods based on Gaussian quadratures for the study of fluids in (2+1) dimensions. The new method is applied to the analysis of electron flow in graphene samples subject to electrostatic drive; we show that the flow displays hydro-electronic whirlpools in accordance with recent analytical calculations as well as experimental results.

We address the problem of forecasting sales for fresh and highly perishable products, in the general context of supply chain management. The forecasting activity refers to the single item in a given store and started from a pre-processing phase for data analysis and normalization. Then data was used as input for a forecasting algorithm designed to be user interactive. We implemented three forecasting methods: ARIMA, ARIMAX and transfer function models. The exogenous components of the forecasting models took the impact of prices into account. The best configuration of these models is dynamically chosen via two alternative methods: (i) a two-step procedure, based on properly selected statistical indicators, (ii) a Sequential Parameter Optimization approach for automatic parameter tuning. The user or the decision maker at the store level should not be exposed to the complexity of the forecasting system which - for this reason - is designed to adaptively select the best model configuration at every forecast session, to be used for each item/store combination. A set of real data based on 19 small and medium sized stores and 156 fresh products was employed to evaluate both quality of forecasting results and their effects on the order planning activity, where sales forecasting is considered as a proxy of the expected demand. Some examples are reported and discussed. Our results confirm that there is no 'one-size-fits-all' forecasting model, whose performance strictly depends on the specific characteristics of the underlying data. This supports the adoption of a data-driven tool to automate the dynamic selection of the most appropriate forecasting model. (C) 2017 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Il contributo della modellistica matematica/computazionale alla bioinformatica

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The angle of directional change of tracer trajectories in rotating Rayleigh-Benard convection is studied as a function of the time increment tau between two instants of time along the trajectories, both experimentally and with direct numerical simulations. Our aim is to explore the geometrical characterization of flow structures in turbulent convection in a wide range of timescales and how it is affected by background rotation. We find that probability density functions (PDFs) of the angle of directional change theta(t, tau) show similar behavior as found in homogeneous isotropic turbulence, up to the timescale of the large-scale coherent flow structures. The scaling of the averaged (over particles and time) angle of directional change Theta(tau) = <vertical bar theta(t, tau)vertical bar > with tau shows a transition from the ballistic regime Theta(tau) similar to tau(c) with c = 1] for tau less than or similar to tau(n), with tau(n) the Kolmogorov timescale, to a scaling with smaller exponent c for tau(n) less than or similar to tau less than or similar to T-L, with T-L the Lagrangian integral timescale. This scaling exponent is approximately constant in the weakly rotating regime (Rossby number Ro greater than or similar to 2.5) and is decreasing for increasing rotation rates when Ro less than or similar to 2.5. We show that this trend in the scaling exponent is related with the large-scale coherent structures in the flow; the large-scale circulation for Ro greater than or similar to 2.5 and vertically aligned vortices emerging from the boundary layers (BLs) near the top and bottom plates and penetrating into the bulk for Ro less than or similar to 2.5. In the viscous BLs, the PDFs of theta(t, tau) and scaling properties of Theta (tau) are in general different from those measured in the bulk and depend on the type of boundary layer, in particular whether the BL is of Prandtl-Blasius type (Ro greater than or similar to 2.5) or of Ekman type (Ro less than or similar to 2.5). When it is of Ekman type, a stronger dynamic coupling exists between the BL and the bulk of the flow, resulting in similar scaling exponents in BL and bulk.

Particle-laden turbulent flows occur in a variety of industrial applications as well as in naturally occurring flows. While the numerical simulation of such flows has seen significant advances in recent years, it still remains a challenging problem. Many studies investigated the rheology of dense suspensions in laminar flows as well as the dynamics of point-particles in turbulence. Here we employ a fully-resolved numerical simulation based on a lattice Boltzmann scheme, to investigate turbulent flow with large neutrally buoyant particles in a pipe flow at low Reynolds number and in dilute regimes. The energy input is kept fixed resulting in a Reynolds number based on the friction velocity around 250. Two different particle radii were used giving a particle-pipe diameter ratio of 0.05 and 0.075. The number of particles is kept constant resulting in a volume fraction of 0.54% and 1.83%, respectively. We investigated Eulerian and Lagrangian statistics along with the stresslet exerted by the fluid on the spherical particles. It was observed that the high particle-to-fluid slip velocity close to the wall corresponds locally to events of high energy dissipation, which are not present in the single-phase flow. The migration of particles from the inner to the outer region of the pipe, the dependence of the stresslet on the particle radial positions and a proxy for the fragmentation rate of the particles computed using the stresslet have been investigated.

Particle laden turbulent flows occur in a variety of industrial applications. While the numerical simulation of such flows has seen significant advances in recent years, it still remains a challenging problem. Many studies investigated the rheology of dense suspensions in laminar flows as well as the dynamics of point-particles in turbulence. Here we will present results on the development of numerical algorithms, based on the lattice Boltzmann method, suitable for the study of suspensions of finite-size particles under turbulent flow conditions. The turbulent flow is modeled by the lattice Boltzmann method, and the interaction between particles and carrier fluid is modeled using the bounce-back rule. Direct contact and lubrication force models for particle-particle interactions and particle-wall interaction are taken into account to allow for a full four-way coupled interaction. The accuracy and robustness of the method is discussed by validating the velocity profile in turbulent pipe flow, the sedimentation velocity of spheres in duct flow and the resistance functions of approaching particles. Preliminary results from the turbulent pipe flow simulations with particles show that the angular and axial velocities of the particles are scattered around values of mean axial velocity and shear rate obtained from the Eulerian velocity field.

We study the deformation and dynamics of droplets in time-dependent flows using 3D numerical simulations of two immiscible fluids based on the lattice Boltzmann model (LBM). Analytical models are available in the literature, which assume the droplet shape to be an ellipsoid at all times (P.L. Maffettone, M. Minale, J. Non-Newton. Fluid Mech 78, 227 (1998); M. Minale, Rheol. Acta 47, 667 (2008)). Beyond the practical importance of using a mesoscale simulation to assess "ab initio" the robustness and limitations of such theoretical models, our simulations are also key to discuss-in controlled situations-some relevant phenomenology related to the interplay between the flow time scales and the droplet time scales regarding the "transparency" transition for high enough shear frequencies for an external oscillating flow. This work may be regarded as a step forward to discuss extensions towards a novel DNS approach, describing the mesoscale physics of small droplets subjected to a generic hydrodynamical strain field, possibly mimicking the effect of a realistic turbulent flow on dilute droplet suspensions.

Anisotropic particles are present in many natural and industrial flows. Here we perform direct numerical simulation (DNS) of turbulent pipe flows with dispersed finite-size prolate spheroids simulated by means of the lattice Boltzmann method (LBM). We consider three different particle shapes: spheroidal (aspect ratio 2 and 3) and spherical. These three simulations are complemented with a reference simulation of a single-phase flow. For the sake of comparison, all simulations, laden or unladen have the same energy input. The flow geometry used is a straight pipe with length eight times its radius where the fluid is randomly seeded with 256 finite-size particles. The volume fraction of particles in the flow has been kept fixed at 0.48% by varying the major and minor axis of each particle such that their volume remains the same. We studied the effect of different particle shapes on particle dynamics and orientation, as well as on the flow modulation. We show that the local accumulation of spheres close to the wall decreases for spheroids with increasing aspect ratio. These spheroidal particles rotate slower than spheres near to the wall and tend to stay with their major axes aligned to the flow streamwise direction. Despite the lower rotation rates, a higher intermittency in the rotational rates was observed for spheroids and this increase at increasing the aspect ratio. The drag reduction observed for particles with higher aspect ratio have also been investigated using the one-dimensional energy and dissipation spectra. These results point to the relevance of particle shapes on their dynamics and their influence on the turbulent flow.

We study the effects of thermally induced capillary waves in the fragmentation of a liquid ligament into multiple nanodroplets. Our numerical implementation is based on a fluctuating lattice Boltzmann (LB) model for nonideal multicomponent fluids, including nonequilibrium stochastic fluxes mimicking the effects of molecular forces at the nano scales. We quantitatively analyze the statistical distribution of the breakup times and the droplet volumes after the fragmentation process at changing the two relevant length scales of the problem, i.e., the thermal length scale and the ligament size. The robustness of the observed findings is also corroborated by quantitative comparisons with the predictions of sharp interface hydrodynamics. Beyond the practical importance of our findings for nanofluidic engineering devices, our study also explores a novel application of LB in the realm of nanofluidic phenomena.

We present the results of a comparative study performed with three numerical methods applied to a flow in a three-dimensional geometry characterized by weak compressibility and large rarefaction effects. The employed methods, all based on the kinetic theory of gases, are the Lattice Boltzmann Method (LBM) in a regularized formulation, the Direct Simulation Monte Carlo (DSMC) approach and a hybrid method coupling the LBM and the DSMC recently developed by Di Staso et al., in this contribution extended to the case of simulations involving many particles and three-dimensional geometries. Owing to the common kinetic nature shared by the employed methods and to their implementation in a single code infrastructure, a detailed comparison of the results can be performed on a quantitative ground. The numerical results permit to determine, for the studied flow problem, the range of applicability in terms of a geometry-based Knudsen number for the present LBM formulation. The need to employ the hybrid method is justified by the very large computational cost of the DSMC simulation. Limitations of the current hybrid method formulation in treating thermal and large compressibility effects are underlined and possible strategies to overcome them are delineated. Finally, good scalability properties of the parallel algorithms, as well as the large computational cost reduction guaranteed by the hybrid method, while providing an accurate solution, are demonstrated. (C) 2018 Elsevier Ltd. All rights reserved.

The alpha-quartz polymorph of SiO2 forms the basis of mineral sands stable down to 100 km depths below the surface, making it of central geoscientific relevance. The characterization of the nanoscale properties of these materials is of importance, especially for elastic properties governing phonon and sound propagation, and is of very high industrial relevance for oil exploration. Here, for the first time, we apply non-equilibrium molecular dynamics simulation to analyze the propagation of an artificial velocity perturbation in silica systems and, in so doing, determine S- and P-wave velocities in a manner redolent of concept to seismic-based oil-exploration approaches. This propagation has been analyzed systematically by means of different metrics in terms of spatiotemporal system response; these produce consistent results, by and large. In particular, we find excellent quantitative agreement with experimental S- and P-wave velocities, in many cases.

Three-dimensional, time-dependent direct simulations of step emulsification microdevices highlight two essential mechanisms for droplet formation: first, the onset of an adverse pressure gradient driving a backflow of the continuous phase from the external reservoir to the microchannel, and second, the stnction of the flowing jet which leads to its subsequent rupture. It is also shown that such a rupture is delayed and eventually suppressed by increasing the flow speed of the dispersed phase within the channel, due to the stabilizing effect of dynamic pressure. This suggests a new criterion for dripping-jetting transition, based on local values of the capillary and Weber numbers.

We point out a formal analogy between lattice kinetic propagators and Haldane-Wu fractional statistics. The analogy could be used to compute the partition function of fractional quantum systems by solving a corresponding lattice kinetic equation for classical dissipative flowing syst erns. Copyright (C)EPLA, 2018

We present a regularized version of the color gradient lattice Boltzmann (LB) scheme for the simulation of droplet formation in microfluidic devices of experimental relevance. The regularized version is shown to provide computationally efficient access to capillary number regimes relevant to droplet generation via microfluidic devices, such as flow-focusers and the more recent microfluidic step emulsifier devices. (C) 2018 Elsevier Ltd. All rights reserved.

We present a new numerical model to simulate settling trajectories of discretized individual or a mixture of particles of different geometrical shapes in a quiescent fluid and their flow trajectories in a flowing fluid. Simulations unveiled diverse particle settling trajectories as a function of their geometrical shape and density. The effects of the surface concavity of a boomerang particle and aspect ratio of a rectangular particle on the periodicity and amplitude of oscillations in their settling trajectories were numerically captured. Use of surrogate circular particles for settling or flowing of a mixture of non-circular particles were shown to miscalculate particle velocities by a factor of 0.9-2.2 and inaccurately determine the particles' trajectories. In a microfluidic chamber with particles of different shapes and sizes, simulations showed that steady vortices do not necessarily always control particle entrapments, nor do larger particles get selectively and consistently entrapped in steady vortices. Strikingly, a change in the shape of large particles from circular to elliptical resulted in stronger entrapments of smaller circular particles, but enhanced outflows of larger particles, which could be an alternative microfluidics-based method for sorting and separation of particles of different sizes and shapes.

We simulate the two-dimensional fluid flow around National Advisory Committee for Aeronautics (NACA) 0012 airfoil using a hybrid lattice Boltzmann method (HLBM), which combines the standard lattice Boltzmann method with an unstructured finite-volume formulation. The aim of the study is to assess the numerical performances and the robustness of the computational method. To this purpose, after providing a convergence study to estimate the overall accuracy of the method, we analyze the numerical solution for different values of the angle of attack at a Reynolds number equal to 10(3). Subsequently, flow fields at Reynolds numbers up to 10(4) are computed for a zero angle of attack configuration. A grid refinement scheme is applied to the uniformly spaced component of the overlapping grid system to further enhance the numerical efficiency of the model. The results demonstrate the capability of the HLBM to achieve high accuracy near solid curved walls, thus providing a viable alternative in the realm of off-lattice Boltzmann methods based on body-fitted mesh. (C) 2018 Elsevier Ltd. All rights reserved.