arXiv subjects
Publications and source records attributed to Sauro Succi.
We outline the main ideas behind the numerical modelling of soft-flowing crystals, with special attention to their application to microfluidic devices for the design of novel mesoscale porous materials.
We present a general framework for constructing trans-scale \emph{discrete Boltzmann models} (DBMs) for high-speed compressible flows ranging from continuum to transition regime. This is achieved by designing a higher-order discrete equilibrium distribution function which satisfies additional nonhydrodynamic kinetic moments. In order to characterize the \emph{% thermodynamic non-equilibrium} (TNE) effects and estimate the condition under which the DBMs at various levels should be used, two novel measures are presented: (i) the relative TNE strength, describing the relative strength of the ($N+1$)-th order TNE effects to the $N$-th order one; (ii) the TNE discrepancy between DBM simulation and relevant theoretical analysis. Whether or not the higher-order TNE effects should be taken into account in the modeling and which level of DBM should be adopted, is best described by the relative TNE intensity and/or the discrepancy, rather than by the value of the Knudsen number. As a model example, a two-dimensional DBM with $26$ discrete velocities at Burnett level is formulated, verified, and validated.
In this paper, we deploy a Lattice Boltzmann - Particle Dynamics (LBPD) method to dissect the transport properties within arterioles and venules. First, the numerical approach is applied to study the transport of Red Blood Cells (RBC) through plasma and validated by means of comparison with the experimental data in the seminal work by Fåhræus and Lindqvist. Then, the presence of micro-scale, soft spheres within the blood flow is considered: the evolution in time of the position of such spheres is studied, in order to highlight the presence of possible \textit{margination} effects. The results of the simulations and the evaluation of the computational eff
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.
We investigate the effects of nanoparticles on the onset of varicose and whipping instabilities in the dynamics of electrified jets. In particular, we show that the non-linear interplay between the mass of the nanoparticles and electrostatic instabilities, gives rise to qualitative changes of the dynamic morphology of the jet, which in turn, drastically affect the final deposition pattern in electrospinning experiments. It is also shown that even a tiny amount of excess mass, of the order of a few percent, may more than double the radius of the electrospun fiber, with substantial implications for the design of experiments involving electrified jets as well as spun organic fibers.
Electrospinning is a nanotechnology process whereby an external electric field is used to accelerate and stretch a charged polymer jet, so as to produce fibers with nanoscale diameters. In quest of a further reduction in the cross section of electrified jets hence of a better control on the morphology of the resulting electrospun fibers, we explore the effects of an external rotating electric field orthogonal to the jet direction. Through extensive particle simulations, it is shown that by a proper tuning of the electric field amplitude and frequency, a reduction of up to a $30 \%$ in the aforementioned radius can be obtained, thereby opening new perspectives in the design of future ultra-thin electrospun fibres. Applications can be envisaged in the fields of nanophotonic components as well as for designing new and improved filtration materials.
We study the time evolution of quenched random-mass Dirac fermions in one dimension by quantum lattice Boltzmann simulations. For nonzero noise strength, the diffusion of an initial wave packet stops after a finite time interval, reminiscent of Anderson localization. However, instead of exponential localization we find algebraically decaying tails in the disorder-averaged density distribution. These qualitatively match $\propto x^{-3/2}$ decay, which has been predicted by analytic calculations based on zero-energy solutions of the Dirac equation.
The dynamics of thermally fluctuating conserved order parameters are described by stochastic conservation laws. Thermal equilibrium in such systems requires the dissipative and stochastic components of the flux to be related by detailed balance. Preserving this relation in spatial and temporal discretization is necessary to obtain solutions that have fidelity to the continuum. Here, we propose a finite-difference discretization that preserves detailed balance on the lattice, has spatial error that is isotropic to leading order in lattice spacing, and can be integrated accurately in time using a delayed difference method. We benchmark the method for model B dynamics with a $ϕ^{4}$ Landau free energy and obtain excellent agreement with analytical results.
We use highly resolved numerical simulations to study turbulent Rayleigh-Bénard convection in a cell with sinusoidally rough upper and lower surfaces in two dimensions for $Pr = 1$ and $Ra = \left[4 \times 10^6, 3 \times 10^9\right]$. By varying the wavelength $λ$ at a fixed amplitude, we find an optimal wavelength $λ_{\text{opt}}$ for which the Nusselt-Rayleigh scaling relation is $\left(Nu-1 \propto Ra^{0.483}\right)$ maximizing the heat flux. This is consistent with the upper bound of Goluskin and Doering \cite{Goluskin:2016} who prove that $Nu$ can grow no faster than ${\cal O} (Ra^{1/2})$ as $Ra \rightarrow \infty$, and thus the concept that roughness facilitates the attainment of the so-called ultimate regime. Our data nearly achieve the largest growth rate permitted by the bound. When $λ\ll λ_{\text{opt}}$ and $λ\gg λ_{\text{opt}}$, the planar case is recovered, demonstrating how controlling the wall geometry manipulates the interaction between the boundary layers and the core flow. Finally, for each $Ra$ we choose the maximum $Nu$ among all $λ$, and thus optimizing over all $λ$, to find $Nu_{\text{opt}} - 1 = 0.01 \times Ra^{0.444}$.
We present quantum Lattice Boltzmann simulations of the Dirac equation for quantum-relativistic particles with random mass. By choosing zero-average random mass fluctuation, the simulations show evidence of localization and ultra-slow Sinai diffusion, due to the interference of oppositely propagating branches of the quantum wavefunction which result from random sign changes of the mass around a zero-mean. The present results indicate that the quantum lattice Boltzmann scheme may offer a viable tool for the numerical simulation of quantum-relativistic transport phenomena in topological materials.
We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte-Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N^6, where N is the resolution per linear phase-space dimension). However, we describe a new technique for achieving N^4 scaling. The method offers promise for investigating the full 6D phase-space of collisionless systems of stars and dark matter.
We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the non-linear Schrodinger equation in the Madelung formulation. The probability density of the wavefunction is discretized into moving particles, whose properties are smoothed by a kernel function. The traditional fluid pressure is replaced by a quantum pressure tensor, for which a novel, robust discretization is found. We demonstrate our numerical method on a variety of numerical test problems involving the simple harmonic oscillator, Bose-Einstein condensates, collapsing singularities, and dark matter halos governed by the Gross-Pitaevskii-Poisson equation. Our method is conservative, applicable to unbounded domains, and is automatically adaptive in its resolution, making it well suited to study problems with collapsing solutions.
The development of high-efficiency porous catalyst membranes critically depends on our understanding of where the majority of the chemical conversions occur within the porous structure. This requires mapping of chemical reactions and mass transport inside the complex nano-scale architecture of porous catalyst membranes which is a multiscale problem in both the temporal and spatial domain. To address this problem, we developed a multi-scale mass transport computational framework based on the Lattice Boltzmann Method (LBM) that allows us to account for catalytic reactions at the gas-solid interface by introducing a new boundary condition. In good agreement with experiments, the simulations reveal that most catalytic reactions occur near the gas-flow facing side of the catalyst membrane if chemical reactions are fast compared to mass transport within the porous catalyst membrane.
Nowadays, several models of unidimensional fluid jets exploit discrete element methods. In some cases, as for models aiming at describing the electrospinning nanofabrication process of polymer fibers, discrete element methods suffer a non constant resolution of the jet representation. We develop a dynamic mesh-refinement method for the numerical study of the electro-hydrodynamic behavior of charged jets using discrete element methods. To this purpose, we import ideas and techniques from the string method originally developed in the framework of free-energy landscape simulations. The mesh-refined discrete element method is demonstrated for the case of electrospinning applications.
We discuss a unified mesoscale framework for the simulation of complex states of flowing matter across scales of motion which requires no explicit coupling between different macro-meso-micro levels. The idea is illustrated through selected examples of complex flows at the micro and nanoscale.
Growth in static and controlled environments such as a Petri dish can be used to study the spatial population dynamics of microorganisms. However, natural populations such as marine microbes experience fluid advection and often grow up in heterogeneous environments. We investigate a generalized Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation describing single species population subject to a constant flow field and quenched random spatially inhomogeneous growth rates with a fertile overall growth condition. We analytically and numerically demonstrate that the non-equilibrium steady-state population density develops a flow-driven striation pattern. The striations are highly asymmetric with a longitudinal correlation length that diverges linearly with the flow speed and a transverse correlation length that approaches a finite velocity-independent value. Linear response theory is developed to study the statistics of the steady states. Theoretical predictions show excellent agreement with the numerical steady states of the generalized FKPP equation obtained from Lattice Boltzmann simulations. These findings suggest that, although the growth disorder can be spatially uncorrelated, correlated population structures with striations emerge naturally at sufficiently strong advection.
We study the effects of a controlled gas flow on the dynamics of electrified jets in the electrospinning process. The main idea is to model the air drag effects of the gas flow by using a non-linear Langevin-like approach. The model is employed to investigate the dynamics of electrified polymer jets at different conditions of air drag force, showing that a controlled gas counterflow can lead to a decrease of the average diameter of electrospun fibers, and potentially to an improvement of the quality of electrospun products. We probe the influence of air drag effects on the bending instabilities of the jet and on its angular fluctuations during the process. The insights provided by this study might prove useful for the design of future electrospinning experiments and polymer nanofiber materials.
The effects of compressibility on Rayleigh-Taylor instability (RTI) are investigated by inspecting the interplay between thermodynamic and hydrodynamic non-equilibrium phenomena (TNE, HNE, respectively) via a discrete Boltzmann model (DBM). Two effective approaches are presented, one tracking the evolution of the \emph{local} TNE effects and the other focussing on the evolution of the mean temperature of the fluid, to track the complex interfaces separating the bubble and the spike regions of the flow. It is found that, both the compressibility effects and the \emph{global} TNE intensity show opposite trends in the initial and the later stages of the RTI. Compressibility delays the initial stage of RTI and accelerates the later stage. Meanwhile, the TNE characteristics are generally enhanced by the compressibility, especially in the later stage. The global or mean thermodynamic non-equilibrium indicators provide physical criteria to discriminate between the two stages of the RTI.