arXiv subjects

Lorenzo Fusi

Publications and source records attributed to Lorenzo Fusi.

4 recordsLinked to original sources

arXiv2026

Discrete versus continuous -- linear lattice models and their exact continuous counterparts

We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence problem for linear nearest neighbour interaction lattice models as well as for linear multiple-neighbour interaction lattice models, while we gradually proceed from infinite lattices to periodic lattices and finally to finite lattices with fixed ends/zero Dirichlet boundary conditions. The whole study is framed as a systematic specialisation of Fourier analysis tools from the continuous to the discrete setting and vice versa, and the correspondence between the discrete and continuous models is examined primarily with regard to the dispersion relation.

physics.class-ph↗

arXiv2025

Linearized instability of Couette flow in stress-power law fluids

This paper examines the linearized stability of plane Couette flow for stress-power law fluids, which exhibit non-monotonic stress-strain rate behavior. The constitutive model is derived from a thermodynamic framework using a non-convex rate of dissipation potential. Under velocity boundary conditions, the system may admit three steady-state solutions. Linearized stability analysis reveals that the two solutions on ascending constitutive branches are unconditionally stable, while the solution on the descending branch is unconditionally unstable. For mixed traction-velocity boundary conditions, the base state is unique. Stability depends solely on whether the prescribed traction lies on an ascending (stable) or descending (unstable) branch of the constitutive curve. The results demonstrate that flow stability in these complex fluids is fundamentally governed by both boundary conditions and constitutive non-monotonicity.

physics.flu-dyn↗

arXiv2025

Viscoplastic flows in narrow channels: Herschel-Bulkley models versus its regularizations

We investigated the two-dimensional flows of a viscoplastic fluid in symmetric channels with impermeable walls under no-slip boundary conditions. As response functions for the Cauchy stress tensor of the viscoplastic fluid, we considered both the celebrated Herschel-Bulkley model and a very general class $\mathcal{C}$ of its regularizations that depend on a positive parameter with the same physical dimensions as the strain rate and known as the \emph{regularization parameter}. Within this class of regularized Herschel-Bulkley models, the response function for the viscosity of the viscoplastic fluid tends to the non-smooth Herschel-Bulkley viscosity function as the regularization parameter tends to zero. To make the equations governing the flow amenable to analysis, we considered channels with small aspect ratio so that the lubrication approximation can be used. In this way, we were able to obtain analytical solutions, perform an asymptotic analysis of the regularized solutions, and compare the results predicted by the Herschel-Bulkley model and its regularizations. We found that for any given channel, the regularized flows predicted by the regularizations in $\mathcal{C}$ tend to the same velocity field in the limit as the regularization parameter tends to zero. Such an asymptotic flow coincides with that predicted by the Herschel-Bulkley model only if the viscoplastic fluid flows in plane channels. Instead, in channels with curved walls, the results are markedly different.

physics.flu-dyn↗

arXiv2017

Mathematical model for acid water neutralization with anomalous and fast diffusion

In this paper we model the neutralization of an acid solution in which the hydrogen ions are transported according to Cattaneo's diffusion. The latter is a modification of classical Fickian diffusion in which the flux adjusts to the gradient with a positive relaxation time. Accordingly the evolution of the ions concentration is governed by the hyperbolic telegraph equation instead of the classical heat equation. We focus on the specific case of a marble slab reacting with a sulphuric acid solution and we consider a one-dimensional geometry. We show that the problem is multi-scale in time, with a reaction time scale that is larger than the diffusive time scale, so that the governing equation is reduced to the one-dimensional wave equation. The mathematical problem turns out to be a hyperbolic free boundary problem where the consumption of the slab is described by a nonlinear differential equation. Global well posedness is proved and some numerical simulations are provided.

physics.chem-ph↗