Gradient-based Monte Carlo methods for relaxation approximations of hyperbolic conservation laws

Giulia Bertaglia, Lorenzo Pareschi, Russel E. Caflisch (preprint arXiv:2308.02904)

Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes, inspired by vortex methods for the Navier--Stokes equations. Such methods, referred to as gradient random walk methods, were extensively studied in the '90s and have several interesting features, such as being grid free, automatically adapting to the solution by concentrating elements where the gradient is large and significantly reducing the variance of the standard random walk approach. In this work, we revive these ideas by showing how to generalize the approach to a larger class of partial differential equations, including hyperbolic systems of conservation laws.

Particle simulation methods for the Landau-Fokker-Planck equation with uncertain data

Andrea Medaglia, Lorenzo Pareschi, Mattia Zanella (preprint arXiv:2306.07701)

The design of particle simulation methods for collisional plasma physics has always represented a challenge due to the unbounded total collisional cross section, which prevents a natural extension of the classical Direct Simulation Monte Carlo (DSMC) method devised for the Boltzmann equation. One way to overcome this problem is to consider the design of Monte Carlo algorithms that are robust in the so-called grazing collision limit. In the first part of this manuscript, we will focus on the construction of collision algorithms for the Landau-Fokker-Planck equation based on the grazing collision asymptotics and which avoids the use of iterative solvers.

Multiscale constitutive framework of 1D blood flow modeling: asymptotic limits and numerical methods

Giulia Bertaglia, Lorenzo Pareschi (SIAM Multiscale Modeling and Simulation to appear. Preprint arXiv:2302.09374)

In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is presented and discussed. By analyzing the asymptotic limits of the proposed model, it is shown that different types of blood propagation phenomena in arteries and veins can be described through an appropriate choice of scaling parameters, which are related to distinct characterizations of the fluid-structure interaction mechanism (whether elastic or viscoelastic) that exist between vessel walls and blood flow. In these asymptotic limits, well-known blood flow models from the literature are recovered. Additionally, by analyzing the perturbation of the local elastic equilibrium of the system, a new viscoelastic blood flow model is derived.

Modeling opinion polarization on social media: application to Covid-19 vaccination hesitancy in Italy

Jonathan Franceschi, Lorenzo Pareschi, Elena Bellodi, Marco Gavanelli, Marco Bresadola (PLOS One to appear. Preprint arXiv:2302.01028)

The SARS-CoV-2 pandemic reminded us how vaccination can be a divisive topic on which the public conversation is permeated by misleading claims, and thoughts tend to polarize, especially on online social networks. In this work, motivated by recent natural language processing techniques to systematically extract and quantify opinions from text messages, we present a differential framework for bivariate opinion formation dynamics that is coupled with a compartmental model for fake news dissemination.

Consensus based optimization with memory effects: random selection and applications

 Giacomo Borghi, Sara Grassi, Lorenzo Pareschi (Chaos, Solitons and Fractals to appear. Preprint arXiv:2301.13242)

In this work we extend the class of Consensus-Based Optimization (CBO) metaheuristic methods by considering memory effects and a random selection strategy. The proposed algorithm iteratively updates a population of particles according to a consensus dynamics inspired by social interactions among individuals. The consensus point is computed taking into account the past positions of all particles. While sharing features with the popular Particle Swarm Optimization (PSO) method, the exploratory behavior is fundamentally different and allows better control over the convergence of the particle system.