Saturday, February 18, 2023

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.

Thursday, February 2, 2023

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

Jonathan Franceschi, Lorenzo Pareschi, Elena Bellodi, Marco Gavanelli, Marco Bresadola (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.

Tuesday, January 31, 2023

Consensus based optimization with memory effects: random selection and applications

 Giacomo Borghi, Sara Grassi, Lorenzo Pareschi (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.

Wednesday, November 30, 2022

The kinetic theory of mutation rates


Lorenzo Pareschi, Giuseppe Toscani (Axioms 12(3), 265, 2023)

The Luria-Delbrück mutation model is a cornerstone of evolution theory and has been mathematically formulated in a number of ways. In this paper we illustrate how this model of mutation rates can be derived by means of classical statistical mechanics tools, in particular by modeling the phenomenon resorting to methodologies borrowed from classical kinetic theory of rarefied gases. The aim is to construct a linear kinetic model that can reproduce the Luria-Delbrück distribution starting from the elementary interactions that qualitatively and quantitatively describe the variation of mutated cells.

Monday, October 31, 2022

Global high-order numerical schemes for the time evolution of the general relativistic radiation magneto-hydrodynamics equations

Manuel R. Izquierdo, Lorenzo Pareschi, Borja Miñano, Joan Massó, Carlos Palenzuela (Classical and Quantum Gravity to appear. Preprint arXiv:2211.00027)

Modeling correctly the transport of neutrinos is crucial in some astrophysical scenarios such as core-collapse supernovae and binary neutron star mergers. In this paper, we focus on the truncated-moment formalism, considering only the first two moments (M1 scheme) within the grey approximation, which reduces Boltzmann seven-dimensional equation to a system of 3+1 equations closely resembling the hydrodynamic ones. Solving the M1 scheme is still mathematically challenging, since it is necessary to model the radiation-matter interaction in regimes where the evolution equations become stiff and behave as an advection-diffusion problem.