arXiv subjects

N. Loy

Publications and source records attributed to N. Loy.

3 recordsLinked to original sources

arXiv2024

Asymptotic and stability analysis of kinetic models for opinion formation on networks: an Allen-Cahn approach

We present the analysis of the stationary equilibria and their stability in case of an opinion formation process in presence of binary opposite opinions evolving according to majority-like rules on social networks. The starting point is a kinetic Boltzmann-type model derived from microscopic interactions rules for the opinion exchange among individuals holding a certain degree of connectivity. The key idea is to derive from the kinetic model an Allen-Cahn type equation for the fraction of individuals holding one of the two opinions. The latter can be studied by means of a linear stability analysis and by exploiting integral operator analysis. While this is true for ternary interactions, for binary interactions the derived equation of interest is a linear scattering equation, that can be studied by means of General Relative Entropy tools and integral operators.

physics.soc-ph↗

arXiv2021

Structure preserving schemes for Fokker-Planck equations with nonconstant diffusion matrices

In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker-Planck-type equations to the case of nonconstant full diffusion matrices. While in existing works the schemes are formulated in a one-dimensional setting, here we consider exclusively the two-dimensional case. We prove that the proposed schemes preserve fundamental structural properties like nonnegativity of the solution without restriction on the size of the mesh and entropy dissipation. Moreover, all the methods presented here are at least second order accurate in the transient regimes and arbitrarily high order for large times in the hypothesis in which the flux vanishes at the stationary state. Suitable numerical tests will confirm the theoretical results.

math.NA↗

arXiv2020

Multi-cue kinetic model with non-local sensing for cell migration on a fibers network with chemotaxis

Cells perform directed motion in response to external stimuli that they detect by sensing the environment with their membrane protrusions. In particular, several biochemical and biophysical cues give rise to tactic migration in the direction of their specific targets. This defines a multi-cue environment in which cells have to sort and combine different, and potentially competitive, stimuli. We propose a non-local kinetic model for cell migration in presence of two external factors both influencing cell polarization: contact guidance and chemotaxis. We propose two different sensing strategies and we analyze the two resulting models by recovering the appropriate macroscopic limit in different regimes, in order to see how the size of the cell, with respect to the variation of both external fields, influences the overall behavior. Moreover, we integrate numerically the kinetic transport equation in a two-dimensional setting in order to investigate qualitatively various scenarios.

q-bio.CB↗