arXiv subjects

Nicola Bellomo

Publications and source records attributed to Nicola Bellomo.

45 records · Page 3Linked to original sources

arXiv2017

Hiding neutrino mass in modified gravity cosmologies

Cosmological observables show a dependence with the neutrino mass, which is partially degenerate with parameters of extended models of gravity. We study and explore this degeneracy in Horndeski generalized scalar-tensor theories of gravity. Using forecasted cosmic microwave background and galaxy power spectrum datasets, we find that a single parameter in the linear regime of the effective theory dominates the correlation with the total neutrino mass. For any given mass, a particular value of this parameter approximately cancels the power suppression due to the neutrino mass at a given redshift. The extent of the cancellation of this degeneracy depends on the cosmological large-scale structure data used at different redshifts. We constrain the parameters and functions of the effective gravity theory and determine the influence of gravity on the determination of the neutrino mass from present and future surveys.

astro-ph.CO↗

arXiv2016

A degenerate chemotaxis system with flux limitation: Finite-time blow-up

This paper is concerned with radially symmetric solutions of the parabolic-elliptic version of the Keller-Segel system with flux limitation, as given by \begin{equation} \left\{ \begin{array}{l} \displaystyle u_t=\nabla \cdot \Big(\frac{u\nabla u}{\sqrt{u^2+|\nabla u|^2}}\Big) - χ\, \nabla \cdot \Big(\frac{u\nabla v}{\sqrt{1+|\nabla v|^2}}\Big), \\[1mm] 0=Δv - μ+ u, \end{array} \right. \qquad \qquad (\star) \end{equation} under the initial condition $u|_{t=0}=u_0>0$ and no-flux boundary conditions in a ball $Ω\subset R^n$, where $χ>0$ and $μ:=\frac{1}{|Ω|} \int_Ωu_0$. A previous result [3] has asserted global existence of bounded classical solutions for arbitrary positive radial initial data $u_0\in C^3(\barΩ)$ when either $n\ge 2$ and $χ<1$, or $n=1$ and $ \int_Ωu_0<\frac{1}{\sqrt{(χ^2-1)_+}}$. This present paper shows that these conditions are essentially optimal: Indeed, it is shown that if the taxis coefficient is large enough in the sense that $χ>1$, then for any choice of \begin{equation} \left\{ \begin{array}{ll} m>\frac{1}{\sqrt{χ^2-1}} \quad & \mbox{if } n=1, \\[2mm] m>0 \mbox{ is arbitrary } \quad & \mbox{if } n\ge 2, \end{array} \right. \end{equation} there exist positive initial data $u_0\in C^3(\barΩ)$ satisfying $ \int_Ωu_0=m$ which are such that for some $T>0$, ($\star$) possesses a uniquely determined classical solution $(u,v)$ in $Ω\times (0,T)$ blowing up at time $T$ in the sense that $\limsup_{t\nearrow T} \|u(\cdot,t)\|_{L^\infty(Ω)}=\infty$.\abs This result is derived by means of a comparison argument applied to the doubly degenerate scalar parabolic equation satisfied by the mass accumulation function associated with ($\star$).

math.AP↗

arXiv2016

A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up

This paper aims at providing a first step toward a qualitative theory for a new class of chemotaxis models derived from the celebrated Keller-Segel system, with the main novelty being that diffusion is nonlinear with flux delimiter features. More precisely, as a prototypical representative of this class we study radially symmetric solutions of the parabolic-elliptic system (see the text). Under the initial condition $u|_{t=0}=u_0>0$ and no-flux boundary conditions in balls $Ω\subset\mathbb{R}^n$, where $χ>0$ and $μ:=\frac{1}{|Ω|} \int_Ωu_0$.\abs The main results assert the existence of a unique classical solution, extensible in time up to a maximal $T_{max} \in (0,\infty]$ which has the property that $$\mbox{if} \quad T_{max}<\infty \quad \mbox{then} \quad\limsup_{t\nearrow T_{max}} \|u(\cdot,t)\|_{L^\infty(Ω)}=\infty. \qquad \qquad (\star)$$ The proof therefore is mainly based on comparison methods, which firstly relate pointwise lower and upper bounds for the spatial gradient $u_r$ to $L^\infty$ bounds for $u$ and to {\em upper bounds} for $z:=\frac{u_t}{u}$; secondly, another comparison argument involving nonlocal nonlinearities provides an appropriate control of $z_+$ in terms of bounds for $u$ and $|u_r|$, with suitably mild dependence on the latter. As a consequence of ($\star$) by means of suitable a priori estimates it is moreover shown that the above solutions are global and bounded when either $$n\ge 2 \ \mbox{ and } χ<1, \qquad \mbox{or} \qquad n=1, \ χ>0 \ \mbox{ and } m 1$ and $m_c:=\infty$ if $χ\le 1$. That these conditions are essentially optimal will be shown in a forthcoming paper in which ($\star$) will be used to derive complementary results on the occurrence of solutions blowing up in finite time with respect to the norm of $u$ in $L^\infty(Ω)$.

math.AP↗

arXiv2015

Stochastic Evolving Differential Games Toward a Systems Theory of Behavioral Social Dynamics

This paper proposes a systems approach to social sciences based on mathematical framework derived from a generalization of the mathematical kinetic theory and on theoretical tools of game theory. Social systems are modeled as a living evolutionary ensemble composed by many individuals, who express specific strategies, cooperate, compete and might aggregate into groups which pursue a common interest. A critical analysis on the complexity features of social system is developed and a differential structure is derived to provide a general framework toward modeling.

physics.soc-ph↗

arXiv2015

First Order Models of Human Crowds with Behavioral-Social Dynamics

This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional process by which walking individuals select their velocity direction. Crowd heterogeneity is modeled by dividing the whole system into subsystems identified by different features. The passage from one subsystem to the other is induced by interactions. It is shown how heterogeneous individual behaviors can modify the collective dynamics, as well as how local unusual behaviors can propagate in the crowd. The paper also proposes a system approach to the modeling of the dynamics in complex venues, where individuals move through areas with different features.

physics.soc-ph↗

arXiv2014

Toward a Mathematical Theory of Behavioral-Social Dynamics for Pedestrian Crowds

This paper presents a new approach to behavioral-social dynamics of pedestrian crowds by suitable development of methods of the kinetic theory. It is shown how heterogeneous individual behaviors can modify the collective dynamics, as well as how local unusual behaviors can propagate in the crowd. The main feature of this approach is a detailed analysis of the interactions between dynamics and social behaviors.

physics.soc-ph↗

arXiv2014

Superfluid hydrodynamics of polytropic gases:dimensional reduction and sound velocity

Motivated by the fact that two-component confined fermionic gases in Bardeen-Cooper-Schrieffer-Bose-Einstein condensate (BCS-BEC) crossover can be described through an hydrodynamical approach, we study these systems - both in the cigar-shaped configuration and in the disk-shaped one - by using a polytropic Lagrangian density. We start from the Popov Lagrangian density and obtain, after a dimensional reduction process, the equations that control the dynamics of such systems. By solving these equations we study the sound velocity as a function of the density by analyzing how the dimensionality affects this velocity

math-ph↗

arXiv2013

From the Micro-scale to Collective Crowd Dynamics

This paper deals with the kinetic theory modeling of crowd dynamics with the aim of showing how the dynamics at the micro-scale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a qualitative analysis of the initial value problem. Existence of solutions is proved for arbitrary large times, while simulations are developed by computational schemes based on splitting methods, where the transport equations treated by finite difference methods for hyperbolic equations. Some preliminary reasonings toward the modeling of panic conditions are proposed.

math-ph↗

arXiv2012

On the dynamics of social conflicts: looking for the Black Swan

This paper deals with the modeling of social competition, possibly resulting in the onset of extreme conflicts. More precisely, we discuss models describing the interplay between individual competition for wealth distribution that, when coupled with political stances coming from support or opposition to a government, may give rise to strongly self-enhanced effects. The latter may be thought of as the early stages of massive, unpredictable events known as Black Swans, although no analysis of any fully-developed Black Swan is provided here. Our approach makes use of the framework of the kinetic theory for active particles, where nonlinear interactions among subjects are modeled according to game-theoretical tools.

math-ph↗