Search results for " Fisica Matematica"
showing 10 items of 384 documents
From classical to operatorial models
2023
Mathematical models for the collective dynamics of interacting and spatially distributed populations find applications in several contexts (biology, ecology, social sciences). Their formulation depends primarily on the (continuous or discrete) description of the space. Reaction-diffusion equations have been widely used in bioecology (morphogenesis, migration of biological species, tumor growth, neuro-degenerative diseases) and in the social sciences (diffusion of opinions or decisionmaking processes), and exhibit complex behaviors (propagation of oscillatory phenomena, pattern formation caused by instability). A reaction–diffusion system exhibits diffusion-driven instability, sometimes call…
Pattern formation and transition to chaos in a chemotaxis model of acute inflammation
2021
We investigate a reaction-diffusion-chemotaxis system that describes the immune response during an inflammatory attack. The model is a modification of the system proposed in Penner, Ermentrout, and Swigon [SIAM J. Appl. Dyn. Syst., 11 (2012), pp. 629-660]. We introduce a logistic term in the immune cell dynamics to reproduce the macrophages' activation, allowing us to describe the disease evolution from the early stages to the acute phase. We focus on the appearance of pattern solutions and their stability. We discover steady-state (Turing) and wave instabilities and classify the bifurcations deriving the corresponding amplitude equations. We study stationary radially symmetric solutions an…
Cross-diffusion effects on stationary pattern formation in the FitzHugh-Nagumo model
2022
<p style='text-indent:20px;'>We investigate the formation of stationary patterns in the FitzHugh-Nagumo reaction-diffusion system with linear cross-diffusion terms. We focus our analysis on the effects of cross-diffusion on the Turing mechanism. Linear stability analysis indicates that positive values of the inhibitor cross-diffusion enlarge the region in the parameter space where a Turing instability is excited. A sufficiently large cross-diffusion coefficient of the inhibitor removes the requirement imposed by the classical Turing mechanism that the inhibitor must diffuse faster than the activator. In an extended region of the parameter space a new phenomenon occurs, namely the exis…
High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex
2013
Abstract We compute the solutions of Prandtl’s and Navier–Stokes equations for the two dimensional flow induced by a rectilinear vortex interacting with a boundary in the half plane. For this initial datum Prandtl’s equation develops, in a finite time, a separation singularity. We investigate the different stages of unsteady separation for Navier–Stokes solution at different Reynolds numbers Re = 103–105, and we show the presence of a large-scale interaction between the viscous boundary layer and the inviscid outer flow. We also see a subsequent stage, characterized by the presence of a small-scale interaction, which is visible only for moderate-high Re numbers Re = 104–105. We also investi…
On critical behaviour in generalized Kadomtsev-Petviashvili equations
2016
International audience; An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev–Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is given in terms of a special solution to an ordinary differential equation of the Painlevé I hierarchy. Several examples are discussed numerically to provide strong evidence for the validity of the conjecture. The numerical study of the long time behaviour of these examples indicates persistence of dispersive shock waves in solutions to the (subcritical) KP equations, while in the supercritical KP equations a blow-up occurs after the formation of the disp…
Fixed Points in Topological *-Algebras of Unbounded Operators
2001
We discuss some results concerning fixed point equations in the setting of topological *-algebras of unbounded operators. In particular, an existence result is obtained for what we have called {\em weak $\tau$ strict contractions}, and some continuity properties of these maps are discussed. We also discuss possible applications of our procedure to quantum mechanical systems.
Lp-Spaces as Quasi *-Algebras
1996
Abstract The Banach space L p ( X , μ), for X a compact Hausdorff measure space, is considered as a special kind of quasi *-algebra (called CQ*-algebra) over the C*-algebra C ( X ) of continuous functions on X . It is shown that, for p ≥2, ( L p ( X , μ), C ( X )) is *-semisimple (in a generalized sense). Some consequences of this fact are derived.
Representable linear functionals on partial *-algebras
2012
A GNS-like *-representation of a partial *-algebra \({{\mathfrak A}}\) defined by certain representable linear functionals on \({{\mathfrak A}}\) is constructed. The study of the interplay with the GNS construction associated with invariant positive sesquilinear forms (ips) leads to the notions of pre-core and of singular form. It is shown that a positive sesquilinear form with pre-core always decomposes into the sum of an ips form and a singular one.
Periodic and quasi-periodic orbits of the dissipative standard map
2011
We present analytical and numerical investigations of the dynamics of the dissipative standard map. We first study the existence of periodic orbits by using a constructive version of the implicit function theorem; then, we introduce a parametric representation, which provides the interval of the drift parameter ensuring the existence of a periodic orbit with a given period. The determination of quasi--periodic attractors is efficiently obtained using the parametric representation combined with a Newton's procedure, aimed to reduce the error of the approximate solution provided by the parametric representation. These methods allow us to relate the drift parameter of the periodic orbits to th…
On the co-orbital asteroids in the solar system: medium-term timescale analysis of the quasi-coplanar objects
2023
The focus of this work is the current distribution of asteroids in co-orbital motion with Venus, Earth and Jupiter, under a quasi-coplanar configuration and for a medium-term timescale of the order of 900 years. A co-orbital trajectory is a heliocentric orbit trapped in a 1:1 mean-motion resonance with a given planet. As such, to model it this work considers the Restricted Three-Body Problem in the planar circular case with the help of averaging techniques. The domain of each co-orbital regime, that is, the quasi-satellite motion, the horseshoe motion and the tadpole motion, can be neatly defined by means of an integrable model and a simple two-dimensional map, that is invariant with respec…