Ricerc@Sapienza

The effects of assumptions about bunch properties on the accuracy of the measurement method of the bunch length based on radio frequency deflectors (RFDs) in electron linear accelerators (LINACs) are investigated. In particular, when the electron bunch at the RFD has a non-negligible energy chirp (i.e. a correlation between the longitudinal positions and energies of the particle), the measurement is affected by a deterministic intrinsic error, which is directly related to the RFD phase offset.

In this work, we study the Lp-risk with p ? 1 of nonparametric density estimators by using wavelet method in the framework of circular data. In particular, these estimators are based on local hard thresholding techniques; furthermore, they are constructed over the so-called Mexican needlet system, which describes a nearly tight frame over the circle.

In this paper we study the tail behavior of Mexican needlets, a class of spherical wavelets introduced by Geller and Mayeli in [12]. More specifically, we provide an explicit upper bound depending on the resolution level j and a parameter s governing the shape of the Mexican needlets.

We study the weak solvability of a system of coupled Allen--Cahn--like equations resembling cross--diffusion which is arising as a model for the consolidation of saturated porous media. Besides using energy like estimates, we cast the special structure of the system in the framework of the Leray--Schauder fixed point principle and ensure this way the local existence of strong solutions to a regularised version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem.

Aim of this note is to study the infinity Laplace operator and the corresponding Absolutely Minimizing Lipschitz Extension problem on the Sierpinski gasket in the spirit of the classical construction of Kigami for the Laplacian. We introduce a notion of infinity harmonic functions on pre-fractal sets and we show that these functions solve a Lipschitz extension problem in the discrete setting. Then we prove that the limit of the infinity harmonic functions on the pre-fractal sets solves the Absolutely Minimizing Lipschitz Extension problem on the Sierpinski gasket.

In this article we consider the Keller-Segel model for chemotaxis on networks, both in the doubly parabolic case and in the parabolic-elliptic one. Introducing appropriate transition conditions at vertices, we prove the existence of a time global and spatially continuous solution for each of the two systems. The main tool we use in the proof of the existence result are optimal decay estimates for the fundamental solution of the heat equation on a weighted network.

In this paper we show that the introduction of an attenuation factor in the brightness equations relative to various perspective shape-from-shading models allows us to make the corresponding differential problems well-posed. We propose a unified approach based on the theory of viscosity solutions and we show that the brightness equations with the attenuation term admit a unique viscosity solution. We also discuss in detail the possible boundary conditions that we can use for the Hamilton–Jacobi equations associated to these models.

In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in the spirit of the Hughes dynamic continuum model. The pedestrians, represented by a density function, move on the graph choosing a route to minimize the instantaneous travel cost to the destination. The density is governed by a conservation law whereas the minimization principle is described by a graph eikonal equation.

We propose a numerical method for stationary Mean Field Games defined on a network.
In this framework a correct approximation of the transition conditions at the vertices plays a crucial
role. We prove existence, uniqueness and convergence of the scheme and we also propose a least squares
method for the solution of the discrete system. Numerical experiments are carried out.

This research aims at ascertaining the existence and characteristics of natural long-term capture orbits around a celestial body of potential interest. The problem is investigated in the dynamical framework of the three-dimensional circular restricted three-body problem. Previous numerical work on two-dimensional trajectories provided numerical evidence of Conley’s theorem, proving that long-term capture orbits are topologically located near trajectories asymptotic to periodic libration point orbits. This work intends to extend the previous investigations to three-dimensional paths.