Ricerc@Sapienza

We discuss the sharp interface limit of the action functional associated with either the Glauber dynamics for Ising systems with Kac potentials or the Glauber+Kawasaki process. The corresponding limiting functionals, for which we provide explicit formulae of the mobility and transport coefficients, describe the large deviation asymptotics with respect to the mean curvature flow.

In this work, we consider a class of recursively grown fractal networks Gn(t) whose topology is controlled by two integer parameters, t and n. We first analyse the structural properties of Gn(t) (including fractal dimension, modularity, and clustering coefficient), and then we move to its transport properties. The latter are studied in terms of first-passage quantities (including the mean trapping time, the global mean first-passage time, and Kemeny’s constant), and we highlight that their asymptotic behavior is controlled by the network’s size and diameter.

We combine Sullivan models from rational homotopy theory with Stasheff's
$L_infty$-algebras to describe a duality in string theory. Namely, what in
string theory is known as topological T-duality between $K^0$-cocycles in type
IIA string theory and $K^1$-cocycles in type IIB string theory, or as Hori's
formula, can be recognized as a Fourier-Mukai transform between twisted
cohomologies when looked through the lenses of rational homotopy theory. We
show this as an example of topological T-duality in rational homotopy theory,

We show that the presence of negative eigenvalues in the spectrum of the angular component of an electromagnetic Schr\"odinger hamiltonian $H$ generically produces a lack of the classical time-decay for the associated Schr\"odinger flow $e^{-itH}$. This is in contrast with the fact that dispersive estimates (Strichartz) still hold, in general, also in this case.

The risk of developing a second malignant cancer as a late time consequence of undergoing a treatment, is one of the main concerns in particle therapy (PT). Since neutrons can release a significant dose far away from the tumour region, a precise characterisation of their production point, kinetic energy and abundance is eagerly needed.

We show how to construct unitary representations of the oriented Thompson group F from oriented link invariants. In particular we show that the suitably normalised HOMFLYPT polynomial defines a positive definite function of F.

A noncommutative KdV-type equation is introduced extending the Bäcklund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived.

The class of nonlinear ordinary differential equations $y^\prime\primey =
F(z,y^2)$, where F is a smooth function, is studied. Various nonlinear ordinary
differential equations, whose applicative importance is well known, belong to
such a class of nonlinear ordinary differential equations. Indeed, the
Emden-Fowler equation, the Ermakov-Pinney equation and the generalized Ermakov
equations are among them. B\"acklund transformations and auto B\"acklund
transformations are constructed: these last transformations induce the

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.