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We call internal-wave billiard the dynamical system of a point particle that moves freely inside a planar domain (the table) and is reflected by its boundary according to this rule: reflections are standard Fresnel reflections but with the pretense that the boundary at any collision point is either horizontal or vertical (relative to a predetermined direction representing gravity). These systems are point particle approximations for the motion of internal gravity waves in closed containers, hence the name. For a class of tables similar to rectangular trapezoids, but with the slanted leg replaced by a general curve with downward concavity, we prove that the dynamics has only three asymptotic regimes: (1) there exist a global attractor and a global repellor, which are periodic and might coincide; (2) there exists a beam of periodic trajectories, whose boundary (if any) comprises an attractor and a repellor for all the other trajectories; (3) all trajectories are dense (that is, the system is minimal). Furthermore, in the prominent case where the table is an actual trapezoid, we study the sets in parameter space relative to the three regimes. We prove in particular that the set for (1) has positive measure (giving a rigorous proof of the existence of Arnol'd tongues for internal-wave billiards), whereas the sets for (2) and (3) are non-empty but have measure zero., Comment: Final preprint for Nonlinearity, 29 pages, 11 figures

We consider the shift transformation on the space of infinite sequences over a finite alphabet endowed with the invariant product measure, and examine the presence of a \emph{hole} on the space. The holes we study are specified by the sequences that do not contain a given finite word as initial sub-string. The measure of the set of sequences that do not fall into the hole in the first $n$ iterates of the shift is known to decay exponentially with $n$, and its exponential rate is called \emph{escape rate}. In this paper we provide a complete characterization of the holes with maximal escape rate. In particular we show that, contrary to the case of equiprobable symbols, ordering the holes by their escape rate corresponds to neither the order by their measure nor by the length of the shortest periodic orbit they contain. Finally, we adapt our technique to the case of shifts endowed with Markov measures, where preliminary results show that a more intricate situation is to be expected., Comment: 18 pages, 3 figures. Final version for Discrete and Continuous Dynamical Systems

We consider the sums TN = Nn=1N F(Sn) where Sn is a random walk on ℤd and F : ℤd → R is a global observable, that is, a bounded function which admits an average value when averaged over large cubes. We show that TN always satisfies the weak Law of Large Numbers but the strong law fails in general except for one dimensional walks with drift. Under additional regularity assumptions on F, we obtain the Strong Law of Large Numbers and estimate the rate of convergence. The growth exponents which we obtain turn out to be optimal in two special cases: for quasiperiodic observables and for random walks in random scenery.

We study a random walk on a point process given by an ordered array of points $(\omega_k, \, k \in \mathbb{Z})$ on the real line. The distances $\omega_{k+1} - \omega_k$ are i.i.d. random variables in the domain of attraction of a $\beta$-stable law, with $\beta \in (0,1) \cup (1,2)$. The random walk has i.i.d. jumps such that the transition probabilities between $\omega_k$ and $\omega_\ell$ depend on $\ell-k$ and are given by the distribution of a $\mathbb{Z}$-valued random variable in the domain of attraction of an $\alpha$-stable law, with $\alpha \in (0,1) \cup (1,2)$. Since the defining variables, for both the random walk and the point process, are heavy-tailed, we speak of a L\'evy flight on a L\'evy random medium. For all combinations of the parameters $\alpha$ and $\beta$, we prove the annealed functional limit theorem for the suitably rescaled process, relative to the optimal Skorokhod topology in each case. When the limit process is not c\`adl\`ag, we prove convergence of the finite-dimensional distributions. When the limit process is deterministic, we also prove a limit theorem for the fluctuations, again relative to the optimal Skorokhod topology., Comment: 30 pages, 3 figures. Final version for Electron. J. Probab

The development of a divertor target for DEMO is of great importance, being able to sustain the harsh environment that is imposed on this component. To fulfill the loading requirements, different concepts were developed within the EUROfusion WPDIV project. The baseline concept is based on the ITER divertor target W-monoblock design. It is made of tungsten as armour material, CuCrZr as structural material and Cu-OFHC as compliant layer. One of the proposed alternative concepts aims to minimize the stress at interfaces by replacing the thick copper interlayer by W/Cu functionally graded material (FGM). In this study, the FGM interlayer, with a thickness of 500 μm, is composed of stacked elementary layers with the following three compositions: 25 vol.%W + 75 vol.%Cu, 50 vol.%W + 50 vol.%Cu, 75 vol.%W + 25 vol.%Cu. Several FGM interlayers were studied. In total three monoblock type mock-ups were manufactured. This paper describes the steps needed to manufacture mock-ups and characterization of elementary layers (composition, porosity, Young’s modulus). HHF tests applying up to 1000 cycles at 20 MW/m² and sub-sequent post-mortem examinations were performed to qualify the concept performance.

We prove that a large class of expanding maps of the unit interval with a $C^2$-regular indifferent point in 0 and full increasing branches are global-local mixing. This class includes the standard Pomeau-Manneville maps $T(x) = x + x^{p+1}$ mod 1 ($p \ge 1$), the Liverani-Saussol-Vaienti maps (with index $p \ge 1$) and many generalizations thereof., Comment: 23 pages. Final version produced for Discrete and Continuous Dynamical Systems - Series A. Numbering of equations, references et alia conforms to the published article

Nel 1828, a Mana in Guyana, Anne-Marie Javouhey fu l’artefice di un esperimento societario complesso, tra suggestioni del socialismo utopistico e riduzioni gesuite del XVII secolo, che sarebbe diventato un laboratorio per il riscatto degli europei emarginati e per l’emancipazione dei neri d’Africa portati nelle colonie. In 1828, in Mana, in French Guyana, Anne-Marie Javouhey was the maker of a complex society experiment, between suggestions of utopian socialism and Jesuit reductions of the seventeenth century, which would become a laboratory for the redemption of marginalized Europeans and for the emancipation of the blacks of Africa brought to the colonies.

International audience; For the development of a divertor for DEMO, the European WPDIV project is underway since 2014. The first phase of the project (2014–2016) aims to provide mock-ups adapted to DEMO operation requirements and the second phase aims to furnish mock-ups, with standardized geometry, which fulfill phase 1 requirements. Within the WPDIV project, several options are under development. One of these aims is to replace the thick copper interlayer, used for ITER divertor components, with a very thin coat (functional gradient material or pure copper) for armor-to-pipe joining. One of the benefits is related to armor temperature which is decreased as the distance of heat conduction path is shortened. Some blocks equipped with thin functional gradient material as interlayer proved, in 2016, to handle high cycling performances without any degradation (no surface change aspect and no decrease of thermal heat exhaust capability). This article gives a brief overview on the recent achievements of the development of thin interlayer concept focusing on the design, mock-up production, inspection, high heat flux (HHF) qualification testing and post-examinations.

We consider a continuous-time random walk which is defined as an interpolation of a random walk on a point process on the real line. The distances between neighboring points of the point process are i.i.d. random variables in the normal domain of attraction of an $\alpha$-stable distribution with $0 < \alpha < 1$. This is therefore an example of a random walk in a L\'evy random medium. Specifically, it is a generalization of a process known in the physical literature as L\'evy-Lorentz gas. We prove that the annealed version of the process is superdiffusive with scaling exponent $1/(\alpha + 1)$ and identify the limiting process, which is not c\`adl\`ag. The proofs are based on the technique of Kesten and Spitzer for random walks in random scenery., Comment: Final version to be published in Stochastic Processes and their Applications. 27 pages

We perform a statistical study of the distances between successive occurrencies of a given dinucleotide in the DNA sequence for a number of organisms of different complexity. Our analysis highlights peculiar features of the dinucleotide CG distribution in mammalian DNA, pointing towards a connection with the role of such dinucleotide in DNA methylation. While the CG distributions of mammals exhibit exponential tails with comparable parameters, the picture for the other organisms studied (e.g., fish, insects, bacteria and viruses) is more heterogeneous, possibly because in these organisms DNA methylation has different functional roles. Our analysis suggests that the distribution of the distances between dinucleotides CG provides useful insights in characterizing and classifying organisms in terms of methylation functionalities., 13 pages, 5 figures. To be published in the Philosophical Transactions A theme issue "DNA as information"

We consider the billiard dynamics in a non-compact set of R^d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called `quenched random Lorentz tube'. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties., Comment: Final version for J. Stat. Phys., 18 pages, 4 figures

In the last twenty years the increasing inequalities determined by the capitalist mode of production - together with the related issues of social integration and social cohesion within the capitalist economy - have been mostly ignored by social sciences and sociology. This is due to the dominance of the ideology of globalization and global corporations, imposed by international neoliberal think tanks; the extreme specialization of social sciences may have had some responsibility for this situation. This is even truer in Italy than in other countries, where the transformations of capitalism have received an increased attention for many years now. A globally dominant rhetoric depicted the welfare state as a "nanny state" marked by waste and inefficiency, thus contributing to its progressive dismantling. In many societies unemployment and inequality, social exclusion and lack of opportunity, sodal and economic discrimination have all increased to the point of threatening social cohesion, democratic participation and civic engagement. In this paper we will try to offer some points for reflection on the current crisis, the extent of which is seriously endangering social bonds. We will also attempt to provide some indications about a possible way out of the crisis, and about the contribution that social sciences and sociology could make in this direction. In particular, we will focus on these questions: 1) which transformations of capitalism contributed to the generation of the tale of globalization, starting from the second half of the 1980s, allowing for the dominance of global corporations and free trade on a global scale; 2) what was the role of sociology in this process of economic, social and cultural change, with respect to the topics of social cohesion and the increasing inequalities in the capitalist mode of production; 3) what role can sociology play to help figuring a way out of the current crisis. The reflections that follow are prelude to a wider study about capitalism and its transformations, and about the role that sociology may play - with its public sociology approach - in identifying the causes of the most disrupting effects of the ongoing social change and in showing what chances are available to strengthen social cohesion.

Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices model a class of L\'evy walks. The assumption that transitions in the scattering phase occur with exponentially-distributed waiting times leads to a description of the process in terms of multiple states, whose distributions evolve according to a set of delay differential equations, amenable to analytic treatment. We obtain an exact expression of the mean squared displacement associated with such processes and discuss the emergence of asymptotic scaling laws in regimes of diffusive and superdiffusive (subballistic) transport, emphasizing, in the latter case, the effect of initial conditions on the transport coefficients. Of particular interest is the case of rare ballistic propagation, in which case a regime of superdiffusion may lurk underneath one of normal diffusion., Comment: 27 pages, 4 figures

We consider a generalization of a one-dimensional stochastic process known in the physical literature as L\'evy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance). The motion is a continuous-time, constant-speed interpolation of a symmetric random walk on the marked points. We first study the quenched random walk on the point process, proving the CLT and the convergence of all the accordingly rescaled moments. Then we derive the quenched and annealed CLTs for the continuous-time process., Comment: Final version to be published in J. Stat. Phys. 23 pages. (Changes from v1: Theorem 2.4 and Corollary 2.6 have been removed.)

We study diffusion on a periodic billiard table with infinite horizon in the limit of narrow corridors. An effective trapping mechanism emerges according to which the process can be modeled by a L\'evy walk combining exponentially-distributed trapping times with free propagation along paths whose precise probabilities we compute. This description yields an approximation of the mean squared displacement of infinite-horizon billiards in terms of two transport coefficients which generalizes to this anomalous regime the Machta-Zwanzig approximation of normal diffusion in finite-horizon billiards [Phys. Rev. Lett. 50, 1959 (1983)]., Comment: 5 pages, 3 figures

Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker, we are led to a description of such L\'evy walks in terms of multistate processes whose time-evolution is shown to obey a set of coupled delay differential equations. Using simple arguments, we obtain asymptotic solutions to these equations and rederive the scaling laws for the mean squared displacement of such processes. Our calculation includes the computation of all relevant transport coefficients in terms of the parameters of the models., Comment: 5 pages, 2 figures. New references added

We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of super-diffusion, in the sense that there is a logarithmic correction to the linear growth in time of the mean-squared displacement. We show numerically that this expected asymptotic behavior is easily overwhelmed by the subleading linear growth throughout the time-range accessible to numerical simulations. We compare our simulations to the known analytical results for the variance of the anomalously-rescaled limiting normal distributions., 10 pages, 4 figures