Effects of concavity on the motion of a body immersed in a Vlasov gas

We consider a body immersed in a perfect gas, moving under the action of a constant force $E$ along the $x$ axis . We assume the gas to be described by the mean-field approximation and interacting elastically with the body. Such a dynamic was studied in previous papers In these studies the asymptotic trend showed no sensitivity whatsoever to the shape of the object moving through the gas. In this work we investigate how a simple concavity in the shape of the body can affect its asymptotic behavior; we thus consider the case of hollow cylinder in three dimensions or a box-like body in two dimensions. We study the approach of the body velocity $V (t)$ to the limiting velocity $V_{\infty}$ and prove that, under suitable smallness assumptions, the approach to equilibrium is $| V_{\infty}-V(t)| \approx C t^{-3}$ both in two or three dimensions, being $C$ a positive constant. This approach is not exponential, as typical in friction problems, and even slower than for the simple disk and the convex body in $\mathbb{R}^2$ or $\mathbb{R}^3$

Three-dimensional Topological Insulators and Bosonization

Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF gauge theory, respectively. We analyze the corresponding field theories of the Dirac fermion and compactified boson and compute their partition functions on the three-dimensional torus geometry. We then find some non-dynamic exact properties of bosonization in (2+1) dimensions, regarding fermion parity and spin sectors. Using these results, we extend the Fu-Kane-Mele stability argument to fractional topological insulators in three dimensions.Comment: 54 pages, 11 figure

Motion among random obstacles on a hyperbolic space

We consider the motion of a particle along the geodesic lines of the Poincar\`e half-plane. The particle is specularly reflected when it hits randomly-distributed obstacles that are assumed to be motionless. This is the hyperbolic version of the well-known Lorentz Process studied by Gallavotti in the Euclidean context. We analyse the limit in which the density of the obstacles increases to infinity and the size of each obstacle vanishes: under a suitable scaling, we prove that our process converges to a Markovian process, namely a random flight on the hyperbolic manifold.Comment: 19 pages, 4 figure

Calibration of a visual method for the analysis of the mechanical properties of historic masonry

The conservation and preservation of historic buildings affords many challenges to those who aim to retain our building heritage. In this area, the knowledge of the mechanical characteristics of the masonry material is fundamental. However, mechanical destructive testing is always expensive and time-consuming, especially when applied to masonry historic structures. In order to overcome such kind of problems, the authors of this article, proposed in 2014 a visual method for the estimation of some critical mechanical parameters of the masonry material. Based on the fact that the mechanical behavior of masonry material depends on many factors, such as compressive or shear strength of components (mortar and masonry units), unit shape, volumetric ratio between components and stone arrangement, that is the result of applying a series of construction solutions which form the "rule of art". Taking into account the complexity of the problem due to the great number of variables, and being on-site testing a not-always viable solution, a visual estimate of the mechanical parameters of the walls can be made on the basis of a qualitative criteria evaluation. A revision of this visual method is proposed in this paper. The draft version of new Italian Building Code have been used to re-calibrate this visual method and more tests results have been also considered for a better estimation of the mechanical properties of masonry

<<LA FILIAZIONE NATURALE>>

La filiazione naturale è il rapporto intercorrente tra la persona fisica e coloro che l'hanno concepito; soggetti del rapporto sono il figlio e i genitori, ma il rapporto prende il nome di filiazione perchè esso gravita attorno alla posizione del figlio

Sunny-Side-Up: Temperature & Lobster Egg Development

Grades: 6-12 Subjects: Biology This lesson allows students to use math and science to characterize the effects of temperature on lobster egg development. Students will measure features of lobster eggs at different time points and plot how they change across development. This development will be compared between lobsters from different environments, and students will be asked to draw conclusions about how these differences may relate to lobster performance and climate change