The Diffusion Problem of Toxic Gases in a Tunnel. The Pump Absorption Model

In this work we study the diffusion of a toxic gas in a tunnel due to an explosion in order to realize a control system—via a wireless network of active sensors—for identification and immediate containment procedures. To this end an aspiration pump is turned on instantaneously at a distance of b meters from the explosion to mitigate the effects of the terroristic act. We exactly find the diffusion concentration in order to provide a solution useful for comparison to other models: numerical ones or models with many aspiration pumps. The model is described by the diffusion partial differential equation (PDE) with a non-homogeneous term which models the aspiration pump. A model with more suction pumps is outlined.     

The blow-up phenomenon for degenerate parabolic equations with variable coefficients and nonlinear source

The Cauchy problem for a degenerate parabolic equation with a source and variable coefficient of the form

     

Vacuum moulding of a superplastic in two dimensions

A mathematical model is proposed for the process of vacuum superplasticforming. The model exploits the fact that in most industrialapplications the sheet aspect ratio (thickness/sheet width)is small. After an initial consideration of some of the moregeneral properties and the literature of superplastic materials,the elastic/plastic deformation of an internally-inflated thin-walledcylinder is examined. Plates of arbitrary geometry are thenconsidered. A quasisteady model in which the sheet moves througha sequence of steady states is developed. Some simplified closed-formsolutions are examined, but for general cases a system of nonlinearpartial differential equations must be solved numerically. Anefficient and accurate semi-explicit numerical scheme is proposedand a simplified stability analysis is presented; the methodis then used to compute properties of superplastic vacuum mouldedsheets in a number of practically motivated cases.     

Modulated optical lattice as an atomic fabry-perot interferometer

We propose to engineer the atomic band structure in optical lattices in order to design a Fabry-Perot interferometer with large mode spacing and strong nonlinear coupling to be employed in atom optics. The use of an optical lattice allows for a significant reduction of the atomic effective mass, while the slow modulation of its parameters spatially confines the matter waves on a length scale of a few dozen optical wavelengths. As a consequence, the mode spacing in such a cavity would be as high as one-tenth of the recoil energy, allowing for a very efficient filter action, while the nonlinear coupling due to interatomic interactions could lead to bistability and limiting effects in the transmission of the atomic beam.     

Spatial projection techniques in general relativity. Remarks about the construction of the spatial tensor analysis

The Eastbrook Whalquist definition of a spatial tensor analysis is compared with Massa's. It is shown that the second approach includes the first one as a special one. Lavoro eseguito nell'ambito dell'attività del Gruppo Nazionale della Fisica Matematica del C.N.R.Lavoro eseguito nell'ambito dell'attività del Gruppo Nazionale della Fisica Matematica del C.N.R.     

A genetic toolbox for creating reversible Ca2+-sensitive materials

A major goal of polymer science is to develop "smart" materials that sense specific chemical signals in complex environments and respond with predictable changes in their mechanical properties. Here, we describe a genetic toolbox of natural and engineered protein modules that can be rationally combined in manifold ways to create reversible self-assembling materials that vary in their composition, architecture, and mechanical properties. Using this toolbox, we produced several materials that reversibly self-assemble in the presence of Ca2+ and characterized these materials using particle-tracking microrheology. The properties of these materials could be predicted from the dilute solution behavior of their component modules, suggesting that this toolbox may be generally useful for creating new stimuli-sensitive materials.     

A weighted interpolation inequality with variable exponent of the Nirenberg-Gagliardo kind

We establish an inequality of the Nirenberg-Gagliardo kind for functions belonging to some degenerate Sobolev space with variable exponents.