Two-Scale Homogenization of Non-Linear Degenerate Evolution Equations

AbstractUsing the notion of two-scale convergence developed by Allaire, the homogenization of a degenerate non-linear evolution equation with periodically oscillating coefficients is presented. A two-scale homogenized system is obtained as the limit of the periodic problem. Monotone operator methods and two-scale convergence are employed to show that the solutions of the periodic problem converge to the unique solution of the homogenized system. Homogenized initial conditions are also obtained and the sense in which they hold for the homogenized initial value problem is made specific

On the viscous Burgers equation in unbounded domain

In this paper we investigate the existence and uniqueness of global solutions, and a rate stability for the energy related with a Cauchy problem to the viscous Burgers equation in unbounded domain $\mathbb{R}\times(0,\infty)$. Some aspects associated with a Cauchy problem are presented in order to employ the approximations of Faedo-Galerkin in whole real line $\mathbb{R}$. This becomes possible due to the introduction of weight Sobolev spaces which allow us to use arguments of compactness in the Sobolev spaces

Extracting Spatial Information from Noise Measurements of Multi-Spatial-Mode Quantum States

We show that it is possible to use the spatial quantum correlations present in twin beams to extract information about the shape of a mask in the path of one of the beams. The scheme, based on noise measurements through homodyne detection, is useful in the regime where the number of photons is low enough that direct detection with a photodiode is difficult but high enough that photon counting is not an option. We find that under some conditions the use of quantum states of light leads to an enhancement of the sensitivity in the estimation of the shape of the mask over what can be achieved with a classical state with equivalent properties (mean photon flux and noise properties). In addition, we show that the level of enhancement that is obtained is a result of the quantum correlations and cannot be explained with only classical correlations

Saturn's icy satellites and rings investigated by Cassini - VIMS. III. Radial compositional variability

In the last few years Cassini-VIMS, the Visible and Infared Mapping Spectrometer, returned to us a comprehensive view of the Saturn's icy satellites and rings. After having analyzed the satellites' spectral properties (Filacchione et al. (2007a)) and their distribution across the satellites' hemispheres (Filacchione et al. (2010)), we proceed in this paper to investigate the radial variability of icy satellites (principal and minor) and main rings average spectral properties. This analysis is done by using 2,264 disk-integrated observations of the satellites and a 12x700 pixels-wide rings radial mosaic acquired with a spatial resolution of about 125 km/pixel. The comparative analysis of these data allows us to retrieve the amount of both water ice and red contaminant materials distributed across Saturn's system and the typical surface regolith grain sizes. These measurements highlight very striking differences in the population here analyzed, which vary from the almost uncontaminated and water ice-rich surfaces of Enceladus and Calypso to the metal/organic-rich and red surfaces of Iapetus' leading hemisphere and Phoebe. Rings spectra appear more red than the icy satellites in the visible range but show more intense 1.5-2.0 micron band depths. The correlations among spectral slopes, band depths, visual albedo and phase permit us to cluster the saturnian population in different spectral classes which are detected not only among the principal satellites and rings but among co-orbital minor moons as well. Finally, we have applied Hapke's theory to retrieve the best spectral fits to Saturn's inner regular satellites using the same methodology applied previously for Rhea data discussed in Ciarniello et al. (2011).Comment: 44 pages, 27 figures, 7 tables. Submitted to Icaru

Finite element analysis of cracking and delamination of concrete beam due to steel corrosion

This paper presents the analytical results to investigate cracking and delamination of concrete beam due to steel corrosion. A series of concrete beams were idealised as two dimensional models via their cross section and analysed using the finite element software – LUSAS. The corrosion of steel bars was simulated using a radial expansion. The FE results show that cracking of beam section due to steel corrosion can be clarified into four types, i.e., Internal Cracking, Internal Penetration, External Cracking (HS) and External Cracking (VB). The amount of corrosion in term of radial expansion required to causes Internal Cracking, Internal Penetration, External Cracking (HS) and External Cracking (VB) varies almost linearly with bar diameter d, bar clear distance s and concrete cover c, respectively. If the ratio s/c was less than the critical value of about 2.2, the delamination of concrete cover could occur before the cracks can be visualised on the concrete surface, which does concern engineers

Cooperation and Self-Regulation in a Model of Agents Playing Different Games

A simple model for cooperation between "selfish" agents, which play an extended version of the Prisoner's Dilemma(PD) game, in which they use arbitrary payoffs, is presented and studied. A continuous variable, representing the probability of cooperation, $p_k(t) \in$ [0,1], is assigned to each agent $k$ at time $t$. At each time step $t$ a pair of agents, chosen at random, interact by playing the game. The players update their $p_k(t)$ using a criteria based on the comparison of their utilities with the simplest estimate for expected income. The agents have no memory and use strategies not based on direct reciprocity nor 'tags'. Depending on the payoff matrix, the systems self-organizes - after a transient - into stationary states characterized by their average probability of cooperation $\bar{p}_{eq}$ and average equilibrium per-capita-income $\bar{p}_{eq},\bar{U}_\infty$. It turns out that the model exhibit some results that contradict the intuition. In particular, some games which - {\it a priory}- seems to favor defection most, may produce a relatively high degree of cooperation. Conversely, other games, which one would bet that lead to maximum cooperation, indeed are not the optimal for producing cooperation.Comment: 11 pages, 3 figures, keybords: Complex adaptive systems, Agent-based models, Social system