1,378 research outputs found
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 . Some aspects associated with a Cauchy problem are presented in order to employ the approximations of Faedo-Galerkin in whole real line . 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, [0,1], is assigned to
each agent at time . At each time step a pair of agents, chosen at
random, interact by playing the game. The players update their 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 and average equilibrium
per-capita-income . 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
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