2,349 research outputs found
On the parametric dependences of a class of non-linear singular maps
We discuss a two-parameter family of maps that generalize piecewise linear,
expanding maps of the circle. One parameter measures the effect of a
non-linearity which bends the branches of the linear map. The second parameter
rotates points by a fixed angle. For small values of the nonlinearity
parameter, we compute the invariant measure and show that it has a singular
density to first order in the nonlinearity parameter. Its Fourier modes have
forms similar to the Weierstrass function. We discuss the consequences of this
singularity on the Lyapunov exponents and on the transport properties of the
corresponding multibaker map. For larger non-linearities, the map becomes
non-hyperbolic and exhibits a series of period-adding bifurcations.Comment: 17 pages, 13 figures, to appear in Discrete and Continuous Dynamical
Systems, series B Higher resolution versions of Figures 5 downloadable at
http://www.glue.umd.edu/~jrd
A Note on the Ruelle Pressure for a Dilute Disordered Sinai Billiard
The topological pressure is evaluated for a dilute random Lorentz gas, in the
approximation that takes into account only uncorrelated collisions between the
moving particle and fixed, hard sphere scatterers. The pressure is obtained
analytically as a function of a temperature-like parameter, beta, and of the
density of scatterers. The effects of correlated collisions on the topological
pressure can be described qualitatively, at least, and they significantly
modify the results obtained by considering only uncorrelated collision
sequences. As a consequence, for large systems, the range of beta-values over
which our expressions for the topological pressure are valid becomes very
small, approaching zero, in most cases, as the inverse of the logarithm of
system size.Comment: 15 pages RevTeX with 2 figures. Final version with some typo's
correcte
On thermostats and entropy production
The connection between the rate of entropy production and the rate of phase
space contraction for thermostatted systems in nonequilibrium steady states is
discussed for a simple model of heat flow in a Lorentz gas, previously
described by Spohn and Lebowitz. It is easy to show that for the model
discussed here the two rates are not connected, since the rate of entropy
production is non-zero and positive, while the overall rate of phase space
contraction is zero. This is consistent with conclusions reached by other
workers. Fractal structures appear in the phase space for this model and their
properties are discussed. We conclude with a discussion of the implications of
this and related work for understanding the role of chaotic dynamics and
special initial conditions for an explanation of the Second Law of
Thermodynamics.Comment: 14 pages, 1 figur
Advanced thermal barrier coating systems
Current state-of-the-art thermal barrier coating (TBC) systems consist of partially stabilized zirconia coatings plasma sprayed over a MCrAlY bond coat. Although these systems have excellent thermal shock properties, they have shown themselves to be deficient for a number of diesel and aircraft applications. Two ternary ceramic plasma coatings are discussed with respect to their possible use in TBC systems. Zirconia-ceria-yttria (ZCY) coatings were developed with low thermal conductivities, good thermal shock resistance and improved resistance to vanadium containing environments, when compared to the baseline yttria stabilized zirconia (YSZ) coatings. In addition, dense zirconia-titania-yttria (ZTY) coatings were developed with particle erosion resistance exceeding conventional stabilized zirconia coatings. Both coatings were evaluated in conjunction with a NiCr-Al-Co-Y2O3 bond coat. Also, multilayer or hybrid coatings consisting of the bond coat with subsequent coatings of zirconia-ceria-yttria and zirconia-titania-yttria were evaluated. These coatings combine the enhanced performance characteristics of ZCY with the improved erosion resistance of ZTY coatings. Improvement in the erosion resistance of the TBC system should result in a more consistent delta T gradient during service. Economically, this may also translate into increased component life simply because the coating lasts longer
Field Driven Thermostated System : A Non-Linear Multi-Baker Map
In this paper, we discuss a simple model for a field driven, thermostated
random walk that is constructed by a suitable generalization of a multi-baker
map. The map is a usual multi-baker, but perturbed by a thermostated external
field that has many of the properties of the fields used in systems with
Gaussian thermostats. For small values of the driving field, the map is
hyperbolic and has a unique SRB measure that we solve analytically to first
order in the field parameter. We then compute the positive and negative
Lyapunov exponents to second order and discuss their relation to the transport
properties. For higher values of the parameter, this system becomes
non-hyperbolic and posseses an attractive fixed point.Comment: 6 pages + 5 figures, to appear in Phys. Rev.
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