244 research outputs found
Generalized Farey trees, transfer Operators and phase transitions
We consider a family of Markov maps on the unit interval, interpolating
between the tent map and the Farey map. The latter map is not uniformly
expanding. Each map being composed of two fractional linear transformations,
the family generalizes many particular properties which for the case of the
Farey map have been successfully exploited in number theory. We analyze the
dynamics through the spectral analysis of generalized transfer operators.
Application of the thermodynamic formalism to the family reveals first and
second order phase transitions and unusual properties like positivity of the
interaction function.Comment: 39 pages, 10 figure
Bodily tides near spin-orbit resonances
Spin-orbit coupling can be described in two approaches. The method known as
"the MacDonald torque" is often combined with an assumption that the quality
factor Q is frequency-independent. This makes the method inconsistent, because
the MacDonald theory tacitly fixes the rheology by making Q scale as the
inverse tidal frequency.
Spin-orbit coupling can be treated also in an approach called "the Darwin
torque". While this theory is general enough to accommodate an arbitrary
frequency-dependence of Q, this advantage has not yet been exploited in the
literature, where Q is assumed constant or is set to scale as inverse tidal
frequency, the latter assertion making the Darwin torque equivalent to a
corrected version of the MacDonald torque.
However neither a constant nor an inverse-frequency Q reflect the properties
of realistic mantles and crusts, because the actual frequency-dependence is
more complex. Hence the necessity to enrich the theory of spin-orbit
interaction with the right frequency-dependence. We accomplish this programme
for the Darwin-torque-based model near resonances. We derive the
frequency-dependence of the tidal torque from the first principles, i.e., from
the expression for the mantle's compliance in the time domain. We also explain
that the tidal torque includes not only the secular part, but also an
oscillating part.
We demonstrate that the lmpq term of the Darwin-Kaula expansion for the tidal
torque smoothly goes through zero, when the secondary traverses the lmpq
resonance (e.g., the principal tidal torque smoothly goes through nil as the
secondary crosses the synchronous orbit).
We also offer a possible explanation for the unexpected frequency-dependence
of the tidal dissipation rate in the Moon, discovered by LLR
Atomic Species Associated with the Portevin–Le Chatelier Effect in Superalloy 718 Studied by Mechanical Spectroscopy
In many Ni-based superalloys, dynamic strain aging (DSA) generates an inhomogeneous plastic deformation resulting in jerky flow known as the Portevin--Le Chatelier (PLC) effect. This phenomenon has a deleterious effect on the mechanical properties and, at high temperature, is related to the diffusion of substitutional solute atoms toward the core of dislocations. However, the question about the nature of the atomic species responsible for the PLC effect at high temperature still remains open. The goal of the present work is to answer this important question; to this purpose, three different 718-type and a 625 superalloy were studied through a nonconventional approach by mechanical spectroscopy. The internal friction (IF) spectra of all the studied alloys show a relaxation peak P718 (at 885 K for 0.1 Hz) in the same temperature range, 700 K to 950 K, as the observed PLC effect. The activation parameters of this relaxation peak have been measured, Ea(P718){\thinspace}={\thinspace}2.68{\thinspace}{\textpm}{\thinspace}0.05 eV, 0{\thinspace}={\thinspace}2{\textperiodcentered}10-15 {\textpm} 1 s as well as its broadening factor {\thinspace}={\thinspace}1.1. Experiments on different alloys and the dependence of the relaxation strength on the amount of Mo attribute this relaxation to the stress-induced reorientation of Mo-Mo dipoles due to the short distance diffusion of one Mo atom by exchange with a vacancy. Then, it is concluded that Mo is the atomic species responsible for the high-temperature PLC effect in 718 superallo
- …