40,287 research outputs found
Partial constraint singularities in elastic rods
We present a unified classical treatment of partially constrained elastic
rods. Partial constraints often entail singularities in both shapes and
reactions. Our approach encompasses both sleeve and adhesion problems, and
provides simple and unambiguous derivations of counterintuitive results in the
literature. Relationships between reaction forces and moments, geometry, and
adhesion energies follow from the balance of energy during quasistatic motion.
We also relate our approach to the balance of material momentum and the concept
of a driving traction. The theory is generalizable and can be applied to a wide
array of contact, adhesion, gripping, and locomotion problems.Comment: edited tex
Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions
We study the thermal conductivity, at fixed positive temperature, of a
disordered lattice of harmonic oscillators, weakly coupled to each other
through anharmonic potentials. The interaction is controlled by a small
parameter . We rigorously show, in two slightly different setups,
that the conductivity has a non-perturbative origin. This means that it decays
to zero faster than any polynomial in as . It
is then argued that this result extends to a disordered chain studied by Dhar
and Lebowitz, and to a classical spins chain recently investigated by
Oganesyan, Pal and Huse.Comment: 21 page
Some remarks on one-dimensional force-free Vlasov-Maxwell equilibria
The conditions for the existence of force-free non-relativistic
translationally invariant one-dimensional (1D) Vlasov-Maxwell (VM) equilibria
are investigated using general properties of the 1D VM equilibrium problem. As
has been shown before, the 1D VM equilibrium equations are equivalent to the
motion of a pseudo-particle in a conservative pseudo-potential, with the
pseudo-potential being proportional to one of the diagonal components of the
plasma pressure tensor. The basic equations are here derived in a different way
to previous work. Based on this theoretical framework, a necessary condition on
the pseudo-potential (plasma pressure) to allow for force-free 1D VM equilibria
is formulated. It is shown that linear force-free 1D VM solutions, which so far
are the only force-free 1D VM solutions known, correspond to the case where the
pseudo-potential is an attractive central potential. A general class of
distribution functions leading to central pseudo-potentials is discussed.Comment: Physics of Plasmas, accepte
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