16,902 research outputs found
Wave asymptotics for waveguides and manifolds with infinite cylindrical ends
We describe wave decay rates associated to embedded resonances and spectral
thresholds for waveguides and manifolds with infinite cylindrical ends. We show
that if the cut-off resolvent is polynomially bounded at high energies, as is
the case in certain favorable geometries, then there is an associated
asymptotic expansion, up to a remainder, of solutions of the wave
equation on compact sets as . In the most general such case we
have , and under an additional assumption on the infinite ends we have
. If we localize the solutions to the wave equation in frequency
as well as in space, then our results hold for quite general waveguides and
manifolds with infinite cylindrical ends.
To treat problems with and without boundary in a unified way, we introduce a
black box framework analogous to the Euclidean one of Sj\"ostrand and Zworski.
We study the resolvent, generalized eigenfunctions, spectral measure, and
spectral thresholds in this framework, providing a new approach to some mostly
well-known results in the scattering theory of manifolds with cylindrical ends.Comment: In this revision we work in a more general black box setting than in
the first version of the paper. In particular, we allow a boundary extending
to infinity. The changes to the proofs of the main theorems are minor, but
the presentation of the needed basic material from scattering theory is
substantially expanded. New examples are included, both for the main results
and for the black box settin
The nonlinear viscoelastic behavior of polypropylene
A series of tensile relaxation tests is performed on isotactic polypropylene
in the sub-yield and post-yield regions at room temperature. Constitutive
equations are derived for the time-dependent response of a semicrystalline
polymer at isothermal loading with small strains. Adjustable parameters in the
stress-strain relations are found by fitting experimental data. It is
demonstrated that the growth of the longitudinal strain results in an increase
in the relaxation rate in a small interval of strains in the sub-yield domain.
When the strain exceeds some critical value which is substantially less than
the apparent yield strain, the relaxation process becomes strain-independent.Comment: 20 pages, 6 figure
Modelling the linear viscoelastic behavior of silicate glasses near the glass transition point
A model is derived for the viscoelastic response of glasses at isothermal
uniaxial deformation with small strains. A glass is treated as an ensemble of
relaxing units with various activation energies for rearrangement. With
reference to the energy-landscape concept, the rearrangement process is thought
of as a series of hops of relaxing units (trapped in their potential wells on
the energy landscape) to higher energy levels. Stress-strain relations are
developed by using the laws of thermodynamics. Adjustable parameters are found
by fitting experimental data in torsional dynamic tests on a multicomponent
silicate glass at several temperatures near the glass transition point.Comment: 17 pages, 17 figure
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