116,065 research outputs found
Qualitative Analysis of Viscous Fluid Cosmological Models satisfying the Israel-Stewart theory of Irreversible Thermodynamics
Isotropic and spatially homogeneous viscous fluid cosmological models are
investigated using the truncated Israel-Stewart theory of irreversible
thermodynamics to model the bulk viscous pressure. The governing system of
differential equations is written in terms of dimensionless variables and a set
of dimensionless equations of state is then utilized to complete the system.
The resulting dynamical system is analyzed using geometric techniques from
dynamical systems theory to find the qualitative behaviour of the
Friedmann-Robertson-Walker models with bulk viscosity. In these models there
exists a free parameter such that the qualitative behaviour of the models can
be quite different (for certain ranges of values of this parameter) from that
found in models satisfying the Eckart theory studied previously. In addition,
the conditions under which the models inflate are investigated.Comment: 29 pages, 8 Encapsulated PostScript Figures, uses the IOP style file
Dilatation of a one-dimensional nonlinear crack impacted by a periodic elastic wave
The interactions between linear elastic waves and a nonlinear crack with
finite compressibility are studied in the one-dimensional context. Numerical
studies on a hyperbolic model of contact with sinusoidal forcing have shown
that the mean values of the scattered elastic displacements are discontinuous
across the crack. The mean dilatation of the crack also increases with the
amplitude of the forcing levels. The aim of the present theoretical study is to
analyse these nonlinear processes under a larger range of nonlinear jump
conditions. For this purpose, the problem is reduced to a nonlinear
differential equation. The dependence of the periodic solution on the forcing
amplitude is quantified under sinusoidal forcing conditions. Bounds for the
mean, maximum and minimum values of the solution are presented. Lastly,
periodic forcing with a null mean value is addressed. In that case, a result
about the mean dilatation of the crack is obtained.Comment: submitted to the SIAM J. App. Mat
Elastic, thermal expansion, plastic and rheological processes - theory and experiment
Rocks are important examples for solid materials where, in various
engineering situations, elastic, thermal expansion, rheological/viscoelastic
and plastic phenomena each may play a remarkable role. Nonequilibrium continuum
thermodynamics provides a consistent way to describe all these aspects in a
unified framework. This we present here in a formulation where the kinematic
quantities allow arbitrary nonzero initial (e.g., in situ) stresses and such
initial configurations which - as a consequence of thermal or remanent stresses
- do not satisfy the kinematic compatibility condition. The various
characteristic effects accounted by the obtained theory are illustrated via
experimental results where loaded solid samples undergo elastic, thermal
expansion and plastic deformation and exhibit rheological behaviour. From the
experimental data, the rheological coefficients are determined, and the
measured temperature changes are also explained by the theory.Comment: 15 pages, to appear in Period. Polytech. Civil En
- …