40 research outputs found
A physical interpretation of Hubble's law and the cosmological redshift from the perspective of a static observer
We derive explicit and exact expressions for the physical velocity of a free
particle comoving with the Hubble flow as measured by a static observer, and
for the frequency shift of light emitted by a comoving source and received,
again, by a static observer. The expressions make it clear that an
interpretation of the redshift as a kind of Doppler effect only makes sense
when the distance between the observer and the source vanishes exactly.Comment: 5 pages, added references; accepted for publication in General
Relativity and Gravitatio
The Cosmic Causal Mass
In order to provide a better understanding of rotating universe models, and
in particular the G\"{o}del universe, we discuss the relationship between
cosmic rotation and perfect inertial dragging. In this connection, the concept
of \emph{causal mass} is defined in a cosmological context, and discussed in
relation to the cosmic inertial dragging effect. Then, we calculate the mass
inside the particle horizon of the flat CDM-model integrated along the
past light cone. The calculation shows that the Schwarzschild radius of this
mass is around three times the radius of the particle horizon. This indicates
that there is close to perfect inertial dragging in our universe. Hence, the
calculation provides an explanation for the observation that the swinging plane
of a Foucault pendulum follows the stars.Comment: 17 pages, 3 figure
Spontaneous thermal runaway as an ultimate failure mechanism of materials
The first theoretical estimate of the shear strength of a perfect crystal was
given by Frenkel [Z. Phys. 37, 572 (1926)]. He assumed that as slip occurred,
two rigid atomic rows in the crystal would move over each other along a slip
plane. Based on this simple model, Frenkel derived the ultimate shear strength
to be about one tenth of the shear modulus. Here we present a theoretical study
showing that catastrophic material failure may occur below Frenkel's ultimate
limit as a result of thermal runaway. We demonstrate that the condition for
thermal runaway to occur is controlled by only two dimensionless variables and,
based on the thermal runaway failure mechanism, we calculate the maximum shear
strength of viscoelastic materials. Moreover, during the thermal
runaway process, the magnitude of strain and temperature progressively localize
in space producing a narrow region of highly deformed material, i.e. a shear
band. We then demonstrate the relevance of this new concept for material
failure known to occur at scales ranging from nanometers to kilometers.Comment: 4 pages, 3 figures. Eq. (6) and Fig. 2a corrected; added references;
improved quality of figure
Spontaneous dissipation of elastic energy by self-localizing thermal runaway
Thermal runaway instability induced by material softening due to shear
heating represents a potential mechanism for mechanical failure of viscoelastic
solids. In this work we present a model based on a continuum formulation of a
viscoelastic material with Arrhenius dependence of viscosity on temperature,
and investigate the behavior of the thermal runaway phenomenon by analytical
and numerical methods. Approximate analytical descriptions of the problem
reveal that onset of thermal runaway instability is controlled by only two
dimensionless combinations of physical parameters. Numerical simulations of the
model independently verify these analytical results and allow a quantitative
examination of the complete time evolutions of the shear stress and the spatial
distributions of temperature and displacement during runaway instability. Thus
we find that thermal runaway processes may well develop under nonadiabatic
conditions. Moreover, nonadiabaticity of the unstable runaway mode leads to
continuous and extreme localization of the strain and temperature profiles in
space, demonstrating that the thermal runaway process can cause shear banding.
Examples of time evolutions of the spatial distribution of the shear
displacement between the interior of the shear band and the essentially
nondeforming material outside are presented. Finally, a simple relation between
evolution of shear stress, displacement, shear-band width and temperature rise
during runaway instability is given.Comment: 16 pages, 7 figures. Extended conclusion; added reference
Seismic evidence for thermal runaway during intermediate-depth earthquake rupture
Intermediate-depth earthquakes occur at depths where temperatures and pressures exceed those at which brittle failure is expected. There are two leading candidates for the physical mechanism behind these earthquakes: dehydration embrittlement and self-localizing thermal shear runaway. A complete energy budget for a range of earthquake sizes can help constrain whether either of these mechanisms might play a role in intermediate-depth earthquake rupture. The combination of high stress drop and low radiation efficiency that we observe for M[subscript w] 4–5 earthquakes in the Bucaramanga Nest implies a temperature increase of 600–1000°C for a centimeter-scale layer during earthquake failure. This suggests that substantial shear heating, and possibly partial melting, occurs during intermediate-depth earthquake failure. Our observations support thermal shear runaway as the mechanism for intermediate-depth earthquakes, which would help explain differences in their behavior compared to shallow earthquakes.National Science Foundation (U.S.) (Grant EAR-1045684
A Physics‐Based Rock Friction Constitutive Law: Steady State Friction
Experiments measuring friction over a wide range of sliding velocities find that the value of the friction coefficient varies widely: friction is high and behaves according to the rate and state constitutive law during slow sliding, yet markedly weakens as the sliding velocity approaches seismic slip speeds. We introduce a physics‐based theory to explain this behavior. Using conventional microphysics of creep, we calculate the velocity and temperature dependence of contact stresses during sliding, including the thermal effects of shear heating. Contacts are assumed to reach a coupled thermal and mechanical steady state, and friction is calculated for steady sliding. Results from theory provide good quantitative agreement with reported experimental results for quartz and granite friction over 11 orders of magnitude in velocity. The new model elucidates the physics of friction and predicts the connection between friction laws to independently determined material parameters. It predicts four frictional regimes as function of slip rate: at slow velocity friction is either velocity strengthening or weakening, depending on material parameters, and follows the rate and state friction law. Differences between surface and volume activation energies are the main control on velocity dependence. At intermediate velocity, for some material parameters, a distinct velocity strengthening regime emerges. At fast sliding, shear heating produces thermal softening of friction. At the fastest sliding, melting causes further weakening. This theory, with its four frictional regimes, fits well previously published experimental results under low temperature and normal stress