11,788 research outputs found
Steady-state, effective-temperature dynamics in a glassy material
We present an STZ-based analysis of numerical simulations by Haxton and Liu
(HL). The extensive HL data sharply test the basic assumptions of the STZ
theory, especially the central role played by the effective disorder
temperature as a dynamical state variable. We find that the theory survives
these tests, and that the HL data provide important and interesting constraints
on some of its specific ingredients. Our most surprising conclusion is that,
when driven at various constant shear rates in the low-temperature glassy
state, the HL system exhibits a classic glass transition, including
super-Arrhenius behavior, as a function of the effective temperature.Comment: 9 pages, 6 figure
On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator
The existence of magnetohydrodynamic mean-field alpha^2-dynamos with
spherically symmetric, isotropic helical turbulence function alpha is related
to a non-self-adjoint spectral problem for a coupled system of two singular
second order ordinary differential equations. We establish global estimates for
the eigenvalues of this system in terms of the turbulence function alpha and
its derivative alpha'. They allow us to formulate an anti-dynamo theorem and a
non-oscillation theorem. The conditions of these theorems, which again involve
alpha and alpha', must be violated in order to reach supercritical or
oscillatory regimes.Comment: 35 pages, 4 figures, to be published in SIAM J. Math. Anal
Novel modelling of ultra-compact X-ray binary evolution - stable mass transfer from white dwarfs to neutron stars
Tight binaries of helium white dwarfs (He WDs) orbiting millisecond pulsars
(MSPs) will eventually "merge" due to gravitational damping of the orbit. The
outcome has been predicted to be the production of long-lived ultra-compact
X-ray binaries (UCXBs), in which the WD transfers material to the accreting
neutron star (NS). Here we present complete numerical computations, for the
first time, of such stable mass transfer from a He WD to a NS. We have
calculated a number of complete binary stellar evolution tracks, starting from
pre-LMXB systems, and evolved these to detached MSP+WD systems and further on
to UCXBs. The minimum orbital period is found to be as short as 5.6 minutes. We
followed the subsequent widening of the systems until the donor stars become
planets with a mass of ~0.005 Msun after roughly a Hubble time. Our models are
able to explain the properties of observed UCXBs with high helium abundances
and we can identify these sources on the ascending or descending branch in a
diagram displaying mass-transfer rate vs. orbital period.Comment: 6 pages, 4 figures, MNRAS Letters, in pres
Are the Models for Type Ia Supernova Progenitors Consistent with the Properties of Supernova Remnants?
We explore the relationship between the models for progenitor systems of Type
Ia supernovae and the properties of the supernova remnants that evolve after
the explosion. Most models for Type Ia progenitors in the single degenerate
scenario predict substantial outflows during the presupernova evolution.
Expanding on previous work, we estimate the imprint of these outflows on the
structure of the circumstellar medium at the time of the supernova explosion,
and the effect that this modified circumstellar medium has on the evolution of
the ensuing supernova remnant. We compare our simulations with the
observational properties of known Type Ia supernova remnants in the Galaxy
(Kepler, Tycho, SN 1006), the Large Magellanic Cloud (0509-67.5, 0519-69.0,
N103B), and M31 (SN 1885). We find that optically thick outflows from the white
dwarf surface (sometimes known as accretion winds) with velocities above 200
km/s excavate large low-density cavities around the progenitors. Such large
cavities are incompatible with the dynamics of the forward shock and the X-ray
emission from the shocked ejecta in all the Type Ia remnants that we have
examined.Comment: To appear in ApJ. 17 pages, 10 figures, emulateap
Simplicity of extremal eigenvalues of the Klein-Gordon equation
We consider the spectral problem associated with the Klein-Gordon equation
for unbounded electric potentials. If the spectrum of this problem is contained
in two disjoint real intervals and the two inner boundary points are
eigenvalues, we show that these extremal eigenvalues are simple and possess
strictly positive eigenfunctions. Examples of electric potentials satisfying
these assumptions are given
Rate dependent shear bands in a shear transformation zone model of amorphous solids
We use Shear Transformation Zone (STZ) theory to develop a deformation map
for amorphous solids as a function of the imposed shear rate and initial
material preparation. The STZ formulation incorporates recent simulation
results [Haxton and Liu, PRL 99 195701 (2007)] showing that the steady state
effective temperature is rate dependent. The resulting model predicts a wide
range of deformation behavior as a function of the initial conditions,
including homogeneous deformation, broad shear bands, extremely thin shear
bands, and the onset of material failure. In particular, the STZ model predicts
homogeneous deformation for shorter quench times and lower strain rates, and
inhomogeneous deformation for longer quench times and higher strain rates. The
location of the transition between homogeneous and inhomogeneous flow on the
deformation map is determined in part by the steady state effective
temperature, which is likely material dependent. This model also suggests that
material failure occurs due to a runaway feedback between shear heating and the
local disorder, and provides an explanation for the thickness of shear bands
near the onset of material failure. We find that this model, which resolves
dynamics within a sheared material interface, predicts that the stress weakens
with strain much more rapidly than a similar model which uses a single state
variable to specify internal dynamics on the interface.Comment: 10 pages, 13 figures, corrected typos, added section on rate
strengthening vs. rate weakening material
Dynamics and Thermodynamics of the Glass Transition
The principal theme of this paper is that anomalously slow, super-Arrhenius
relaxations in glassy materials may be activated processes involving chains of
molecular displacements. As pointed out in a preceding paper with A. Lemaitre,
the entropy of critically long excitation chains can enable them to grow
without bound, thus activating stable thermal fluctuations in the local density
or molecular coordination of the material. I argue here that the intrinsic
molecular-scale disorder in a glass plays an essential role in determining the
activation rate for such chains, and show that a simple disorder-related
correction to the earlier theory recovers the Vogel-Fulcher law in three
dimensions. A key feature of this theory is that the spatial extent of
critically long excitation chains diverges at the Vogel-Fulcher temperature. I
speculate that this diverging length scale implies that, as the temperature
decreases, increasingly large regions of the system become frozen and do not
contribute to the configurational entropy, and thus ergodicity is partially
broken in the super-Arrhenius region above the Kauzmann temperature . This
partially broken ergodicity seems to explain the vanishing entropy at and
other observed relations between dynamics and thermodynamics at the glass
transition.Comment: 20 pages, no figures, some further revision
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