417 research outputs found
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Instability Criteria for Steady Flows of a Perfect Fluid
An instability criterion based on the positivity of a Lyapunov-type exponent is used to study the stability of the Euler equations governing the motion of an inviscid incompressible fluid. It is proved that any flow with exponential stretching of the fluid particles is unstable. In the case of an arbitrary axisymmetric steady integrable flow, a sufficient condition for instability is exhibited in terms of the curvature and the geodesic torsion of a stream line and the helicity of the flow.NSF DMS 9000137, DMS 9105688Mathematic
Topology Change in (2+1)-Dimensional Gravity
In (2+1)-dimensional general relativity, the path integral for a manifold
can be expressed in terms of a topological invariant, the Ray-Singer torsion of
a flat bundle over . For some manifolds, this makes an explicit computation
of transition amplitudes possible. In this paper, we evaluate the amplitude for
a simple topology-changing process. We show that certain amplitudes for spatial
topology change are nonvanishing---in fact, they can be infrared
divergent---but that they are infinitely suppressed relative to similar
topology-preserving amplitudes.Comment: 19 pages of text plus 4 pages of figures, LaTeX (using epsf),
UCD-11-9
Dynamo effect in parity-invariant flow with large and moderate separation of scales
It is shown that non-helical (more precisely, parity-invariant) flows capable
of sustaining a large-scale dynamo by the negative magnetic eddy diffusivity
effect are quite common. This conclusion is based on numerical examination of a
large number of randomly selected flows. Few outliers with strongly negative
eddy diffusivities are also found, and they are interpreted in terms of the
closeness of the control parameter to a critical value for generation of a
small-scale magnetic field. Furthermore, it is shown that, for parity-invariant
flows, a moderate separation of scales between the basic flow and the magnetic
field often significantly reduces the critical magnetic Reynolds number for the
onset of dynamo action.Comment: 44 pages,11 figures, significantly revised versio
Ultrafast dynamics in the presence of antiferromagnetic correlations in electron-doped cuprate LaCeCuO
We used femtosecond optical pump-probe spectroscopy to study the photoinduced
change in reflectivity of thin films of the electron-doped cuprate
LaCeCuO (LCCO) with dopings of x0.08 (underdoped) and
x0.11 (optimally doped). Above T, we observe fluence-dependent
relaxation rates which onset at a similar temperature that transport
measurements first see signatures of antiferromagnetic correlations. Upon
suppressing superconductivity with a magnetic field, it is found that the
fluence and temperature dependence of relaxation rates is consistent with
bimolecular recombination of electrons and holes across a gap (2)
originating from antiferromagnetic correlations which comprise the pseudogap in
electron-doped cuprates. This can be used to learn about coupling between
electrons and high-energy () excitations in these
compounds and set limits on the timescales on which antiferromagnetic
correlations are static
ARPES studies of cuprate Fermiology: superconductivity, pseudogap, and quasiparticle dynamics
We present angle-resolved photoemission spectroscopy (ARPES) studies of the
cuprate high-temperature superconductors which elucidate the relation between
superconductivity and the pseudogap and highlight low-energy quasiparticle
dynamics in the superconducting state. Our experiments suggest that the
pseudogap and superconducting gap represent distinct states, which coexist
below T. Studies on Bi-2212 demonstrate that the near-nodal and
near-antinodal regions behave differently as a function of temperature and
doping, implying that different orders dominate in different momentum-space
regions. However, the ubiquity of sharp quasiparticles all around the Fermi
surface in Bi-2212 indicates that superconductivity extends into the
momentum-space region dominated by the pseudogap, revealing subtlety in this
dichotomy. In Bi-2201, the temperature dependence of antinodal spectra reveals
particle-hole asymmetry and anomalous spectral broadening, which may constrain
the explanation for the pseudogap. Recognizing that electron-boson coupling is
an important aspect of cuprate physics, we close with a discussion of the
multiple 'kinks' in the nodal dispersion. Understanding these may be important
to establishing which excitations are important to superconductivity.Comment: To appear in a focus issue on 'Fermiology of Cuprates' in New Journal
of Physic
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Doping-Dependent Nodal Fermi Velocity in Bi-2212 Revealed by High-Resolution ARPES
The improved resolution of laser-based angle-resolved photoemission spectroscopy (ARPES) allows reliable access to fine structures in the spectrum. We present a systematic, doping-dependent study of a recently discovered low-energy kink in the nodal dispersion of Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} (Bi-2212), which demonstrates the ubiquity and robustness of this kink in underdoped Bi-2212. The renormalization of the nodal velocity due to this kink becomes stronger with underdoping, revealing that the nodal Fermi velocity is non-universal, in contrast to assumed phenomenology. This is used together with laser-ARPES measurements of the gap velocity, v{sub 2}, to resolve discrepancies with thermal conductivity measurements
Fold-Saddle Bifurcation in Non-Smooth Vector Fields on the Plane
This paper presents results concerning bifurcations of 2D piecewise-smooth
dynamical systems governed by vector fields. Generic three parameter families
of a class of Non-Smooth Vector Fields are studied and its bifurcation diagrams
are exhibited. Our main result describes the unfolding of the so called
Fold-Saddle singularity
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