784 research outputs found
A model problem for the initial-boundary value formulation of Einstein's field equations
In many numerical implementations of the Cauchy formulation of Einstein's
field equations one encounters artificial boundaries which raises the issue of
specifying boundary conditions. Such conditions have to be chosen carefully. In
particular, they should be compatible with the constraints, yield a well posed
initial-boundary value formulation and incorporate some physically desirable
properties like, for instance, minimizing reflections of gravitational
radiation.
Motivated by the problem in General Relativity, we analyze a model problem,
consisting of a formulation of Maxwell's equations on a spatially compact
region of spacetime with timelike boundaries. The form in which the equations
are written is such that their structure is very similar to the
Einstein-Christoffel symmetric hyperbolic formulations of Einstein's field
equations. For this model problem, we specify a family of Sommerfeld-type
constraint-preserving boundary conditions and show that the resulting
initial-boundary value formulations are well posed. We expect that these
results can be generalized to the Einstein-Christoffel formulations of General
Relativity, at least in the case of linearizations about a stationary
background.Comment: 25 page
Connes distance by examples: Homothetic spectral metric spaces
We study metric properties stemming from the Connes spectral distance on
three types of non compact noncommutative spaces which have received attention
recently from various viewpoints in the physics literature. These are the
noncommutative Moyal plane, a family of harmonic Moyal spectral triples for
which the Dirac operator squares to the harmonic oscillator Hamiltonian and a
family of spectral triples with Dirac operator related to the Landau operator.
We show that these triples are homothetic spectral metric spaces, having an
infinite number of distinct pathwise connected components. The homothetic
factors linking the distances are related to determinants of effective Clifford
metrics. We obtain as a by product new examples of explicit spectral distance
formulas. The results are discussed.Comment: 23 pages. Misprints corrected, references updated, one remark added
at the end of the section 3. To appear in Review in Mathematical Physic
Note on Global Regularity for 2D Oldroyd-B Fluids with Diffusive Stress
We prove global regularity of solutions of Oldroyd-B equations in 2 spatial
dimensions with spatial diffusion of the polymeric stresses
The Johnson-Segalman model with a diffusion term in Couette flow
We study the Johnson-Segalman (JS) model as a paradigm for some complex
fluids which are observed to phase separate, or ``shear-band'' in flow. We
analyze the behavior of this model in cylindrical Couette flow and demonstrate
the history dependence inherent in the local JS model. We add a simple gradient
term to the stress dynamics and demonstrate how this term breaks the degeneracy
of the local model and prescribes a much smaller (discrete, rather than
continuous) set of banded steady state solutions. We investigate some of the
effects of the curvature of Couette flow on the observable steady state
behavior and kinetics, and discuss some of the implications for metastability.Comment: 14 pp, to be published in Journal of Rheolog
Coexistence and Phase Separation in Sheared Complex Fluids
We demonstrate how to construct dynamic phase diagrams for complex fluids
that undergo transitions under flow, in which the conserved composition
variable and the broken-symmetry order parameter (nematic, smectic,
crystalline, etc.) are coupled to shear rate. Our construction relies on a
selection criterion, the existence of a steady interface connecting two stable
homogeneous states. We use the (generalized) Doi model of lyotropic nematic
liquid crystals as a model system, but the method can be easily applied to
other systems, provided non-local effects are included.Comment: 4 pages REVTEX, 5 figures using epsf macros. To appear in Physical
Review E (Rapid Communications
Global generalized solutions for Maxwell-alpha and Euler-alpha equations
We study initial-boundary value problems for the Lagrangian averaged alpha
models for the equations of motion for the corotational Maxwell and inviscid
fluids in 2D and 3D. We show existence of (global in time) dissipative
solutions to these problems. We also discuss the idea of dissipative solution
in an abstract Hilbert space framework.Comment: 27 pages, to appear in Nonlinearit
Pearling and Pinching: Propagation of Rayleigh Instabilities
A new category of front propagation problems is proposed in which a spreading
instability evolves through a singular configuration before saturating. We
examine the nature of this front for the viscous Rayleigh instability of a
column of one fluid immersed in another, using the marginal stability criterion
to estimate the front velocity, front width, and the selected wavelength in
terms of the surface tension and viscosity contrast. Experiments are suggested
on systems that may display this phenomenon, including droplets elongated in
extensional flows, capillary bridges, liquid crystal tethers, and viscoelastic
fluids. The related problem of propagation in Rayleigh-like systems that do not
fission is also considered.Comment: Revtex, 7 pages, 4 ps figs, PR
Oscillations of a solid sphere falling through a wormlike micellar fluid
We present an experimental study of the motion of a solid sphere falling
through a wormlike micellar fluid. While smaller or lighter spheres quickly
reach a terminal velocity, larger or heavier spheres are found to oscillate in
the direction of their falling motion. The onset of this instability correlates
with a critical value of the velocity gradient scale
s. We relate this condition to the known complex rheology of wormlike
micellar fluids, and suggest that the unsteady motion of the sphere is caused
by the formation and breaking of flow-induced structures.Comment: 4 pages, 4 figure
Heisenberg Picture Approach to the Stability of Quantum Markov Systems
Quantum Markovian systems, modeled as unitary dilations in the quantum
stochastic calculus of Hudson and Parthasarathy, have become standard in
current quantum technological applications. This paper investigates the
stability theory of such systems. Lyapunov-type conditions in the Heisenberg
picture are derived in order to stabilize the evolution of system operators as
well as the underlying dynamics of the quantum states. In particular, using the
quantum Markov semigroup associated with this quantum stochastic differential
equation, we derive sufficient conditions for the existence and stability of a
unique and faithful invariant quantum state. Furthermore, this paper proves the
quantum invariance principle, which extends the LaSalle invariance principle to
quantum systems in the Heisenberg picture. These results are formulated in
terms of algebraic constraints suitable for engineering quantum systems that
are used in coherent feedback networks
Search for CP Violation in the Decay Z -> b (b bar) g
About three million hadronic decays of the Z collected by ALEPH in the years
1991-1994 are used to search for anomalous CP violation beyond the Standard
Model in the decay Z -> b \bar{b} g. The study is performed by analyzing
angular correlations between the two quarks and the gluon in three-jet events
and by measuring the differential two-jet rate. No signal of CP violation is
found. For the combinations of anomalous CP violating couplings, and , limits of \hat{h}_b < 0.59h^{\ast}_{b} < 3.02$ are given at 95\% CL.Comment: 8 pages, 1 postscript figure, uses here.sty, epsfig.st
- …