768 research outputs found
Standing wave oscillations in binary mixture convection: from onset via symmetry breaking to period doubling into chaos
Oscillatory solution branches of the hydrodynamic field equations describing
convection in the form of a standing wave (SW) in binary fluid mixtures heated
from below are determined completely for several negative Soret coefficients.
Galerkin as well as finite-difference simulations were used. They were
augmented by simple control methods to obtain also unstable SW states. For
sufficiently negative Soret coefficients unstable SWs bifurcate subcritically
out of the quiescent conductive state. They become stable via a saddle-node
bifurcation when lateral phase pinning is exerted. Eventually their invariance
under time-shift by half a period combined with reflexion at midheight of the
fluid layer gets broken. Thereafter they terminate by undergoing a
period-doubling cascade into chaos
Traveling Wave Fronts and Localized Traveling Wave Convection in Binary Fluid Mixtures
Nonlinear fronts between spatially extended traveling wave convection (TW)
and quiescent fluid and spatially localized traveling waves (LTWs) are
investigated in quantitative detail in the bistable regime of binary fluid
mixtures heated from below. A finite-difference method is used to solve the
full hydrodynamic field equations in a vertical cross section of the layer
perpendicular to the convection roll axes. Results are presented for
ethanol-water parameters with several strongly negative separation ratios where
TW solutions bifurcate subcritically. Fronts and LTWs are compared with each
other and similarities and differences are elucidated. Phase propagation out of
the quiescent fluid into the convective structure entails a unique selection of
the latter while fronts and interfaces where the phase moves into the quiescent
state behave differently. Interpretations of various experimental observations
are suggested.Comment: 46 pages, 11 figures. Accepted for publication in Phys. Rev.
Pattern selection as a nonlinear eigenvalue problem
A unique pattern selection in the absolutely unstable regime of driven,
nonlinear, open-flow systems is reviewed. It has recently been found in
numerical simulations of propagating vortex structures occuring in
Taylor-Couette and Rayleigh-Benard systems subject to an externally imposed
through-flow. Unlike the stationary patterns in systems without through-flow
the spatiotemporal structures of propagating vortices are independent of
parameter history, initial conditions, and system length. They do, however,
depend on the boundary conditions in addition to the driving rate and the
through-flow rate. Our analysis of the Ginzburg-Landau amplitude equation
elucidates how the pattern selection can be described by a nonlinear eigenvalue
problem with the frequency being the eigenvalue. Approaching the border between
absolute and convective instability the eigenvalue problem becomes effectively
linear and the selection mechanism approaches that of linear front propagation.
PACS: 47.54.+r,47.20.Ky,47.32.-y,47.20.FtComment: 18 pages in Postsript format including 5 figures, to appear in:
Lecture Notes in Physics, "Nonlinear Physics of Complex Sytems -- Current
Status and Future Trends", Eds. J. Parisi, S. C. Mueller, and W. Zimmermann
(Springer, Berlin, 1996
PCT, spin and statistics, and analytic wave front set
A new, more general derivation of the spin-statistics and PCT theorems is
presented. It uses the notion of the analytic wave front set of
(ultra)distributions and, in contrast to the usual approach, covers nonlocal
quantum fields. The fields are defined as generalized functions with test
functions of compact support in momentum space. The vacuum expectation values
are thereby admitted to be arbitrarily singular in their space-time dependence.
The local commutativity condition is replaced by an asymptotic commutativity
condition, which develops generalizations of the microcausality axiom
previously proposed.Comment: LaTeX, 23 pages, no figures. This version is identical to the
original published paper, but with corrected typos and slight improvements in
the exposition. The proof of Theorem 5 stated in the paper has been published
in J. Math. Phys. 45 (2004) 1944-195
Noise sensitivity of sub- and supercritically bifurcating patterns with group velocities close to the convective-absolute instability
The influence of small additive noise on structure formation near a forwards
and near an inverted bifurcation as described by a cubic and quintic Ginzburg
Landau amplitude equation, respectively, is studied numerically for group
velocities in the vicinity of the convective-absolute instability where the
deterministic front dynamics would empty the system.Comment: 16 pages, 7 Postscript figure
A New Derivation of the CPT and Spin-Statistics Theorems in Non-Commutative Field Theories
We propose an alternative axiomatic description for non-commutative field
theories (NCFT) based on some ideas by Soloviev to nonlocal quantum fields. The
local commutativity axiom is replaced by the weaker condition that the fields
commute at sufficiently large spatial separations, called asymptotic
commutativity, formulated in terms of the theory of analytic functionals. The
question of a possible violation of the CPT and Spin-Statistics theorems caused
by nonlocality of the commutation relations
is investigated. In spite of this
inherent nonlocality, we show that the modification aforementioned is
sufficient to ensure the validity of these theorems for NCFT. We restrict
ourselves to the simplest model of a scalar field in the case of only
space-space non-commutativity.Comment: The title is new, and the analysis in the manuscript has been made
more precise. This revised version is to be published in J.Math.Phy
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