175 research outputs found
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.
Influence of the Dufour effect on convection in binary gas mixtures
Linear and nonlinear properties of convection in binary fluid layers heated
from below are investigated, in particular for gas parameters. A Galerkin
approximation for realistic boundary conditions that describes stationary and
oscillatory convection in the form of straight parallel rolls is used to
determine the influence of the Dufour effect on the bifurcation behaviour of
convective flow intensity, vertical heat current, and concentration mixing. The
Dufour--induced changes in the bifurcation topology and the existence regimes
of stationary and traveling wave convection are elucidated. To check the
validity of the Galerkin results we compare with finite--difference numerical
simulations of the full hydrodynamical field equations. Furthermore, we report
on the scaling behaviour of linear properties of the stationary instability.Comment: 14 pages and 10 figures as uuencoded Postscript file (using uufiles
Two classes of generalized functions used in nonlocal field theory
We elucidate the relation between the two ways of formulating causality in
nonlocal quantum field theory: using analytic test functions belonging to the
space (which is the Fourier transform of the Schwartz space )
and using test functions in the Gelfand-Shilov spaces . We prove
that every functional defined on has the same carrier cones as its
restrictions to the smaller spaces . As an application of this
result, we derive a Paley-Wiener-Schwartz-type theorem for arbitrarily singular
generalized functions of tempered growth and obtain the corresponding extension
of Vladimirov's algebra of functions holomorphic on a tubular domain.Comment: AMS-LaTeX, 12 pages, no figure
Influence of the Soret effect on convection of binary fluids
Convection in horizontal layers of binary fluids heated from below and in
particular the influence of the Soret effect on the bifurcation properties of
extended stationary and traveling patterns that occur for negative Soret
coupling is investigated theoretically. The fixed points corresponding to these
two convection structures are determined for realistic boundary conditions with
a many mode Galerkin scheme for temperature and concentration and an accurate
one mode truncation of the velocity field. This solution procedure yields the
stable and unstable solutions for all stationary and traveling patterns so that
complete phase diagrams for the different convection types in typical binary
liquid mixtures can easily be computed. Also the transition from weakly to
strongly nonlinear states can be analyzed in detail. An investigation of the
concentration current and of the relevance of its constituents shows the way
for a simplification of the mode representation of temperature and
concentration field as well as for an analytically manageable few mode
description.Comment: 30 pages, 12 figure
Nonlocal looking equations can make nonlinear quantum dynamics local
A general method for extending a non-dissipative nonlinear Schr\"odinger and
Liouville-von Neumann 1-particle dynamics to an arbitrary number of particles
is described. It is shown at a general level that the dynamics so obtained is
completely separable, which is the strongest condition one can impose on
dynamics of composite systems. It requires that for all initial states
(entangled or not) a subsystem not only cannot be influenced by any action
undertaken by an observer in a separated system (strong separability), but
additionally that the self-consistency condition is fulfilled. It is shown that a correct
extension to particles involves integro-differential equations which, in
spite of their nonlocal appearance, make the theory fully local. As a
consequence a much larger class of nonlinearities satisfying the complete
separability condition is allowed than has been assumed so far. In particular
all nonlinearities of the form are acceptable. This shows that
the locality condition does not single out logarithmic or 1-homeogeneous
nonlinearities.Comment: revtex, final version, accepted in Phys.Rev.A (June 1998
Influence of through-flow on linear pattern formation properties in binary mixture convection
We investigate how a horizontal plane Poiseuille shear flow changes linear
convection properties in binary fluid layers heated from below. The full linear
field equations are solved with a shooting method for realistic top and bottom
boundary conditions. Through-flow induced changes of the bifurcation thresholds
(stability boundaries) for different types of convective solutions are deter-
mined in the control parameter space spanned by Rayleigh number, Soret coupling
(positive as well as negative), and through-flow Reynolds number. We elucidate
the through-flow induced lifting of the Hopf symmetry degeneracy of left and
right traveling waves in mixtures with negative Soret coupling. Finally we
determine with a saddle point analysis of the complex dispersion relation of
the field equations over the complex wave number plane the borders between
absolute and convective instabilities for different types of perturbations in
comparison with the appropriate Ginzburg-Landau amplitude equation
approximation. PACS:47.20.-k,47.20.Bp, 47.15.-x,47.54.+rComment: 19 pages, 15 Postscript figure
Why honey is effective as a medicine. 1. Its use in modern medicine
Honey has been used as a medicine for thousands of years and its curative properties are well documented. However, modern medicine turned its back on honey and it is only now, with the advent of multi-resistant bacteria, that the antibiotic properties of honey are being rediscovered
Convection in Binary Fluid Mixtures. II. Localized Traveling Waves. (Physical Review E, in press)
Nonlinear, spatially localized structures of traveling convection rolls are
investigated in quantitative detail as a function of Rayleigh number for two
different Soret coupling strengths (separation ratios) with Lewis and Prandtl
numbers characterizing ethanol-water mixtures. A finite-difference method was
used to solve the full hydrodynamic field equations numerically. Structure and
dynamics of these localized traveling waves (LTW) are dominated by the
concentration field. Like in the spatially extended convective states ( cf.
accompanying paper), the Soret-induced concentration variations strongly
influence, via density changes, the buoyancy forces that drive convection. The
spatio-temporal properties of this feed-back mechanism, involving boundary
layers and concentration plumes, show that LTW's are strongly nonlinear states.
Light intensity distributions are determined that can be observed in side-view
shadowgraphs. Detailed analyses of all fields are made using colour-coded
isoplots, among others. In the frame comoving with their drift velocity, LTW's
display a nontrivial spatio-temporal symmetry consisting of time-translation by
half an oscillation period combined with vertical reflection through the
horizontal midplane of the layer. A time-averaged concentration current is
driven by a phase difference between the waves of concentration and vertical
velocity in the bulk of the LTW state. The associated large-scale concentration
redistribution stabilizes the LTW and controls its drift velocity into the
quiescent fluid by generating a buoyancy-reducing concentration "barrier" ahead
of the leading LTW front. The selection of the width of the LTW's is
investigated and comparisons with experiments are presented.Comment: 18 pages and 6 figures as uuencoded Postscript file (using uufiles) 1
color figure as uuencoded Postscript file, a high resolution version of the
color figure (about 10MB) can be requested from [email protected] or
[email protected].: (Barten)present address: PSI, CH-5232 Villigen
PSI, Switzerlan
A Structured Model of Video Reproduces Primary Visual Cortical Organisation
The visual system must learn to infer the presence of objects and features in the world from the images it encounters, and as such it must, either implicitly or explicitly, model the way these elements interact to create the image. Do the response properties of cells in the mammalian visual system reflect this constraint? To address this question, we constructed a probabilistic model in which the identity and attributes of simple visual elements were represented explicitly and learnt the parameters of this model from unparsed, natural video sequences. After learning, the behaviour and grouping of variables in the probabilistic model corresponded closely to functional and anatomical properties of simple and complex cells in the primary visual cortex (V1). In particular, feature identity variables were activated in a way that resembled the activity of complex cells, while feature attribute variables responded much like simple cells. Furthermore, the grouping of the attributes within the model closely parallelled the reported anatomical grouping of simple cells in cat V1. Thus, this generative model makes explicit an interpretation of complex and simple cells as elements in the segmentation of a visual scene into basic independent features, along with a parametrisation of their moment-by-moment appearances. We speculate that such a segmentation may form the initial stage of a hierarchical system that progressively separates the identity and appearance of more articulated visual elements, culminating in view-invariant object recognition
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