121 research outputs found
Numerical solution of scattering problems using a Riemann--Hilbert formulation
A fast and accurate numerical method for the solution of scalar and matrix
Wiener--Hopf problems is presented. The Wiener--Hopf problems are formulated as
Riemann--Hilbert problems on the real line, and a numerical approach developed
for these problems is used. It is shown that the known far-field behaviour of
the solutions can be exploited to construct numerical schemes providing
spectrally accurate results. A number of scalar and matrix Wiener--Hopf
problems that generalize the classical Sommerfeld problem of diffraction of
plane waves by a semi-infinite plane are solved using the approach
Short- and Long- Time Transport Structures in a Three Dimensional Time Dependent Flow
Lagrangian transport structures for three-dimensional and time-dependent
fluid flows are of great interest in numerous applications, particularly for
geophysical or oceanic flows. In such flows, chaotic transport and mixing can
play important environmental and ecological roles, for examples in pollution
spills or plankton migration. In such flows, where simulations or observations
are typically available only over a short time, understanding the difference
between short-time and long-time transport structures is critical. In this
paper, we use a set of classical (i.e. Poincar\'e section, Lyapunov exponent)
and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent
structures) tools from dynamical systems theory that analyze chaotic transport
both qualitatively and quantitatively. With this set of tools we are able to
reveal, identify and highlight differences between short- and long-time
transport structures inside a flow composed of a primary horizontal
contra-rotating vortex chain, small lateral oscillations and a weak Ekman
pumping. The difference is mainly the existence of regular or extremely slowly
developing chaotic regions that are only present at short time.Comment: 9 pages, 9 figure
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Generation of bulk vorticity and current density in current-vortex sheet models
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The motion of a buoyant vortex filament
We investigate the motion of a thin vortex filament in the presence of buoyancy. The asymptotic model of Moore & Saffman (Phil. Trans. R. Soc. Lond.A, vol. 272, 1972, pp. 403–429) is extended to take account of buoyancy forces in the force balance on a vortex element. The motion of a buoyant vortex is given by the transverse component of force balance, while the tangential component governs the dynamics of the structure in the core. We show that the local acceleration of axial flow is generated by the external pressure gradient due to gravity. The equations are then solved for vortex rings. An analytic solution for a buoyant vortex ring at a small initial inclination is obtained and asymptotically agrees with the literature
The Nusselt numbers of horizontal convection
We consider the problem of horizontal convection in which non-uniform
buoyancy, , is imposed on the top surface of a container and
all other surfaces are insulating. Horizontal convection produces a net
horizontal flux of buoyancy, , defined by vertically and temporally
averaging the interior horizontal flux of buoyancy. We show that
; overbar denotes a
space-time average over the top surface, angle brackets denote a volume-time
average and is the molecular diffusivity of buoyancy . This
connection between and
justifies the definition of the
horizontal-convective Nusselt number, , as the ratio of to the corresponding quantity produced
by molecular diffusion alone. We discuss the advantages of this definition of
over other definitions of horizontal-convective Nusselt number currently
in use. We investigate transient effects and show that equilibrates more rapidly than other
global averages, such as the domain averaged kinetic energy and bottom
buoyancy. We show that is
essentially the volume-averaged rate of Boussinesq entropy production within
the enclosure. In statistical steady state, the interior entropy production is
balanced by a flux of entropy through the top surface. This leads to an
equivalent "surface Nusselt number", defined as the surface average of vertical
buoyancy flux through the top surface times the imposed surface buoyancy
. In experiments it is likely easier to evaluate the surface
entropy flux, rather than the volume integral of
demanded by .Comment: 16 pages, 7 figure
An Arabidopsis rhomboid protease has roles in the chloroplast and in flower development
Increasing numbers of cellular pathways are now recognized to be regulated via proteolytic processing events. The rhomboid family of serine proteases plays a pivotal role in a diverse range of pathways, activating and releasing proteins via regulated intramembrane proteolysis. The prototype rhomboid protease, rhomboid-1 in Drosophila, is the key activator of epidermal growth factor (EGF) receptor pathway signalling in the fly and thus affects multiple aspects of development. The role of the rhomboid family in plants is explored and another developmental phenotype, this time in a mutant of an Arabidopsis chloroplast-localized rhomboid, is reported here. It is confirmed by GFP-protein fusion that this protease is located in the envelope of chloroplasts and of chlorophyll-free plastids elsewhere in the plant. Mutant plants lacking this organellar rhomboid demonstrate reduced fertility, as documented previously with KOM—the one other Arabidopsis rhomboid mutant that has been reported in the literature—along with aberrant floral morphology
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