1,209 research outputs found
Bipartite partial duals and circuits in medial graphs
It is well known that a plane graph is Eulerian if and only if its geometric
dual is bipartite. We extend this result to partial duals of plane graphs. We
then characterize all bipartite partial duals of a plane graph in terms of
oriented circuits in its medial graph.Comment: v2: minor changes. To appear in Combinatoric
Ribbon Graph Minors and Low-Genus Partial Duals
We give an excluded minor characterisation of the class of ribbon graphs that
admit partial duals of Euler genus at most one
On knotted streamtubes in incompressible hydrodynamical flow and a restricted conserved quantity
For certain families of fluid flow, a new conserved quantity --
stream-helicity -- has been established.Using examples of linked and knotted
streamtubes, it has been shown that stream-helicity does, in certain cases,
entertain itself with a very precise topological meaning viz, measure of the
degree of knottedness or linkage of streamtubes.As a consequence,
stream-helicity emerges as a robust topological invariant.Comment: This extended version is the basically a more clarified version of
the previous submission physics/0611166v
Optimization of the magnetic dynamo
In stars and planets, magnetic fields are believed to originate from the
motion of electrically conducting fluids in their interior, through a process
known as the dynamo mechanism. In this Letter, an optimization procedure is
used to simultaneously address two fundamental questions of dynamo theory:
"Which velocity field leads to the most magnetic energy growth?" and "How large
does the velocity need to be relative to magnetic diffusion?" In general, this
requires optimization over the full space of continuous solenoidal velocity
fields possible within the geometry. Here the case of a periodic box is
considered. Measuring the strength of the flow with the root-mean-square
amplitude, an optimal velocity field is shown to exist, but without limitation
on the strain rate, optimization is prone to divergence. Measuring the flow in
terms of its associated dissipation leads to the identification of a single
optimal at the critical magnetic Reynolds number necessary for a dynamo. This
magnetic Reynolds number is found to be only 15% higher than that necessary for
transient growth of the magnetic field.Comment: Optimal velocity field given approximate analytic form. 4 pages, 4
figure
Evaluations of topological Tutte polynomials
We find new properties of the topological transition polynomial of embedded
graphs, . We use these properties to explain the striking similarities
between certain evaluations of Bollob\'as and Riordan's ribbon graph
polynomial, , and the topological Penrose polynomial, . The general
framework provided by also leads to several other combinatorial
interpretations these polynomials. In particular, we express , ,
and the Tutte polynomial, , as sums of chromatic polynomials of graphs
derived from ; show that these polynomials count -valuations of medial
graphs; show that counts edge 3-colourings; and reformulate the Four
Colour Theorem in terms of . We conclude with a reduction formula for the
transition polynomial of the tensor product of two embedded graphs, showing
that it leads to additional relations among these polynomials and to further
combinatorial interpretations of and .Comment: V2: major revision, several new results, and improved expositio
A new proof that alternating links are non-trivial
We use a simple geometric argument and small cancellation properties of link
groups to prove that alternating links are non-trivial. This proof uses only
classic results in topology and combinatorial group theory.Comment: Minor changes. To appear in Fundamenta Mathematica
Responses of Rat P2X2 Receptors to Ultrashort Pulses of ATP Provide Insights into ATP Binding and Channel Gating
To gain insight into the way that P2X2 receptors localized at synapses might function, we explored the properties of outside-out patches containing many of these channels as ATP was very rapidly applied and removed. Using a new method to calibrate the speed of exchange of solution over intact patches, we were able to reliably produce applications of ATP lasting <200 ÎŒs. For all concentrations of ATP, there was a delay of at least 80 ÎŒs between the time when ATP arrived at the receptor and the first detectable flow of inward current. In response to 200-ÎŒs pulses of ATP, the time constant of the rising phase of the current was âŒ600 ÎŒs. Thus, most channel openings occurred when no free ATP was present. The current deactivated with a time constant of âŒ60 ms. The amplitude of the peak response to a brief pulse of a saturating concentration of ATP was âŒ70% of that obtained during a long application of the same concentration of ATP. Thus, ATP leaves fully liganded channels without producing an opening at least 30% of the time. Extensive kinetic modeling revealed three different schemes that fit the data well, a sequential model and two allosteric models. To account for the delay in opening at saturating ATP, it was necessary to incorporate an intermediate closed state into all three schemes. These kinetic properties indicate that responses to ATP at synapses that use homomeric P2X2 receptors would be expected to greatly outlast the duration of the synaptic ATP transient produced by a single presynaptic spike. Like NMDA receptors, P2X2 receptors provide the potential for complex patterns of synaptic integration over a time scale of hundreds of milliseconds
Analytical theory of forced rotating sheared turbulence: The perpendicular case
Rotation and shear flows are ubiquitous features of many astrophysical and geophysical bodies. To understand their origin and effect on turbulent transport in these systems, we consider a forced turbulence and investigate the combined effect of rotation and shear flow on the turbulence properties. Specifically, we study how rotation and flow shear influence the generation of shear flow (e.g., the direction of energy cascade), turbulence level, transport of particles and momentum, and the anisotropy in these quantities. In all the cases considered, turbulence amplitude is always quenched due to strong shear (Ο=Îœky2/AâȘĄ1, where A is the shearing rate, Îœ is the molecular viscosity, and ky is a characteristic wave number of small-scale turbulence), with stronger reduction in the direction of the shear than those in the perpendicular directions. Specifically, in the large rotation limit (ΩâȘąA), they scale as Aâ1 and Aâ1|lnâΟ|, respectively, while in the weak rotation limit (ΩâȘĄA), they scale as Aâ1 and Aâ2/3, respectively. Thus, flow shear always leads to weak turbulence with an effectively stronger turbulence in the plane perpendicular to shear than in the shear direction, regardless of rotation rate. The anisotropy in turbulence amplitude is, however, weaker by a factor of Ο1/3|lnâΟ| (âAâ1/3|lnâΟ|) in the rapid rotation limit (ΩâȘąA) than that in the weak rotation limit (ΩâȘĄA) since rotation favors almost-isotropic turbulence. Compared to turbulence amplitude, particle transport is found to crucially depend on whether rotation is stronger or weaker than flow shear. When rotation is stronger than flow shear (ΩâȘąA), the transport is inhibited by inertial waves, being quenched inversely proportional to the rotation rate (i.e., âΩâ1) while in the opposite case, it is reduced by shearing as Aâ1. Furthermore, the anisotropy is found to be very weak in the strong rotation limit (by a factor of 2) while significant in the strong shear limit. The turbulent viscosity is found to be negative with inverse cascade of energy as long as rotation is sufficiently strong compared to flow shear (ΩâȘąA) while positive in the opposite limit of weak rotation (ΩâȘĄA). Even if the eddy viscosity is negative for strong rotation (ΩâȘąA), flow shear, which transfers energy to small scales, has an interesting effect by slowing down the rate of inverse cascade with the value of negative eddy viscosity decreasing as |ÎœT|âAâ2 for strong shear. Furthermore, the interaction between the shear and the rotation is shown to give rise to a nondiffusive flux of angular momentum (Î effect), even in the absence of external sources of anisotropy. This effect provides a mechanism for the existence of shearing structures in astrophysical and geophysical systems
Convective plan-form two-scale dynamos in a plane layer
We study generation of magnetic fields, involving large spatial scales, by
convective plan-forms in a horizontal layer. Magnetic modes and their growth
rates are expanded in power series in the scale ratio, and the magnetic eddy
diffusivity (MED) tensor is derived for flows, symmetric about the vertical
axis in a layer. For convective rolls magnetic eddy correction is demonstrated
to be always positive. For rectangular cell patterns, the region in the
parameter space of negative MED coincides with that of small-scale magnetic
field generation. No instances of negative MED in hexagonal cells are found. A
family of plan-forms with a smaller symmetry group than that of rectangular
cell patterns has been found numerically, where MED is negative for molecular
magnetic diffusivity over the threshold for the onset of small-scale magnetic
field generation.Comment: Latex. 24 pages with 3 Postscript figures, 19 references. Final
version (expanded Appendix 2, 4 references added, notation changed to a more
"user-friendly"), accepted in Geophysical and Astrophysical Fluid Dynamic
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