Pulsed Gradient Spin Echo Nuclear Magnetic Resonance Measurement and Simulation of Two-Fluid Taylor Vortex Flow in a Vertically Oriented Taylor–Couette Device

Magnetic resonance microscopy and Ansys Fluent^? computational fluid dynamics simulation have been used to classify Taylor vortex flows (TVF) for several single fluid and axially stratified two-fluid systems in a vertically oriented Taylor–Couette device. A Rheo-NMR (nuclear magnetic resonance) Couette system (Magritek Ltd, New Zealand) with a 1.05-mm gap was used to evaluate the transition from Couette flow to TVF in 1.65 cSt silicone oil, 1 cSt deionized water, and 0.65 cSt silicone oil. The rotation rate at which instability onset occurred agreed between experiment and simulation, as did the critical wavelength. Velocities were mapped for axially stratified two-fluid systems. The vortex containing the two-fluid interface was found to form with a significantly longer wavelength than that observed in the pure fluids. For experiments and simulations in the TVF regime, a region with no secondary flows was found at the interface, indicating interface stabilization by surface tension forces.     

Thermologic investigations of three species of <Emphasis Type="Italic">Amorphophallus</Emphasis>

Thermologic investigations were carried out on three species of Amorphophallus: A. konjac, A. paeoniifolius and A. titanum, all the three strongly thermogenic. Moreover, their breeding system is described as protogynous, the heat production occurs in the appendix and male florets, no warming is seen in the female florets and pollen is shed after the end of heat dissipation. All the three have large, impressive inflorescences developed from big corms and have considerable sizes. During their inflorescence, they have a strong scent like rotting meat with carrion smell. Amorphophallus konjac (K. Koch) has a large, exposed appendix that produces a disgusting scent during the day of the female phase of blooming. The appendix produces about 3 W for several hours, and the temperature elevation is about 2.9 K. The low temperature elevation is attributed to a high surface area and a high evaporative heat loss from the appendix. During the male phase of blooming, a second episode of thermogenesis occurs during the same time of day, apparently from the male florets, reaching a maximum of 1.6 W. Amorphophallus paeoniifolius (Dennst.) Nicolson has a spadix that varies considerably from that of A. konjac and A. titanum with an amorphous upper end of the appendix like a shrunken red pepper instead of cone-like appendices for the two others. It shows thermogenic temperature increases of up to +9.1 K in the male florets and +2.6 K for a short time in the appendix. Amorphophallus titanum (Becc.) Becc. ex Arcang is the largest inflorescence of the world, growing up to 300 cm high and 250 cm across. A much smaller plant was observed during its thermogenic period by means of infrared (IR) thermography, IR thermometry, and thermometric data logger. The temperature maximum showed 36.6 °C at ambient 24.0 °C, which means a temperature difference of about +12.6 K. In the morning of the next day, all temperatures are back to ambient at about 24 °C. Estimates of the heat production (about 74 W) were made from the geometric data and special assumptions with respect to the heat transfer.     

Packing seagulls

A seagull in a graph is an induced three-vertex path. When does a graph G have k pairwise vertex-disjoint seagulls? This is NP-complete in general, but for graphs with no stable set of size three we give a complete solution. This case is of special interest because of a connection with Hadwiger’s conjecture which was the motivation for this research; and we deduce a unification and strengthening of two theorems of Blasiak [2] concerned with Hadwiger’s conjecture. Our main result is that a graph G (different from the five-wheel) with no three-vertex stable set contains k disjoint seagulls if and only if

1. |V (G)|≥3k
2. G is k-connected
3. for every clique C of G, if D denotes the set of vertices in V (G)\C that have both a neighbour and a non-neighbour in C then |D|+|V (G)\C|≥2k, and
4. the complement graph of G has a matching with k edges.

We also address the analogous fractional and half-integral packing questions, and give a polynomial time algorithm to test whether there are k disjoint seagulls.     

Dynamic NMR microscopy measurement of the dynamics and flow partitioning of colloidal particles in a bifurcation

The flow and distribution of Newtonian, polymeric and colloid suspension fluids at low Reynolds numbers in bifurcations has importance in a wide range of disciplines, including microvascular physiology and microfluidic devices. A bifurcation consisting of circular capillaries laser etched into a hard polymer with inlet diameter 2.50 ± 0.01 mm, bifurcating to a small diameter outlet of 0.76 ± 0.01 mm and a large diameter outlet of 1.25 ± 0.01 mm is examined. Four distinct fluids (water, 0.25%wt xanthan gum, 8 and 22%vol hard-sphere colloidal suspensions) are flowed at flow rates from 10 to 30 ml/h corresponding to Reynolds numbers based on the entry flow from 0.001 to 8. PGSE NMR techniques are applied to obtain dynamic images of the fluids inside the bifurcation with spatial resolution of 59 × 59 μm/pixel in plane over a 200-μm-thick slice. Velocity in all three spatial directions is examined to determine the impact of secondary flows and characterize the transport in the bifurcation. The velocity data provide direct measurement of the volumetric distribution of the flow between the two channels as a function of flow rate. Water and the 8% colloidal suspension show a constant distribution with increasing flow rate, the xanthan gum shows an increase in fluid going into the larger outlet with higher flow rate, and the 22% colloidal suspension shows a decrease in fluid entering the larger channel with higher flow rate. For the colloidal particle flow, the distribution of colloid particles down the capillary is determined by examining the spectrally resolved propagator for the oil inside the core–shell particles in a direction perpendicular to the axial flow. Using dynamic magnetic resonance microscopy, the potential for using magnetic resonance for “particle counting” in a microscale bifurcation is thus demonstrated.     

On Turner’s theorem and first-order theory

A theorem of E.C. Turner states that if F is a finitely generated free group, then the test words are precisely the elements not contained in any proper retract. In this paper, we examine some ideas in model theory and logic related to Turner’s characterization of test words and introduce Turner groups, a class of groups containing all finite groups and all stably hyperbolic groups satisfying this characterization. We show that Turner’s theorem is not first-order expressible. However, we prove that every finitely generated elementary free group is a Turner group.     

Heavy quark production in jets

Zeitschrift für Physik C Particles and Fields - We study possible deviations from the Standard Model in the reactione + e ?→Z?, where ? denotes a spinless neutral boson....     

Generating Multiset Permutations in Constant Time

An algorithm is presented that generates multiset permutations taking constant time between each permutation.     

Graph Minors. XX. Wagner''s conjecture

In a previous paper (J. Combin. Theory 48 (1990) 255) we showed that for any infinite set of (finite) graphs drawn in a fixed surface, one of the graphs is isomorphic to a minor of another. In this paper we extend that result in two ways:

• we generalize from graphs to hypergraphs drawn in a fixed surface, in which each edge has two or three ends, and

• the edges of our hypergraphs are labelled from a well-quasi-order, and the minor relation is required to respect this order.

This result is another step in the proof of Wagner's conjecture, that for any infinite set of graphs, one is isomorphic to a minor of another.     

Bad news for chordal partitions

Reed and Seymour [1998] asked whether every graph has a partition into induced connected nonempty bipartite subgraphs such that the quotient graph is chordal. If true, this would have significant ramifications for Hadwiger's Conjecture. We prove that the answer is “no.” In fact, we show that the answer is still “no” for several relaxations of the question.