Hamiltonian flows on null curves

The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the KdV hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, it is shown that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio

Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations

We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.Comment: 33 pages, 5 figures; submitted to Journal of Nonlinear Scienc

A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow

Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time simulation of smoke. Here we introduce a time-discrete evolution equation for arbitrary closed polygons in 3-space that is a discretisation of the localised induction approximation of filament motion. This discretisation shares with its continuum limit the property that it is a completely integrable system. We apply this polygon evolution to a significant improvement of the numerical algorithms used in Computer Graphics.Comment: 15 pages, 3 figure

Ricci Solitons and Einstein-Scalar Field Theory

B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimension. As well, solutions of Euclidean-signature Einstein gravity coupled to a free massless scalar field with nonzero cosmological constant are associated to shrinking or expanding Ricci solitons. We exhibit examples, including an explicit family of complete expanding solitons which can be thought of as a Ricci flow for a complete Lorentzian metric. The possible generalization to Ricci-flat stationary metrics leads us to consider an alternative to Ricci flow.Comment: 17 pages, 1 figure; Revised version (organizational changes, other minor revisions and corrections, citations corrected and added), to appear in CQ

MHz-rate nitric oxide planar laser-induced fluorescence imaging in a Mach 10 hypersonic wind tunnel

Nitric oxide planar laser-induced fluorescence (NO PLIF) imaging at repetition rates as high as 1 MHz is demonstrated in the NASA Langley 31 in. Mach 10 hypersonic wind tunnel. Approximately 200 timecorrelated image sequences of between 10 and 20 individual frames were obtained over eight days of wind tunnel testing spanning two entries in March and September of 2009. The image sequences presented were obtained from the boundary layer of a 20° flat plate model, in which transition was induced using a variety of different shaped protuberances, including a cylinder and a triangle. The high-speed image sequences captured a variety of laminar and transitional flow phenomena, ranging from mostly laminar flow, typically at a lower Reynolds number and/or in the near wall region of the model, to highly transitional flow in which the temporal evolution and progression of characteristic streak instabilities and/or corkscrew-shaped vortices could be clearly identified

Differential systems associated with tableaux over Lie algebras

We give an account of the construction of exterior differential systems based on the notion of tableaux over Lie algebras as developed in [Comm. Anal. Geom 14 (2006), 475-496; math.DG/0412169]. The definition of a tableau over a Lie algebra is revisited and extended in the light of the formalism of the Spencer cohomology; the question of involutiveness for the associated systems and their prolongations is addressed; examples are discussed.Comment: 16 pages; to appear in: "Symmetries and Overdetermined Systems of Partial Differential Equations" (M. Eastwood and W. Miller, Jr., eds.), IMA Volumes in Mathematics and Its Applications, Springer-Verlag, New Yor

Variability in plasma concentrations of methylprednisolone 6 days after intrasynovial injection of methylprednisolone acetate in racing horses: A field study

Background: Methylprednisolone (MP) acetate is a commonly used corticosteroid for suppression of inflammation in synovial structures in horses. Its use is often regulated in equine sports by plasma MP concentrations. Objectives: To describe variability in MP plasma concentrations after MP acetate injection in different synovial structures and with co-administration with hyaluronic acid (HA). Study design: Field study in actively racing horses in three disciplines (Thoroughbred, Standardbred and Quarter Horse). Methods: Seventy-six horses (15 Thoroughbreds, 20 Standardbreds and 41 Quarter Horses) were included in the study. Injection of any synovial structure with a total body dose of 100 mg MP acetate was permitted, data were grouped according to the synovial structure injected and coadministration with HA. Plasma was collected before injection and at 6 days post-injection. Per cent censored data (below the limit of quantification) for each synovial structure were determined, and summary statistics generated by Robust Regression on Order. Differences between synovial structures and co-administration with HA were identified by ANOVA with Tukey’s post hoc testing. Results: Metacarpophalangeal (MCP) plasma concentrations contained 86% censored data and could not be included in the statistical analysis. The carpal joints (CJO) group had a lower plasma MP concentration (P \u3c 0.05) than the distal tarsal joints (DTJ) or medial femorotibial (MFT), the no HA (NHA) group had a lower plasma MP concentration (P \u3c 0.05) than HA. Main limitations: The synovial structures injected varied by racing discipline, so this study was unable to identify any differences between disciplines. Conclusions: Practitioners should be aware that injection of DTJ, CS and MFT joints, and combining MP acetate with HA may prolong its clearance, and withdrawal times for competition in regulated equine sports

Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space

Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a restricted class of topologies is consistent with the metric and the dilaton. A particular case of string motivated Liouville gravity is studied in detail. Path integral quantisation in generic Euclidean dilaton gravity is performed non-perturbatively by analogy to the Minkowskian case.Comment: 27 p., LaTeX, v2: included new refs. and a footnot

Synchronizing Cardiac Cycle Phase with Foot Strike to Optimize Cardiac Performance in Patients with Chronic Systolic Heart Failure and Cardiac Resynchronization Therapy (CRT)

Despite advances in medical and Cardiac Resynchronization Therapy (CRT), patients with chronic systolic heart failure (HF) have persistent symptoms including dyspnea on exertion and exercise intolerance. Novel strategies to improve exercise performance in these patients, such as optimizing cardio-locomotor coupling, could be particularly beneficial to improve functional capacity. For example, runners display a lower heart rate and higher oxygen pulse, suggestive of a higher stroke volume (SV), when foot strike occurs in diastole. Whether patients with HF undergoing CRT can similarly increase SV is unknown. PURPOSE: To compare the effects of diastolic versus systolic foot strike timing on exercise hemodynamics in patients with HF and CRT. METHODS: Ten patients (Age: 58 ± 17 years, 40% Female) with HF and previously implanted CRT pacemakers completed repeated 5-minute bouts of walking on a treadmill at a fixed but individualized speed (range: 1.5-3mph). Participants were randomized to walking to an auditory tone to synchronize their foot strike to either the systolic (ECG R-wave; 0 or 100%±15% or R-R interval) or diastolic phase (45±15% of the R-R interval) of their cardiac cycle. Participants were included if ≥50% of their steps were valid (i.e. in time). Patients wore a chest strap with an attached ECG sensor and accelerometer (CounterpaceR). Foot strike timing and associated valid step counts were assessed via CounterpaceR or post-hoc analysis of foot strike waveforms. Cardiopulmonary parameters were measured breath by breath via indirect calorimetry and cardiac output was measured via acetylene rebreathing, with SV calculated as the quotient of cardiac output and heart rate. RESULTS: There was no difference in oxygen uptake between conditions (1.02 ± 0.44 vs. 1.04 ± 0.44 L/min, P=0.298). When compared to systolic walking, stepping in diastole was associated with higher SV (Diastolic: 80 ± 28 vs. Systolic: 74 ± 26 ml, P=0.003) and cardiac output (8.3 ± 3.5 vs. 7.9 ± 3.4 L/min, P=0.004); heart rate (paced) was not different between conditions (101 ± 15 vs. 103 ± 14 bpm, P=0.300). Mean arterial pressure was significantly lower during diastolic walking (85 ± 12 vs. 98 ± 20 mmHg, P=0.007). CONCLUSION: In patients with HF and previous CRT, synchronizing foot strike with diastole during walking increased SV and cardiac output and reduced arterial pressure. Our findings indicate that in such paced hearts, diastolic stepping increases oxygen delivery and decreases afterload, which may facilitate increased exercise capacity. Therefore, if added to pacemakers, this cardio-locomotor coupling technology may maximize CRT efficiency and increase exercise participation and quality of life in patients with HF