Spiral Waves in Media with Complex Excitable Dynamics

The structure of spiral waves is investigated in super-excitable reaction-diffusion systems where the local dynamics exhibits multi-looped phase space trajectories. It is shown that such systems support stable spiral waves with broken symmetry and complex temporal dynamics. The main structural features of such waves, synchronization defect lines, are demonstrated to be similar to those of spiral waves in systems with complex-oscillatory dynamics.Comment: to appear in International Journal of Bifurcation and Chao

The rise of fully turbulent flow

Over a century of research into the origin of turbulence in wallbounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow. At slightly higher speeds the situation changes distinctly and the entire flow is turbulent. Neither the origin of the different states encountered during transition, nor their front dynamics, let alone the transformation to full turbulence could be explained to date. Combining experiments, theory and computer simulations here we uncover the bifurcation scenario organising the route to fully turbulent pipe flow and explain the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence and fully turbulent flows.Comment: 31 pages, 9 figure

Computational Study of Turbulent-Laminar Patterns in Couette Flow

Turbulent-laminar patterns near transition are simulated in plane Couette flow using an extension of the minimal flow unit methodology. Computational domains are of minimal size in two directions but large in the third. The long direction can be tilted at any prescribed angle to the streamwise direction. Three types of patterned states are found and studied: periodic, localized, and intermittent. These correspond closely to observations in large aspect ratio experiments.Comment: 4 pages, 5 figure

Characterization of aerosol associated with enhanced small particle number concentrations in a suburban forested environment

Two elevated particle number/mass growth events associated with Aitken‐mode particles were observed during a sampling campaign (13–29 September 2004) at the Duke University Free‐Air CO2 Enrichment facility, a forested field site located in suburban central North Carolina. Aerosol growth rates between 1.2 and 4.9 nm hr−1 were observed, resulting in net increases in geometric mean diameter of 21 and 37 nm during events. Growth was dominated by addition of oxidized organic compounds. Campaign‐average aerosol mass concentrations measured by an Aerodyne quadrupole aerosol mass spectrometer (Q‐AMS) were 1.9 ± 1.6 (σ), 1.6 ± 1.9, 0.1 ± 0.1, and 0.4 ± 0.4 μg m−3 for organic mass (OM), sulfate, nitrate, and ammonium, respectively. These values represent 47%, 40%, 3%, and 10%, respectively, of the measured submicron aerosol mass. Based on Q‐AMS spectra, OM was apportioned to hydrocarbon‐like organic aerosol (HOA, likely representing primary organic aerosol) and two types of oxidized organic aerosol (OOA‐1 and OOA‐2), which constituted on average 6%, 58%, and 36%, respectively, of the apportioned OM. OOA‐1 probably represents aged, regional secondary organic aerosol (SOA), while OOA‐2 likely reflects less aged SOA. Organic aerosol characteristics associated with the events are compared to the campaign averages. Particularly in one event, the contribution of OOA‐2 to overall OM levels was enhanced, indicating the likelihood of less aged SOA formation. Statistical analyses investigate the relationships between HOA, OOA‐1, OOA‐2, other aerosol components, gas‐phase species, and meteorological data during the campaign and individual events. No single variable clearly controls the occurrence of a particle growth event

Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications

In a weakly excitable medium, characterized by a large threshold stimulus, the free end of an isolated broken plane wave (wave tip) can either rotate (steadily or unsteadily) around a large excitable core, thereby producing a spiral pattern, or retract causing the wave to vanish at boundaries. An asymptotic analysis of spiral motion and retraction is carried out in this weakly excitable large core regime starting from the free-boundary limit of the reaction-diffusion models, valid when the excited region is delimited by a thin interface. The wave description is shown to naturally split between the tip region and a far region that are smoothly matched on an intermediate scale. This separation allows us to rigorously derive an equation of motion for the wave tip, with the large scale motion of the spiral wavefront slaved to the tip. This kinematic description provides both a physical picture and exact predictions for a wide range of wave behavior, including: (i) steady rotation (frequency and core radius), (ii) exact treatment of the meandering instability in the free-boundary limit with the prediction that the frequency of unstable motion is half the primary steady frequency (iii) drift under external actions (external field with application to axisymmetric scroll ring motion in three-dimensions, and spatial or/and time-dependent variation of excitability), and (iv) the dynamics of multi-armed spiral waves with the new prediction that steadily rotating waves with two or more arms are linearly unstable. Numerical simulations of FitzHug-Nagumo kinetics are used to test several aspects of our results. In addition, we discuss the semi-quantitative extension of this theory to finite cores and pinpoint mathematical subtleties related to the thin interface limit of singly diffusive reaction-diffusion models

Global atmospheric budget of acetaldehyde: 3-D model analysis and constraints from in-situ and satellite observations

We construct a global atmospheric budget for acetaldehyde using a 3-D model of atmospheric chemistry (GEOS-Chem), and use an ensemble of observations to evaluate present understanding of its sources and sinks. Hydrocarbon oxidation provides the largest acetaldehyde source in the model (128 Tg a<sup>−1</sup>, a factor of 4 greater than the previous estimate), with alkanes, alkenes, and ethanol the main precursors. There is also a minor source from isoprene oxidation. We use an updated chemical mechanism for GEOS-Chem, and photochemical acetaldehyde yields are consistent with the Master Chemical Mechanism. We present a new approach to quantifying the acetaldehyde air-sea flux based on the global distribution of light absorption due to colored dissolved organic matter (CDOM) derived from satellite ocean color observations. The resulting net ocean emission is 57 Tg a<sup>−1</sup>, the second largest global source of acetaldehyde. A key uncertainty is the acetaldehyde turnover time in the ocean mixed layer, with quantitative model evaluation over the ocean complicated by known measurement artifacts in clean air. Simulated concentrations in surface air over the ocean generally agree well with aircraft measurements, though the model tends to overestimate the vertical gradient. PAN:NO<sub>x</sub> ratios are well-simulated in the marine boundary layer, providing some support for the modeled ocean source. We introduce the Model of Emissions of Gases and Aerosols from Nature (MEGANv2.1) for acetaldehyde and ethanol and use it to quantify their net flux from living terrestrial plants. Including emissions from decaying plants the total direct acetaldehyde source from the land biosphere is 23 Tg a<sup>−1</sup>. Other terrestrial acetaldehyde sources include biomass burning (3 Tg a<sup>−1</sup>) and anthropogenic emissions (2 Tg a<sup>−1</sup>). Simulated concentrations in the continental boundary layer are generally unbiased and capture the spatial gradients seen in observations over North America, Europe, and tropical South America. However, the model underestimates acetaldehyde levels in urban outflow, suggesting a missing source in polluted air. Ubiquitous high measured concentrations in the free troposphere are not captured by the model, and based on present understanding are not consistent with concurrent measurements of PAN and NO<sub>x</sub>: we find no compelling evidence for a widespread missing acetaldehyde source in the free troposphere. We estimate the current US source of ethanol and acetaldehyde (primary + secondary) at 1.3 Tg a<sup>−1</sup> and 7.8 Tg a<sup>−1</sup>, approximately 60{%} and 480% of the corresponding increases expected for a national transition from gasoline to ethanol fuel

Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states

Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are seen to be unstable in different regions of parameter space. The corresponding bifurcations and bifurcated states are characterized by performing direct numerical simulations. In addition, computations of the adjoint linear stability operator eigenmodes are also performed and serve to obtain a number of matrix elements characterizing the long-wavelength deformations of scroll waves.Comment: 30 pages 16 figures, submitted to Phys. Rev.

Twist and writhe dynamics of stiff filaments

This letter considers the dynamics of a stiff filament, in particular the coupling of twist and bend via writhe. The time dependence of the writhe of a filament is $W_r^2\sim L t^{1/4}$ for a linear filament and $W_r^2\sim t^{1/2} / L$ for a curved filament. Simulations are used to study the relative importance of crankshaft motion and tube like motion in twist dynamics. Fuller's theorem, and its relation with the Berry phase, is reconsidered for open filamentsComment: 7 Pages with 2 figure

Entry in the ADHD drugs market: Welfare impact of generics and me-toos

Recent decades have seen a growth in treatments for attention deficit hyperactivity disorder (ADHD) including many branded and generic drugs. In the early 2000's, new drug entry dramatically altered market shares. We estimate a demand system for ADHD drugs and assess the welfare impact of new drugs. We find that entry induced large welfare gains by reducing prices of substitute drugs, and by providing alternative delivery mechanisms for existing molecules. Our results suggest that the success of follow-on patented drugs may come from unanticipated innovations like delivery mechanisms, a factor ignored by proposals to retard new follow-on drug approvals

Helicoidal instability of a scroll vortex in three-dimensional reaction-diffusion systems

We study the dynamics of scroll vortices in excitable reaction-diffusion systems analytically and numerically. We demonstrate that intrinsic three-dimensional instability of a straight scroll leads to the formation of helicoidal structures. This behavior originates from the competition between the scroll curvature and unstable core dynamics. We show that the obtained instability persists even beyond the meander core instability of two-dimensional spiral wave.Comment: 4 pages, 5 figures, revte