Convergent Chaos

Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion should be refined. Despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods, as revealed by our investigation of a simple chaotic system (a realistic model for small bodies in a turbulent flow). We establish that this strong convergence is a multi-facetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions. Power laws, indicative of scale-free features, characterize the distribution of particles in the system. We use large-deviation and extreme-value statistics to explain the effect. Our results show that the interpretation of the 'butterfly effect' needs to be carefully qualified. We argue that the combination of mixing and clustering processes makes our specific model relevant to understanding the evolution of simple organisms. Lastly, this notion of convergent chaos, which implies the existence of conditions for which uncertainties are unexpectedly small, may also be relevant to the valuation of insurance and futures contracts

Invariance and plasticity in the Drosophila melanogaster metabolomic network in response to temperature

BACKGROUND: Metabolomic responses to extreme thermal stress have recently been investigated in Drosophila melanogaster. However, a network level understanding of metabolomic responses to longer and less drastic temperature changes, which more closely reflect variation in natural ambient temperatures experienced during development and adulthood, is currently lacking. Here we use high-resolution, non-targeted metabolomics to dissect metabolomic changes in D. melanogaster elicited by moderately cool (18°C) or warm (27°C) developmental and adult temperature exposures. RESULTS: We find that temperature at which larvae are reared has a dramatic effect on metabolomic network structure measured in adults. Using network analysis, we are able to identify modules that are highly differentially expressed in response to changing developmental temperature, as well as modules whose correlation structure is strongly preserved across temperature. CONCLUSIONS: Our results suggest that the effect of temperature on the metabolome provides an easily studied and powerful model for understanding the forces that influence invariance and plasticity in biological networks. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12918-014-0139-6) contains supplementary material, which is available to authorized users

Conditional stability of unstable viscous shock waves in compressible gas dynamics and MHD

Extending our previous work in the strictly parabolic case, we show that a linearly unstable Lax-type viscous shock solution of a general quasilinear hyperbolic--parabolic system of conservation laws possesses a translation-invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small $L^1\cap H^3$ perturbations, converging time-asymptotically to a translate of the unperturbed wave. That is, for a shock with $p$ unstable eigenvalues, we establish conditional stability on a codimension-$p$ manifold of initial data, with sharp rates of decay in all $L^p$. For $p=0$, we recover the result of unconditional stability obtained by Mascia and Zumbrun. The main new difficulty in the hyperbolic--parabolic case is to construct an invariant manifold in the absence of parabolic smoothing.Comment: 32p

The effects of water and microstructure on the performance of polymer electrolyte fuel cells

n this paper, we present a comprehensive non-isothermal, one-dimensional model of the cathode side of a Polymer Electrolyte Fuel Cell. We explicitly include the catalyst layer, gas diffusion layer and the membrane. The catalyst layer and gas diffusion layer are characterized by several measurable microstructural parameters. We model all three phases of water, with a view to capturing the effect that each has on the performance of the cell. A comparison with experiment is presented, demonstrating excellent agreement, particularly with regard to the effects of water activity in the channels and how it impacts flooding and membrane hydration. We present several results pertaining to the effects of water on the current density (or cell voltage), demonstrating the role of micro-structure, liquid water removal from the channel, water activity, membrane and gas diffusion layer thickness and channel temperature. These results provide an indication of the changes that are required to achieve optimal performance through improved water management and MEA-component design. Moreover, with its level of detail, the model we develop forms an excellent basis for a multi-dimensional model of the entire membrane electrode assembly

Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential

The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger equation. Their stability is examined using analytic and numerical methods. All trivial-phase stable solutions are deformations of the ground state of the linear Schr\"odinger equation. Our results show that a large number of condensed atoms is sufficient to form a stable, periodic condensate. Physically, this implies stability of states near the Thomas-Fermi limit.Comment: 12 pages, 17 figure

Inhomogeneous magnetization in dipolar ferromagnetic liquids

At high densities fluids of strongly dipolar spherical particles exhibit spontaneous long-ranged orientational order. Typically, due to demagnetization effects induced by the long range of the dipolar interactions, the magnetization structure is spatially inhomogeneous and depends on the shape of the sample. We determine this structure for a cubic sample by the free minimization of an appropriate microscopic density functional using simulated annealing. We find a vortex structure resembling four domains separated by four domain walls whose thickness increases proportional to the system size L. There are indications that for large L the whole configuration scales with the system size. Near the axis of the mainly planar vortex structure the direction of the magnetization escapes into the third dimension or, at higher temperatures, the absolute value of the magnetization is strongly reduced. Thus the orientational order is characterized by two point defects at the top and the bottom of the sample, respectively. The equilibrium structure in an external field and the transition to a homogeneous magnetization for strong fields are analyzed, too.Comment: 17 postscript figures included, submitted to Phys. Rev.

Genetic and metabolomic architecture of variation in diet restriction-mediated lifespan extension in Drosophila.

In most organisms, dietary restriction (DR) increases lifespan. However, several studies have found that genotypes within the same species vary widely in how they respond to DR. To explore the mechanisms underlying this variation, we exposed 178 inbred Drosophila melanogaster lines to a DR or ad libitum (AL) diet, and measured a panel of 105 metabolites under both diets. Twenty four out of 105 metabolites were associated with the magnitude of the lifespan response. These included proteinogenic amino acids and metabolites involved in α-ketoglutarate (α-KG)/glutamine metabolism. We confirm the role of α-KG/glutamine synthesis pathways in the DR response through genetic manipulations. We used covariance network analysis to investigate diet-dependent interactions between metabolites, identifying the essential amino acids threonine and arginine as hub metabolites in the DR response. Finally, we employ a novel metabolic and genetic bipartite network analysis to reveal multiple genes that influence DR lifespan response, some of which have not previously been implicated in DR regulation. One of these is CCHa2R, a gene that encodes a neuropeptide receptor that influences satiety response and insulin signaling. Across the lines, variation in an intronic single nucleotide variant of CCHa2R correlated with variation in levels of five metabolites, all of which in turn were correlated with DR lifespan response. Inhibition of adult CCHa2R expression extended DR lifespan of flies, confirming the role of CCHa2R in lifespan response. These results provide support for the power of combined genomic and metabolomic analysis to identify key pathways underlying variation in this complex quantitative trait

Immunosenescence in wild animals:Meta-analysis and outlook

Immunosenescence, the decline in immune defense with age, is an important mortality source in elderly humans but little is known of immunosenescence in wild animals. We systematically reviewed and meta-analysed evidence for age-related changes in immunity in captive and free-living populations of wild species (321 effect sizes in 62 studies across 44 species of mammals, birds and reptiles). As in humans, senescence was more evident in adaptive (acquired) than innate immune functions. Declines were evident for cell function (antibody response), the relative abundance of naive immune cells and an in vivo measure of overall immune responsiveness (local response to phytohaemagglutinin injection). Inflammatory markers increased with age, similar to chronic inflammation associated with human immunosenescence. Comparisons across taxa and captive vs free-living animals were difficult due to lack of overlap in parameters and species measured. Most studies are cross-sectional, which yields biased estimates of age-effects when immune function co-varies with survival. We therefore suggest longitudinal sampling approaches, and highlight techniques from human cohort studies that can be incorporated into ecological research. We also identify avenues to address predictions from evolutionary theory and the contribution of immunosenescence to age-related increases in disease susceptibility and mortality

A Signaling Protease Required for Melanization in Drosophila Affects Resistance and Tolerance of Infections

Organisms evolve two routes to surviving infections—they can resist pathogen growth (resistance) and they can endure the pathogenesis of infection (tolerance). The sum of these two properties together defines the defensive capabilities of the host. Typically, studies of animal defenses focus on either understanding resistance or, to a lesser extent, tolerance mechanisms, thus providing little understanding of the relationship between these two mechanisms. We suggest there are nine possible pairwise permutations of these traits, assuming they can increase, decrease, or remain unchanged in an independent manner. Here we show that by making a single mutation in the gene encoding a protease, CG3066, active in the melanization cascade in Drosophila melanogaster, we observe the full spectrum of changes; these mutant flies show increases and decreases in their resistance and tolerance properties when challenged with a variety of pathogens. This result implicates melanization in fighting microbial infections and shows that an immune response can affect both resistance and tolerance to infections in microbe-dependent ways. The fly is often described as having an unsophisticated and stereotypical immune response where single mutations cause simple binary changes in immunity. We report a level of complexity in the fly's immune response that has strong ecological implications. We suggest that immune responses are highly tuned by evolution, since selection for defenses that alter resistance against one pathogen may change both resistance and tolerance to other pathogens