Controlling Chaos: Periodic Defect Braiding in Active Nematics Confined to a Cardioid.

This work examines self-mixing in active nematics, a class of fluids in which mobile topological defects drive chaotic flows in a system comprised of biological filaments and molecular motors. We present experiments that demonstrate how geometrical confinement can influence the braiding dynamics of the defects. Notably, we show that confinement in cardioid-shaped wells leads to realization of the golden braid, a maximally efficient mixing state of exactly three defects with no defect creation or annihilation. We characterize the golden braid state using different measures of topological entropy and the Lyapunov exponent. In particular, topological entropy measured from the stretching rate of material lines agrees well with an analytical computation from braid theory. Increasing the size of the confining cardioid produces a transition from the golden braid, to the fully chaotic active turbulent state.

Fractal generation in a two-dimensional active-nematic fluid.

Active fluids, composed of individual self-propelled agents, can generate complex large-scale coherent flows. A particularly important laboratory realization of such an active fluid is a system composed of microtubules, aligned in a quasi-two-dimensional (2D) nematic phase and driven by adenosine-triphosphate-fueled kinesin motor proteins. This system exhibits robust chaotic advection and gives rise to a pronounced fractal structure in the nematic contours. We characterize such experimentally derived fractals using the power spectrum and discover that the power spectrum decays as k-ß for large wavenumbers k. The parameter ß is measured for several experimental realizations. Though ß is effectively constant in time, it does vary with experimental parameters, indicating differences in the scale-free behavior of the microtubule-based active nematic. Though the fractal patterns generated in this active system are reminiscent of passively advected dye in 2D chaotic flows, the underlying mechanism for fractal generation is more subtle. We provide a simple, physically inspired mathematical model of fractal generation in this system that relies on the material being locally compressible, though the total area of the material is conserved globally. The model also requires that large-scale density variations are injected into the material periodically. The model reproduces the power-spectrum decay k-ß seen in experiments. Linearizing the model of fractal generation about the equilibrium density, we derive an analytic relationship between ß and a single dimensionless quantity r, which characterizes the compressibility.

Trapping of swimmers in a vortex lattice.

We examine the motion of rigid, ellipsoidal swimmers subjected to a steady vortex flow in two dimensions. Numerical simulations of swimmers in a spatially periodic array of vortices reveal a range of possible behaviors, including trapping inside a single vortex and motility-induced diffusion across many vortices. While the trapping probability vanishes at a sufficiently high swimming speed, we find that it exhibits surprisingly large oscillations as this critical swimming speed is approached. Strikingly, at even higher swimming speeds, we find swimmers that swim perpendicular to their elongation direction can again become trapped. To explain this complex behavior, we investigate the underlying swimmer phase-space geometry. We identify the fixed points and periodic orbits of the swimmer equations of motion that regulate swimmer trapping inside a single vortex cell. For low to intermediate swimming speeds, we find that a stable periodic orbit surrounded by invariant tori forms a transport barrier to swimmers and can trap them inside individual vortices. For swimming speeds approaching the maximum fluid speed, we find instead that perpendicular swimmers can be trapped by asymptotically stable fixed points. A bifurcation analysis of the stable periodic orbit and the fixed points explains the complex and non-monotonic breakdown and re-emergence of swimmer trapping as the swimmer speed and shape are varied.

Ensemble-based topological entropy calculation (E-tec).

Topological entropy measures the number of distinguishable orbits in a dynamical system, thereby quantifying the complexity of chaotic dynamics. One approach to computing topological entropy in a two-dimensional space is to analyze the collective motion of an ensemble of system trajectories taking into account how trajectories "braid" around one another. In this spirit, we introduce the Ensemble-based Topological Entropy Calculation, or E-tec, a method to derive a lower-bound on topological entropy of two-dimensional systems by considering the evolution of a "rubber band" (piece-wise linear curve) wrapped around the data points and evolving with their trajectories. The topological entropy is bounded below by the exponential growth rate of this band. We use tools from computational geometry to track the evolution of the rubber band as data points strike and deform it. Because we maintain information about the configuration of trajectories with respect to one another, updating the band configuration is performed locally, which allows E-tec to be more computationally efficient than some competing methods. In this work, we validate and illustrate many features of E-tec on a chaotic lid-driven cavity flow. In particular, we demonstrate convergence of E-tec's approximation with respect to both the number of trajectories (ensemble size) and the duration of trajectories in time.

Mode-locking in advection-reaction-diffusion systems: An invariant manifold perspective.

Fronts propagating in two-dimensional advection-reaction-diffusion systems exhibit a rich topological structure. When the underlying fluid flow is periodic in space and time, the reaction front can lock to the driving frequency. We explain this mode-locking phenomenon using the so-called burning invariant manifolds (BIMs). In fact, the mode-locked profile is delineated by a BIM attached to a relative periodic orbit (RPO) of the front element dynamics. Changes in the type (and loss) of mode-locking can be understood in terms of local and global bifurcations of the RPOs and their BIMs. We illustrate these concepts numerically using a chain of alternating vortices in a channel geometry.

Using periodic orbits to compute chaotic transport rates between resonance zones.

Transport properties of chaotic systems are computable from data extracted from periodic orbits. Given a sufficient number of periodic orbits, the escape rate can be computed using the spectral determinant, a function that incorporates the eigenvalues and periods of periodic orbits. The escape rate computed from periodic orbits converges to the true value as more and more periodic orbits are included. Escape from a given region of phase space can be computed by considering only periodic orbits that lie within the region. An accurate symbolic dynamics along with a corresponding partitioning of phase space is useful for systematically obtaining all periodic orbits up to a given period, to ensure that no important periodic orbits are missing in the computation. Homotopic lobe dynamics (HLD) is an automated technique for computing accurate partitions and symbolic dynamics for maps using the topological forcing of intersections of stable and unstable manifolds of a few periodic anchor orbits. In this study, we apply the HLD technique to compute symbolic dynamics and periodic orbits, which are then used to find escape rates from different regions of phase space for the Hénon map. We focus on computing escape rates in parameter ranges spanning hyperbolic plateaus, which are parameter intervals where the dynamics is hyperbolic and the symbolic dynamics does not change. After the periodic orbits are computed for a single parameter value within a hyperbolic plateau, periodic orbit continuation is used to compute periodic orbits over an interval that spans the hyperbolic plateau. The escape rates computed from a few thousand periodic orbits agree with escape rates computed from Monte Carlo simulations requiring hundreds of billions of orbits.

Using heteroclinic orbits to quantify topological entropy in fluid flows.

Topological approaches to mixing are important tools to understand chaotic fluid flows, ranging from oceanic transport to the design of micro-mixers. Typically, topological entropy, the exponential growth rate of material lines, is used to quantify topological mixing. Computing topological entropy from the direct stretching rate is computationally expensive and sheds little light on the source of the mixing. Earlier approaches emphasized that topological entropy could be viewed as generated by the braiding of virtual, or "ghost," rods stirring the fluid in a periodic manner. Here, we demonstrate that topological entropy can also be viewed as generated by the braiding of ghost rods following heteroclinic orbits instead. We use the machinery of homotopic lobe dynamics, which extracts symbolic dynamics from finite-length pieces of stable and unstable manifolds attached to fixed points of the fluid flow. As an example, we focus on the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow. Over a certain parameter range, the topological entropy is primarily due to the braiding of a period-three orbit. However, this orbit does not explain the topological entropy for parameter values where it does not exist, nor does it explain the excess of topological entropy for the entire range of its existence. We show that braiding by heteroclinic orbits provides an accurate computation of topological entropy when the period-three orbit does not exist, and that it provides an explanation for some of the excess topological entropy when the period-three orbit does exist. Furthermore, the computation of symbolic dynamics using heteroclinic orbits has been automated and can be used to compute topological entropy for a general 2D fluid flow.

Thermorudis pharmacophila sp. nov., a novel member of the class Thermomicrobia isolated from geothermal soil, and emended descriptions of Thermomicrobium roseum, Thermomicrobium carboxidum, Thermorudis peleae and Sphaerobacter thermophilus.

An aerobic, thermophilic and cellulolytic bacterium, designated strain WKT50.2T, was isolated from geothermal soil at Waikite, New Zealand. Strain WKT50.2T grew at 53-76 °C and at pH 5.9-8.2. The DNA G+C content was 58.4 mol%. The major fatty acids were 12-methyl C18 : 0 and C18 : 0. Polar lipids were all linked to long-chain 1,2-diols, and comprised 2-acylalkyldiol-1-O-phosphoinositol (diolPI), 2-acylalkyldiol-1-O-phosphoacylmannoside (diolP-acylMan), 2-acylalkyldiol-1-O-phosphoinositol acylmannoside (diolPI-acylMan) and 2-acylalkyldiol-1-O-phosphoinositol mannoside (diolPI-Man). Strain WKT50.2T utilized a range of cellulosic substrates, alcohols and organic acids for growth, but was unable to utilize monosaccharides. Robust growth of WKT50.2T was observed on protein derivatives. WKT50.2T was sensitive to ampicillin, chloramphenicol, kanamycin, neomycin, polymyxin B, streptomycin and vancomycin. Metronidazole, lasalocid A and trimethoprim stimulated growth. Phylogenetic analysis of 16S rRNA gene sequences showed that WKT50.2T belonged to the class Thermomicrobia within the phylum Chloroflexi, and was most closely related to Thermorudis peleae KI4T (99.6% similarity). DNA-DNA hybridization between WKT50.2T and Thermorudis peleae DSM 27169T was 18.0%. Physiological and biochemical tests confirmed the phenotypic and genotypic differentiation of strain WKT50.2T from Thermorudis peleae KI4T and other members of the Thermomicrobia. On the basis of its phylogenetic position and phenotypic characteristics, we propose that strain WKT50.2T represents a novel species, for which the name Thermorudis pharmacophila sp. nov. is proposed, with the type strain WKT50.2T ( = DSM 26011T = ICMP 20042T). Emended descriptions of Thermomicrobium roseum, Thermomicrobium carboxidum, Thermorudis peleae and Sphaerobacter thermophilus are also proposed, and include the description of a novel respiratory quinone, MK-8 2,3-epoxide (23%), in Thermomicrobium roseum.

Finite-time barriers to front propagation in two-dimensional fluid flows.

Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid. These barriers form one-dimensional curves in a two-dimensional fluid flow. In prior studies, the fluid velocity field was required to be either time-independent or time-periodic. In the present study, we develop an approach to identify prominent one-way barriers based only on fluid velocity data over a finite time interval, which may have arbitrary time-dependence. We call such a barrier a burning Lagrangian coherent structure (bLCS) in analogy to Lagrangian coherent structures (LCSs) commonly used in passive advection. Our approach is based on the variational formulation of LCSs using curves of stationary "Lagrangian shear," introduced by Farazmand et al. [Physica D 278-279, 44 (2014)] in the context of passive advection. We numerically validate our technique by demonstrating that the bLCS closely tracks the BIM for a time-independent, double-vortex channel flow with an opposing "wind."

Maximally mixing active nematics.

Active nematics are an important new paradigm in soft condensed matter systems. They consist of rodlike components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in which a small patch of fluid is stretched exponentially in length. Using simulation, this paper shows that this system can exhibit stable periodic motion when confined to a sufficiently small square with periodic boundary conditions. Moreover, employing tools from braid theory, we show that this motion is maximally mixing, in that it optimizes the (dimensionless) "topological entropy"-the exponential stretching rate of a material line advected by the fluid. That is, this periodic motion of the defects, counterintuitively, produces more chaotic mixing than chaotic motion of the defects. We also explore the stability of the periodic state. Importantly, we show how to stabilize this orbit into a larger periodic tiling, a critical necessity for it to be seen in future experiments.

A turnstile mechanism for fronts propagating in fluid flows.

We consider the propagation of fronts in a periodically driven flowing medium. It is shown that the progress of fronts in these systems may be mediated by a turnstile mechanism akin to that found in chaotic advection. We first define the modified ("active") turnstile lobes according to the evolution of point sources across a transport boundary. We then show that the lobe boundaries may be constructed from stable and unstable burning invariant manifolds (BIMs)--one-way barriers to front propagation analogous to traditional invariant manifolds for passive advection. Because the BIMs are one-dimensional curves in a three-dimensional (xyθ) phase space, their projection into xy-space exhibits several key differences from their advective counterparts: (lobe) areas are not preserved, BIMs may self-intersect, and an intersection between stable and unstable BIMs does not map to another such intersection. These differences must be accommodated in the correct construction of the new turnstile. As an application, we consider a lobe-based treatment protocol for protecting an ocean bay from an invading algae bloom.

Invariant manifolds and the geometry of front propagation in fluid flows.

Recent theoretical and experimental work has demonstrated the existence of one-sided, invariant barriers to the propagation of reaction-diffusion fronts in quasi-two-dimensional periodically driven fluid flows. These barriers were called burning invariant manifolds (BIMs). We provide a detailed theoretical analysis of BIMs, providing criteria for their existence, a classification of their stability, a formalization of their barrier property, and mechanisms by which the barriers can be circumvented. This analysis assumes the sharp front limit and negligible feedback of the front on the fluid velocity. A low-dimensional dynamical systems analysis provides the core of our results.

Demonstration of turnstiles as a chaotic ionization mechanism in Rydberg atoms.

We present an experimental and theoretical study of the chaotic ionization of quasi-one-dimensional potassium Rydberg wave packets via a classical phase-space turnstile mechanism. Turnstiles form a general transport mechanism for numerous chaotic systems, and this study explicitly illuminates their relevance to atomic ionization. We create time-dependent Rydberg wave packets, subject them to alternating applied electric-field pulses, and measure the electron survival probability. Ionization depends not only on the initial electron energy, but also on the classical phase-space position of the electron with respect to the turnstile--that part of the electron packet inside the turnstile ionizes after the applied ionization sequence, while that part outside the turnstile does not. The survival data thus encode information on the shape and location of the turnstile, in good agreement with theoretical predictions.

Metabolic products of European-type propolis. Synthesis and analysis of glucuronides and sulfates.

ETHNOPHARMACOLOGICAL RELEVANCE: Propolis is a bee-derived product used since antiquity for its general health-giving properties and is especially noted for its anti-bacterial activity. In more recent times, propolis has been employed against more specific targets such as antiproliferative effects vs cancer cells, wound healing and type-2 diabetes. AIM OF THE STUDY: European (poplar)-type propolis from New Zealand contains a number of hydroxy cinnamic acid esters and a set of aglycone flavonoid compounds, mainly chrysin, galangin, pinocembrin and pinobanksin. Propolis is usually taken orally and propolis metabolites quickly appear in the plasma of the ingested. In this work we aimed to identify the major flavonoid plasma metabolites by direct analysis of the plasma. MATERIALS AND METHODS: After consumption of a large dose of propolis in a single sitting, blood samples were taken and analysed using LCMS/MS. The major flavonoid metabolites identified were also synthesised using chemical (sulfates) or enzymatic methods (glucuronides). RESULTS: Both the sulfate and glucuronide conjugates of the four major propolis flavonoids are readily detected in human plasma after propolis ingestion. Preparation of the sulfates and glucuronides of the four major flavonoids allowed the relative proportions of the various metabolites to be determined. Although the sulfates are seen as large peaks in the LCMS/MS, the glucuronides are the dominant conjugate species. CONCLUSIONS: This study shows most of the flavonoids in the plasma are present as 7-O-glucuronides with only galangin showing some di-glucuronidation (3,7-O-diglucuronide). No evidence was found for hydroxy cinnamic acid type metabolites in the plasma samples.

Reference intervals and values for fecal cortisol, aldosterone, and the ratio of cortisol to dehydroepiandrosterone metabolites in four species of cetaceans.

The goal of the current study was to create reference intervals and values for several common and one potential novel physiological indicators of animal welfare for four species of cetaceans. The subjects included 189 bottlenose dolphins (Tursiops truncatus), 27 Indo-Pacific bottlenose dolphins (Tursiops aduncus), eight Pacific white-sided dolphins (Lagenorhynchus obliquidens), and 13 beluga whales (Delphinapterus leucas) at Alliance of Marine Mammal Parks and Aquariums and/or Association of Zoos and Aquariums accredited facilities. During two sampling time periods between July and November of 2018 and between January and April of 2019, fecal samples were collected weekly for five weeks from all animals. Samples were processed and analyzed using enzyme immunoassay for fecal cortisol, aldosterone, and dehydroepiandrosterone (DHEA) metabolites. Linear mixed models were used to examine demographic and time factors impacting hormone metabolite concentrations. Age, sex, and time of year were all significant predictors for some of the models (p < 0.01). An iOS mobile application ZooPhysioTrak was created for easy access to species-specific reference intervals and values accounting for significant predictors. For facilities without access to this application, additional reference intervals and values were constructed without accounting for significant predictors. Information gained from this study and the use of the application can provide reference intervals and values to make informed management decisions for cetaceans in zoological facilities.

Health reference intervals and values for common bottlenose dolphins (Tursiops truncatus), Indo-Pacific bottlenose dolphins (Tursiops aduncus), Pacific white-sided dolphins (Lagenorhynchus obliquidens), and beluga whales (Delphinapterus leucas).

This study reports comprehensive clinical pathology data for hematology, serum, and plasma biochemistry reference intervals for 174 apparently healthy common bottlenose dolphins (Tursiops truncatus) and reference values for 27 Indo-Pacific bottlenose dolphins (Tursiops aduncus), 13 beluga whales (Delphinapterus leucas), and 6 Pacific white-sided dolphins (Lagenorhynchus obliquidens) in zoos and aquariums accredited by the Alliance for Marine Mammal Parks and Aquariums and the Association of Zoos & Aquariums. Blood samples were collected as part of a larger study titled "Towards understanding the welfare of cetaceans in zoos and aquariums" (colloquially called the Cetacean Welfare Study). Two blood samples were collected following a standardized protocol, and two veterinarian examinations were conducted approximately six months apart between July to November 2018 and January to April 2019. Least square means, standard deviations, and 95% confidence intervals were calculated for hematology, serum, and plasma biochemical variables. Comparisons by age, gender, and month revealed statistically significant differences (p < 0.01) for several variables. Reference intervals and values were generated for samples tested at two laboratories for up to 56 hematologic, serum, and plasma biochemical variables. To apply these data, ZooPhysioTrak, an iOS mobile software application, was developed to provide a new resource for cetacean management. ZooPhysioTrak provides species-specific reference intervals and values based on user inputs of individual demographic and sample information. These data provide a baseline from which to compare hematological, serum, and plasma biochemical values in cetaceans in zoos and aquariums.

Barriers to front propagation in laminar, three-dimensional fluid flows.

We present experiments on one-way barriers that block reaction fronts in a fully three-dimensional (3D) fluid flow. Fluorescent Belousov-Zhabotinsky reaction fronts are imaged with laser-scanning in a laminar, overlapping vortex flow. The barriers are analyzed with a 3D extension to burning invariant manifold (BIM) theory that was previously applied to two-dimensional advection-reaction-diffusion processes. We discover tube and sheet barriers that guide the front evolution. The experimentally determined barriers are explained by BIMs calculated from a model of the flow.

Escape of trajectories from a vase-shaped cavity.

We consider the escape of ballistic trajectories from an open, vase-shaped cavity. Such a system serves as a model for microwaves escaping from a cavity or electrons escaping from a microjunction. Fixing the initial position of a particle and recording its escape time as a function of the initial launch direction, the resulting escape-time plot shows "epistrophic fractal" structure--repeated structure within structure at all levels of resolution with new features appearing in the fractal at longer time scales. By launching trajectories simultaneously in all directions (modeling an outgoing wave), a detector placed outside the cavity would measure a train of escaping pulses. We connect the structure of this chaotic pulse train with the fractal structure of the escape-time plot.

Frozen reaction fronts in steady flows: A burning-invariant-manifold perspective.

The dynamics of fronts, such as chemical reaction fronts, propagating in two-dimensional fluid flows can be remarkably rich and varied. For time-invariant flows, the front dynamics may simplify, settling in to a steady state in which the reacted domain is static, and the front appears "frozen." Our central result is that these frozen fronts in the two-dimensional fluid are composed of segments of burning invariant manifolds, invariant manifolds of front-element dynamics in xyθ space, where θ is the front orientation. Burning invariant manifolds (BIMs) have been identified previously as important local barriers to front propagation in fluid flows. The relevance of BIMs for frozen fronts rests in their ability, under appropriate conditions, to form global barriers, separating reacted domains from nonreacted domains for all time. The second main result of this paper is an understanding of bifurcations that lead from a nonfrozen state to a frozen state, as well as bifurcations that change the topological structure of the frozen front. Although the primary results of this study apply to general fluid flows, our analysis focuses on a chain of vortices in a channel flow with an imposed wind. For this system, we present both experimental and numerical studies that support the theoretical analysis developed here.

Age-induced diminution of free radical scavenging capacity in bee pollens and the contribution of constituent flavonoids.

Bee-collected pollen ("bee pollen") is promoted as a health food with a wide range of nutritional and therapeutic properties. The objective of the current study is to evaluate the contribution made through the free radical scavenging capability of bee-collected floval pollens by their flavonoid/phenolics constituents, and to determine whether this capability is affected by aging. The free radical scavenging effectiveness of a bee pollen (EC(50)) as measured by the DPPH method is shown to be determined by the nature and levels of the constituent floral pollens, which can be assayed via their phenolics profiles by HPLC. Each pure floral pollen has been found to possess a consistent EC(50) value, irrespective of its geographic origin or date of collection, and the EC(50) value is determined to a large extent (ca. 50%) by the nature and the levels of the pollen's flavonoids and phenolic acids. Non-phenolic antioxidants, possibly proteins, account for the balance of the activity. Pollen aging over 3 years is demonstrated to reduce the free radical scavenging activity by up to 50% in the most active floral pollens, which tend to contain the highest levels of flavonoids/phenolic acids. It is suggested that the freshness of a bee pollen may be determined from its free radical scavenging capacity relative to that of fresh bee pollen containing the same floral pollen mix.