Predicting chaotic statistics with unstable invariant tori.

It has recently been speculated that long-time average quantities of hyperchaotic dissipative systems may be approximated by weighted sums over unstable invariant tori embedded in the attractor, analogous to equivalent sums over periodic orbits, which are inspired by the rigorous periodic orbit theory and which have shown much promise in fluid dynamics. Using a new numerical method for converging unstable invariant two-tori in a chaotic partial differential equation (PDE), and exploiting symmetry breaking of relative periodic orbits to detect those tori, we identify many quasiperiodic, unstable, invariant two-torus solutions of a modified Kuramoto-Sivashinsky equation. The set of tori covers significant parts of the chaotic attractor and weighted averages of the properties of the tori-with weights computed based on their respective stability eigenvalues-approximate average quantities for the chaotic dynamics. These results are a step toward exploiting higher-dimensional invariant sets to describe general hyperchaotic systems, including dissipative spatiotemporally chaotic PDEs.

Jacobian-free variational method for computing connecting orbits in nonlinear dynamical systems.

One approach for describing spatiotemporal chaos is to study the unstable invariant sets embedded in the chaotic attractor of the system. While equilibria, periodic orbits, and invariant tori can be computed using existing methods, the numerical identification of heteroclinic and homoclinic connections between them remains challenging. We propose a robust matrix-free variational method for computing connecting orbits between equilibrium solutions. Instead of a common shooting-based approach, we view the identification of a connecting orbit as a minimization problem in the space of smooth curves in the state space that connect the two equilibria. In this approach, the deviation of a connecting curve from an integral curve of the vector field is penalized by a non-negative cost function. Minimization of the cost function deforms a trial curve until, at a global minimum, a connecting orbit is obtained. The method has no limitation on the dimension of the unstable manifold at the origin equilibrium and does not suffer from exponential error amplification associated with time-marching a chaotic system. Owing to adjoint-based minimization techniques, no Jacobian matrices need to be constructed. Therefore, the memory requirement scales linearly with the size of the problem, allowing the method to be applied to high-dimensional dynamical systems. The robustness of the method is demonstrated for the one-dimensional Kuramoto-Sivashinsky equation.

Invariant tori in dissipative hyperchaos.

One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's chaotic attractor. The significance of zero-dimensional unstable fixed points and one-dimensional unstable periodic orbits capturing time-periodic dynamics is widely accepted for high-dimensional chaotic systems, including fluid turbulence, while higher-dimensional invariant tori representing quasiperiodic dynamics have rarely been considered. We demonstrate that unstable 2-tori are generically embedded in the hyperchaotic attractor of a dissipative system of ordinary differential equations; tori can be numerically identified via bifurcations of unstable periodic orbits and their parameteric continuation and characterization of stability properties are feasible. As higher-dimensional tori are expected to be structurally unstable, 2-tori together with periodic orbits and equilibria form a complete set of relevant invariant solutions on which to base a dynamical description of chaos.

Constructing periodic orbits of high-dimensional chaotic systems by an adjoint-based variational method.

Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatiotemporal systems including fluid turbulence is supported by nonchaotic, exactly recurring time-periodic solutions of the governing equations. These unstable periodic orbits capture key features of the turbulent dynamics and sufficiently large sets of orbits promise a framework to predict the statistics of the chaotic flow. Computing periodic orbits for high-dimensional spatiotemporally chaotic systems remains challenging as known methods either show poor convergence properties because they are based on time-marching of a chaotic system causing exponential error amplification, or they require constructing Jacobian matrices which is prohibitively expensive. We propose a new matrix-free method that is unaffected by exponential error amplification, is globally convergent, and can be applied to high-dimensional systems. The adjoint-based variational method constructs an initial value problem in the space of closed loops such that periodic orbits are attracting fixed points for the loop dynamics. We introduce the method for general autonomous systems. An implementation for the one-dimensional Kuramoto-Sivashinsky equation demonstrates the robust convergence of periodic orbits underlying spatiotemporal chaos. Convergence does not require accurate initial guesses and is independent of the period of the respective orbit.

Superspreading events suggest aerosol transmission of SARS-CoV-2 by accumulation in enclosed spaces.

Viral transmission pathways have profound implications for public safety; it is thus imperative to establish a complete understanding of viable infectious avenues. Mounting evidence suggests SARS-CoV-2 can be transmitted via the air; however, this has not yet been demonstrated. Here we quantitatively analyze virion accumulation by accounting for aerosolized virion emission and destabilization. Reported superspreading events analyzed within this framework point towards aerosol mediated transmission of SARS-CoV-2. Virion exposure calculated for these events is found to trace out a single value, suggesting a universal minimum infective dose (MID) via aerosol that is comparable to the MIDs measured for other respiratory viruses; thus, the consistent infectious exposure levels and their commensurability to known aerosol-MIDs establishes the plausibility of aerosol transmission of SARS-CoV-2. Using filtration at a rate exceeding the destabilization rate of aerosolized SARS-CoV-2 can reduce exposure below this infective dose.

Nondestructive Prediction of the Buckling Load of Imperfect Shells.

From soda cans to space rockets, thin-walled cylindrical shells are abundant, offering exceptional load carrying capacity at relatively low weight. However, the actual load at which any shell buckles and collapses is very sensitive to imperceptible defects and cannot be predicted, which challenges the of such structures. Consequently, probabilistic descriptions in terms of empirical design rules are used and designing reliable structures requires the use of conservative strength estimates. We introduce a nonlinear description where finite-amplitude perturbations trigger buckling. Drawing from the analogy between imperfect shells which buckle and imperfect pipe flow which becomes turbulent, we experimentally show that lateral probing of cylindrical shells reveals their strength nondestructively. A new ridge-tracking method is applied to commercial cylinders with a hole showing that when the location where buckling nucleates is known we can accurately predict the buckling load of each individual shell, within ±5%. Our study provides a new promising framework to understand shell buckling, and more generally, imperfection-sensitive instabilities.

Buckling instabilities and spatio-temporal dynamics of active elastic filaments.

Biological filaments driven by molecular motors tend to experience tangential propulsive forces also known as active follower forces. When such a filament encounters an obstacle, it deforms, which reorients its follower forces and alters its entire motion. If the filament pushes a cargo, the friction on the cargo can be enough to deform the filament, thus affecting the transport properties of the cargo. Motivated by cytoskeletal filament motility assays, we study the dynamic buckling instabilities of a two-dimensional slender elastic filament driven through a dissipative medium by tangential propulsive forces in the presence of obstacles or cargo. We observe two distinct instabilities. When the filament's head is pinned or experiences significant translational but little rotational drag from its cargo, it buckles into a steadily rotating coiled state. When it is clamped or experiences both significant translational and rotational drag from its cargo, it buckles into a periodically beating, overall translating state. Using minimal analytically tractable models, linear stability theory and fully nonlinear computations, we study the onset of each buckling instability, characterize each buckled state, and map out the phase diagram of the system. Finally, we use particle-based Brownian dynamics simulations to show our main results are robust to moderate noise and steric repulsion. Overall, our results provide a unified framework to understand the dynamics of tangentially propelled filaments and filament-cargo assemblies.

Origin of localized snakes-and-ladders solutions of plane Couette flow.

Spatially localized invariant solutions of plane Couette flow are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations [Schneider, Gibson, and Burke, Phys. Rev. Lett. 104, 104501 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.104501]. We demonstrate the mechanism by which these snaking solutions originate from well-known periodic states of the Taylor-Couette system. They are formed by a localized slug of wavy-vortex flow that emerges from a background of Taylor vortices via a modulational sideband instability. This mechanism suggests a close connection between pattern-formation theory and Navier-Stokes flow.

Rational design of a high-throughput droplet sorter.

The high-throughput selection of individual droplets is an essential function in droplet-based microfluidics. Fluorescence-activated droplet sorting is achieved using electric fields triggered at rates up to 30 kHz, providing the ultra-high throughput relevant in applications where large libraries of compounds or cells must be analyzed. To achieve such sorting frequencies, electrodes have to create an electric field distribution that generates maximal actuating forces on the droplet while limiting the induced droplet deformation and avoid disintegration. We propose a metric characterizing the performance of an electrode design relative to the theoretical optimum and analyze existing devices using full 3D simulations of the electric fields. By combining parameter optimization with numerical simulation we derive rational design guidelines and propose optimized electrode configurations. When tested experimentally, the optimized design show significantly better performance than the standard designs.

Exact invariant solution reveals the origin of self-organized oblique turbulent-laminar stripes.

Wall-bounded shear flows transitioning to turbulence may self-organize into alternating turbulent and laminar regions forming a stripe pattern with non-trivial oblique orientation. Different experiments and flow simulations identify oblique stripe patterns as the preferred solution of the well-known Navier-Stokes equations, but the origin of stripes and their oblique orientation remains unexplained. In concluding his lectures, Feynman highlights the unexplained stripe pattern hidden in the solution space of the Navier-Stokes equations as an example demonstrating the need for improved theoretical tools to analyze the fluid flow equations. Here we exploit dynamical systems methods and demonstrate the existence of an exact equilibrium solution of the fully nonlinear 3D Navier-Stokes equations that resembles oblique stripe patterns in plane Couette flow. The stripe equilibrium emerges from the well-studied Nagata equilibrium and exists only for a limited range of pattern angles. This suggests a mechanism selecting the non-trivial oblique orientation angle of turbulent-laminar stripes.

High-throughput multiplexed fluorescence-activated droplet sorting.

Fluorescence-activated droplet sorting (FADS) is one of the most important features provided by droplet-based microfluidics. However, to date, it does not allow to compete with the high-throughput multiplexed sorting capabilities offered by flow cytometery. Here, we demonstrate the use of a dielectrophoretic-based FADS, allowing to sort up to five different droplet populations simultaneously. Our system provides means to select droplets of different phenotypes in a single experimental run to separate initially heterogeneous populations. Our experimental results are rationalized with the help of a numerical model of the actuation of droplets in electric fields providing guidelines for the prediction of sorting designs for upscaled or downscaled microsystems.

Stability Landscape of Shell Buckling.

We measure the response of cylindrical shells to poking and identify a stability landscape, which fully characterizes the stability of perfect shells and imperfect ones in the case where a single defect dominates. We show that the landscape of stability is independent of the loading protocol and the poker geometry. Our results suggest that the complex stability of shells reduces to a low dimensional description. Tracking ridges and valleys of this landscape defines a natural phase-space coordinates for describing the stability of shells.

Fully localized post-buckling states of cylindrical shells under axial compression.

We compute nonlinear force equilibrium solutions for a clamped thin cylindrical shell under axial compression. The equilibrium solutions are dynamically unstable and located on the stability boundary of the unbuckled state. A fully localized single dimple deformation is identified as the edge state-the attractor for the dynamics restricted to the stability boundary. Under variation of the axial load, the single dimple undergoes homoclinic snaking in the azimuthal direction, creating states with multiple dimples arranged around the central circumference. Once the circumference is completely filled with a ring of dimples, snaking in the axial direction leads to further growth of the dimple pattern. These fully nonlinear solutions embedded in the stability boundary of the unbuckled state constitute critical shape deformations. The solutions may thus be a step towards explaining when the buckling and subsequent collapse of an axially loaded cylinder shell is triggered.

Is delayed surgical revascularization in acute myocardial infarction useful or dangerous? New insights into an old problem.

OBJECTIVES: Haemodynamically stable patients admitted for coronary artery bypass grafting in acute myocardial infarction often undergo delayed surgery in order to avoid the risks of emergency surgery. However, initially stable patients undergoing delayed surgery may develop low cardiac output syndrome (LCOS) during the waiting period, which might be a major drawback of this strategy. We aim to define risk factors and clinical consequences of LCOS during the waiting period. METHODS: A total of 530 consecutive patients with acute myocardial infarction (33% non-ST-segment elevation myocardial infarction and 67% ST-segment-elevation myocardial infarction) underwent isolated coronary artery bypass grafting between 2008 and 2013. Outcomes after either immediate (<48 h after onset of symptoms) or delayed (>48 h after onset of symptoms) therapy were compared. Predictors of preoperative development of LCOS were identified using multivariate regression analysis. RESULTS: Of the 327 patients undergoing delayed therapy, 39 (12%) developed preoperative LCOS, resulting in increased mortality compared with patients who remained stable (21 vs 7.6%, P < 0.001). Immediate therapy resulted in similar mortality compared with delayed therapy (6.4 vs 7.6%; P = 0.68) and better 7-year survival (70 vs 55%; P < 0.001). Predictors of developing LCOS were reduced left ventricular function (odds ratio 4.4), renal impairment (odds ratio 3.0), acute pulmonary infection (odds ratio 3.4) and the extent of troponin elevation at admission (odds ratio 1.01 per increase by 1 µg/l). CONCLUSIONS: In patients with acute myocardial infarction undergoing delayed coronary artery bypass grafting, preoperative LCOS is a relevant and dangerous condition that can be avoided by operating immediately or by carefully selecting patients to be delayed according to the risk parameters identified preoperatively.

Taking the Perfect Selfie: Investigating the Impact of Perspective on the Perception of Higher Cognitive Variables.

Taking selfies is now becoming a standard human habit. However, as a social phenomenon, research is still in the fledgling stage and the scientific framework is sparse. Selfies allow us to share social information with others in a compact format. Furthermore, we are able to control important photographic and compositional aspects, such as perspective, which have a strong impact on the assessment of a face (e.g., demonstrated by the height-weight illusion, effects of gaze direction, faceism-index). In Study 1, we focused on the impact of perspective (left/right hemiface, above/below vs. frontal presentation) on higher cognitive variables and let 172 participants rate the perceived attractiveness, helpfulness, sympathy, dominance, distinctiveness, and intelligence, plus important information on health issues (e.g., body weight), on the basis of 14 3D faces. We could show that lateral snapshots yielded higher ratings for attractiveness compared to the classical frontal view. However, this effect was more pronounced for left hemifaces and especially female faces. Compared to the frontal condition, 30° right hemifaces were rated as more helpful, but only for female faces while faces viewed from above were perceived as significant less helpful. Direct comparison between left vs. right hemifaces revealed no effect. Relating to sympathy, we only found a significant effect for 30° right male hemifaces, but only in comparison to the frontal condition. Furthermore, female 30° right hemifaces were perceived as more intelligent. Relating to body weight, we replicated the so-called "height-weight illusion." Other variables remained unaffected. In Study 2, we investigated the impact of a typical selfie-style condition by presenting the respective faces from a lateral (left/right) and tilted (lower/higher) vantage point. Most importantly, depending on what persons wish to express with a selfie, a systematic change of perspective can strongly optimize their message; e.g., increasing their attractiveness by shooting from above left, and in contrast, decreasing their expressed helpfulness by shooting from below. We could further extent past findings relating to the height-weight illusion and showed that an additional rotation of the camera positively affected the perception of body weight (lower body weight). We discuss potential explanations for perspective-related effects, especially gender-related ones.

Increasing lifetimes and the growing saddles of shear flow turbulence.

In linearly stable shear flows, turbulence spontaneously decays with a characteristic lifetime that varies with Reynolds number. The lifetime sharply increases with Reynolds number so that a possible divergence marking the transition to sustained turbulence at a critical point has been discussed. We present a mechanism by which the lifetimes increase: in the system's state space, turbulent motion is supported by a chaotic saddle. Inside this saddle a locally attracting periodic orbit is created and undergoes a traditional bifurcation sequence generating chaos. The formed new "turbulent bubble" is initially an attractor supporting persistent chaotic dynamics. Soon after its creation, it collides with its own boundary, by which it becomes leaky and dynamically connected with the surrounding structures. The complexity of the chaotic saddle that supports transient turbulence hence increases by incorporating the remnant of a new bubble. As a a result, the time it takes for a trajectory to leave the saddle and decay to the laminar state is increased. We demonstrate this phenomenon in plane Couette flow and show that characteristic lifetimes vary nonsmoothly and nonmonotonically with Reynolds number.

Judging body weight from faces: the height-weight illusion.

Being able to exploit features of the human face to predict health and fitness can serve as an evolutionary advantage. Surface features such as facial symmetry, averageness, and skin colour are known to influence attractiveness. We sought to determine whether observers are able to extract more complex features, namely body weight. If possible, it could be used as a predictor for health and fitness. For instance, facial adiposity could be taken to indicate a cardiovascular challenge or proneness to infections. Observers seem to be able to glean body weight information from frontal views of a face. Is weight estimation robust across different viewing angles? We showed that participants strongly overestimated body weight for faces photographed from a lower vantage point while underestimating it for faces photographed from a higher vantage point. The perspective distortions of simple facial measures (e.g., width-to-height ratio) that accompany changes in vantage point do not suffice to predict body weight. Instead, more complex patterns must be involved in the height-weight illusion.

Sequencing by hybridization of long targets.

Sequencing by Hybridization (SBH) reconstructs an n-long target DNA sequence from its biochemically determined l-long subsequences. In the standard approach, the length of a uniformly random sequence that can be unambiguously reconstructed is limited to n = O(2(l)) due to repetitive subsequences causing reconstruction degeneracies. We present a modified sequencing method that overcomes this limitation without the need for different types of biochemical assays and is robust to error.

Algorithm for a microfluidic assembly line.

Microfluidic technology has revolutionized the control of flows at small scales giving rise to new possibilities for assembling complex structures on the microscale. We analyze different possible algorithms for assembling arbitrary structures, and demonstrate that a sequential assembly algorithm can manufacture arbitrary 3D structures from identical constituents. We illustrate the algorithm by showing that a modified Hele-Shaw cell with 7 controlled flow rates can be designed to construct the entire English alphabet from particles that irreversibly stick to each other.

Transient turbulence in plane Couette flow.

Plane Couette flow, the flow between two parallel plates moving in opposite directions, belongs to the group of shear flows where turbulence occurs while the laminar profile is stable. Experimental and numerical studies show that at intermediate Reynolds numbers turbulence is transient and that the lifetimes are distributed exponentially. However, these studies have remained inconclusive about a divergence in lifetimes above a critical Reynolds number. The extensive numerical results for flow in a box of width 2pi and length 8pi presented here cover observation times up to 12,000 units and show that while the lifetimes increase rapidly with Reynolds number, they do not indicate a divergence and therefore no transition to persistent turbulence.