Ecological models: higher complexity in, higher feasibility out

Finding a compromise between tractability and realism has always been at the core of ecological modelling. The introduction of nonlinear functional responses in two-species models has reconciled part of this compromise. However, it remains unclear whether this compromise can be extended to multispecies models. Yet, answering this question is necessary in order to differentiate whether the explanatory power of a model comes from the general form of its polynomial or from a more realistic description of multispecies systems. Here, we study the probability of feasibility (the existence of at least one positive real equilibrium) in complex models by adding higher-order interactions and nonlinear functional responses to the linear Lotka-Volterra model. We characterize complexity by the number of free-equilibrium points generated by a model, which is a function of the polynomial degree and system's dimension. We show that the probability of generating a feasible system in a model is an increasing function of its complexity, regardless of the specific mechanism invoked. Furthermore, we find that the probability of feasibility in a model will exceed that of the linear Lotka-Volterra model when a minimum level of complexity is reached. Importantly, this minimum level is modulated by parameter restrictions, but can always be exceeded via increasing the polynomial degree or system's dimension. Our results reveal that conclusions regarding the relevance of mechanisms embedded in complex models must be evaluated in relation to the expected explanatory power of their polynomial forms.

Clockwise and counterclockwise hysteresis characterize state changes in the same aquatic ecosystem

Incremental increases in a driver variable, such as nutrients or detritus, can trigger abrupt shifts in aquatic ecosystems that may exhibit hysteretic dynamics and a slow return to the initial state. A model system for understanding these dynamics is the microbial assemblage that inhabits the cup-shaped leaves of the pitcher plant Sarracenia purpurea. With enrichment of organic matter, this system flips within three days from an oxygen-rich state to an oxygen-poor state. In a replicated greenhouse experiment, we enriched pitcher-plant leaves at different rates with bovine serum albumin (BSA), a molecular substitute for detritus. Changes in dissolved oxygen (DO) and undigested BSA concentration were monitored during enrichment and recovery phases. With increasing enrichment rates, the dynamics ranged from clockwise hysteresis (low), to environmental tracking (medium), to novel counter-clockwise hysteresis (high). These experiments demonstrate that detrital enrichment rate can modulate a diversity of hysteretic responses within a single aquatic ecosystem, and suggest different management strategies may be needed to mitigate the effects of high vs. low rates of detrital enrichment.

Tipping point and noise-induced transients in ecological networks

A challenging and outstanding problem in interdisciplinary research is to understand the interplay between transients and stochasticity in high-dimensional dynamical systems. Focusing on the tipping-point dynamics in complex mutualistic networks in ecology constructed from empirical data, we investigate the phenomena of noise-induced collapse and noise-induced recovery. Two types of noise are studied: environmental (Gaussian white) noise and state-dependent demographic noise. The dynamical mechanism responsible for both phenomena is a transition from one stable steady state to another driven by stochastic forcing, mediated by an unstable steady state. Exploiting a generic and effective two-dimensional reduced model for real-world mutualistic networks, we find that the average transient lifetime scales algebraically with the noise amplitude, for both environmental and demographic noise. We develop a physical understanding of the scaling laws through an analysis of the mean first passage time from one steady state to another. The phenomena of noise-induced collapse and recovery and the associated scaling laws have implications for managing high-dimensional ecological systems.

Functional advantages of Lévy walks emerging near a critical point

A special class of random walks, so-called Lévy walks, has been observed in a variety of organisms ranging from cells, insects, fishes, and birds to mammals, including humans. Although their prevalence is considered to be a consequence of natural selection for higher search efficiency, some findings suggest that Lévy walks might also be epiphenomena that arise from interactions with the environment. Therefore, why they are common in biological movements remains an open question. Based on some evidence that Lévy walks are spontaneously generated in the brain and the fact that power-law distributions in Lévy walks can emerge at a critical point, we hypothesized that the advantages of Lévy walks might be enhanced by criticality. However, the functional advantages of Lévy walks are poorly understood. Here, we modeled nonlinear systems for the generation of locomotion and showed that Lévy walks emerging near a critical point had optimal dynamic ranges for coding information. This discovery suggested that Lévy walks could change movement trajectories based on the magnitude of environmental stimuli. We then showed that the high flexibility of Lévy walks enabled switching exploitation/exploration based on the nature of external cues. Finally, we analyzed the movement trajectories of freely moving Drosophila larvae and showed empirically that the Lévy walks may emerge near a critical point and have large dynamic range and high flexibility. Our results suggest that the commonly observed Lévy walks emerge near a critical point and could be explained on the basis of these functional advantages.

Law of Mass Action Type Chemical Mechanisms for Modeling Autocatalysis and Hypercycles: Their Role in the Evolutionary Race

One of our most appealing challenge is to unravel the role of a presumably autocatalytic system in controlling the origin and spreading of Life on our entire planet. Here we show that in the simplest autocatalytic loop involving reactions capable of self-replication and obeying law of mass action kinetics, concentration growth of the autocatalyst may be characterized by parametrization of direct and autocatalytic pathways rather than by kinetic orders of the autocatalyst. Extending this model by feasible elementary steps allows us to outline super-exponential growth where kinetic order of the autocatalyst is higher than unity. Furthermore, it is shown in case of the simplest hypercycle that such a situation might appear where the otherwise more sluggish autocatalytic route receives a decisive support from the crosscatalytic pathway to become an apparently stronger autocatalytic loop even if the other route contains a more efficient autocatalysis. If the hypercycle is performed under flow conditions selection of autocatalyst depends on kinetic and flow parameters influenced by external factors mimicking that the most adaptive loop of hypercycle eventually finds its wining way in the evolutionary race.

Nonlinear dynamics of fires in Africa over recent decades controlled by precipitation

Dynamics of fires in Africa are of critical importance for understanding changes in ecosystem properties and effects on the global carbon cycle. Given increasing fire risk from projected warming on the one hand and a documented human-driven decline in fires on the other, it is still unknown how the complex interplay between climate and human factors affects recent changes of fires in Africa. Moreover, the impact of recent strong El Niño events on fire dynamics is not yet known. By applying an ensemble empirical mode decomposition method to satellite-derived fire burned area, we investigated the spatio-temporal evolution of fires in Africa over 2001-2016 and identified the potential dominant drivers. Our results show an overall decline of fire rates, which is continuous over the time period and mainly caused by cropland expansion in northern sub-Saharan Africa. However, we also find that years of high precipitation have caused an initial increase in fire rates in southern Africa, which reversed to a decline in later years. This decline is caused by a high frequency of dry years leading to very low fuel loads, suggesting that recent drought causes a general reduction of burned areas, in particular in xeric savannas. In some mesic regions (10°-15°S), solar radiation and increased temperature caused increase in fires. These findings show that climate change overrules the impact of human expansion on fire rates at the continental scale in Africa, reducing the fire risk.

Periodic propagating waves coordinate RhoGTPase network dynamics at the leading and trailing edges during cell migration

Migrating cells need to coordinate distinct leading and trailing edge dynamics but the underlying mechanisms are unclear. Here, we combine experiments and mathematical modeling to elaborate the minimal autonomous biochemical machinery necessary and sufficient for this dynamic coordination and cell movement. RhoA activates Rac1 via DIA and inhibits Rac1 via ROCK, while Rac1 inhibits RhoA through PAK. Our data suggest that in motile, polarized cells, RhoA–ROCK interactions prevail at the rear, whereas RhoA-DIA interactions dominate at the front where Rac1/Rho oscillations drive protrusions and retractions. At the rear, high RhoA and low Rac1 activities are maintained until a wave of oscillatory GTPase activities from the cell front reaches the rear, inducing transient GTPase oscillations and RhoA activity spikes. After the rear retracts, the initial GTPase pattern resumes. Our findings show how periodic, propagating GTPase waves coordinate distinct GTPase patterns at the leading and trailing edge dynamics in moving cells.

Phase Entropy Analysis of Electrohysterographic Data at the Third Trimester of Human Pregnancy and Active Parturition

Phase Entropy (PhEn) was recently introduced for evaluating the nonlinear features of physiological time series. PhEn has been demonstrated to be a robust approach in comparison to other entropy-based methods to achieve this goal. In this context, the present study aimed to analyze the nonlinear features of raw electrohysterogram (EHG) time series collected from women at the third trimester of pregnancy (TT) and later during term active parturition (P) by PhEn. We collected 10-min longitudinal transabdominal recordings of 24 low-risk pregnant women at TT (from 35 to 38 weeks of pregnancy) and P (>39 weeks of pregnancy). We computed the second-order difference plots (SODPs) for the TT and P stages, and we evaluated the PhEn by modifying the k value, a coarse-graining parameter. Our results pointed out that PhEn in TT is characterized by a higher likelihood of manifesting nonlinear dynamics compared to the P condition. However, both conditions maintain percentages of nonlinear series higher than 66%. We conclude that the nonlinear features appear to be retained for both stages of pregnancy despite the uterine and cervical reorganization process that occurs in the transition from the third trimester to parturition.

Leveraging Machine Learning Techniques and Engineering of Multi-Nature Features for National Daily Regional Ambulance Demand Prediction

The accurate prediction of ambulance demand provides great value to emergency service providers and people living within a city. It supports the rational and dynamic allocation of ambulances and hospital staffing, and ensures patients have timely access to such resources. However, this task has been challenging due to complex multi-nature dependencies and nonlinear dynamics within ambulance demand, such as spatial characteristics involving the region of the city at which the demand is estimated, short and long-term historical demands, as well as the demographics of a region. Machine learning techniques are thus useful to quantify these characteristics of ambulance demand. However, there is generally a lack of studies that use machine learning tools for a comprehensive modeling of the important demand dependencies to predict ambulance demands. In this paper, an original and novel approach that leverages machine learning tools and extraction of features based on the multi-nature insights of ambulance demands is proposed. We experimentally evaluate the performance of next-day demand prediction across several state-of-the-art machine learning techniques and ambulance demand prediction methods, using real-world ambulatory and demographical datasets obtained from Singapore. We also provide an analysis of this ambulatory dataset and demonstrate the accuracy in modeling dependencies of different natures using various machine learning techniques.

On the modelling and testing of a laboratory-scale Foucault pendulum as a precursor for the design of a high-performance measurement instrument

An integrated study is presented on the dynamic modelling and experimental testing of a mid-length Foucault pendulum with the aim of confirming insights from the literature on the reliable operation of this device and setting markers for future research in which the pendulum may be used for the measurement of relativistic effects due to terrestrial gravity. A tractable nonlinear mathematical model is derived for the dynamics of a practical laboratory Foucault pendulum and its performance with and without parametric excitation, and with coupling to long-axis torsion is investigated numerically for different geographical locations. An experimental pendulum is also tested, with and without parametric excitation, and it is shown that the model closely predicts the general precessional performance of the pendulum, for the case of applied parametric excitation of the length, when responding to the Newtonian rotation of the Earth. Many of the principal inherent performance limitations of Foucault pendulums from the literature have been confirmed and a general prescription for design is evolved, placing the beneficial effect of principal parametric resonance of this inherently nonlinear system in a central mitigating position, along with other assistive means of response moderation such as excitational phase control through electromagnetic pushing, enclosure, and the minimization of seismic and EMC noise. It is also shown, through a supporting analysis and calculation, that although the terrestrial measurement of the Lense–Thirring (LT) precession by means of a Foucault pendulum is certainly still within the realms of possibility, there remains a very challenging increase in resolution capability required, in the order of 2 × 10⁹ to be sure of reliable detection, notwithstanding the removal of extraneous motions and interferences. This study sets the scene for a further investigation in the very near future in which these challenges are to be met, so that a new assault can be made on the terrestrial measurement of LT precession.

A Review of Bolt Tightening Force Measurement and Loosening Detection

Pre-stressed bolted joints are widely used in civil structures and industries. The tightening force of a bolt is crucial to the reliability of the joint connection. Loosening or over-tightening of a bolt may lead to connectors slipping or bolt strength failure, which are both harmful to the main structure. In most practical cases it is extremely difficult, even impossible, to install the bolts to ensure there is a precise tension force during the construction phase. Furthermore, it is inevitable that the bolts will loosen due to long-term usage under high stress. The identification of bolt tension is therefore of great significance for monitoring the health of existing structures. This paper reviews state-of-the-art research on bolt tightening force measurement and loosening detection, including fundamental theories, algorithms, experimental set-ups, and practical applications. In general, methods based on the acoustoelastic principle are capable of calculating the value of bolt axial stress if both the time of incident wave and reflected wave can be clearly recognized. The relevant commercial instrument has been developed and its algorithm will be briefly introduced. Methods based on contact dynamic phenomena such as wave energy attenuation, high-order harmonics, sidebands, and impedance, are able to correlate interface stiffness and the clamping force of bolted joints with respective dynamic indicators. Therefore, they are able to detect or quantify bolt tightness. The related technologies will be reviewed in detail. Potential challenges and research trends will also be discussed.

Spatiotemporal Integrity and Spontaneous Nonlinear Dynamic Properties of the Salience Network Revealed by Human Intracranial Electrophysiology: A Multicohort Replication

The salience network (SN) plays a critical role in cognitive control and adaptive human behaviors, but its electrophysiological foundations and millisecond timescale dynamic temporal properties are poorly understood. Here, we use invasive intracranial EEG (iEEG) from multiple cohorts to investigate the neurophysiological underpinnings of the SN and identify dynamic temporal properties that distinguish it from the default mode network (DMN) and dorsolateral frontal-parietal network (FPN), two other large-scale brain networks that play important roles in human cognition. iEEG analysis of network interactions revealed that the anterior insula and anterior cingulate cortex, which together anchor the SN, had stronger intranetwork interactions with each other than cross-network interactions with the DMN and FPN. Analysis of directionality of information flow between the SN, DMN, and FPN revealed causal outflow hubs in the SN consistent with its role in fast temporal switching of network interactions. Analysis of regional iEEG temporal fluctuations revealed faster temporal dynamics and higher entropy of neural activity within the SN, compared to the DMN and FPN. Critically, these results were replicated across multiple cohorts. Our findings provide new insights into the neurophysiological basis of the SN, and more broadly, foundational mechanisms underlying the large-scale functional organization of the human brain.

Energy Drink before Exercise Did Not Affect Autonomic Recovery Following Moderate Aerobic Exercise: A Crossover, Randomized and Controlled Trial

Introduction: Energy drink (ED) intake could initiate physiological changes owing to its stimulant characteristics and, it improves endurance and athletic performance. We evaluated the acute effects of ED on autonomic heart rate (HR) control during recovery after a session of submaximal aerobic exercise.Method: The study was completed by submitting 29 healthy males between 18 and 30 years old to three conventions: (A) Maximum exercise test by the adapted Bruce protocol; (B) Placebo protocol (PP) - water intake 15 minutes prior to exercise, rest in dorsal decubitus for 15 minutes followed by 5 minutes of treadmill running at 1% inclination, initial speed of 5 km/h for 5 minutes 25 minutes with 60% of the velocity consistent to the maximum oxygen consumption (VO2max), and finally 60 minutes of recovery at rest in the supine position; (C) Experimental protocol (PE) - similar to PP previously, but with ED intake 15 minutes before physical exercise. The time, frequency and geometric indexes of HR variability (HRV) were inspected before and after exercise.Results: There was a significant (p < 0.05, <5%) effect on the HRV index (HR-nu and ms², LF-nu and ms², LF/HF, SD1, SDNN and RMSSD), indicating a reduction in HRV in the first 5 minutes after exercise in both protocols (PP and PE). Yet, no protocol interaction was detected, suggesting no effect of ED on HRV throughout recovery after submaximal aerobic exercise.Conclusion: There was no significant effect of ED on the autonomic control of HR in the recovery phase after submaximal aerobic exercise.

Sex-Specific Dependence of Linear and Nonlinear Postural Control Metrics on Anthropometrics During Clinical Balance Tests in Healthy Young Adults

CONTEXT

Previous work suggests that balance behavior is a sex-dependent, complex process that can be characterized by linear and nonlinear metrics. Although a certain degree of center of pressure variability may be expected based on sexual dimorphism, there is evidence to suggest that these effects are obscured by potential interactions between sex and anthropometric factors. To date, no study has accounted for such interactive effects using both linear and nonlinear measures.

OBJECTIVE

This investigation sought to analyze interactive models featuring sex, height, and weight as predictors of linear and nonlinear aspects of postural control.

DESIGN

Cross-sectional study.

SETTING

Controlled laboratory.

PARTICIPANTS

A total of 26 males (23.80 [3.44] y, 177.87 [6.44] cm, 81.70 [10.80] kg) and 28 females (21.14 [2.03] y, 169.57 [8.80] cm, 64.48 [8.86] kg) were sampled from a healthy university population.

MAIN OUTCOME MEASURES

Linear (range [RNG], velocity [VEL], and SD) and nonlinear (detrended fluctuation analysis scaling exponent, multivariate multiscale sample entropy [MMSECI]) summary metrics of center of pressure time series.

PROCEDURE

Participants stood on a force plate for 20 seconds in 3 conditions: double (D), single (S), and tandem (T) stance. Data for each stance condition were analyzed using regression models with interaction terms for sex × height and sex × weight. In D, weight had a positive, significant main effect on VELy, MMSECId, and MMSECIv. In men, height was observed to have a positive effect on SDy (S), RNGy (S), and RNGx (T) and a negative effect on MMSECIv (T). In women, weight was observed to have a positive effect on SDy and VELx (both T).

CONCLUSIONS

Our findings suggest that men and women differ with respect to certain linear and nonlinear aspects of balance behavior, and that these differences may reflect sex-specific behavioral patterns in addition to effects related to sexual dimorphism.

Fractal Analysis of Human Gait Variability via Stride Interval Time Series

Fractal analysis of stride interval time series is a useful tool in human gait research which could be used as a marker for gait adaptability, gait disorder, and fall risk among patients with movement disorders. This study is designed to systematically and comprehensively investigate two practical aspects of fractal analysis which significantly affect the outcome: the series length and the parameters used in the algorithm. The Hurst exponent, scaling exponent, and/or fractal dimension are computed from both simulated and experimental data using three fractal methods, namely detrended fluctuation analysis, box-counting dimension, and Higuchi's fractal dimension. The advantages and drawbacks of each method are discussed, in terms of biases and variability. The results demonstrate that a careful selection of fractal analysis methods and their parameters is required, which is dependent on the aim of study (either analyzing differences between experimental groups or estimating an accurate determination of fractal features). A set of guidelines for the selection of the fractal methods and the length of stride interval time series is provided, along with the optimal parameters for a robust implementation for each method.

Obtaining Information about Operation of Centrifugal Compressor from Pressure by Combining EEMD and IMFE

Based on entropy characteristics, some complex nonlinear dynamics of the dynamic pressure at the outlet of a centrifugal compressor are analyzed, as the centrifugal compressor operates in a stable and unstable state. First, the 800-kW centrifugal compressor is tested to gather the time sequence of dynamic pressure at the outlet by controlling the opening of the anti-surge valve at the outlet, and both the stable and unstable states are tested. Then, multi-scale fuzzy entropy and an improved method are introduced to analyze the gathered time sequence of dynamic pressure. Furthermore, the decomposed signals of dynamic pressure are obtained using ensemble empirical mode decomposition (EEMD), and are decomposed into six intrinsic mode functions and one residual signal, and the intrinsic mode functions with large correlation coefficients in the frequency domain are used to calculate the improved multi-scale fuzzy entropy (IMFE). Finally, the statistical reliability of the method is studied by modifying the original data. After analysis of the relationships between the dynamic pressure and entropy characteristics, some important intrinsic dynamics are captured. The entropy becomes the largest in the stable state, but decreases rapidly with the deepening of the unstable state, and it becomes the smallest in the surge. Compared with multi-scale fuzzy entropy, the curve of the improved method is smoother and could show the change of entropy exactly under different scale factors. For the decomposed signals, the unstable state is captured clearly for higher order intrinsic mode functions and residual signals, while the unstable state is not apparent for lower order intrinsic mode functions. In conclusion, it can be observed that the proposed method can be used to accurately identify the unstable states of a centrifugal compressor in real-time fault diagnosis.

Interfering with influenza: nonlinear coupling of reactive and static mitigation strategies

When new, highly infectious strains of influenza emerge, global pandemics can occur before an effective vaccine is developed. Without a strain-specific vaccine, pandemics can only be mitigated by employing combinations of low-efficacy pre-pandemic vaccines and reactive response measures that are carried out as the pandemic unfolds. Unfortunately, the application of reactive interventions can lead to unintended consequences that may exacerbate unpredictable spreading dynamics and cause more drawn-out epidemics. Here, we employ a detailed model of pandemic influenza in Australia to simulate the combination of pre-pandemic vaccination and reactive antiviral prophylaxis. This study focuses on population-level coupling effects between the respective methods, and the associated spatio-temporal fluctuations in pandemic dynamics produced by reactive strategies. Our results show that combining strategies can produce either mutual improvement of performance or interference that reduces the effectiveness of each strategy when they are used together. We demonstrate that these coupling effects between intervention strategies are extremely sensitive to delay times, compliance rates and the type of contact targeting used to administer prophylaxis.

Conley Index Approach to Sampled Dynamics

The topological method for the reconstruction of dynamics from time series [K. Mischaikow et al., Phys. Rev. Lett., 82 (1999), pp. 1144-1147] is reshaped to improve its range of applicability, particularly in the presence of sparse data and strong expansion. The improvement is based on a multivalued map representation of the data. However, unlike the previous approach, it is not required that the representation has a continuous selector. Instead of a selector, a recently developed new version of Conley index theory for multivalued maps [B. Batko, SIAM J. Appl. Dyn. Syst., 16 (2017), pp. 1587-1617; B. Batko and M. Mrozek, SIAM J. Appl. Dyn. Syst., 15 (2016), pp. 1143-1162] is used in computations. The existence of a continuous, single valued generator of the relevant dynamics is guaranteed in the vicinity of the graph of the multivalued map constructed from data. Some numerical examples based on time series derived from the iteration of Hénon-type maps are presented.

Interaction mechanisms quantified from dynamical features of frog choruses

We employ a mathematical model (a phase oscillator model) to describe the deterministic and stochastic features of frog choruses in which male frogs attempt to avoid call overlaps. The mathematical model with a general interaction term is identified using a Bayesian approach, and it qualitatively reproduces the stationary and dynamical features of the empirical data. In addition, we quantify the magnitude of attention paid among the male frogs from the identified model, and then analyse the relationship between attention and behavioural parameters using a statistical approach. Our analysis demonstrates a negative correlation between attention and inter-frog distance, and also suggests a behavioural strategy in which male frogs selectively attend to a less attractive male frog (i.e. a male producing calls at longer intervals) in order to more effectively advertise their superior relative attractiveness to females.

Opto-chemo-mechanical transduction in photoresponsive gels elicits switchable self-trapped beams with remote interactions

Next-generation photonics envisions circuitry-free, rapidly reconfigurable systems powered by solitonic beams of self-trapped light and their particlelike interactions. Progress, however, has been limited by the need for reversibly responsive materials that host such nonlinear optical waves. We find that repeatedly switchable self-trapped visible laser beams, which exhibit strong pairwise interactions, can be generated in a photoresponsive hydrogel. Through comprehensive experiments and simulations, we show that the unique nonlinear conditions arise when photoisomerization of spiropyran substituents in pH-responsive poly(acrylamide-co-acrylic acid) hydrogel transduces optical energy into mechanical deformation of the 3D cross-linked hydrogel matrix. A Gaussian beam self-traps when localized isomerization-induced contraction of the hydrogel and expulsion of water generates a transient waveguide, which entraps the optical field and suppresses divergence. The waveguide is erased and reformed within seconds when the optical field is sequentially removed and reintroduced, allowing the self-trapped beam to be rapidly and repeatedly switched on and off at remarkably low powers in the milliwatt regime. Furthermore, this opto-chemo-mechanical transduction of energy mediated by the 3D cross-linked hydrogel network facilitates pairwise interactions between self-trapped beams both in the short range where there is significant overlap of their optical fields, and even in the long range--over separation distances of up to 10 times the beam width--where such overlap is negligible.

An update on dimensions of consciousness

Evidence is presented to support the hypothesis that "binding" of the senses to produce a combined sensory experience is made possible by the allocation of each sense to its own dimension.

Dynamics of Postural Control in Elite Sport Rifle Shooters

Thirteen shooters and eleven non-shooters completed two-legged and single-legged stance on a force platform. The dynamics of the center of pressure trajectory was assessed using sample entropy, correlation dimension and entropic half-life. Additionally, the body sway was quantified as the elliptical area of the trajectory. The shooters had lower sample entropy and tended to have longer entropic half-life during the single-legged stance. Across the two tasks, the correlation dimension in the anterior-posterior direction and the body sway in both directions were lower in the shooters. This suggests that extensive training in quiet stance is associated with altered postural control, especially during challenging single-legged stance and to a lesser extend during two-legged stance.

Guided transition waves in multistable mechanical metamaterials

Transition fronts, moving through solids and fluids in the form of propagating domain or phase boundaries, have recently been mimicked at the structural level in bistable architectures. What has been limited to simple one-dimensional (1D) examples is here cast into a blueprint for higher dimensions, demonstrated through 2D experiments and described by a continuum mechanical model that draws inspiration from phase transition theory in crystalline solids. Unlike materials, the presented structural analogs admit precise control of the transition wave's direction, shape, and velocity through spatially tailoring the underlying periodic network architecture (locally varying the shape or stiffness of the fundamental building blocks, and exploiting interactions of transition fronts with lattice defects such as point defects and free surfaces). The outcome is a predictable and programmable strongly nonlinear metamaterial motion with potential for, for example, propulsion in soft robotics, morphing surfaces, reconfigurable devices, mechanical logic, and controlled energy absorption.

Assessing the predictability of nonlinear dynamics under smooth parameter changes

Short-term forecasts of nonlinear dynamics are important for risk-assessment studies and to inform sustainable decision-making for physical, biological and financial problems, among others. Generally, the accuracy of short-term forecasts depends upon two main factors: the capacity of learning algorithms to generalize well on unseen data and the intrinsic predictability of the dynamics. While generalization skills of learning algorithms can be assessed with well-established methods, estimating the predictability of the underlying nonlinear generating process from empirical time series remains a big challenge. Here, we show that, in changing environments, the predictability of nonlinear dynamics can be associated with the time-varying stability of the system with respect to smooth changes in model parameters, i.e. its local structural stability. Using synthetic data, we demonstrate that forecasts from locally structurally unstable states in smoothly changing environments can produce significantly large prediction errors, and we provide a systematic methodology to identify these states from data. Finally, we illustrate the practical applicability of our results using an empirical dataset. Overall, this study provides a framework to associate an uncertainty level with short-term forecasts made in smoothly changing environments.

Precise modeling of complex tooth surface microtopography and multi-degree-of-freedom nonlinear friction dynamics for high-performance face gear

Face gear transmission is a kind of space-meshing mechanism that is mainly used in the field of aviation. Compared with traditional transmission, it has the advantages of stability, reliability, low noise, and strong carrying capacity. However, owing to its complex tooth surface, there are no means to accurately model the face gear. Likewise, research based on the geometry is difficult. Therefore, the tooth surface equation of the face gear is derived in this article based on the meshing theory. Based on the equations, the point cloud of the face gear tooth surface is calculated, the complex tooth surface is generated, and the face gear is accurately modeled. Moreover, taking tooth surface friction excitation into consideration, a multi-degree-of-freedom nonlinear dynamic model of face gear transmission system is established, using the adaptive variable step length Runge-Kutta method. As shown in the results, the bifurcation diagram, phase diagram, time history diagram, and Poincaré section diagram are combined to analyze the influence of tooth surface friction and meshing frequency on the dynamic characteristics of the system.