Complex Spatiotemporal Behavior Research Articles

Joint input-state estimation of structures subjected to complex loads via augmented Kalman Filter with physics informed latent force models

Joint input-state estimation algorithms such as the Augmented Kalman Filter (AKF) rely on the assumption that the distribution of the input loads follows simple spatial patterns, which are either spatially distributed or sparse. However, in many real situations the spatial distribution of the loads is complex and time-varying, which poses a significant challenge. To tackle this issue, this paper introduces a novel method named the Augmented Kalman Filter with Physics Informed Latent Force Models (AKF-PILFM), which incorporates knowledge about the physics underlying the dynamics of the input loads in the estimation based on training data. In the paper, the general formulation of the AKF-PILFM is described, followed by its tailored application to structures subjected to loads with a complex spatiotemporal behavior such as wave loads. The dominant characteristics of the wave loads are identified from training data via the Dynamic Mode Decomposition, enabling the development of a state space model of the loads that can be integrated with the AKF-PILFM. To demonstrate the effectiveness of the proposed methodology, a numerical example is provided consisting of a 3D steel jacket structure subjected to nonlinear irregular waves. The AKF-PILFM shows accurate estimation results and, in the example, outperforms an existing method based on the Gaussian Process Latent Force Models and equivalent modal loads, signifying that the load’s spatiotemporal behavior substantially influences the structural response.

Mechanical and biochemical feedback combine to generate complex contractile oscillations in cytokinesis

The actomyosin cortex is an active material that generates force to drive shape changes via cytoskeletal remodeling. Cytokinesis is the essential cell division event during which a cortical actomyosin ring closes to separate two daughter cells. Our active gel theory predicted that actomyosin systems controlled by a biochemical oscillator and experiencing mechanical strain would exhibit complex spatiotemporal behavior. To test whether active materials invivo exhibit spatiotemporally complex kinetics, we imaged the C.elegans embryo with unprecedented temporal resolution and discovered that sections of the cytokinetic cortex undergo periodic phases of acceleration and deceleration. Contractile oscillations exhibited a range of periodicities, including those much longer periods than the timescale of RhoA pulses, which was shorter in cytokinesis than in any other biological context. Modifying mechanical feedback invivo or in silico revealed that the period of contractile oscillation is prolonged as a function of the intensity of mechanical feedback. Fast local ring ingression occurs where speed oscillations have long periods, likely due to increased local stresses and, therefore, mechanical feedback. Fast ingression also occurs where material turnover is high, invivo and in silico. We propose that downstream of initiation by pulsed RhoA activity, mechanical feedback, including but not limited to material advection, extends the timescale of contractility beyond that of biochemical input and, therefore, makes it robust to fluctuations in activation. Circumferential propagation of contractility likely allows for sustained contractility despite cytoskeletal remodeling necessary to recover from compaction. Thus, like biochemical feedback, mechanical feedback affords active materials responsiveness and robustness.

Clocked dynamics in artificial spin ice

Artificial spin ice (ASI) are nanomagnetic metamaterials with a wide range of emergent properties. Through local interactions, the magnetization of the nanomagnets self-organize into extended magnetic domains. However, controlling when, where and how domains change has proven difficult, yet is crucial for technological applications. Here, we introduce astroid clocking, which offers significant control of ASI dynamics in both time and space. Astroid clocking unlocks a discrete, step-wise and gradual dynamical process within the metamaterial. Notably, our method employs global fields to selectively manipulate local features within the ASI. Sequences of these clock fields drive domain dynamics. We demonstrate, experimentally and in simulations, how astroid clocking of pinwheel ASI enables ferromagnetic domains to be gradually grown or reversed at will. Richer dynamics arise when the clock protocol allows both growth and reversal to occur simultaneously. With astroid clocking, complex spatio-temporal behaviors of magnetic metamaterials become easily controllable with high fidelity.

Resource limitation and population fluctuation drive spatiotemporal order in microbial communities.

Microbial communities display complex spatiotemporal behaviors leading to spatially-structured and ordered organization driven by species interactions and environmental factors. Resource availability plays a pivotal role in shaping the dynamics of bacterial colonies. In this study, we delve into the intricate interplay between resource limitation and the emergent properties of a growing colony of two visually distinct bacterial strains having similar growth and mechanical properties. Employing an agent-based modeling and computer simulations, we analyze the resource-driven effect on segregation and sectoring, cell length regulation and nematic ordering within a growing colony. We introduce a dimensionless parameter referred to as the active layer thickness, derived from nutrient diffusion equations, indicating effective population participation due to local resource availability. Our results reveal that lower values of active layer thickness arising from decreased resource abundance lead to rougher colony fronts, fostering heightened population fluctuations within the colony and faster spatial genetic diversity loss. Our temporal analyses unveil the dynamics of mean cell length and fluctuations, showcasing how initial disturbances evolve as colonies are exposed to nutrients and subsequently settle. Furthermore, examining microscopic details, we find that lower resource levels yield diverse cell lengths and enhanced nematic ordering, driven by the increased prevalence of longer rod-shaped cells. Our investigation sheds light on the multifaceted relationship between resource constraints and bacterial colony dynamics, revealing insights into their spatiotemporal organization.

Turing-Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator-Prey Model with Allee Effect and Predator Harvesting.

This paper investigates the complex dynamics of a ratio-dependent predator-prey model incorporating the Allee effect in prey and predator harvesting. To explore the joint effect of the harvesting effort and diffusion on the dynamics of the system, we perform the following analyses: (a) The stability of non-negative constant steady states; (b) The sufficient conditions for the occurrence of a Hopf bifurcation, Turing bifurcation, and Turing-Hopf bifurcation; (c) The derivation of the normal form near the Turing-Hopf singularity. Moreover, we provide numerical simulations to illustrate the theoretical results. The results demonstrate that the small change in harvesting effort and the ratio of the diffusion coefficients will destabilize the constant steady states and lead to the complex spatiotemporal behaviors, including homogeneous and inhomogeneous periodic solutions and nonconstant steady states. Moreover, the numerical simulations coincide with our theoretical results.

Simulations of driven breathing modes of a magnetically shielded Hall thruster

The operation of a 5 kW-class magnetically shielded Hall effect thruster with sinusoidal modulation of the discharge voltage is investigated through simulations with a 2D axisymmetric hybrid (particle-in-cell/fluid) code. The dynamic response of the thruster for different modulation amplitudes and frequencies is presented and discussed. The analysis of partial efficiencies contributing to thrust efficiency allows identifying counteracting effects limiting net gains in performance figures. Voltage modulation enhances the amplitude of plasma oscillations and can effectively control their frequency when the modulation frequency is close to that of the natural breathing mode (BM) of the thruster. The 2D plasma solution reveals that the dynamics of the ionization cycle are governed by the electron temperature response, enabling a driven BM at the modulation frequency. For modulation frequencies far from the natural BM one, voltage modulation fails to control the plasma production via the electron temperature, and the natural BM of the thruster is recovered. High order dynamic mode decomposition applied to the 2D plasma solution permits analyzing the complex spatio-temporal behavior of the plasma discharge oscillations, revealing the main characteristics of natural and externally driven modes.

Bifurcations in a diffusive predator–prey system with linear harvesting

Complex spatiotemporal dynamical behaviors of a diffusive predator–prey system with Michaelis–Menten type functional response and linear harvesting are investigated. Firstly, the critical conditions for the occurrence of Turing instability, which are necessary and sufficient, are derived in a novel way. Then, the existence conditions of codimension-1 Turing bifurcation, Hopf bifurcation, and codimension-2 Turing–Turing bifurcation, Turing–Hopf bifurcation are established. Furthermore, the detailed bifurcation set is given by calculating the amplitude equation with the method of the multiple time scale near the Turing–Hopf bifurcation. We find that the system may exhibit nonconstant steady-state solutions, spatially homogeneous periodic solutions, and spatially inhomogeneous periodic solutions, which can be verified by a series of numerical simulations. These investigations not only explain the effect of diffusion and harvesting on the dynamic behavior of the system, but also reveal the mechanism of spatiotemporal complexity in the diffusive predator–prey system.

Spatiotemporal dynamics of a diffusive predator-prey model with delay and Allee effect in predator.

It has been shown that Allee effect can change predator-prey dynamics and impact species persistence. Allee effect in the prey population has been widely investigated. However, the study on the Allee effect in the predator population is rare. In this paper, we investigate the spatiotemporal dynamics of a diffusive predator-prey model with digestion delay and Allee effect in the predator population. The conditions of stability and instability induced by diffusion for the positive equilibrium are obtained. The effect of delay on the dynamics of system has three different cases: (a) the delay doesn't change the stability of the positive equilibrium, (b) destabilizes and stabilizes the positive equilibrium and induces stability switches, or (c) destabilizes the positive equilibrium and induces Hopf bifurcation, which is revealed (numerically) to be corresponding to high, intermediate or low level of Allee effect, respectively. To figure out the joint effect of delay and diffusion, we carry out Turing-Hopf bifurcation analysis and derive its normal form, from which we can obtain the classification of dynamics near Turing-Hopf bifurcation point. Complex spatiotemporal dynamical behaviors are found, including the coexistence of two stable spatially homogeneous or inhomogeneous periodic solutions and two stable spatially inhomogeneous quasi-periodic solutions. It deepens our understanding of the effects of Allee effect in the predator population and presents new phenomena induced be delay with spatial diffusion.

Cis-Regulation by NACs: A Promising Frontier in Wheat Crop Improvement.

Crop traits are controlled by multiple genes; however, the complex spatio-temporal transcriptional behavior of genes cannot be fully understood without comprehending the role of transcription factors (TFs) and the underlying mechanisms of the binding interactions of their cis-regulatory elements. NAC belongs to one of the largest families of plant-specific TFs and has been associated with the regulation of many traits. This review provides insight into the cis-regulation of genes by wheat NACs (TaNACs) for the improvement in yield-related traits, including phytohormonal homeostasis, leaf senescence, seed traits improvement, root modulation, and biotic and abiotic stresses in wheat and other cereals. We also discussed the current potential, knowledge gaps, and prospects of TaNACs.

Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion Model

A constructive approach is provided for the reconstruction of stationary and non-stationary patterns in the one-dimensional Gray-Scott model, utilizing measurements of the system state at a finite number of locations. Relations between the parameters of the model and the density of the sensor locations are derived that ensure the exponential convergence of the estimated state to the original one. The designed observer is capable of tracking a variety of complex spatiotemporal behaviors and self-replicating patterns. The theoretical findings are illustrated in particular numerical case studies. The results of the paper can be used for the synchronization analysis of the master–slave configuration of two identical Gray–Scott models coupled via a finite number of spatial points and can also be exploited for the purposes of feedback control applications in which the complete state information is required.

A quasi-periodic route to chaos in a parametrically driven nonlinear medium

Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of damped nonlinear oscillators, we investigate a route to spatiotemporal chaos emerging from standing waves. The route from the stationary to the chaotic state proceeds through quasiperiodic dynamics. The standing wave undergoes the onset of oscillatory instability, which subsequently exhibits a different critical frequency, from which the complexity originates. A suitable amplitude equation, valid close to the parametric resonance, makes it possible to produce universe results. The respective phase-space structure and bifurcation diagrams are produced in a numerical form. We characterize the relevant dynamical regimes by means of the largest Lyapunov exponent, the power spectrum, and the evolution of the total intensity of the wave field.

Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds.

Gamma frequency oscillations (25–140 Hz), observed in the neural activities within many brain regions, have long been regarded as a physiological basis underlying many brain functions, such as memory and attention. Among numerous theoretical and computational modeling studies, gamma oscillations have been found in biologically realistic spiking network models of the primary visual cortex. However, due to its high dimensionality and strong non-linearity, it is generally difficult to perform detailed theoretical analysis of the emergent gamma dynamics. Here we propose a suite of Markovian model reduction methods with varying levels of complexity and apply it to spiking network models exhibiting heterogeneous dynamical regimes, ranging from nearly homogeneous firing to strong synchrony in the gamma band. The reduced models not only successfully reproduce gamma oscillations in the full model, but also exhibit the same dynamical features as we vary parameters. Most remarkably, the invariant measure of the coarse-grained Markov process reveals a two-dimensional surface in state space upon which the gamma dynamics mainly resides. Our results suggest that the statistical features of gamma oscillations strongly depend on the subthreshold neuronal distributions. Because of the generality of the Markovian assumptions, our dimensional reduction methods offer a powerful toolbox for theoretical examinations of other complex cortical spatio-temporal behaviors observed in both neurophysiological experiments and numerical simulations.

Spatio-temporal complexity of power-grid frequency fluctuations

Power-grid systems constitute one of the most complex man-made spatially extended structures. These operate with strict operational bounds to ensure synchrony across the grid. This is particularly relevant for power-grid frequency, which operates strictly at 50 Hz (60 Hz). Nevertheless, small fluctuations around the mean frequency are present at very short time scales <2 s and can exhibit highly complex spatio-temporal behaviour. Here we apply superstatistical data analysis techniques to measured frequency fluctuations in the Nordic grid. We study the increment statistics and extract the relevant time scales and superstatistical distribution functions from the data. We show that different synchronous recordings of power-grid frequency have very distinct stochastic fluctuations with different types of superstatistics at different spatial locations, and with transitions from one superstatistics to another when the time lag of the increment statistics is changed.

Autonomous Transient pH Flips Shaped by Layered Compartmentalization of Antagonistic Enzymatic Reactions

AbstractTransient signaling orchestrates complex spatiotemporal behaviour in living organisms via (bio)chemical reaction networks (CRNs). Compartmentalization of signal processing is an important aspect for controlling such networks. However, artificial CRNs mostly focus on homogeneous solutions to program autonomous self‐assembling systems, which limits their accessible behaviour and tuneability. Here, we introduce layered compartments housing antagonistic pH‐modulating enzymes and demonstrate that transient pH signals in a supernatant solution can be programmed based on spatial delays. This overcomes limitations of activity mismatches of antagonistic enzymes in solution and allows to flexibly program acidic and alkaline pH lifecycles beyond the possibilities of homogeneous solutions. Lag time, lifetime, and the pH minima and maxima can be precisely programmed by adjusting spatial and kinetic conditions. We integrate these spatially controlled pH flips with switchable peptides, furnishing time‐programmed self‐assemblies and hydrogel material system.

Autonomous Transient pH Flips Shaped by Layered Compartmentalization of Antagonistic Enzymatic Reactions.

Transient signaling orchestrates complex spatiotemporal behaviour in living organisms via (bio)chemical reaction networks (CRNs). Compartmentalization of signal processing is an important aspect for controlling such networks. However, artificial CRNs mostly focus on homogeneous solutions to program autonomous self‐assembling systems, which limits their accessible behaviour and tuneability. Here, we introduce layered compartments housing antagonistic pH‐modulating enzymes and demonstrate that transient pH signals in a supernatant solution can be programmed based on spatial delays. This overcomes limitations of activity mismatches of antagonistic enzymes in solution and allows to flexibly program acidic and alkaline pH lifecycles beyond the possibilities of homogeneous solutions. Lag time, lifetime, and the pH minima and maxima can be precisely programmed by adjusting spatial and kinetic conditions. We integrate these spatially controlled pH flips with switchable peptides, furnishing time‐programmed self‐assemblies and hydrogel material system.

Bridging the gap: Machine learning to resolve improperly modeled dynamics

We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex spatio-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the system and the dynamics given by a model of the system that is either inaccurately or inadequately described. Our machine learning strategy leverages data generated from the improper system model and observational data from the actual system to create a neural network to model the dynamics of the actual system. We evaluate the proposed framework using numerical solutions obtained from three increasingly complex dynamical systems. Our results show that our system is capable of learning a data-driven model that provides accurate estimates of the system states both in previously unobserved regions as well as for future states. Our results show the power of state-of-the-art machine learning frameworks in estimating an accurate prior of the system’s true dynamics that can be used for prediction up to a finite horizon.

On the Regional Variability of dB/dt and Its Significance to GIC

AbstractFaraday's law of induction is responsible for setting up a geoelectric field due to the variations in the geomagnetic field caused by ionospheric currents. This drives geomagnetically induced currents (GICs) which flow in large ground‐based technological infrastructure such as high‐voltage power lines. The geoelectric field is often a localized phenomenon exhibiting significant variations over spatial scales of only hundreds of kilometers. This is due to the complex spatiotemporal behavior of electrical currents flowing in the ionosphere and/or large gradients in the ground conductivity due to highly structured local geological properties. Over some regions, and during large storms, both of these effects become significant. In this study, we quantify the regional variability of dB/dt using closely placed IMAGE stations in northern Fennoscandia. The dependency between regional variability, solar wind conditions, and geomagnetic indices are also investigated. Finally, we assess the significance of spatial geomagnetic variations to modeling GICs across a transmission line. Key results from this study are as follows: (1) Regional geomagnetic disturbances are important in modeling GIC during strong storms; (2) dB/dt can vary by several times up to a factor of three compared to the spatial average; (3) dB/dt and its regional variation is coupled to the energy deposited into the magnetosphere; and (4) regional variability can be more accurately captured and predicted from a local index as opposed to a global one. These results demonstrate the need for denser magnetometer networks at high latitudes where transmission lines extending hundreds of kilometers are present.

Transition to Spatiotemporal Intermittency and Defect Turbulence in Systems under Translational Coupling.

Out of equilibrium systems under the influence of enough energy injection exhibit complex spatiotemporal behaviors. Based on a liquid crystal light valve experiment with translational optical feedback, we observe propagation, spatiotemporal intermittency, and defect turbulence of striped waves. A prototype model of pattern formation with translational coupling shows the same phenomenology. Close to the spatial instability, a local amplitude equation is derived. This amplitude equation allows us to reveal the origin and bifurcation diagram of the observed complex spatiotemporal dynamics. Experimental observations have a qualitative agreement with theoretical findings.

Bifurcation and nonlinear evolution of convection in binary fluid mixtures with weak Soret effect

Rayleigh-Bénard (RB) convection in binary fluid mixtures, which shows rich and interesting pattern formation behavior, is a paradigm for understanding instabilities, bifurcations, self-organization with complex spatiotemporal behavior and turbulence, with many applications in atmospheric and environmental physics, astrophysics, and process technology. In this paper, by using a high-order compact finite difference method to solve the full hydrodynamic field equations, we study numerically the RB convection in binary fluid mixtures such as ethanol-water with a very weak Soret effect (separation ratio &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$\psi=-0.02$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191836_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191836_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;) in a rectangular container heated uniformly from below. The direct numerical simulations are conducted in the rectangular container with aspect ratio of &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$\varGamma=12$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191836_M3.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191836_M3.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; and with four no-slip and impermeable boundaries, isothermal horizontal and perfectly insulated vertical boundaries. The bifurcation and the origin and evolution of pattern in RB convection for the considered physical parameters are studied, and the bifurcation diagram is presented. By performing two-dimensional simulations, we observe three stable states of Blinking state, localized traveling wave and stationary overturning convection (SOC) state, and discuss the transitions between them. The results show that there is a hysteresis in the transition from the Blinking state to the localized traveling wave state for the considered separation ratio, and the evolution of the oscillation frequency, convection amplitude and Nusselt number are discontinuous. Near the lower bound of the Rayleigh number range where the Blinking state exists, a asymmetric initial disturbance is the inducement for the formation of the Blinking state. Inside the range, its inducing effect is weakened, and the oscillatory instability becomes the main reason. It is further confirmed that reflections of lateral walls are responsible for the survival of the stable Blinking state. With the increase of the Rayleigh number, the critical SOC state undergoes multiple bifurcations and forms multiple SOC states with different wave numbers, and then transitions to a chaotic state. There are no stable undulation traveling wave states at both ends of the critical SOC branch.

Pattern Formation With Locally Active S-Type NbOx Memristors

The main focus of this paper is the evolution of complex behavior in a system of coupled nonlinear memristor circuits depending on the applied coupling conditions. Thereby, the parameter space for the local activity and the edge-of-chaos domain will be determined to enable the emergence of the pattern formation in locally coupled cells according to Chua’s principle. Each cell includes a Niobium oxide-based memristor, which may feature a locally active behavior once it is suitably biased on the negative differential resistance region of its DC current-voltage characteristic. It will be shown that there exists a domain of parameters under which each uncoupled cell may become locally active around a stable bias state. More specifically, under these conditions, the coupled cells are on the edge-of-chaos, and can support the static and dynamic pattern formation. The emergence of such complex spatio-temporal behavior in homogeneous structures is a prerequisite for information processing. The theoretical results are confirmed by measurements as well as by the numerical simulations of the accurate device and circuit models.