Spatiotemporal Instability Research Articles

Suppression of Spatiotemporal Instabilities in Broad-Area Lasers with Pump Modulation by External Optical Injection

Suppression of Spatiotemporal Instabilities in Broad-Area Lasers with Pump Modulation by External Optical Injection

Effect of Mach number on the absolute/convective stability of compressible planar wakes

In this paper, the influence of the Mach number on the stability of two-dimensional compressible planar wakes is studied to gain physical insight into the turbine wakes. Two-dimensional instabilities of compressible wakes are studied using local spatiotemporal instability analyses. The absolute/convective boundary of a family of wake profiles is obtained at different Mach numbers. Then, local stability analyses of compressible wakes behind flat plates are performed. It is found that in the subsonic region increasing Mach number acts in two ways to modify the instability characteristics in the near wake region: it lengthens the recirculation zone and it reduces the absolute growth rate. These two mechanisms work against each other, which explains why the linear global growth rate varies slightly as Mach number changes in the subsonic region. Further increasing Mach number to 1 would greatly reduce the length of the absolute unstable region due to the occurrence of expansion waves around the trailing edge corner. As a result, the wake is strongly stabilized at $$\hbox {Ma}=1$$ .

Modeling pedestrian-injury severities in pedestrian-vehicle crashes considering spatiotemporal patterns: Insights from different hierarchical Bayesian random-effects models

To systematically account for the spatiotemporal features and unobserved heterogeneity within pedestrian-vehicle crashes, this paper employs the spatiotemporal analysis and hierarchical Bayesian random-effects models to explore the factors contributing to pedestrian-injury severities of pedestrian-vehicle crashes involving single vehicle in North Carolina from 2007 to 2018. Ten spatiotemporal patterns of the crashes are identified by applying an improved spatiotemporal analysis. Significant temporal instability and the spatiotemporal instability of the factors to the pedestrian-injury crashes are identified by the likelihood ratio tests. A hierarchical Bayesian random intercept logit model with random-effects across the spatiotemporal groups is firstly employed for the whole dataset. The comparison between different hierarchical models indicates that addressing random-effects across observations and increasing the number of random parameters could both improve the model performance. Then a hierarchical Bayesian random-effects-only logit model, which allows all parameters to be randomly distributed across observations, is developed to further investigate the unobserved heterogeneity in spatiotemporal segmented datasets. The significant improvements in terms of model fit and the hit accuracy underscore the superiority of the random-effects-only model. The marginal effects of the human, vehicle, crash, locality, roadway, environment, time, and traffic control factors for each spatiotemporal dataset also provide insights into possible inherent reasons for the spatiotemporal instability/tendency of the crash and correlated factors. Meanwhile, specific countermeasures are given to locations especially in which the spatially aggregated patterns of the crashes have new, consecutive, and intensifying temporal tendencies. This study provides a framework for engineers and researchers to identify spatiotemporal patterns of the crashes and explore the factors affecting pedestrian-injury severities especially in those existing crash-prone areas.

Theory of mechanochemical patterning and optimal migration in cell monolayers

Collective cell migration offers a rich field of study for non-equilibrium physics and cellular biology, revealing phenomena such as glassy dynamics, pattern formation and active turbulence. However, how mechanical and chemical signalling are integrated at the cellular level to give rise to such collective behaviours remains unclear. We address this by focusing on the highly conserved phenomenon of spatiotemporal waves of density and extracellular signal-regulated kinase (ERK) activation, which appear both in vitro and in vivo during collective cell migration and wound healing. First, we propose a biophysical theory, backed by mechanical and optogenetic perturbation experiments, showing that patterns can be quantitatively explained by a mechanochemical coupling between active cellular tensions and the mechanosensitive ERK pathway. Next, we demonstrate how this biophysical mechanism can robustly induce long-ranged order and migration in a desired orientation, and we determine the theoretically optimal wavelength and period for inducing maximal migration towards free edges, which fits well with experimentally observed dynamics. We thereby provide a bridge between the biophysical origin of spatiotemporal instabilities and the design principles of robust and efficient long-ranged migration. Spatiotemporal waves appear during collective cell migration and are affected by mechanical forces and biochemical signalling. Here the authors develop a biophysical model that can quantitatively account for complex mechanochemical patterns, and predict how they can be used for optimal collective migration.

Spatiotemporal Gradient and Instability of Wnt Induce Heterogeneous Growth and Differentiation of Human Intestinal Organoids.

SummaryIn a conventional culture of three-dimensional human intestinal organoids, extracellular matrix hydrogel has been used to provide a physical space for the growth and morphogenesis of organoids in the presence of exogenous morphogens such as Wnt3a. We found that organoids embedded in a dome-shaped hydrogel show significant size heterogeneity in different locations inside the hydrogel. Computational simulations revealed that the instability and diffusion limitation of Wnt3a constitutively generate a concentration gradient inside the hydrogel. The location-dependent heterogeneity of organoids in a hydrogel dome substantially perturbed the transcriptome profile associated with epithelial functions, cytodifferentiation including mucin 2 expression, and morphological characteristics. This heterogeneous phenotype was significantly mitigated when the Wnt3a was frequently replenished in the culture medium. Our finding suggests that the morphological, transcriptional, translational, and functional heterogeneity in conventional organoid cultures may lead to a false interpretation of the experimental results in organoid-based studies.

Investigation and Analysis of Spatiotemporal Instability of the Earth’s Atmosphere Based on Real-Time GNSS Data Processing

One of the options for the practical application of GNSS technology, in addition to geodetic and navigation needs, is remote sensing of the atmosphere by radio signals from navigation satellites in order to improve the quality and detail of weather forecasts. The propagation of a radio signal from GNSS satellites to a ground receiving device (GNSS receiver) through a neutral atmosphere is accompanied by a decrease in the phase velocity of the radio waves (additional atmospheric delays). This is due to the presence of nitrogen, oxygen, carbon dioxide, and water vapor molecules in the atmosphere. Therefore, measurements of the additional delay of the radio signal in the atmosphere (tropospheric delay) provide information on the integral properties of the atmosphere along the propagation path of the radio signal. As a result of the primary processing of the GNSS measurement results, the distances from the observation station to GNSS satellites are determined. Secondary processing of GNSS measurements consists in solving a navigation problem and provides information on the location of the station. In order to obtain meteorological information, it is necessary to develop special methods of secondary data processing based on solving inverse problems. The combination of primary and secondary data (processing) along with meteorological information makes it possible to obtain a global model of the atmosphere in near-real time. The efficiency of this approach, the complete automation, and the absence of consumables during remote sensing provide opportunities for the widespread implementation of operational monitoring of the state of the atmosphere in order to improve the data’s detail and accuracy of regional short-term weather forecasts. Currently, due to cross-border cooperation with European countries in conducting joint GNSS observations in the UA-EUPOS/ZAKPOS network of stations, we are able to have an accurate, dense, and continuous sampling of tropospheric delay values, which allows us to determine and predict the dynamics of atmospheric changes in real time. The main goal of the work is to study the spatio-temporal instability of the atmosphere over an area covered by active reference stations. The results of the study can be used to improve the quality of weather prediction.

Instability threshold in a large balanced magneto-optical trap

Large clouds of cold atoms prepared in a magneto-optical trap can develop spatiotemporal instabilities when the frequency of the trapping lasers is brought close to the atomic resonance. This system bears close similarities with trapped plasmas, whereby effective Coulomb interactions are induced by the exchange of scattered photons and lead to collective nonlinear dynamics of the trapped atoms. We report in this paper a detailed experimental study of the instability threshold, and comparisons with three-dimensional simulations of the interacting, laser-driven cloud.

Stability analysis for a new model of multi-species convection-diffusion-reaction in poroelastic tissue

We perform the linear stability analysis of a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes convected in the medium. We find parameter regions that lead to spatio-temporal instabilities of the coupled system. The mutual dependences between deformation and diffusive patterns are of substantial relevance in the study of morphoelastic changes in bio-materials. We provide a set of computational examples in 2D and 3D (related to brain mechanobiology) that can be used to form a better understanding on how, and up to which extent, the deformations of the porous structure dictate the generation and suppression of spatial patterning dynamics, also related to the onset of mechano-chemical waves.

Spatiotemporal linear instability analysis for arbitrary dispersion relations on the Lefschetz thimble in multidimensional spacetime

In linear stability analysis of field quantities described by partial differential equations, the well-established classical theory is all but impossible to apply to concrete problems in its entirety even for uniform backgrounds when the spatial dimension is more than 1. In this study, using the Lefschetz thimble method, we develop a new formalism to give an explicit expression to the asymptotic behavior of linear perturbations. It is not only more mathematically rigorous than the previous theory but also useful practically in its applications to realistic problems, and, as such, has an impact on broad subjects in physics.

Spatiotemporal variation in the relationship between boreal forest productivity proxies and climate data

The impacts of climate change on high-latitude forest ecosystems are still uncertain. Divergent forest productivity trends have recently been reported both at the local and regional level challenging the projections of boreal tree growth dynamics. The present study investigated (i) the responses of different forest productivity proxies to monthly climate (temperature and precipitation) through space and time; and (ii) the local coherency between these proxies through time at four high-latitude boreal Scots pine sites (coastal and inland) in Norway. Forest productivity proxies consisted of two proxies representing stem growth dynamics (radial and height growth) and one proxy representing canopy dynamics (cumulative May-to-September Normalized Difference Vegetation Index (NDVI)). Between-proxy and climate-proxy correlations were computed over the 1982–2011 period and over two 15-yr sub-periods. Over the entire period, radial growth significantly correlated with current year July temperature, and height growth and cumulative NDVI significantly correlated with previous and current growing season temperatures. Significant climate responses were quite similar across sites, despite some higher sensitivity to non-growing season climate at inland sites. Significant climate-proxy correlations identified over the entire period were temporarily unstable. Local coherency between proxies was generally insignificant. The spatiotemporal instability in climate-proxy correlations observed for all proxies underlines evolving responses to climate and challenges the modelling of forest productivity. The general lack of local coherency between proxies at our four study sites suggests that forest productivity estimations based on a single proxy should be considered with great caution. The combined use of different forest growth metrics may help circumvent uncertainties in capturing responses of forest productivity to climate variability and improve estimations of carbon sequestration by forest ecosystems.

Emergent spatiotemporal instabilities in reactive spatially extended systems by thermodiffusion.

Thermodiffusion or thermophoresis or Soret effect, i.e., mass-transport induced by thermal gradient, has immense application in segregation of species in two or multicomponent gaseous, liquid, or colloidal mixtures. Here, we show that an external thermal gradient can be effectively utilized in creation and modification of patterns in spatially extended systems. We consider Brusselator and chlorine-dioxide iodine malonic acid (CDIMA) reaction-diffusion systems, which follow activator-inhibitor kinetics subjected to an external thermal gradient. We find that the conspicuous interaction of emergent thermodiffusive flux with reaction kinetics and diffusion can lead to various spatiotemporal instabilities in these two models. Specifically, our result reveals formation of Turing-like spatial patterns even for equal diffusivities of the activator and inhibitor components in the Brusselator model under the influence of differential thermodiffusion, whereas formation of such stationary patterns in the CDIMA system from a homogenous stable steady state, which is also stable under differential diffusion, requires the same sign and magnitude of Soret coefficients. However, with equal diffusivities of the components of the CDIMA system and without starch in the medium, our result identifies formation of drifting spiral waves which finally disappears at longer times under the influence of thermodiffusion. We also show formation of propagating patterns of spotlike or stripelike heterogeneity in both the model systems under appropriate conditions. Our study provides a route to pattern formation beyond Turing space and reveals remarkable influence of thermodiffusion to modify the pattern types just by employing an external thermal gradient which also opens up the possibility to set up new related experiments.

Spatio-temporal secondary instabilities near the Turing-Hopf bifurcation

In this work, we provide a framework to understand and quantify the spatiotemporal structures near the codimension-two Turing-Hopf point, resulting from secondary instabilities of Mixed Mode solutions of the Turing-Hopf amplitude equations. These instabilities are responsible for solutions such as (1) patterns which change their effective wavenumber while they oscillate as well as (2) phase instability combined with a spatial pattern. The quantification of these instabilities is based on the solution of the fourth order polynomial for the dispersion relation, which is solved using perturbation techniques. With the proposed methodology, we were able to identify and numerically corroborate that these two kinds of solutions are generalizations of the well known Eckhaus and Benjamin-Feir-Newell instabilities, respectively. Numerical simulations of the coupled system of real and complex Ginzburg-Landau equations are presented in space-time maps, showing quantitative and qualitative agreement with the predicted stability of the solutions. The relation with spatiotemporal intermittency and chaos is also illustrated.

Bifurcation and nonlinear dynamics in passive Q-switched optical vortex lasers

In a laser resonator with an intra-cavity spiral phase plate, a passive Q-switched pulsed vortex laser carrying a positive unit topological charge is formed by the coherent superposition of the supported off-axis multiple-pass transverse (MPT) resonant modes. Under different pumping conditions, the modal interaction induces spatiotemporal instability and results in periodic and aperiodic oscillations in the vortex laser pulses while the vortex structure remains stable. The constituting off-axis MPT modes that form the vortex strongly overlap in the time domain and can be simulated by a modified Tang–Statz–DeMars model including coherent modal interactions. Expected potential applications using this vortex laser include the manipulation of laser chaos and stochastic events.

On the transition to secondary Kerr combs in whispering-gallery mode resonators.

We demonstrate that extended dissipative structures in Kerr-nonlinear whispering-gallery mode resonators undergo a spatiotemporal instability, as the pumping parameters are varied. We show that the dynamics of the patterns beyond this bifurcation yield specific Kerr comb and sub-comb spectra that can be subjected to a phase of frequency-locking when optimal conditions are met. Our numerical results are found to be in agreement with experimental measurements.

Spatio-temporal instability in negative index materials

In this paper, we investigate spatiotemporal instability in negative index materials (NIMs) made of split ring resonators and arrays of wires embedded in a Kerr medium. The pulse propagation in NIM is modeled by nonlinear Schrödinger type equation. The linear stability analysis is carried out to obtain the instability gain. We study the influence of electric and magnetic self steepening effects and coupling between electric and magnetic fields on MI gain. We report additional ways to generate solitons or ultrashort pulses in negative index artificial materials.

Instability analysis of the cone–jet flow in liquid-driven flow focusing

The instability behaviors of a liquid jet issuing from a cone in liquid-driven flow focusing for droplet generation are studied. The experiment, numerical simulation by solving the Navier–Stokes equation coupled with a diffuse interface method, and linear spatio-temporal instability analysis based on non-uniform velocity profiles are performed. Typical flow modes and transitions are obtained by adjusting the flow rates of focused and focusing phases. The cone instability is examined and the flow patterns in the vicinity of the cone are presented numerically. The result shows that the liquid cone can be always stable in a wide range of process parameters when the viscous shear stress overcomes the interfacial tension stress and a scaling law is given. In addition, the spatial evolution of velocity profiles of the flow is numerically investigated. Finally, the jetting–dripping (J–D) transition is studied through the dimensional analysis and the linear instability theory in comparison with experiments and good agreements among them are achieved. It is also indicated that the J–D transition boundary can be approximately given by the scaling law of $$We_{\mathrm{i}}+Ca_{\mathrm{o}}\approx 1,$$ where $$We_{\mathrm{i}}$$ and $$Ca_{\mathrm{o}}$$ reflect the competitions of inertia force and viscous shear stress to the interfacial tension along the jet, respectively.

Explore a deep learning multi-output neural network for regional multi-step-ahead air quality forecasts

Timely regional air quality forecasting in a city is crucial and beneficial for supporting environmental management decisions as well as averting serious accidents caused by air pollution. Artificial Intelligence-based models have been widely used in air quality forecasting. The Shallow Multi-output Long Short-Term Memory (SM-LSTM) model is suitable for regional multi-step-ahead air quality forecasting, while it commonly encounters spatio-temporal instabilities and time-lag effects. To overcome these bottlenecks and overfitting issues, this study proposed a Deep Multi-output LSTM (DM-LSTM) neural network model that were incorporated with three deep learning algorithms (i.e., mini-batch gradient descent, dropout neuron and L2 regularization) to configure the model for extracting the key factors of complex spatio-temporal relations as well as reducing error accumulation and propagation in multi-step-ahead air quality forecasting. The proposed DM-LSTM model was evaluated by three time series of PM2.5, PM10, and NOx simultaneously at five air quality monitoring stations in Taipei City of Taiwan. Results indicated that the loss function values (mean-square-error) of the SM-LSTM and DM-LSTM models in the testing stages at horizon t+4 were 0.87 and 0.72, respectively. The Gbench values of the DM-LSTM model in the testing stages for PM2.5, PM10, and NOx reached 0.95 at horizon t+1 and exceeded 0.81 at horizon t+4, respectively. Results demonstrated that the proposed DM-LSTM model incorporated with three deep learning algorithms could significantly improve the spatio-temporal stability and accuracy of regional multi-step-ahead air quality forecasts.

Spatio-temporal instability of two superposed fluids in a channel with boundary slip

Spatio-temporal stability analysis of a viscosity and density stratified two-fluid flow in a channel with hydrophobic walls, which experience a finite tangential velocity slip, is considered for a range of parameters for which Squire’s theorem is not valid. The study restricted only to temporal stability analysis of two/three-dimensional infinitesimal disturbances reveals that three-dimensional disturbances are more unstable than the corresponding two-dimensional disturbances. We examine the role of different types of slip boundary conditions at the channel walls on the temporal growth rate. The influence of velocity slip at the upper wall on the nature of instability in the spatio-temporal framework for low density ratio is investigated, and the boundary that demarcates the convective/absolute instabilities are presented for both two and three-dimensional disturbances. In a configuration with a thinner lower layer away from the upper wall with slip, we found that the flow in the entire domain is absolutely unstable, except for two strips at low and high Reynolds numbers. For the parameters considered in the present study, it is found that the absolutely unstable region shrinks with decrease in velocity slip. The absolute growth rate exhibits a non-monotonic behavior with respect to velocity slip. The role of velocity slip in promoting absolute instability in some parameter regimes suggests that by designing the walls of the channel as hydrophobic/rough/porous surfaces, which can be modelled as smooth surfaces with tangential velocity slip, it may be possible to achieve early transition to turbulence in two-layer flow systems.

Spatiotemporal instability in a diffusively relaxed dynamics

The diffusion equation fails to offer a satisfactory description of dynamics when the correlation between successive motions of dispersive particle is large. Further, the equation is associated with the pitfall of predicting the infinite propagation speed of the diffusive particles. Both limitations arise as the Brownian picture (on which the equation is based on) does not take into account the inertia of the diffusive particles. This could be overcome by introducing a delay in the diffusive flux. The resultant delay-diffusion equation may be converted to an ordinary differential equation by linearizing the flux with respect to the delay, a technique valid in general for small delays. In this article I show that the condition for a spatial bifurcation induced by diffusive delay in the delay differential model is significantly different from the condition derived in an earlier work modifying the reaction-telegraphic equation based on a microscopic approach. The latter necessitates criteria not realizable in common reaction-diffusion models and therefore effectively rules out such kinds of instability in these models. I show here that the instability condition derived with the original nontruncated version of the delayed reaction-diffusion equation does not impose any constraint on the model kinetics, but only requires the diffusive memory to be large enough. Numerical simulation with three well-known reaction-diffusion models corroborates with the predictions of the linear analysis and ensures the that spatiotemporal structure generated is stable in the long term.

Thermal Reaction Norms of Locomotor Performance in Lacertid Lizards of the Genus Takydromus

Thermal reaction norms of sprint speed were examined in three lacertid lizard species (Takydromus tachydromoides, T. smaragdinus, and T. dorsalis). We found inter- and intraspecific variations in maximum sprint speed, optimal body temperature, and thermal performance breadth for the best sprints. The thermal performance breadth of T. smaragdinus was broader than that of T. tachydromoides or T. dorsalis, whereas T. dorsalis sprinted faster than the others. In T. smaragdinus, individuals with narrower performance breadths run faster within their thermal range of expertise. There were “specialist” individuals of which performance depended heavily on high temperatures, as well as “generalist” individuals that performed well over a broad range of temperatures even within a single population. We discussed that the spatiotemporal instability of habitats might favor more than one type of thermal reaction norm of sprint performance, and this phenomenon may be driven by specialist-generalist trade-offs.