Spatiotemporal Disorder Research Articles

Spatiotemporalized Hydrogel Microspheres Promote Vascularized Osteogenesis via Ultrasound Oxygen Delivery

AbstractDisturbance of spatiotemporal oxygen balance is the main cause of delayed healing or nonhealing of large bone defects. The accurate administration of oxygen to regulate disruptions in the spatiotemporal oxygen equilibrium during 9 h of hypoxia is imperative for bone tissue regeneration. Herein, oxygen‐loaded nanobubbles prepared by double emulsification are successfully embedded in GelMA/HepMA microsphere macromolecular meshwork by microfluidic techniques, and a spatiotemporalized hydrogel microsphere is constructed by noncovalently binding bone morphogenetic protein 2 (BMP‐2). The spatiotemporalized hydrogel microspheres precisely “remote control” oxygen release by ultrasound in vitro 9 h after bone injury to regulate spatiotemporal oxygen homeostasis disorder, maintain a high level of vascular endothelial growth factor (VEGF) expression, and accelerate bone repair. The spatiotemporalized hydrogel microspheres possess good oxygen‐carrying capacity and ultrasonic responsiveness, and the oxygen concentration increases to 1.63, 1.95, 2.11, and 2.29 times under the ultrasound action at different intensities of 1, 2, 3, and 4 W, respectively, providing the conditions for the precise regulation of spatiotemporal oxygen balance disorder by ultrasound. In the in vitro hypoxia model and in vivo rat femoral defect model, the spatiotemporal hydrogel microspheres show good vascularization and osteogenesis capabilities, which provide a new strategy for the clinical treatment of large bone defects.

Ultrasonic-controlled “explosive” hydrogels to precisely regulate spatiotemporal osteoimmune disturbance

Spatiotemporal Immune disorder is a key factor leading to the failure of bone tissue healing. It is of vital importance to accurately suppress excessive peak immune response within 24-48 h of the injury and so regulate the spatiotemporal osteoimmune disturbance of bones. In this study, Ultrasound Controlled “Explosive” (UCE) hydrogels were prepared from gelatin-hyaluronic acid methacrylate hydrogels loaded with resveratrol nanobubbles produced by double emulsification through a condensation reaction. Such materials innovatively enable ultrasound-controlled RES release for precise regulation of spatiotemporal osteoimmune disorders. Under an ultrasonic power level of 1.5 W/cm2, the rate of effectively released RES through the blast of UCE hydrogels reached 38.14 %. And compared with the control group, the in vivo inhibition of inflammation and osteogenesis effects of UCE hydrogels were more effective, respectively. As suggested by the results, the excessive local inflammatory response was inhibited by the release of resveratrol, the temporospatial disorder of bone immune was precisely regulated, and as a result, the process of bone repair was accelerated. Altogether, this study confirms that the newly created UCE Hydrogels effectively promote bone repair by intervening peak inflammation during the early phase of fracture healing.

Weak ergodicity breaking and anomalous diffusion in collective motion of active particles under spatiotemporal disorder.

The effects of spatiotemporal disorder, i.e., both the noise and quenched disorder, on the dynamics of active particles in two dimensions are investigated. We demonstrate that within the tailored parameter regime, nonergodic superdiffusion and nonergodic subdiffusion occur in the system, identified by the observable quantities (the mean squared displacement and ergodicity-breaking parameter) averaged over both the noise and realizations of quenched disorder. Their origins are attributed to the competition effects between the neighbor alignment and spatiotemporal disorder on the collective motion of active particles. These results may be helpful for further understanding the nonequilibrium transport process of active particles, as well as for detection of the transport of self-propelled particles in complex and crowded environments.

Floquet-induced localization in long-range many-body systems

The fate of many-body localization in long-range interacting systems is not fully settled. For instance, the phase boundary between ergodic and many-body localized regimes is still under debate. Here, we use Floquet dynamics which can induce many-body localization in a clean long-range interacting system through spatiotemporal disorder, which are realized by regular operation of random local rotations. The phase diagram has been determined for two types of uniform and nonuniform long-range couplings. Our Floquet mechanism shows more localizing power than conventional static disorder methods as it pushes the phase boundary in favor of the localized phase. Moreover, our comprehensive long-time simulations provide strong support for obtained results based on static analysis.

Dissipative solitons stabilized by nonlinear gradients in one spatial dimension: From deterministic to stochastic aspects, and a perspective

The purpose of this article is twofold. Firstly, to investigate the formation of localized spatiotemporal chaos in the complex cubic Ginzburg–Landau equation including nonlinear gradient terms. We found a transition to spatiotemporal disorder via quasiperiodicity accompanied by the fact that incommensurate satellite peaks arise around the fundamental frequency and its harmonics. Secondly, we review the influence of multiplicative noise on stationary pulses stabilized by nonlinear gradients. Numerical simulations show surprising results that are explained analytically. We found that multiplicative noise can induce a velocity change of propagating dissipative solitons. This completes previous communications on the two issues addressed in O. Descalzi et al., (2019, 2021, 2022).

Oscillatory dissipative solitons stabilized by nonlinear gradient terms: The transition to localized spatiotemporal disorder.

We investigate properties of oscillatory dissipative solitons (DSs) in a cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. As a main result we find a transition to dissipative solitons with spatiotemporal disorder as a function of the diffusion coefficient. This transition proceeds via quasiperiodicity and shows incommensurate satellites next to the fundamental frequency and its harmonics indicating a possible route to localized spatiotemporal chaos. The transition back to oscillatory DSs follows a similar scenario.

Ultracold Bose Gases in Dynamic Disorder with Tunable Correlation Time.

We study experimentally the dissipative dynamics of ultracold bosonic gases in a dynamic disorder potential with tunable correlation time. First, we measure the heating rate of thermal clouds exposed to the dynamic potential and present a model of the heating process, revealing the microscopic origin of dissipation from a thermal, trapped cloud of bosons. Second, for Bose-Einstein condensates, we measure the particle loss rate induced by the dynamic environment. Depending on the correlation time, the losses are either dominated by heating of residual thermal particles or the creation of excitations in the superfluid, a notion we substantiate with a rate model. Our results illuminate the interplay between superfluidity and time-dependent disorder and on more general grounds establish ultracold atoms as a platform for studying spatiotemporal noise and time-dependent disorder.

Initiation and maintenance of arrhythmogenic action potential waves near the infarct zone in heart failure

Cardiac arrhythmias are thought to be a complex spatiotemporal disorder of the cardiac action potential (AP) in the heart. The transition from normal sinus rhythm to arrhythmias includes many steps: the genesis of triggers, the initiation of reentry by the trigger, the transition from reentry to multiple wavelets fibrillation, and the maintenance of fibrillation. While it is known that reentries and successive spiral waves often arise from the infarct border zone, the detailed mechanisms of these phenomena are not well understood.

Lagrangian Transport and Chaotic Advection in Three-Dimensional Laminar Flows

AbstractTransport and mixing of scalar quantities in fluid flows is ubiquitous in industry and Nature. While the more familiar turbulent flows promote efficient transport and mixing by their inherent spatio-temporal disorder, laminar flows lack such a natural mixing mechanism and efficient transport is far more challenging. However, laminar flow is essential to many problems, and insight into its transport characteristics of great importance. Laminar transport, arguably, is best described by the Lagrangian fluid motion (“advection”) and the geometry, topology, and coherence of fluid trajectories. Efficient laminar transport being equivalent to “chaotic advection” is a key finding of this approach. The Lagrangian framework enables systematic analysis and design of laminar flows. However, the gap between scientific insights into Lagrangian transport and technological applications is formidable primarily for two reasons. First, many studies concern two-dimensional (2D) flows, yet the real world is three-dimensional (3D). Second, Lagrangian transport is typically investigated for idealized flows, yet practical relevance requires studies on realistic 3D flows. The present review aims to stimulate further development and utilization of know-how on 3D Lagrangian transport and its dissemination to practice. To this end, 3D practical flows are categorized into canonical problems. First, to expose the diversity of Lagrangian transport and create awareness of its broad relevance. Second, to enable knowledge transfer both within and between scientific disciplines. Third, to reconcile practical flows with fundamentals on Lagrangian transport and chaotic advection. This may be a first incentive to structurally integrate the “Lagrangian mindset” into the analysis and design of 3D practical flows.

Long-range exciton diffusion in a non-fullerene acceptor: approaching the incoherent limit

Low energetic disorder enables the accurate and high-speed prediction of exciton diffusion parameters in a non-fullerene acceptor.

Bedload Sediment Rate Prediction for the Sand Transport Along Coastal Waters in Ocean Management Strategy

Interactions among different landforms and varied complicated physical processes cause sediment transport in coastal regions being the interest of ocean management planning studies. In coastal zones, the derivation of the bedload sediment transport rate and the flow velocity distribution is done by entropy theory which assumes the modified spatiotemporal disorder power index (MSTDPI) and the time-averaged flow velocity (as a random variable). Studying the deposition trend of bedload sediment transport rate for the sand particle (BLSTRS) and estimating the coastal erosion rate as a case study, the Makran coast is selected. To analyze the spatiotemporal patterns, the disorder power index (entropy-power) method is applied in this study where the monthly data of six Makran coastal sections from January 1970 to December 2015 are used. The studied data are mainly focused on the correlation of the flow rate of the sediment from the Makran River, and the spatiotemporal patterns of BLSTRS. Despite their meaningful spatiotemporal variability, it is not very easy to explain how the abovementioned variables perform together; the entropy-power index allows a better understanding of the combined performance of such parameters as the flow velocity and sediment transport by showing clearer signals for the assessment of coastal engineering issues at very large (coastal) scales.

Spatiotemporal Variation in Total Sediment Load Concentration and Related Factors of Shoreline Waters Based on Disorder Power Index

Entropy is a property of a system which measures the uncertainty or disorder within the system. In hydraulics, uncertainties occur in flow variables, such as velocity, sediment concentration, wave. Using entropy, it is possible to establish connections between deterministic and probabilistic domains. To describe sediment transport distributional/autocorrelation properties, including scaling behavior both in state and in time, the well-founded physical and mathematical entropy theory is generally used wherein the spatiotemporal disorder power index (STDPI) is considered to have the maximum uncertainty. Effort has been made in this research to propose a novel entropy method capable of accurately calculating the total sediment load concentration (TSLC) in the shoreline region. Accordingly, STDPI and entropy method have been suggested for finding the TSLC to analyze the spatiotemporal patterns/reports based on a shoreline zone case study because STDPI is quite suitable for marine and hydrological ecosystem components analyses. The method makes use of the monthly data of six shoreline sections in Makran Ocean region in the time period between 1970 and 2015 and investigates the spatiotemporal patterns of the wave height and TLSC variables both of which depend on time and play important parts in terrestrial hydrological studies. These variables usually show meaningful spatiotemporal variability, but explanation of their combined performance is not an easy task. As the results show, STDPI can simulate TSLC and wave when concentration, flow conditions, and granulometry vary.

Simultaneous influence of additive and multiplicative noise on stationary dissipative solitons.

We investigate the simultaneous influence of spatially homogeneous multiplicative noise as well as of spatially δ-correlated additive noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. Depending on the ratio between the strength of additive and multiplicative noise we find a number of distinctly different types of behavior including explosions, collapse, filling in, and spatio-temporal disorder as well as intermittent behavior of all types listed. Techniques used to analyze the results include snapshots, x-t plots and plots of the spatially and temporally averaged amplitude as a function of the strength of multiplicative noise while keeping the strength of additive noise fixed. Typically 50 realizations are used for averaging to obtain the corresponding data points in these diagrams. For the widths of these distribution as a function of additive noise we obtain a linear decrease in the limit of fairly large, but fixed values of the multiplicative noise. To summarize our findings concisely we show three-dimensional plots of the mean pattern amplitude and the generalized susceptibility as a function of the strengths of additive and multiplicative noise. We critically compare the results of our investigations with those obtained in the two limiting cases of purely additive and of purely multiplicative noise.

Collisions of non-explosive dissipative solitons can induce explosions.

We investigate the interaction of stationary and oscillatory dissipative solitons in the framework of two coupled cubic-quintic complex Ginzburg-Landau equation for counter-propagating waves. We analyze the case of a stabilizing as well as a destabilizing cubic cross-coupling between the counter-propagating dissipative solitons. The three types of interacting localized solutions investigated are stationary, oscillatory with one frequency, and oscillatory with two frequencies. We show that there is a large number of different outcomes as a result of these collisions including stationary as well as oscillatory bound states and compound states with one and two frequencies. The two most remarkable results are (a) the occurrence of bound states and compound states of exploding dissipative solitons as outcome of the collisions of stationary and oscillatory pulses; and (b) spatiotemporal disorder due to the creation, interaction, and annihilation of dissipative solitons for colliding oscillatory dissipative solitons as initial conditions.

Turbulence and turbulent pattern formation in a minimal model for active fluids

Active matter systems display a fascinating range of dynamical states, including stationary patterns and turbulent phases. While the former can be tackled with methods from the field of pattern formation, the spatio-temporal disorder of the active turbulence phase calls for a statistical description. Borrowing techniques from turbulence theory, we here establish a quantitative description of correlation functions and spectra of a minimal continuum model for active turbulence. Further exploring the parameter space, we also report on a surprising type of turbulence-driven pattern formation far beyond linear onset: the emergence of a dynamic hexagonal vortex lattice state after an extended turbulent transient, which can only be explained taking into account turbulent energy transfer across scales.

Spatio-temporal scaling effects on longshore sediment transport pattern along the nearshore zone

A measure of uncertainties, entropy has been employed in such different applications as coastal engineering probability inferences. Entropy sediment transport integration theories present novel visions in coastal analyses/modeling the application and development of which are still far-reaching. Effort has been made in the present paper to propose a method that needs an entropy-power index for spatio-temporal patterns analyses. Results have shown that the index is suitable for marine/hydrological ecosystem components analyses based on a beach area case study. The method makes use of six Makran Coastal monthly data (1970–2015) and studies variables such as spatio-temporal patterns, LSTR (long-shore sediment transport rate), wind speed, and wave height all of which are time-dependent and play considerable roles in terrestrial coastal investigations; the mentioned variables show meaningful spatio-temporal variability most of the time, but explanation of their combined performance is not easy. Accordingly, the use of an entropy-power index can show considerable signals that facilitate the evaluation of water resources and will provide an insight regarding hydrological parameters’ interactions at scales as large as beach areas. Results have revealed that an STDDPI (entropy based spatio-temporal disorder dynamics power index) can simulate wave, long-shore sediment transport rate, and wind when granulometry, concentration, and flow conditions vary.

Nonergodic subdiffusion from transient interactions with heterogeneous partners.

Spatiotemporal disorder has been recently associated to the occurrence of anomalous nonergodic diffusion of molecular components in biological systems, but the underlying microscopic mechanism is still unclear. We introduce a model in which a particle performs continuous Brownian motion with changes of diffusion coefficients induced by transient molecular interactions with diffusive binding partners. In spite of the exponential distribution of waiting times, the model shows subdiffusion and nonergodicity similar to the heavy-tailed continuous time random walk. The dependence of these properties on the density of binding partners is analyzed and discussed. Our work provides an experimentally testable microscopic model to investigate the nature of nonergodicity in disordered media.

Spatiotemporal generalization of the Harris criterion and its application to diffusive disorder.

We investigate how a clean continuous phase transition is affected by spatiotemporal disorder, i.e., by an external perturbation that fluctuates in both space and time. We derive a generalization of the Harris criterion for the stability of the clean critical behavior in terms of the space-time correlation function of the external perturbation. As an application, we consider diffusive disorder, i.e., an external perturbation governed by diffusive dynamics, and its effects on a variety of equilibrium and nonequilibrium critical points. We also discuss the relation between diffusive disorder and diffusive dynamical degrees of freedom in the example of model C of the Hohenberg-Halperin classification and comment on Griffiths singularities.

Brownian motion on random dynamical landscapes

We present a study of overdamped Brownian particles moving on a random landscape of dynamic and deformable obstacles (spatio-temporal disorder). The obstacles move randomly, assemble, and dissociate following their own dynamics. This landscape may account for a soft matter or liquid environment in which large obstacles, such as macromolecules and organelles in the cytoplasm of a living cell, or colloids or polymers in a liquid, move slowly leading to crowding effects. This representation also constitutes a novel approach to the macroscopic dynamics exhibited by active matter media. We present numerical results on the transport and diffusion properties of Brownian particles under this disorder biased by a constant external force. The landscape dynamics are characterized by a Gaussian spatio-temporal correlation, with fixed time and spatial scales, and controlled obstacle concentrations.

A universal transition to turbulence in channel flow

Transition from laminar to turbulent flow drastically changes the mixing, transport, and drag properties of fluids, yet when and how turbulence emerges is elusive even for simple flow within pipes and rectangular channels. Unlike the onset of temporal disorder, which is identified as the universal route to chaos in confined flows, characterization of the onset of spatio-temporal disorder has been an outstanding challenge because turbulent domains irregularly decay or spread as they propagate downstream. Here, through extensive experimental investigation of channel flow, we identify a distinctive transition with critical behavior. Turbulent domains continuously injected from an inlet ultimately decayed, or in contrast, spread depending on flow rates. Near a transition point, critical behavior was observed. We investigate both spatial and temporal dynamics of turbulent clusters, measuring four critical exponents, a universal scaling function and a scaling relation, all in agreement with the (2+1)-dimensional directed percolation universality class.