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Summary: Background: Stroke and dementia are the leading causes of neurological disease burden. Detrimental effects of air pollution on both conditions are increasingly recognised, while the impacts on the dynamic transitions have not yet been explored, and whether critical time intervals exist is unknown. Methods: This prospective study was conducted based on the UK Biobank. Annual average air pollution concentrations at baseline year 2010 estimated by land-use regression models were used as a proxy for long-term air pollution exposure. Associations between multiple air pollutants (PM2.5, PM2.5-10, and NO2) indicated by air pollution score and the dynamic transitions of stroke and dementia were estimated, and the impacts during critical time intervals were explored. The date cutoff of this study was February 29, 2020. Findings: During a median follow-up of 10.9 years in 413,372 participants, 6484, 3813, and 376 participants developed incident stroke, dementia, and comorbidity of stroke and dementia. For the overall transition from stroke to comorbid dementia, the hazard ratio (HR) for each interquartile range (IQR) increase in air pollution score was 1.38 (95% CI, 1.15, 1.65), and the risks were limited to two time intervals (within 1 year and over 5 years after stroke). As for the transition from dementia to comorbid stroke, increased risk was only observed during 2–3 years after dementia. Interpretation: Our findings suggested that air pollution played an important role in the dynamic transition of stroke and dementia even at concentrations below the current criteria. The findings provided new evidence for alleviating the disease burden of neurological disorders related to air pollution during critical time intervals. Funding: The State Scholarship Fund of China Scholarship Council.

We consider a 2-layer quasi-geostrophic ocean model where the upper layer is forced by a steady Kolmogorov wind stress in a periodic channel domain, which allows to mathematically study the nonlinear development of the resulting flow. The model supports a steady parallel shear flow as a response to the wind stress. As the maximal velocity of the shear flow (equivalently the maximal amplitude of the wind forcing) exceeds a critical threshold, the zonal jet destabilizes due to baroclinic instability and we numerically demonstrate that a first transition occurs. We obtain reduced equations of the system using the formalism of dynamic transition theory and establish two scenarios which completely describe this first transition. The generic scenario is that a conjugate pair of modes loses stability and a Hopf bifurcation occurs as a result. Under an appropriate set of parameters describing related midlatitude oceanic flows, we show that this first transition is continuous: a supercritical Hopf bifurcation occurs and a stable time periodic solution bifurcates. We also investigate the case of double Hopf bifurcations which occur when four modes of the linear stability problem simultaneously destabilize the zonal jet. In this case, we prove that, in the relevant parameter regime, the flow exhibits a continuous transition accompanied by a bifurcated attractor homeomorphic to S 3 . The topological structure of this attractor is analyzed in detail and is shown to depend on the system parameters. In particular, this attractor contains (stable or unstable) time-periodic solutions and a quasi-periodic solution. [ABSTRACT FROM AUTHOR]

This paper deals with the classification of transition phenomena in the most basic dissipative system possible, namely, the 1D reaction–diffusion equation. The emphasis is on the relation between the linear and nonlinear terms and the effect of the boundaries which influence the first transitions. We consider the cases where the linear part is self‐adjoint with second‐order and fourth‐order derivatives which is the case which most often arises in applications. We assume that the nonlinear term depends on the unknown function and its first derivative which is basically the semilinear case for the second‐order reaction–diffusion system. As for the boundary conditions, we consider the typical Dirichlet, Neumann, and periodic boundary settings. In all the cases, the equations admit a trivial steady state which loses stability at a critical parameter. We aim to classify all possible transitions and bifurcations that take place. Our analysis shows that these systems display all three types of transitions: continuous, jump and mixed. Moreover they exhibit transcritical, supercritical bifurcations with bifurcated states such as finitely many equilibria, circle of equilibria, and slowly rotating limit cycle. Many applications found in the literature are basically corollaries of our main results. We apply our results to classify the first transitions of the Chaffee–Infante equation, the Fisher‐KPP equation, the Kuramoto–Sivashinsky equation, and the Swift–Hohenberg equation. [ABSTRACT FROM AUTHOR]

The Swift-Hohenberg equation is ubiquitous in the study of bistable dynamics. In this paper, we study the dynamic transitions of the Swift-Hohenberg equation with a third-order dispersion term in one spacial dimension with a periodic boundary condition. As a control parameter crosses a critical value, the trivial stable equilibrium solution will lose its stability, and undergoes a dynamic transition to a new physical state, described by a local attractor. The main result of this paper is to fully characterize the type and detailed structure of the transition using dynamic transition theory [ 7 ]. In particular, employing techniques from center manifold theory, we reduce this infinite dimensional problem to a finite one since the space on which the exchange of stability occurs is finite dimensional. The problem then reduces to analysis of single or double Hopf bifurcations, and we completely classify the possible phase changes depending on the dispersion for every spacial period. [ABSTRACT FROM AUTHOR]

In this article, we aim to classify the dynamic transitions and bifurcations for a family of axisymmetric geophysical fluid problems of a generic fourth-second order structure. A transition theorem is established by reducing the governing partial differential equations to a complex-valued ordinary differential equation, derived by employing approximate invariant manifolds. We develop an algorithm for the numerical determination of the transition/bifurcation types. Finally we apply the transition theorem and algorithm to examine the baroclinic instability in a two-layer quasi-geostrophic system in an annular channel and with different bathymetry profiles. Our numerical results show that with concave bathymetry the transition (bifurcation) is always continuous (supercritical Hopf bifurcation), whereas for convex bathymetry a jump transition (subcritical Hopf bifurcation) may occur in the basic azimuthal currents that rotate in the same direction. [ABSTRACT FROM AUTHOR]

The structural superlubricity (SSL), a state of near-zero friction between two contacted solid surfaces, has been attracting rapidly increasing research interest since it was realized in microscale graphite in 2012. An obvious question concerns the implications of SSL for micro- and nanoscale devices such as actuators. The simplest actuators are based on the application of a normal load; here we show that this leads to remarkable dynamical phenomena in microscale graphite mesas. Under an increasing normal load, we observe mechanical instabilities leading to dynamical states, the first where the loaded mesa suddenly ejects a thin flake and the second characterized by peculiar oscillations, during which a flake repeatedly pops out of the mesa and retracts back. The measured ejection speeds are extraordinarily high (maximum of 294 m/s), and correspond to ultrahigh accelerations (maximum of 1.1x1010 m/s²). These observations are rationalized using a simple model, which takes into account SSL of graphite contacts and sample microstructure and considers a competition between the elastic and interfacial energies that defines the dynamical phase diagram of the system. Analyzing the observed flake ejection and oscillations, we conclude that our system exhibits a high speed in SSL, a low friction coefficient of 3.6x10-6, and a high quality factor of 1.3x107 compared with what has been reported in literature. Our experimental discoveries and theoretical findings suggest a route for development of SSL-based devices such as high-frequency oscillators with ultrahigh quality factors and optomechanical switches, where retractable or oscillating mirrors are required. [ABSTRACT FROM AUTHOR]

We study the transitions in friction-induced vibrations (FIV) experimentally. The measurement data stem from a highly sophisticated setup specifically designed to study FIV problems and where the relative motion between the samples is achieved using air bearings and a voice-coil motor. This peculiarity ensures avoiding parasitic vibrations and makes the setup particularly suitable to perform measurements of very low vibration levels. The relative sliding velocity decays along the measurement to zero, which provokes several types of FIV. We employ advanced time-series analysis techniques, such as spectral analysis, attractor reconstruction and recurrence plot analysis to study the dynamical transition from steady sliding to high-frequency FIV and stick-slip vibrations in detail. For different specimens, self-excited vibrations are observed stemming from an instability that is driven by a negative friction-velocity slope characteristic as well as for constant friction values. Prior to instability, it is observed that highly irregular oscillations decay and most of the vibration energy focuses in a low-frequency mode of the experimental setup. The analysis of the FIV range illustrates a plethora of qualitatively different dynamics that can be detected, characterized and visualized using advanced signal processing. Particularly, we report on period-1 and period-2 limit cycles, quasi-periodic motion, weakly chaotic attractors and different types of stick-slip vibrations. The analysis of transitions between those dynamic regimes reveals beating phenomena, sudden energy exchange between different modes and intermittent dynamics. The results of this study aim to provide a step forward on the application of nonlinear dynamics post-processing tools for identifying and characterizing the different frictional stable and unstable scenarios. [ABSTRACT FROM AUTHOR]

Background: Stroke and dementia are the leading causes of neurological disease burden. Detrimental effects of air pollution on both conditions are increasingly recognised, while the impacts on the dynamic transitions have not yet been explored, and whether critical time intervals exist is unknown., Methods: This prospective study was conducted based on the UK Biobank. Annual average air pollution concentrations at baseline year 2010 estimated by land-use regression models were used as a proxy for long-term air pollution exposure. Associations between multiple air pollutants (PM 2.5 , PM 2.5-10 , and NO 2 ) indicated by air pollution score and the dynamic transitions of stroke and dementia were estimated, and the impacts during critical time intervals were explored. The date cutoff of this study was February 29, 2020., Findings: During a median follow-up of 10.9 years in 413,372 participants, 6484, 3813, and 376 participants developed incident stroke, dementia, and comorbidity of stroke and dementia. For the overall transition from stroke to comorbid dementia, the hazard ratio (HR) for each interquartile range (IQR) increase in air pollution score was 1.38 (95% CI, 1.15, 1.65), and the risks were limited to two time intervals (within 1 year and over 5 years after stroke). As for the transition from dementia to comorbid stroke, increased risk was only observed during 2-3 years after dementia., Interpretation: Our findings suggested that air pollution played an important role in the dynamic transition of stroke and dementia even at concentrations below the current criteria. The findings provided new evidence for alleviating the disease burden of neurological disorders related to air pollution during critical time intervals., Funding: The State Scholarship Fund of China Scholarship Council., Competing Interests: None reported., (© 2023 The Author(s).)

In a standard bifurcation of a dynamical system, the stationary points (or more generally attractors) change qualitatively when varying a control parameter. Here we describe a novel unusual effect, when the change of a parameter, e.g. a growth rate, does not influence the stationary states, but nevertheless leads to a qualitative change of dynamics. For instance, such a dynamic transition can be between the convergence to a stationary state and a strong increase without stationary states, or between the convergence to one stationary state and that to a different state. This effect is illustrated for a dynamical system describing two symbiotic populations, one of which exhibits a growth rate larger than the other one. We show that, although the stationary states of the dynamical system do not depend on the growth rates, the latter influence the boundary of the basins of attraction. This change of the basins of attraction explains this unusual effect of the qualitative change of dynamics by growth rate variation. [ABSTRACT FROM AUTHOR]

• A mixed-integer dynamic model for multitask catalytic distillation design is studied. • The proposed formulation considers both steady-state and transient operation. • The problem was solved using an enhanced Discrete-Steepest Descent Algorithm. • The production of ethyl tert‑butyl ether at multiple grades was intensified. This work presents the optimal design and operation of catalytic distillation (CD) units considering discrete and continuous design and operation variables combined with rigorous non-linear dynamic process models. The key novelty in this work is that optimal process design and dynamic transitions between different product grades in CD units are simultaneously intensified using a deterministic optimization framework. The proposed optimization method is based on a Discrete-Steepest Descent Algorithm (D-SDA), which enables the designer to improve an initial feasible design, while providing local optimality guarantees. The D-SDA has been effective to handle the optimal steady-state design of CD columns. The present study brings dynamic transitions into consideration thus providing theoretical foundations regarding the optimal design of CD columns in the transient domain. The production of ethyl tert-butyl-ether (ETBE) is considered as a case study, where dynamic transitions between different grades of ETBE coupled with design considerations are investigated. This work shows that a single CD unit can be optimally designed to produce multiple ETBE grades, while simultaneously optimizing its dynamic performance to attain different steady states. Accordingly, this study provides new insights regarding the economic and operational benefits of performing the simultaneous optimal design of multitask CD columns with dynamic transitions. [Display omitted] [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study the dynamic transitions in flows described by the two-dimensional, barotropic vorticity equation in a periodic zonal channel. In [Z.-M. Chen et al, SIAM J. Appl. Math., 64 (2003), pp. 343-368], the existence of a Hopf bifurcation in this model as the Reynolds number crosses a critical value was proven. In this paper, we extend these results by addressing the stability problem of the bifurcated periodic solutions. Our main result is the explicit expression of a nondimensional parameter γ which controls the transition behavior. We prove that depending on γ, the modeled flow exhibits either a continuous (Type I) or catastrophic (Type II) transition. Numerical evaluation of γ for a physically realistic region of parameter space suggests that a catastrophic transition is preferred in this flow, which may lead to chaotic flow regimes. [ABSTRACT FROM AUTHOR]

The analysis of biomedical signals demonstrating complexity through recurrence plots is challenging. Quantification of recurrences is often biased by sojourn points that hide dynamic transitions. To overcome this problem, time series have previously been embedded at high dimensions. However, no one has quantified the elimination of sojourn points and rate of detection, nor the enhancement of transition detection has been investigated. This paper reports our on-going efforts to improve the detection of dynamic transitions from logistic maps and fetal hearts by reducing sojourn points. Three signal-based recurrence plots were developed, i.e. embedded with specific settings, derivative-based and m-time pattern. Determinism, cross-determinism and percentage of reduced sojourn points were computed to detect transitions. For logistic maps, an increase of 50% and 34.3% in sensitivity of detection over alternatives was achieved by m-time pattern and embedded recurrence plots with specific settings, respectively, and with a 100% specificity. For fetal heart rates, embedded recurrence plots with specific settings provided the best performance, followed by derivative-based recurrence plot, then unembedded recurrence plot using the determinism parameter. The relative errors between healthy and distressed fetuses were 153%, 95% and 91%. More than 50% of sojourn points were eliminated, allowing better detection of heart transitions triggered by gaseous exchange factors. This could be significant in improving the diagnosis of fetal state. [ABSTRACT FROM AUTHOR]

The main objective of this article is to establish a new mechanism of ENSO, as a self-organizing and selfexcitation system, with two highly coupled processes. The first is the oscillation between the two metastable warm (El Niño phase) and cold events (La Niña phase), and the second is the spatiotemporal oscillation of the sea surface temperature (SST) field. The symbiotic interplay between these two processes gives rises the climate variability associated with the ENSO, leads to both the random and deterministic features of the ENSO, and defines a new natural feedback mechanism, which drives the sporadic oscillation of the ENSO. The new mechanism is rigorously derived using a dynamic transition theory developed recently by the authors, which has also been successfully applied to a wide range of problems in nonlinear sciences. [ABSTRACT FROM AUTHOR]

The motions of large systems such as the ribosome are not fully accessible with conventional molecular simulations. A coarse-grained, less-than-atomic-detail model such as the anisotropic network model (ANM) is a convenient informative tool to study the cooperative motions of the ribosome. The motions of the small 30S subunit, the larger 50S subunit, and the entire 70S assembly of the two subunits have been analyzed using ANM. The lowest frequency collective modes predicted by ANM show that the 50S subunit and 30S subunit are strongly anti-correlated in the motion of the 70S assembly. A ratchet-like motion is observed that corresponds well to the experimentally reported ratchet motion. Other slow modes are also examined because of their potential links to the translocation steps in the ribosome. We identify several modes that may facilitate the E-tRNA exiting from the assembly. The A-site t-RNA and P-site t-RNA are found to be strongly coupled and positively correlated in these slow modes, suggesting that the translocations of these two t-RNAs occur simultaneously, while the motions of the E-site t-RNA are less correlated, and thus less likely to occur simultaneously. Overall the t-RNAs exhibit relatively large deformations. Animations of these slow modes of motion can be viewed at . [Copyright &y& Elsevier]

• A method to perform dynamic transitions in reactive distillation units is presented. • A trichlorosilane decomposition reaction is used to illustrate the method. • Two different process designs of the reactive distillation unit are considered. • Temperature control is used to ensure on-spec production of the desired products. • Economic analysis was performed to assess dynamic transition costs during operation. This work presents a new methodology to perform dynamic transitions among different chemical products in an intensified reactive distillation column. The procedure consists of a switchability analysis to identify the actions needed to switch between different products. This is followed by a dynamic analysis that aims to seek for feasible control schemes that allow smooth product transitions while keeping the products specifications on target. The times to switch from one chemical product to another, their dynamic performance to reach new steady states, and the feasibility to meet operational constraints, are taken into consideration in the proposed method. A case study involving the decomposition of trichlorosilane into three products in a reactive distillation column was used to show the application of the methodology. Two process designs were considered, and control strategies based on a sensitivity analysis and on process operational constraints, in this case the maximum temperature allowed to prevent catalyst degradation, were implemented. The proposed framework was able to identify suitable control policies that meet composition targets while keeping the reactive zone under feasible temperature ranges. The results show the importance to develop control schemes that perform feasible dynamic transitions for the production scheduling of multiproduct systems. [ABSTRACT FROM AUTHOR]

The structural superlubricity (SSL), a state of near-zero friction between two contacted solid surfaces, has been attracting rapidly increasing research interest since it was realized in microscale graphite in 2012. An obvious question concerns the implications of SSL for micro- and nanoscale devices such as actuators. The simplest actuators are based on the application of a normal load; here we show that this leads to remarkable dynamical phenomena in microscale graphite mesas. Under an increasing normal load, we observe mechanical instabilities leading to dynamical states, the first where the loaded mesa suddenly ejects a thin flake and the second characterized by peculiar oscillations, during which a flake repeatedly pops out of the mesa and retracts back. The measured ejection speeds are extraordinarily high (maximum of 294 m/s), and correspond to ultrahigh accelerations (maximum of 1.1×10 10 m/s 2 ). These observations are rationalized using a simple model, which takes into account SSL of graphite contacts and sample microstructure and considers a competition between the elastic and interfacial energies that defines the dynamical phase diagram of the system. Analyzing the observed flake ejection and oscillations, we conclude that our system exhibits a high speed in SSL, a low friction coefficient of 3.6×10 -6 , and a high quality factor of 1.3×10 7 compared with what has been reported in literature. Our experimental discoveries and theoretical findings suggest a route for development of SSL-based devices such as high-frequency oscillators with ultrahigh quality factors and optomechanical switches, where retractable or oscillating mirrors are required., Competing Interests: The authors declare no competing interest., (Copyright © 2020 the Author(s). Published by PNAS.)