Slow Time Scale Research Articles

Major depressive disorder and bistability in an HPA-CNS toggle switch.

Major depressive disorder (MDD) is the most common psychiatric disorder. It has a complex and heterogeneous etiology. Most treatments take weeks to show effects and work well only for a fraction of the patients. Thus, new concepts are needed to understand MDD and its dynamics. One of the strong correlates of MDD is increased activity and dysregulation of the hypothalamic-pituitary-adrenal (HPA) axis which produces the stress hormone cortisol. Existing mathematical models of the HPA axis describe its operation on the scale of hours, and thus are unable to explore the dynamic on the scale of weeks that characterizes many aspects of MDD. Here, we propose a mathematical model of MDD on the scale of weeks, a timescale provided by the growth of the HPA hormone glands under control of HPA hormones. We add to this the mutual inhibition of the HPA axis and the hippocampus and other regions of the central nervous system (CNS) that forms a toggle switch. The model shows bistability between euthymic and depressed states, with a slow timescale of weeks in its dynamics. It explains why prolonged but not acute stress can trigger a self-sustaining depressive episode that persists even after the stress is removed. The model explains the weeks timescale for drugs to take effect, as well as the dysregulation of the HPA axis in MDD, based on gland mass changes. This understanding of MDD dynamics may help to guide strategies for treatment.

Non-equilibrium steady states as saddle points and EDP-convergence for slow-fast gradient systems

The theory of slow-fast gradient systems leads in a natural way to non-equilibrium steady states, because on the slow time scale the fast subsystem stays in steady states that are controlled by the interaction with the slow system. Using the theory of convergence of gradient systems depending on a small parameter ɛ (here the ratio between the slow and the fast time scale) in the sense of the energy-dissipation principle shows that there is a natural characterization of these non-equilibrium steady states as saddle points of a so-called B-function where the slow variables are fixed. We give applications to slow-fast reaction-diffusion systems based on the so-called cosh-type gradient structure for reactions. It is shown that two binary reactions give rise to a ternary reaction with a state-dependent reaction coefficient. Moreover, we show that a reaction-diffusion equation with a thin membrane-like layer convergences to a transmission condition, where the formerly quadratic dissipation potential for diffusion convergences to a cosh-type dissipation potential for the transmission in the membrane limit.

Two-time scale dynamic closed-loop scheduling for gas supply network with multiple air separation units

The gas supply network with multiple air separation units (ASUs) in steel enterprises provides the essential gas products for iron- and steel-making processes. Steel enterprises must make scheduling decisions for their gas supply networks to meet the fast-changing downstream demands. Therefore, the dynamic characteristics of the process must be considered during short-interval production scheduling to ensure more reasonable scheduling decisions. A two-scale dynamic scheduling method is first developed in this paper to consider the process dynamics. In this method, scheduling decisions are made in the slow time scale, and the nonlinear dynamic characteristics are described using a varied time constant dynamic model in the fast time scale. Then, an autoregressive moving average (ARMA) model is established to address the unavoidable model mismatch, which explicitly predicts and integrates future mismatches into the scheduling model. Moreover, a moving horizon closed-loop framework is designed to integrate the state feedback, mismatch modeling, and scheduling decision modification so that scheduling decisions can be modified in real time to avoid potential safety hazards. The results of the industrial application indicate that the proposed method can provide better scheduling decisions in case studies of model mismatch and unknown leakage compared with existing methods.

On the locomotion of the slider within a self-adaptive beam–slider system

A beam–slider system is considered whose passive self-adaption relies on an intricate locomotion process involving both frictional and unilateral contact. The system also exploits geometric nonlinearity to achieve broadband efficacy. The dynamics of the system take place on three distinct time scales: On the fast time scale of the harmonic base excitation are the vibrations and the locomotion cycle. On the slow time scale, the slider changes its position along the beam, and the overall vibration level varies. Finally, on an intermediate time scale, strong modulations of the vibration amplitude may take place. In the present work, first, an analytical approximation of the beam’s response on the slow time scale is derived as function of the slider position, which is a crucial prerequisite for identifying the main drivers of the slider’s locomotion. Then, the most important forms of locomotion are described and approximations of their individual contribution to the overall slider transport are estimated. Finally, the theoretical results are compared against numerical results obtained from an experimentally validated model.

Exciton-polaron interactions in metal halide perovskite nanocrystals revealed via two-dimensional electronic spectroscopy.

Metal halide perovskite nanocrystals have been under intense investigation for their promise in optoelectronic devices due to their remarkable physics, such as liquid/solid duality. This liquid/solid duality may give rise to their defect tolerance and other such useful properties. This duality means that the electronic states are fluctuating in time, on a distribution of timescales from femtoseconds to picoseconds. Hence, these lattice induced energy fluctuations that are connected to polaron formation are also connected to exciton formation and dynamics. We observe these correlations and dynamics in metal halide perovskite nanocrystals of CsPbI3 and CsPbBr3 using two-dimensional electronic (2DE) spectroscopy, with its unique ability to resolve dynamics in heterogeneously broadened systems. The 2DE spectra immediately reveal a previously unobserved excitonic splitting in these 15nm NCs that may have a coarse excitonic structure. 2D lineshape dynamics reveal a glassy response on the 300fs timescale due to polaron formation. The lighter Br system shows larger amplitude and faster timescale fluctuations that give rise to dynamic line broadening. The 2DE signals enable 1D transient absorption analysis of exciton cooling dynamics. Exciton cooling within this doublet is shown to take place on a slower timescale than within the excitonic continuum. The energy dissipation rates are the same for the I and Br systems for incoherent exciton cooling but are very different for the coherent dynamics that give rise to line broadening. Exciton cooling is shown to take place on the same timescale as polaron formation, revealing both as coupled many-body excitation.

Digital Adaptive Behavioral Interventions to Improve HIV Prevention and Care: Innovations in Intervention Approach and Experimental Design.

Recent advances in digital technologies can be leveraged to adapt HIV prevention and treatment services to the rapidly changing needs of individuals in everyday life. However, to fully take advantage of these technologies, it is critical to effectively integrate them with human-delivered components. Here, we introduce a new experimental approach for optimizing the integration and adaptation of digital and human-delivered behavioral intervention components for HIV prevention and treatment. Typically, human-delivered components can be adapted on a relatively slow timescale (e.g., every few months or weeks), while digital components can be adapted much faster (e.g., every few days or hours). Thus, the systematic integration of these components requires an experimental approach that involves sequential randomizations on multiple timescales. Selecting an experimental approach should be motivated by the type of adaptive intervention investigators would like to develop, and the scientific questions they have about its construction.

Self-excited intermittent thermoacoustic fluctuations in an annular combustor exhibiting flame transient phenomena: Physical mechanisms and modeling

We experimentally examine the physical mechanisms causing intermittent thermoacoustic fluctuations in a turbulent annular combustor exhibiting flame transient phenomena (FTP). The combustor consists of 12 burners. Flames are stabilized by conical bluff bodies, resembling the afterburner and ramjet burner configurations. The combustor exhibits a dominant 1A–1L (first azimuthal–first longitudinal, ∼630 Hz) thermoacoustic mode. Instability manifests as intermittent fluctuations in acoustic pressure. From the heat release and acoustic pressure measurements, FTPs are found to create large amplitude heat release fluctuations occurring on a slow timescale compared with 1A–1L thermoacoustic mode. The heat release, in turn, leads to the observed intermittent acoustic pressure fluctuations. Four FTPs are found to occur in the combustor: (1) near blow-off, (2) flame extinction, (3) successful reignition, and (4) unsuccessful reignition. Their occurrences and the associated time spans are found to be random. The time span follows an unimodal probability distribution, peaking around 100 ms. A low-order model is developed by incorporating the distribution for the FTP time span in the heat release. An additive Gaussian white noise is added to represent background turbulent fluctuations. The model qualitatively reproduces the experimentally observed probability density function of the acoustic pressure fluctuations. This indicates that the stochastic FTP time span and turbulence are essential for reproducing intermittent thermoacoustic fluctuations.

An efficient method for the anisotropic diffusion equation in magnetic fields

We solve the anisotropic diffusion equation in 2D, where the dominant direction of diffusion is defined by a vector field which does not conform to a Cartesian grid. Our method uses operator splitting to separate the diffusion perpendicular and parallel to the vector field. The slow time scale is solved using a provably stable finite difference formulation in the perpendicular to the vector field, and an integral operator for the diffusion parallel to it. Energy estimates are shown to for the continuous and semi-discrete cases. Numerical experiments are performed showing convergence of the method, and examples is given to demonstrate the capabilities of the method.

Photoexcitation Control of Excitation Relaxation in Mixed‐Phase Ruddlesden‐Popper Hybrid Organic‐Inorganic Lead‐Iodide Perovskites

AbstractThe electronic states and exciton binding energies of layered Ruddlesden‐Popper (RP) metal‐halide perovskites can be tailored through changes of their chemical composition, yielding multi‐phase systems with complex energy cascades. Ultrafast photoexcitation relaxation with transfer dynamics into domains of increasing layer number has been reported for these materials. Here, ultrafast optical spectroscopy is used to report an unexpected excitation energy dependence of photoexcitation relaxation dynamics in mixed‐dimensional benzylammonium cesium lead iodide RP perovskite (BeA2CsPb2I7) thin films, which gives rise to spectrally broadband luminescence over the visible region. Using transient absorption and photoluminescence spectroscopy it is found that excitations, which are formed in the n = 2 RP‐phase after photoexcitation with ≈0.2 electron volt excess energy, transfer to higher layer number RP‐phases on unexpectedly slow timescales of tens of picoseconds. Further, it is observed that such excitations are initially optically passive. Notably, luminescence occurs under these conditions from multiple RP‐phases with optical bandgaps across the visible range, yielding broadband luminescence. The results hold potential for realization of broadband white‐light emitters and other light‐emitting devices.

Reliability and robustness of oscillations in some slow-fast chaotic systems.

A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or internal conditions. Motivated by the subtle dynamics of cell activity in a crustacean central pattern generator (CPG), this paper proposes a refinement of the notion of chaos that reconciles homeostasis and chaos in systems with multiple timescales. We show that systems displaying relaxation cycles while going through chaotic attractors generate chaotic dynamics that are regular at macroscopic timescales and are, thus, consistent with physiological function. We further show that this relative regularity may break down through global bifurcations of chaotic attractors such as crises, beyond which the system may also generate erratic activity at slow timescales. We analyze these phenomena in detail in the chaotic Rulkov map, a classical neuron model known to exhibit a variety of chaotic spike patterns. This leads us to propose that the passage of slow relaxation cycles through a chaotic attractor crisis is a robust, general mechanism for the transition between such dynamics. We validate this numerically in three other models: a simple model of the crustacean CPG neural network, a discrete cubic map, and a continuous flow.

Data-driven safe control via finite-time Koopman identifier

In this paper, a novel data-driven invariant-based safe control scheme for control of a nonlinear vehicle is developed. First, a novel incremental finite-time Koopman representation-based identifier is introduced to learn approximated lifted-states linear system model of system from a limited budget of incrementally sampled data points which not only minimises the instantaneous Koopman representation's identification errors but also the identification errors for a batch of past samples collected in a history stack. A great advantage of the presented identifier is that the uncertainty of the identified system is also quantified and updated over time on a slower time scale. Using set-theoretic tools, then, the quantified uncertainty will be leveraged in conjunction with the learned model in order to impose robust contractivity on the safe set, which guarantees its safety and stability. The proposed approach significantly reduces conservativeness through quantifying and updating the uncertainty level of the learned model over time.

Large deviations for the two-time-scale stochastic convective Brinkman-Forchheimer equations

The convective Brinkman-Forchheimer (CBF) equations are employed to characterize the motion of incompressible fluid in a saturated porous medium. This work investigates the small noise asymptotic of two-time-scale stochastic CBF equations in two and three dimensional bounded domains. More precisely, we establish a Wentzell-Freidlin type large deviation principle for stochastic partial differential equations that have slow and fast time-scales. The slow component is the stochastic CBF equations in two or three dimensions perturbed by a small multiplicative Gaussian noise, while the fast component is a stochastic reaction-diffusion equation with damping. The results are obtained by using a variational method (based on weak convergence approach) developed by Budhiraja and Dupuis, Khasminkii's time discretization approach and stopping time arguments. In particular, the findings from this study are also applicable to two-dimensional stochastic Navier-Stokes equations.

ICVS-Inferring Cardio-Vascular hidden States from physiological signals available at the bedside.

Intensive care medicine is complex and resource-demanding. A critical and common challenge lies in inferring the underlying physiological state of a patient from partially observed data. Specifically for the cardiovascular system, clinicians use observables such as heart rate, arterial and venous blood pressures, as well as findings from the physical examination and ancillary tests to formulate a mental model and estimate hidden variables such as cardiac output, vascular resistance, filling pressures and volumes, and autonomic tone. Then, they use this mental model to derive the causes for instability and choose appropriate interventions. Not only this is a very hard problem due to the nature of the signals, but it also requires expertise and a clinician's ongoing presence at the bedside. Clinical decision support tools based on mechanistic dynamical models offer an appealing solution due to their inherent explainability, corollaries to the clinical mental process, and predictive power. With a translational motivation in mind, we developed iCVS: a simple, with high explanatory power, dynamical mechanistic model to infer hidden cardiovascular states. Full model estimation requires no prior assumptions on physiological parameters except age and weight, and the only inputs are arterial and venous pressure waveforms. iCVS also considers autonomic and non-autonomic modulations. To gain more information without increasing model complexity, both slow and fast timescales of the blood pressure traces are exploited, while the main inference and dynamic evolution are at the longer, clinically relevant, timescale of minutes. iCVS is designed to allow bedside deployment at pediatric and adult intensive care units and for retrospective investigation of cardiovascular mechanisms underlying instability. In this paper, we describe iCVS and inference system in detail, and using a dataset of critically-ill children, we provide initial indications to its ability to identify bleeding, distributive states, and cardiac dysfunction, in isolation and in combination.

Global error estimates in zero-relaxation limit of Euler–Poisson system for ion dynamics

The zero-relaxation limit of Euler–Poisson systems for ion dynamics in a slow time scale leads to drift-diffusion equations. This fact was justified in previous works. This paper concerns global error estimates between solutions of Euler–Poisson systems and that of drift-diffusion equations. In the proof, we use Sobolev inequalities and employ a multiplier related to the electric potential.

(Invited) In-Situ Time-Resolved Probe of Charge Carrier Dynamics at Planar Semiconductor Photoelectrode/Liquid Interface

Photoelectrochemistry is a promising approach for converting solar energy to storable chemical energy in chemical fuels. The efficiency of photoelectrochemcial devices depends critically on efficient transfer of charge carrier across the electrode liquid interface and the efficiency and selectivity of the catalytic reaction on electrode surface. Although transient absorption spectroscopy is a powerful tool for probing interfacial dynamics in high surface area electrodes, it is often not applicable on planar electrodes because the observed signal is often dominated by carrier dynamics in the bulk. In this talk, we discuss our recent effort in developing in situ time-resolved linear and nonlinear spectroscopic tools that can be used to probe carrier dynamics and reactions at planar electrode/liquid interfaces, focusing on transient reflection spectroscopy and electric field induced second harmonic generation (EFISH) spectroscopy. Compared to transient absorption, transient reflection spectroscopy is more sensitive to surface carrier density that can be more directly correlated to catalysis. We showed that transient reflectance change can be used to follow charge carrier dynamics and their amplitude can be directly correlated to efficiency of initial interfacial charge separation on p-GaP single crystals protected by TiO2 ALD layer. Our finding suggests that IPCE is determined by the product of the efficiency of initial ultrafast (< hundreds of ps) charge separation across the GaP/TiO2 interface and the efficiency of water reduction reaction on the slower time scale. Key loss pathways that limit these efficiencies are discussed. In a second approach, we showed the EFISH signal in a n-doped single crystal TiO2 can be used to probe the accumulation of photogenerated carriers at surface states and these trapped carriers are responsible for the water oxidation reaction.

Memory Effects, Multiple Time Scales and Local Stability in Langevin Models of the S&P500 Market Correlation.

The analysis of market correlations is crucial for optimal portfolio selection of correlated assets, but their memory effects have often been neglected. In this work, we analyse the mean market correlation of the S&P500, which corresponds to the main market mode in principle component analysis. We fit a generalised Langevin equation (GLE) to the data whose memory kernel implies that there is a significant memory effect in the market correlation ranging back at least three trading weeks. The memory kernel improves the forecasting accuracy of the GLE compared to models without memory and hence, such a memory effect has to be taken into account for optimal portfolio selection to minimise risk or for predicting future correlations. Moreover, a Bayesian resilience estimation provides further evidence for non-Markovianity in the data and suggests the existence of a hidden slow time scale that operates on much slower times than the observed daily market data. Assuming that such a slow time scale exists, our work supports previous research on the existence of locally stable market states.

Understanding elevated CO2 concentrations in East Asia relative to the global mean during boreal spring on the slow and interannual timescales

It is important to examine the physical processes that regulate current CO2 concentrations in East Asia to understand the global carbon cycle. To do this, we begin by defining the difference between East Asian and global CO2 concentrations (East Asian CO2 concentration minus global CO2 concentration), which is referred to as East Asian local CO2 concentration (i.e., EA_LCO2). Then, we examine the physical processes associated with the variability of EA_LCO2 during boreal spring (March–April–May) on the slow and interannual timescales. Our results indicate that there are two key factors leading to elevated CO2 concentrations in East Asia relative to the global mean during boreal spring; one is higher emissions in East Asia, which mostly explains the increasing in EA_LCO2 on the slow timescales. The other is a cool sea surface temperature (SST) in the eastern tropical Pacific (La-Nina-like SST), which is associated with an interannual higher CO2 concentration in East Asia than the global mean. Enhanced convective activity in the western tropical Pacific, which is associated with a La-Nina-like SST forcing, induces low-pressure circulation in the western North Pacific with northerly winds, leading to suppressed precipitation and cool surface temperature in East Asia. Subsequently, those suppress vegetation growth as well as gross primary product, resulting in relatively high CO2 concentrations in East Asia compared to the global mean.

Interpolating Nonadiabatic Molecular Dynamics Hamiltonian with Bidirectional Long Short-Term Memory Networks.

Essential for understanding far-from-equilibrium processes, nonadiabatic (NA) molecular dynamics (MD) requires expensive calculations of the excitation energies and NA couplings. Machine learning (ML) can simplify computation; however, the NA Hamiltonian requires complex ML models due to its intricate relationship to atomic geometry. Working directly in the time domain, we employ bidirectional long short-term memory networks (Bi-LSTM) to interpolate the Hamiltonian. Applying this multiscale approach to three metal-halide perovskite systems, we achieve two orders of magnitude computational savings compared to direct ab initio calculation. Reasonable charge trapping and recombination times are obtained with NA Hamiltonian sampling every half a picosecond. The Bi-LSTM-NAMD method outperforms earlier models and captures both slow and fast time scales. In combination with ML force fields, the methodology extends NAMD simulation times from picoseconds to nanoseconds, comparable to charge carrier lifetimes in many materials. Nanosecond sampling is particularly important in systems containing defects, boundaries, interfaces, etc. that can undergo slow rearrangements.

Time rescaling of nonadiabatic transitions

Applying time-dependent driving is a basic way of quantum control. Driven systems show various dynamics as its time scale is changed due to the different amount of nonadiabatic transitions. The fast-forward scaling theory enables us to observe slow (or fast) time-scale dynamics during moderate time by applying additional driving. Here we discuss its application to nonadiabatic transitions. We derive mathematical expression of additional driving and also find a formula for calculating it. Moreover, we point out relation between the fast-forward scaling theory for nonadiabatic transitions and shortcuts to adiabaticity by counterdiabatic driving.

Is the Madden‐Julian Oscillation a Moisture Mode?

AbstractThe governing thermodynamics of the Madden‐Julian Oscillation (MJO) is examined using sounding and reanalysis data. On the basis of four objective criteria, results suggest that the MJO behaves like a moisture mode–a system whose thermodynamics is governed by moisture–only over the Indian Ocean. Over this basin, the MJO shows a slow convective adjustment timescale, its zonal scale is smaller, and it exhibits slow propagation, allowing moisture modes to exist. Elsewhere, the faster‐propagating wavenumber 1–2 components are more prominent preventing weak temperature gradient (WTG) balance to be established. As a result, temperature and moisture play similar roles in the MJO's thermodynamics outside the Indian Ocean.