Slow Time Scale Research Articles

Batch-screening guided continuous flow synthesis of the metal-organic framework HKUST-1 in a millifluidic droplet reactor

Metal-organic frameworks (MOFs) are a class of crystalline and porous adsorbents, with wide-ranging applications in gas separations, membrane materials as well as sensors. Commonly used batch synthesis techniques for MOF production are limited by low productivity, high operating costs, and slow crystallization timescales, severely impeding the large-scale manufacturing of these materials. However, batch synthesis is a useful and easy technique to screen multiple reaction parameters to find an optimal chemistry. Therefore, in this study, we have used the batch process and screened a multidimensional reaction space consisting of 45 sample variations based on the crystallinity, yield, and instantaneous precipitation, which could lead to tube clogging under flow conditions. We have found one optimized reaction chemistry, that could be used in flow conditions, which in this study is a novel millifluidic droplet-based reactor for the continuous synthesis of HKUST-1 crystals. The biphasic flow in the millifluidic reactor consisted of droplets of the reactant solution, dispersed in a continuous phase of silicone oil. We investigate the differences in the quality and quantity of HKUST-1 synthesized via the continuous and batch techniques. Moreover, we have demonstrated that the HKUST-1 samples prepared via the continuous synthesis in a droplet based millifluidic reactor, at an ultra-low residence time exhibit excellent physical properties comparable to that obtained for the samples prepared by the traditional batch process. A clean, easy-to-install, and reusable millifluidic reactor presented in this work may pave the path for an economically viable, large-scale synthesis of HKUST-1.

Predicting slow relaxation timescales in open quantum systems

Predicting slow relaxation timescales in open quantum systems

Multiple time scale state-of-charge and capacity-based equalisation strategy for lithium-ion battery pack with passive equaliser

The cycle life of a lithium-ion battery pack is much shorter than that of a single cell because of their different external operating environments and internal characteristic parameters. Equalisation management is essential for reducing the difference between battery cells, improving capacity, and prolonging the cycle life. Passive equalisation is also widely used in electric vehicles and energy storage systems because of its comparative advantages including the low cost, simple structure, and easy control. Compared with the mature development of the passive equalisation hardware circuits, the evolution of high-performance equalisation strategies is relatively backward. Along these lines, a multiple time scale state-of-charge (SOC) and capacity-based equalisation strategy for lithium-ion battery packs with passive equalisers was proposed in this work. Firstly, the minimum-capacity differential model (MCDM) consisting of a cell minimum-capacity model (CMCM) and a cell differential model (CDM) was established to improve the computational efficiency and accuracy of the dynamic behaviour of the minimum-capacity cell, as well as all the other cells in a battery pack. Secondly, the SOC and capacity of a battery pack were estimated on multiple time scales with the use of a dual extended Kalman filter and MCDM. The fast time scale based on CMCM and the slow time scale based on CDM can balance the efficiency and accuracy of the estimation algorithm. Based on the accurate estimation of both SOC and capacity, a SOC-and-capacity-based equalisation strategy was designed. Finally, a high-fidelity multicell model was used to simulate and verify the proposed equalisation strategy under the guidance of actual battery pack degradation data. The extracted experimental results show that the proposed method can efficiently and accurately estimate the SOC and capacity of new and aged batteries while a high-accuracy estimation in the entire life cycle is achieved. Compared with the traditional voltage-based and SOC-based strategies, the proposed SOC-and-capacity-based strategy can reconcile the maximization of battery pack capacity, the minimization of equalisation energy consumption, and the-equalisation duration to achieve high-efficiency balancing in the entire life cycle.

Large deviations of mean-field interacting particle systems in a fast varying environment

This paper studies large deviations of a “fully coupled” finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment evolves in the fast time scale. Our main result is the path-space large deviation principle for the joint law of the empirical measure process of the particles and the occupation measure process of the fast environment. This extends previous results known for two time scale diffusions to two time scale mean-field models with jumps. Our proof is based on the method of stochastic exponentials. We characterise the rate function by studying a certain variational problem associated with an exponential martingale.

Voltage Regulation With High Penetration of Low-Carbon Energy in Distribution Networks: A Source–Grid–Load-Collaboration-Based Perspective

In this article, a source–grid–load-collabora tion-based control framework is proposed to improve the power quality of active distribution networks (ADNs) with high penetration of low-carbon energy. First, hybrid dynamics of ADNs are characterized by addressing the voltage regulation and operation economics in each operation mode, and the mode switching control is designed in line with the operation principle of the on-load tap changer, where voltage security events are used to build the event-triggered functions. Second, multiobjective optimization is formulated with consideration of the system-wide operation cost and distribution circuit loss of the ADN in a relatively slow time scale, while in the fast time scale, all the inverter-based distributed generators, energy storages, and static var compensator devices are coordinated at the source–load side, through which multiple voltage issues, including voltage profile issue and voltage increment issue, can be addressed in a fully distributed manner. Finally, simulation results validate the effectiveness and robustness of the proposed method based on the modified IEEE 33-bus system.

Critical Parameters in Dynamic Network Modeling of Sepsis.

In this work, we propose a dynamical systems perspective on the modeling of sepsis and its organ-damaging consequences. We develop a functional two-layer network model for sepsis based upon the interaction of parenchymal cells and immune cells via cytokines, and the coevolutionary dynamics of parenchymal, immune cells, and cytokines. By means of the simple paradigmatic model of phase oscillators in a two-layer system, we analyze the emergence of organ threatening interactions between the dysregulated immune system and the parenchyma. We demonstrate that the complex cellular cooperation between parenchyma and stroma (immune layer) either in the physiological or in the pathological case can be related to dynamical patterns of the network. In this way we explain sepsis by the dysregulation of the healthy homeostatic state (frequency synchronized) leading to a pathological state (desynchronized or multifrequency cluster) in the parenchyma. We provide insight into the complex stabilizing and destabilizing interplay of parenchyma and stroma by determining critical interaction parameters. The coupled dynamics of parenchymal cells (metabolism) and nonspecific immune cells (response of the innate immune system) is represented by nodes of a duplex layer. Cytokine interaction is modeled by adaptive coupling weights between nodes representing immune cells (with fast adaptation timescale) and parenchymal cells (slow adaptation timescale), and between pairs of parenchymal and immune cells in the duplex network (fixed bidirectional coupling). The proposed model allows for a functional description of organ dysfunction in sepsis and the recurrence risk in a plausible pathophysiological context.

Quasi-static limit for the asymmetric simple exclusion

We study the one-dimensional asymmetric simple exclusion process on the lattice $\{1, \dots,N\}$ with creation/annihilation at the boundaries. The boundary rates are time dependent and change on a slow time scale $N^{-a}$ with $a>0$. We prove that at the time scale $N^{1+a}$ the system evolves quasi-statically with a macroscopic density profile given by the entropy solution of the stationary Burgers equation with boundary densities changing in time, determined by the corresponding microscopic boundary rates. We consider two different types of boundary rates: the "Liggett boundaries" that correspond to the projection of the infinite dynamics, and the reversible boundaries, that correspond to the contact with particle reservoirs in equilibrium. The proof is based on the control of the Lax boundary entropy--entropy flux pairs and a coupling argument.

Quantum Dynamics with Electronic Friction.

A theory of electronic friction is developed using the exact factorization of the electronic-nuclear wave function. No assumption is made regarding the electronic bath, which can be made of independent or interacting electrons, and the nuclei are treated quantally. The ensuing equation of motion for the nuclear wave function is a nonlinear Schrödinger equation including a friction term. The resulting friction kernel agrees with a previously derived mixed quantum-classical result by Dou etal., [Phys. Rev. Lett. 119, 046001 (2017)]PRLTAO0031-900710.1103/PhysRevLett.119.046001, except for a pseudomagnetic contribution in the latter that is here removed. More specifically, it is shown that the electron dynamics generally washes out the gauge fields appearing in the adiabatic dynamics. However, these are fully re-established in the typical situation where the electrons respond rapidly on the slow time scale of the nuclear dynamics (Markov limit). Hence, we predict Berry's phase effects to be observable also in the presence of electronic friction. Application to a model vibrational relaxation problem proves that the proposed approach represents a viable way to account for electronic friction in a fully quantum setting for the nuclear dynamics.

Quantum theory of electronic friction

Electronic friction is an important energy loss channel for atoms and molecules scattering off, reacting, or simply vibrating at metallic surfaces. It is usually well described by mixed classical-quantum approaches where the nuclei evolve classically according to Langevin-type equations of motion, and Born-Oppenheimer forces and friction kernels are obtained from first-principles electronic structure calculations. However, classical dynamics falls short when light atoms are involved, which is also the situation where electronic friction becomes the dominant dissipation channel and its role in the dynamics can be unambiguously assessed. Furthermore, the interplay between electronic friction and nuclear quantum effects in molecular processes at surfaces is largely unknown; in fact, it is not even clear how to include electronic friction in a quantum setting. Here we fill this gap by developing a fully quantum theory of electronic friction at $T=0\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The electronic bath is considered to be entirely general and can be made of interacting electrons, potentially in a strongly correlated state. The derived friction kernel agrees with a recently obtained mixed quantum-classical result [Dou, Miao, and Subotnik, Phys. Rev. Lett. 119, 046001 (2017)], except for a pseudomagnetic contribution in the latter that is removed here. The ensuing equation of motion for the nuclear wave function is a nonlinear Schr\"odinger equation with a frictional vector potential that depends on the past wave function behavior. The equation becomes local-in-time in the typical situation where the electrons respond rapidly on the slow timescale of the nuclear dynamics (Markov limit) and generalizes previously known Schr\"odinger-Langevin equations to coordinate-dependent, tensorial friction kernels.

Classification of KPI lumps

A large family of nonsingular rational solutions of the Kadomtsev–Petviashvili (KP) I equation are investigated. These solutions are constructed via the Gramian method and are identified as points in a complex Grassmannian. Each solution is a traveling wave moving with a uniform background velocity but have multiple peaks which evolve at a slower time scale in the co-moving frame. For large times, these peaks separate and form well-defined wave patterns in the xy-plane. The pattern formation are described by the roots of well-known polynomials arising in the study of rational solutions of Painlevé II and IV equations. This family of solutions are shown to be described by the classical Schur functions associated with partitions of integers and irreducible representations of the symmetric group of N objects. It is then shown that there exists a one-to-one correspondence between the KPI rational solutions considered in this article and partitions of a positive integer N.

Primary Parametric Amplification in a Weakly Forced Mathieu Equation

Abstract The present study deals with the response of a forced Mathieu equation with damping, with weak harmonic direct excitation at the same frequency as the parametric excitation. A second-order perturbation analysis using the method of multiple scales unfolds parametric amplification at primary resonance. The parametric effect on the primary resonance behavior occurs with a slow time scale of second-order, although the effect on the steady-state response is of order 1. As the parametric excitation level increases, the response at primary resonance stretches before becoming unbounded and unstable. Analytical expressions for predicting the response amplitudes are presented and compared with numerical results for a specific set of system parameters. Dependence of the amplification behavior, and indeed possible deamplification, on parameters is examined. The effect of parametric excitation on the response phase behavior is also presented.

Linear Active Disturbance Rejection Control for Two-Mass Systems Via Singular Perturbation Approach

This article presents a linear active disturbance rejection control (LADRC) scheme for two-mass systems (TMSs) based on a singular perturbation (SP) approach. In the proposed scheme, the dynamics of TMSs are separated into a quasi-steady-state system at a slow time scale and a boundary-layer system at a fast time scale via the SP method. The quasi-steady-state model is used as the nominal model to design the LADRC, where internal model control (IMC) rules are employed for prescribed tracking performance. This not only reduces the model order but also makes the gain tuning straightforward, which is crucial for practical use. Based on the boundary-layer model, the active damping method is designed for vibration suppression, which aims at achieving a higher stable bandwidth of the IMC to better attenuate the residual disturbance of linear extended state observer such that the tracking accuracy can be improved. Stability of the full system was analyzed via the extended Tikhonov's theorem. Comparative experiments were carried out to verify the effectiveness of the proposed scheme.

Unique structural and dynamic properties of the HNH nuclease in mesophilic and thermophilic Cas9 revealed by NMR

CRISPR‐Cas9 is a widely utilized biochemical tool with applications in biotechnology and in medicine. Target DNA recognition and nuclease sites of Cas9 are spatially separated yet functionally coupled, indicative of an allosteric crosstalk throughout the enzyme. There are structural and dynamic changes occuring throughout Cas9 that are critical for this signal propagation. However, an understanding of the molecular motions guiding Cas9 and how this influences its mechanism are unknown. In this study we report on the structural and dynamic properties of the HNH domain between the extensively studied SpCas9 from Streptococcus pyogenes, and a recently discovered thermostable Cas9 homolog from a thermophilic bacterium Geobacillus stearothermophilus(GeoCas9). Here we show that despite sequential and structural conservation, SpHNH and GeoHNH have different dynamic profiles. We found the intrinsic dynamics of SpHNH to be on the slow (ms) timescale, while GeoHNH is highly influenced by fast (ps‐ns) timescale dynamics. Furthermore, we found that when the residue with the highest flexibility on the ps‐ns timescale is mutated in GeoHNH, its protein solubility, thermal stability, and dynamic profile are all drastically distorted. Our results demonstrate how there are mechanistic differences between the HNH domain of mesophilic and thermophilic Cas9 species. Our results also highlight how these fast timescale motions that regulate GeoHNH play a role in giving GeoCas9 its thermophilic characteristic.

HVAC system dynamic management in communities via an aggregation–disaggregation framework

The aggregation and disaggregation problem of Heating Ventilation and Air Conditioning (HVAC) systems in the building at the community-level have been considered in this work. The aim is to provide capacity reserves as a Virtual Power Plant (VPP) to support power system operation, improving grid reliability and efficiency in the face of increased use of renewable energy. Motivated by the layered operating structure of the power grid, an aggregation–disaggregation framework which operates at both slow and fast time-scales is proposed. At the slow time-scale, each building forecasts its HVAC system future electric power consumption information using predictions of disturbance and information of thermal zone via solving certain optimization problems. These values will be collected by a control center such as a community aggregator. Acting as a VPP, the control center determines each HVAC system future nominal electric power consumption by participating in the real-time electricity market or an independent power allocation plan. At the fast time-scale, a modified primal–dual gradient method based distributed control scheme is designed such that under real disturbances, the system can track the nominal consumption as closely as possible using only neighboring communications and local measurements. Finally, a numerical study demonstrates the effectiveness of the proposed framework.

Epigenetic fluctuations underlie gene expression timescales and variability.

Isogenic populations of mammalian cells exhibit significant gene expression variability. This variability can be separated into two components. Variance arises from events specific to the transcribed gene (i.e., cis or allele-specific sources) and variance from events that impact many genes at once (i.e., trans and global processes). Furthermore, the activity of the different regulatory factors that influence gene expression fluctuates at different timescales. Fast timescales will result in rapid fluctuation of gene expression, whereas slow timescales will result in longer persistence of gene expression levels over time. Here, we investigated sources of gene expression that are intrinsic, i.e., coming from cis-regulatory factors and follow slow timescales. To do so, we developed a reporter system that isolates allele-specific variability and measures its persistence in imaging and long-term fluctuation analysis experiments. Our results identify a new source of gene expression variability that is allele-specific but that fluctuates on timescales of days. We hypothesized that allele-specific fluctuations of epigenetic regulatory factors are responsible for the newly discovered allele-specific and slow source of gene expression variability. Using mathematical modeling, we showed that adding this effect to the two-state model is sufficient to account for all empirical observations. Furthermore, using direct assays of chromatin markers, we find fluctuation in H3K4me3 levels that match the observed changes in gene expression levels providing direct experimental support of our model. Collectively, our work shows that slow fluctuations of regulatory chromatin modifications contribute to the variability in gene expression.

Surprising Rigidity of Functionally Important Water Molecules Buried in the Lipid Headgroup Region.

Understanding water dynamics and structure is an important topic in biological systems. It is generally held in the literature that the interfacial water of hydrated phospholipids is highly mobile, in fast exchange with the bulk water ranging from the nano- to femtosecond timescale. Although nuclear magnetic resonance (NMR) is a powerful tool for structural and dynamic studies, direct probing of interfacial water in hydrated phospholipids is formidably challenging due to the extreme population difference between bulk and interfacial water. We developed a novel 17O solid-state NMR technique in combination with an ultra-high-field magnet (35.2 T) to directly probe the functionally important interfacial water. By selectively suppressing the dominant bulk water signal, we observed two distinct water species in the headgroup region of hydrated dimyristoylphosphatidylcholine (DMPC) lipid bilayers for the first time. One water species denoted as "confined water" is chemically and dynamically different from the bulk water (∼0.17 ppm downfield and a slightly shorter spin-lattice relaxation time). Another water species denoted as "bound water" has severely restricted motion and a distinct chemical shift (∼12 ppm upfield). Additionally, the bulk water is not as "free" as pure water, resulting from the fast exchange with the water molecules that weakly and transiently interact with the lipid choline groups. These new discoveries clearly indicate the existence of the interfacial water molecules that are relatively stable over the NMR timescale (on the order of milliseconds), providing an opportunity to characterize water dynamics on the millisecond or slower timescale in biomacromolecules.

Using AGN light curves to map accretion disc temperature fluctuations

ABSTRACT We introduce a new model for understanding AGN continuum variability. We start from a Shakura–Sunyaev thin accretion disc with a steady-state radial temperature profile T(R) and assume that the variable flux is due to axisymmetric temperature perturbations δT(R, t). After linearizing the equations, we fit UV–optical AGN light curves to determine δT(R, t) for a sample of seven AGNs. We see a diversity of |δT/T| ∼ 0.1 fluctuation patterns which are not dominated by outgoing waves travelling at the speed of light as expected for the ‘lamppost’ model used to interpret disc reverberation mapping studies. Rather, the most common pattern resembles slow (v ≪ c) ingoing waves. An explanation for our findings is that these ingoing waves trigger central temperature fluctuations that act as a lamppost, producing lower amplitude temperature fluctuations moving outwards at the speed of light. The light curves are dominated by the lamppost signal – even though the temperature fluctuations are dominated by other structures with similar variability time-scales – because the discs exponentially smooth the contributions from the slower moving (v ≪ c) fluctuations to the observed light curves. This leads to light curves that closely resemble the expectations for a lamppost model but with the slow variability time-scales of the ingoing waves. This also implies that longer time-scale variability signals will increasingly diverge from lamppost models because the smoothing of slower moving waves steadily decreases as their period or spatial wavelength increases.

Dynamics of KPI lumps

A family of nonsingular rational solutions of the Kadomtsev–Petviashvili (KP) I equation are investigated. These solutions have multiple peaks whose heights are time-dependent and the peak trajectories in the xy-plane are altered after collision. Thus they differ from the standard multi-peaked KPI simple n-lump solutions whose peak heights as well as peak trajectories remain unchanged after interaction. The anomalous scattering occurs due to a non-trivial internal dynamics among the peaks in a slow time scale. This phenomena is explained by relating the peak locations to the roots of complex heat polynomials. It follows from the long time asymptotics of the solutions that the peak trajectories separate as as |t| → ∞, and all the peak heights approach the same constant value corresponding to that of the simple one-lump solution. Consequently, a multi-peaked n-lump solution evolves to a superposition of n one-lump solutions asymptotically as |t| → ∞.

Time Evolution of the Millisecond Allosteric Activation of Imidazole Glycerol Phosphate Synthase.

Deciphering the molecular mechanisms of enzymatic allosteric regulation requires the structural characterization of functional states and also their time evolution toward the formation of the allosterically activated ternary complex. The transient nature and usually slow millisecond time scale interconversion between these functional states hamper their experimental and computational characterization. Here, we combine extensive molecular dynamics simulations, enhanced sampling techniques, and dynamical networks to describe the allosteric activation of imidazole glycerol phosphate synthase (IGPS) from the substrate-free form to the active ternary complex. IGPS is a heterodimeric bienzyme complex whose HisH subunit is responsible for hydrolyzing glutamine and delivering ammonia for the cyclase activity in HisF. Despite significant advances in understanding the underlying allosteric mechanism, essential molecular details of the long-range millisecond allosteric activation of IGPS remain hidden. Without using a priori information of the active state, our simulations uncover how IGPS, with the allosteric effector bound in HisF, spontaneously captures glutamine in a catalytically inactive HisH conformation, subsequently attains a closed HisF:HisH interface, and finally forms the oxyanion hole in HisH for efficient glutamine hydrolysis. We show that the combined effector and substrate binding dramatically decreases the conformational barrier associated with oxyanion hole formation, in line with the experimentally observed 4500-fold activity increase in glutamine hydrolysis. The allosteric activation is controlled by correlated time-evolving dynamic networks connecting the effector and substrate binding sites. This computational strategy tailored to describe millisecond events can be used to rationalize the effect of mutations on the allosteric regulation and guide IGPS engineering efforts.

Optical and photophysical properties of platinum benzoporphyrins with C2v and D2h symmetry

Platinum(II) mono- and di-benzoporphyrins carrying either ester or imide peripheral groups have been successfully synthesized. These benzoporphyrins possessing C[Formula: see text] and D[Formula: see text] symmetry were investigated using a range of techniques including UV-Vis and phosphorescence spectroscopy, differential pulse voltammetry, and transient absorption spectroscopy covering wide spatial and temporal ranges. Up to three oxidation and three reductions within the accessible potential window of dichlorobenzene were observed. Facile reductions for both mono- and dibenzoporphyrin derivatives, more so with imide peripheral substituents were witnessed. Computational studies were supportive of push-pull type interactions within these molecular systems. The formation of triplet excited states within 5 ps after laser excitation was confirmed by femtosecond transient absorption studies. Nanosecond transient absorption studies coupled with phosphorescence lifetime studies revealed relatively rapid relaxation of the triplet excited states as compared to a controlled platinum porphyrin suggesting push-pull type interactions on a slower time scale.