Slow Variations Research Articles

A modified dual time integration technique for aerodynamic quasi-static and dynamic stall hysteresis

Simulation of the aerodynamic stall phenomenon in both quasi-static and dynamic conditions requires expensive computational resources. The computations become even more costly for static stall hysteresis using an unsteady solver with very slow variation of angle of attack at low reduced frequencies. In an explicit time-marching solver that satisfies the low Courant number condition, that is, [Formula: see text], the computational cost for such simulations becomes prohibitive, especially at higher Reynolds numbers due to the presence of thin-stretched cells with large aspect ratio in the boundary layer. In this paper, a segregated solver method such as the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) is modified as a dual pseudo-time marching method so that the unsteady problem at each time step is reformulated as a steady state problem. The resulting system of equations in the discretized finite volume formulation is then reduced to zero or near-zero residuals using available convergence acceleration methods such as local time stepping, multi-grid acceleration and residual smoothing. The performance and accuracy of the implemented algorithm was tested for three different airfoils at low to moderate Reynolds numbers in both incompressible and compressible flow conditions covering both attached and separated flow regimes. The results obtained are in close agreement with the published experimental and computational results for both quasi-static and dynamic stall and have demonstrated significant savings in computational time.

Rate of convergence for singular perturbations of Hamilton-Jacobi equations in unbounded spaces

We prove rate of convergence results for singular perturbations of Hamilton-Jacobi equations in unbounded spaces where the fast operator is linear, uniformly elliptic and has an Ornstein-Uhlenbeck-type drift. The slow operator is a fully nonlinear elliptic operator while the source term is assumed only locally Hölder continuous in both fast and slow variables. We obtain several rates of convergence according to the regularity of the source term.

New Insights on Ground Deformation at Campi Flegrei Caldera Inferred From Kinematics and Dynamics Investigation of Borehole Tilt

AbstractThe study of the ground deformation in active calderas provides valuable indications of the ongoing dynamical processes. In this framework, we analyze the borehole tiltmeter data recorded at Campi Flegrei (Southern Italy) from their first installation (1 April 2015), in order to retrieve the kinematics of the ground deformation and its main anomalies. Our approach involves the nonlinear dynamics analysis aimed at the identification of the degrees of freedom of the system and thus its complexity. Starting from the second part of the year 2020, the behavior of the dynamical system becomes collective, and a locally significant deviation of the deformative pattern from the background trend is observed. In particular, a series of 15 slow tilt variations (like jumps lasting a few days) appears in the ground deformation. They are associated with a very low‐dimensional system likely generated by a local second‐order source. The latter is related to fluid migration and it is superimposed on the primary one located in Pozzuoli town and driving the current uplift of Campi Flegrei. The effects of such a local, second‐order stress field are, indeed, evident in the area of the volcanic dome of Mt. Olibano, where they are measured as tilt steps. The superposition of primary and second‐order sources of deformation acting contemporaneously can justify the recent variations in geophysical and geochemical parameters. Our approach based on the joint dynamical and kinematical analyses of the tiltmeter data can be applied to other volcanic/tectonic areas or extended to other geophysical and geochemical variables.

An Improved Setting-Free Scheme for Fast and Reliable Detection of Complete and Partial Loss-of-Excitation

In this article, an improved setting-free loss-of-excitation (LOE) protection is developed for fast and reliable classification of various events. In the proposed scheme, the internal voltage and reactive power of the synchronous generator (SG) have been exploited to fulfill the condition of not needing the threshold amount because they are directly dependent on the rotor field and continuously reduced during the LOE, leading to having a negative polarity of variation. However, due to slow dynamic variation during the LOE condition, they are multiplied to accelerate and highlight the reduction changes, giving rise to increasing the detection speed. Meanwhile, owing to the considerable difference between the value of internal voltage and reactive power and to highlight the effect of multiplication function, an adaptive gain on the basis of steady-state parameters of SG is suggested. Furthermore, given that the negative polarity of the multiplied parameters can be affected during the hybrid events, the limited integral function is implemented to eliminate the happened swings, resulting in keeping the negative polarity and thus clustering the hybrid events reliably. The performed simulations on the IEEE 9-bus and 39-bus test systems prove that the provided setting-free protection can detect all types of the events reliably and quickly than other schemes.

Ingestion kinetics of mixotrophic and heterotrophic flagellates

AbstractIn sunlit waters, significant predation is performed by unicellular, phagotrophic mixotrophs, that is, predators that also possess plastids. The success of a mixotrophic lifestyle will depend in part on how well mixotrophs acquire prey relative to specialized heterotrophs. Likewise, consequences of mixotrophy for productivity and element cycling will depend on the rate and efficiency at which mixotrophs consume prey biomass relative to heterotrophs. However, trait differences between mixotrophs and heterotrophs are not well characterized. In addition, cell size of mixotrophs varies widely, and constitutive mixotrophs include small flagellates deriving from diverse taxa, while larger species are primarily dinoflagellates. To determine whether similar constraints apply to phagotrophs across this broad range of size and taxa, we compiled 83 measurements of flagellate functional responses and compared maximum clearance rates (Cmax) and maximum ingestion rates (Imax) between trophic modes. We found that the average mixotroph has a 3.7‐fold lower Cmax and 7.8‐fold lower Imax than the average heterotroph, after controlling for cell size. The smaller penalty for Cmax suggests that relative fitness of mixotrophs will be enhanced under dilute prey concentrations that are common in pelagic ecosystems. We also find that growth efficiency is greater for mixotrophs and for flagellates with lower Cmax, indicating a spectrum of trophic strategies that may be driven by phototrophy vs. phagotrophy allocation as well as fast vs. slow metabolic variation. Allometric scaling shows that Imax is constrained by a common relationship among dinoflagellates and other taxa, but dinoflagellates achieve a greater volume‐specific Cmax. These results should aid in interpreting protistan communities and modeling mixotrophy.

Separation of scales and a thermodynamic description of feature learning in some CNNs

Deep neural networks (DNNs) are powerful tools for compressing and distilling information. Their scale and complexity, often involving billions of inter-dependent parameters, render direct microscopic analysis difficult. Under such circumstances, a common strategy is to identify slow variables that average the erratic behavior of the fast microscopic variables. Here, we identify a similar separation of scales occurring in fully trained finitely over-parameterized deep convolutional neural networks (CNNs) and fully connected networks (FCNs). Specifically, we show that DNN layers couple only through the second cumulant (kernels) of their activations and pre-activations. Moreover, the latter fluctuates in a nearly Gaussian manner. For infinite width DNNs, these kernels are inert, while for finite ones they adapt to the data and yield a tractable data-aware Gaussian Process. The resulting thermodynamic theory of deep learning yields accurate predictions in various settings. In addition, it provides new ways of analyzing and understanding DNNs in general.

Enhancing the resilience of ecosystem services under extreme events in socio-hydrological systems: A spatio-temporal analysis

Due to the adverse impacts of severe droughts on various aspects of human life and ecosystem services (ESs), the spatio-temporal assessment of the resilience of ESs under droughts is essential. In this paper, we propose a new methodology for assessing ESs-based resilience, taking into account the seven resilience principles: a) redundancy and diversity, b) managing connectivity, c) managing slow variables and their feedback, d) complex adaptive system (CAS) thinking, e) experimentation and learning, f) broadening participation, and g) polycentric governance. These principles enable us to consider the main social, political, hydrological, economic, and environmental aspects concerning resilience which have been overlooked in previous studies. The methodology is evaluated by applying it to Zarrinehroud River Basin (ZRB) in north-western Iran. A set of qualitative and quantitative criteria and their sub-criteria are proposed for quantifying the ES-based resilience and generating time series of resilience against severe droughts in several sub-basins in the study area. To evaluate the criteria and sub-criteria, the required data are derived from calibrated SWAT and MODSIM models as well as experts’ judjments. The time series of ES-based resilience under 128 Water and Environmental Resources Management (WERM) scenarios (for enhancing agricultural practices, altering and modernizing irrigation methods, improving irrigation network and drainage facilities) and Climate Change (CC) scenarios (RCP 4.5, RCP6.0, and RCP 8.5) are derived for each sub-basin based on short-term (2020–2049) and long-term (2020–2098) periods. The low resilience values (0.53–0.6) of all sub-basins under the base management scenario (the status quo scenario (SC0)) illustrate the need for implementing some projects to enhance the ESs in the study area. The results show that the WERM scenario SC12346 can improve the values of the resilience criterion in sub-basins up to 0.85 and reduce the vulnerability of the study area to droughts. By evaluating all management scenarios, scenario SC12346 is reported as the best scenario, since it can significantly increase the resilience of all sub-basins against extreme droughts with an acceptable cost of 636 million US dollars compared to other scenarios. Under this WERM scenario, the resilience values of sub-basins increase up to 40%. This scenario suggests implementing a set of projects such as improving irrigation networks and drainage facilities.

Ginzburg Landau Model for Nanofluid Convection in the Presence of Time Periodic Plate Modulation

Here we study thermal modulation effect on nanofluid convection and discuss heat and mass transfer in the layer. The non-uniform time periodic boundary conditions of the system are considered. A weak non-linear stability analysis has been performed and obtained heat and mass transfer coefficients as a function of the system parameters. The Ginzburg Landau model was employed to derive nanofluid convective amplitude at different stages of flow disturbances and modulation. Slow variations of time scale shows that thermal modulation impact on transport phenomenon for the case of out phase modulation (OPM) and (lower boundary modulation) LBM. Also the effect of IPM (in-phase modulation) is observed low effect on Nu and which are similar to un-modulation case. It is also justified that LBM restuls are similar to gravity modulation results. It is found that thermal modulation and concentration Rayleigh numbers are either stabilize or destabilize the system. Further, GL model shows better results on regulation of transport process

АСИМПТОТИЧЕСКИЕ МЕТОДЫ В ЗАДАЧАХ СУПЕРВИЗОРНОГО УПРАВЛЕНИЯ АВТОНОМНЫХ ПОДВОДНЫХ РОБОТОВ

The work is devoted to the relevant problem of control synthesis for autonomous underwater vehicles(AUVs). Since AUVs must perform actions in accordance with a given program under conditionsof a volatile predictable environment, it is necessary to provide working tools, the use of which, togetherwith the AUV position and orientation control requires, along with continuous local stabilization means,implementation of supervising and coordinated control algorithms at the upper level. Such a two-levelcontrol scheme, which can be called supervisory, is proposed in this paper to be implemented using twotypes of asymptotic methods: to separate movements into fast and slow, an apparatus for analyzing singularly perturbed differential equations is used, and the upper level control is based on the principleof large deviations. The general synthesis task is to control slow movements and stabilize fast movements.At the same time, in the stochastic problem formulation, it is assumed that there is a randomperturbation in fast movements. Given that fast movements are stabilized, it is high probable that thenoise influence averaged and does not significantly affect the behavior of slow variables. However, withsufficiently long observation it is possible to find a situation where at some period the perturbation valuesare not only uncompensated, but, on the contrary, line up in a sequence as specially intended toform an apparent deviation of the slow sub-vector from equilibrium. It is known from the theory of largedeviations that such a trajectory is the only and most likely of all those leading to a certain critical event.At the same time, the phase of this process can be used to judge the critical event proximity. For thisreason, the large deviations theory usage makes it possible to organize the control of deviations from aiven object’ t jecto y, capable of giving estimates on the probability of the controlled deviationscritical values. As a result, it is shown that if accelerations are formed by fast subsystems, then in slowsubsystems it is possible not only to achieve acceptable quality and accuracy at a fixed interval, but alsoto ensure this regardless of the disturbances. The validity of the proposed approach to synthesis, basedon the separation of movements and the large deviations theory, is shown on the example of an autonomousunderwater vehicle with two rudders (fore and aft) in the task of controlling longitudinal motion ata given depth. Simulation results and their discussion are presented.

Intelligent fault detection algorithm based on Hi/H∞ optimization and a cascaded neural networks

Autonomous surface ships (ASSs) have attracted attention owing to their ability to perform various tasks in complex and challenging aquatic environments without relying on a crew. However, they require reliable sensors to ensure navigational safety. In this study, a robust and intelligent fault detection algorithm was designed for the integrated navigation system of an ASS. First, a residual observer-based fault detection algorithm using Hi/H∞ optimization is proposed to deal with process disturbances and measurement noise. Such noise can be modeled under the condition of a bounded l2-norm to account for the sensitivity and robustness of the residual observer against random noise with unknown properties. However, this fault detection algorithm is insensitive to soft faults, which manifest as noise characterized by a small amplitude and slow variation. Conventional strategies for evaluating the fault detection threshold rely on human experience, which is insufficiently sophisticated for fault detection. Therefore, a cascaded neural network is proposed for optimizing the fault detection algorithm when the amount of training data is limited. The cascaded neural network consists of a multi-feature time domain network, a frequency-domain fault detection network as well as a decision-level fusion network. The proposed algorithm was verified in simulations as well as on historical data collected from real ship sensors. The results demonstrated that the proposed algorithm offers intelligent fault detection, including soft faults, with a low false alarm rate for integrated navigation systems.

Resonance and bifurcation of fractional quintic Mathieu-Duffing system.

In this paper, the main subharmonic resonance of the Mathieu-Duffing system with a quintic oscillator under simple harmonic excitation, the route to chaos, and the bifurcation of the system under the influence of different parameters is studied. The amplitude-frequency and phase-frequency response equations of the main resonance of the system are determined by the harmonic balance method. The amplitude-frequency and phase-frequency response equations of the steady solution to the system under the combined action of parametric excitation and forced excitation are obtained by using the average method, and the stability conditions of the steady solution are obtained based on Lyapunov's first method. The necessary conditions for heteroclinic orbit cross section intersection and chaos of the system are given by the Melnikov method. Based on the separation of fast and slow variables, the bifurcation phenomena of the system under different conditions are obtained. The amplitude-frequency characteristics of the total response of the system under different excitation frequencies are investigated by analytical and numerical methods, respectively, which shows that the two methods achieve consistency in the trend. The influence of fractional order and fractional derivative term coefficient on the amplitude-frequency response of the main resonance of the system is analyzed. The effects of nonlinear stiffness coefficient, parametric excitation term coefficient, and fractional order on the amplitude-frequency response of subharmonic resonance are discussed. Through analysis, it is found that the existence of parametric excitation will cause the subharmonic resonance of the Mathieu-Duffing oscillator to jump. Finally, the subcritical and supercritical fork bifurcations of the system caused by different parameter changes are studied. Through analysis, it is known that the parametric excitation coefficient causes subcritical fork bifurcations and fractional order causes supercritical fork bifurcations.

Electrical Charge Coupling Dominates the Hysteresis Effect of Halide Perovskite Devices.

Hysteresis effects in ionic-electronic devices are a valuable resource for the development of switching memory devices that can be used in information storage and brain-like computation. Halide perovskite devices show frequent hysteresis in current-voltage curves that can be harnessed to build effective memristors. These phenomena can be often described by a set of highly nonlinear differential equations that involve current, voltage, and internal state variables, in the style of the famous Hodgkin-Huxley model that accounts for the initiation and temporal response of action potentials in biological neurons. Here we extend the neuron-style models that lead to chemical inductors by introducing a capacitive coupling in the slow relaxation variable. The extended model is able to explain naturally previous observations concerning the transition from capacitor to inductor in impedance spectroscopy of MAPbBr solar cells and memristors in the dark. The model also generates new types of oscillating systems by the generation of a truly negative capacitance distinct from the usual inductive effect.

Supporting data for "Girsanov Reweighting Enhanced Sampling Technique (GREST): On-the-fly data-driven discovery of and enhanced sampling in slow collective variables"

Supporting data for "Girsanov Reweighting Enhanced Sampling Technique (GREST): On-the-fly data-driven discovery of and enhanced sampling in slow collective variables"

Asymptotics of Solutions of Linear Singularly Perturbed Optimal Control Problems with a Convex Integral Performance Index and a Cheap Control

We consider an optimal control problem for a linear system with constant coefficients with an integral convex performance index containing a small parameter multiplying the integral term in the class of piecewise continuous controls with smooth geometric constraints. Such problems are called cheap control problems. It is shown that the limit problem will be a problem with a terminal performance index. It is established that if the terminal term of the performance index is a convex (strictly convex) and continuously differentiable function, then the performance functional in the limit problem has similar properties. It is proved that, in the general case, convergence with respect to the performance functional is valid, and under the condition of strict convexity of the terminal term of the performance index in the original problem, convergence to the minimum point of the terminal summand of the performance index in the limit problem is valid. The limit of the defining vector in the original problem is found as the small parameter tends to zero. In particular, it is shown that the first component of the defining vector in the original problem converges to the defining vector in the limit problem. The problems of controlling a point of low mass in a medium with and without resistance with a terminal part depending on both slow and fast variables are considered in detail, and complete asymptotic expansions of the defining vectors in these problems are constructed.

Online feedforward parameter learning with robustness to set-point variations

High-tech motion system development is driven by increasingly accurate and fast positioning requirements. Feedforward compensation together with high bandwidth feedback control are essential to achieve these ever tightening performance demands. In particular, online adaptation of the feedforward parameters, to correct for small position dependencies and slow variations, is crucial to approach zero error tracking. The aim of this paper is a framework that provides robust recursive learning of feedforward parameters for any bounded reference trajectory. The convergence of the parameter learning strategy exploits the difference in time-scale between the parameter variation rate and the bandwidth of the servo controlled system. This enables to describe a servo-error-based objective function for varying trajectories as a static sector bounded nonlinearity. Subsequently, the circle criterion is employed to derive stability guarantees on the learning with explicit robustness to reference trajectory variation. A numerical case study demonstrates that a significant performance improvement can be achieved.

Forecasting Solar Cycle 25 with Physical Model-Validated Recurrent Neural Networks

The Sun’s activity, which is associated with the solar magnetic cycle, creates a dynamic environment in space known as space weather. Severe space weather can disrupt space-based and Earth-based technologies. Slow decadal-scale variations on solar-cycle timescales are important for radiative forcing of the Earth’s atmosphere and impact satellite lifetimes and atmospheric dynamics. Predicting the solar magnetic cycle is therefore of critical importance for humanity. In this context, a novel development is the application of machine-learning algorithms for solar-cycle forecasting. Diverse approaches have been developed for this purpose; however, with no consensus across different techniques and physics-based approaches. Here, we first explore the performance of four different machine-learning algorithms – all of them belonging to a class called Recurrent Neural Networks (RNNs) – in predicting simulated sunspot cycles based on a widely studied, stochastically forced, nonlinear time-delay solar dynamo model. We conclude that the algorithm Echo State Network (ESN) performs the best, but predictability is limited to only one future sunspot cycle, in agreement with recent physical insights. Subsequently, we train the ESN algorithm and a modified version of it (MESN) with solar-cycle observations to forecast Cycles 22 – 25. We obtain accurate hindcasts for Solar Cycles 22 – 24. For Solar Cycle 25 the ESN algorithm forecasts a peak amplitude of 131 ± 14 sunspots around July 2024 and indicates a cycle length of approximately 10 years. The MESN forecasts a peak of 137 ± 2 sunspots around April 2024, with the same cycle length. Qualitatively, both forecasts indicate that Cycle 25 will be slightly stronger than Cycle 24 but weaker than Cycle 23. Our novel approach bridges physical model-based forecasts with machine-learning-based approaches, achieving consistency across these diverse techniques.

Clearing function in the context of the invariant manifold method

Clearing functions (CFs), which express a mathematical relationship between the expected throughput of a production facility in a planning period and its workload (or work-inprogress, WIP) in that period have shown considerable promise for modeling WIP-dependent cycle times in production planning. While steady-state queueing models are commonly used to derive analytic expressions for CFs, the finite length of planning periods calls their validity into question. We apply a different approach to propose a mechanistic model for one-resource, one-product factory shop based on the analogy between the operation of machine and enzyme molecule. The model is reduced to a singularly perturbed system of two differential equations for slow (WIP) and fast (busy machines) variables, respectively. The analysis of this slow-fast system finds that CF is nothing but a result of the asymptotic expansion of the slow invariant manifold. The validity of CF is ultimately determined by how small is the parameter multiplying the derivative of the fast variable. It is shown that sufficiently small characteristic ratio ’working machines: WIP’ guarantees the applicability of CF approximation in unsteady-state operation.

Impact of Channel Aging on Reconfigurable Intelligent Surface Aided Massive MIMO Systems With Statistical CSI

The incorporation of reconfigurable intelligent surface (RIS) into massive multiple-input-multiple-output (mMIMO) systems can unleash the potential of next-generation networks by improving the performance of user equipments (UEs) in service dead zones. However, their requirement for accurate channel state information (CSI) is critical, and especially, applications with UE mobility that induce channel aging make challenging the achievement of adequate quality of service. Hence, in this work, we investigate the impact of channel aging on the performance of RIS-assisted mMIMO systems under both spatial correlation and imperfect CSI conditions. Specifically, by accounting for channel aging during both uplink training and downlink data transmission phases, we first perform minimum mean square error (MMSE) channel estimation to obtain the UE effective channels with low overhead similar to conventional systems without RIS. Next, we derive the downlink achievable sum spectral efficiency (SE) with regularized zero-forcing (RZF) precoding in closed-form being dependent only on large-scale statistics by using the deterministic equivalent (DE) analysis. Subsequently, we present the attractive optimization of the achievable sum SE with respect to the phase shifts and the total transmit power that can be performed every several coherence intervals due to the slow variation of the large-scale statistics. Numerical results validate the analytical expressions and demonstrate the performance while allowing the extraction of insightful design conclusions for common scenarios including UE mobility. In particular, channel aging degrades the performance but its impact can be controlled by choosing appropriately the frame duration or by increasing the number of RIS elements.

Differential resonant MEMS accelerometer: Synchronization characteristics of weakly coupled microbeam sensing elements

This work is devoted to studying the conditions and scenarios for synchronizing oscillations of weakly coupled microbeam elements of a differential resonant MEMS accelerometer operating in the dual-loop self-oscillator mode. The model of a system of two Van der Pol self-oscillators with a nonlinear elastic coupling between moving elements, obtained using the Galerkin method, was studied using the multiscale method. The modes of beats and synchronization of oscillations of two resonators are found analytically and numerically, and the boundary between these modes in the space of system parameters is determined. Along with a local bifurcation analysis of the considered stationary regimes, a global analysis of the evolution and branching of limit cycles in the space of slow variables was also carried out, which made it possible to detect zones of coexistence of stable synchronization and beat regimes with their basins of attraction. The influence of the factor of the designed or technologically determined non-identity of the design of two resonators on the location of the parametric zones of synchronization and beats is studied.

Discovering dynamical features of Hodgkin–Huxley-type model of physiological neuron using artificial neural network

We consider Hodgkin–Huxley-type model that is a stiff ODE system with two fast and one slow variables. For the parameter ranges under consideration the original version of the model has unstable fixed point and the oscillating attractor that demonstrates bifurcation from bursting to spiking dynamics. Also, a modified version is considered where the bistability occurs such that an area in the parameter space appears where the fixed point becomes stable and coexists with the bursting attractor. For these two systems we create artificial neural networks that are able to reproduce their dynamics. The created networks operate as recurrent maps and are trained on trajectory cuts sampled at random parameter values within a certain range. Although the networks are trained only on oscillatory trajectory cuts, they also discover the fixed point of the considered systems. The position and even the eigenvalues coincide very well with the fixed point of the initial ODEs. For the bistable model it means that the network being trained only on one brunch of the solutions recovers another brunch without seeing it during the training. These results, as we see it, are able to trigger the development of new approaches to complex dynamics reconstruction and discovering. From the practical point of view reproducing dynamics with the neural network can be considered as a sort of alternative method of numerical modeling intended for use with contemporary parallel hard- and software.