Critical Speeding Research Articles

Fuzzy model predictive control for frequency regulation of temporary microgrids during load restoration

AbstractTemporary microgrids containing a high proportion of distributed renewable generations can offer great benefits during the recovery stage after large‐scale power system blackout, by picking up critical load and speeding up the entire grid recovery process. To solve the frequency security problem of temporary microgrids faced in the load restoration process, this paper proposes an adaptive fuzzy model predictive control (adaptive fuzzy‐MPC) strategy to obtain effective frequency regulation to suit the special characteristics of this process. First, the load restoration plan within a short time frame is regarded as the feedforward information and assists in the establishment of the MPC model. Then, considering the uncertainty of renewable distributed generations, the regulation resources are cooperated by an adaptive fuzzy controller which provides the weights of different regulation resources adopted in MPC. Specifically, the base weights of the energy storage system and renewable distributed generations are obtained from fuzzy rules, and then the weight for each regulation resource is modified by the designed adjustment rules. Simulation results illustrate that the proposed strategy can efficiently improve frequency performance while making various frequency regulation resources with different regulation capacities cooperate properly, which can further accelerate the load restoration progress and enhance system resilience.

Enhancing the Output Performance of a Triboelectric Nanogenerator Based on Modified Polyimide and Sandwich-Structured Nanocomposite Film

Recently, scientists have been facing major obstacles in terms of improving the performances of dielectric materials for triboelectric nanogenerators. The triboelectric nanogenerator (TENG) is one of the first green energy technologies that can convert random mechanical kinetic energy into electricity. The surface charge density of TENGs is a critical factor speeding up their commercialization, so it is important to explore unique methods to increase the surface charge density. The key to obtaining a high-performance TENG is the preparation of dielectric materials with good mechanical properties, thermal stability and output performance. To solve the problem of the low output performance of PI-based triboelectric nanogenerators, we modified PI films by introducing nanomaterials and designed a new type of sandwich-shaped nanocomposite film. Herein, we used polyimide (PI) with ideal mechanical properties, excellent heat resistance and flexibility as the dielectric material, prepared an A-B-A sandwich structure with PI in the outer layer and modified a copper calcium titanate/polyimide (CCTO/PI) storage layer in the middle to improve the output of a TENG electrode. The doping amount of the CCTO was tailored. The results showed that at 8 wt% CCTO content, the electrical output performance was the highest, and the open-circuit voltage of CCTO/PI was 42 V. In the TENG, the open-circuit voltage, short-circuit current and transfer charge of the prepared sandwich-structured film were increased by 607%, 629% and 672% compared to the TENG with the PI thin film, respectively. This study presents a novel strategy of optimizing dielectric materials for triboelectric nano-generators and has great potential for the future development of high output-performance TENGs.

Exploring the role of the potential surface in the behaviour of early warning signals

The theory of critical slowing down states that a system displays increasing relaxation times as it approaches a critical transition. These changes can be seen in statistics generated from timeseries data, which can be used as early warning signals of a transition. Such early warning signals would be of value for emerging infectious diseases or to understand when an endemic disease is close to elimination. However, in applications to a variety of epidemiological models there is frequent disagreement with the general theory of critical slowing down, with some indicators performing well on prevalence data but not when applied to incidence data. Furthermore, the alternative theory of critical speeding up predicts contradictory behaviour of early warning signals prior to some stochastic transitions. To investigate the possibility of observing critical speeding up in epidemiological models we characterise the behaviour of common early warning signals in terms of a system’s potential surface and noise around a quasi-steady state. We then describe a method to obtain these key features from timeseries data, taking as a case study a version of the SIS model, adapted to demonstrate either critical slowing down or critical speeding up. We show this method accurately reproduces the analytic potential surface and diffusion function, and that these results can be used to determine the behaviour of early warning signals and correctly identify signs of both critical slowing down and critical speeding up.

Squeezing by critical speeding up: Applications in quantum metrology

We present an alternative protocol allowing for the preparation of critical states that instead of suffering from the critical slowing down benefits from the critical speeding up. Paradoxically, we prepare these states by going away from the critical point which allows for the speed-up. We apply the protocol to the paradigmatic quantum Rabi model and its classical oscillator limit as well as the Lipkin-Meshkov-Glick model. Subsequently, we discuss the application of the adiabatic speed-up protocol in quantum metrology and compare its performance with critical quantum metrology. We show that critical quantum metrology with the Lipkin-Meshkov-Glick model cannot even overcome the standard quantum limit, and we argue that, even though critical metrology protocols can overcome it in some cases, critical metrology is a suboptimal metrological strategy. Finally, we conclude that systems exhibiting a phase transition are indeed interesting from the viewpoint of quantum technologies; however, it may not be the critical point that should attract the most attention.

Critical speeding up as an early warning signal of stochastic regime shifts

The use of critical slowing down as an early warning indicator for regime switching in observations from noisy dynamical systems and models has been widely studied and implemented in recent years. Some systems, however, have been shown to avoid critical slowing down prior to a transition between equilibria (Ditlevsen and Johnsen, Geophysical Research Letters, 37(19), 2010; Hastings and Wysham, Ecol Lett 13(4):464–472, 2010). Possible explanations include a non-smooth potential driving the dynamic (Hastings and Wysham, Ecol Lett 13(4):464–472, 2010) or large perturbations driving the system out of the initial basin of attraction (Boettiger and Batt 2020). In this paper, we discuss a phenomenon analogous to critical slowing down, where a slow parameter change leads to a high likelihood of a regime shift and creates signature warning signs in the statistics of the process’s sample paths. This effect, which we dub “critical speeding up,” is demonstrated using a simple population model exhibiting an Allee effect. In short, if a basin of attraction is compressed under a parameter change then the potential well steepens, leading to a drop in the time series’ variance and autocorrelation; precisely the opposite warning signs exhibited by critical slowing down. The fact that either falling or rising variance / autocorrelation can indicate imminent state change should underline the need for reliable modeling of any empirical system where one desires to forecast regime change.

Activated drops: Self-excited oscillation, critical speeding and noisy transport

A small drop (∼10μl) of water exhibits critical speeding dynamics on an inclined super-hydrophobic pillared surface, in that it moves very slowly at first, but speeds up rapidly after a critical velocity is reached. During the mobile phase, some of the natural vibration modes of the drops are self-excited on a pillared surface, but not on a smooth hydrophobic surface. Additional experiments were carried out with glycerin and the solutions of water and glycerin that allowed their density and surface tension to be held more or less constant, while their viscosity could be varied. The terminal velocities of these drops following the critical speeding did not exhibit the expected decrease with increasing viscosity, but showed a highly non-linear behavior, exhibiting a maximum at an intermediate viscosity. Any of these drops moves steadily on a sub-critically inclined pillared substrate when it is subjected to a mechanical noise, the dynamics of which is remarkably similar to that obtained from another designed experiment in which the drops were made to cross a physical barrier assisted by an external noise. The dynamics of the low viscosity (1mPa s to 5.3mPa s) drops are amenable to a Kramers-like transition rate in the low friction limit, although the overall dynamics is found to be sub-Arrhenius. This work highlights the importance of the fluctuation of a drop that is either self-excited or that induced by an external noise in its motion on a surface.

The effects of feeding on the swimming performance and metabolic response of juvenile southern catfish, Silurus meridionalis, acclimated at different temperatures

To test whether the effects of feeding on swimming performance vary with acclimation temperature in juvenile southern catfish (Silurus meridionalis), we investigated the specific dynamic action (SDA) and swimming performance of fasting and feeding fish at acclimation temperatures of 15, 21, 27, and 33 degrees C. Feeding had no effect on the critical swimming speeding (U(crit)) of fish acclimated at 15 degrees C (p=0.66), whereas it elicited a 12.04, 18.70, and 20.98% decrease in U(crit) for fish acclimated at 21, 27 and 33 degrees C, respectively (p<0.05). Both the maximal postprandial oxygen consumption rate (VO2peak) and the active metabolic rate (VO2active, maximal aerobic sustainable metabolic rate of fasting fish) increased significantly with temperature (p<0.05). The postprandial maximum oxygen consumption rates during swimming (VO2max) were higher than the VO2active of fasting fish at all temperature groups (p<0.05). The VO2max increased with increasing temperature, but the relative residual metabolic scope (VO2max-VO2peak) during swimming decreased with increasing in temperature. The present study showed that the impairment of postprandial swimming performance increased with increasing temperature due to the unparalleled changes in the catfish's central cardio-respiratory, peripheral digestive and locomotory capacities. The different metabolic strategies of juvenile southern catfish at different temperatures may relate to changes in oxygen demand, imbalances in ion fluxes and dissolved oxygen levels with changes in temperature.

Critical phenomena in microgravity: Past, present, and future

This review provides an overview of the progress in using the low-gravity environment of space to explore critical phenomena and test modern theoretical predictions. Gravity-induced variations in the hydrostatic pressure and the resulting density gradients adversely affect ground-based measurements near fluid critical points. Performing measurements in a low-gravity environment can significantly reduce these difficulties. A number of significant experiments have been performed in low-Earth orbit. Experiments near the lambda transition in liquid helium explored the regime of large correlation lengths and tested the theoretical predictions to a level of precision that could not be obtained on Earth. Other studies have validated theoretical predictions for the divergence in the viscosity as well as the unexpected critical speeding up of the thermal equilibrium process in pure fluids near the liquid-gas critical point. We describe the scientific content of previously flown low-gravity investigations of critical phenomena as well as those in the development stage, and associated ground-based work.

Two typical time scales of the piston effect

The existence of a fourth mode of heat transfer near the critical point, named the piston effect, has been known for more than a decade. The typical time scale of temperature relaxation due to this effect was first predicted by Onuki [Phys. Rev A 41, 2256 (1990)], and this author's formula has been extensively used since then to predict the thermal behavior of near-critical fluids. Recent studies, however, pointed out that the critical divergence of the bulk viscosity could have a strong influence on piston-effect-related processes. In this paper, we conduct a theoretical analysis of near-critical temperature relaxation showing that the piston effect is not governed by one (as was until now believed) but by two typical time scales. These two time scales exhibit antagonistic asymptotic behaviors as the critical point is approached: while the classical piston-effect time scale (as predicted by Onuki ) goes to zero at the critical point (critical speeding up), the second time scale (related to bulk viscosity) goes to infinity (critical slowing down). Based on this property, an alternative method for measuring near-critical bulk viscosity is proposed.

Electron spin resonance and relaxation studies of double-layered manganites

Electronic properties of ${\mathrm{La}}_{2\ensuremath{-}2x}{\mathrm{Sr}}_{1+2x}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ $(x=0.4$ and 0.5) single crystals are studied by electron spin resonance (ESR) and spin-lattice relaxation time measurements. Spin susceptibility $\ensuremath{\chi}(T)$ determined from the ESR signal intensity and macroscopically measured static-susceptibility data are in good agreement, thus ESR detects all spin species in the system. In both compounds, the ESR spectra contain a single, nearly isotropic Lorentzian line associated with the exchange coupled ${\mathrm{Mn}}^{3+}$ and ${\mathrm{Mn}}^{4+}$ ions. For the $x=0.5$ compound, the fingerprints of charge ordering (CO) transition at ${T}_{\mathrm{CO}}=226\mathrm{K}$ are detected. In addition, strongly anisotropic ferromagnetic resonance spectra are found in both materials, suggesting the presence of extrinsic ferromagnetic phases. For $x=0.4,$ the longitudinal relaxation time ${T}_{1}$ and the transversal relaxation time ${T}_{2}$ are equal around room temperature that is a sign of exchange narrowing. The ${T}_{1}{/T}_{2}$ ratio increases to about 5 approaching the Curie temperature ${T}_{C}=126\mathrm{K}.$ No sign of critical speeding up of ${T}_{1}$ is detected. Instead, the slowing down of the relaxation rate takes place and ${T}_{1}$ is proportional to $T\ensuremath{\chi}(T).$ This is attributed to the freezing of short-range magnetic correlations in the external field.

Rapid thermal relaxation in near-critical fluids and critical speeding up: discrepancies caused by boundary effects

We present one-dimensional numerical simulations reporting the temperature evolution of a pure fluid subjected to heating near its liquid-vapor critical point under weightlessness. In this model, thermal boundary conditions are imposed at the outer edges of the solids in contact with the fluid. Our investigations concern the thermal conditions at the edges of the fluid and their consequences on the fluid's global response. The results for piston effect heating are shown to be significantly affected by the simulation of the solid boundaries. Concerning critical speeding up, it is even found that taking conductive solids into account can make the bulk fluid temperature change in a way opposed to that predicted in their absence.

Simulation numérique de l'Effet Piston avec prise en compte des échanges thermiques pariétaux

The Piston Effect and heat transfer at the boundaries of the near-critical fluid are modelled together. At the non-heated wall, the conditions at the edge of the fluid are close to a thermostat. Heat diffusion into the heating solid leads to much lower heating of the fluid by Piston Effect. This discrepancy increases when moving away from the critical point. Regarding the critical speeding up, our results do not agree with the theory.

The effect of bulk viscosity on temperature relaxation near the critical point

The heat transfer near the critical point is governed not only by diffusion, convection, and radiation, but also by a thermomechanical coupling called the Piston Effect. This fourth mode of heat transfer is responsible for the so-called critical speeding up, which contradicts the first expectation of a critical slowing down of the heat diffusion. So far, the viscosity has been neglected in all the existing theoretical models of the Piston Effect. The aim of this paper is to present a comprehensive model of the Piston Effect, written for a real-fluid equation of state and including the critical divergence of the bulk viscosity. It is shown in particular that when the critical point is neared, the heat transfer goes faster and faster, until a point is reached where viscous stresses are no longer negligible. When going closer to the critical point, the heat transfer then slows down again; a regime of critical slowing down is entered. This phenomenon should happen sufficiently far from the critical temperature to allow experimental checks. Moreover, it could be used as an indirect way of measuring the critical divergence of the bulk viscosity.

Acoustic saturation of the critical speeding up

It has recently been found that the heat transfer in the vicinity of the liquid-vapor critical point is governed by a fourth heat transfer process called Piston Effect. This effect has been described as the strong expansion of a thin initial thermal boundary layer (due to the diverging compressibility of near-critical fluids), driving in the rest of the fluid a set of compression waves which adiabatically increase the temperature, on a shorter and shorter time-scale as the critical point is approached (Critical Speeding Up). In the present work, matched asymptotic descriptions techniques applied to the Navier-Stokes equations show that very near the critical point, a new regime of heat transfer appears where thermal equilibration is governed only by acoustic phenomena. In this new regime, temperature relaxation takes place within a few acoustic typical times only, showing that the Piston-Effect mechanism can be as fast as the acoustic propagation, but no faster. This phenomenon is called the Acoustic Saturation of the Piston Effect.

Dynamic temperature propagation in a pure fluid near its critical point observed under microgravity during the German Spacelab Mission D-2.

Diverging thermodynamic and transport properties of a near critical fluid have significant effects on heat and mass transport; the effects are still under investigation. These effects become visible especially in experiments carried out under microgravity conditions because in the absence of gravity, buoyancy induced convection is suppressed. According to the ``critical slowing down'' hypothesis, even longer thermal relaxation times are predicted for experiments under reduced gravity conditions than for that on earth. Early experiments under microgravity showed a fast dynamic temperature propagation. More recently, this effect has been called the ``piston effect,'' or ``critical speeding up.'' The final thermodynamic equilibration of temperature and density is still very slow according to a diffusion process of heat and mass. During the German Spacelab Mission D-2 in 1993, the calorimeter HPT-HYDRA, which was designed for measurements of the specific heat at constant volume ${\mathit{c}}_{\mathit{V}}$, was also used for investigations of the dynamic temperature propagation. The spherical cell filled with ${\mathrm{SF}}_{6}$ at critical density was pulsewise heated, which caused a temperature increase in the fluid of about 10 mK. The temperature propagation in the fluid was monitored with a resolution of 10 \ensuremath{\mu}K at three different radial positions in the fluid and at the wall of the cell. The experiments were carried out at 39 different temperatures in the region of 0.03 K\ensuremath{\Vert}T-${\mathit{T}}_{\mathit{C}}$\ensuremath{\Vert}5.25 K. Approaching the critical temperature ${\mathit{T}}_{\mathit{C}}$, the temperature difference between the wall and the fluid decreases to zero in both the one phase and two phase regions. The experimental results in both the one phase region and two phase regions are in remarkably good agreement with numerical simulations and confirm the fast temperature propagation, which is predicted by the ``piston effect'' model quantitatively. In addition the phase separation process during cooling is explained with this model.

Temperature propagation in near-critical fluids prior to and during phase separation.

Temperature propagation in a near-critical fluid sample (${\mathrm{SF}}_{6}$) is experimentally studied under reduced gravity in space. Onset of phase separation is indicated by the appearance of a spinodal scattering ring. Critical speeding up of temperature equilibration prior to phase separation and markedly slowed-down temperature equilibration during phase separation are observed.

Critical speeding up observed.

The extreme compressibility of a fluid near its liquid-vapor critical point significantly alters its dynamic response to temperature changes. Adiabatic processes allow a fluid of constant volume to thermalize in a matter of seconds, compared with the hours or days that thermal diffusion would require. Moreover, the adiabatic transient is faster as the temperature of the fluid approaches the critical temperature. We present experimental measurements of turbidity in critical xenon which show the fast time scale of the adiabatic transient and the phenomenon of critical speeding up.

Critical speeding up in pure fluids.

We show how the extreme compressibility of a pure fluid near its critical point significantly affects its bulk dynamic response to temperature changes through adiabatic processes. We develop equations that describe the dynamics in the absence of gravity, and illustrate the magnitude of the effect with numerical solutions in one dimension. The results are remarkable: 5 mm of critical xenon, quenched from 20 to 10 mK above its critical temperature, cools by over 99% in less than 5 sec. Moreover, adiabatic cooling is faster when the fluid is closer to the critical point.