Frequency Fluctuations Research Articles

Non-linear MHD investigations of high-confinement regimes without type-I ELMs in ASDEX Upgrade and JT-60SA

Large edge localised modes (ELMs) would cause an unacceptable reduction of material lifetime in future large tokamaks due to the significant amount of energy expelled from the magnetically confined region towards the plasma facing components. Thoroughly validated modelling of regimes devoid of large ELMs is crucial as it may then provide predictive insights prior to tokamak operation and design. This paper describes recent efforts pursued with the non-linear extended MHD code JOREK in the modelling of three scenarios without large ELMs: quiescent H-mode (QH-mode), quasi-continuous exhaust regime (QCE regime), and the enhanced D-alpha H-mode (EDA H-mode). For each of these regimes, the non-linear dynamics observed in the simulations are detailed and compared to experimental observations of the underlying instabilities of each regime (edge harmonic oscillation for QH-mode, small ELMs for QCE regime, and quasi-coherent mode for EDA H-mode). For QH-mode, the kink-peeling mode is found to govern the dynamics and a transition to a large ELM is obtained above the same density threshold as in the modelled experiment. For the QCE regime and EDA H-mode, resistive peeling–ballooning modes dominate and pedestal fluctuation frequencies correspond well to experimental observations. The dominant mechanisms for the excitation and suppression of these instabilities are presented and their influence on simulation dynamics is shown. Finally, predictive simulations of edge instabilities at different values of plasma resistivity in a 4.60 MA scenario with low edge safety factor in JT-60SA are presented.

Load Frequency Control Strategy of Interconnected Power System Based on Tube DMPC

Solar thermal power generation shares technical characteristics with traditional thermal power generation. This enables rapid adjustment of turbine generator output to meet the demands of the power grid load for frequency modulation. However, fluctuations in light intensity lead to variations in interconnected power system parameters, posing challenges for load frequency control (LFC). In this study, we propose a Robust Distributed Model Predictive Control (RDMPC) method. This method achieves system trajectory tracking by solving the nominal system optimization problem. It also flexibly adjusts the weights of different Tube models to determine the optimal control law using the standard Tube online combination with various gain values. Additionally, we incorporate the states of adjacent areas into the feedback control law to achieve effective coordination between these areas. Using MATLAB/Simulink, we simulated the power system in two areas. Compared to standard Tube DMPC, our proposed algorithm effectively mitigates the impact of light intensity, enhances adjustment speed, reduces frequency fluctuation, and demonstrates superior control effectiveness.

Bulimia nervosa selectively reshapes the structure and intrinsic function of anterior insula subregions associated with cognition-emotion integration

BackgroundExisting evidence suggests that anterior insula plays a crucial role in cognitive control and emotional regulation and is implicated in the onset and maintenance of bulimia nervosa (BN). However, it remains unclear how structural and functional abnormalities in specific subregions of anterior insula contribute to BN. MethodsIn this study, we analyzed structural MRI and resting-state functional MRI data from 54 BN patients and 56 healthy controls (HCs). We conducted voxel-based morphometry, amplitude of low frequency fluctuation (conventional band: 0.01–0.08 Hz, slow-5: 0.01–0.027 Hz) and seed-based whole-brain functional connectivity (FC) analysis of the anterior insula subregions for both groups. Additionally, we investigated the correlation between neuroimaging findings and clinical characteristics in the BN group. ResultsOur findings revealed that BN patients exhibited reduced gray matter volume in the right dorsal anterior insula (dAI) and bilateral ventral anterior insula (vAI) and demonstrated decreased ALFF in slow-5 band of bilateral dAI. The BN group also showed increased FC between bilateral dAI and precuneus or right superior frontal gyri which significantly correlated with the severity of BN or its key symptom. In addition, the decreased FC between bilateral vAI and anterior cingulate and paracingulate gyri and/or median cingulate and paracingulate gyri were both significantly correlated with the severity and its restrained eating behavior. ConclusionsOur findings further indicate that the functional separation of anterior insula subregions may underlie the pathophysiology of BN. Notably, the vAI associated with emotional processing may serve as a promising neuroimaging biomarker which could inform therapeutic strategy.

Suppressing Thermal Noise to Sub-Millikelvin Level in a Single-Spin Quantum System Using Realtime Frequency Tracking.

A single nitrogen-vacancy (NV) center in a diamond can be used as a nanoscale sensor for magnetic field, electric field or nuclear spins. Due to its low photon detection efficiency, such sensing processes often take a long time, suffering from an electron spin resonance (ESR) frequency fluctuation induced by the time-varying thermal perturbations noise. Thus, suppressing the thermal noise is the fundamental way to enhance single-sensor performance, which is typically achieved by utilizing a thermal control protocol with a complicated and highly costly apparatus if a millikelvin-level stabilization is required. Here, we analyze the real-time thermal drift and utilize an active way to alternately track the single-spin ESR frequency drift in the experiment. Using this method, we achieve a temperature stabilization effect equivalent to sub-millikelvin (0.8 mK) level with no extra environmental thermal control, and the spin-state readout contrast is significantly improved in long-lasting experiments. This method holds broad applicability for NV-based single-spin experiments and harbors the potential for prospective expansion into diverse nanoscale quantum sensing domains.

Robust and fast microwave-driven quantum logic for trapped-ion qubits

Microwave-driven logic is a promising alternative to laser control in scaling trapped-ion based quantum processors. We implement Mølmer-Sørensen two-qubit gates on 43Ca+ hyperfine clock qubits in a cryogenic (≈25 K) surface trap, driven by near-field microwaves. We achieve gate durations of 154 µs [with 1.0(2)% error] and 331 µs [0.5(1)% error], which approaches the performance of typical laser-driven gates. In the 331 µs gate, we demonstrate a Walsh-modulated dynamical decoupling scheme which suppresses errors due to fluctuations in the qubit frequency as well as imperfections in the decoupling drive itself. Published by the American Physical Society 2024

Evaluating High-Frequency Fluctuations And Its Effect On Hemodynamics At Varying Heart Rates In Intracranial Aneurysms Via 4D PTV

Hemodynamics have been shown to affect the growth and rupture of intracranial aneurysms (IA). Studies have increasingly reported the presence of high frequency velocity fluctuations in aneurysms. However, it remains undetermined how transient physiological factors like heart rate and inflow blood waveform amplitude affect the hemodynamic parameters and high frequency fluctuations in and around an IA, as well as the risk of IA progression. In this work, we address this question using a volumetric particle tracking velocimetry (PTV) study where a patient-specific right middle cerebral artery (R MCA) aneurysm model was subjected to two heart rate conditions (60 bpm and 137 bpm). The input waveform amplitude for the 137 bpm case was increased by a factor of 1.6 to be physiologically consistent. Captured PTV images were processed using the Shake-the-Box (STB) workflow. Flow parameters including velocity, vorticity, and turbulent kinetic energy (TKE) were evaluated. To evaluate the presence of high frequency fluctuations, a direct numerical simulation (DNS) using the R MCA geometry and same two heart rate cases was conducted and a method for use with STB particle tracks was proposed. As compared to the 60 bpm case, the 137 bpm case had a more concentrated inflow jet that extended further into the aneurysmal sac and a stronger and larger vortical flow structure in the aneurysmal sac. The 60 bpm case maintained a region of slightly elevated TKE at the main junction point where the aneurysmal sac and all vessels merge. In the 137 bpm case, TKE in this region was dramatically higher. Using probe points, the DNS data revealed high frequency velocity fluctuations in an outflow vessel during the deceleration phase of the cycle. Notably, these fluctuations were only observed for the 137 bpm case. For both the DNS and STB data, high frequency components were more prevalent and stronger outside of the aneurysmal sac as opposed to inside the aneurysmal sac. Overall, these results suggest that changes in heart rate induce changes to the flow structure and can induce significant increases in TKE and high frequency fluctuations. Based on our findings, a higher heart rate would be expected to yield a flow field more akin to IA progression. The specific correlation between the high frequency components computed using our proposed STB-based method and the high frequency fluctuations in the flow field could not be well understood. Thus, additional analysis and development of this method is needed.

Effect of tip clearance on non-synchronous propagating flow disturbances of compressor rotors under high aerodynamic loading conditions

The complex tip flow instability and its induced non-synchronous vibration have become significant challenges, especially as aerodynamic loading continues to increase. This study investigates the effects of tip clearance on non-synchronous propagating flow disturbances of compressor rotors under high aerodynamic loading conditions by conducting full-annulus unsteady numerical simulations with three typical tip clearance values for a 1-1/2 stage transonic compressor. The non-synchronous aerodynamic excitation frequency, circumferential mode characteristics, and annular unstable flow structures are analyzed under near stall conditions. The results show that the total pressure ratio and normalized mass flow parameters first increase and then decrease as the tip clearance increases from 0.5%C (where C represents the tip chord length) to 2%C under high aerodynamic loading conditions, instead of constantly decreasing. For the 0.5%C tip clearance case, the traveling large-scale tornado-like separation vortices cause a low non-synchronous aerodynamic excitation frequency and severe pressure fluctuations. The periodic shedding and reattachment processes of the rotor blades separated by 2 – 3 pitches result in 19 dominant mode orders in the circumferential direction. As the tip clearance increases from 1%C to 2%C, the difference of tip flow structures in each blade passage is significantly weakened, and the dominant mode order of the disturbance is equal to the rotor blade-passing number. The pressure fluctuation is mainly caused by cross-channel tip leakage flow, and the aerodynamic excitation frequency exhibits evident broadband hump characteristics, which has been reported as a rotating instability phenomenon.

Inertia–Active Power Filter Design Based on Repetitive Control

The advent of distributed generation has brought with it a plethora of challenges for the nascent power systems that are being deployed on a large scale. Firstly, the majority of power electronic converters connected to the grid are in current source mode, which results in a lack of inertia and an inability to provide effective inertia or achieve damping support during fluctuations in grid frequency. Secondly, the issue of power quality, caused by the presence of harmonics, is becoming increasingly severe. This is particularly problematic in microgrids or systems with high line impedance, where harmonics can be amplified, thereby further compromising the stability of the power system. To address the deficiency in system inertia, numerous scholars are currently utilizing grid-forming (GFM) technology to achieve virtual inertia. In order to address the issue of system harmonics, it is possible to install active power filter (APF) devices at the point of common coupling (PCC), which serve to mitigate the effects of harmonics. This paper puts forth a proposal for the implementation of an APF with virtual inertia, based on PR + RC composite control. This composite control mechanism serves to enhance the harmonic suppression capabilities of the APF. The introduction of a frequency droop enables the capacitor voltage amplitude to be adjusted during fluctuations in system frequency, thereby achieving virtual inertia and providing active support for system frequency. The experimental results demonstrate that this strategy not only reduces the total harmonic distortion (THD) by 13% in comparison to PI control, indicating excellent harmonic suppression performance, but also allows the system to be inert, achieving positive results in suppressing frequency fluctuations during transients.

Multiple cognition associated multimodal brain networks in major depressive disorder.

Major depressive disorder frequently leads to cognitive impairments, significantly affecting patients' quality of life. However, the neurobiological mechanisms underlying cognitive deficits remain unclear. This study aimed to explore multimodal imaging biomarkers associated with cognitive function in major depressive disorder. Five cognitive scores (sustained attention, visual recognition memory, pattern recognition memory, executive function, and working memory) were used as references to guide the fusion of gray matter volume and amplitude of the low frequency fluctuation. Social function was assessed after 2yr. Linear regression analysis was performed to identify brain features that were associated with social function of patients with major depressive disorder. Finally, we included 131 major depressive disorder and 145 healthy controls. A multimodal frontal-insula-occipital network associated with sustained attention was found to be associated with social functioning in major depressive disorders. Analysis across different cognitive domains revealed that gray matter volume exhibited greater sensitivity to differences, while amplitude of the low frequency fluctuation consistently decreased in the right temporal-occipital-hippocampus circuit. The consistent functional changes across the 5 cognitive domains were related to symptom severity. Overall, these findings provide insights into biomarkers associated with multiple cognitive domains in major depressive disorder. These results may contribute to the development of effective treatment targeting cognitive deficits and social function.

Adaptive VSG-Based power allocation strategy for hybrid energy storage

Abstract Aiming at the stochasticity of photovoltaic output and the problem of power, voltage, and frequency fluctuation caused by the lack of system inertia and damping parameters, a photovoltaic storage microgrid is constructed as a research object. Firstly, a virtual synchronous motor VSG is used to control the grid-connected inverter and to improve the dynamic performance of the system further. The inertia and damping parameters of the VSG are adjusted adaptively. Secondly, the hybrid energy storage device composed of a supercapacitor and battery adopts a second-order filter to avoid the integrating effect of the first-order filter on the high-frequency power and improve the poor performance of the first-order filter at the cutoff frequency to improve the accuracy of power distribution. Moreover, two negative feedback links of power error are added in the power distribution link to correct the reference power of the energy storage device, which further improves the power tracking effect of the energy storage system. Finally, the effectiveness of the above strategy is verified by a Matlab simulation session.

The spiking output of the mouse olfactory bulb encodes large-scale temporal features of natural odor environments.

In natural odor environments, odor travels in plumes. Odor concentration dynamics change in characteristic ways across the width and length of a plume. Thus, spatiotemporal dynamics of plumes have informative features for animals navigating to an odor source. Population activity in the olfactory bulb (OB) has been shown to follow odor concentration across plumes to a moderate degree (Lewis et al., 2021). However, it is unknown whether the ability to follow plume dynamics is driven by individual cells or whether it emerges at the population level. Previous research has explored the responses of individual OB cells to isolated features of plumes, but it is difficult to adequately sample the full feature space of plumes as it is still undetermined which features navigating mice employ during olfactory guided search. Here we released odor from an upwind odor source and simultaneously recorded both odor concentration dynamics and cellular response dynamics in awake, head-fixed mice. We found that longer timescale features of odor concentration dynamics were encoded at both the cellular and population level. At the cellular level, responses were elicited at the beginning of the plume for each trial, signaling plume onset. Plumes with high odor concentration elicited responses at the end of the plume, signaling plume offset. Although cellular level tracking of plume dynamics was observed to be weak, we found that at the population level, OB activity distinguished whiffs and blanks (accurately detected odor presence versus absence) throughout the duration of a plume. Even ~20 OB cells were enough to accurately discern odor presence throughout a plume. Our findings indicate that the full range of odor concentration dynamics and high frequency fluctuations are not encoded by OB spiking activity. Instead, relatively lower-frequency temporal features of plumes, such as plume onset, plume offset, whiffs, and blanks, are represented in the OB.

Correlations versus noise in the NFT market.

The non-fungible token (NFT) market emerges as a recent trading innovation leveraging blockchain technology, mirroring the dynamics of the cryptocurrency market. The current study is based on the capitalization changes and transaction volumes across a large number of token collections on the Ethereum platform. In order to deepen the understanding of the market dynamics, the inter-collection dependencies are examined by using the multivariate formalism of detrended correlation coefficient and correlation matrix. It appears that correlation strength is lower here than that observed in previously studied markets. Consequently, the eigenvalue spectra of the correlation matrix more closely follow the Marchenko-Pastur distribution, still, some departures indicating the existence of correlations remain. The comparison of results obtained from the correlation matrix built from the Pearson coefficients and, independently, from the detrended cross-correlation coefficients suggests that the global correlations in the NFT market arise from higher frequency fluctuations. Corresponding minimal spanning trees for capitalization variability exhibit a scale-free character while, for the number of transactions, they are somewhat more decentralized.

Influence of polymer types on the performance of piezoelectric ceramic/polymer composite arrays based on 1–3 type structure

Piezoelectric ceramic/polymer composite array elements based on a 1–3 structure are widely used in high-frequency transducers. This study selected three commonly used polymers (epoxy resin, silicone rubber, and polyurethane) to prepare three types of piezoelectric ceramic/polymer composite array elements. These elements were tested using a concentric ring sampling scheme from the inside to the outside and analyzed through finite element simulation to explain the performance differences in piezoelectric ceramic/polymer composite arrays. The test results demonstrate that compared to composite arrays made with piezoelectric ceramic and epoxy resin or polyurethane, piezoelectric ceramic/silicone rubber composite arrays exhibit superior resonance characteristics and consistency. The resonance frequency fluctuation is within 6 kHz, with a maximum deviation factor of 1.22 %, and an average effective electromechanical coupling factor of up to 0.69. The experimental results also show significant performance differences between edge and non-edge elements, suggesting that in practical applications, edge elements of the array can be set as dummy elements to ensure array consistency.

Fluctuating pressure gradients and corrugated surfaces effects on wind turbines power output

This paper investigates the effect of corrugated surfaces on the wind turbines power output for both laminar and turbulent flows. Conservation principles including continuity and momentum equations, wind turbine power equations, and the corrugated surface equation have been implemented to build up a theoretical model then which has been solved using MATLAB. This model simulates wind turbines power output and analyzes several case studies implementing different parameters such as air pressure wave amplitude (Po), air wave fluctuation frequency (n), and wind layer turbulence (b). Also, different complex terrains in two main scenarios representing two different positions (X) of the wind turbine are analyzed. This analysis indicates the importance of wind turbines micro siting. In addition, it is found that increasing the pressure ratio increased wind turbine power output, while increasing the frequency decreased the power ratio of the wind turbines for both laminar and turbulent flow conditions. Increasing turbulence for the turbulent model increased the power ratio.

Cyclic Electron Flow Alleviates the Stress of Light Fluctuation on Soybean Photosynthesis

Crops often face light intensity fluctuations in natural settings. Intercropping is widely used to improve crop yield and resource utilization worldwide, but crops suffer from high-frequency and high-intensity light fluctuations due to mutual crop influence. Soybean is an important legume crop and is often intercropped with other crops, but little is known about soybean’s response to light fluctuation environments. Herein, three fluctuation frequencies (1, 10, and 20 min/cycle) were used to analyze soybean photosynthesis responses by measuring leaf growth, chlorophyll content, gas exchange, and electron transfer. Our data revealed that faster fluctuation frequencies led to the stronger suppression of soybean morphology and photosynthesis, with significant reductions of 31.31% and 21.58%, respectively. Damage to photosystems II (PSII) and I (PSI) also intensified, with significant decreases of 18.52% and 18.38% in their effective quantum yields Y(II) and Y(I). Additionally, increased fluctuation frequency exacerbated the consumption of the plastoquinone pool and linear electron flow but enhanced the cyclic electron flow across the thylakoid membrane and, thus, increased heat dissipation in PSII. Our findings indicate that an increased fluctuation frequency inflicted more severe damage on the soybean photosynthesis system. However, PSI-enhanced CEF improved NPQ and coordinated photoprotection to some extent.

In Ukrainian

Brownian motors belong to the class of nanoscale devices that use the thermal noise of the environment as one of the necessary components in the mechanism of their operation. Today, there are a lot of practical implementations of such nanomachines, both inorganic, fairly simple mechanisms produced artificially, and more complex ones created from separate biological components available at the cellular level. One of the options for implementing the mechanism of straightening the chaotic thermal noise of the environment into unidirectional motion is the presence of a motor particle in the field of action of an asymmetric periodic stationary potential, which undergoes certain small disturbances (fluctuations) periodically over time. To describe such asymmetric one-dimensional structures (for example, dipole chains or fibers of the cytoskeleton) in the theory of Brownian motors, two model potentials are most often used: piecewise linear sawtooth and double sinusoidal. In this work, within the framework of the approximation of small fluctuations, a model of a pulsating Brownian motor with a stationary double sinusoidal potential and a disturbing small harmonic signal is considered. A new method of parametrization of such a problem is proposed, which allows to separate the contributions from various factors affecting the operation of the ratchet, and the numerical procedure for calculating the average speed of the directional movement of nanoparticles for the selected type of model potentials is specified. A number of numerical dependences of the average speed on the main parameters of the system were obtained. Peculiarities of the behavior of the motor as dependent on the parameter responsible for asymmetry and the number of potential wells on the spatial period of the stationary potential have been investigated. It is shown that the direction of the generated flux of nanoparticles depends not only on the phase shift between the stationary and fluctuating components of the potential, but also on the temperature of the system and the frequency of fluctuations, i.e., a possibility of temperature-frequency control of the direction of movement in the considered model has been found. Diagrams have been constructed that allow you to choose the ratio between the parameters of the nanomotor to create a flux of particles in the desired direction.

Aberrant associations between neuronal resting-state fluctuations and working memory-induced activity in major depressive disorder.

Previous investigations have revealed performance deficits and altered neural processes during working-memory (WM) tasks in major depressive disorder (MDD). While most of these studies used task-based functional magnetic resonance imaging (fMRI), there is an increasing interest in resting-state fMRI to characterize aberrant network dynamics involved in this and other MDD-associated symptoms. It has been proposed that activity during the resting-state represents characteristics of brain-wide functional organization, which could be highly relevant for the efficient execution of cognitive tasks. However, the dynamics linking resting-state properties and task-evoked activity remain poorly understood. Therefore, the present study investigated the association between spontaneous activity as indicated by the amplitude of low frequency fluctuations (ALFF) at rest and activity during an emotional n-back task. 60 patients diagnosed with an acute MDD episode, and 52 healthy controls underwent the fMRI scanning procedure. Within both groups, positive correlations between spontaneous activity at rest and task-activation were found in core regions of the central-executive network (CEN), whereas spontaneous activity correlated negatively with task-deactivation in regions of the default mode network (DMN). Compared to healthy controls, patients showed a decreased rest-task correlation in the left prefrontal cortex (CEN) and an increased negative correlation in the precuneus/posterior cingulate cortex (DMN). Interestingly, no significant group-differences within those regions were found solely at rest or during the task. The results underpin the potential value and importance of resting-state markers for the understanding of dysfunctional network dynamics and neural substrates of cognitive processing.

Versatile, fast, and accurate frequency excursions with a semiconductor laser

Achieving accurate arbitrary frequency excursions with a laser can be quite a technical challenge, especially when steep slopes (GHz/µs) are required, due to both deterministic and stochastic frequency fluctuations. In this work we present a multistage correction combining four techniques: pre-distorsion of the laser modulation, iterative correction, opto-electronic feedback loop, and feed-forward correction. This combination allows us not only to compensate for the non-instantaneous response of the laser to an input modulation but also to correct in real time the stochastic frequency fluctuations. We implement this multistage architecture on a commercial DBR laser and verify its efficiency, first, with monochromatic operation, and second, with highly demanding frequency excursions. We demonstrate that our multistage correction not only enables a strong reduction of the laser linewidth but also allows steep frequency excursions with a relative RMS frequency error well below 1% and a laser spectral purity consistently better than 100 kHz, even in the midst of gigahertz-scale frequency excursions.

VSG-LFC on multi-area power system under unsecured communication channel using hybrid trigger mechanism

This paper studies the frequency fluctuation problems of a multi-area power system with renewable energy sources (RESs) under denial-of-service (DoS) attacks. (i) Due to the decoupling of the RESs from power system using electronic devices, the RESs have no natural frequency response capability, which result in decreasing of entire power system equivalent inertia with large penetration of RESs. (ii) DoS attacks cause the insecurity of network communication, which can vanish data transmission and yield data packet dropout. To address the above issues, a virtual synchronous generator (VSG) incorporated with load frequency control (LFC) method (VSG-LFC) is proposed by introducing a hybrid-triggered mechanism (HTM) to (i) reduce the system sensitivity to the penetration level of RESs; (ii) compromise between frequency regulation performance and the reasonable usage of network resource under unsecured communication environments. Then, a switched system model is constructed considering non-identical DoS attack situations. Furthermore, theoretical analyses using Lyapunov functional related methods are carry out for asymptotical mean-square stability with H∞ performance on frequency regulation. Simulation evaluations of power system verify the effectiveness of this development. It shows that in a two-area power system frequency derivation performance indicators (IAE, ITAT, ISE) in Area1 are reduced by (82.996%, 86.273%, 85.823%) and in Area2 are reduces by (77.996%, 83.613%, 82.315%).

The Role of Precursor Disturbances on the Modulation of Western Pacific Tropical Cyclogenesis by the Madden‐Julian Oscillation

AbstractThe present study considers tropical cyclogenesis as a multi‐stage process in which pre‐cursor disturbances develop first and a fraction of them further strengthen to become a tropical cyclone (TC). Using this framework, we analyze the impact of Madden‐Julian oscillation (MJO)‐ associated anomalous large‐scale environmental conditions on the triggering of tropical convective clusters (TCCs)—a type of pre‐cursor disturbance—and the TCC‐to‐TC transition in the western Pacific. We find that, within the MJO's lifecycle, the modulation of the TCC frequency by the MJO drives TC genesis frequency anomalies earlier than the TCC‐to‐TC transition rate. Also, the fluctuation of TCC occurrence frequency is most strongly associated with the MJO's large‐scale ascent and relative humidity anomalies, while that of the transition of TCCs to a TC is mainly associated with the MJO's vorticity anomalies. Our results suggest the distinct roles of large‐scale environmental variables in different stages of tropical cyclogenesis.