Low-frequency Cycles Research Articles

Analysis of Global and Key PM2.5 Dynamic Mode Decomposition Based on the Koopman Method

Understanding the spatiotemporal dynamics of atmospheric PM2.5 concentration is highly challenging due to its evolution processes have complex and nonlinear patterns. Traditional mode decomposition methods struggle to accurately capture the mode features of PM2.5 concentrations. In this study, we utilized the global linearization capabilities of the Koopman method to analyze the hourly and daily spatiotemporal processes of PM2.5 concentration in the Beijing–Tianjin–Hebei (BTH) region from 2019 to 2021. This approach decomposes the data into the superposition of different spatial modes, revealing their hierarchical spatiotemporal structure and reconstructing the dynamic processes. The results show that PM2.5 concentrations exhibit high-frequency cycles of 12 and 24 h, as well as low-frequency cycles of 124 and 353 days, while also revealing spatiotemporal modes of growth, recession, and oscillation. The superposition of these modes enables the reconstruction of spatiotemporal dynamics with a mean absolute percentage error (MAPE) of only 0.6%. Unlike empirical mode decomposition (EMD), Koopman mode decomposition (KMD) method avoids mode aliasing and provides a clearer identification of global and key modes compared to wavelet analysis. These findings underscore the effectiveness of KMD method in analyzing and reconstructing the spatiotemporal dynamics of PM2.5 concentration, offering new insights into the understanding and reconstruction of other complex spatiotemporal phenomena.

Experimental investigation on the mode transition characteristics of a phase-change thermofluidic oscillator with external loads

Phase-change thermofluidic oscillator has drawn significant attention thanks to its low operating temperature, which is beneficial for recovering low-grade heat. The vapor–liquid coupling oscillation in the thermofluidic oscillator leads to complex non-linear mode transition phenomenon that affects the steady operation. In this work, the mode transition characteristics of a thermofluidic oscillator with external loads (i.e., a needle valve and a load reservoir) are experimentally investigated through bifurcation analysis. A low-order van der Pol model is employed to examine the effect of acoustic resistance on mode transition. Experimental results demonstrate that modifying the valve opening and load volume under a constant temperature difference can trigger bifurcation, resulting in high-frequency limit cycle, low-frequency limit cycle and quasi-periodic modes. The non-linear features of each mode are revealed through phase space and Poincaré section, with Neimark-Sacker bifurcation, second bifurcation and inverse Neimark-Sacker bifurcation observed. Steady-state performance of oscillator is then characterized under different oscillation modes. The maximum pressure amplitudes measured are 11.54 kPa during the high-frequency oscillation and 1.35 kPa during the low-frequency oscillation, while the maximum displacement amplitudes obtained are 45.5 mm during the high-frequency oscillation and 91.4 mm during the low-frequency oscillation. The oscillation modes can be adjusted by external load to maximize output performance. This study offers comprehensive guidelines for constructing phase-change thermofluidic oscillators.

Forecasting the solar modulation potential: Tests of time series models

This study analyzes the predictability of the solar modulation potential using time series models. Recently, new data sets for the modulation potential have become available, at daily, monthly, and annual resolutions. At lower frequencies, the data show the well-known 11-22-year cycle. Both the periodicity and amplitude vary over time. At higher resolutions, the probability distribution has heavy tails, while the data show the intermittent outliers characteristic of multifractal processes. Forecasting experiments are run using regressions in levels and differences, frequency domain methods, models with sinusoidal terms and neural networks. For the daily data, all the models achieve high degrees of accuracy at proximate horizons. As the horizon extends, accuracy falls away rapidly. At 27 days, corresponding to one solar rotation, a transfer function in differences achieves a more accurate forecast than either regressions or neural nets, since it is able to replicate the range of the data. At the annual resolution, both the regression and neural net predict well at horizons of 1 year. Again, forecast accuracy deteriorates sharply as the forecast horizon extends. At the monthly resolution, forecasting is problematic. The resolution is not low enough to bring out the low frequency cycles, but there is so much short-term dependence that the data are completely dominated by serial correlation. Any model incorporating proximate lags will generate inertial forecasts. Any model using lower frequency cyclical terms will be unable to pick up on near-term patterns. The forecasting skill of time series models appears limited to short horizons. The recommendation for forecasting over longer intervals is some combination of physics and statistical models.

The development and application of a novel E-commerce recommendation system used in electric power B2B sector.

The advent of the digital era has transformed E-commerce platforms into critical tools for industry, yet traditional recommendation systems often fall short in the specialized context of the electric power industry. These systems typically struggle with the industry's unique challenges, such as infrequent and high-stakes transactions, prolonged decision-making processes, and sparse data. This research has developed a novel recommendation engine tailored to these specific conditions, such as to handle the low frequency and long cycle nature of Business-to-Business (B2B) transactions. This approach includes algorithmic enhancements to better process and interpret the limited data available, and data pre-processing techniques designed to enrich the sparse datasets characteristic of this industry. This research also introduces a methodological innovation that integrates multi-dimensional data, combining user E-commerce activities, product specifics, and essential non-tendering information. The proposed engine employs advanced machine learning techniques to provide more accurate and relevant recommendations. The results demonstrate a marked improvement over traditional models, offering a more robust and effective tool for facilitating B2B transactions in the electric power industry. This research not only addresses the sector's unique challenges but also provides a blueprint for adapting recommendation systems to other industries with similar B2B characteristics.

INVESTIGATION OF CYCLIC PROPERTIES OF SOLAR AND GEOMAGNETIC ACTIVITIES: IMPLICATION FOR GLOBAL SURFACE TEMPERATURE VARIABILITY

The cyclic properties of solar-geomagnetic activity and global surface temperature have been investigated using trend, frequency and time-frequency analyses. Results reveal that on decadal-to-centennial timescales, low-frequency cycles in the half-century (~49 to 56 years per cycle) and Gleisberg (~99 to 114 years per cycle) range run in the background of the Schwabe (~9 to 11 years per cycle) as the dominant cycle of solar-geomagnetic activity. The only dominant cycle in the global surface temperature series is the half-century cycle and suggests a possible causal link between it and solar-geomagnetic activity phenomena. Evolution of the amplitudes of the cycles is such that the Schwabe and Gleisberg periods have increased in power from the beginning of the series until the mid-20th century after which they declined. The half-century cycle decreased in amplitude after 1800 to the present. For geomagnetic activity, the amplitude of Gleisberg cycle increased from the beginning of the series around 2000 while the amplitudes of Schwabe and half-century cycles declined within the same interval, except the Schwabe cycle which amplitude increased rapidly after 1980 to the present. For the global surface temperature, the amplitudes of Gleisberg and half-century cycles have continuously increased from the beginning of the series while Schwabe cycle oscillates with very low amplitudes until 1980 after which it increased slightly. Evolution of the amplitudes of cycles of solar-gemagnetic activity suggests a recovery from Maunder Minimum and decline into a grand epsode most likely to be a minimum.

Influence of the RF voltage amplitude on the space- and time-resolved properties of RF–LF dielectric barrier discharges in α–γ mode

This work reports the results of an experimental and modeling study on dual-frequency Ar–NH3 dielectric barrier discharges (DBDs) exhibiting the α–γ transition. A combination of space- and time-resolved optical absorption and emission spectroscopy is used to record spatio-temporal mappings of the Ar metastable number density, Ar 750.4 nm line emission intensity, and electron–Ar bremsstrahlung continuum emission intensity. With the increase of the radio frequency (RF) voltage amplitude in a 50 kHz–5 MHz DBD, maximum populations of Ar excited species (1s and 2p states, linked to the population of high-energy electrons) observed in the γ mode decrease and appear earlier in the low-frequency cycle. On the other hand, the density of the bulk electrons, monitored from the continuum emission intensity, increases, with a more prominent rise in the RF-α mode than in the γ regime. Such behaviors are consistent with the predictions of 1D fluid model and results from a decrease of the gas voltage required for self-maintenance of the cathode sheath in the γ breakdown.

Characterizing the mode transition features of a two-phase thermofluidic oscillator

Two-phase thermofluidic oscillator (TPTO) is a promising technology for harvesting low-grade heat. The multi-physics coupling within TPTO adds to the complex nonlinear dynamic characteristics that affect the operation, while not yet sufficiently analyzed. The mode transition features of a TPTO were experimentally characterized via nonlinear dynamic analysis. The bifurcations were studied with regards to the effect of temperature ratio and relative thermal penetration depth. Mass-spring and acoustic-electric analogy models were developed to predict the incommensurate resonant frequencies, which were then experimentally verified. The experimental results show that the TPTO experiences a series of bifurcations by increasing the temperature ratio, leading to the occurrence of oscillation modes such as the high-frequency limit cycle (HFLC) oscillation, quasiperiodic oscillation and low-frequency limit cycle (LFLC) oscillation. The high frequency in HFLC is approximately 3.1 Hz, which is the natural frequency of the TPTO. The low frequency close to 0.9 Hz in LFLC is the intrinsic frequency of the looped tube. The stability curves of the 2nd, 3rd, and 4th bifurcations show a trend of first growing and then dropping with the increasing relative thermal penetration depth of working fluid along the regenerator. The potential applications of TPTO are then discussed. This study offers insights for comprehending the mechanism of mode transition and provides recommendations for the design and operation of TPTO.

Re-Examining Bitcoin’s Price–Volume Relationship: A Time-Varying Spectral Analysis

This study employs continuous wavelet transforms to model the relationship between Bitcoin volume and prices across time and frequency space using daily data for the period between 17 September 2014 and 10 April 2023. The results show that Bitcoin price and volume have a long-term relationship at low frequency cycles mostly during the period after 2019. A statistically insignificant relationship between the price and volume of Bitcoin is observed prior to 2019 which coincides with a time of limited regulatory oversight of Bitcoin markets globally. Positive correlation is observed in the aftermath of this period, with stronger correlation recorded during and post the period of the Covid-19 pandemic. Furthermore, the findings reveal that fluc-tuations in the Bitcoin volume tends to affect the price at higher frequency synchronizations (short-term); whereas, at lower frequencies (long-term), a feedback loop is observed, whereby the price changes lead to alterations in the volume.

The impact of oil price shocks on the U.S. and Chinese stock markets: A quantitative structural analysis

This paper applies sign restrictions to identify oil structural shocks by imposing nonzero restrictions on the short-term price elasticity of oil supply. With the help of oil inventory data, flow supply, flow demand and speculative demand shocks in the global oil market are identified. Then, the impact of different kinds of oil price shocks on fluctuations of the U.S. and Chinese stock markets is examined and some insights from the perspective of frequency domain are provided. We observe that the U.S. and Chinese stock markets are extensively influenced by the three types of oil structural shocks. In particular, oil price shocks induced by speculation can significantly affect the performance of stock markets in both countries. Under the frequency domain, we notice that the flow demand shock is the most important driver of the variance in U.S. and Chinese stock returns and volatility, particularly at low and business cycle frequencies. Meanwhile, we note that short-term fluctuations in Chinese stock market returns and volatility are more vulnerable to speculative demand shocks. These analysis results are not only useful for policymakers to take targeted measures to deal with the impact of oil price shocks on the stock market, but also useful for investors to adjust their stock portfolios to achieve excess returns.

Ultrafast, room temperature rejuvenation of SiC Schottky diodes from forward current-induced degradation

In this work, we demonstrate the rejuvenation of Ti/4H-SiC Schottky barrier diodes after forward current-induced degradation, at room temperature and in a few seconds, by exploiting the physics of high-energy electron interactions with defects. The diodes were intentionally degraded to a 42% decrease in forward current and a 9% increase in leakage current through accelerated electrical stressing. The key feature of our proposed rejuvenation process is very high current density electrical pulsing with low frequency and duty cycle to suppress any temperature rise. The primary stimulus is, therefore, the electron wind force, which is derived from the loss of the momentum of the high energy electrons upon collision with the defects. Such defect-specific or “just in location” mobilization of atoms allows a significant decrease in defect concentration, which is not possible with conventional thermal annealing that requires higher temperatures and longer times. We show evidence of rejuvenation with additional improvement in leakage current (16%) and forward current (38%) beyond the pristine condition. Transmission electron microscopy, geometric phase analysis, Raman spectroscopy, and energy dispersive x-ray-spectroscopy reveal the enhancement of defects and interfaces. The ultrafast and room temperature process has the potential for rejuvenating electronic devices operating in high power and harsh environmental conditions.

Diagenetic characterization and the influence on the porosity properties of a mixed bioclastic-siliciclastic rift lacustrine deposit of the Sergipe-Alagoas Basin, northeastern Brazil

Bioclastic and siliciclastic deposits of the Morro do Chaves Formation, Early Cretaceous of the Sergipe-Alagoas Basin, northeastern Brazil, show depositional and diagenetic analogies with the Brazilian Pre-salt rift reservoirs. A detailed petrographic study carried out on 221 thin sections from four well-cores were used to define the stratigraphic and sedimentological controls of the diagenetic events on coquinas supported by cathodoluminescence and EDS-MEV analysis. The study of cement distribution allowed identification in high- and low-frequency cycles of the subaerial exposure zones and intervals with porosity and permeability enhancement. The eodiagenetic processes and products show a good correlation with the maximum regressive events marked in the lower carbonate-dominated sequence, by the occurrence of nodules, micritization, pseudomicrokarst, mechanical compaction, three types of calcite fringes, coarse calcite cement, and three dissolution events. This sequence shows less than 25% of terrigenous constituents, thus favoring a pervasive early calcite cement precipitation and consequently an occlusion of the porosity. The upper sequence displays a predominance of poikilotopic and blocky calcite cement related to the mesogenetic stage. This sequence shows a dominance of mixed carbonate and siliciclastic constituents, which reflects directly the reduced early cementation, and the higher porosity and permeability relatively to the lower sequence. This study on cement occurrence and distribution on mixed deposits and their relationships with sedimentological and stratigraphic controls adds new and useful data for helping in the understanding of the complex coquina successions of the analogous lacustrine bioclastic reservoirs of the Pre-salt interval. The diagenetic model can support further studies regarding to predictive models of porosity and permeability distribution in other bioclastic lacustrine reservoirs.

Are emerging economies’ credit cycles synchronized? Fresh evidence from time–frequency analysis

PurposeTo the best of our knowledge, no study has examined credit cycle synchronizations in the context of emerging economies. Studying the credit cycles synchronization across BRICS (Brazil, Russia, India, China and South Africa) countries is crucial given the magnitude of trade and financial integration among member counties. The enormity of the trade and financial linkages among BRICS countries and growth spillovers from emerging economies to advanced and low-income countries provide the rationale and motivation to study the synchronization of credit cycles across BRICS.Design/methodology/approachThe study investigates the credit cycles coherence across BRICS economies from 1996Q2 to 2020Q4. The synchronization analysis is done using the noval wavelet approach. The analysis examines not only the coherence but also the extent of credit cycle synchronization that varies across frequencies and over time among different pairs of nations.FindingsThe authors find heterogeneity in the credit cycles' synchronization among the member nations. China and India are very much in sync with the other BRICS countries. China's high-frequency credit cycle mostly leads the other countries' credit cycles before the global financial crisis and shows a mix of lead/lag relationships post-financial crisis. Interestingly, most of the time, India's low-frequency credit cycles lead the member countries' credit cycles, and Brazil's low frequency credit cycle lag behind the other BRICS countries' credit cycles, except for Russia. The results are crucial from the macroprudential policymaker's perspective.Research limitations/implicationsThe empirical design is applicable to a similar set of countries and may not directly fit each emerging economy.Practical implicationsThe findings will help understand the marked deepening of trade, technology, investment and financial interdependence across the world. BRICS acronym requires no introduction, but such analysis may help understand the interaction at the monetary policy level.Originality/valueThis is the first study that highlights the need to understand the credit variable interactions for BRICS nations.

Intrinsic water-use efficiency influences establishment in Encelia farinosa.

We describe establishment of Encelia farinosa, a drought-deciduous shrub common to the Mojave and Sonoran Deserts, based on annual observations of two populations between 1980 and 2020. Only 11 establishment events of 50 + yearlings (0.02-0.03 individuals m-2) occurred during this monitoring period; in 68% of the years fewer than 10 yearlings were established. Yearling survival to adulthood (age 4) ranged from 88 to 5% and was significantly related to cumulative precipitation. Juvenile survival rates were lowest during the current megadrought period. We calculated intrinsic water-use efficiency (iWUE) and observed the widest variations in iWUE values among the youngest plants. Among juveniles, surviving yearlings with the lowest iWUE values exhibited upward ontogenetic shifts in iWUE values, whereas those yearlings with the highest initial iWUE values exhibited little if any change. Juvenile size, higher iWUE values, and greater likelihood of surviving were all positively related with each other over the past several decades. Furthermore, iWUE and photosynthetic capacity were positively related to each other, providing a mechanistic explanation for why increased iWUE values among juveniles could lead to greater survival rates and to larger plants under water-deficit conditions. We posit that there is bi-directional selection for genotypic variations in iWUE values among E. farinosa and that this variation is selected for because of interannual environmental heterogeneity in precipitation and VPD associated with both high- and low-frequency climate cycles. Extreme drought cycles may favor plants with higher iWUE values, whereas more mesic periods may allow for greater persistence of lower iWUE genotypes.

Identification and reconstruction of high-frequency fluctuations evolving on a low-frequency periodic limit cycle: application to turbulent cylinder flow

Oftentimes, turbulent flows exhibit a high-frequency turbulent component developing on a strong low-frequency periodic motion. In such cases, the low-frequency motion may strongly influence the spatio-temporal features of the high-frequency component. A typical example of such behaviour is the flow around bluff bodies, for which the high-frequency turbulent component, characterized by Kelvin–Helmholtz structures associated with thin shear layers, depends on the phase of the low-frequency vortex-shedding motion. In this paper, we propose extended versions of spectral proper orthogonal decomposition (SPOD) and of resolvent analysis that respectively extract and reconstruct the high-frequency turbulent fluctuation field as a function of the phase of the low-frequency periodic motion. These approaches are based on a quasi-steady (QS) assumption, which may be justified by the supposedly large separation between the frequencies of the periodic and turbulent components. After discussing their relationship to more classical Floquet-like analyses, the new tools are illustrated on a simple periodically varying linear Ginzburg–Landau model, mimicking the overall characteristics of a turbulent bluff-body flow. In this simple model, we in particular assess the validity of the QS approximation. Then, we consider the case of turbulent flow around a squared-section cylinder at a Reynolds number of $Re=22\,000$ , for which we show reasonable agreement between the extracted spatio-temporal fluctuation field and the prediction of QS resolvent analysis at the various phases of the periodic vortex-shedding motion.

Fatigue damage calculation of offshore wind turbines’ long-term data considering the low-frequency fatigue dynamics

The mutual and simultaneous action of external variable forces on (offshore) wind support structures causes fatigue. Fatigue analysis in this context relies on 10-minute-long strain signals. Cycle-counting allows capturing the fatigue cycles nested within these signals but inevitably leaves some open loops called half-cycles or residuals. Some other loops are not even cycle-counted because the algorithm cannot catch low-frequency (LF) cycles spanning more than 10 minutes, as caused, e.g., by wind speed variations. Notwithstanding, LF cycles are also the most damaging since they always contain the highest range in the variable amplitude signal. Therefore, counting multiple 10-minute signals and merging the resulting histograms into one inevitably has some non-conservative effects, for it leaves the LF cycles uncounted. In this work, we avoid signal concatenation to recover the LF effect. To do so, we use the residuals sequence from the 10-minute signals as it embeds the LF information. As method validation, we compare the impact of LF fatigue dynamics recovery on the linearly accumulated damage using a real-life dataset measured at a Belgian offshore wind turbine. By defining a factor that incorporates the LF effect, we observe that after 300 days of observation, the factor converges to a fixed value.

A laboratory study on fracture initiation and propagation of granite under cyclic-injection hydraulic fracturing

The abundant geothermal energy in hot dry rock (HDR) geothermal reservoirs is an attractive renewable energy resource with great potential. Cyclic injection in hydraulic fracturing has been proved to be a suitable way for the geothermal energy exploitation. However, the fracture initiation and propagation regimes induced by cyclic injection have been inadequately studied, and the fracturing optimization for HDR is often by experience. For this reason, true tri-axial hydraulic-fracturing tests were conducted to study the initiation and propagation of hydraulic fractures, while the specimens were subjected to the cyclic injection with different cycle time duration and injection rate. The results revealed that the initiation of hydraulic fracture was displayed as three basic patterns, and these fracture-initiation patterns were developed into two fracture geometries: simple fracture with only 2–4 strands and complex fracture network with >4 strands. The main reason for this difference is that the initiation and propagation of hydraulic fracture is controlled by the way of fluid circulation, and the cycle time duration and injection rate each played a different role in hydraulic fracturing. At a low injection rate, the initiation and propagation of hydraulic fractures under the high-frequency cycle (cycle time duration = 10 and 20 s) are mainly controlled by the change of injection pressure. Here, the hydraulic energy mainly acts on the rock near the well. The frequent change of injection pressure promotes the initiation of micro-fractures and forms a complex but short hydraulic fracture network. However, when high injection rate is subjected, too high and too low cycle frequencies (cycle time duration = 5 and 40 s) both tend to form a simple fracture, but the fracture has strong extension ability. With that, the similarity criterion of physical phenomena between the on-site prototype and the experimental model were discussed, and these lab-scale results were translated into the fracturing site of HDR.

Fractal dimension and area of seismicity in the Baikal Rift System: Implications for modern geodynamics

The fractal geometry and extent of seismicity in the Baikal Rift System (BRS) are estimated from data on 52,700 instrumental events of MLH ≥ 2.5 magnitudes for fifty years (1964–2013). The seismic pattern is characterized by the box-counting Hausdorff dimension D0, multifractal spectra f(α), and surface area S of seismicity at three scales: the rift system as a whole, its three zones, and six subzones. The multifractal spectra record a self-similar hierarchical structure of the BRS seismicity pattern. The space and time variations in the fractal dimension (D0) and area of seismicity (S), which are mapped and plotted as a function of time, show good correlation. The two parameters depend on three related factors: progressive increase in the amount of instrumental data (dataset size), structure of seismogenic fault network, and geodynamic activity. They increase as ever more data appear with time and acquire high local values at increasing extent and density of quakes. Moreover, the obtained D0 estimates reflect statistical self-similarity of earthquake patterns being in the range ≈ 1.45–1.55 over most of BRS, except one zone and one subzone in the rift flanks. They are the highest in the southwest and the lowest in the northeast of the rift system (D0 ≈ 1.60 ± 0.02 and D0 ≈ 1.37 ± 0.02 respectively). This dissimilarity indicates that seismogenic faulting occurs by different mechanisms: distributed failure as a result of superposed global-scale collisional compression and regional rifting in the SW flank and quasi-linear rift propagation in the NE flank. In general, D0 decreases toward the northeastern part of the BRS, where the pattern of earthquakes becomes localized along lineaments instead of being distributed over an area. The space and time variations of D0 and S revealed in the earthquake data are consistent with the location and activity pulses of rifting attractors and provide a realistic explanation of BRS geodynamics and tectonophysics. The global lithospheric compression and the regional pulse-like activity of rifting attractors control the network of seismogenic faults which, in turn, govern the fractal geometry and 2D structure of seismicity in the region. The obtained results confirm the oscillatory dynamics of the regional seismicity at a decadal period correlated with activity pulses of rifting attractors. The oscillations stand out against the background of decreasing global low-frequency secular cycle of the BRS seismicity. The BRS lithospheric geodynamics fits the model of a nonlinear oscillator with dissipation. The suggested analysis of the fractal geometry and extent of seismicity as proxies of the faulting evolution provides insights into modern geodynamics of the Baikal Rift System and its constituents.

Full-field monitoring methods for damage analysis on aeronautical CFRP specimens under fatigue loads

The present paper is focused on full-field experimental monitoring procedures to be employed during HCF fatigue testing on two series of CFRP open hole samples. Two different experimental methodologies based on thermographic techniques and displacement measurements with Digital Image Correlation (DIC) analysis are employed for damage settlement and evolution to be detected up to failure, together with correspondent compliance analysis. Combined monitoring approaches, based on thermo-elastic and dissipative phenomena, together with stiffness properties variations, are claimed to offer precise damage state localization during tests in real time; in addition, DIC analysis is performed during low-frequency fatigue cycle is studied for better failure prediction and damage location. The thermal parameters and experimental compliance correlation seem to indicate similar signal variation during damage progress and after proper data elaboration; contemporaneous raw thermal measurements in critical zones of specimens under fatigue life offer a kind of delamination recognition at specific layer interface and location, as well as propagation before final failure. Sample under tensile load on the other hand reveal delaminations indirectly on the surface. In addition, non-destructive thermographic and ultrasound tests are performed at regular intervals during fatigue life.

Low frequency instability in a H2/air plane-radial rotating detonation engine

To investigate low frequency instability in a H2/air plane-radial rotating detonation engine, simultaneous visualization, pressure, and ion measurements are performed. Changing reactants mass flow rate and equivalence ratio, two low frequency instabilities, amplitude low frequency instability (ALFI) and amplitude-frequency low frequency instability (AFLFI) are discovered, characterized by periodic sinusoidal oscillations of detonation-wave parameters. The operating conditions of low frequency instabilities are also summarized. The ALFI with periodic fluctuations of detonation-wave pressure peak mostly occurs in single-wave modes and symmetric dual-wave modes, operating near the critical conditions of modes switching. Almost all asymmetric dual-wave modes and some triple-wave modes exhibit some degree of AFLFI characterized by periodic waxing and waning of detonation-wave pressure peak and velocity. Each low-frequency cycle contains several to dozens of rotating detonation laps. Obvious high-frequency and low-frequency oscillations are observed in air plenum, with exactly the same frequency as that in the combustor but lower amplitudes and some phase difference. The interaction between plenum and combustor affects detonation stability.

Interannual and intra-annual cycles of satellite-derived chlorophyll-a concentrations in the Caspian Sea

Variability of phytoplankton in the Caspian Sea (CS) is related to the complex orography, the variety of physical and chemical processes, and climatic indices. Here, interannual and intra-annual variability of satellite-derived chlorophyll-a concentrations (Chl-a) were studied using wavelet analysis during 2002–2019 in different regions of the CS. Self-Organizing Maps (SOM) analysis performed to classify the CS into the areas of similar variability of satellite-derived Chl-a. Wavelet spectral analysis showed that the Chl-a variability regulated by four primary periodic cycles: 0.5-year, 1-year, 2 to 2.5-year, and 3 to 5-year. The 0.5 and 1-year wavelet cycles mostly depicted the intensity of seasonality patterns. The 2–2.5-year and 3–5-year cycles of Chl-a showed non-stationary coherence with corresponding low-frequency cycles of NAO and ENSO. The 3–5-year wavelet amplitudes of Chl-a strongly correlated with NAO and ENSO in the southern CS. Weak correlations of 2–2.5-year cycle wavelet amplitudes of Chl-a with NAO and ENSO suggested that variations do not always directly translate to a biological response. A negative anomaly in the Chl-a autumn peaks observed during 2011–2016 in the middle and southern CS, when NAO phases were persistently positive. The interannual variations of summer peaks in the northern CS, and autumn peaks in the middle and southern CS were broadly related to the precipitation. SST and wind stress. Moreover, it was shown that the Volga discharge has a significant influence on Chl-a variability in the northern CS.