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Search Results (1,860)

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Keywords = period-one oscillations

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18 pages, 2280 KiB  
Article
Theoretical Modeling of a Bionic Arm with Elastomer Fiber as Artificial Muscle Controlled by Periodic Illumination
by Changshen Du, Shuhong Dai and Qinglin Sun
Polymers 2025, 17(15), 2122; https://doi.org/10.3390/polym17152122 - 31 Jul 2025
Viewed by 211
Abstract
Liquid crystal elastomers (LCEs) have shown great potential in the field of soft robotics due to their unique actuation capabilities. Despite the growing number of experimental studies in the soft robotics field, theoretical research remains limited. In this paper, a dynamic model of [...] Read more.
Liquid crystal elastomers (LCEs) have shown great potential in the field of soft robotics due to their unique actuation capabilities. Despite the growing number of experimental studies in the soft robotics field, theoretical research remains limited. In this paper, a dynamic model of a bionic arm using an LCE fiber as artificial muscle is established, which exhibits periodic oscillation controlled by periodic illumination. Based on the assumption of linear damping and angular momentum theorem, the dynamics equation of the model oscillation is derived. Then, based on the assumption of linear elasticity model, the periodic spring force of the fiber is given. Subsequently, the evolution equations for the cis number fraction within the fiber are developed, and consequently, the analytical solution for the light-excited strain is derived. Following that, the dynamics equation is numerically solved, and the mechanism of the controllable oscillation is elucidated. Numerical calculations show that the stable oscillation period of the bionic arm depends on the illumination period. When the illumination period aligns with the natural period of the bionic arm, the resonance is formed and the amplitude is the largest. Additionally, the effects of various parameters on forced oscillation are analyzed. The results of numerical studies on the bionic arm can provide theoretical support for the design of micro-machines, bionic devices, soft robots, biomedical devices, and energy harvesters. Full article
(This article belongs to the Section Polymer Physics and Theory)
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13 pages, 2254 KiB  
Article
Mechanistic Study and Regulatory Effects of Chloride Ions on the B-Z Oscillating Reaction
by Lidan Niu, Lijuan Zhou, Qihui Wang and Wenjing Yang
Molecules 2025, 30(15), 3210; https://doi.org/10.3390/molecules30153210 - 31 Jul 2025
Viewed by 171
Abstract
This work investigated the mechanistic role of chloride ions (Cl) in the Belousov–Zhabotinsky (B-Z) oscillating reaction. We conducted a multivariate statistical analysis of the B-Z response, established a quadratic polynomial regression model, and determined the contributions of the experimental parameters to [...] Read more.
This work investigated the mechanistic role of chloride ions (Cl) in the Belousov–Zhabotinsky (B-Z) oscillating reaction. We conducted a multivariate statistical analysis of the B-Z response, established a quadratic polynomial regression model, and determined the contributions of the experimental parameters to the induction time. The results indicate that the relationship between the experimental parameters and the induction time is often nonmonotonic, exhibiting secondary dependence. Then, we studied the influence mechanism by which Cl affects the B-Z reaction system. Both experimental and theoretical studies indicate that as the concentration of Cl increases, the system becomes more active as the activation energy increases. When the Cl concentration is less than 1 mmol/L, the induced apparent activation energy remains relatively constant. However, as the Cl concentration increases from 1.00 mmol/L to 2.00 mmol/L, the induced apparent activation energy increases rapidly from 50 kJ/mol to 120 kJ/mol, which severely hinders the induction period and then increases the induction time. Full article
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14 pages, 3505 KiB  
Article
The Influence of Operating Pressure Oscillations on the Machined Surface Topography in Abrasive Water Jet Machining
by Dejan Ž. Veljković, Jelena Baralić, Predrag Janković, Nedeljko Dučić, Borislav Savković and Aleksandar Jovičić
Materials 2025, 18(15), 3570; https://doi.org/10.3390/ma18153570 - 30 Jul 2025
Viewed by 193
Abstract
The aim of this study was to determine the connection between oscillations in operating pressure values and the appearance of various irregularities on machined surfaces. Such oscillations are a consequence of the high water pressure generated during abrasive water jet machining. Oscillations in [...] Read more.
The aim of this study was to determine the connection between oscillations in operating pressure values and the appearance of various irregularities on machined surfaces. Such oscillations are a consequence of the high water pressure generated during abrasive water jet machining. Oscillations in the operating pressure values are periodic, namely due to the cyclic operation of the intensifier and the physical characteristics of water. One of the most common means of reducing this phenomenon is installing an attenuator in the hydraulic system or a phased intensifier system. The main hypothesis of this study was that the topography of a machined surface is directly influenced by the inability of the pressure accumulator to fully absorb water pressure oscillations. In this study, we monitored changes in hydraulic oil pressure values at the intensifier entrance and their connection with irregularities on the machined surface—such as waviness—when cutting aluminum AlMg3 of different thicknesses. Experimental research was conducted in order to establish this connection. Aluminum AlMg3 of different thicknesses—from 6 mm to 12 mm—was cut with different traverse speeds while hydraulic oil pressure values were monitored. The pressure signals thus obtained were analyzed by applying the fast Fourier transform (FFT) algorithm. We identified a single-sided pressure signal amplitude spectrum. The frequency axis can be transformed by multiplying inverse frequency data with traverse speed; in this way, a single-sided amplitude spectrum can be obtained, examined against the period in which striations are expected to appear (in millimeters). In the lower zone of the analyzed samples, striations are observed at intervals determined by the dominant hydraulic oil pressure harmonics, which are transferred to the operating pressure. In other words, we demonstrate how the machined surface topography is directly induced by water jet pressure frequency characteristics. Full article
(This article belongs to the Special Issue High-Pressure Water Jet Machining in Materials Engineering)
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46 pages, 7184 KiB  
Article
Climate in Europe and Africa Sequentially Shapes the Spring Passage of Long-Distance Migrants at the Baltic Coast in Europe
by Magdalena Remisiewicz and Les G. Underhill
Diversity 2025, 17(8), 528; https://doi.org/10.3390/d17080528 - 29 Jul 2025
Viewed by 268
Abstract
Since the 1980s, earlier European springs have led to the earlier arrival of migrant passerines. We predict that arrival is related to a suite of climate indices operating during the annual cycle (breeding, autumn migration, wintering, spring migration) in Europe and Africa over [...] Read more.
Since the 1980s, earlier European springs have led to the earlier arrival of migrant passerines. We predict that arrival is related to a suite of climate indices operating during the annual cycle (breeding, autumn migration, wintering, spring migration) in Europe and Africa over the year preceding arrival. The climate variables include the Indian Ocean Dipole (IOD), Southern Oscillation Index (SOI), and North Atlantic Oscillation (NAO). Furthermore, because migrants arrive sequentially from different wintering areas across Africa, we predict that relationships with climate variables operating in different parts of Africa will change within the season. We tested this using daily ringing data at Bukowo, a spring stopover site on the Baltic coast. We calculated an Annual Anomaly (AA) of spring passage (26 March–15 May, 1982–2024) for four long-distance migrants (Blackcap, Lesser Whitethroat, Willow Warbler, Chiffchaff). We decomposed the anomaly in two ways: into three independent main periods and nine overlapping periods. We used multiple regression to explore the relationships of the arrival of these species at Bukowo. We found sequential effects of climate indices. Bukowo is thus at a crossroads of populations arriving from different wintering regions. The drivers of phenological shifts in passage of wide-ranging species are related to climate indices encountered during breeding, wintering, and migration. Full article
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33 pages, 4686 KiB  
Article
Modeling of Dynamics of Nonideal Mixer at Oscillation and Aperiodic Damped Mode of Driving Member Motion
by Kuatbay Bissembayev, Zharilkassin Iskakov, Assylbek Jomartov and Akmaral Kalybayeva
Appl. Sci. 2025, 15(15), 8391; https://doi.org/10.3390/app15158391 - 29 Jul 2025
Viewed by 242
Abstract
The dynamics of the vibrational mode of motion of the driving member of a nonideal system, a mixing–whipping device based on a simple slide-crank mechanism, was studied. The highly nonlinear differential equations of motion were solved numerically by the Runge–Kutta method. The interaction [...] Read more.
The dynamics of the vibrational mode of motion of the driving member of a nonideal system, a mixing–whipping device based on a simple slide-crank mechanism, was studied. The highly nonlinear differential equations of motion were solved numerically by the Runge–Kutta method. The interaction of the mixing–whipping device with the nonideal excitation source causes the rotational speed of the engine shaft and the rotation angle of the driving member to fluctuate, accomplishing a damped process. The parameters of the device and the nonideal energy source have an effect on the kinematic, vibrational and energy characteristics of the system. An increase in the engine’s torque, crank length, number and radius of piston holes, and piston mass, as well as a decrease in the fluid’s density, leads to a reduction in the oscillation range of the crank angle, amplitude and period of angular velocity oscillations of the engine shaft and the mixing–whipping force power. The effects of a nonideal energy source may be used in designing a mixing–whipping device based on a slider-crank mechanism to select effective system parameters and an energy-saving motor in accordance with the requirements of technological processes and products. Full article
(This article belongs to the Special Issue Dynamics and Vibrations of Nonlinear Systems with Applications)
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19 pages, 704 KiB  
Article
Semi-Analytical Solutions for the Shimizu–Morioka Dynamical System
by Remus-Daniel Ene, Nicolina Pop and Rodica Badarau
Axioms 2025, 14(8), 580; https://doi.org/10.3390/axioms14080580 - 26 Jul 2025
Viewed by 106
Abstract
The Shimizu–Morioka dynamical system is analytically investigated in this paper by means of the Optimal Auxiliary Functions Method (OAFM). This system has a chaotic dynamical behavior, specified for more physical applications as chaos synchronization, an attractive phenomenon involving various real-life processes. Semi-analytical solutions [...] Read more.
The Shimizu–Morioka dynamical system is analytically investigated in this paper by means of the Optimal Auxiliary Functions Method (OAFM). This system has a chaotic dynamical behavior, specified for more physical applications as chaos synchronization, an attractive phenomenon involving various real-life processes. Semi-analytical solutions for the Shimizu–Morioka system are provided. A comparative analysis between the obtained results via the OAFM method and the corresponding numerical solution highlights the accuracy and efficiency of the involved method. The choice of the OAFM method is justified by the performance in comparison with the iterative method with 7–10 iterations. The physical parameters’ influence is investigated on damped oscillations and periodical behaviors of the obtained solutions. Full article
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11 pages, 1320 KiB  
Article
Power Scaling of a Narrowband-Seeded, Non-Resonant Optical Parametric Oscillator Based on Periodically Poled LiNbO3
by Tugba Temel, Subhasis Das, Gerhard Spindler, André Schirrmacher, Robert T. Murray, Marcin Piotrowski, Li Wang, Weidong Chen and Valentin Petrov
Photonics 2025, 12(8), 743; https://doi.org/10.3390/photonics12080743 - 23 Jul 2025
Viewed by 259
Abstract
A periodically poled LiNbO3 (PPLN) non-resonant optical parametric oscillator injectionseeded by narrowband sub-50-mW CW radiation at the signal wavelength produces a >3 W average idler power at 2376 nm for a 20 kHz repetition rate, with a ~2 nm spectral linewidth. Seed [...] Read more.
A periodically poled LiNbO3 (PPLN) non-resonant optical parametric oscillator injectionseeded by narrowband sub-50-mW CW radiation at the signal wavelength produces a >3 W average idler power at 2376 nm for a 20 kHz repetition rate, with a ~2 nm spectral linewidth. Seed levels as low as 5 mW are sufficient to produce the desired spectral narrowing effect, and spectral tuning is possible by changing the seed wavelength and simultaneously adjusting the crystal temperature. The spectral features are in good agreement with numerical simulations based on the plane wave approximation. Full article
(This article belongs to the Section Lasers, Light Sources and Sensors)
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26 pages, 9566 KiB  
Article
How Does Energy Harvesting from a Fluttering Foil Influence Its Nonlinear Dynamics?
by Dilip Thakur, Faisal Muhammad and Muhammad Saif Ullah Khalid
Energies 2025, 18(15), 3897; https://doi.org/10.3390/en18153897 - 22 Jul 2025
Viewed by 221
Abstract
This study investigates the nonlinear aeroelastic behavior and energy harvesting performance of a two-degrees-of-freedom NACA 0012 airfoil under varying reduced velocities and electrical load resistances. The system exhibits a range of dynamic responses, including periodic and chaotic states, governed by strong fluid–structure interactions. [...] Read more.
This study investigates the nonlinear aeroelastic behavior and energy harvesting performance of a two-degrees-of-freedom NACA 0012 airfoil under varying reduced velocities and electrical load resistances. The system exhibits a range of dynamic responses, including periodic and chaotic states, governed by strong fluid–structure interactions. Nonlinear oscillations first appear near the critical reduced velocity Ur*=6, with large-amplitude limit-cycle oscillations emerging around Ur*=8 in the absence of the electrical loading. As the load resistance increases, this transition shifts to higher Ur*, reflecting the damping effect of the electrical load. Fourier spectra reveal the presence of odd and even superharmonics in the lift coefficient, indicating nonlinearities induced by fluid–structure coupling, which diminishes at higher resistances. Phase portraits and Poincaré maps capture transitions across dynamical regimes, from periodic to chaotic behavior, particularly at a low resistance. The voltage output correlates with variations in the lift force, reaching its maximum at an intermediate resistance before declining due to a suppressing nonlinearity. Flow visualizations identify various vortex shedding patterns, including single (S), paired (P), triplet (T), multiple-pair (mP) and pair with single (P + S) that weaken at higher resistances and reduced velocities. The results demonstrate that nonlinearity plays a critical role in efficient voltage generation but remains effective only within specific parameter ranges. Full article
(This article belongs to the Section A3: Wind, Wave and Tidal Energy)
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24 pages, 50503 KiB  
Article
Quantifying the Influence of Sea Surface Temperature Anomalies on the Atmosphere and Precipitation in the Southwestern Atlantic Ocean and Southeastern South America
by Mylene Cabrera, Luciano Pezzi, Marcelo Santini and Celso Mendes
Atmosphere 2025, 16(7), 887; https://doi.org/10.3390/atmos16070887 - 19 Jul 2025
Viewed by 240
Abstract
Oceanic mesoscale activity influences the atmosphere in the southwestern and southern sectors of the Atlantic Ocean. However, the influence of high latitudes, specifically sea ice, on mid-latitudes and a better understanding of mesoscale ocean–atmosphere thermodynamic interactions still require further study. To quantify the [...] Read more.
Oceanic mesoscale activity influences the atmosphere in the southwestern and southern sectors of the Atlantic Ocean. However, the influence of high latitudes, specifically sea ice, on mid-latitudes and a better understanding of mesoscale ocean–atmosphere thermodynamic interactions still require further study. To quantify the effects of oceanic mesoscale activity during the periods of maximum and minimum Antarctic sea ice extent (September 2019 and February 2020), numerical experiments were conducted using a coupled regional model and an online two-dimensional spatial filter to remove high-frequency sea surface temperature (SST) oscillations. The largest SST anomalies were observed in the Brazil–Malvinas Confluence and along oceanic fronts in September, with maximum SST anomalies reaching 4.23 °C and −3.71 °C. In February, the anomalies were 2.18 °C and −3.06 °C. The influence of oceanic mesoscale activity was evident in surface atmospheric variables, with larger anomalies also observed in September. This influence led to changes in the vertical structure of the atmosphere, affecting the development of the marine atmospheric boundary layer (MABL) and influencing the free atmosphere above the MABL. Modulations in precipitation patterns were observed, not only in oceanic regions, but also in adjacent continental areas. This research provides a novel perspective on ocean–atmosphere thermodynamic coupling, highlighting the mesoscale role and importance of its representation in the study region. Full article
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28 pages, 12894 KiB  
Article
Evolution of Rainfall Characteristics in Catalonia, Spain, Using a Moving-Window Approach (1950–2022)
by Carina Serra, María del Carmen Casas-Castillo, Raül Rodríguez-Solà and Cristina Periago
Hydrology 2025, 12(7), 194; https://doi.org/10.3390/hydrology12070194 - 19 Jul 2025
Viewed by 558
Abstract
A comprehensive analysis of the evolution of rainfall characteristics in Catalonia, NE Spain, was conducted using monthly data from 72 rain gauges over the period 1950–2022. A moving-window approach was applied at annual, seasonal, and monthly scales, calculating mean values, coefficients of variation [...] Read more.
A comprehensive analysis of the evolution of rainfall characteristics in Catalonia, NE Spain, was conducted using monthly data from 72 rain gauges over the period 1950–2022. A moving-window approach was applied at annual, seasonal, and monthly scales, calculating mean values, coefficients of variation (CV), and trends across 43 overlapping 31-year periods. To assess trends in these moving statistics, a modified Mann–Kendall test was applied to both the 31-year means and CVs. Results revealed a significant 10% decrease in annual rainfall, with summer showing the most pronounced decline, as nearly 90% of stations exhibited negative trends, while the CV showed negative trends in coastal areas and mostly positive trends inland. At the monthly scale, February, March, June, August, and December exhibited negative trends at more than 50% of stations, with rainfall reductions ranging from 20% to 30%. Additionally, the temporal evolution of Mann–Kendall trend coefficients within each 31-year moving window displayed a fourth-degree polynomial pattern, with a periodicity of 30–35 years at annual and seasonal scales, and for some months. Finally, at the annual scale and in two centennial series, the 80-year oscillations found were inversely correlated with the large-scale climate indices North Atlantic Oscillation (NAO) and Atlantic Multidecadal Oscillation (AMO). Full article
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19 pages, 9601 KiB  
Article
Two-Hour Sea Level Oscillations in Halifax Harbour
by Dan Kelley, Clark Richards, Ruby Yee, Alex Hay, Knut Klingbeil, Phillip MacAulay and Ruth Musgrave
J. Mar. Sci. Eng. 2025, 13(7), 1366; https://doi.org/10.3390/jmse13071366 - 17 Jul 2025
Viewed by 255
Abstract
Halifax Harbour, a major seaport in Nova Scotia that is approximately 100 km southeast of the Bay of Fundy, comprises a deep inner region called Bedford Basin, connected to the adjacent ocean by a shallow channel called The Narrows. A study of sea [...] Read more.
Halifax Harbour, a major seaport in Nova Scotia that is approximately 100 km southeast of the Bay of Fundy, comprises a deep inner region called Bedford Basin, connected to the adjacent ocean by a shallow channel called The Narrows. A study of sea level and currents reveals the presence of episodic oscillations in The Narrows, with a period of approximately 2 h. The oscillation strength varies from day to day and, to some extent, through the seasons. The median amplitude of the associated sea level variation is 18% that of the de-tided signal, rising to 32% at the 95-th percentile. Values this large may be of concern for the transit of deep-draft vessels through shallow parts of the harbour and for the clearance of tall vessels under the two bridges that span The Narrows. Another concerning issue is the matter of oscillations being superimposed on storm surges. In addition to such direct effects of sea level variation, shear associated with the oscillations may increase the turbulent mixing in the region, affecting the overall state of this estuarine system. We explore the nature of the oscillations as a first step towards the improvement of prediction schemes for sea level and currents in the region. This involves an analysis of the oscillations in the context of seiche and Helmholtz resonance theories and the use of a 2D numerical model to handle realistic bathymetric conditions and other complications that the simpler theories cannot address. We conclude that the predictions of Helmholtz resonance theory are in reasonable agreement with both the observations and the predictions of the numerical model. Full article
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18 pages, 2314 KiB  
Article
Deletion of Clock Gene Period 2 (Per2) in Astrocytes Shortens Clock Period but Does Not Affect Light-Mediated Phase Shifts in Mice
by Soha A. Hassan, Katrin S. Wendrich and Urs Albrecht
Clocks & Sleep 2025, 7(3), 37; https://doi.org/10.3390/clockssleep7030037 - 17 Jul 2025
Viewed by 304
Abstract
The circadian clock is a self-sustaining oscillator with a period of approximately 24 h, enabling organisms to anticipate daily recurring events, such as sunrise and sunset. Since the circadian period is not exactly 24 h and the environmental day length varies throughout the [...] Read more.
The circadian clock is a self-sustaining oscillator with a period of approximately 24 h, enabling organisms to anticipate daily recurring events, such as sunrise and sunset. Since the circadian period is not exactly 24 h and the environmental day length varies throughout the year, the clock must be periodically reset to align an organism’s physiology with the natural light/dark cycle. This synchronization, known as entrainment, is primarily regulated by nocturnal light, which can be replicated in laboratory settings using a 15 min light pulse (LP) and by assessing locomotor activity. An LP during the early part of the dark phase delays the onset of locomotor activity, resulting in a phase delay, whereas an LP in the late dark phase advances activity onset, causing a phase advance. The clock gene Period 2 (Per2) plays a key role in this process. To investigate its contributions, we examined the effects of Per2 deletion in neurons versus astrocytes using glia-specific GPer2 (Per2/GfapCre) knockout (KO) and neuronal-specific NPer2KO (Per2/NesCre) mice. All groups were subjected to Aschoff type II protocol, where an LP was applied at ZT14 or ZT22 and the animals were released into constant darkness. As control, no LP was applied. Phase shift, period, amplitude, total activity count, and rhythm instability were assessed. Our findings revealed that mice lacking Per2 in neurons (NPer2) exhibited smaller phase delays and larger phase advances compared to control animals. In contrast, mice with Per2 deletion specifically in glial cells including astrocytes (GPer2) displayed normal clock resetting. Interestingly, the absence of Per2 in either of the cell types resulted in a shorter circadian period compared to control animals. These results suggest that astrocytic Per2 is important for maintaining the circadian period but is not required for phase adaptation to light stimuli. Full article
(This article belongs to the Section Animal Basic Research)
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24 pages, 8373 KiB  
Article
Simple Strain Gradient–Divergence Method for Analysis of the Nanoindentation Load–Displacement Curves Measured on Nanostructured Nitride/Carbonitride Coatings
by Uldis Kanders, Karlis Kanders, Artis Kromanis, Irina Boiko, Ernests Jansons and Janis Lungevics
Coatings 2025, 15(7), 824; https://doi.org/10.3390/coatings15070824 - 15 Jul 2025
Viewed by 584
Abstract
This study investigates the fabrication, nanomechanical behavior, and tribological performance of nanostructured superlattice coatings (NSCs) composed of alternating TiAlSiNb-N/TiCr-CN bilayers. Deposited via High-Power Ion-Plasma Magnetron Sputtering (HiPIPMS) onto 100Cr6 steel substrates, the coatings achieved nanohardness values of ~25 GPa and elastic moduli up [...] Read more.
This study investigates the fabrication, nanomechanical behavior, and tribological performance of nanostructured superlattice coatings (NSCs) composed of alternating TiAlSiNb-N/TiCr-CN bilayers. Deposited via High-Power Ion-Plasma Magnetron Sputtering (HiPIPMS) onto 100Cr6 steel substrates, the coatings achieved nanohardness values of ~25 GPa and elastic moduli up to ~415 GPa. A novel empirical method was applied to extract stress–strain field (SSF) gradient and divergence profiles from nanoindentation load–displacement data. These profiles revealed complex, depth-dependent oscillations attributed to alternating strain-hardening and strain-softening mechanisms. Fourier analysis identified dominant spatial wavelengths, DWL, ranging from 4.3 to 42.7 nm. Characteristic wavelengths WL1 and WL2, representing fine and coarse oscillatory modes, were 8.2–9.2 nm and 16.8–22.1 nm, respectively, aligning with the superlattice period and grain-scale features. The hyperfine structure exhibited non-stationary behavior, with dominant wavelengths decreasing from ~5 nm to ~1.5 nm as the indentation depth increased. We attribute the SSF gradient and divergence spatial oscillations to alternating strain-hardening and strain-softening deformation mechanisms within the near-surface layer during progressive loading. This cyclic hardening–softening behavior was consistently observed across all NSC samples, suggesting it represents a general phenomenon in thin film/substrate systems under incremental nanoindentation loading. The proposed SSF gradient–divergence framework enhances nanoindentation analytical capabilities, offering a tool for characterizing thin-film coatings and guiding advanced tribological material design. Full article
(This article belongs to the Section Ceramic Coatings and Engineering Technology)
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18 pages, 2458 KiB  
Article
Periodic Oscillatory Solutions for a Nonlinear Model with Multiple Delays
by Chunhua Feng
Mathematics 2025, 13(14), 2275; https://doi.org/10.3390/math13142275 - 15 Jul 2025
Viewed by 228
Abstract
For systems such as the van der Pol and van der Pol–Duffing oscillators, the study of their oscillation is currently a very active area of research. Many authors have used the bifurcation method to try to determine oscillatory behavior. But when the system [...] Read more.
For systems such as the van der Pol and van der Pol–Duffing oscillators, the study of their oscillation is currently a very active area of research. Many authors have used the bifurcation method to try to determine oscillatory behavior. But when the system involves n separate delays, the equations for bifurcation become quite complex and difficult to deal with. In this paper, the existence of periodic oscillatory behavior was studied for a system consisting of n coupled equations with multiple delays. The method begins by rewriting the second-order system of differential equations as a larger first-order system. Then, the nonlinear system of first-order equations is linearized by disregarding higher-degree terms that are locally small. The instability of the trivial solution to the linearized equations implies the instability of the nonlinear equations. Periodic behavior often occurs when the system is unstable and bounded, so this paper also studied the boundedness here. It follows from previous work on the subject that the conditions here did result in periodic oscillatory behavior, and this is illustrated in the graphs of computer simulations. Full article
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19 pages, 7129 KiB  
Article
Dendroclimatic Reconstruction of Seasonal Precipitation from Two Endangered Spruce Species in Northeastern Mexico
by Christian Wehenkel, Oscar A. Díaz-Carrillo and Jose Villanueva-Díaz
Atmosphere 2025, 16(7), 863; https://doi.org/10.3390/atmos16070863 - 15 Jul 2025
Viewed by 309
Abstract
Water availability is a major constraint on socioeconomic development in northeastern Mexico, highlighting the need for effective water resource planning that accounts for the variability and extremes of precipitation. In this study, seasonal precipitation reconstructions were developed using tree-ring chronologies from spruce species [...] Read more.
Water availability is a major constraint on socioeconomic development in northeastern Mexico, highlighting the need for effective water resource planning that accounts for the variability and extremes of precipitation. In this study, seasonal precipitation reconstructions were developed using tree-ring chronologies from spruce species (Picea spp.). A representative chronology for Picea mexicana Martínez was developed from two populations and spans the period 1786–2020, while a chronology for Picea martinezii T.F. Patterson was established from three populations covering 1746–2020. Both species exhibited significant positive correlations with January–May precipitation (r = 0.65 and 0.71, respectively; p < 0.01) and negative correlations with maximum temperature over the same period (r = −0.52 and −0.59, respectively). Two January–May precipitation reconstructions were produced for periods with adequate sample depth (EPS > 0.85): 1851–2020 for P. mexicana and 1821–2020 for P. martinezii. Both reconstructions revealed pronounced interannual variability, with recurrent droughts and persistently dry conditions, particularly evident in the P. mexicana series. Spatial correlation analyses indicated a historical link between reconstructed precipitation and the El Niño–Southern Oscillation (ENSO). These results highlight the value of spruce species for dendroclimatic reconstruction and their sensitivity to precipitation variability, especially as rising maximum temperatures may compromise their persistence in the Sierra Madre Oriental. Full article
(This article belongs to the Special Issue Forest Ecosystems in a Changing Climate)
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