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Keywords = system of difference equations

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26 pages, 2804 KB  
Article
An Improved Particle Swarm Optimization for Three-Dimensional Indoor Positioning with Ultra-Wideband Communications for LOS/NLOS Channels
by Yung-Fa Huang, Tung-Jung Chan, Guan-Yi Chen and Hsing-Wen Wang
Mathematics 2026, 14(3), 493; https://doi.org/10.3390/math14030493 - 30 Jan 2026
Abstract
In this study, an improved particle swarm optimization (PSO) algorithm is designed to construct a weighting model for line-of-sight (LOS) and non-line-of-sight (NLOS) channels in an ultra-wideband (UWB) indoor positioning system. In the proposed algorithm, the particle position represents candidate weight vectors, and [...] Read more.
In this study, an improved particle swarm optimization (PSO) algorithm is designed to construct a weighting model for line-of-sight (LOS) and non-line-of-sight (NLOS) channels in an ultra-wideband (UWB) indoor positioning system. In the proposed algorithm, the particle position represents candidate weight vectors, and the fitness function is defined by the 3D positioning error over multiple test points. An optimized weight modeling framework is proposed for a multi-anchor, three-dimensional UWB indoor positioning system under LOS and NLOS channels. First, the three-dimensional positioning problem is formulated as a multilateration model, and the tag coordinates are estimated via a linearized matrix equation solved by the least-squares method, which explicitly links anchor geometry and ranging errors to the positioning accuracy. To evaluate the proposed method, extensive ranging and positioning experiments are conducted in a realistic indoor environment using up to eight anchors with different LOS/NLOS configurations, including dynamic scenarios with varying numbers of NLOS anchors. The results show that, compared with the conventional unweighted multi-anchor scheme, the PSO-based weighting model can reduce the average 3D positioning error by more than 30% in typical LOS-dominant settings and significantly suppress error bursts in severe NLOS conditions. These findings demonstrate that the combination of mathematical modeling, least-squares estimation, and swarm intelligence optimization provides an effective tool for designing intelligent engineering positioning systems in complex indoor environments, which aligns with the development of smart factories and industrial Internet-of-Things (IIoT) applications. Full article
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18 pages, 2352 KB  
Article
Divergent Responses of Soil CO2 and N2O Fluxes to Simulated Rainfall in a Restored Arid Ecosystem
by Chunming Xin, Jing Zhou, Zhanwu Zhu, Huijun Qin, Rui Hu and Mingzhu He
Sustainability 2026, 18(3), 1383; https://doi.org/10.3390/su18031383 - 30 Jan 2026
Abstract
Precipitation pulses refer to discrete and intermittent precipitation events that significantly influence ecosystem carbon and nitrogen cycling processes. However, the mechanisms by which different vegetation types modulate the sensitivity of carbon dioxide (CO2) and nitrous oxide (N2O) fluxes to [...] Read more.
Precipitation pulses refer to discrete and intermittent precipitation events that significantly influence ecosystem carbon and nitrogen cycling processes. However, the mechanisms by which different vegetation types modulate the sensitivity of carbon dioxide (CO2) and nitrous oxide (N2O) fluxes to short-term rainfall pulses remain poorly elucidated. To address this knowledge gap, we conducted a controlled rainfall simulation experiment across four representative surface types (moss-dominated biological soil crusts, Artemisia-ordosica-dominated soil, Caragana-korshinskii-dominated soil, and bare sandy soil), applying two precipitation pulses (5 mm and 10 mm) to quantify soil CO2 and N2O flux responses. The results showed that: (1) CO2 emissions increased significantly with precipitation intensity, with the 10 mm treatment producing higher mean fluxes than the 5 mm treatment. Emission peaks (1200–1600 mg m−2 h−1) occurred within 24 h after rainfall and returned to baseline levels within three days; (2) Surface cover exerted a strong regulatory effect on CO2 emissions, with moss crust soils (~400 mg m−2 h−1) and A. ordosica soils (~350 mg m−2 h−1) exhibiting CO2 fluxes 2.5–3 times higher than those of bare sandy soils (~120 mg m−2 h−1); (3) Structural equation modeling indicated that precipitation indirectly enhanced CO2 emissions by increasing soil carbon availability, with total organic carbon emerging as the strongest direct driver. Together, these findings clarify the primary controls on precipitation-induced CO2 emissions in restored desert systems and highlight the decoupled and weak short-term response of N2O, providing critical insights for managing carbon–nitrogen processes under increasing precipitation variability. Full article
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15 pages, 3170 KB  
Article
Rapid Measurement of Liquid Diffusion Coefficients of β-Alanine Varying with Concentration at Different Temperatures
by Bolin Geng, Xinfei Cao, Yuan Li, Xiaoyun Pu and Weidong Meng
Photonics 2026, 13(2), 132; https://doi.org/10.3390/photonics13020132 - 30 Jan 2026
Abstract
The liquid diffusion coefficient is a critical parameter for studying mass transfer processes, calculating mass transfer rates, and facilitating chemical engineering design and development, with its value strongly influenced by factors such as temperature and concentration. Conventionally, determining the concentration-dependent diffusion coefficient relationship [...] Read more.
The liquid diffusion coefficient is a critical parameter for studying mass transfer processes, calculating mass transfer rates, and facilitating chemical engineering design and development, with its value strongly influenced by factors such as temperature and concentration. Conventionally, determining the concentration-dependent diffusion coefficient relationship D(C) requires multiple measurements across various concentrations followed by fitting, which is time-consuming and prone to cumulative errors, especially under varying thermal conditions encountered in industrial applications. To address this limitation, this study proposes an optimized finite difference numerical method that enables rapid determination of D(C) using only a single diffusion image, significantly enhancing measurement efficiency. This approach was validated by comparison with the shift of equivalent refractive index slice method and ray-tracing simulations. Diffusion coefficients for β-alanine aqueous solutions at different concentrations were measured over the temperature range of 288.15 K to 318.15 K using both techniques. The results from the two methods showed excellent consistency, with diffusion coefficients well described by the Arrhenius equation across temperatures, allowing for the rapid derivation of activation energies. Numerical simulations based on the derived D(C) relationship yielded images that closely matched experimental observations, confirming the accuracy and reliability of the finite difference method. This innovative technique not only offers a streamlined pathway for characterizing concentration-dependent diffusion in amino acid systems like β-alanine—relevant to pharmaceutical and biochemical processes—but also demonstrates broad applicability for obtaining diffusion coefficients and activation energies with minimal experimental effort. Full article
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12 pages, 2261 KB  
Article
Fractional Modeling of Coupled Heat and Moisture Transfer with Gas-Pressure-Driven Flow in Raw Cotton
by Normakhmad Ravshanov and Istam Shadmanov
Processes 2026, 14(3), 481; https://doi.org/10.3390/pr14030481 - 29 Jan 2026
Abstract
This study introduces a multidimensional mathematical model and a robust numerical algorithm with second-order accuracy for modeling the complex coupled processes of heat and moisture transfer with gas-pressure-driven flow, based on time-fractional differential equations (with Caputo derivatives of order 0 < α ≤ [...] Read more.
This study introduces a multidimensional mathematical model and a robust numerical algorithm with second-order accuracy for modeling the complex coupled processes of heat and moisture transfer with gas-pressure-driven flow, based on time-fractional differential equations (with Caputo derivatives of order 0 < α ≤ 1), which capture the memory effects and anomalous diffusion inherent in heterogeneous porous media. The proposed model integrates conductive and convective heat transfer; moisture diffusion and phase change; and pressure dynamics within the pore space and their bidirectional couplings. It also incorporates environmental interactions through boundary conditions for heat and moisture exchange with the ambient air; internal heat and moisture release; transient influx of solar radiation; and material heterogeneity, where all transport coefficients are spatially variable functions. To solve this nonlinear and coupled system, we developed a high-order, stable finite-difference scheme. The numerical algorithm employs an alternating direction-implicit approach, which ensures computational efficiency while maintaining numerical stability. We demonstrate the algorithm’s capability through numerical simulations that monitor and predict the spatiotemporal evolution of coupled transport temperature, moisture content, and pressure fields. The results reveal how heterogeneity, diurnal solar radiation, and internal sources create localized hot spots, moisture accumulation zones, and pressure gradients that significantly influence the overall dynamics of storage and drying processes. Full article
(This article belongs to the Section Process Control and Monitoring)
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14 pages, 3979 KB  
Article
Spatial-Multiplexed Four-Channel Optical Amplification via Multiple Four-Wave Mixing in a Double-Λ Atomic System
by Xin Li, Dan Song, Yu-Xia Fan, Rong Miao, Dan Wang, Bao-Dong Yang, Hai-Tao Zhou and Jun-Xiang Zhang
Nanomaterials 2026, 16(3), 184; https://doi.org/10.3390/nano16030184 - 29 Jan 2026
Abstract
Optical amplification and spatial multiplexing technologies have important applications in quantum communication, quantum networks, and optical information processing. In this paper, based on the non-reciprocal amplification of a pair of co-propagating conjugate four-wave mixing (FWM) signals induced by a one-way pump field in [...] Read more.
Optical amplification and spatial multiplexing technologies have important applications in quantum communication, quantum networks, and optical information processing. In this paper, based on the non-reciprocal amplification of a pair of co-propagating conjugate four-wave mixing (FWM) signals induced by a one-way pump field in a double-Λ-type hot atomic system, we demonstrate spatially multiplexed multiple FWM processes by introducing a counter-propagating collinear pump field. This configuration enables simultaneous amplification of bidirectional four-channel FWM signals. Furthermore, when the injected signal and pump beams are modulated to Laguerre–Gaussian beams carrying different optical orbital angular momentum (OAM), the OAM of the pump beam is transferred to each amplified field. Through the tilted lens method, we experimentally demonstrate that the OAM of the amplified signal light remains identical to that of the original injected signal light. In contrast, the OAM of the other three newly generated FWM fields is governed by the angular momentum conservation law of their respective FWM processes, which enables the precise manipulation of the OAM for the other generated amplified fields. Theoretical analysis of the dynamical transport equation for the density operator in light–matter interaction processes fully corroborates the experimental results. These findings establish a robust framework for developing OAM-compatible optical non-reciprocal devices based on complex structured light. Full article
(This article belongs to the Special Issue Optical Properties of Nanomaterials: Linear and Nonlinear Behavior)
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16 pages, 1286 KB  
Article
Organic Carbon Pools and Their Association with Cadmium in Sediments of Small Freshwater Ecosystems
by Kateryna Fastovetska, Olgirda Belova, Joanna Gmitrowicz-Iwan, Barbara Futa, Aida Skersiene, Alvyra Slepetiene and Egidijus Vigricas
Water 2026, 18(3), 332; https://doi.org/10.3390/w18030332 - 29 Jan 2026
Viewed by 59
Abstract
Understanding how different pools of sediment organic carbon (OC) are associated with trace metals is essential for interpreting biogeochemical processes in small freshwater ecosystems. This study examines spatial and interannual patterns of total organic carbon (TOC), water-extractable organic carbon (WEOC), and cadmium (Cd) [...] Read more.
Understanding how different pools of sediment organic carbon (OC) are associated with trace metals is essential for interpreting biogeochemical processes in small freshwater ecosystems. This study examines spatial and interannual patterns of total organic carbon (TOC), water-extractable organic carbon (WEOC), and cadmium (Cd) in sediments collected from streams, natural ponds, and drying ditches across three contrasting regions of Lithuania during 2022–2024. TOC and WEOC exhibited pronounced spatial gradients and a marked increase in 2023, while Cd showed a similar but more moderate temporal response. Correlation analysis, principal component analysis, regression modelling, and structural equation modelling consistently indicated that WEOC is more strongly associated with sediment Cd concentrations than bulk TOC. The results suggest that TOC influences Cd distribution primarily indirectly, through its control on the water-extractable OC pool. Multivariate analyses revealed a dominant organic–metal association gradient shared by TOC, WEOC, and Cd, as well as a secondary axis reflecting partial geochemical independence of Cd. These findings highlight the functional relevance of WEOC as an interface between sediment organic matter and Cd accumulation in small freshwater systems. Incorporating WEOC into sediment monitoring may improve interpretation of trace-metal patterns under conditions of hydrological variability. Full article
(This article belongs to the Section Soil and Water)
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25 pages, 2728 KB  
Article
A Full-Time-Domain Analysis Based Method for Fault Transient Characteristic and Optimization Control in New Distribution System
by Wanxing Sheng, Xiaoyu Yang, Dongli Jia, Keyan Liu, Chengfeng Li and Qing Han
Energies 2026, 19(3), 669; https://doi.org/10.3390/en19030669 - 27 Jan 2026
Viewed by 113
Abstract
In new distribution systems with high penetration of renewable energy, inverter-based sources exhibit significant differences in fault characteristics compared to traditional power sources due to the absence of a constant electromotive force and their operation under nonlinear control links, rendering conventional fault current [...] Read more.
In new distribution systems with high penetration of renewable energy, inverter-based sources exhibit significant differences in fault characteristics compared to traditional power sources due to the absence of a constant electromotive force and their operation under nonlinear control links, rendering conventional fault current calculation methods inadequate. To address these challenges, a full-time-domain analysis-based method for modelling and calculating fault transient characteristics is proposed. First, a dynamic model of inverter-based sources accounting for current loop saturation effects is established, and phase plane analysis is employed to resolve nonlinear control regions. On this basis, a full-time-domain fault current calculation method is proposed, wherein the steady-state operating point after a fault is determined by iteratively solving the network node voltage equations. By integrating control strategies and derived transient differential equations, the fault current expression across the full-time-domain scope is formulated. Furthermore, a multi-objective optimization control strategy is proposed to achieve effective fault current suppression, and an improved Simulated Annealing-Particle Swarm Optimization (SA-IPSO) hybrid algorithm is adopted for efficient solution. Finally, SIMULINK-based simulation experiments validate the accuracy and effectiveness of the proposed method in transient characteristic analysis and current suppression. Full article
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21 pages, 3861 KB  
Article
A Five-Year Field Investigation of Conservation Tillage on Soil Hydrothermal Regimes and Crop Yield Stability in Semi-Arid Agroecosystems
by Fahui Jiang, Jia Xu, Hao Zhang, Chunlei Hao, Wei Zheng, Yanyan Zuo, Liyan Zhang, Zhe Dong, Limei Bian, Yuhan Yao, Yanhua Ci, Qinglin Li and Fansheng Meng
Agriculture 2026, 16(3), 312; https://doi.org/10.3390/agriculture16030312 - 27 Jan 2026
Viewed by 161
Abstract
The sustainable management of Northern China’s vulnerable agro-pastoral ecotone requires a clearer understanding of how tillage systems affect crop productivity through local soil-climate interactions. Therefore, this study was conducted to quantify and compare the long term effects of different tillage practices on soil [...] Read more.
The sustainable management of Northern China’s vulnerable agro-pastoral ecotone requires a clearer understanding of how tillage systems affect crop productivity through local soil-climate interactions. Therefore, this study was conducted to quantify and compare the long term effects of different tillage practices on soil hydrothermal regimes, resource use efficiency, and maize yield stability in a semi-arid agroecosystem. A long term five-year field experiment with maize was conducted in this ecotone to assess three tillage methods: no tillage (NT), deep ploughing (DP), and conventional rotary tillage (RT). Seasonal monitoring included soil moisture, temperature, bulk density, and straw cover. Analyses focused on soil water use efficiency (WUE), the production efficiency per soil thermal unit (PEsoil), and pathways affecting theoretical calculated yield. Results show that relative to RT and DP, NT consistently elevated soil water content within the 0–30 cm profile during the growing season, with the most marked increases from pre-sowing to the V12 stage. This water-conserving effect was stronger in wet years, highlighting the role of precipitation in NT’s performance. DP also retained more soil water than RT, particularly in deeper layers, though its effect was less pronounced than NT’s. Regarding temperature, NT lowered the daily mean soil temperature and accumulated growing degree days (GDD) in early growth phases, a result of residue cover buffering thermal changes. Despite reduced heat accumulation, NT achieved the greatest efficiencies for both heat and water use (PEsoil and WUE), showing increases of 62.03% and 16.64% over RT, respectively, without yield penalty. Key mechanisms include permanent straw mulch under NT, which curtails evaporation, promotes water infiltration, and stabilizes soil structure, thereby modulating hydrothermal dynamics. Structural equation modeling indicated that soil water content, ear number per hectare, and hundred-kernel weight directly and positively determined final yield. Tillage methods exerted indirect effects on yield by modifying soil physical traits and microclimatic conditions. In this semi-arid setting, both NT and DP outperformed RT in conserving soil water, moderating soil temperature, and boosting resource use efficiency. These practices present viable strategies for strengthening crop resilience and sustaining productivity amid climatic variability. Full article
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15 pages, 5730 KB  
Article
A Binary Correlation-Based Ultrasonic Ranging System with Cross-Measurement Interference Mitigation
by Ashish Mahanta, Gil Powers, Dulini H. S. Hewage, Jacob Powers and Haibo Wang
Sensors 2026, 26(3), 834; https://doi.org/10.3390/s26030834 - 27 Jan 2026
Viewed by 189
Abstract
This work presents a binary correlation-based ultrasonic ranging system that supports versatile signal modulation schemes. It transmits ultrasonic waves with distinct characteristics in consecutive measurement operations and employs a set of signal detectors to identify the originating excitation of the received echo signals, [...] Read more.
This work presents a binary correlation-based ultrasonic ranging system that supports versatile signal modulation schemes. It transmits ultrasonic waves with distinct characteristics in consecutive measurement operations and employs a set of signal detectors to identify the originating excitation of the received echo signals, thereby effectively mitigating cross-measurement interference. Design equations supporting diverse modulation schemes are presented, and the factors affecting system performance are discussed. Experimental results obtained with the developed hardware system demonstrate its ability to perform accurate measurements over extended distances and under low signal-to-noise ratio conditions. Furthermore, the system effectively distinguishes echo signals generated by different excitation waves. Full article
(This article belongs to the Section Navigation and Positioning)
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21 pages, 4251 KB  
Article
Comparative Analysis of Unsteady Natural Convection and Thermal Performance in Rectangular and Square Cavities Filled with Stratified Air
by Syed Mehedi Hassan Shaon, Md. Mahafujur Rahaman, Suvash C. Saha and Sidhartha Bhowmick
Fluids 2026, 11(2), 33; https://doi.org/10.3390/fluids11020033 - 27 Jan 2026
Viewed by 72
Abstract
A comprehensive numerical analysis has been conducted to investigate unsteady natural convection (UNC), bifurcation behavior, and heat transfer (HT) in a rectangular enclosure containing thermally stratified air. The enclosure comprises a uniformly heated bottom wall, thermally stratified vertical sidewalls, and a cooled top [...] Read more.
A comprehensive numerical analysis has been conducted to investigate unsteady natural convection (UNC), bifurcation behavior, and heat transfer (HT) in a rectangular enclosure containing thermally stratified air. The enclosure comprises a uniformly heated bottom wall, thermally stratified vertical sidewalls, and a cooled top wall. To assess thermal performance, square and rectangular cavities with identical boundary conditions and working fluid are considered. The finite volume method (FVM) is used to solve the governing equations over a wide range of Rayleigh numbers (Ra = 101 to 109) for air with a Prandtl number (Pr) of 0.71. Flow dynamics and thermal performance are analyzed using temperature time series (TTS), limit point–limit cycle behavior, average Nusselt number (Nuavg), average entropy generation (Savg), average Bejan number (Beavg), and the ecological coefficient of performance (ECOP). In the rectangular cavity, the transition from steady to chaotic flow exhibits three bifurcations: a pitchfork bifurcation at Ra = 3 × 104–4 × 104, a Hopf bifurcation at Ra = 3 × 106–4 × 106, and the onset of chaotic flow at Ra = 9 × 107–2 × 108. The comparative analysis indicates that Nuavg remains nearly identical for both cavities within Ra = 105 to 107. However, at Ra = 108, the HT rate in the rectangular cavity is 29.84% higher than that of the square cavity, while Savg and Beavg differ by 39.32% and 37.50%, respectively. Despite higher HT and Savg in the rectangular enclosure, the square cavity demonstrates superior overall thermal performance by 13.52% at Ra = 108. These results offer significant insights for optimizing cavity geometries in thermal system design based on energy efficiency and entropy considerations. Full article
(This article belongs to the Special Issue Convective Flows and Heat Transfer)
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17 pages, 2629 KB  
Article
Simulated Oxygen Supply Efficiency Assessment to Represent Stored Red Blood Cells Quality
by Zongtang Chu, Guoxing You, Weidan Li, Peilin Shu, Dong Qin, Lian Zhao, Hong Zhou and Ying Wang
Life 2026, 16(2), 205; https://doi.org/10.3390/life16020205 - 26 Jan 2026
Viewed by 113
Abstract
Hemolysis rate is usually used as the acceptance criterion for stored red blood cells (RBCs) in clinical practice. However, there is a current lack of parameters for the characterization of hemoglobin quality. This study aimed to incorporate oxygen affinity, cooperativity, and the Bohr [...] Read more.
Hemolysis rate is usually used as the acceptance criterion for stored red blood cells (RBCs) in clinical practice. However, there is a current lack of parameters for the characterization of hemoglobin quality. This study aimed to incorporate oxygen affinity, cooperativity, and the Bohr effect into a parameter system to monitor oxygen supply efficiency in stored RBCs, potentially serving as a basis for quality assessment. Han Chinese blood from plains, Tibetan blood from plateau, bovine hemoglobin (bHb), and a dextran–bovine hemoglobin conjugate (Dex20-bHb) were analyzed using the BLOODOX-2018. Oxygen affinity (P50) was determined by oxygen dissociation curves (ODCs) at pH = 7.4. Cooperativity was assessed through the Hill coefficient, calculated from the fitting range of the Hill equation. The Bohr effect was evaluated by the acid-base sensitivity index (SI) under simulated pH conditions of the lungs (pH = 7.6) and tissues (pH = 7.2) to calculate corresponding P50 values. Oxygen partial pressures (PO2) simulating lungs (PO2 = 100 mmHg for plains and 60 mmHg for plateau) and tissues (PO2 = 40 mmHg for plains and 30 mmHg for plateau) were used to calculate theoretical oxygen-release capacities in both environments. Multiple regression analysis explored relationships among parameters, constructing a system to assess changes in rat RBCs during storage. Optimized test methods determined P50, Hill coefficient, SI, and theoretical oxygen-release capacities for Han Chinese blood, Tibetan blood, bHb, and Dex20-bHb samples in various environments. We constructed a parameter system to characterize blood’s oxygen supply efficiency, revealing the significant influence of the Bohr effect. This influence varied with environmental changes in oxygen affinity. We validated the system using stored rat RBCs, finding consistent P50 trends with predictions, and initial increases in Hill coefficient and SI followed by decreases. Theoretical oxygen-release capacities varied significantly between plateau and plain environments. These results support using oxygen supply efficiency to assess RBC storage quality for developing transfusion strategies. P50, Hill coefficient, SI, and theoretical oxygen-release capacity in different environments can be incorporated into blood oxygen supply efficiency characterization systems to assess the quality changes in RBCs during storage. Full article
(This article belongs to the Section Physiology and Pathology)
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27 pages, 8712 KB  
Article
Resonant Forcing of Oceanic and Atmospheric Rossby Waves in (Sub)Harmonic Modes: Climate Impacts
by Jean-Louis Pinault
Atmosphere 2026, 17(2), 127; https://doi.org/10.3390/atmos17020127 - 26 Jan 2026
Viewed by 101
Abstract
Baroclinic wave resonance, particularly Rossby waves, has attracted great interest in ocean and atmospheric physics since the 1970s. Research on Rossby wave resonance covers a wide variety of phenomena that can be unified when focusing on quasi-stationary Rossby waves traveling at the interface [...] Read more.
Baroclinic wave resonance, particularly Rossby waves, has attracted great interest in ocean and atmospheric physics since the 1970s. Research on Rossby wave resonance covers a wide variety of phenomena that can be unified when focusing on quasi-stationary Rossby waves traveling at the interface of two stratified fluids. This assumes a clear differentiation of the pycnocline, where the density varies strongly vertically. In the atmosphere, such stationary Rossby waves are observable at the tropopause, at the interface between the polar jet and the ascending air column at the meeting of the polar and Ferrel cell circulation, or between the subtropical jet and the descending air column at the meeting of the Ferrel and Hadley cell circulation. The movement of these air columns varies according to the declination of the sun. In oceans, quasi-stationary Rossby waves are observable in the tropics, at mid-latitudes, and around the subtropical gyres (i.e., the gyral Rossby waves GRWs) due to the buoyant properties of warm waters originating from tropical oceans, transported to high latitudes by western boundary currents. The thermocline oscillation results from solar irradiance variations induced by the sun’s declination, as well as solar and orbital cycles. It is governed by the forced, linear, inviscid shallow water equations on the β-plane (or β-cone for GRWs), namely the momentum, continuity, and potential vorticity equations. The coupling of multi-frequency wave systems occurs in exchange zones. The quasi-stationary Rossby waves and the associated zonal/polar and meridional/radial geostrophic currents modify the geostrophy of the basin. Here, it is shown that the ubiquity of resonant forcing in (sub)harmonic modes of Rossby waves in stratified media results from two properties: (1) the natural period of Rossby wave systems tunes to the forcing period, (2) the restoring forces between the different multi-frequency Rossby waves assimilated to inertial Caldirola–Kanai (CK) oscillators are all the stronger when the imbalance between the Coriolis force and the horizontal pressure gradients in the exchange zones is significant. According to the CK equations, this resonance mode ensures the sustainability of the wave systems despite the variability of the forcing periods. The resonant forcing of quasi-stationary Rossby waves is at the origin of climate variations, as well-known as El Niño, glacial–interglacial cycles or extreme events generated by cold drops or, conversely, heat waves. This approach attempts to provide some new avenues for addressing climate and weather issues. Full article
(This article belongs to the Special Issue Ocean Climate Modeling and Ocean Circulation)
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19 pages, 1858 KB  
Article
Exploring Dynamic Behavior in the Fractional-Order Reaction–Diffusion Model
by Wei Zhang and Haolu Zhang
Fractal Fract. 2026, 10(2), 77; https://doi.org/10.3390/fractalfract10020077 - 23 Jan 2026
Viewed by 145
Abstract
This paper presents a novel high-order numerical method. The proposed scheme utilizes polynomial generating functions to achieve p order accuracy in time for the Grünwald–Letnikov fractional derivatives, while maintaining second-order spatial accuracy. By incorporating a short-memory principle, the method remains computationally efficient for [...] Read more.
This paper presents a novel high-order numerical method. The proposed scheme utilizes polynomial generating functions to achieve p order accuracy in time for the Grünwald–Letnikov fractional derivatives, while maintaining second-order spatial accuracy. By incorporating a short-memory principle, the method remains computationally efficient for long-time simulations. The authors rigorously analyze the stability of equilibrium points for the fractional vegetation–water model and perform a weakly nonlinear analysis to derive amplitude equations. Convergence analysis confirms the scheme’s consistency, stability, and convergence. Numerical simulations demonstrate the method’s effectiveness in exploring how different fractional derivative orders influence system dynamics and pattern formation, providing a robust tool for studying complex fractional systems in theoretical ecology. Full article
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31 pages, 15772 KB  
Article
Effects of Diffusion Limitations and Partitioning on Signal Amplification and Sensitivity in Bienzyme Electrochemical Biosensors Employing Cyclic Product Conversion
by Romas Baronas and Karolis Petrauskas
Appl. Sci. 2026, 16(3), 1171; https://doi.org/10.3390/app16031171 - 23 Jan 2026
Viewed by 109
Abstract
In this study, the nonlinear and non-monotonic behavior of amperometric bienzyme biosensors employing an enzymatic trigger reaction is investigated analytically and computationally using a two-compartment model comprising an enzymatic layer and an outer diffusion layer. The trigger enzymatic reaction is coupled with a [...] Read more.
In this study, the nonlinear and non-monotonic behavior of amperometric bienzyme biosensors employing an enzymatic trigger reaction is investigated analytically and computationally using a two-compartment model comprising an enzymatic layer and an outer diffusion layer. The trigger enzymatic reaction is coupled with a cyclic electrochemical–enzymatic conversion (CEC) process. The model is formulated as a system of reaction–diffusion equations incorporating nonlinear Michaelis–Menten kinetics and interlayer partitioning effects. Exact steady-state analytical solutions for substrate and product concentrations, as well as for the output current, are obtained for specific cases of first- and zero-order reaction kinetics. At the transition conditions, biosensor performance is further analyzed numerically using the finite difference method. The CEC biosensor exhibits the highest signal gain when the first enzyme has low activity and the second enzyme has high activity; however, under these conditions, the response time is the longest. When the first enzyme possesses a higher substrate affinity (lower Michaelis constant) than the second, the biosensor demonstrates severalfold higher current and gain compared to the reverse configuration under identical diffusion limitations. Furthermore, increasing external mass transport resistance or interfacial partitioning can enhance the apparent signal gain. Full article
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21 pages, 831 KB  
Article
Exploring the Roles of Age and Gender in User Satisfaction and Usage of AI-Driven Chatbots in Digital Health Services: A Multigroup Analysis
by Latifa Alzahrani and Vishanth Weerakkody
Systems 2026, 14(1), 113; https://doi.org/10.3390/systems14010113 - 22 Jan 2026
Viewed by 108
Abstract
As chatbot technology becomes increasingly prevalent across a wide range of industries, it is crucial to explore the factors that shape user satisfaction with this AI-driven innovation. This research provides insights into how age and gender impact user perceptions and engagement with AI-driven [...] Read more.
As chatbot technology becomes increasingly prevalent across a wide range of industries, it is crucial to explore the factors that shape user satisfaction with this AI-driven innovation. This research provides insights into how age and gender impact user perceptions and engagement with AI-driven health technologies in Saudi Arabia. The information systems success model has been utilised to determine the effect of age and gender on user satisfaction. A self-administered questionnaire was distributed in two hospitals in Makkah City, Saudi Arabia, and 527 responses were collected from chatbot users. Structural equation modelling via analysis of moment structures validated the model constructs. The findings revealed that the privacy issue on user satisfaction has been significantly greater with males than with females. However, the correlation between user satisfaction and continuance usage intention, as well as net benefits, has been much higher among the females. Also, notable differences were found between user satisfaction and net benefits and continuance usage intention and net benefits, especially when comparing younger and older participants. Across all age groups, user satisfaction consistently emerged as a central driver of continuance usage intention and net benefits, underscoring the importance of fostering satisfaction to enhance the effectiveness of AI-driven chatbots in digital health services. This study can serve as a guide to highlight the importance of chatbot user satisfaction and provide implications, limitations, and future research opportunities. Full article
(This article belongs to the Section Artificial Intelligence and Digital Systems Engineering)
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