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Keywords = time-varying difference equations

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26 pages, 8897 KiB  
Article
Numerical Study of Wave-Induced Longshore Current Generation Zones on a Circular Sandy Sloping Topography
by Mohammad Shaiful Islam, Tomoaki Nakamura, Yong-Hwan Cho and Norimi Mizutani
Water 2025, 17(15), 2263; https://doi.org/10.3390/w17152263 - 29 Jul 2025
Viewed by 192
Abstract
Wave deformation and sediment transport nearest the shoreside are among the main reasons for sand erosion and beach profile changes. In particular, identifying the areas of incident-wave breaking and longshore current generation parallel to the shoreline is important for understanding the morphological changes [...] Read more.
Wave deformation and sediment transport nearest the shoreside are among the main reasons for sand erosion and beach profile changes. In particular, identifying the areas of incident-wave breaking and longshore current generation parallel to the shoreline is important for understanding the morphological changes of coastal beaches. In this study, a two-phase incompressible flow model along with a sandy sloping topography was employed to investigate the wave deformation and longshore current generation areas in a circular wave basin model. The finite volume method (FVM) was implemented to discretize the governing equations in cylindrical coordinates, the volume-of-fluid method (VOF) was adopted to differentiate the air–water interfaces in the control cells, and the zonal embedded grid technique was employed for grid generation in the cylindrical computational domain. The water surface elevations and velocity profiles were measured in different wave conditions, and the measurements showed that the maximum water levels per wave were high and varied between cases, as well as between cross-sections in a single case. Additionally, the mean water levels were lower in the adjacent positions of the approximated wave-breaking zones. The wave-breaking positions varied between cross-sections in a single case, with the incident-wave height, mean water level, and wave-breaking position measurements indicating the influence of downstream flow variation in each cross-section on the sloping topography. The cross-shore velocity profiles became relatively stable over time, while the longshore velocity profiles predominantly moved in the alongshore direction, with smaller fluctuations, particularly during the same time period and in measurement positions near the wave-breaking zone. The computed velocity profiles also varied between cross-sections, and for the velocity profiles along the cross-shore and longshore directions nearest the wave-breaking areas where the downstream flow had minimal influence, it was presumed that there was longshore-current generation in the sloping topography nearest the shoreside. The computed results were compared with the experimental results and we observed similar characteristics for wave profiles in the same wave period case in both models. In the future, further investigations can be conducted using the presented circular wave basin model to investigate the oblique wave deformation and longshore current generation in different sloping and wave conditions. Full article
(This article belongs to the Special Issue Numerical Modeling of Hydrodynamics and Sediment Transport)
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14 pages, 577 KiB  
Article
Social Cognitive Theory and Physical Activity: Examining Gender-Based Prediction Patterns and Theoretical Validity
by Viktoria Sophie Egele and Robin Stark
Sports 2025, 13(8), 249; https://doi.org/10.3390/sports13080249 - 29 Jul 2025
Viewed by 73
Abstract
This study explored gender-specific nuances in the applicability of Social Cognitive Theory (SCT) to predict physical activity behavior. This study aimed to determine whether similar or different prediction patterns emerge for men and women, particularly emphasizing the tenability of the SCT model’s theoretical [...] Read more.
This study explored gender-specific nuances in the applicability of Social Cognitive Theory (SCT) to predict physical activity behavior. This study aimed to determine whether similar or different prediction patterns emerge for men and women, particularly emphasizing the tenability of the SCT model’s theoretical assumptions across gender. Six hundred fifty-four participants (58.1% women, 41.1% men) completed two validated questionnaires at separate time points (t1 = social cognitive and demographic variables; t2 = physical activity behavior). We employed a multigroup Structural Equation Model (SEM) to examine the validity of the theoretical assumptions and the influence of gender. The results suggest that SCT’s theoretical assumptions hold true for men and women, indicated by a highly satisfactory fit of the SEM despite the variance explained being small (R2women = 11.9%, R2men = 7.3%). However, the importance of the specific theoretical paths and the underlying mechanisms of action might differ between genders, and the interplay of the social and cognitive variables to predict physical activity may vary significantly for men and women. The use of SCT can be recommended for explaining and predicting physical activity behavior, although gender-specific differences in the underlying theoretical relationships should be taken into consideration when designing interventions or when being used to explain physical activity behavior. Full article
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20 pages, 4420 KiB  
Article
Perception of Light Environment in University Classrooms Based on Parametric Optical Simulation and Virtual Reality Technology
by Zhenhua Xu, Jiaying Chang, Cong Han and Hao Wu
Buildings 2025, 15(15), 2585; https://doi.org/10.3390/buildings15152585 - 22 Jul 2025
Viewed by 277
Abstract
University classrooms, core to higher education, have indoor light environments that directly affect students’ learning efficiency, visual health, and psychological states. This study integrates parametric optical simulation and virtual reality (VR) to explore light environment perception in ordinary university classrooms. Forty college students [...] Read more.
University classrooms, core to higher education, have indoor light environments that directly affect students’ learning efficiency, visual health, and psychological states. This study integrates parametric optical simulation and virtual reality (VR) to explore light environment perception in ordinary university classrooms. Forty college students (18–25 years, ~1:1 gender ratio) participated in real virtual comparative experiments. VR scenarios were optimized via real-time rendering and physical calibration. The results showed no significant differences in subjects’ perception evaluations between environments (p > 0.05), verifying virtual environments as effective experimental carriers. The analysis of eight virtual conditions (varying window-to-wall ratios and lighting methods) revealed that mixed lighting performed best in light perception, spatial perception, and overall evaluation. Light perception had the greatest influence on overall evaluation (0.905), with glare as the core factor (0.68); closure sense contributed most to spatial perception (0.45). Structural equation modeling showed that window-to-wall ratio and lighting power density positively correlated with subjective evaluations. Window-to-wall ratio had a 0.412 direct effect on spatial perception and a 0.84 total mediating effect (67.1% of total effect), exceeding the lighting power density’s 0.57 mediating effect sum. This study confirms mixed lighting and window-to-wall ratio optimization as keys to improving classroom light quality, providing an experimental paradigm and parameter basis for user-perception-oriented design. Full article
(This article belongs to the Section Building Energy, Physics, Environment, and Systems)
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20 pages, 5297 KiB  
Article
The Validation and Discussion of a Comparative Method Based on Experiment to Determine the Effective Thickness of Composite Glass
by Dake Cao, Xiaogen Liu, Zhe Yang, Jiawei Huang, Ming Xu and Detian Wan
Buildings 2025, 15(14), 2542; https://doi.org/10.3390/buildings15142542 - 19 Jul 2025
Viewed by 224
Abstract
This study introduces and validates a comparative experiment-based method for determining the effective thickness of composite glass, including polymeric laminated glass (with polyvinyl butyral (PVB) and SentryGlas® (SGP) interlayers) and vacuum glazing. This method employs comparative four-point bending tests, defining effective thickness [...] Read more.
This study introduces and validates a comparative experiment-based method for determining the effective thickness of composite glass, including polymeric laminated glass (with polyvinyl butyral (PVB) and SentryGlas® (SGP) interlayers) and vacuum glazing. This method employs comparative four-point bending tests, defining effective thickness by equating the bending stress of a composite specimen to that of a reference monolithic glass specimen under identical loading and boundary conditions. Specimens with varying configurations (glass thicknesses of 5 mm, 6 mm and 8 mm) were tested using non-destructive four-point bending tests under a multi-stage loading protocol (100 N–1000 N). Strain rosettes measured maximum strains at each loading stage to calculate bending stress. Analysis of the bending stress state revealed that vacuum glazing and SGP laminated glass exhibit superior load-bearing capacity compared to PVB laminated glass. The proposed method successfully determined the effective thickness for both laminated glass and vacuum glazing. Furthermore, results demonstrate that employing a 12 mm monolithic reference glass provides the highest accuracy for effective thickness determination. Theoretical bending stress calculations using the effective thickness derived from the 12 mm reference glass showed less than 10% deviation from experimental values. Conversely, compared to established standards and empirical formulas, the proposed method offers superior accuracy, particularly for vacuum glazing. Additionally, the mechanical properties of the viscoelastic interlayers (PVB and SGP) were investigated through static tensile tests and dynamic thermomechanical analysis (DMA). Distinct tensile behaviors and differing time-dependent shear transfer capacities between the two interlayer materials are found out. Key factors influencing the reliability of the method are also discussed and analyzed. This study provides a universally practical and applicable solution for accurate and effective thickness estimation in composite glass design. Full article
(This article belongs to the Section Building Materials, and Repair & Renovation)
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15 pages, 2165 KiB  
Article
Study on the High-Temperature Reaction Kinetics of Solid Waste-Based High Belite Sulphoaluminate Cement Containing Residual Gypsum in Clinker
by Dunlei Su, Mingxin Yang, Yani Hao, Jiahui Wang, Xin Liu, Haojian Tang, Fengyuan Dong, Dejin Xing and Weiyi Kong
Materials 2025, 18(14), 3369; https://doi.org/10.3390/ma18143369 - 17 Jul 2025
Viewed by 330
Abstract
In order to elucidate the high-temperature reaction process of solid waste-based high belite sulphoaluminate cement containing residual gypsum in clinker (NHBSAC) and obtain the formation laws of each mineral in clinker, this article studied its high-temperature reaction kinetics. Through QXRD analysis and numerical [...] Read more.
In order to elucidate the high-temperature reaction process of solid waste-based high belite sulphoaluminate cement containing residual gypsum in clinker (NHBSAC) and obtain the formation laws of each mineral in clinker, this article studied its high-temperature reaction kinetics. Through QXRD analysis and numerical fitting methods, the formation of C4A3S¯, β-C2S, and CaSO4 in clinker under different calcination systems was quantitatively characterized, the corresponding high-temperature reaction kinetics models were established, and the reaction activation energies of each mineral were obtained. The results indicate that the content of C4A3S¯ and β-C2S increases with the prolongation of holding time and the increase in calcination temperature, while CaSO4 is continuously consumed. Under the control mechanism of solid-state reaction, the formation and consumption of minerals follow the kinetic equation. C4A3S¯ and β-C2S satisfy the D4 equation under diffusion mechanism control, and CaSO4 satisfies the R3 equation under interface chemical reaction mechanism control. The activation energy required for mineral formation varies with different temperature ranges. The activation energies required to form C4A3S¯ at 1200–1225 °C, 1225–1275 °C, and 1275–1300 °C are 166.28 kJ/mol, 83.14 kJ/mol, and 36.58 kJ/mol, respectively. The activation energies required to form β-C2S at 1200–1225 °C and 1225–1300 °C are 374.13 kJ/mol and 66.51 kJ/mol, respectively. This study is beneficial for achieving flexible control of the mineral composition of NHBSAC clinker, providing a theoretical basis and practical experience for the preparation of low-carbon cement and the optimization design of its mineral composition. Full article
(This article belongs to the Special Issue Characterization and Optimization of Cement-Based Materials)
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21 pages, 661 KiB  
Article
Semi-Analytical Solutions of the Rayleigh Oscillator Using Laplace–Adomian Decomposition and Homotopy Perturbation Methods: Insights into Symmetric and Asymmetric Dynamics
by Emad K. Jaradat, Omar Alomari, Audai A. Al-Zgool and Omar K. Jaradat
Symmetry 2025, 17(7), 1081; https://doi.org/10.3390/sym17071081 - 7 Jul 2025
Viewed by 233
Abstract
This study investigates the solution structure of the nonlinear Rayleigh oscillator equation through two widely used semi-analytical techniques: the Laplace–Adomian Decomposition Method (LADM) and the Homotopy Perturbation Method (HPM). The Rayleigh oscillator exhibits inherent asymmetry in its nonlinear damping term, which disrupts the [...] Read more.
This study investigates the solution structure of the nonlinear Rayleigh oscillator equation through two widely used semi-analytical techniques: the Laplace–Adomian Decomposition Method (LADM) and the Homotopy Perturbation Method (HPM). The Rayleigh oscillator exhibits inherent asymmetry in its nonlinear damping term, which disrupts the time-reversal symmetry present in linear oscillatory systems. Applying the LADM and HPM, we derive approximate solutions for the Rayleigh oscillator. Due to the absence of exact analytical solutions in the literature, these approximations are benchmarked against high-precision numerical results obtained using Mathematica’s NDSolve function. We perform a detailed error analysis across different damping parameter values ε and time intervals. Our results reveal how the asymmetric damping influences the accuracy and convergence behavior of each method. This study highlights the role of nonlinear asymmetry in shaping the solution dynamics and provides insight into the suitability of the LADM and HPM under varying conditions. Full article
(This article belongs to the Section Physics)
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19 pages, 1361 KiB  
Article
Evaporation and Ignition of Isolated Fuel Drops in an Oxidizing Environment: Analytical Study Based on Varshavskii’s ‘Diffusion Theory’
by Laurencas Raslavičius
Appl. Sci. 2025, 15(13), 7488; https://doi.org/10.3390/app15137488 - 3 Jul 2025
Viewed by 317
Abstract
Varshavskii’s ‘Diffusion Theory’, less investigated due to its limited international visibility, can offer one of the simplest and, on the other hand, high-accuracy methods for evaluating the ignition delay of fossil fuel and biofuel droplets, including their blend. In this study, experimental pre-tests [...] Read more.
Varshavskii’s ‘Diffusion Theory’, less investigated due to its limited international visibility, can offer one of the simplest and, on the other hand, high-accuracy methods for evaluating the ignition delay of fossil fuel and biofuel droplets, including their blend. In this study, experimental pre-tests were conducted to determine pre-existing subject knowledge on stationary droplet combustion at ambient pressure and temperatures varying from 935 to 1010 K followed by simulation of droplet ignition times. The test fuels were mineral diesel (DF), RME and a 20% RME blend with DF. Simulations were performed for isobaric conditions. Using the detailed transport model and detailed chemical kinetics, the necessary rearrangements were made for the governing equations to meet the criteria for modern fuels (biodiesel, diesel, and blend). The influence of different physical parameters, such as droplet radius, or initial conditions, on the ignition delay time was investigated. The high sensitivity of the proposed methodology to experimental results was substantiated. Full article
(This article belongs to the Special Issue Advances in Combustion Science and Engineering)
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16 pages, 4017 KiB  
Article
Tailoring Dialdehyde Bacterial Cellulose Synthesis for Versatile Applications
by Krittanan Kadsanit, Malinee Sriariyanun, Muenduen Phisalaphong and Suchata Kirdponpattara
Polymers 2025, 17(13), 1836; https://doi.org/10.3390/polym17131836 - 30 Jun 2025
Viewed by 255
Abstract
Dialdehyde bacterial cellulose (DBC) has been implemented in versatile applications. DBC was prepared from bacterial cellulose (BC) through periodate oxidation with varying parameters, including the mole ratio of BC and NaOI4, temperature, and reaction time. The relationship between the degree of [...] Read more.
Dialdehyde bacterial cellulose (DBC) has been implemented in versatile applications. DBC was prepared from bacterial cellulose (BC) through periodate oxidation with varying parameters, including the mole ratio of BC and NaOI4, temperature, and reaction time. The relationship between the degree of oxidation (DO)/aldehyde content and these parameters was proposed as a quadratic equation to predict the oxidation conditions needed to achieve a specific DO using Response Surface Methodology (RSM). The chemical structure and morphology of DBC were influenced by DO. DBC with different DO levels was used as a crosslinker and a reinforcing agent for gelatin sponge fabrication. Results indicated that a high DO of DBC could enhance the tensile strength and structural stability of the gelatin matrix. Selecting the proper DO level could control the morphological structure of the gelatin sponge, which is crucial for biomedical applications. Full article
(This article belongs to the Special Issue Polysaccharide-Based Materials: Developments and Properties)
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15 pages, 1027 KiB  
Article
Formation Mechanisms and Kinetic Modeling of Key Aroma Compounds During Qidan Tea Roasting
by Xing Gao, Siyuan Wang, Ying Wang and Huanlu Song
Foods 2025, 14(12), 2125; https://doi.org/10.3390/foods14122125 - 18 Jun 2025
Viewed by 403
Abstract
Understanding the changes in tea aroma and non-volatile substances during roasting is essential for optimizing tea processing and enhancing tea quality. In this study, the Carbon Module Labeling (CAMOLA) technique was employed to simulate the roasting conditions of Qidan, thereby elucidating the formation [...] Read more.
Understanding the changes in tea aroma and non-volatile substances during roasting is essential for optimizing tea processing and enhancing tea quality. In this study, the Carbon Module Labeling (CAMOLA) technique was employed to simulate the roasting conditions of Qidan, thereby elucidating the formation pathway of the theanine-glucose Maillard system. Combined with sensory evaluation, the results indicated that the floral and fruity aromas of Qidan tea decreased, while the woody, roasted, smoky, and herbal aromas increased with prolonged roasting time. Kinetic modeling demonstrated that higher temperatures favored the production of benzaldehyde, which was directly proportional to the heating temperature. In contrast, pyrazines exhibited zero-order kinetics, influenced by both temperature and time. An increasing trend in furans was observed with rising temperature and extended heating time. The kinetic equations effectively describe the changes in aroma compounds associated with merad, highlighting the differences in the production patterns of aroma compounds under varying roasting conditions. This study provides a theoretical foundation for optimizing roasting parameters to enhance tea quality. Full article
(This article belongs to the Section Food Engineering and Technology)
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10 pages, 223 KiB  
Article
Gait Metrics in Elderly Fallers and Non-Fallers with Varying Levels of Glaucoma: A Longitudinal Prospective Cohort Study
by Louay Almidani, José G. Vargas, Zhuochen Yuan, Seema Banerjee, Xindi Chen, Mariah Diaz, Rhonda Miller, Aleksandra Mihailovic and Pradeep Y. Ramulu
Sensors 2025, 25(12), 3712; https://doi.org/10.3390/s25123712 - 13 Jun 2025
Viewed by 467
Abstract
To understand the impact of falls on gait in those with poor sight, we examined how gait changed after falls in older adults with varying degrees of visual impairment from glaucoma. Participants were classified as fallers or non-fallers based on prospective falls data [...] Read more.
To understand the impact of falls on gait in those with poor sight, we examined how gait changed after falls in older adults with varying degrees of visual impairment from glaucoma. Participants were classified as fallers or non-fallers based on prospective falls data from the first study year. Injurious fallers were those who suffered injuries from falls. The GAITRite Electronic Walkway characterized gait at baseline and three annual follow-ups. Parameters examined included stride length, variability in stride length (CV), stride velocity, stride velocity CV, base of support, base of support CV, and cadence. Longitudinal gait changes were assessed using generalized estimating equation models. Stride length significantly decreased in both fallers (β = −0.09 z-score unit/year) and non-fallers (β = −0.08 z-score unit/year), stride velocity slowed only among fallers (β = −0.08 z-score unit/year), and, in contrast, stride velocity CV decreased only among non-fallers (β = −0.07 z-score unit/year). No longitudinal differences were noted between groups. Additionally, no significant differences in gait metrics were observed between non-fallers, one-time fallers, and multiple fallers, nor between those with and without an injurious fall. Amongst older adults, and enriched for those with visual impairment, fallers and non-fallers adopted a more cautious gait over time, with similar gait changes across groups. Our results suggest that, in visual impairment, many falls may not lead to significant changes in gait. Full article
(This article belongs to the Special Issue Fall Detection Based on Wearable Sensors)
11 pages, 261 KiB  
Article
A Result Regarding the Existence and Attractivity for a Class of Nonlinear Fractional Difference Equations with Time-Varying Delays
by Shihan Wang and Danfeng Luo
Fractal Fract. 2025, 9(6), 362; https://doi.org/10.3390/fractalfract9060362 - 31 May 2025
Viewed by 337
Abstract
In this paper, we are studying a class of nonlinear fractional difference equations with time-varying delays in Banach space. By means of mathematical induction and the Picard iteration method, we first obtain the existence result of this fractional difference system. Under some new [...] Read more.
In this paper, we are studying a class of nonlinear fractional difference equations with time-varying delays in Banach space. By means of mathematical induction and the Picard iteration method, we first obtain the existence result of this fractional difference system. Under some new criteria along with the Schauder’s fixed point theorem, we then derive the attractivity conclusions. Subsequently, with the aid of Grönwall’s inequality, we prove that the system is globally attractive. Finally, we give two examples to prove the validity of our theorems. Full article
40 pages, 2146 KiB  
Article
Global Dynamics of a Predator–Prey System with Variation Multiple Pulse Intervention Effects
by Gang Wang, Ming Yi and Zaiyun Zhang
Mathematics 2025, 13(10), 1597; https://doi.org/10.3390/math13101597 - 13 May 2025
Viewed by 268
Abstract
A continuous point of a trajectory for an ordinary differential equation can be viewed as a special impulsive point; i.e., the pulsed proportional change rate and the instantaneous increment for the prey and predator populations can be taken as 0. By considering the [...] Read more.
A continuous point of a trajectory for an ordinary differential equation can be viewed as a special impulsive point; i.e., the pulsed proportional change rate and the instantaneous increment for the prey and predator populations can be taken as 0. By considering the variation multiple pulse intervention effects (i.e., several indefinite continuous points are regarded as impulsive points), an impulsive predator–prey model for characterizing chemical and biological control processes at different fixed times is first proposed. Our modeling approach can describe all possible realistic situations, and all of the traditional models are some special cases of our model. Due to the complexity of our modeling approach, it is essential to examine the dynamical properties of the periodic solutions using new methods. For example, we investigate the permanence of the system by constructing two uniform lower impulsive comparison systems, indicating the mathematical (or biological) essence of the permanence of our system; furthermore, the existence and global attractiveness of the pest-present periodic solution is analyzed by constructing an impulsive comparison system for a norm V(t), which has not been addressed to date. Based on the implicit function theorem, the bifurcation of the pest-present periodic solution of the system is investigated under certain conditions, which is more rigorous than the corresponding traditional proving method. In addition, by employing the variational method, the eigenvalues of the Jacobian matrix at the fixed point corresponding to the pest-free periodic solution are determined, resulting in a sufficient condition for its local stability, and the threshold condition for the global attractiveness of the pest-free periodic solution is provided in terms of an indicator Ra. Finally, the sensitivity of indicator Ra and bifurcations with respect to several key parameters are determined through numerical simulations, and then the switch-like transitions among two coexisting attractors show that varying dosages of insecticide applications and the numbers of natural enemies released are crucial. Full article
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18 pages, 5531 KiB  
Article
A Comparative Study of Solvers and Preconditioners for an SPE CO2 Storage Benchmark Reservoir Simulation Model
by Cenk Temizel, Gökhan Karcıoğlu, Ali Behzadan, Coşkun Çetin and Yusuf Ziya Pamukçu
Geosciences 2025, 15(5), 169; https://doi.org/10.3390/geosciences15050169 - 8 May 2025
Viewed by 510
Abstract
This study analyzes and evaluates the performance of various solvers and preconditioners for reservoir simulations of CO2 injection and long-term storage using the model 11B of SPE CSP (Society of Petroleum Engineers, 11th Comparative Solution Project) and the MATLAB Reservoir Simulation Toolbox [...] Read more.
This study analyzes and evaluates the performance of various solvers and preconditioners for reservoir simulations of CO2 injection and long-term storage using the model 11B of SPE CSP (Society of Petroleum Engineers, 11th Comparative Solution Project) and the MATLAB Reservoir Simulation Toolbox (MRST). The SPE CSP 11 model serves as a benchmark for testing numerical methods for solving partial differential equations (PDEs) in reservoir simulations. The research focuses on the Biconjugate Gradient Stabilized (BiCGSTAB) and Loose Generalized Minimum Residual (LGMRES) solver methods, as well as multiple preconditioning techniques designed to improve convergence rates and reduce computational effort for CO2 storage. Extensive simulations were performed to compare the performance of different solver-preconditioner combinations under varying reservoir conditions, leveraging MRST’s flexible simulation capabilities. Key performance metrics, including iteration counts and computational time, were analyzed for the project. The results reveal trade-offs between computational efficiency and solution accuracy, providing valuable insights into the effectiveness of each approach. This study offers practical guidance for reservoir engineers and researchers seeking to analyze and optimize simulation workflows within MRST by identifying the strengths and limitations of specific solver-preconditioner combinations for complex linear systems. Full article
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20 pages, 7137 KiB  
Article
Design and Analysis of a Serial Position-Controlled Variable Stiffness Rotating Mechanism Based on Multi-Stage Torsional Compliant Mechanisms
by Kai Wen and Guanglei Wu
Actuators 2025, 14(5), 236; https://doi.org/10.3390/act14050236 - 8 May 2025
Viewed by 613
Abstract
This work presents the design and experimental validation of a position-controlled rotating mechanism featuring multi-stage variable stiffness. Before designing the overall mechanism, three different compliant mechanisms, based on flexible beams, are parametrically optimized using a SolidWorks–Ansys co-simulation technique. The flexible beams are composed [...] Read more.
This work presents the design and experimental validation of a position-controlled rotating mechanism featuring multi-stage variable stiffness. Before designing the overall mechanism, three different compliant mechanisms, based on flexible beams, are parametrically optimized using a SolidWorks–Ansys co-simulation technique. The flexible beams are composed of multiple straight segments, Bezier curves, and multiple arc segments. The corresponding torque–deflection curves of the compliant mechanisms are collected and fitted into analytical expressions, from which the stiffness equation varying with the angular position is derived for stiffness regulation. A combination of three-stage compliant mechanisms connected in serial is realized to prototype the physical mechanism, which can have three different stiffness ranges of the output shaft. The maximum stiffness is about nine times higher than the lowest one, leading to a broader bandwidth of varying stiffness, which can make the mechanism more adaptive to the external payloads for safety consideration. Experimental measurements are carried out, and the comparison shows a good agreement between the experimental and simulation results, which experimentally validated the design concept. The compact and simple structure, as well as the multi-stage variable stiffness ranges, implies high adaptability of the designed mechanism. Full article
(This article belongs to the Section Actuators for Robotics)
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14 pages, 617 KiB  
Article
Iterative Forecasting of Financial Time Series: The Greek Stock Market from 2019 to 2024
by Evangelos Bakalis and Francesco Zerbetto
Entropy 2025, 27(5), 497; https://doi.org/10.3390/e27050497 - 4 May 2025
Viewed by 1031
Abstract
Predicting the evolution of financial data, if at all possible, would be very beneficial in revealing the ways in which different aspects of a global environment can impact local economies. We employ an iterative stochastic differential equation that accurately forecasts an economic time [...] Read more.
Predicting the evolution of financial data, if at all possible, would be very beneficial in revealing the ways in which different aspects of a global environment can impact local economies. We employ an iterative stochastic differential equation that accurately forecasts an economic time series’s next value by analysing its past. The input financial data are assumed to be consistent with an α-stable Lévy motion. The computation of the scaling exponent and the value of α, which characterises the type of the α-stable Lévy motion, are crucial for the iterative scheme. These two indices can be determined at each iteration from the form of the structure function, for the computation of which we use the method of generalised moments. Their values are used for the creation of the corresponding α-stable Lévy noise, which acts as a seed for the stochastic component. Furthermore, the drift and diffusion terms are calculated at each iteration. The proposed model is general, allowing the kind of stochastic process to vary from one iterative step to another, and its applicability is not restricted to financial data. As a case study, we consider Greece’s stock market general index over a period of five years, from September 2019 to September 2024, after the completion of bailout programmes. Greece’s economy changed from a restricted to a free market over the chosen era, and its stock market trading increments are likely to be describable by an α-stable L’evy motion. We find that α=2 and the scaling exponent H varies over time for every iterative step we perform. The forecasting points follow the same trend, are in good agreement with the actual data, and for most of the forecasts, the percentage error is less than 2%. Full article
(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics II)
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