Search Results (1,094)

This paper addresses the problem of optimal stabilization for stochastic dynamical systems characterized by Markov switches and concentration points of jumps, which is a scenario not adequately covered by classical stability conditions. Unlike traditional approaches requiring a strictly positive minimal interval between jumps, we allow jump moments to accumulate at a finite point. Utilizing Lyapunov function methods, we derive sufficient conditions for exponential stability in the mean square and asymptotic stability in probability. We provide explicit constructions of Lyapunov functions adapted to scenarios with jump concentration points and develop conditions under which these functions ensure system stability. For linear stochastic differential equations, the stabilization problem is further simplified to solving a system of Riccati-type matrix equations. This work provides essential theoretical foundations and practical methodologies for stabilizing complex stochastic systems that feature concentration points, expanding the applicability of optimal control theory. Full article

This paper explores the complex dynamics of mixed convective flow in a Casson fluid saturated in a non-Darcy porous medium, focusing on the influence of gyrotactic microorganisms, internal heat generation, and multiple convective mechanisms. Casson fluids, known for their non-Newtonian behavior, are relevant in various industrial and biological contexts where traditional fluid models are insufficient. This study addresses the limitations of the standard Darcy’s law by examining non-Darcy flow, which accounts for nonlinear inertial effects in porous media. The governing equations, derived from conservation laws, are transformed into a system of no linear ordinary differential equations (ODEs) using similarity transformations. These ODEs are solved numerically using a finite differencing method that incorporates central differencing, tridiagonal matrix manipulation, and iterative procedures to ensure accuracy across various convective regimes. The reliability of this method is confirmed through validation with the MATLAB (R2024b) bvp4c scheme. The investigation analyzes the impact of key parameters (such as the Casson fluid parameter, Darcy number, Biot numbers, and heat generation) on velocity, temperature, and microorganism concentration profiles. This study reveals that the Casson fluid parameter significantly improves the velocity, concentration, and motile microorganism profiles while decreasing the temperature profile. Additionally, the Biot number is shown to considerably increase the concentration and dispersion of motile microorganisms, as well as the heat transfer rate. The findings provide valuable insights into non-Newtonian fluid behavior in porous environments, with applications in bioengineering, environmental remediation, and energy systems, such as bioreactor design and geothermal energy extraction. Full article

Sediment accumulation in irrigation channels poses a significant challenge to water resource management, impacting hydraulic efficiency and agricultural sustainability. This study introduces an innovative multidisciplinary framework that integrates advanced image analysis (FIJI/ImageJ 1.54p), statistical validation (RStudio), and vector field modeling with a novel Sinusoidal Morphodynamic Bedload Transport Equation (SMBTE) to predict sediment deposition patterns with high precision. Conducted along the Malacatos River in La Tebaida Linear Park, Loja, Ecuador, the research captured a natural sediment transport event under controlled flow conditions, transitioning from pressurized pipe flow to free-surface flow. Observed sediment deposition reduced the hydraulic cross-section by approximately 5 cm, notably altering flow dynamics and water distribution. The final SMBTE model (Model 8) demonstrated exceptional predictive accuracy, achieving RMSE: 0.0108, R²: 0.8689, NSE: 0.8689, MAE: 0.0093, and a correlation coefficient exceeding 0.93. Complementary analyses, including heatmaps, histograms, and vector fields, revealed spatial heterogeneity, local gradients, and oscillatory trends in sediment distribution. These tools identified high-concentration sediment zones and quantified variability, providing actionable insights for optimizing canal design, maintenance schedules, and sediment control strategies. By leveraging open-source software and real-world validation, this methodology offers a scalable, replicable framework applicable to diverse water conveyance systems. The study advances understanding of sediment dynamics under subcritical (Fr ≈ 0.07) and turbulent flow conditions (Re ≈ 41,000), contributing to improved irrigation efficiency, system resilience, and sustainable water management. This research establishes a robust foundation for future advancements in sediment transport modeling and hydrological engineering, addressing critical challenges in agricultural water systems. Full article

Uncertain singular non-causal systems represent a class of singular systems distinguished by the presence of regularity constraints and the involvement of uncertain variables. This paper considers optimal control problems for such systems under the Hurwicz criterion. By integrating dynamic programming with uncertainty theory, a recurrence equation is developed to address these problems. This equation has been shown to be effective in handling the optimal control problems of both linear and nonlinear uncertain singular non-causal systems, thereby enabling the derivation of analytical expressions for their corresponding optimal solutions. Moreover, the transformation of the original system into forward and backward subsystems reveals a fundamental temporal and structural symmetry, which significantly contributes to problem simplification. A detailed example is presented to illustrate the proposed results. Full article

The objective of the present study is to detect chirped optical solitons of the perturbed Chen–Lee–Liu equation with full nonlinearity. By virtue of the traveling wave hypothesis, the discussed model is reduced to a simple form known as an elliptic equation. The latter equation, which is a second-order ordinary differential equation, is handled by the undetermined coefficient method of two forms expressed in terms of the hyperbolic secant and tangent functions. Additionally, the auxiliary equation method is applied to derive several miscellaneous solutions. Various types of chirped solitons are revealed such as W-shaped, bright, dark, gray, kink and anti-kink waves. Taking into consideration the existence conditions, the dynamical behaviors of optical solitons and their corresponding chirp are illustrated. The modulation instability of the perturbed CLL equation is examined by means of the linear stability analysis. It is found that all solutions are stable against small perturbations. These entirely new results, compared to previous works, can be employed to understand pulse propagation in optical fiber mediums and dynamic characteristics of waves in plasma. Full article

Wind erosion poses a major threat to ecosystem stability and land productivity in arid and semi-arid regions. Accurate identification of its spatiotemporal dynamics and underlying driving mechanisms is a critical prerequisite for effective risk forecasting and targeted erosion control. This study applied the Revised Wind Erosion Equation (RWEQ) model to assess the spatial distribution, interannual variation, and seasonal dynamics of the Soil Wind Erosion Modulus (SWEM) across Inner Mongolia from 1990 to 2022. The GeoDetector model was further employed to quantify dominant drivers, key interactions, and high-risk zones via factor, interaction, and risk detection. The results showed that the average SWEM across the study period was 35.65 t·ha⁻¹·yr⁻¹ and showed a decreasing trend over time. However, localised increases were observed in the Horqin and Hulun Buir sandy lands and central grasslands. Wind erosion was most intense in spring (17.64 t·ha⁻¹·yr⁻¹) and weakest in summer (5.57 t·ha⁻¹·yr⁻¹). Gale days, NDVI, precipitation, and wind speed were identified as dominant drivers. Interaction detection revealed non-linear synergies between gale days and temperature (q = 0.40) and wind speed and temperature (q = 0.36), alongside a two-factor interaction between NDVI and precipitation (q = 0.19). Risk detection indicated that areas with gale days > 58, wind speed > 3.01 m/s, NDVI < 0.2, precipitation of 30.17–135.59 mm, and temperatures of 3.01–4.23 °C are highly erosion-prone. Management should prioritise these sensitive and intensifying areas by implementing site-specific strategies to enhance ecosystem resilience. Full article

A comprehensive framework for ultrasound imaging simulations is presented. Solutions to an inhomogeneous wave equation are provided, yielding a linear model for characterizing ultrasound propagation and scattering in soft tissue. This simulation approach, which is based upon the fast nearfield method, is implemented in the Fast Object-oriented C++ Ultrasound Simulator (FOCUS) and is extended to a range of imaging modalities, including synthetic aperture, B-mode, plane wave, and color Doppler imaging. The generation of radiofrequency (RF) data and the receive beamforming techniques employed for each imaging modality, along with background on color Doppler imaging, are described. Simulation results demonstrate rapid convergence and lower error rates compared to conventional spatial impulse response methods and Field II, resulting in substantial reductions in computation time. Notably, the framework effectively simulates hundreds of thousands of scatterers without the need for a full three-dimensional (3D) grid, and the inherent randomness in the scatterer distributions produces realistic speckle patterns. A plane wave imaging example, for instance, achieves high fidelity using 100,000 scatterers with five steering angles, and the simulation is completed on a personal computer in a few minutes. Furthermore, by modeling scatterers as moving particles, the simulation framework captures dynamic flow conditions in vascular phantoms for color Doppler imaging. These advances establish FOCUS as a robust, versatile tool for the rapid prototyping, validation, and optimization of both established and novel ultrasound imaging techniques. Full article

This paper establishes some links between Sturm–Liouville problems and the well-known controllability property in linear dynamic systems, together with a control law design that allows any prefixed arbitrary final state finite value to be reached via feedback from any given finite initial conditions. The scheduled second-order dynamic systems are equivalent to the stated second-order differential equations, and they are used for analysis purposes. In the first study, a control law is synthesized for a forced time-invariant nominal version of the current time-varying one so that their respective two-point boundary values are coincident. Afterward, the parameter that fixes the set of eigenvalues of the Sturm–Liouville system is replaced by a time-varying parameter that is a control function to be synthesized without performing, in this case, any comparison with a nominal time-invariant version of the system. Such a control law is designed in such a way that, for given arbitrary and finite initial conditions of the differential system, prescribed final conditions along a time interval of finite length are matched by the state trajectory solution. As a result, the solution of the dynamic system, and thus that of its differential equation counterpart, is subject to prefixed two-point boundary values at the initial and at the final time instants of the time interval of finite length under study. Also, some algebraic constraints between the eigenvalues of the Sturm–Liouville system and their evolution operators are formulated later on. Those constraints are based on the fact that the solutions corresponding to each of the eigenvalues match the same two-point boundary values. Full article

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 paper presents a modeling framework for hysteretically nonlinear piezoelectric composite beams using functional differential equations (FDEs). While linear piezoelectric models are well established, they fail to capture the complex nonlinear behaviors that emerge at higher electric field strengths, particularly history-dependent hysteresis effects. This paper develops a cascade model that integrates a high-dimensional linear piezoelectric composite beam representation with a nonlinear Krasnosel’skii–Pokrovskii (KP) hysteresis operator. The resulting system is formulated using a state-space model where the input voltage undergoes a history-dependent transformation. Through modal expansion and discretization of the Preisach plane, we derive a tractable numerical implementation that preserves essential nonlinear phenomena. Numerical investigations demonstrate how system parameters, including the input voltage amplitude, and hysteresis parameters significantly influence the dynamic response, particularly the shape and amplitude of limit cycles. The results reveal that while the model accurately captures memory-dependent nonlinearities, it depends on numerous real and distributed parameters, highlighting the need for efficient reduced-order modeling approaches. This work provides a foundation for understanding and predicting the complex behavior of piezoelectric systems with hysteresis, with potential applications in vibration control, energy harvesting, and precision actuation. Full article

Vibration control has long been a key concern in engineering, with low-frequency vibration isolation remaining particularly challenging. Traditional linear isolators are limited in their ability to provide high load-bearing capacity and effective low-frequency isolation simultaneously. In contrast, quasi-zero stiffness (QZS) isolators offer low dynamic stiffness near equilibrium while maintaining high static stiffness, thereby enabling superior isolation performance in the low and ultra-low frequency range. This paper proposes a novel vibration isolation system that combines a grounded dynamic absorber with a QZS isolator, incorporating time-delay feedback control to enhance performance. The dynamic equations of the system are derived using Newton’s second law. The harmonic balance method combined with the arc-length continuation technique is employed to obtain steady-state responses under harmonic force excitation. The influence of feedback gain and time delay on vibration isolation effectiveness and dynamic behavior is analyzed, demonstrating the ability of time-delay feedback to modulate system responses and suppress primary resonance peaks. To further enhance performance, a genetic algorithm is used to optimize the control parameters under harmonic force excitation. The force transmissibility is defined as fitness functions, and the effects of control parameters on these metrics are examined. The results show that the optimized time-delay feedback parameters significantly reduce the transmitted force, improving the overall isolation efficiency. The proposed system provides a promising approach for achieving high-performance vibration isolation in low-frequency environments. Full article

We investigate the bridge problem for stochastic processes, that is, we analyze the statistical properties of trajectories constrained to begin and terminate at a fixed position within a time interval $\tau$. Our primary focus is the time-reversal symmetry of these trajectories: under which conditions do the statistical properties remain invariant under the transformation $t\to \tau -t$? To address this question, we compare the stochastic differential equation describing the bridge, derived equivalently via Doob’s transform or stochastic optimal control, with the corresponding equation for the time-reversed bridge. We aim to provide a concise overview of these well-established derivation techniques and subsequently obtain a local condition for the time-reversal asymmetry that is specifically valid for the bridge. We are specifically interested in cases in which detailed balance is not satisfied and aim to eventually quantify the bridge asymmetry and understand how to use it to derive useful information about the underlying out-of-equilibrium dynamics. To this end, we derived a necessary condition for time-reversal symmetry, expressed in terms of the current velocity of the original stochastic process and a quantity linked to detailed balance. As expected, this formulation demonstrates that the bridge is symmetric when detailed balance holds, a sufficient condition that was already known. However, it also suggests that a bridge can exhibit symmetry even when the underlying process violates detailed balance. While we did not identify a specific instance of complete symmetry under broken detailed balance, we present an example of partial symmetry. In this case, some, but not all, components of the bridge display time-reversal symmetry. This example is drawn from a minimal non-equilibrium model, namely Brownian Gyrators, that are linear stochastic processes. We examined non-equilibrium systems driven by a "mechanical” force, specifically those in which the linear drift cannot be expressed as the gradient of a potential. While Gaussian processes like Brownian Gyrators offer valuable insights, it is known that they can be overly simplistic, even in their time-reversal properties. Therefore, we transformed the model into polar coordinates, obtaining a non-Gaussian process representing the squared modulus of the original process. Despite this increased complexity and the violation of detailed balance in the full process, we demonstrate through exact calculations that the bridge of the squared modulus in the isotropic case, constrained to start and end at the origin, exhibits perfect time-reversal symmetry. Full article

This paper studies an averaged Linear Quadratic Regulator (LQR) problem for a parabolic partial differential equation (PDE), where the system dynamics are affected by uncertain parameters. Instead of assuming a deterministic operator, we model the uncertainty using a probability distribution over a set of possible system dynamics. This approach extends classical optimal control theory by incorporating an averaging framework to account for parameter uncertainty. We establish the existence and uniqueness of the optimal control solution and analyze its convergence as the probability distribution governing the system parameters changes. These results provide a rigorous foundation for solving optimal control problems in the presence of parameter uncertainty. Our findings lay the groundwork for further studies on optimal control in dynamic systems with uncertainty. Full article

Land degradation neutrality is crucial for sustainable mining, necessitating a comprehensive assessment of mining and land restoration performance. Current assessments of mining development and land degradation neutrality are isolated. Therefore, this study formulated a comprehensive framework for economic development and land governance, integrating a Dynamic Network Directional Distance Function (DDF) model with structural equation modeling (SEM), using China’s mining development and land restoration governance as a case study, to evaluate the efficiency and its determinants of mining and land restoration systems. The findings are as follows: there are significant regional differences in mining efficiency; the overall land restoration efficiency is higher than mining efficiency; the development of the two stages is unbalanced, and there is no obvious linear correlation between efficiencies; policy and economic factors negatively impact both mining and land restoration efficiency; technological innovation strongly boosts mining efficiency but has a weaker effect on land restoration efficiency; and climate factors slightly hinder land restoration and mildly enhance mining. Therefore, comprehensively analyzing the mining-land restoration system and considering exogenous factors to internalize externalities are crucial for promoting ecological protection, achieving the LDN target in mining areas, and realizing harmonious human-nature development in China. Full article

This study introduces a novel analytical technique known as the double local fractional Yang–Laplace transform method ($LF{L}_{\zeta }^2$) and rigorously investigates its foundational properties, including linearity, differentiation, and convolution. The proposed method is formulated via double local fractional integrals, enabling a robust mechanism for addressing local fractional partial differential equations defined on fractal domains, particularly Cantor sets. Through a series of illustrative examples, we demonstrate the applicability and efficacy of the $LF{L}_{\zeta }^2$ transform in solving complex local fractional partial differential equation models. Special emphasis is placed on the local fractional Laplace equation, the linear local fractional Klein–Gordon equation, and other models, wherein the method reveals significant computational and analytical advantages. The results substantiate the method’s potential as a powerful tool for broader classes of problems governed by local fractional dynamics on fractal geometries. Full article