Search Results (29)

Parabolic trough collector (PTC) systems, often deployed in arid regions, are vulnerable to dust accumulation (soiling), which reduces mirror reflectivity and energy output. This study presents a physically based soiling forecast algorithm (SFA) designed to estimate soiling levels. The model was calibrated and validated using three meteorological data sources—numerical forecasts (YR), METAR observations, and on-site measurements—from a PTC facility in Limassol, Cyprus. Field campaigns covered dry, rainy, and red-rain conditions. The model demonstrated robust performance, particularly under dry summer conditions, with normalized root mean square errors (NRMSE) below 1%. Sedimentation emerged as the dominant soiling mechanism, while the contributions of impaction and Brownian motion varied according to site-specific environmental conditions. Under dry deposition conditions, the reflectivity change rate during spring and autumn was approximately twice that of summer, indicating a need for more frequent cleaning during transitional seasons. A red-rain event resulted in a pronounced drop in reflectivity, showcasing the model’s ability to capture abrupt soiling dynamics associated with extreme weather episodes. The proposed SFA offers a practical, adaptable tool for reducing soiling-related losses and supporting seasonally adjusted maintenance strategies for solar thermal systems. Full article

The article presents a new method for evaluating investment projects in uncertain conditions, assuming that uncertainty may have two origins: aleatory (related to randomness) and epistemic (due to incomplete knowledge). Epistemic uncertainty is rarely considered in investment analysis, which can result in undervaluing the future opportunities and risks. Our contribution is built around a correlated random–fuzzy Geometric Brownian Motion, a hybrid Monte Carlo engine that propagates mixed uncertainty into a probability box, combined with three p-box-to-CDF transformations (pignistic, ambiguity-based and credibility-based) to reflect decision-maker attitudes. Our approach utilizes the Datar–Mathews method (DM method) to gather relevant information regarding the potential value of a real option. By combining probabilistic and possibilistic approaches, the proposed valuation model incorporates hybrid Monte Carlo simulation and a random–fuzzy Geometric Brownian Motion, considering the interdependence between parameters. The result of the hybrid simulation is a pair of upper and lower cumulative probability distributions, known as a p-box, which represents the uncertainty range of the Net Present Value (NPV). We propose three transformations of the p-box into a subjective probability distribution, which allow decision makers to incorporate their subjective beliefs and risk preferences when performing real option valuation. Thus, our approach allows the combination of objective available information about valuation of investment with the decision maker’s attitude in front of partial ignorance. To demonstrate the effectiveness of our approach in practical scenarios, we provide a numerical illustration that clearly showcases how our approach delivers a more precise valuation of real options. Full article

This study examines the price dynamics of the UK Emission Trading Scheme (UK ETS) by integrating advanced computational methods, including deep learning and statistical modelling, to analyze and simulate carbon market behaviour. By analyzing long-memory effects and price volatility, it assesses whether UK carbon prices align with theoretical expectations from carbon pricing mechanisms and market efficiency theories. Findings indicate that UK carbon prices exhibit persistent long-memory effects, contradicting the Efficient Market Hypothesis, which assumes price movements are random and fully reflect available information. Furthermore, regulatory interventions exert significant downward pressure on prices, suggesting that policy uncertainty disrupts price equilibrium in cap-and-trade markets. Deep learning models, such as Time-series Generative Adversarial Networks (TGANs) and adjusted fractional Brownian motion, outperform traditional approaches in capturing price dependencies but are prone to overfitting, highlighting trade-offs in AI-based forecasting for carbon markets. These results underscore the need for predictable regulatory frameworks, hybrid pricing mechanisms, and data-driven approaches to enhance market efficiency. By integrating empirical findings with economic theory, this study contributes to the carbon finance literature and provides insights for policymakers on improving the stability and effectiveness of emissions trading systems. Full article

In this study, we present a novel mathematical framework for pricing financial derivates and modelling asset behaviour by bringing together fractional Brownian motion (fBm), fuzzy logic, and jump processes, all aligned with no-arbitrage principle. In particular, our mathematical developments include fBm defined through Mandelbrot-Van Ness kernels, and advanced mathematical tools such Molchan martingale and BDG inequalities ensuring rigorous theoretical validity. We bring together these different concepts to model uncertainties like sudden market shocks and investor sentiment, providing a fresh perspective in financial mathematics and derivatives pricing. By using fuzzy logic, we incorporate subject factors such as market optimism or pessimism, adjusting volatility dynamically according to the current market environment. Fractal mathematics with the Hurst exponent close to zero reflecting rough market conditions and fuzzy set theory are combined with jumps, representing sudden market changes to capture more realistic asset price movements. We also bridge the gap between complex stochastic equations and solvable differential equations using tools like Feynman-Kac approach and Girsanov transformation. We present simulations illustrating plausible scenarios ranging from pessimistic to optimistic to demonstrate how this model can behave in practice, highlighting potential advantages over classical models like the Merton jump diffusion and Black-Scholes. Overall, our proposed model represents an advancement in mathematical finance by integrating fractional stochastic processes with fuzzy set theory, thus revealing new perspectives on derivative pricing and risk-free valuation in uncertain environments. Full article

This paper presents an original and comprehensive comparative analysis of eight fractal analysis methods, including Box Counting, Compass, Detrended Fluctuation Analysis, Dynamical Fractal Approach, Hurst, Mass, Modified Mass, and Persistence. These methods are applied to artificially generated fractal data, such as Weierstrass–Mandelbrot functions and fractal Brownian motion, as well as natural datasets related to environmental and geophysical domains. The objectives of this research are to evaluate the methods’ capabilities in capturing fractal properties, their computational efficiency, and their sensitivity to data fluctuations. Main findings indicate that the Dynamical Fractal Approach consistently demonstrated the highest accuracy across different datasets, particularly for artificial data. Conversely, methods like Mass and Modified Mass showed limitations in complex fractal structures. For natural datasets, including meteorological and geological data, the fractal dimensions varied significantly across methods, reflecting their differing sensitivities to structural complexities. Computational efficiency analysis revealed that methods with linear or logarithmic complexity, such as Persistence and Compass, are most suited for larger datasets, while methods like DFA and Dynamic Fractal Approaches required higher computational resources. This study provides an original comparative study for researchers to select appropriate fractal analysis techniques based on dataset characteristics and computational limitations. Full article

Aiming at the problem of high failure rate and inconvenient maintenance of wind turbine gearboxes, this paper establishes a stochastic differential equation model that can be used to fit the change of gearbox oil temperature and adopts an iterative computational method and Markov-based modified optimization to fit the prediction sequence in order to realize the accurate prediction of gearbox oil temperature. The model divides the oil temperature change of the gearbox into two parts, internal aging and external random perturbation, adopts the approximation theorem to establish the internal aging model, and uses Brownian motion to simulate the external random perturbation. The model parameters were calculated by the Newton–Raphson iterative method based on the gearbox oil temperature monitoring data. Iterative calculations and Markov-based corrections were performed on the model prediction data. The gearbox oil temperature variations were simulated in MATLAB, and the fitting and testing errors were calculated before and after the iterations. By comparing the fitting and testing errors with the ordinary differential equations and the stochastic differential equations before iteration, the iterated model can better reflect the gear oil temperature trend and predict the oil temperature at a specific time. The accuracy of the iterated model in terms of fitting and prediction is important for the development of preventive maintenance. Full article

The mean square synchronization problem of the complex dynamical network (CDN) with the stochastic link dynamics is investigated. In contrast to previous literature, the CDN considered in this paper can be viewed as consisting of two subsystems coupled to each other. One subsystem consists of all nodes, referred to as the nodes subsystem, and the other consists of all links, referred to as the network topology subsystem, where the weighted values can quantitatively reflect changes in the network’s topology. Based on the above understanding of CDN, two vector stochastic differential equations with Brownian motion are used to model the dynamic behaviors of nodes and links, respectively. The control strategy incorporates not only the controller in the nodes but also the coupling term in the links, through which the CDN is synchronized in the mean-square sense. Meanwhile, the dynamic stochastic signal is proposed in this paper, which is regarded as the auxiliary reference tracking target of links, such that the links can track the reference target asymptotically when synchronization occurs in nodes. This implies that the eventual topological structure of CDN is stochastic. Finally, a comparison simulation example confirms the superiority of the control strategy in this paper. Full article

This paper presents a hybrid algorithm based on the slime mould algorithm (SMA) and the mixed dandelion optimizer. The hybrid algorithm improves the convergence speed and prevents the algorithm from falling into the local optimal. (1) The Bernoulli chaotic mapping is added in the initialization phase to enrich the population diversity. (2) The Brownian motion and Lévy flight strategy are added to further enhance the global search ability and local exploitation performance of the slime mould. (3) The specular reflection learning is added in the late iteration to improve the population search ability and avoid falling into local optimality. The experimental results show that the convergence speed and precision of the improved algorithm are improved in the standard test functions. At last, this paper optimizes the parameters of the Extreme Learning Machine (ELM) model with the improved method and applies it to the power load forecasting problem. The effectiveness of the improved method in solving practical engineering problems is further verified. Full article

The application of convective heat transport holds great significance in physiological studies, particularly in preventing the overheating of birds and mammals living in warm climates. This process involves the transfer of heated blood from the body’s core to the nearest blood vessels, effectively dissipating the excess heat into the environment. As a result, analyzing convective boundary conditions becomes crucial for understanding heat and solutal profiles in the flow of a two-phase nanofluid model (Darcy–Forchheimer), which also takes into account heat sources and chemical reactions. This model encompasses the combined effects of Brownian and thermophoresis phenomena on flow behavior. The development of a three-dimensional model leads to a set of nonlinear ODEs, which can be tackled using appropriate similarity variables and traditional numerical techniques, i.e., the Runge–Kutta fourth-order combined with shooting technique is adopted to obtain the solutions. To ensure the model’s accuracy, physical parameters are carefully chosen within their appropriate ranges to reflect real-world behavior. This approach helps to capture the physical essence of the system under study. It is observed that the streamlines for the proposed stream function shows the flow pattern of the fluid particles within the domain for the variation of the kinematic viscosity and stream values, and enhanced Brownian motion controls the fluid concentration. Full article

We consider symmetric fuzzy stochastic differential equations where diffusion and drift terms arise in a symmetric way at both sides of the equations and diffusion parts are driven by fractional Brownian motions. Such equations can be used in real-life hybrid systems, which include properties of being both random and fuzzy and reflecting long-range dependence. By imposing on the mappings occurring in the equation the conditions of Lipschitzian continuity and additional constraints by an integrable stochastic process, we construct an approximation sequence of fuzzy stochastic processes and apply this to prove the existence of a unique solution to the studied equation. Finally, a model from population dynamics is considered to illustrate the potential application of our equations. Full article

Preventive maintenance is widely used in wind turbine equipment to ensure their safe and reliable operation, and this mainly includes time-based maintenance (TBM) and condition-based maintenance (CBM). Most wind farms only use TBM as the main maintenance strategy in engineering practice. Although this can meet certain reliability requirements, it cannot fully utilize the characteristics of TBM and CBM. For this, a state model based on the stochastic differential equation (SDE) is established in this paper to describe the spatio-temporal evolution process of the degradation behavior of wind turbine generators, in which the components’ failure is represented by a proportional hazards model, the random fluctuation of the state is simulated by the Brownian motion, and the SDE model is solved by a function transformation method. Based on the model, the characteristics of TBM and CBM, and the asymptotic relationship between them, are discussed and analyzed, the necessity and feasibility of their combination are expounded, and a joint maintenance strategy is proposed and analyzed. The results show that the stochastic model can better reflect the real deterioration state of the generator. Moreover, TBM has a fixed maintenance interval, depending on global sample tracks and, only depending on the local sample track, CBM can follow the component state. Finally, the rationality and effectiveness of the proposed model and results are verified by a practical example. Full article

Mathematical difficulty remains in many classical financial problems, especially for a closed-form expression of asset value. The European option evaluation problem based on a regime-switching has been formally modeled since early 2000, for which a recursive algorithm was developed to solve it. The key mathematical difficulty of this problem relies on the expectation $\mathrm{I}\mathrm{E}\left[h\left(Y_T\right)\right]$, where h is a payoff function and ${\left\{Y_t\right\}}_{t\in [0,T]}$ denotes a geometric Brownian motion with Markovian regime-switching. It is long since attempted to conclude this problem with closed form formulas. Towards the same target, this paper applies some novel techniques to draw explicit formulas for cases with more states for regime-switching (whereas the former deals the cases with two states) for any integrable function h (whereas the former only applies to the payoff of a European option). This paper combines the technique of occupation time of Markov chains and inverse Laplace transform to achieve the density function of geometric Brownian motion with Markovian regime-switching. Extension along this technique creates potential for probabilistic computations in addition to European option pricing. The reflection from the inverse Laplace transform to the expression of a moment-generating function is the core technique developed by this paper, and it is presented in symmetric forms. Full article

The current research study is focusing on the investigation of the physical effects of thermal radiation on heat and mass transfer of a nanofluid located around a sphere. The configuration is investigated by solving the partial differential equations governing the phenomenon. By using suitable non-dimensional variables, the governing set of partial differential equations is transformed into a dimensionless form. For numerical simulation, the attained set of dimensionless partial differential equations is discretized by using the finite difference method. The effects of the governing parameters, such as the Brownian motion parameter, the thermophoresis parameter, the radiation parameter, the Prandtl number, and the Schmidt number on the velocity field, temperature distribution, and mass concentration, are presented graphically. Moreover, the impacts of these physical parameters on the skin friction coefficient, the Nusselt number, and the Sherwood number are displayed in the form of tables. Numerical outcomes reflect that the effects of the radiation parameter, thermophoresis parameter, and the Brownian motion parameter intensify the profiles of velocity, temperature, and concentration at different circumferential positions on the sphere. Full article

In this paper, the mixed convective heat transfer mechanism of nanofluids is investigated. Based on the Buongiorno model, we develop a novel Cattaneo–Buongiorno model that reflects the non-local properties as well as Brownian motion and thermophoresis diffusion. Due to the highly non-linear character of the equations, the finite difference method is employed to numerically solve the governing equations. The effectiveness of the numerical method and the convergence order are presented. The results show that the rise in the fractional parameter $\delta$ enhances the energy transfer process of nanofluids, while the fractional parameter $\gamma$ has the opposite effect. In addition, the effects of Brownian motion and thermophoresis diffusion parameters are also discussed. We infer that the flow and heat transfer mechanism of the viscoelastic nanofluids can be more clearly revealed by controlling the parameters in the Cattaneo–Buongiorno model. Full article

Stochastic SIRS models play a key role in formulating and analyzing the transmission of infectious diseases. These models reflect the environmental changes of the diseases and their biological mechanisms. Therefore, it is very important to study the uniqueness and existence of the global positive solution to investigate the asymptotic properties of the model. In this article, we investigate the dynamics of the stochastic SIRS epidemic model with a saturated incidence rate. The effects of both deterministic and stochastic distribution from infectious to susceptible are analyzed. Our findings show that the occurrence of symmetry breaking as a function of the stochastic noise has a significant advantage over the deterministic one to prevent the spread of the infectious diseases. The larger stochastic noise will guarantee the control of epidemic diseases with symmetric Brownian motion. Periodic outbreaks and re-infection may occur due to the existence of feedback memory. It is shown that the endemic equilibrium is stable under some suitable initial conditions, taking advantage of the symmetry of the large amount of contact structure. A numerical method based on Legendre polynomials that converts the given stochastic SIRS model into a nonlinear algebraic system is used for the approximate solution. Finally, some numerical experiments are performed to verify the theoretical results and clearly show the sharpness of the obtained conditions and thresholds. Full article