Search Results (275)

In this study, we develop and investigate a novel fractional discrete-time computer virus dynamics model in two dimensions with a memristive nonlinear coupling mechanism. The memristor introduces nonlinearity by having memory regulation that depends on the state and enhances the propagation dynamics of virus spread. By investigating both matching and non-matching fractional orders, it is then possible to derive useful knowledge with respect to cooperating roles in terms of fractional memory and memristive effects. The complexity behind it is confirmed via 3D phase portraits, bifurcation analysis with LE_max calculation, 0–1 chaos test, and SE complexity. Numerical results reveal rich dynamical phenomena, including periodic oscillations, quasi-periodicity, and strong chaos. In fact, positive LE_max values, Brownian-like trajectories, and high-complexity SE corroborate the chaotic nature of the regimes. Thereby, the fractional-order separation in noncommensurate conditions is a marker of chaotic motion, magnified in the emergently high-dimensional space introduced by the memristive element. As these results indicate that the derivative model proposed here provides an excellent fit for complex viruses present in scaffolds, it may prove to be a useful modeling tool. Full article

Under dynamic loading conditions, the output voltage of proton exchange membrane fuel cells (PEMFCs) exhibits nonlinear degradation characterized by non-Gaussian fluctuations, abrupt changes, and long-range temporal dependence, which are difficult to model using conventional short-correlation or remaining useful life (RUL) prediction approaches. To capture both historical dependency and stochastic jump behavior, this study proposes a SHAP-driven mechanism–data fusion fractional stochastic degradation model based on fractional Brownian motion (fBm) and fractional Poisson process (fPp) for degradation trend forecasting. A terminal voltage mechanism model considering activation, ohmic, and concentration polarization losses is first established, and SHapley Additive exPlanations (SHAP) analysis is employed to quantify the contributions of multi-source operational variables and enhance interpretability. The Hurst exponent is then used to verify long-range dependence and jump characteristics in the voltage sequence. Subsequently, fBm is integrated with a fPp to construct a unified stochastic degradation framework capable of jointly describing continuous decay and discrete abrupt variations, enabling multi-step probabilistic prediction with confidence intervals. Validation on the publicly available FCLAB FC1 and FC2 datasets shows that the proposed model achieves superior overall performance under both steady and dynamic conditions, with MAPE/RMSE/R² of 0.027%/0.00178/0.9895 and 0.056%/0.00259/0.9896, respectively, outperforming fBm, Wiener, WTD-RS-LSTM, and CNN-LSTM methods. The proposed approach provides accurate and interpretable degradation forecasting for PEMFC health management and maintenance decision support. Full article

Micro heat exchangers (MHXs) have emerged as a critical technology for advanced thermal management in the food and pharmaceutical industries due to their high surface area-to-volume ratios, compact design, and precise temperature control. This review provides a systematic and integrated analysis of MHX technology, covering their fundamental principles, classification, design methodologies, performance enhancement techniques, and industrial applications. Unlike existing reviews, the present work establishes a unified framework that links microscale heat transfer mechanisms, such as Brownian motion, surface corrugation effects, and non-dimensional parameters, with practical design choices, manufacturing routes, and the process requirements specific to food and pharmaceutical systems. The subsequent sections explore the key performance-influencing factors, including channel geometry, surface enhancement strategies, nanofluid utilization, and governing non-dimensional numbers (e.g., Nusselt, Reynolds, and Knudsen numbers), which are systematically compared across different operating regimes. Recent advances in materials and fabrication techniques, such as laser ablation, lithography, micro-milling, embossing, and additive manufacturing, are analyzed with respect to their scalability, thermal–hydraulic performance, and industrial feasibility. Furthermore, the review highlights the emerging trends in micro heat exchanger (MHX) optimization, including computational fluid dynamics (CFD)-driven design, smart monitoring systems, and energy-efficient integration within processing lines. Finally, the paper also identifies the key challenges and limitations of micro heat exchangers, including pressure drop, fouling, scaling, manufacturing complexity, and cost constraints. These are critically discussed along with future research directions aimed at improving reliability and sustainability. By consolidating the dispersed research outcomes into a coherent, design-oriented perspective, this review offers new insights and practical guidance for researchers, engineers, and industry practitioners seeking to advance the deployment of MHXs in food and pharmaceutical processing. Full article

Although many studies have focused on the initial adhesion of bacteria, there have been few that looked at responses to changing environmental conditions. To more closely examine the viscoelastic nature of initial adhesion, surface-associated bacteria were quantified and monitored for their Brownian motion vibrations. This study used a flow chamber to observe the surface association of Enterobacter cloacae BS 1037, Staphylococcus aureus ATCC 12600, Klebsiella pneumoniae–1, Acinetobacter baumannii–1, Pseudomonas aeruginosa PA O1, and Enterococcus faecalis 1396 to glass under dynamic shear rates of 7–15–30 s⁻¹, 15–30–60 s⁻¹, and 30–15–7 s⁻¹. Comparing increasing and decreasing shear rates, information about retention and recovery became apparent. Coccoid bacteria primarily reacted to directional changes in shear rates with changes in either surface-associated bacterial densities or surface-associated strength independently. A. baumannii and E. faecalis did not change their associated strength, whereas S. aureus did not change its associated density. Bacillus bacteria demonstrated differences in both associations with directional changes in shear rates. We demonstrate that retention and recovery are different methods of adaptation to environmental conditions utilised by different bacterial species. These adaptations may form the basis of upregulation and downregulation responses used for survival. Full article

This paper develops a unified analytical approach for pricing a broad class of volatility-linked financial derivatives under the sub-mixed fractional geometric Brownian motion model. The proposed framework captures key empirical features of financial markets, including correlated non-stationary Gaussian increments and long-memory dependence, while preserving the semimartingale property required for arbitrage-free pricing. We present the exact distribution of the realized variance as a quadratic form of correlated non-stationary Gaussian increments, which leads to a closed-form expression for the cumulative distribution function via a Laguerre-series expansion. These distributional results enable analytical pricing formulas for an extensive family of volatility-linked derivatives. Monte Carlo simulations confirm the accuracy and computational efficiency of the proposed formulas, while numerical investigations illustrate the significant impact of non-stationarity, long-memory effects, and the Hurst parameter on derivative values. These results contribute to a deeper theoretical understanding and more effective computational methods for pricing nonlinear volatility derivatives in markets characterized by persistent temporal dependence and non-stationary stochastic dynamics. Full article

As a critical carbon offset mechanism, China’s Certified Emission Reduction (CCER) plays a pivotal role in achieving the “dual carbon” targets. With the relaunch of its trading market, refining the CCER valuation framework has become imperative. This study develops a multidimensional CCER valuation methodology based on both the income and market approaches. Under the income approach, two probabilistic models—discrete and continuous emission distribution frameworks—are proposed to quantify CCER value. Under the market approach, a Geometric Brownian Motion (GBM) model and a Long Short-Term Memory (LSTM) neural network model are constructed to capture nonlinear temporal dynamics in CCER pricing. Through a systematic comparative analysis of the outputs and methodologies of these models, this study identifies optimal pricing strategies to enhance CCER valuation. Results reveal significant disparities among models in predictive accuracy, computational efficiency, and adaptability to market dynamics. Each model exhibits distinct strengths and limitations, necessitating scenario-specific selection based on data availability, application context, and timeliness requirements to strike a balance between precision and efficiency. These findings offer both theoretical and practical insights to support the development of the CCER market. Full article

This paper focuses on the Caputo-Hadamard fractional uncertain differential equations (CH-FUDEs) governed by Liu processes, which combine the Caputo–Hadamard fractional derivative with uncertain differential equations to describe dynamic systems involving memory characteristics and uncertain information. Within the framework of uncertain theory, this Liu process serves as the counterpart to Brownian motion. We establish some new Bihari type fractional inequalities that are easy to apply in practice and can be considered as a more general tool in some situations. As applications of those inequalities, we establish the well-posedness of a proposed class of equations under specified non-Lipschitz conditions. Building upon this result, we establish the notions of stability in distribution and stability in measure solutions to CH-FUDEs, deriving sufficient conditions to ensure these stability properties. Finally, the theoretical findings are verified through two numerical examples. Full article

In PAC spectroscopy, hyperfine interactions of a radioactive probe nucleus with its surroundings are measured, providing information about the local atomic structure and dynamics at the probe site. In the so-called fast reorientation time regime for fluctuating nuclear quadrupole interactions (NQIs), the PAC signal is an exponentially decaying function, with decay constant λ depending on both the hyperfine interaction and dynamics. For a molecular system in solution, dynamics may originate from Brownian molecular tumbling (rotational diffusion) with rotational correlation time τ_c and from local dynamics at the probe site, occurring at a characteristic time scale τ_loc. The τ_c and the τ_loc cannot be discriminated in a single PAC spectrum; however, assuming that they scale differently with viscosity and temperature, a series of experiments in which these parameters are varied may allow for discrimination of τ_c and the τ_loc. Three models are presented for the effect of dynamics on the PAC signal: (1) the Stokes–Einstein–Debye model with linear scaling of λ with viscosity ξ; (2) a more general model presenting a power law scaling of λ with (ξ/ξ₀)ⁿ; and (3) a model that includes rotational and local dynamics leading to an expression for λ that scales with ξ/(ξ + c), where c is a constant that depends on temperature, molecular volume, and τ_loc. These models may serve as different approaches to analyze PAC data and their dependence on temperature and solvent viscosity in the fast reorientation time regime, and they can be applied to design experiments for optimal discrimination of global rotational diffusion and local dynamics at the probe site. Full article

Cascade reservoir optimization faces significant challenges due to multi-dimensional, non-convex, and nonlinear characteristics with coupled constraints. As reservoir numbers increase, computational complexity escalates dramatically, limiting conventional optimization methods’ effectiveness. This paper proposes HHONMPA, a hybrid algorithm combining Harris Hawks Optimization (HHO) with Marine Predators Algorithm (MPA). The method uses SPM chaotic mapping for population initialization to enhance diversity and integrates both algorithms’ predatory behaviors. During exploration, it employs Brownian motion and improved Lévy flight strategies for global search, while exploitation uses enhanced HHO for local optimization. A novel Dual-Period Oscillation Attenuation Strategy dynamically adjusts parameters to balance exploration-exploitation. Performance validation using CEC2017 benchmark functions shows HHONMPA significantly outperforms the original HHO and MPA in solution accuracy and convergence speed, confirmed through statistical testing. Engineering validation applies the algorithm to the Lower Jinsha River—Three Gorges four-reservoir system, conducting experiments across various hydrological scenarios. Results demonstrate substantial improvements in search accuracy and convergence efficiency compared to existing methods. HHONMPA effectively addresses large-scale cascade reservoir optimization challenges, offering promising prospects for water resource management and hydropower scheduling applications. Full article

Using molecular dynamics simulations, we explore the impact of correlated monomer activity and star topology on the structure and dynamics of active polymers. Unlike uncorrelated active Brownian particle (ABP) stars, correlated activity induces a rather steep stretching of the star polymer at intermediate activity levels. This stretching is characterized by transitions between distinct, metastable states defined by the coordinated movement of the arms, leading to novel collective dynamics. The behavior is consistent with experimental observations of active oligomers, highlighting the critical role of activity correlations for the understanding and modeling of active polymers. Full article

This study investigates the valuation of defaultable corporate bonds using a two-factor model of Markov-modulated stochastic volatility with double exponential jumps (2FMMSVDEJ). This model captures long- and short-term SV and asymmetrical jumps in the underlying asset value. Concurrently, the firm’s debt dynamics are governed by a Markov-modulated GBM (MMGBM) model to reflect state transitions. A dynamic measure change technique is employed to determine the pricing kernel, and the resulting credit spreads and default probabilities are analyzed. Full article

This paper investigates the existence of square-mean S-asymptotically $(\omega ,c)$-periodic solutions for a class of neutral impulsive stochastic differential equations driven by fractional Brownian motion, addressing the challenge of modeling long-range dependencies, delayed feedback, and abrupt changes in systems like biological networks or mechanical oscillators. By employing semigroup theory to derive mild solution representations and the Banach contraction principle, we establish sufficient conditions–such as Lipschitz continuity of nonlinear terms and growth bounds on the resolvent operator—that guarantee the uniqueness and existence of such solutions in the space ${\mathcal{S}AP}_{\omega ,c}([0,\infty ),L^2(\Omega ,\mathbb{H}))$. The important results demonstrate that under these assumptions, the mild solution exhibits square-mean S-asymptotic $(\omega ,c)$-periodicity, enabling robust asymptotic analysis beyond classical periodicity. We illustrate these findings with examples, such as a neutral stochastic heat equation with impulses, revealing stability thresholds and decay rates and highlighting the framework’s utility in predicting long-term dynamics. These outcomes advance stochastic analysis by unifying neutral, impulsive, and fractional noise effects, with potential applications in control theory and engineering. Full article

We first investigate the dynamical behavior of an active Brownian particle influenced by a viscoelastic memory effect characterized by a power-law kernel, under the effects of thermal and active noises. We then analyze the dynamics of an active Brownian particle confined in a harmonic trap in the presence of the same noise sources. To derive the Fokker–Planck equation for the joint probability density of the active particle, we obtain analytical solutions for the joint probability density and its moments using double Fourier transforms in the limits $t\ll \tau$, $t\gg \tau$, and $\tau =0$. As a result, the mean squared displacement of an active Brownian particle driven by thermal noise exhibits a super-diffusive scaling of $t^{2h+1}$ in the short-time regime ($t\ll \tau$). In contrast, for a particle in a harmonic trap driven by active noise, the mean squared velocity scales linearly with $t$ when $\tau =0$. Moreover, the higher-order moments of an active Brownian particle in a harmonic trap with thermal noise scale with $t^{4h+2}$ in the long-time limit ($t\gg \tau$) and for $\tau =0$, consistent with our analytical results. Full article

Recent denoising methods based on diffusion models typically formulate the task as a conditional generation process initialized from a standard Gaussian distribution. However, such stochastic initialization often leads to redundant sampling steps and unstable results due to the neglect of structured noise characteristics. To address these limitations, we propose a novel framework that directly bridges the probabilistic distributions of noisy and clean images while jointly modeling structured noise. We introduce Dual-diffusion Brownian Bridge Coupled Sampling (DBBCS) the first framework to incorporate Brownian bridge diffusion into image denoising. DBBCS synchronously models the distributions of clean images and structural noise via two coupled diffusion processes. Unlike conventional diffusion models, our method starts sampling directly from noisy observations and jointly optimizes image reconstruction and noise estimation through a coupled posterior sampling scheme. This allows for dynamic refinement of intermediate states by adaptively updating the sampling gradients using residual feedback from both image and noise paths. Specifically, DBBCS employs two parallel Brownian bridge models to learn the distributions of clean images and noise. During inference, their respective residual processes regulate each other to progressively enhance both denoising and noise estimation. A consistency constraint is enforced among the estimated noise, the reconstructed image, and the original noisy input to ensure stable and physically coherent results. Extensive experiments on standard benchmarks demonstrate that DBBCS achieves superior performance in both visual fidelity and quantitative metrics, offering a robust and efficient solution to image denoising. Full article

Magnetic nanoparticles (MNPs) perturb magnetic field homogeneity, influencing transverse relaxation and the full width at half maximum (FWHM) of nuclear magnetic resonance (NMR) spectra. In Nuclear Magnetic Resonance (NMR), this appears as decay of the free induction decay (FID) signal, whose relaxation rate determines spectral FWHM. In D₂O containing MNPs, both nanoparticles and solvent molecules undergo Brownian motion and diffusion. Under a vertical main field ($B_0$), MNPs respond to their magnetization behavior, evolving toward a dynamic steady state in which the time-averaged distribution of local field fluctuations remains stable. The resulting spatial magnetic field can thus characterize field homogeneity. Within this framework, Monte Carlo simulations of spatial field distributions approximate the dynamic environment experienced by nuclear spins. NMR experiments confirm that increasing MNP concentration and particle size significantly broadens FWHM, while stronger $B_0$ enhances sensitivity to MNP-induced inhomogeneities. Full article