Search Results (6,021)

Divinylisoprene rubber, a copolymer of butadiene and isoprene, is used as raw material for rubber technical products, combining isoprene rubber’s elasticity and butadiene rubber’s wear resistance. These properties depend quantitatively on the copolymer composition, which depends on the kinetics of its synthesis. This work aims to theoretically describe how the monomer mixture composition in the butadiene–isoprene copolymerization affects the activity of the TiCl₄–Al(i-C₄H₉)₃ catalytic system (expressed by active sites concentration) via kinetic modeling. This enables development of a reliable kinetic model for divinylisoprene rubber synthesis, predicting reaction rate, molecular weight, and composition, applicable to reactor design and process intensification. Active sites concentrations were calculated from experimental copolymerization rates and known chain propagation constants for various monomer compositions. Kinetic equations for active sites formation were based on mass-action law and Langmuir monomolecular adsorption theory. An analytical equation relating active sites concentration to monomer composition was derived, analyzed, and optimized with experimental data. The results show that monomer composition’s influence on active sites concentration is well described by a two-step kinetic model (physical adsorption followed by Ti–C bond formation), accounting for competitive adsorption: isoprene adsorbs more readily, while butadiene forms more stable active sites. Full article

This paper addresses an attraction–repulsion chemotaxis system governed by Neumann boundary conditions within a bounded domain $\Omega \subset {\mathbb{R}}^3$ that has a smooth boundary. The primary focus of the study is the chemotactic response of a species (cell population) to two competing signals. We establish the existence and uniqueness of a weak solution to the system by analyzing the solvability of an approximate problem and utilizing the Leray–Schauder fixed-point theorem. By deriving appropriate a priori estimates, we demonstrate that the solution of the approximate problem converges to a weak solution of the original system. Additionally, we conduct computational studies of the model using the finite element method. The accuracy of our numerical implementation is evaluated through error analysis and numerical convergence, followed by various numerical simulations in a two-dimensional domain to illustrate the dynamics of the system and validate the theoretical findings. Full article

Because artificially cemented granular (ACG) materials employ diverse combinations of aggregates and binders—including cemented soil, low-cement-content cemented sand and gravel (LCSG), and concrete—their stress–strain responses vary widely. In LCSG, the binder dosage is typically limited to 40–80 kg/m³ and the sand–gravel skeleton is often obtained directly from on-site or nearby excavation spoil, endowing the material with a markedly lower embodied carbon footprint and strong alignment with current low-carbon, green-construction objectives. Yet, such heterogeneity makes a single material-specific constitutive model inadequate for predicting the mechanical behavior of other ACG variants, thereby constraining broader applications in dam construction and foundation reinforcement. This study systematically summarizes and analyzes the stress–strain and volumetric strain–axial strain characteristics of ACG materials under conventional triaxial conditions. Generalized hyperbolic and parabolic equations are employed to describe these two families of curves, and closed-form expressions are proposed for key mechanical indices—peak strength, elastic modulus, and shear dilation behavior. Building on generalized plasticity theory, we derive the plastic flow direction vector, loading direction vector, and plastic modulus, and develop a concise, transferable elastoplastic model suitable for the full spectrum of ACG materials. Validation against triaxial data for rock-fill materials, LCSG, and cemented coal–gangue backfill shows that the model reproduces the stress and deformation paths of each material class with high accuracy. Quantitative evaluation of the peak values indicates that the proposed constitutive model predicts peak deviatoric stress with an error of 1.36% and peak volumetric strain with an error of 3.78%. The corresponding coefficients of determination R² between the predicted and measured values are 0.997 for peak stress and 0.987 for peak volumetric strain, demonstrating the excellent engineering accuracy of the proposed model. The results provide a unified theoretical basis for deploying ACG—particularly its low-cement, locally sourced variants—in low-carbon dam construction, foundation rehabilitation, and other sustainable civil engineering projects. Full article

We establish a rigorous kinetic-theoretical framework to analyze causal propagation in thermal transport phenomena within relativistic ideal fluids, building a more rigorous framework based on the kinetic theory of gases. Specifically, we provide a refined derivation of the wave equation governing thermal and density fluctuations, clarifying its hyperbolic nature and the associated characteristic propagation speeds. The analysis confirms that thermal fluctuations in a simple non-degenerate relativistic fluid satisfy a causal wave equation in the Euler regime, and it recovers the classical expression for the speed of sound in the non-relativistic limit. This work offers enhanced mathematical and physical insights, reinforcing the validity of the hyperbolic description and suggesting a foundation for future studies in dissipative relativistic hydrodynamics. Full article

The aim of our work is to theoretically model the conversion of C6 and C5 carbohydrates derived from lignocellulosic biomass waste into C1–C5 carboxylic acids such as levulinic, oxalic, lactic, and formic acids. Understanding the mechanism of these processes will provide the necessary knowledge to better plan the structure of zeolite. In this article, we focus on the theoretical modeling of two carbohydrates, representing C5 and C6, namely xylose and fructose, into levulinic acid (LE) and formic acid (FA). The modeling was carried out with the participation of Na-BEA zeolite in a hierarchical form, due to the large size of the carbohydrates. The density functional theory (DFT) method (StoBe program) was used, employing non-local generalized gradient-corrected functions according to Perdew, Burke, and Ernzerhof (RPBE) to account for electron exchange and correlation and using the nudged elastic band (NEB) method to determine the structure and energy of the transition state. The modeling was performed using cluster representations of hierarchical Na-Al₂Si₁₂O₃₉H₂₃ and ideal Al₂Si₂₂O₆₄H₃₄ beta zeolite. However, to accommodate the size of the carbohydrate molecules in reaction paths, only hierarchical Na-Al₂Si₁₂O₃₉H₂₃ was used. Sodium ions were positioned above the aluminum centers within the zeolite framework. Full article

This study introduces two novel methodologies for solving systems of Fredholm integral equations, with particular emphasis on second-kind equations. The first method integrates the Sinc-collocation technique with a newly developed singular exponential transformation, enhancing convergence behavior and numerical stability. A comprehensive convergence analysis is conducted to support this approach. The second method employs a double exponential transformation, leading to a pair of linear equations whose solvability is established using the double projection method. Rigorous theoretical analysis is presented, including convergence theorems and newly derived error bounds. A system of two Fredholm integral equations is treated as a practical case study. Numerical examples are provided to illustrate the effectiveness and accuracy of the proposed methods, substantiating the theoretical results. Full article

Ecosystem services—the benefits humans derive from nature—are foundational to environmental sustainability and economic well-being, with carbon sequestration and storage standing out as critical regulating services in the fight against climate change. This study presents a comprehensive financial valuation of the carbon sequestration, storage and product substitution ecosystem services provided by the Hungarian forest-based sector. Using a multi-scenario framework, four complementary valuation concepts are assessed: total carbon storage (biomass, soil, and harvested wood products), annual net sequestration, emissions avoided through material and energy substitution, and marketable carbon value under voluntary carbon market (VCM) and EU Carbon Removal Certification Framework (CRCF) mechanisms. Data sources include the National Forestry Database, the Hungarian Greenhouse Gas Inventory, and national estimates on substitution effects and soil carbon stocks. The total carbon stock of Hungarian forests is estimated at 1289 million tons of CO₂ eq, corresponding to a theoretical climate liability value of over EUR 64 billion. Annual sequestration is valued at approximately 380 million EUR/year, while avoided emissions contribute an additional 453 million EUR/year in mitigation benefits. A comparative analysis of two mutually exclusive crediting strategies—improved forest management projects (IFMs) avoiding final harvesting versus long-term carbon storage through the use of harvested wood products—reveals that intensified harvesting for durable wood use offers higher revenue potential (up to 90 million EUR/year) than non-harvesting IFM scenarios. These findings highlight the dual role of forests as both carbon sinks and sources of climate-smart materials and call for policy frameworks that integrate substitution benefits and long-term storage opportunities in support of effective climate and bioeconomy strategies. Full article

Quarry dust (QD) landfill causes environmental issues that cannot be ignored. In this study, we systematically explore its potential application as a supplementary cementitious material (SCM) in cemented paste backfill (CPB), revealing the activated mechanism of modified QD (MQD) and exploring the hydration process and workability of CPB containing QD/MQD. The experimental results show that quartz, clinochlore and amphibole components react with CaO to form reactive dicalcium silicate (C₂S) and amorphous glass phases, promoting pozzolanic reactivity in MQD. QD promotes early aluminocarbonate (M_c) formation through CaCO₃-derived CO₃²⁻ release but shifts to hemicarboaluminate (H_c) dominance at 28 d. MQD releases active Al³⁺/Si⁴⁺ due to calcination and deconstruction, significantly increasing the amount of ettringite (AFt) in the later stage. With the synergistic effect of coarse–fine particle gradation, MQD-type fresh backfill can achieve a 161 mm flow spread at 20% replacement. Even if this replacement rate reaches 50%, a strength of 19.87 MPa can still be maintained for 28 days. The good workability and low carbon footprint of MQD-type backfill provide theoretical support for—and technical paths toward—QD recycling and the development of low-carbon building materials. Full article

This paper develops a unified framework for mathematical finance under general semimartingale models that allow for dividend payments, negative asset prices, and unbounded jumps. We present a rigorous approach to the mathematical modeling of financial markets with dividend-paying assets by defining appropriate concepts of numéraires, discounted processes, and self-financing trading strategies. While most of the mathematical results are not new, this unified framework has been missing in the literature. We carefully examine the transition between nominal and discounted price processes and define appropriate notions of admissible strategies that work naturally in both settings. By establishing the equivalence between these models and providing clear conditions for their applicability, we create a mathematical foundation that encompasses a wide range of realistic market scenarios and can serve as a basis for future work on mathematical finance and derivative pricing. We demonstrate the practical relevance of our framework through a comprehensive application to dividend-paying equity markets where the framework naturally handles discrete dividend payments. This application shows that our theoretical framework is not merely abstract but provides the rigorous foundation for pricing derivatives in real-world markets where classical assumptions need extension. Full article

Liquid crystal elastomers (LCEs) have shown great potential in the field of soft robotics due to their unique actuation capabilities. Despite the growing number of experimental studies in the soft robotics field, theoretical research remains limited. In this paper, a dynamic model of a bionic arm using an LCE fiber as artificial muscle is established, which exhibits periodic oscillation controlled by periodic illumination. Based on the assumption of linear damping and angular momentum theorem, the dynamics equation of the model oscillation is derived. Then, based on the assumption of linear elasticity model, the periodic spring force of the fiber is given. Subsequently, the evolution equations for the cis number fraction within the fiber are developed, and consequently, the analytical solution for the light-excited strain is derived. Following that, the dynamics equation is numerically solved, and the mechanism of the controllable oscillation is elucidated. Numerical calculations show that the stable oscillation period of the bionic arm depends on the illumination period. When the illumination period aligns with the natural period of the bionic arm, the resonance is formed and the amplitude is the largest. Additionally, the effects of various parameters on forced oscillation are analyzed. The results of numerical studies on the bionic arm can provide theoretical support for the design of micro-machines, bionic devices, soft robots, biomedical devices, and energy harvesters. Full article

Measuring weak magnetic fields proposes significant challenges to the sensing capabilities of magnetic field sensors. The magnetic field detection capacity of tunnel magnetoresistance (TMR) sensors is often insufficient for such applications, necessitating targeted optimization strategies to improve their performance in weak-field measurements. Utilizing magnetic flux concentrators (MFCs) offers an effective approach to enhance TMR sensitivity. In this study, the finite element method was employed to analyze the effects of different MFC geometric structures on the uniformity of the magnetic field in the air gap and the magnetic circuit gain (MCG). It was determined that the MCG of the MFC is not directly related to the absolute values of its parameters but rather to their ratios. Simulation analyses evaluated the impact of these parameter ratios on both the MCG and its spatial distribution uniformity, leading to the formulation of MFC design optimization principles. Building on these simulation-derived principles, several MFCs were fabricated using the 1J85 material, and an experimental platform was established to validate the simulation findings. The fabricated MFCs achieved an MCG of 7.325 times. Based on the previously developed TMR devices, a detection sensitivity of 2.46 nT/$\sqrt{\mathrm{Hz}}$ @1Hz was obtained. By optimizing parameter configurations, this work provides theoretical guidance for further enhancing the performance of TMR sensors in magnetic field measurements. Full article

Research on reliability control for enhancing power systems under random loads holds significant and undeniable importance in maintaining system stability, performance, and safety. The primary challenge lies in determining the reliability index while optimizing system parameters. To effectively address this challenge, we developed a novel intelligent algorithm and conducted an optimal reliability assessment for a Negative Stiffness Device (NSD) seismic isolation structure incorporating fractional-order damping. This algorithm combines the Gaussian Radial Basis Function Neural Network (GRBFNN) with the Particle Swarm Optimization (PSO) algorithm. It takes the reliability function with unknown parameters as the objective function, while using the Backward Kolmogorov (BK) equation, which governs the reliability function and is accompanied by boundary and initial conditions, as the constraint condition. During the operation of this algorithm, the neural network is employed to solve the BK equation, thereby deriving the fitness function in each iteration of the PSO algorithm. Then the PSO algorithm is utilized to obtain the optimal parameters. The unique advantage of this algorithm is its ability to simultaneously achieve the optimization of implicit objectives and the solution of time-dependent BK equations.To evaluate the performance of the proposed algorithm, this study compared it with the algorithm combines the GRBFNN with Genetic Algorithm (GA-GRBFNN)across multiple dimensions, including performance and operational efficiency. The effectiveness of the proposed algorithm has been validated through numerical comparisons and Monte Carlo simulations. The control strategy presented in this paper provides a solid theoretical foundation for improving the reliability performance of mechanical engineering systems and demonstrates significant potential for practical applications. Full article

This study addresses the practical stability analysis of Riemann-Liouville fractional-order nonlinear systems with time delays. We first establish a rigorous formulation of initial conditions that aligns with the properties of Riemann-Liouville fractional derivatives. Subsequently, a generalized definition of practical stability is introduced, specifically tailored to accommodate the hybrid dynamics of fractional calculus and time-delay phenomena. By constructing appropriate Lyapunov-Krasovskii functionals and employing an enhanced Razumikhin-type technique, we derive sufficient conditions ensuring practical stability in the $L_p$-norm sense. The theoretical findings are validated through illustrative example for fractional order nonlinear systems with time delays. Full article

In this study, we focus on solving the nonlinear time-fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) and modified Korteweg–de Vries (MKdV) equations, using the Yang transform iterative method (YTIM). This method combines the Yang transform with a new iterative scheme to construct reliable and efficient solutions. Readers can understand the procedures clearly, since the implementation of Yang transform directly transforms fractional derivative sections into algebraic terms in the given problems. The new iterative scheme is applied to generate series solutions for the provided problems. The fractional derivatives are considered in the Caputo sense. To validate the proposed approach, two numerical examples are analysed and compared with exact solutions, as well as with the results obtained from the fractional reduced differential transform method (FRDTM) and the q-homotopy analysis transform method (q-HATM). The comparisons, presented through both tables and graphical illustrations, confirm the enhanced accuracy and reliability of the proposed method. Moreover, the effect of varying the fractional order is explored, demonstrating convergence of the solution as the order approaches an integer value. Importantly, the time-fractional Hirota–Satsuma coupled KdV and modified Korteweg–de Vries (MKdV) equations investigated in this work are not only of theoretical and computational interest but also possess significant implications for achieving global sustainability goals. Specifically, these equations contribute to the Sustainable Development Goal (SDG) “Life Below Water” by offering advanced modelling capabilities for understanding wave propagation and ocean dynamics, thus supporting marine ecosystem research and management. It is also relevant to SDG “Climate Action” as it aids in the simulation of environmental phenomena crucial to climate change analysis and mitigation. Additionally, the development and application of innovative mathematical modelling techniques align with “Industry, Innovation, and Infrastructure” promoting advanced computational tools for use in ocean engineering, environmental monitoring, and other infrastructure-related domains. Therefore, the proposed method not only advances mathematical and numerical analysis but also fosters interdisciplinary contributions toward sustainable development. Full article

Optical solitons have emerged as a highly active research domain in nonlinear fiber optics, driving significant advancements and enabling a wide range of practical applications. This study investigates the dynamics of dark solitons in systems governed by the resonant nonlinear Schrödinger equation (RNLSE). For the RNLSE with third-order (3OD) and fourth-order (4OD) dispersions, the dark soliton solution of the equation in the (1+1)-dimensional case is derived using the F-expansion method, and the analytical study is extended to the (2+1)-dimensional case via the self-similar method. Subsequently, the nonlinear equation incorporating perturbation terms is further studied, with particular attention given to the dark soliton solutions in both one and two dimensions. The soliton dynamics are illustrated through graphical representations to elucidate their propagation characteristics. Finally, modulation instability analysis is conducted to evaluate the stability of the nonlinear system. These theoretical findings provide a solid foundation for experimental investigations of dark solitons within the systems governed by the RNLSE model. Full article