Search Results (630)

Previous studies have extensively applied the generalized consolidation theory, which incorporates a two-stress state variable framework, to predict the volumetric behavior of unsaturated expansive soils under varying mechanical stress and matric suction. A key requirement for this approach is a constitutive surface that links the soil void ratio to both net stress and matric suction. A large number of fitting parameters are typically needed to accurately fit a two-variable void ratio surface equation to laboratory test data. In this study, a single-stress state variable framework was adopted to describe the void ratio as a function of effective stress for unsaturated soils. The proposed approach was applied to fit void ratio–effective stress constitutive curves to laboratory test data for two different expansive clays. Additionally, a finite element model coupling variably saturated flow and stress–strain analysis was developed to simulate the volume change behavior of expansive clay subjected to moisture fluctuations. The model utilizes suction stress to compute the effective stress field and incorporates the dependency of soil modulus on volumetric water content based on the proposed void ratio–effective stress relationship. The developed numerical model was validated against a benchmark problem in which a layer of Regina expansive clay was subjected to a constant infiltration rate. The results demonstrate the effectiveness of the proposed model in simulating expansive soil deformations under varying moisture conditions over time. Full article

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

In this article, we propose a novel nonlinear cross-diffusion framework to model the distribution of susceptible and infected individuals within their habitat using a reduced SIR model that incorporates saturated incidence and treatment rates. The study investigates solution boundedness through the theory of parabolic partial differential equations, thereby validating the proposed spatio-temporal model. Through the implementation of the suggested cross-diffusion mechanism, the model reveals at least one non-constant positive equilibrium state within the susceptible–infected (SI) system. This work demonstrates the potential coexistence of susceptible and infected populations through cross-diffusion and unveils Turing instability within the system. By analyzing codimension-2 Turing–Hopf bifurcation, the study identifies the Turing space within the spatial context. In addition, we explore the results for Turing–Bogdanov–Takens bifurcation. To account for seasonal disease variations, novel perturbations are introduced. Comprehensive numerical simulations illustrate diverse emerging patterns in the Turing space, including holes, strips, and their mixtures. Additionally, the study identifies non-Turing and Turing–Bogdanov–Takens patterns for specific parameter selections. Spatial series and surfaces are graphed to enhance the clarity of the pattern results. This research provides theoretical insights into the implications of cross-diffusion in epidemic modeling, particularly in contexts characterized by localized mobility, clinically evident infections, and community-driven isolation behaviors. Full article

Dry jack pine forests exposed to elevated nitrogen (N) deposition do not necessarily exhibit traditional N saturation responses. Using empirical results from a five year above-canopy N deposition experiment, a simple nitrogen (N) saturation model was developed for jack pine (Pinus banksiana Lamb.) forests dominated by cryptogams. For the model, a series of differential equations using empirically derived rate constants (k) were applied to estimate changes in net N pools in biotic and abiotic components across a narrow N deposition gradient (0, 5, 10, 15, 20, and 25 kg N ha⁻¹ yr⁻¹). Critical soil C:N ratios were used as the model limit to signify saturation. We explored the saturation response time by priming the model to mineralize approximately one percent of the soil N pool after the critical C:N ratio was reached. A portion of this pool was made available to jack pine trees. Nitrogen leaching below the rooting zone occurred when the mass of N mineralized from the soil organic- and A horizon layers exceeded the theoretical mass required by jack pine, driving the mineral soil below the critical C:N ratio. The model suggests that N leaching below the rooting zone could happen around 50 (1% LFH N mineralization) years after the onset of deposition at 25 kg N ha⁻¹ yr⁻¹. In contrast, N deposition rates ≤ 20 kg N ha⁻¹ yr⁻¹ are not expected to be associated with N leaching over this timeframe. The modeled results are consistent with empirical surveys of jack pine forests exposed to elevated N deposition for several decades. Full article

This study evaluated the synergistic effects of microbial decomposition agents and deep rotary tillage on rice straw decomposition, soil nutrient dynamics, and microbial communities in paddy fields of southern China. A two-factor randomized block experiment was conducted, with straw decomposition dynamics modeled using a modified Olson decay model, and microbial communities were assessed via high-throughput sequencing and network analysis. The combined treatment significantly increased the decomposition rate constant, reduced the time for 50% decomposition to 81 days, and enhanced soil nutrient availability, especially total nitrogen, phosphorus, and potassium. Microbial richness, diversity, and network complexity were also improved. Structural equation modeling indicated that nutrient availability, rather than microbial α-diversity, was the main driver of decomposition processes. These findings suggest that integrating microbial agents with deep tillage offers an effective strategy for optimizing straw return, improving soil fertility, and enhancing microbial functional resilience in rice systems. Full article

In this paper, we develop an HIV/AIDS epidemic model that incorporates a saturated incidence rate to reflect the limited transmission capacity and the impact of behavioral saturation in contact patterns. The model is formulated as a system of seven non-linear ordinary differential equations representing key population compartments. In addition to model formulation, we introduce an optimal control problem involving three control measures: educational campaigns, screening of unaware infected individuals, and antiretroviral treatment for aware infected individuals. We begin by establishing the positivity and boundedness of the model solutions under constant control inputs. The existence and local and global stability of both the disease-free and endemic equilibrium points are analyzed, depending on the effective reproduction number (${\mathcal{R}}_e$). Bifurcation analysis reveals that the model undergoes a forward bifurcation at ${\mathcal{R}}_e=1$. A local sensitivity analysis of ${\mathcal{R}}_e$ identifies the disease transmission rate as the most sensitive parameter. The optimal control problem is then formulated by incorporating the dynamics of infected subpopulations, control costs, and time-dependent controls. The existence of optimal control solutions is proven, and the necessary conditions for optimality are derived using Pontryagin’s Maximum Principle. Numerical simulations support the theoretical analysis and confirm the stability of the equilibrium points. The optimal control strategies, evaluated using the Incremental Cost-Effectiveness Ratio (ICER), indicate that implementing both screening and treatment (Strategy D) is the most cost-effective intervention. These results provide important insights for designing effective and economically sustainable HIV/AIDS intervention policies. Full article

Fluid flow and mass transfer processes in some fractured aquifers are negligible in the low-permeability rock matrix and occur mainly in the fracture network. In this work, we consider coupled variable-density flow (VDF) and mass transport with dissolution in discrete fracture networks (DFNs). These three processes are ruled by nonlinear and strongly coupled partial differential equations (PDEs) due to the (i) density variation induced by concentration and (ii) fracture aperture evolution induced by dissolution. In this study, we develop an efficient model to solve the resulting system of nonlinear PDEs. The new model leverages the method of lines (MOL) to combine the robust finite volume (FV) method for spatial discretization with a high-order method for temporal discretization. A suitable upwind scheme is used on the fracture network to eliminate spurious oscillations in the advection-dominated case. The time step size and the order of the time integration are adapted during simulations to reduce the computational burden while preserving accuracy. The developed VDF-DFN model is validated by simulating saltwater intrusion and dissolution in a coastal fractured aquifer. The results of the VDF-DFN model, in the case of a dense fracture network, show excellent agreement with the Henry semi-analytical solution for saltwater intrusion and dissolution in a coastal aquifer. The VDF-DFN model is then employed to investigate coupled flow, mass transfer and dissolution for an injection/extraction well pair problem. This test problem enables an exploration of how dissolution influences the evolution of the fracture aperture, considering both constant and variable dissolution rates. Full article

Biochar has garnered considerable attention for its potential to improve soil properties due to its unique characteristics. However, the precise measurement of soil water content using electromagnetic sensors becomes challenging after biochar is incorporated. This study investigated the impact of biochar on soil water content measurement by adding biochar of varying dosages and particle sizes to a typical loess, under both room and subzero temperature conditions by using time domain reflectometry (TDR) and frequency domain reflectometry (FDR) techniques. The results demonstrate that biochar amendment significantly influenced the measurement accuracy of both TDR and FDR. A clear dosage-dependent relationship was observed, with measurement errors exhibiting progressive escalation as biochar addition rates increased. At room temperature, the root mean square error (RMSE) values for loess were remarkably low (TDR: 0.029; FDR: 0.093). In contrast, the 9% coarse-grained biochar-amended soil (BAS-9%C) showed substantially elevated RMSE values (TDR: 0.2006; FDR: 0.1468). Furthermore, comparative analysis revealed that particle size significantly affected measurement precision, with coarse-grained biochar demonstrating more pronounced interference effects than fine-grained biochar at equivalent application rates. At subzero temperatures, BAS-6%C exhibited significantly higher RMSE values (TDR: 0.1753; FDR: 0.2022) compared to BAS-6%F (TDR: 0.079; FDR: 0.1872). A dielectric mixing model was established for calculating the dielectric constant of BAS. In addition, calibration equations for accurately determining the water content of biochar-amended loess under both room and subzero temperature conditions were established. Furthermore, the mechanisms by which biochar influenced the performance of the TDR and FDR sensors are comprehensively discussed. These findings can provide valuable theoretical foundation and practical guidance for future soil improvement with biochar and accurate water content measurement in BAS. Full article

This study presents a high-order shear deformation theory (HSDT)-based model for evaluating the energy harvesting performance of functionally graded material (FGM) beams integrated with a piezoelectric layer and subjected to a moving concentrated load at constant velocity. The governing equations are derived using Hamilton’s principle, and the dynamic response is obtained through the State Function Method with trigonometric mode shapes. The output voltage and harvested power are calculated based on piezoelectric constitutive relations. A comparative analysis with homogeneous isotropic beams demonstrates that HSDT yields more accurate predictions than the Classical Beam Theory (CBT), especially for thick beams; for instance, at a span-to-thickness ratio of h/L = 12.5, HSDT predicts increases of approximately 6%, 7%, and 12% in displacement, voltage, and harvested power, respectively, compared to CBT. Parametric studies further reveal that increasing the load velocity significantly enhances the strain rate in the piezoelectric layer, resulting in higher voltage and power output, with the latter exhibiting quadratic growth. Moreover, increasing the material gradation index n reduces the beam’s effective stiffness, which amplifies vibration amplitudes and improves energy conversion efficiency. These findings underscore the importance of incorporating shear deformation and material gradation effects in the design and optimization of piezoelectric energy harvesting systems using FGM beams subjected to dynamic loading. Full article

The cure kinetics in frontal polymerization (FP) of short carbon-fiber-reinforced composites are investigated numerically, focusing on the influence of fiber aspect ratio, volume fraction, and orientation. A classical heat conduction equation is used in FP, where the enthalpic reaction generates heat. The heat generation term is expressed in terms of the rate of degree of cure ($\mathrm{d}\mathsf{\alpha }/\mathrm{d}\mathrm{t}$) in thermoset resin. A rate equation of the degree of cure for epoxy is established in terms of a pre-exponential factor, activation energy, Avogadro’s gas constant, and temperature. The cure kinetics parameters for epoxy resin used in this study are determined using the Ozawa method. The numerical model was validated with experimental data. The results reveal that the aspect ratio of fibers has a minimal effect on the polymerization time. The volume percentage of fibers significantly influences the curing time and temperature distribution, with higher fiber volume fractions leading to faster curing due to enhanced heat transfer. Additionally, fiber orientation plays a critical role in cure kinetics, with specific angles facilitating more effective heat transfer, thereby influencing the curing rate and frontal velocity. The results offer valuable insights into optimizing the design and manufacturing processes for high-performance epoxy-based composites through FP, where precise control over curing is critical. Full article

In recent years, an increasing number of published articles on biocatalysis have reported new enzymes that exhibit biotechnologically interesting catalytic activities. Some authors rush to publish their work in an attempt to ensure “novelty” and often present their results with various types of graphs, such as scatter plots or line-and-symbol plots using nonexistent parameters as ordinates, e.g., “Relative Activity (%)” and the like, vs. abscissae such as pH value, temperature, etc. Nevertheless, in vitro enzyme kinetics remains a valuable tool for understanding, optimizing, and effectively applying these biocatalysts under diverse reaction conditions, taking advantage of all available experimental results. This work aims to emphasize the importance of processing experimental data from enzymatic reactions through appropriate fitting with known kinetic equations and to discourage the use of nonexistent parameters. To support this integrated approach, specific examples are provided for the calculation of significant kinetic and thermodynamic parameters, as well as rate constants. Full article

This study investigates the effects of varying hydrogen percentages in fuel blends on combustion dynamics, engine performance, and emissions. Experimental data and analytical equations were used to evaluate combustion parameters such as equivalent lambda, in-cylinder pressure, heat release rate, and ignition timing. The findings demonstrate that hydrogen blending enhances combustion stability, shortens ignition delay, and shifts peak heat release to be closer to the top dead center (TDC). These changes improve thermal efficiency and reduce cycle-to-cycle variation. Hydrogen blending also significantly lowers carbon dioxide (CO₂) and hydrocarbon (HC) emissions, particularly at higher blend levels (H0–H5), while lower blends increase nitrogen oxides (NO_x) emissions and risk pre-ignition due to advanced start of combustion (SOC). Engine performance improved with an average hydrogen energy contribution of 12% under a constant load. However, the optimal hydrogen blending range is crucial to balancing efficiency gains and emission reductions. These results underline the potential of hydrogen as a cleaner additive fuel and the importance of optimizing blend ratios to harness its benefits effectively. Full article

Tensile tests are a common method for characterizing plastic behavior for sheet metal forming applications. During tensile testing at the beginning of the deformation, the stress state is uniaxial; however, as the deformation proceeds, the state changes to triaxial, making the post-processing of experimental data challenging using analytical methods. In contrast, inverse approaches in which the behavior is represented by constitutive equations and the parameters are fitted using an iterative procedure are extremely dependent on the empirical equation chosen at the outset and can be computationally expensive. The inverse piecewise flow curve determination method, previously developed for compression tests, is extended in this paper to tensile testing. A stepwise approach is proposed to calculate constant strain rate flow curves accounting for the unique characteristics of tensile deformation. To capture the effects of localized strain rate variations during necking, a parallel flow curve determination strategy is introduced. Tensile test flow curves for manganese-boron steel 22MnB5, a material commonly used in hot stamping applications, are determined, and the approach is demonstrated for virtual force–displacement curves. It has been shown that these curves can replicate the virtual experimental flow curves data with a maximum deviation of 1%. Full article

A food pasteurization or sterilization process was treated as a system comprising a target microorganism, a food medium, and applied lethal agents (both thermal and nonthermal). So, the state of such a system was defined by the target microorganism’s concentration, the food medium parameters (food composition, pH, and water activity), and the magnitudes of temperature and nonthermal lethal agents. Further, a path was defined as a series of profiles that describe the changes in state factors over time when a food process system changes from its initial state to any momentary state. Using the Weibull model as an example, results showed that, if the microbial inactivation rate depends on path, then there exists an infinite number of rate equations that can result in the same algebraic primary model under constant conditions but, theoretically, only one of them is true. Considering the infinite possibilities, there is no way to find the most suitable or true rate equation. However, the inactivation rate equation can be uniquely derived from the algebraic primary model if the inactivation rate does not depend on path, which was demonstrated to be true by most microbial survival data reported in previous studies. Full article

We survey developments in the use of entropy maximization for applying the Gibbs Canonical Ensemble to finite situations. Biological insights are invoked along with physical considerations. In the game-theoretic approach to entropy maximization, the interpretation of the two player roles as predator and prey provides a well-justified and symmetric analysis. The main focus is placed on the Lagrange multiplier approach. Using natural physical units with Planck’s constant set to unity, it is recognized that energy has the dimensions of inverse time. Thus, the conjugate Lagrange multiplier, traditionally related to absolute temperature, is now taken with time units and oriented to follow the Arrow of Time. In quantum optics, where energy levels are bounded above and below, artificial singularities involving negative temperatures are eliminated. In a biological model where species compete in an environment with a fixed carrying capacity, use of the Canonical Ensemble solves an instance of Eigen’s phenomenological rate equations. The Lagrange multiplier emerges as a statistical measure of the ecological age. Adding a weak inequality on an order parameter for the entropy maximization, the phase transition from initial unconstrained growth to constrained growth at the carrying capacity is described, without recourse to a thermodynamic limit for the finite system. Full article