Search Results (154)

A Lotka–Volterra-type system with porous diffusion, which can be used as an alternative model to the classical Lotka–Volterra system, is under study. Multiparameter families of exact solutions of the system in question are constructed and their properties are established. It is shown that the solutions obtained can satisfy the zero Neumann conditions, which are typical conditions for mathematical models describing real-world processes. It is proved that the system possesses two stable steady-state points provided its coefficients are correctly specified. In particular, this occurs when the system models the prey–predator interaction. The exact solutions are used for solving boundary-value problems. The analytical results are compared with numerical solutions of the same boundary-value problems but perturbed initial profiles. It is demonstrated that the numerical solutions coincide with the relevant exact solutions with high exactness in the case of sufficiently small perturbations of the initial profiles. Full article

In the context of the current global transition toward low-carbon energy, the issue of $C{O}_2$ utilization has become increasingly important. One of the most promising natural targets for $C{O}_2$ sequestration is the terrigenous sedimentary formations found in oil, gas, and coal basins. It is generally assumed that $C{O}_2$ injected into such formations can be stored indefinitely in a stable form. However, the dissolution of $C{O}_2$ into subsurface water leads to a reduction in pH, which may cause partial dissolution of the host formation, altering the structure of the subsurface in the injection zone. This process is relatively slow, potentially unfolding over decades or even centuries, and its long-term consequences require careful investigation through mathematical modeling. The geological formation is treated as a partially soluble porous medium, where the dissolution rate is governed by surface chemical reactions occurring at the pore boundaries. In this study, we present an applied mathematical model that captures the coupled processes of mass transport, surface chemical reactions, and the resulting microscopic changes in the pore structure of the formation. To ensure the model remains grounded in realistic geological conditions, we based it on exploration data characterizing the composition and microstructure of the pore space typical of the Cenomanian suite in northern Western Siberia. The model incorporates the dominant geochemical reactions involving calcium carbonate (calcite, $CaC{O}_3$), characteristic of Cenomanian reservoir rocks. It describes the dissolution of $C{O}_2$ in the pore fluid and the associated evolution of ion concentrations, specifically $H^{+}$, $C{a}^{2+}$, and $HC{O}_3^{-}$. The input parameters are derived from experimental data. While the model focuses on calcite-based formations, the algorithm can be adapted to other mineralogies with appropriate modifications to the reaction terms. The simulation domain is defined as a cubic region with a side length of 1 $\mathsf{\mu }$m, representing a fragment of the geological formation with a porosity of 0.33. The pore space is initially filled with a mixture of liquid $C{O}_2$ and water at known saturation levels. The mathematical framework consists of a system of diffusion–reaction equations describing the dissolution of $C{O}_2$ in water and the subsequent mineral dissolution, coupled with a model for surface evolution of the solid phase. This model enables calculation of surface reaction rates within the porous medium and estimates the timescales over which significant changes in pore structure may occur, depending on the relative saturations of water and liquid $C{O}_2$. Full article

The paradigm-shift idea of murburn concept is no hypothesis but developed directly from fundamental facts of cellular/ecological existence. Murburn involves spontaneous and stochastic interactions (mediated by murzymes) amongst the molecules and unbound ions of cells. It leads to effective charge separation (ECS) and formation/recruitment of diffusible reactive species (DRS, like radicals whose reactions enable ATP-synthesis and thermogenesis) and emission of radiations (UV/Vis to ELF). These processes also lead to a chemo-electromagnetic matrix (CEM), ascertaining that living cell/organism react/function as a coherent unit. Murburn concept propounds the true utility of oxygen: generating DRS (with catalytic and electrical properties) on the way to becoming water, the life solvent, and ultimately also leading to phase-based macroscopic homeostatic outcomes. Such a layout enables cells to become simple chemical engines (SCEs) with powering, coherence, homeostasis, electro-mechanical and sensing–response (PCHEMS; life’s short-term “intelligence”) abilities. In the current review, we discuss the coacervate nature of cells and dwell upon the ways and contexts in which various radiations (either incident or endogenously generated) could interact in the new scheme of cellular function. Presenting comparative evidence/arguments and listing of systems with murburn models, we argue that the new perceptions explain life processes better and urge the community to urgently adopt murburn bioenergetics and adapt to its views. Further, we touch upon some distinct scientific and sociological contexts with respect to the outreach of murburn concept. It is envisaged that greater awareness of murburn could enhance the longevity and quality of life and afford better approaches to therapies. Full article

A Cournot triopoly is a type of oligopoly market involving three firms that produce and sell homogeneous or similar products without cooperating with one another. In Cournot models, firms’ decisions about production levels play a crucial role in determining overall market output. Compared to duopoly models, oligopolies with more than two firms have received relatively less attention in the literature. Nevertheless, triopoly models are more reflective of real-world market conditions, even though analyzing their dynamics remains a complex challenge. A reaction–diffusion system of PDEs generalizing a nonlinear triopoly model describing a master–slave Cournot game is introduced. The effect of diffusion on the stability of Nash equilibrium is investigated. Self-diffusion alone cannot induce Turing pattern formation. In fact, linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. The conditions for the onset of cross-diffusion-driven instability are obtained via linear stability analysis, and the formation of several Turing patterns is investigated through numerical simulations. Full article

Plasma non-transferrin-bound iron (NTBI) comprises multiple subspecies, classified by their composition, chemical reactivity, and susceptibility to chelation. The redox-active and chelatable fraction of NTBI is referred to as labile plasma iron (LPI). The pathophysiological significance of NTBI and LPI lies in their ability to enter cells via alternative transport pathways that are not regulated by the transferrin receptor system or by cellular iron levels. Several mechanisms have been proposed for their cellular entry, including the hijacking of divalent metal transporters and passive diffusion. This unregulated uptake can lead to iron accumulation in vulnerable tissues such as the liver and the heart. NTBI and LPI bypassing normal cellular control mechanisms can rapidly exceed the cell’s capacity to safely store excess iron, leading to toxicity. Both NTBI and LPI contribute to oxidative stress by participating in free-radical-generating reactions. However, LPI concentration in the bloodstream may be differentially affected by the mode and extent of iron overload, the presence of residual serum iron-binding activity, and the antioxidant capacity of individual sera. In summary, both NTBI and LPI contribute to iron-mediated toxicity but differ in terms of reactivity, availability, and pathogenic potential depending on the pathophysiological conditions that influence the degree of toxicity. Full article

Nitric oxide (NO) is a well-known member of the reactive oxygen species (ROS) family. The extent of its concentration influences whether it produces beneficial physiological effects or harmful toxic reactions. In a blood system, NO is generally produced by nitric oxide synthase (NOS) in the endothelium. Then, it diffuses into the smooth muscle wall causing a vasodilatation, and it can also be diluted in a lumen blood stream. In the present study, we analyzed a convectional reaction–diffusion of NO in a 3D digital phantom of a short segment of small arteries. NO concentrations were analyzed by applying numerical solutions to the boundary problems, which included the Navier–Stokes equation, Darcy’s law, varying consumption of NO, and the dependence of NOS activity on shear stress. All the boundary problems were evaluated using COMSOL Multiphysics software ver. 5.5. The role of two diffusive barriers surrounding the endothelium producing NO was theoretically proven. When the eNOS rate remains unchanged, an increase in the fenestration of the internal elastic lamina (IEL) and a decrease in the diffusive permeability of a thin layer of endothelial surface glycocalyx (ESG) lead to a notable rise in the NO concentration in the vascular wall. The alterations in pore count in IEL and the viscosity of ESG are considered to be involved in the physiological and pathological regulation of NO concentrations. Full article

This study investigates the early hydration characteristics and kinetics of ordinary Portland cement (OPC) and calcium sulfoaluminate cement (CSA) composite pastes. The hydration mechanisms of OPC-CSA systems with different proportions are analyzed through zonal analysis and the Krstulović–Dabić method. The experimental results show that in OPC-dominated systems, an appropriate amount of CSA promotes the rapid hydration of ye’elimite and optimizes the cumulative hydration heat and pore structure. However, excessive CSA inhibits hydration due to alkalinity imbalance. In CSA-dominated systems, 10% OPC increases the alkalinity, promoting ye’elimite to hydrate into ettringite. Higher OPC content hinders the hydration process due to ion concentration imbalance. The kinetics model indicates that CSA accelerates the interfacial reaction and diffusion in the OPC system, while OPC reduces the overall hydration rate of the CSA system. Microscopic analysis confirms that the composite system improves the pore structure through mineral interaction. In the OPC-dominated area, the pore structure is mainly composed of small and dense pores. In the CSA-dominated area, the characteristics of large pores are affected by the expansion properties of CSA and hydration heat. This study constructs a coupling mechanism of alkalinity regulation and crystal nucleus generation, providing a theoretical basis for the design of high-performance composite cement materials. Full article

The textile industry encounters serious environmental challenges from wastewater with persistent organic pollutants, demanding sustainable solutions for remediation. Herein, we report a novel green synthesis of flexible BiOBr@PZT nanocomposite membranes via electrospinning and successive ionic layer adsorption and reaction (SILAR) for visible-light-driven photocatalytic degradation. The hierarchical structure integrates leaf-like BiOBr nanosheets with PAN/ZnO/TiO₂ (PZT) nanofibers, forming a Z-scheme heterojunction. This enhances the separation of photogenerated carriers while preserving mechanical integrity. SILAR-enabled low temperature deposition ensures eco-friendly fabrication by avoiding toxic precursors and cutting energy use. Optimized BiOBr@PZT-5 shows exceptional photocatalytic performance, achieving 97.6% tetracycline hydrochloride (TCH) degradation under visible light in 120 min. It also has strong tensile strength (4.29 MPa) and cycling stability. Mechanistic studies show efficient generation of O₂⁻ and OH radicals through synergistic light absorption, charge transfer, and turbulence-enhanced mass diffusion. The material’s flexibility allows reusable turbulent flow applications, overcoming rigid catalyst limitations. Aligning with green chemistry and UN SDGs, this work advances multifunctional photocatalytic systems for scalable, energy-efficient wastewater treatment, offering a paradigm that integrates environmental remediation with industrial adaptability. Full article

In this research, we investigate the phenomenon of multistability and complex dynamic behaviors in plasma waves by utilizing advanced mathematical techniques. We examine how fractional-order derivatives influence plasma wave stability by applying the fractional diffusion–reaction model, the framework of nonlinear dynamical systems, and the $\left({\displaystyle \frac{G^{\prime }}{G^2}}\right)$ method. The principal direction of our work is associated with different forms of oscillations in the plasma wave: non-linear periodic, solitons, and kink waves. This leads to the study of small amplitude pulses and solitary waves, which are significant in plasma activities. Using bifurcation analysis, we discuss how these waves appear and develop under different conditions, as well as determine which conditions generate the chaotic behavior or highly complex patterns of waves. We study the details of transitions between waves and their chaotic behavior to characterize the laws that govern their plasma environment. Moreover, we have used non-linear modeling and numerical simulations to understand in detail the complex patterns and the factors of stability underlying the phenomena of plasma waves. In addition, our study also investigates the correspondence between non-linearity, multi-stability, and the birth of complex structures such as solitons and kink waves. The solutions of the dynamical system produced by the proposed nonlinear model generate different patterns of response based on system parameter variation. These patterns include oscillations and decay behaviors. Research results about system stability and solution convergence under various parameter settings provide an extended performance evaluation of the proposed method through a better understanding of system dynamics. They increase our understanding of chaotic behavior in plasma systems and pave the way for applications in plasma physics and energy systems, as well as advanced technologies. Full article

Electrocoagulation (EC) systems are regaining attention as a promising wastewater treatment technology due to their numerous advantages, including low system and operational costs and environmental friendliness. However, the widespread adoption and further development of EC systems have been hindered by a lack of fundamental understanding, necessitating systematic research to provide essential insights for system developers. In this study, a continuous EC system with a realistic setup is analyzed using an unsteady, two-dimensional physics-based model that incorporates multiphysics. The model captures key mechanisms, such as arsenic adsorption onto flocs, electrochemical reactions at the electrodes, chemical reactions in the bulk solution, and ionic species transport via diffusion and convection. Additionally, it accounts for bulk wastewater flow circulating between the EC cell and an external storage tank. This comprehensive modeling approach enables a fundamental analysis of how operating conditions influence arsenic removal efficiency, providing crucial insights for optimizing system utilization. Furthermore, the developed model is used to generate data under various operating conditions. Seven machine learning models are trained on this data after hyperparameter optimization. These high-accuracy models are then employed to develop processing maps that identify the conditions necessary to achieve acceptable removal efficiency. This study is the first to generate processing maps by synergistically integrating physics-based and data-driven models. These maps provide clear design and operational guidelines, helping researchers and engineers optimize EC systems. This research establishes a framework for combining physics-based and data-driven modeling approaches to generate processing maps that serve as essential guidelines for wastewater treatment applications. Full article

Reaction–diffusion equations can model complex systems where randomness plays a role, capturing the interaction between diffusion processes and random fluctuations. The Kolmogorov equations associated with these systems play an important role in understanding the long-term behavior, stability, and control of such complex systems. In this paper, we investigate the existence of a classical solution for the Kolmogorov equation associated with a stochastic reaction–diffusion equation driven by nonlinear multiplicative trace-class noise. We also establish the existence of an invariant measure $\nu$ for the corresponding transition semigroup $P_t$, where the infinitesimal generator in $L^2(H,\nu )$ is identified as the closure of the Kolmogorov operator $K_0$. Full article

The performance and durability of proton-exchange membrane fuel cells (PEMFCs) are dependent on fuel flow, humidifying water, and outgoing water management. Unlike conventional flow fields with linear channels, the complex 3D flow field—featuring repeating baffles along the channel, known as the baffle design—induces a micro-scale interface flux between the gas diffusion layer (GDL) and the flow fields. Thus, an intensive oxygen flow is created that removes excess water from the GDL, thereby improving the fuel cell efficiency. Another approach for channel design is the Turing flow field, which resembles the organization of fluid flows in natural objects such as leaves, lungs, and the blood system. This design enhances the distribution of inlet flow significantly compared with traditional designs. The present study aims to combine the advantages of both Turing and baffle flow field designs and to provide model investigations on the influence of the mixed flow field design on the efficiency of PEMFCs. It was established that the mixed design achieves the highest electrode current density of 1.2 A/cm², outperforming the other designs. Specifically, it achieves 20% improvement over the Turing design, reaching 1.0 A/cm² and generating three times more current than the baffle design, which delivers 0.4 A/cm². In contrast, the conventional serpentine designs exhibit the lowest current density. The mixed flow field design provides better oxygen utilization in the electrochemical reaction, offers optimal membrane hydration, and contributes to superior electrode current density performance. These data illustrate how flow field structure directly impacts fuel cell efficiency through enhancement of current density. Full article

This article investigates the boundary value problem for an extended stationary system of Nernst–Planck–Poisson equations, corresponding to a mathematical model of the influence of changes in the equilibrium coefficient on the transport of ions of a binary salt in the diffusion layer. Dimensionless variables were introduced using characteristic parameter values. As a result, a dimensionless boundary value problem was obtained, which is singularly perturbed, containing a small parameter in the derivative of the Poisson equation and, additionally, another regular small parameter. A similarity theory was developed: trivial and non-trivial similarity criteria and their physical meaning were determined, which allowed for the identification of general properties of the solutions. A numerical investigation of the boundary value problem was conducted using the finite element method. With an increase in the initial solution concentration, the value of the small parameter entering singularly decreases, reaching values on the order of 10⁻¹² and below, leading to computational difficulties that prevent a comprehensive analysis of the influence of changes in the equilibrium coefficient on salt ion transport. In this regard, an analytical solution to the problem was constructed, based on dividing the solution domain into several subdomains (regions of electroneutrality, extended space charge region, quasi-equilibrium region, recombination region, intermediate layer), in each of which the problem is solved differently, followed by matching these solutions. Verification of the analytical solution was carried out by comparing it with the numerical solution. The advantage of the obtained analytical solution is the possibility of a comprehensive analysis of the influence of the dissociation/recombination reaction of water molecules on salt ion transport over a wide range of real changes in the concentration and composition of the electrolyte solution and other input parameters. This boundary value problem serves as a benchmark for constructing asymptotic solutions for other singularly perturbed boundary value problems in membrane electrochemistry. Full article

In numerical simulations of combustion flow fields, tabulated chemistry models are widely used to reduce computational cost compared to rigorous reaction calculation methods such as detailed chemical reaction calculations. Tabulated combustion data are generated by performing low-dimensional combustion calculations prior to simulating the combustion flow field. The results are then stored in a database indexed by parameters such as mixture fraction and reaction progress variables. In recent years, significant advancements have been made in the tabulation of combustion data to accommodate diverse fuels and replicate the complex conditions observed in practical combustion systems. This review paper provides an overview of recent developments in tabulated chemistry models, particularly those based on the flamelet/progress-variable method. It specifically addresses scenarios involving multi-point fuel injection, the presence of heat loss factors in combustion flow fields, the consideration of varying diffusion coefficients, and other complex phenomena. Full article

Oscillations in animate and inanimate systems are ubiquitous phenomena driven by sophisticated chemical reaction networks. Non-autonomous chemical oscillators have been designed to mimic oscillatory behavior using programmable syringe pumps. Here, we investigated the non-autonomous oscillations, pattern formation, and front propagation of amphoteric hydroxide (aluminum (III), zinc (II), tin (II), and lead (II)) precipitates under controlled pH conditions. A continuous stirred-tank reactor with modulated inflows of acidic and alkaline solutions generated pH oscillations, leading to periodic precipitation and dissolution of metal hydroxides in time. The generated turbidity oscillations exhibited ion-specific patterns, enabling their characterization through quantitative parameters such as peak width (W) and asymmetry (As). The study of mixed metal cationic systems showed that turbidity patterns contained signatures of both hydroxides due to the formation of mixed hydroxides and oxyhydroxides. The reaction–diffusion setup in solid hydrogel columns produced spatial precipitation patterns depending on metal cations and their concentrations. Additionally, in the case of tin (II), a propagating precipitation front was observed in a thin precipitation layer. These findings provide new insights into precipitation pattern formation and open avenues for metal ion identification and further exploration of complex reaction–diffusion systems. Full article