Terms Of Reactions Research Articles

Numerical Solution of Two-Dimensional Nonlinear Unsteady Advection-Diffusion-Reaction Equations with Variable Coefficients

The advection-diffusion-reaction (ADR) equation is a fundamental mathematical model used to describe various processes in many different areas of science and engineering. Due to wide applicability of the ADR equation, finding accurate solution is very important to better understand a physical phenomenon represented by the equation. In this study, a numerical scheme for solving two-dimensional unsteady ADR equations with spatially varying velocity and diffusion coefficients is presented. The equations include nonlinear reaction terms. To discretize the ADR equations, the Crank–Nicolson finite difference method is employed with a uniform grid. The resulting nonlinear system of equations is solved using Newton’s method. At each iteration of Newton’s method, the Gauss–Seidel iterative method with sparse matrix computation is utilized to solve the block tridiagonal system and obtain the error correction vector. The consistency and stability of the numerical scheme are investigated. MATLAB codes are developed to implement this combined numerical approach. The validation of the scheme is verified by solving a two-dimensional advection-diffusion equation without reaction term. Numerical tests are provided to show the good performances of the proposed numerical scheme in simulation of ADR problems. The numerical scheme gives accurate results. The obtained numerical solutions are presented graphically. The result of this study may provide insights to apply numerical methods in solving comprehensive models of physical phenomena that capture the underlying situations.

Spreading speeds for time heterogeneous prey-predator systems with nonlocal diffusion on a lattice

We investigate the spreading behaviour for the solutions of a non-autonomous prey-predator system on a discrete lattice. These time variations are assumed to enjoy an averaging property. This includes periodicity, almost periodicity and unique ergodicity as special cases. The spatial motion of individuals from one site to another is modelled by a discrete convolution operator. In order to take into account external fluctuations such as seasonality, daily variations and so on, the convolution kernels and reaction terms may vary with time. Our analysis of the spreading speeds of invasion of the species is based on the careful and detailed study of the hair-trigger effect and spreading speed for a non-autonomous scalar Fisher-KPP equation on a lattice. Then, we are able to compare the solutions of the prey-predator system with those of a suitable scalar Fisher-KPP equation and derive the invasion speeds of the prey and of the predator.

Normal forms of a class of partial functional differential equations

In this paper, we investigate the normal form a class of partial functional differential equations, which takes account of delays in the diffusion terms as well as a wider scope of nonlinear terms. We first study the associated linear theory, mainly including the spectral properties of infinitesimal generator, formal adjoint and decomposition of phase space. Based on these results, the normal form theory for nonlinear equation is established, which can be used to study the local dynamics near the steady state for such equations. As an application, we consider the Hopf bifurcation problem of a scalar diffusive equation with delay not only involved in the diffusive term but also in reaction terms. The normal form, depending on the original coefficients, up to the third order term is calculated, which allows us to determine the direction of Hopf bifurcation and stability of bifurcated periodic solutions. The results are then applied to study the scalar population model with memory-based diffusion for modeling the movement of highly-developed animals.

Experimentally Closing the Balance of Progress of Reaction in Premixed Turbulent Combustion in the Thin Flame Regime

We investigate the possibility of determining the local turbulent flame speed by measuring the individual terms in the balance of a mean progress of reaction variable for the case of a low turbulence methane-air Bunsen flame in the thin flame regime. Velocity distributions and flame edge positions were measured by particle image velocimetry techniques at 3 kHz for a flame stabilized by a surrounding pilot of the same stoichiometry, for a turbulent Reynolds number around 66 and Karlovitz numbers of the order of 4. The conservation equation for mean progress variable was analyzed along different streamlines as a balance of terms expressed as velocities, including terms for convection, turbulent diffusion, mean reaction, and turbulent and molecular diffusion. Each term was estimated from local velocities and flame locations using a thin flame approximation, and their uncertainty was evaluated based on propagation of experimentally measured statistical correlations. The largest terms were the convective and reaction terms, as expected, with smaller roles for turbulent and molecular diffusion across the flame brush. Countergradient diffusion and transition to gradient diffusion were observed across the flame brush. Closure of the balance of terms in the conservation equations using independently measured terms was not consistently achieved across the flame brush within the reckoned uncertainties, arriving at a balance within 20–30% of the absolute value. Testable hypotheses are offered for the possible reasons for the mismatch, including the role of spatial filtering and 3D effects on the reaction rate term. Finally, the experiments identify the inaccuracies in measuring a true local turbulent flame speed, and suggest a consistent methodology to reduce errors in such estimations. This is the first time such a detailed experimental closure is attempted for any configuration. The results suggest that the significant improvements in spatial resolution are necessary for a full closure.

Localization of energies in Navier–Stokes models with reaction terms

We analyze a general class of coupled systems of stationary Navier–Stokes type equations with variable coefficients and non-homogeneous terms of reaction type in the incompressible case. Existence of solutions satisfying the homogeneous Dirichlet condition in a bounded domain in [Formula: see text], [Formula: see text], and localization results for the corresponding kinetic energy and enstrophy are obtained by using a variational approach and the fixed point index theory.

Evaluation of Cherts in Gumushane Province in Terms of Alkali Silica Reaction

Alkali–silica reaction (ASR) occurs when alkali oxides coming from the cement composition in concrete come together with reactive silica and moisture coming from the aggregate. Additional maintenance and repair costs caused by the development of ASR in concrete cause the cost to increase. However, thanks to the measures taken against ASR in the early period, it contributes to the creation of sustainable and durable concrete structures. The article investigated the usability of cherts with eight different chemical compositions as aggregates in ready-mixed concrete plants in Gümüşhane. Cherts have been investigated for alkaline reactivity and are intended to be used largely as a source for concrete plants. ASR length changes of the samples prepared according to ASTM C1260 standard were determined after 3, 7, 14, and 28 days of the curing period. Microstructural examination, ultrasonic P-wave velocity, and bending and compressive strength experiments supporting ASR were carried out. The obtained test results were compared between the reference (limestone) sample and each other, as well as with the values specified in the standards. The compressive and bending strength values of the samples increase depending on their ASR. It was observed that the crack structures and types increased depending on the increase in the crack values.

Lagrangian modelling of reactive contaminant transport in the multi-component marine medium

The particle-tracking method for transporting radionuclides in multicomponent ocean medium (water and multifractional suspended and deposited sediments) is considered using a probabilistic approach for simulating interaction processes between several states of radioactivity. The state transformations as a result of reactions of the first order were described using the master equation for the probability of the particle being in the given state. Transition probabilities between all possible states can be obtained from the numerical solution of the matrix master equation that is derived in the paper. In the first approximation, the Euler method was used to obtain a solution for the next time step. This approach can be applied to any linear system of equations describing phase transitions with any number of states, but it requires small values of the transition probabilities to ensure only a single-phase change during one time step. The paper also focuses on deriving the Lagrangian interface conditions between the water column and bottom deposition. To apply the probabilistic approach, the boundary conditions were considered as the reaction terms in a thin near-bottom interface layer in which boundary conditions were converted into source terms. For this layer, the corresponding master equation was derived to obtain transitional probabilities for particle states. The developed approaches were tested on numerical and analytical solutions of two test cases. It was found that the optimal thickness of the interface layer must be larger than the maximum vertical displacement of the particle during the one-time step, but it must be small enough to approximate the condition of uniform distribution of concentration in this layer.

A Crank-Nicolson WG-FEM for unsteady 2D convection-diffusion equation with nonlinear reaction term on layer adapted mesh

This paper is contributed to explore how a Crank-Nicolson weak Galerkin finite element method (WG-FEM) addresses the singularly perturbed unsteady convection-diffusion equation with a nonlinear reaction term in 2D. The problem and some asymptotic behavior results are given for the exact solution and its derivatives with the parameter ε. These results are essential for proving the uniform convergence of the proposed WG-FEM. A tensor product Shishkin mesh featuring piece-wise discontinuous bilinear polynomials is employed to handle the layers for uniform convergence at different parameter values of ε. An error estimate ‖uN−INu‖WG is presented, where INu denotes the vertex-edge-cell interpolation of the solution u, and ‖⋅‖WG denotes the Weak Galerkin norm. The optimal uniform convergence order is demonstrated for semi-discrete and fully discrete schemes. Various numerical experiments are conducted to validate the optimal order of convergence demonstrated by the proposed method.

Analysis and application of MLPG7 for diffusion equations with nonlinear reaction terms

This paper extends the recently proposed variant of meshless local Petrov Galerkin (MLPG) method, i.e., MLPG7, for solving time dependent PDEs. As test function, the method uses a novel modification of fundamental solution of Laplace operator that not only the test function itself but also its derivative vanish on boundary of local subdomains. Therefore, more stable local integral equations are obtained by replacing a boundary integral of derivatives of field variables with a domain integral of field variables itself. MLPG7 formulation converts the nonlinear governing equation into a system of first order ordinary differential equations (ODEs). For this system of ODEs, a theoretical stability analysis is carried out for the case of regularly spaced nodal points. Stability and convergence conditions for fully discretized equations by Euler (forward and backward) and Crank–Nicolson methods are investigated. The nonlinear term is treated iteratively. A numerical study investigates the convergence and stability of the method. A comparison is also done with some well-known methods and the results reveal the excellence of MLPG7. The convergence of the iterative approach is numerically verified by another illustrative test example. As nonlinear test problems, Allen–Cahn equations are studied.

Multidimensional assessment of adverse events of bupropion: A large-scale data analysis from the FAERS database

ObjectiveBupropion, a monocyclic antidepressant, aids in smoking cessation, treats major depression, and prevents severe depression in seasonal affective disorder patients. Yet, its adverse reactions remain insufficiently studied. MethodsAll data from the raw data packages for 78 quarters from the 1st quarter of 2004 to the 2nd quarter of 2023 were extracted from the FDA Adverse Event Reporting System (FAERS) database and imported into the SAS9.4 software for data cleaning and analysis. The Reporting Odds Ratio (ROR), Proportional Reporting Ratio (PRR), Bayesian Confidence Propagation Neural Network (BCPNN), and Multi-item Gamma Poisson Shrinker (MGPS) methods were used to analyze drug adverse events and assess their compliance with various screening criteria. ResultsThe results showed a total of 36,862 reports related to Bupropion use, identifying 364 positive reaction terms (PT) covering 23 System Organ Classes (SOCs). In addition to known side effects, some new potential adverse reactions were found, such as Stool analysis abnormal, Oculocephalogyric reflex absent, Suspected suicide, and so on. At the same time, reactions like Encephalopathy neonatal, Hyponatraemic coma, and Electrocardiogram QRS complex prolonged were prominently ranked. Notably, occurrences such as Urine amphetamine positive and Amphetamines positive were relatively high, suggesting extra caution for these potential adverse reactions during clinical use of Bupropion. ConclusionThese findings highlight the potential health risks of long-term Bupropion use, especially concerning efficacy, positive drug tests, and suicidal tendencies. Therefore, it is recommended to monitor and assess patients using Bupropion more stringently to use this therapeutically potential drug more safely and effectively.

An improved nonlinear anisotropic model with p(x)‐growth conditions applied to image restoration and enhancement

This work proposes a novel nonlinear parabolic equation with ‐growth conditions for image restoration and enhancement. Based on the generalized Lebesgue and Sobolev spaces with variable exponent, we demonstrate the well‐posedness of the proposed model. As a first result, we prove the existence of a weak solution to our model when the reaction term is bounded by a suitable function. Secondly, we use the approximations method to establish the existence of a nonnegative weak SOLA (Solution Obtained as Limit of Approximations) solution to the proposed model. We illustrate our theoretical results in the context of image denoising and enhancement. Specifically, we present various numerical implementations on a set of grayscale images. To further enrich these simulations, we assess the efficiency of the proposed model on several color images. The obtained numerical results strongly suggest that our model outperforms existing state‐of‐the‐art methods in terms of both visual and quantitative comparison, demonstrating superior efficiency and robustness in noise removal and contrast enhancement.

Effect of unfavorable regions on the spreading solution in a diffusion equation

We consider a diffusion equation on the real line with growth rates (reaction terms) being negative in a bounded unfavorable region and bistable on two sides. The equation can be used to model a species living in a habitat with a polluted or hunting zone but still tries to survive or even spread to the whole space. Using the zero number argument, we first show the general convergence to stationary solution for any nonnegative global solutions, and then we prove a spreading–transition–vanishing trichotomy result for the asymptotic behavior of global solutions. The key point is to find a quite special stationary solution to distinguish the spreading and transition solutions. Finally, we construct precise upper and lower solutions to estimate the asymptotic speed for the spreading solution.

Mathematical modeling of non-linear reaction-diffusion process in autocatalytic reaction: Akbari-Ganji method

A theoretical model of the electroreduction of halogen oxoanions via autocatalytic redox mediation by halide anions is discussed. This autocatalytic process depends upon a system reaction-diffusion equation including a nonlinear term for homogeneous reactions. This study solves these equations using the robust and user-friendly analytical technique, the Akbari-Ganji method. The current and the redox component concentration are presented in terms of the rate constant. The influence of variables on current is examined using sensitivity analysis. The most important factor affecting current is the ratio between the bulk concentrations of halogen molecules and non-electroactive halogen oxoanions. The theoretically predicted results are compared with the numerical results. These approximate results enhance our understanding of system behavior.

Global dynamics of a time-delayed nonlocal reaction-diffusion model of within-host viral infections.

In this paper, we study a time-delayed nonlocal reaction-diffusion model of within-host viral infections. We introduce the basic reproduction number and show that the infection-free steady state is globally asymptotically stable when , while the disease is uniformly persistent when . In the case where all coefficients and reaction terms are spatially homogeneous, we obtain an explicit formula of and the global attractivity of the positive constant steady state. Numerically, we illustrate the analytical results, conduct sensitivity analysis, and investigate the impact of drugs on curtailing the spread of the viruses.

Olivine-Hosted Melt Inclusions Track Progressive Dehydration Reactions in Subducting Slabs Across Volcanic Arcs

Abstract The stability and breakdown of mineral phases in subducting slabs control the cycling of trace elements through subduction zones. Stability of key minerals and the partitioning of trace elements between these minerals and liquid phases of interests have been charted by natural sample analysis and experimental constraints. However, systematic study from arc front to far back arc has rarely shown that the expected geochemical variations of the slab liquid are actually recorded by natural samples. Complexities arise by uncertainties on the nature of the slab component (melts, fluids and supercritical liquids), source heterogeneities and transport processes. Using data from olivine-hosted melt inclusions sampled along and across the NE Japan and southern Kurile arcs, we demonstrate that experimentally and thermodynamically constrained phase stabilities in subducted materials indeed control the trace element signatures as predicted by these models and experiments. The main reactions that can be traced across arc are progressive breakdown of light rare earth element-rich accessory phases (e.g. allanite), enhanced dehydration of the lithospheric mantle (serpentine breakdown) and changes in the nature of the slab component. This work elucidates subduction zone elemental cycling in a well-characterized petrogenetic setting and provides important constraints on the interpretation of trace element ratios in arc magmas in terms of the prograde metamorphic reactions within the subducting slab.

On propagation in networks, promising models beyond network diffusion to describe degenerative brain diseases and traumatic brain injuries.

Introduction: Connections among neurons form one of the most amazing and effective network in nature. At higher level, also the functional structures of the brain is organized as a network. It is therefore natural to use modern techniques of network analysis to describe the structures of networks in the brain. Many studies have been conducted in this area, showing that the structure of the neuronal network is complex, with a small-world topology, modularity and the presence of hubs. Other studies have been conducted to investigate the dynamical processes occurring in brain networks, analyzing local and large-scale network dynamics. Recently, network diffusion dynamics have been proposed as a model for the progression of brain degenerative diseases and for traumatic brain injuries. Methods: In this paper, the dynamics of network diffusion is re-examined and reaction-diffusion models on networks is introduced in order to better describe the degenerative dynamics in the brain. Results: Numerical simulations of the dynamics of injuries in the brain connectome are presented. Different choices of reaction term and initial condition provide very different phenomenologies, showing how network propagation models are highly flexible. Discussion: The uniqueness of this research lies in the fact that it is the first time that reaction-diffusion dynamics have been applied to the connectome to model the evolution of neurodegenerative diseases or traumatic brain injury. In addition, the generality of these models allows the introduction of non-constant diffusion and different reaction terms with non-constant parameters, allowing a more precise definition of the pathology to be studied.

Culture dependent analysis of bacterial activity, biofilm-formation and oxidative stress of seawater with the contamination of microplastics under climate change consideration

Temperature changes due to climate change and microplastic contamination are worldwide concerns, creating various problems in the marine environment. Therefore, this study was carried out to discover the impact of different temperatures of seawater exposed to different types of plastic materials on culture dependent bacterial responses and oxidative characteristics. Seawater was exposed to microplastics obtained from various plastic materials at different temperature (−18, +4, +20, and +35 °C) for seven days. Then microplastics were removed from the suspension and microplastic-exposed seawater samples were analyzed for bacterial activity, biofilm formation and oxidative characteristics (antioxidant, catalase, glutathione, and superoxide dismutase) using Gram-negative Pseudomonas aeruginosa and Gram-positive Staphylococcus aureus. The results showed that the activity and biofilm formation of Pseudomonas aeruginosa and Staphylococcus aureus were affected through oxidative stress by catalase, glutathione, and superoxide dismutase due to the microplastic deformation by temperature changes. This study confirms that temperature changes as a result of climate change might influence microplastic degradation and their contamination impact in seawater in terms of bacterial metabolic and oxidation reactions.

Green, solventless debromination of C70Br10 to C70 with CsI

A smooth, solventless and solid state debromination of C70Br10 can be achieved in a CsI matrix with the restoration of the pristine C70 in quantitative yields. Such debromination reaction was studied with FT-IR spectroscopy and its kinetics was fitted by a pseudofirst order law, with a rate constant in the range of 3.6-5.2 x 10−5 s−1. The thermal properties of the compound C70Br10 were studied with TGA and DSC analysis focusing on the thermal decomposition processes. From the DSC data both the activation energy for the thermal decomposition of C70Br10 as well as its enthalpy of formation were determined. Some considerations on the relative weakness of C-Br bonds in brominated fullerenes compounds were made. Accordingly, the debromination mechanism is discussed in terms of unimolecular elimination reaction (E1) in a concerted mechanism which leads to the restoration of the pristine C70 fullerene.

Reaction-diffusion equations on metric graphs with edge noise

We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given. The vertex conditions are the standard continuity and generalized, non-local Neumann-Kirchhoff-type law in each vertex. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily of the same degree on each edge, with possibly stochastic coefficients and negative leading term. The model is a generalization of the problem in [14] where polynomials with much more restrictive assumptions are considered and no first order differential operator is involved. We utilize the semigroup approach from [15] to obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph.

Green, solventless debromination of C70Br10 To C70 with CsI

A smooth, solventless and solid state debromination of C70Br10 can be achieved in a CsI matrix with quantitative restoration of the pristine C70 in quantitative yields. The debromination kinetics was studied with FT-IR spectroscopy and according to the pseudofirst order kinetics law, the rate constant was found in the range 3.6–5.2 × 10−5 s−1. The compound C70Br10 was studied with TGA and its thermal decomposition by DSC analysis. From the DSC data both the activation energy for the thermal decomposition of C70Br10 was determined as well as its enthalpy of formation, which has led to some considerations on the relative weakness of C–Br bonds in brominated fullerenes compounds. The debromination mechanism is discussed in terms of unimolecular elimination reaction (E1) in a concerted mechanism which leads to the restoration of the pristine C70 fullerene.