Nonlinear Reaction Research Articles

Coupled nonlinear surface reactions in random walk particle tracking

Random walk particle tracking (RWPT) methods employ a Lagrangian discretization of transported scalars into point particles to numerically solve the advection–dispersion equation. Their recognized advantages regarding numerical stability and numerical dispersion make them ideal candidates to tackle reactive transport problems. However, limitations in the classes of boundary conditions that can currently be treated restrict the range of interface processes that can be simulated. Here, we derive and verify a new collision-based approach to implement a broad class of generalized Robin-type boundary conditions, representing the balance between diffusive fluxes and an arbitrary nonlinear function of the transported and surface reactant concentrations. This formulation allows for modeling coupled sets of surface reactions with arbitrary nonlinear kinetics within the classical RWPT framework. The collision-based nature of the proposed technique allows for estimating surface reaction rates based on single-particle collisions with the reactive interface, relying only on a discretization of the boundary as commonly used for collision detection under conservative transport. Thus, the method does not require concentration field reconstructions within the transport domain or multi-particle searches.

A Harnack inequality for a class of 1D nonlinear reaction–diffusion equations and applications to wave solutions

In this paper, a differential-geometric method is applied to build some Li–Yau–Hamilton-type Harnack inequalities for the positive solutions to a one spatial dimensional nonlinear reaction–diffusion equation in a plane geometry. The class of reaction–diffusion equation that is considered here contains several important equations some of which are Newel–Whitehead–Segel, Allen–Cahn and Fisher–KPP equations. The Harnack inequalities so derived are used to discuss some other important properties of positive solutions and in the characterization of positive wave solutions.

Mixed finite element methods for nonlinear reaction–diffusion equations with interfaces

We develop mixed finite element methods for nonlinear reaction–diffusion equations with interfaces which have Robin-type interface conditions. We introduce the velocity of chemicals as new variables and reformulate the governing equations. The stability of semidiscrete solutions, existence and the a priori error estimates of fully discrete solutions are proved by fixed point theorem and continuous/discrete Grönwall inequalities. Numerical results illustrating our theoretical analysis are included.

Recovery of waste cooking palm oil as a crosslinker for inverse vulcanized adsorbent to remove iron (Fe3+) ions

Gas and oil reservoirs around the world leave megatons of unused elemental sulfur as industrial byproducts which has been successfully used in inverse vulcanization. We reported the successful application of inverse vulcanized porous adsorbent from waste cooking palm oil (WCO) to remove ferric (Fe3+) ions. Sodium chloride (NaCl) acted as a porogen to get the porous polysulfide. The removal of Fe3+ was observed through the atomic absorption spectroscopic (AAS) technique. The effects of pH (3,7, and 11) and initial concentration (35, 40, 45 mg/L) of Fe3+ solution, and dosage (10, 15, and 20 g/100 mL) on Fe3+ adsorption were studied to determine the best removal condition. Later, fixing the best parameters (pH 3, 40 mg/L, 20 g/100 mL), Langmuir and Freundlich equations were used to study the adsorption isotherm. Adsorption kinetics were described using linear and nonlinear pseudo-first and second-order reactions. The Freundlich isothermal model and linear pseudo-second-order kinetics fit best for the removal process. The comparison between the pre and post-adsorption analyses using FTIR, SEM-EDX, and the isothermal model confirmed the physisorption of Fe3+. The current study concluded with some further scopes of the adsorbent for diverse removal applications.

Radical chain mechanism for the S2O8 2--S2O3 2--Cu(ii) flow system explains high-amplitude pH oscillations in the NH4OH-modified version.

Peroxodisulfate is well known as an important reagent in analytical, environmental and other branches of chemistry, as well as in industrial processes. One of the most studied oxidative reactions peroxodisulfate participates in as an oxidizer is the Cu(ii)-catalyzed peroxodisulfate-thiosulfate reaction. When carried out in a flow reactor, this system shows oscillatory dynamics characterized by periodic changes in the Pt-potential and [O2] while it only displays variation in the pH with a few tenths of unit magnitude. Our recent experiments unveiled an increase of the amplitude of the pH oscillations that exceeds 4 units when NH4OH was introduced into the oscillatory flow system. The dynamics of Cu(ii)-catalyzed peroxodisulfate-thiosulfate reaction has been described in detail but the chemical mechanism explaining the oscillatory behavior has not been established. Based on what is known about the uncatalyzed reaction between peroxodisulfate and thiosulfate in the literature, we have developed a mechanism that includes radical chain reactions which can explain the oscillatory phenomena. The proposed mechanism includes 13 reactions with the radical ions SO4˙-, S2O3˙-, S2O8˙-, OH˙ and two acid-base equilibria, including the dissociation equilibrium of NH4OH accounting for its effect on the amplitude of pH oscillations. Using this model, we successfully simulated the behavior of this system: (1) the evolution of the concentrations of the initial reagents, radicals, and catalyst over time in batch configuration, (2) the periodic changes in the concentrations of radicals and the oxidized and reduced forms of the catalyst, pH and [O2] in flow conditions. Our model also explains the amplification of the pH cycles without impacting the redox processes when NH4OH is added, which is a novel phenomenon observed in nonlinear chemical reactions. The high amplitude pH oscillations we report in the peroxodisulfate-thiosulfate-Cu(ii)-NH4OH flow reaction may enable future applications where this system may serve (a) as a core oscillator in coupled chemical systems, or (b) as a pH oscillator capable of running in a closed reactor configuration.

A kinetic non-steady state analysis of immobilized enzyme systems with external mass transfer resistance

<abstract><p>The goal of this paper is to utilize the homotopy perturbation method (HPM) and Laplace transform to provide an approximate analytical expression to the non-linear time-dependent reaction diffusion equation arising in a mathematical model of an immobilized enzyme system with external mass transfer resistance. This mathematical model is a non-steady, non-linear reaction diffusion equation based on Michaelis–Menten kinetics. Approximate analytical expressions are also provided for various geometries of the enzyme catalytic pellets, namely, planar, cylindrical, and spherical. Obtained semi-analytical expressions are proven to fit for all the parameters appearing in the system and for all the geometries of enzyme catalytic pellets. When comparing the numerical and approximate analytical solutions, satisfactory results are obtained. Also, approximate analytical expressions of the effectiveness factor (EF) of the immobilized system are presented, and the effect of parameters on the EF is also analyzed.</p></abstract>

Self-organization of active colloids mediated by chemical interactions.

Self-propelled colloidal particles exhibit rich non-equilibrium phenomena and have promising applications in fields such as drug delivery and self-assembled active materials. Previous experimental and theoretical studies have shown that chemically active colloids that consume or produce a chemical can self-organize into clusters with diverse characteristics depending on the effective phoretic interactions. In this paper, we investigate self-organization in systems with multiple chemical species that undergo a network of reactions and multiple colloidal species that participate in different reactions. Active colloids propelled by complex chemical reactions with potentially nonlinear kinetics can be realized using enzymatic reactions that occur on the surface of enzyme-coated particles. To demonstrate how the self-organizing behavior depends on the chemical reactions active colloids catalyze and their chemical environment, we consider first a single type of colloid undergoing a simple catalytic reaction, and compare this often-studied case with self-organization in binary mixtures of colloids with sequential reactions, and binary mixtures with nonlinear autocatalytic reactions. Our results show that in general active colloids at low particle densities can form localized clusters in the presence of bulk chemical reactions and phoretic attractions. The characteristics of the clusters, however, depend on the reaction kinetics in the bulk and on the particles and phoretic coefficients. With one or two chemical species that only undergo surface reactions, the space for possible self-organizations are limited. By considering the additional system parameters that enter the chemical reaction network involving reactions on the colloids and in the fluid, the design space of colloidal self-organization can be enlarged, leading to a variety of non-equilibrium structures.

A first-order fractional–steps–type method to approximate a nonlinear reaction–diffusion equation with homogeneous Cauchy–Neumann boundary conditions

A first-order fractional–steps–type method to approximate a nonlinear reaction–diffusion equation with homogeneous Cauchy–Neumann boundary conditions

Supply, Demand and Asymmetric Adjustment of House Prices in Poland

Abstract In recent years, a lot of empirical effort has been made to search for potential nonlinear responses of house prices to various demand and supply factors. This paper examines Poland's heterogeneous regional housing market reactions to key economic variables from 2000 to 2022. The study raises two research questions related to the asymmetric adjustment of housing markets to selected demand and supply shocks. Firstly, we ask whether the house price adjustments to negative shocks are relatively minor (for example, during an economic downturn) when compared to positive shocks (prevalent in booming markets), mainly due to the loss aversion behavior theory and nominal rigidity of house prices. In particular, we test the hypothesis that house prices react more to positive impulses from supply and demand than negative ones. Secondly, we investigate whether market reactions are similar for large and small metropolitan markets. The second hypothesis posits that metropolitan housing markets adjust asymmetrically to demand and supply shocks based on the city size (population and housing stock in a given city). The study uses a nonlinear ARDL model to test the research hypotheses empirically. This paper provides new insights into the nonlinear reactions of house prices to exogenous shocks and adds to the limited empirical evidence from less developed economies.

Methylene glycol-sulfite pH-clocks for the time-programming of soft materials: advantages, limitations, and yet unexplored opportunities.

Coupling nonlinear reaction networks with soft matter building blocks holds great potential for the design of life-mimicking, time-programmable dissipative self-assembly systems. In this regard, clock reactions are especially useful triggers since they allow to autonomously generate in situ chemical stimuli such as pH changes. The methylene glycol-sulfite (MGS) is a well-known acid-to-base pH-clock reaction which is able to produce sharp and intense pH jumps (up to 5 pH units) after a reliable, yet relatively short (tens of seconds rather than minutes), induction time. Here, after an introductory discussion on the main chemical aspects of MGS and MGS-based systems, their applications for the time-programming of soft matter will be showcased - from micelles, vesicles, and droplets to supramolecular aggregates, polymers and gels. Hopefully, this will help attracting more attention and foster research on the broader field of materials programming with chemical reaction networks.

Simultaneous blow-up of the solution for a singular parabolic system with concentrated sources

<abstract> <p>A singular parabolic system with homogeneous Dirichlet boundary conditions and concentrated nonlinear reaction sources was examined. This paper investigated the existence and uniqueness of the solution. The sufficient conditions for the solution being blown up simultaneously in a finite time were determined. In addition, it was shown that the solution blew up everywhere in the domain except boundary points.</p> </abstract>

Mathematical analysis of urea amperometric biosensor with Non-Competitive inhibition for Non-Linear Reaction-Diffusion equations with Michaelis-Menten kinetics

This article examines a mathematical model for stable urea amperometric biosensors with non-competitive inhibition under homogenous conditions. The system is based on reaction and diffusion equations with a non-linear component associated with the Michaelis-Menten kinetics of the enzyme reaction. Theoretical findings in this study can be used to examine the impact of various factors, including the Michaelis-Menten constant and the Thiele modulus. The steady-state non-linear reaction–diffusion equations were solved using two effective and widely used analytical approaches, the Akbari-Ganji method (AGM) and the differential transform method (DTM). The generalized approximation analytical solution for the concentrations of the substrate, inhibitor, and product, as well as the current for the experimental values of the parameter, is developed. The current can also be used to analyze the resistance and sensitivity of biosensors. The digital simulation was carried out utilizing MATLAB software. The numerical results help to validate the analytical results. The impact of membrane thickness, maximum enzymatic rate, and substrate concentration on biosensor response was evaluated.

Smart Tumor Cell-Derived DNA Nano-Tree Assembly for On-Demand Macrophages Reprogramming.

Without coordinated strategies to balance the population and activity of tumor cells and polarized macrophages, antitumor immunotherapy generally offers limited clinical benefits. Inspired by the "eat me" signal, a smart tumor cell-derived proximity anchored non-linear hybridization chain reaction (Panel-HCR) strategy is established for on-demand regulation of tumor-associated macrophages (TAMs). The Panel-HCR is composed of a recognition-then-assembly module and a release-then-regulation module. Upon recognizing tumor cells, a DNA nano-tree is assembled on the tumor cell surface and byproduct strands loaded with CpG oligodeoxynucleotides (CpG-ODNs) are released depending on the tumor cell concentration. The on-demand release of CpG-ODNs can achieve efficient regulation of M2 TAMs into the M1 phenotype. Throughout the recognition-then-assembly process, tumor cell-targeted bioimaging is implemented in single cells, fixed tissues, and living mice. Afterward, the on-demand release of CpG-ODNs regulate the transformation of M2 TAMs into the M1 phenotype by stimulating toll-like receptor 9 to activate the NF-κB pathway and increasing inflammatory cytokines. This release-then-regulation process is verified to induce strong antitumor immune responses both in vitro and in vivo. Altogether, this proposed strategy holds tremendous promise for on-demand antitumor immunotherapy.

Reaction-diffusion modelling of petrological mixing mechanisms in the evolution of continental crusts

Petrological assimilation is a key process in the evolution of high-grade metamorphic terrains in the continental crusts. This study examines the mechanisms of such macroscopic assimilation between felsic (F) and mafic (M) constituents as two petrologically interacting continuum phases, as observed in the Chotanagpur Granite Gneissic Complex (CGGC), India, which underwent amphibolite to granulite facies metamorphism (∼775 to 900°C and 7 to 11 kb) between from the Paleoproterozoic to the late Mesoproterozoic. From field investigation we could recognized four interface patterns: planar, wavy, fingering and incoherent, which are generated at the interface between the F and M units. We have adopted the Turing type reaction-diffusion (RD) approach, which is a well established theoretical model to interpret any complex auto-regulatory pattern in natural and physical sciences, to understand the physics of the self-organizing interface geometries observed across the CGGC. The RD model findings suggest that these patterns are constrained by a combination of: diffusion coefficients (DF, DM) of F and M, a linear or non-linear reaction term (R) that describes phase interactions and a pinning field (W) that introduces microscale heterogeneity. For linear interactions, F − M undergo homogeneous mixing and show planar/wavy interfaces, when DF = DM and W = 0. The mixing turns heterogeneous as DF ≠ DM and W > 0, resulting in phase boundary migration with a fingering pattern. Non-linear reaction coupling enhances heterogeneous mixing and produces incoherent phase boundaries where F-phases host relics of M-phases, following a power-law size distribution. Striking similarities of interface patterns and fractal dimensions estimated from model and CGGC validate the proposed mechanism of macroscopic petrological assimilation. We argue that RD model provides a new insight into the genesis of hybrid rocks in metamorphic terrains.

Information geometry of dynamics on graphs and hypergraphs

We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces, respectively. The former is the conventional duality between density and potential, e.g., the probability density and its logarithmic form induced by a convex thermodynamic function. The latter is the duality between flux and force induced by a convex and symmetric dissipation function, which drives the dynamics of the density. These two are connected topologically by the homological algebraic relation induced by the underlying discrete objects. The generalized gradient flow in this doubly dual flat structure is an extension of the gradient flows on Riemannian manifolds, which include Markov jump processes and nonlinear chemical reaction dynamics as well as the natural gradient. The information-geometric projections on this doubly dual flat structure lead to information-geometric extensions of the Helmholtz–Hodge decomposition and the Otto structure in L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^{2}$$\\end{document}-Wasserstein geometry. The structure can be extended to non-gradient nonequilibrium flows, from which we also obtain the induced dually flat structure on cycle spaces. This abstract but general framework can broaden the applicability of information geometry to various problems of linear and nonlinear dynamics.

Finite Difference Modeling of Time Fractal Impact on Unsteady Magneto-hydrodynamic Darcy–Forchheimer Flow in Non-Newtonian Nanofluids with the q-Derivative

This contribution addresses a fractal numerical scheme that can be employed for handling fractal time-dependent parabolic equations. The numerical scheme presented in this contribution can be used to discretize integer order and fractal derivatives in a given differential equation. Therefore, the scheme and results can be used for both cases. The proposed finite difference scheme is based on two stages. Fractal time derivatives are discretized by employing the proposed approach. For the scalar convection–diffusion equation, we derive the stability condition of the proposed fractal scheme. Using a nonlinear chemical reaction, the approach is also used to solve the Quantum Calculus model of a Williamson nanofluid’s unsteady Darcy–Forchheimer flow over flat and oscillatory sheets. The findings indicate a negative correlation between the velocity profile and the porosity parameter and inertia coefficient, with an increase in these factors resulting in a drop in the velocity profile. Additionally, the fractal scheme under consideration is being compared to the fractal Crank–Nicolson method, revealing that the proposed scheme exhibits a superior convergence speed compared to the fractal Crank–Nicolson method. Several problems involving the motion of non-Newtonian nanofluids through magnetic fields and porous media can be investigated with the help of the proposed numerical scheme. This research has implications for developing more efficient heat transfer and energy conversion devices based on nanofluids.

The Holby–Morgan Model of Platinum Catalyst Degradation in PEM Fuel Cells: Range of Feasible Parameters Achieved Using Voltage Cycling

Loss of electrochemical surface area in proton-exchange membrane is of large practical importance, since membrane degradation largely affects the durability and life of fuel cells. In this paper, the electrokinetic model developed by Holby and Morgan is considered. The paper describes degradation mechanisms in membrane catalyst presented by platinum dissolution, platinum diffusion, and platinum oxide formation. A one-dimensional model is governed by nonlinear reaction–diffusion equations given in a cathodic catalyst layer using Butler–Volmer relationships for reaction rates. The governing system is endowed with initial conditions, mixed no-flux boundary condition at the interface with gas diffusion layer, and a perfectly absorbing condition at the membrane boundary. In cyclic voltammetry tests, a non-symmetric square waveform is applied for the electric potential difference between 0.6 and 0.9 V held for 10 and 30 s, respectively, according to the protocol of European Fuel Cell and Hydrogen Joint Undertaking. Aimed at mitigation strategies, the impact of cycling operating conditions and model parameters on the loss rate of active area is investigated. The global behavior with respect to variation of parameters is performed using the method of sensitivity analysis. Finding feasible and unfeasible values helps to determine the range of test parameters employed in the model. Comprehensive results of numerical simulation tests are presented and discussed.

Nonlinear dynamics in eyring-powell fluid flow with darcy-forchheimer effects. An asymptotic analysis

We provide a mathematical treatment, analytical and numerical, for a fluid constructed as an hybrid of the Eyring-Powell and Darcy-Forchheimer fluid models. The Eyring-Powell model departs from the kinetic theory of liquids and it allows for a description of shear stresses and viscous terms. The Darcy-Forchheimer model permits to describe the fluid effects given in a porous media, and it provides non-linear reaction terms when considered as part of the momentum equations. Hence, it is natural to investigate mathematical characteristics of solutions for a fluid flow formulated as a combination of these two fluid models. First of all, we prove boundedness and uniqueness of solutions arising from rough (i.e. in L 1(R) ∩ L ∞(R)) initial data. This is physically relevant, since it means that we are considering general descriptions of the velocity distribution of the fluid, in a media with particular porosity distributions. Afterwards, stationary profiles are obtained by using a Hamiltonian description, and our construction is supported by numerical validating evidences. Furthermore, asymptotic solutions are explored based on an exponential scaling and a non-linear transport Jacobi equation. Finally, a region of validity for this asymptotic approach is provided, and a numerical validation of our asymptotic analysis is presented. Our main conclusion is that a fluid model combining Eyring-Powell and Darcy-Forchheimer characteristics is indeed possible to introduce, and that solutions of potential physical interest, can be obtained.

Exploration of nonlinear radiative heat energy on Buongiorno modeled nano liquid toward an inclined porous plate with heat source and variable chemical reaction

Nanofluids are fluid suspensions of nanoparticles that exhibit a considerable improvement in their characteristics at low nanoparticle concentrations. Numerous research on nanofluids focuses on interpreting their behavior in order to use them in applications where improving straight heat transmission is crucial, such as in various industrial settings, nuclear reactors, transportation, biology, food, and electronics. Thus, this study examines the implementation of a novel numerical technique, namely the shooting method for nonlinear radiative heat energy study on Buongiorno modeled nano liquid confined by an inclined porous plate. The Brownian and thermophoresis diffusions impacts are also accounted. The transmission of thermal and solutal energy is regulated by the considerable influence of nonlinear thermal radiation, heat source, and variable chemical reactions. The dimensional modeled partial differential equations (PDEs), by using precise similarity functions, have been mutated into ordinary differential equations (ODEs). The outcomes for the flow field, thermal, and solutal outlines are captured graphically. The values of the dimensionless parameters are chosen from the literature in such a way that they have significantly affected the dimensionless boundary layer (BL) profiles. Also, the non-dimensional profiles of velocity, temperature, and concentration observe two different trends (increasing and decreasing) for diverse values of the dimensionless parameters.

Very high-order finite difference method on arbitrary geometries with Cartesian grids for non-linear convection diffusion reaction equations

An arbitrary order finite difference method for solving non-linear convection Diffusion Reaction equations in curved boundary domains with Cartesian grid is proposed. Ghost points' values are determined with the Reconstruction Off-Site Data based on a polynomial interpolation using the least square method with constraints to enforce the boundary conditions. We propose a second-, fourth-, and sixth-order schemes for linear non-constant coefficients problem in both the conservative and non-conservative scalar equations. Extensions to non-linear scalar problems and systems are then implemented while preserving the optimal orders. Numerical simulations are carried out to provide evidence about the convergence order and the stability of the method.