Solutions Of Reaction Research Articles

A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems

A simple flux reconstruction for finite element solutions of reaction–diffusion problems is shown to yield fully computable upper bounds on the energy norm of error in an approximation of singularly perturbed reaction–diffusion problem. The flux reconstruction is based on simple, independent post-processing operations over patches of elements in conjunction with standard Raviart–Thomas vector fields. We prove that the corresponding local error indicators are locally efficient and robust (up to a nonstandard oscillation term) with respect to any mesh size and any size of the reaction coefficient, including the singularly perturbed limit.

Polymeric and non‐crosslinked acid self‐thickening agent based on hydrophobically associating water‐soluble polymer during the acid rock reaction

ABSTRACTDifferent from traditional crosslinked polymer diverting agents, a polymeric and non‐crosslinked acid self‐thickening agent (ZPAM) based on hydrophobically associating water‐soluble polymer of acrylamide (AM), [2‐(methacryloyloxy)ethyl]trimethylammonium chloride (DMC) andN,N′‐dimethyl octadecyl allyl ammonium chloride (DOAC) was synthesized. The apparent viscosity variation of ZPAM acid solutions in acid rock reaction and rheological properties of ZPAM spent acid solutions were studied. Results showed that ZPAM acid solutions demonstrated good uninterruptedly thickening ability from low apparent viscosity to high apparent viscosity during the acid rock reaction. Meanwhile, ZPAM spent acid solutions showed good shear resistance, viscoelasticity and high temperature resistance. The thickening mechanism of ZPAM acid solutions during the acid rock reaction was explained by apparent viscosity change, rheological properties of simulative ZPAM acid solutions, and ZPAM aqueous solutions with different concentrations of CaCl2. The results showed increasing calcium chloride concentration enhanced the hydrophobic association strength of the thickener solution, resulting in increasing solution viscosity, in other words, the self‐thickening agent showed excellent salt resistance and acid resistance. In addition, the change of association strength of ZPAM acid solutions during the acid rock reaction was further confirmed via environmental scanning electron micrographs and UV spectrum. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci.2019,136, 47907.

Analysis of differential equations involving Caputo\u2013Fabrizio fractional operator and its applications to reaction\u2013diffusion equations

This manuscript deals with fractional differential equations including Caputo–Fabrizio differential operator. The conditions for existence and uniqueness of solutions of fractional initial value problems is established using fixed point theorem and contraction principle, respectively. As an application, the iterative Laplace transform method (ILTM) is used to get an approximate solutions for nonlinear fractional reaction–diffusion equations, namely the Fitzhugh–Nagumo equation and the Fisher equation in the Caputo–Fabrizio sense. The obtained approximate solutions are compared with other available solutions from existing methods by using graphical representations and numerical computations. The results reveal that the proposed method is most suitable in terms of computational cost efficiency, and accuracy which can be applied to find solutions of nonlinear fractional reaction–diffusion equations.

In situ construction of Co/Co3O4 with N-doped porous carbon as a bifunctional electrocatalyst for oxygen reduction and oxygen evolution reactions

Abstract The development of low-cost electrocatalyst with high efficiency is crucial in energy conversion and storage. The Co/Co3O4 nanoparticles are encapsulated into N-doped porous carbon (Co/Co3O4/NPC) by one-step dual-template method. Co/Co3O4/NPC possesses hierarchically porous structure consisting of 3D ordered macroporous carbon frameworks and mesopores with large BET surface areas, and Co/Co3O4 nanoparticles are uniformly enclosed in the carbon walls. Co/Co3O4/NPC exhibits better durability in alkaline solution for oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) compared to commercial Pt/C and Ir/C. Such superior catalytic performance could be ascribed to the synergistic effects between embedded Co/Co3O4 nanoparticles and the unique hierarchically porous structure.

Stability of reaction–diffusion systems with stochastic switching

In this paper, we investigate the stability for reaction systems with stochastic switching. Two types of switched models are considered: (i) Markov switching and (ii) independent and identically distributed switching. By means of the ergodic property of Markov chain, Dynkin formula and Fubini theorem, together with the Lyapunov direct method, some sufficient conditions are obtained to ensure that the zero solution of reaction–diffusion systems with Markov switching is almost surely exponential stable or exponentially stable in the mean square. By using Theorem 7.3 in [R. Durrett, Probability: Theory and Examples, Duxbury Press, Belmont, CA, 2005], we also investigate the stability of reaction–diffusion systems with independent and identically distributed switching. Meanwhile, an example with simulations is provided to certify that the stochastic switching plays an essential role in the stability of systems.

Surface fractal dimension of bentonite affected by long-term corrosion in alkaline solution

To study the change mechanisms of the fractal dimension of bentonite affected by a corrosion process in alkaline solution, sodium bentonite was mixed with 1 mol/L NaOH solution and sealed for reaction for up to 720 d (days). The fractal dimensions of bentonite specimens at different stages of the corrosion process were obtained from N2 adsorption and swelling deformation tests, and the results of both methods suggested that the fractal dimension tends to increase with duration of the corrosion process. From X-ray diffraction (XRD) tests, it was found that montmorillonite, the main component of bentonite, was dissolved gradually in the alkaline solution. However, the decline in montmorillonite content had no relation to the change in fractal dimension, which was validated by swelling deformation tests of bentonite–quartz mixtures, as the swelling characteristics of the bentonite–quartz mixtures could be expressed by a unique curve of the em–ps relation (em is the void ratio of montmorillonite, ps is the vertical stress) with an identical fractal dimension. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) images were used to observe the surface microscopic morphology of the original and alkaline-corroded bentonite. It was found that montmorillonite layers in the original bentonite were often aggregated into plate-like particles. However, after corrosion in the alkaline solution, these montmorillonite aggregates were cracked into small stacks and the surface of montmorillonite layers became more uneven, resulting in a more complicated surface and a higher fractal dimension.

Reduction approach to the dynamics of interacting front solutions in a bistable reaction–diffusion system and its application to heterogeneous media

The dynamics of pulse solutions in a bistable reaction-diffusion system are studied analytically by reducing partial differential equations (PDEs) to finite-dimensional ordinary differential equations (ODEs). For the reduction, we apply the multiple-scales method to the mixed ODE-PDE system obtained by taking a singular limit of the PDEs. The reduced equations describe the interface motion of a pulse solution formed by two interacting front solutions. This motion is in qualitatively good agreement with that observed for the original PDE system. Furthermore, it is found that the reduction not only facilitates the analytical study of the pulse solution, especially the specification of the onset of local bifurcations, but also allows us to elucidate the global bifurcation structure behind the pulse behavior. As an application, the pulse dynamics in a heterogeneous bump-type medium are explored numerically and analytically. The reduced ODEs clarify the transition mechanisms between four pulse behaviors that occur at different parameter values.

Asymptotic Stability of a Stationary Solution of a Multidimensional Reaction–Diffusion Equation with a Discontinuous Source

A two-dimensional reaction–diffusion equation in a medium with discontinuous characteristics is considered; the existence, local uniqueness, and asymptotic stability of its stationary solution, which has a large gradient at the interface, is proved. This paper continues the authors’ works concerning the existence and stability of solutions with internal transition layers of boundary value problems with discontinuous terms to multidimensional problems. The proof of the existence and stability of a solution is based on the method of upper and lower solutions. The methods of analysis proposed in this paper can be generalized to equations of arbitrary dimension of the spatial variables, as well as to more complex problems, e.g., problems for systems of equations. The results of this work can be used to develop numerical algorithms for solving stiff problems with discontinuous coefficients.

Fabrication of 3D microporous amorphous metallic phosphides for high-efficiency hydrogen evolution reaction

The design and prediction of composition and structure is critical for the development of robust and efficient oxygen evolution reaction (OER) catalysts for water splitting. To enhance electrochemical catalytic activity of catalyst, a series of 3D microporous amorphous metallic phosphides, such as NiP, FeP, CoP, NiFeP, FeCoP, NiCoP and NiFeCoP, were electrodeposited on nickel mesh (dubbed NM) via hydrogen bubbles electroplating technique. The electrocatalytic performances of all as-prepared phosphides in alkaline solution for hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) were investigated. The optimal 3D microporous NiFeCoP/NM electrode exhibits remarkable catalytic activity for HER and delivers a current density of 10 mA cm−2 only required an extremely low overpotential (33 mV) and a small Tafel slope (71.1 mV dec−1) in 1.0 M KOH solution. Meanwhile the NiFeCoP/NM electrode also shows outstanding strong durability and robustness in alkaline water electrolysis. Further, the NiFeCoP/NM electrode displays superior catalytic activity towards OER. In a two-electrode water electrolytic cell, the bi-functional NiFeCoP/NM electrodes could obtain current densities of 10 and 50 mA cm−2 at overall cell potentials of only 1.64 and 1.82 V, respectively. The remarkable electrocatalytic activities of the NiFeCoP/NM electrode both for HER and OER are attributed to the synergistic effect of tri-metal elements in metallic phosphide, amorphous phase structure, and the superlarge electrochemical surface area fabricated by the hydrogen bubbles electroplating.

Ultrasensitive detection of hERG potassium channel in single-cell with photocleavable and entropy-driven reactions by using an electrochemical biosensor

Ion channel is a pore-forming membrane protein that allows ions to pass through the cell membrane, which is essential for the continuation of life. Analysis of ion channel characteristics at the single cell level will help to study the role of cellular heterogeneity in disease progression and cellular signaling processes. In this study, we fabricate a photocleavable and entropy-driven reaction based electrochemical biosensor for ultrasensitive detection of human ether-a-go-go related gene (hERG) potassium channel activity on HEK293 cell. We employed an antibody-DNA1 to conjugate the hERG channel in the cell membrane via antibody-antigen reaction. The release of the DNA1 by photocleavable reaction will trigger an amplification reaction by using the Exonuclease III (Exo III) to generate intermediate DNA. In addition, two hairpin DNA (DNA3 and DNA4) was employed for the signal amplification. We well designed a toehold on DNA3 for intermediate DNA hybridization to form double-strand DNA that opens the DNA3 hairpin. The free DNA3 exposed the relocked toehold domain to open the DNA4. After the entropy-driven toehold-mediated displacement amplification reaction by using intermediate DNA, DNA4 hybridized with DNA3 effectively, making the ferrocene labeled on the 5′-termini DNA4 close to the Au electrode surface to produce the electrochemical response. Then, the displaced intermediate DNA was released from the cell surface into solution for the next entropy-driven reaction. After two steps amplification reaction, one ion channel triggered thousands of DNA3/DNA4 duplex on the biosensor surface. By using this biosensor, electrochemical curve of hERG ion channels on a single cell was obtained.

Existence of weak solutions for the nonlocal energy-weighted fractional reaction–diffusion equations

For any bounded smooth domain $$\Omega \subset \mathbb {R}^n$$ , we establish the global existence of weak solutions $$u\in L^2(0,T;H^s_{\Omega ,0})$$ with $$u_t\in L^2(0,T;H^{-s}_{\Omega })$$ to the initial boundary value problem of the nonlocal energy-weighted fractional reaction–diffusion equations for any initial data $$u_0\in H^s_{\Omega ,0}$$ .

An efficient wavelet-based method for the numerical solutions of nonlinear coupled reaction–diffusion equations in biochemical engineering

The theoretical model of Saranya et al. (Bioprocess Biosyst Eng 41:281–294, 2017) glucose oxidation and hydrogen peroxide production in the Chitosan-alginate microsphere membrane is discussed. In this paper, an accurate and efficient Ultra-Spherical Wavelet Method (USWM) is successfully employed to investigate the numerical solutions for a set of nonlinear reaction–diffusion equations. The sensitivity analysis of various parameters on the concentrations of gluconic acid and hydrogen peroxide is also discussed. The numerical solutions are compared with Homotopy Perturbation Method and numerical simulation. Moreover, the use of USWM is found to be accurate, efficient, simple, flexible, and requires less computation costs.

Dynamic soil reactions around pile-fictitious soil pile coupled model and its application in parallel seismic method

The parallel seismic (PS) method is a nondestructive test technique for evaluating pile integrity, which has a wide range of applications for detection of reinforced concrete pile length and defects. In recent years, this method has been increasingly applied in practice; however, its theoretical model still requires further refinement. In this paper, a pile-fictitious soil pile coupled model considering three-dimensional effect of surrounding soil is established, and the analytical solution for the dynamic reaction of soil around and beneath the pile is solved. The developed solution is then employed to investigate the effects of pile-soil properties and technical aspects of PS method on the dynamic response of surrounding soil. The results are used to derive some conclusions in order to provide practical guidance for application of PS test in engineering practice.

Construction of exact solutions in implicit form for PDEs: New functional separable solutions of non-linear reaction–diffusion equations with variable coefficients

The paper deals with different classes of non-linear reaction–diffusion equations with variable coefficients c(x)ut=[a(x)f(u)ux]x+b(x)g(u),that admit exact solutions. The direct method for constructing functional separable solutions to these and more complex non-linear equations of mathematical physics is described. The method is based on the representation of solutions in implicit form ∫h(u)du=ξ(x)ω(t)+η(x),where the functions h(u), ξ(x), η(x), and ω(t) are determined further by analyzing the resulting functional-differential equations. Examples of specific reaction–diffusion type equations and their exact solutions are given. The main attention is paid to non-linear equations of a fairly general form, which contain several arbitrary functions dependent on the unknown u and /or the spatial variable x (it is important to note that exact solutions of non-linear PDEs, that contain arbitrary functions and therefore have significant generality, are of great practical interest for testing various numerical and approximate analytical methods for solving corresponding initial–boundary value problems). Many new generalized traveling-wave solutions and functional separable solutions are described.

Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation

In the present article, the advection–diffusion equation (ADE) having a nonlinear type source/sink term with initial and boundary conditions is solved using finite difference method (FDM). The solution of solute concentration is calculated numerically and also presented graphically for conservative and nonconservative cases. The emphasis is given for the stability analysis, which is an important aspect of the proposed mathematical model. The accuracy and efficiency of the proposed method are validated by comparing the results obtained with existing analytical solutions for a conservative system. The novelty of the article is to show the damping nature of the solution profile due to the presence of the nonlinear reaction term for different particular cases in less computational time by using the reliable and efficient finite difference method.

Dynamic Compressor Optimization in Natural Gas Pipeline Systems

The growing dependence of electric power systems on gas-fired generators to balance fluctuating and intermittent production by renewable energy sources has increased the variation and volume of flows withdrawn from natural gas transmission pipelines. Adapting pipeline operations to maintain efficiency and security under these dynamic conditions requires optimization methods that account for substantial intraday transients and can rapidly compute solutions in reaction to generator re-dispatch. Here, we present a computationally efficient method for minimizing gas compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flows. The optimization method uses a simplified representation of gas flow physics, provides a choice of discretization schemes in time and space, and exploits a two-stage approach to minimize energy costs and ensure smooth and physically meaningful solutions. The resulting large-scale NLPs are solved using an interior point method. The optimization scheme is validated by comparing the solutions with an integration of the dynamic equations using an adaptive timestepping differential equation solver, as well as a different, recently proposed optimal control scheme. The comparison shows that solutions to the discretized problem are feasible for the continuous problem and also practical from an operational standpoint. The results also indicate that our scheme produces at least an order of magnitude reduction in computation time relative to the state of the art and scales to large gas transmission networks with more than 6,000 kilometers of total pipeline. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0821 .

Epidemic spreading of random walkers in metapopulation model on an alternating graph

Much literature exists on temporal networks for epidemic spreading. We present a metapopulation dynamic model on a temporal network; a subpopulation (patch) is represented by a node on a graph, and a link represents a migration path between patches. We consider the alternating graph as a temporal network. It alternates between star and complete graphs, where the nodes do not change but links vary temporally and periodically. Mobile individuals move by random walk through a link between nodes. Each individual is either susceptible (S) or infected (I). The reaction–diffusion equations are presented as ordinary differential equations with time-dependent coefficients. To evaluate the infection risk of each patch (node), we obtain the solutions of reaction–diffusion equations numerically. The temporal behavior of infected individuals depends highly on the frequency of the alternating graph. At low frequency, infected densities exhibit an oscillating behavior, while they keep a constant value at high frequencies. The crossover occurs from the oscillating state to the frozen state with increasing frequency. The SIS epidemic threshold is derived for the alternating graph. The epidemic threshold is lower than that on the star graph and higher than that on the complete graph.

Existence of Peregrine type solutions in fractional reaction–diffusion equations

Fil: Besteiro, Agustin Tomas. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria. Instituto de Investigaciones Matematicas Luis A. Santalo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matematicas Luis A. Santalo; Argentina

On Error Control in the Numerical Solution of Reaction–Diffusion Equation

On Error Control in the Numerical Solution of Reaction–Diffusion Equation

Blow-up and global solutions for a class of time fractional nonlinear reaction–diffusion equation with weakly spatial source

This paper investigates the blow-up of solutions for a time fractional nonlinear reaction–diffusion equation with weakly spatial source. We first derive two sufficient conditions under which the solutions may blow up in finite time. Then, we prove the existence of global solution when the initial data are small enough. Moreover, the long time behavior of bounded solutions will be analyzed.