The architecture of hydrogel composites results in not only synergistic property enhancement but also superior functionality. The reaction–diffusion (RD) process is acommon phenomenon throughout nature which induced ordered structure on a lengt...
In this paper we propose and compare two methods to optimize the numerical computations for the diffusion term in a nonlocal formulation for a reaction-diffusion equation. The diffusion term is particularly computationally intensive due to the integr...
Rare-earth permanent magnets, such as Nd2Fe14B, have been widely used in electric vehicle and wind turbine motors due to their high anisotropy field (Ha), saturation magnetization (Ms) and coercivity (Hc). Cerium (Ce) has gained attention as a potent...
General Purpose (use of) Graphics Processing Units (GPGPU) is a promising technology for simulation upscaling; in particular for bottom–up modelling approaches seeking to translate micro-scale system processes to macro-scale properties. Many existing...
A qualitative study for a second-order boundary value problem with local or nonlocal diffusion and a cubic nonlinear reaction term, endowed with in-homogeneous Cauchy–Neumann (Robin) boundary conditions, is addressed in the present paper. Provi...
In this article, we analyze a category of time-fractional variable-order reaction-diffusion equations coupled in the Caputo sense that are created with the modeling of complicated biological and chemical processes. Furthermore, it is shown that the s...
Water-based perovskite solar cells (W-PSCs) provide a promising route toward reducing the use of hazardous organic solvents during perovskite fabrication. However, their development remains limited by sluggish precursor conversion, incomplete phase t...
The exact time–space correlation function of the
Metal atoms or ions originating from interconnects, electrodes, or diffusion-barrier layers can migrate into oxide dielectrics during thermal annealing, causing insulation degradation, leakage-path formation, capacitance variation, and interfacial re...
Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of diff...
This manuscript addresses a new multivariate generalized predictive control strategy using the least squares support vector machine for parabolic distributed parameter systems. First, a set of proper orthogonal decomposition-based spatial basis funct...
The majority of literature sources dedicated to dissimilar Al-Cu friction stir welding testifies to the formation of intermetallic compounds (IMC) according to diffusion-controlled reactions, i.e., without liquation on the Al/Cu interfaces. Fewer sou...
Objective: Schizophrenia is a complex functionally debilitating neurodevelopmental disorder, with associated social cognitive impairment. Corpus Callosum (CC) white matter tracts deficits are reported for people with schizophrenia; however, few studi...
Since the time of Buckingham in 1914, dimensional analysis and similarity arguments based on dimensionless groups have served as powerful tools for the analysis of systems in all branches of science and engineering. Dimensionless groups are generally...
A standard reaction–diffusion equation consists of two additive terms, a diffusion term and a reaction rate term. The latter term is obtained directly from a reaction rate equation which is itself derived from known reaction kinetics, together with m...
DNA nanotechnology offers a fine control over biochemistry by programming chemical reactions in DNA templates. Coupled to microfluidics, it has enabled DNA-based reaction-diffusion microsystems with advanced spatio-temporal dynamics such as traveling...
The mathematical model of diffusion in powder oxide catalysts during the process of temperature programmed oxygen isotopic exchange is proposed. The diffusion is considered together with the homogeneous and heterogeneous oxygen isotopic exchange proc...
In this paper, we study a fractional Brusselator reaction–diffusion model with the help of the residual power series transform method. Specific reaction–diffusion chemical processes are modeled by applying the fractional Brusselator react...
The study considers a nonlinear multi-parameter reaction–diffusion system of two Lotka–Volterra-type equations with several delays. It treats both cases of different diffusion coefficients and identical diffusion coefficients. The study d...
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 i...
This study presents two novel methods for in situ characterization of the reaction-diffusion process during the co-curing of a polyetherimide thermoplastic interlayer with an epoxy-amine thermoset. The first method was based on hot stage experiments...
This study uses a combination of conventional and high resolution field and laboratory methods to investigate processes causing attenuation of a hexavalent chromium (Cr(VI)) plume in sedimentary bedrock at a former industrial facility. Groundwater pl...
In this paper, we study the local stability of an incommensurate fractional reaction–diffusion glycolysis model. The glycolysis process, fundamental to cellular metabolism, exhibits complex dynamical behaviors when formulated as a nonlinear rea...
The paper deals with a system of two nonlinear second-order parabolic equations. Similar systems, also known as reaction-diffusion systems, describe different chemical processes. In particular, two unknown functions can represent concentrations of ef...
In this work, we present a novel strategy for the numerical solution of a coupled system of partial differential equations that describe reaction–diffusion processes of a mixture of metals and ligands that can be absorbed by a sensor or a micro...
In this work, we consider extended irreversible thermodynamics in assuming that the entropy density is a function of both common thermodynamic variables and their higher-order time derivatives. An expression for entropy production, and the linear phe...
This article is focused on investigating the mathematical model calibration of a reaction–diffusion system arising in the mathematical model of the spread of an epidemic in a society. We consider that the total population is divided into two classes...
This work fabricated a double hollow structural component of Mg-8.3Gd-2.9Y-0.8Zn-0.2Zr alloy by superplastic forming (SPF) and reaction-diffusion bonding (RDB). The superplastic characteristic and mechanical properties of Mg-8.3Gd-2.9Y-0.8Zn-0.2Zr al...
Discrete fractional models with reaction-diffusion have gained significance in the scientific field in recent years, not only due to the need for numerical simulation but also due to the stated biological processes. In this paper, we investigate the...
This paper uses the attached flow method for solving nonlinear second-order differential equations of the reaction–diffusion type. The key steps of the method consist of the following: (i) reducing the differentiability order by defining the fi...
Two main topics are addressed in the present paper, first, a rigorous qualitative study of a second-order reaction–diffusion problem with non-linear diffusion and cubic-type reactions, as well as inhomogeneous dynamic boundary conditions. Under...
Tungsten leaching kinetics were investigated for three concentrates of Spanish origin containing wolframite, scheelite and mixed mineral phases under their respective optimum processing conditions. Experimental conversion data were analysed using cla...
The interplay of diffusion with phenomena like stochastic adsorption–desorption, absorption, and reaction–diffusion is essential for life and manifests in diverse natural contexts. Many factors must be considered, including geometry, dime...
This review describes the subjective experience of visual aura in migraine, outlines theoretical models of this phenomenon, and explores how these may be linked to neurochemical, electrophysiological, and psychophysical differences in sensory process...
Reaction–diffusion equations provide a fundamental framework for modelling spatial population dynamics and invasion processes in mathematical biology. Among these, Fisher’s equation combines diffusion with logistic growth to describe the...
The formulation of mathematical models using differential equations has become crucial in predicting the evolution of viral diseases in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (...
Approximate analytical solutions to doubly degenerate reaction-diffusion models pertinent to population dynamics and chemical kinetics have been developed. The double integral-balance method applied to preliminary transformed models and by a direct i...
We review a coherent mesoscopic presentation of thermodynamics and fluctuations far from and near equilibrium, applicable to chemical reactions, energy transfer and transport processes, and electrochemical systems. Both uniform and spatially dependen...
The debate about what causes the generation of form and structure in embryological development goes back to antiquity. Most recently, it has focused on the divergent views as to whether the generation of patterns and form in development is a largely...
This paper is devoted to the study of the chemotaxis model for drug delivery purposes. The pattern formation for a volume-filling with nonlinear diffusive terms is investigated. The proposed mathematical model is governed by a reaction–diffusion syst...
A stochastic reaction–diffusion model was developed to describe the binding of labeled monoclonal antibodies (mAbs) to CD4 receptors on the surface of T cells. The mAbs diffused to, adsorbed on, and underwent monovalent and bivalent binding to...
Non-enzymatic electrochemical glucose sensors are of great importance in biomedical applications, for the realization of portable diabetic testing kits and continuous glucose monitoring systems. Nanostructured materials show a number of advantages in...
The review is devoted to an analysis of mathematical models used for describing epidemic processes. Our main focus is on the models that are based on partial differential equations (PDEs), especially those that were developed and used for the COVID-1...
We studied the properties of a reaction front that forms in irreversible reaction–diffusion systems with concentration-dependent diffusivities during the synthesis of polymer brushes. A coarse-grained model of the polymerization process during the fo...
In this study, the nonlinear and non-monotonic behavior of amperometric bienzyme biosensors employing an enzymatic trigger reaction is investigated analytically and computationally using a two-compartment model comprising an enzymatic layer and an ou...
In this study, we developed a novel water quality model that integrated hydrodynamic, solute transport, and geochemical reactions processes. This model was built upon the open-source ELCIRC hydrodynamic model, the TVD-format solute transport model, a...
We propose a reaction–diffusion phase-field model to simulate the microstructure evolution of voids in systems with low vacancy concentration under irradiation. In this model, void growth and shrinkage are governed by reactions between vacancie...
This paper studies the spatial joint evolution of cooperative behavior and a partially assortative matching institution that protects cooperators. We consider cooperation as characterized by a cultural trait transmitted via an endogenous socializatio...
Holographic photopolymers are a new technology to create passive diffractive optical elements by a pure laser interference recording. In this review, we explain the chemistry concepts of light harvesting in an interference pattern and the subsequent...
Percolation, in its most general interpretation, refers to the “flow” of something (a physical agent, data or information) in a network, possibly accompanied by some nonlinear dynamical processes on the network nodes (sometimes denoted re...
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