Papers by Keyword: Reaction-Diffusion

Abstract: A reaction-diffusion framework (RDF) is used to synthesize and control the size and morphology of single crystals of metal-organic framework-199 (MOF-199). The framework consists of diffusing copper ions (Cu²⁺, outer electrolyte) into a hydrogel medium containing the organic linker, 1,3,5-benzenetricarboxylic acid (BTC, inner electrolyte). The resulting supersaturation gradient, and its nonlinear coupling with nucleation and growth kinetics, provides means to control the crystal size, distrubution and morphology along the diffusion flux. This method is rapid, efficient, scalable, and environmentally friendly. By using this method we demonstrate how assorted experimental parameters, such as temperature, concentrations, and nature of the gel matrix can be easily tuned to produce different particle size distributions and various morphologies.

Abstract: By the methods of Auger-spectroscopy and mass-spectrometry of secondary ions, small-angle electron diffraction, X-ray and resistometry analyses the solid-state reactions in the Ti(5 nm)/ Ni(24 nm)/Si₍₀₀₁₎ thin film system at annealing in running nitrogen in the temperature interval of 723 – 1273 К are investigated. Regularities of phase transformations, consistency of solid-state reactions, layer-by-layer redistribution of components during annealing, features of surface morphology during formation of inclusions of silicide phases are established.

Abstract: Dynamical behaviors of stochastic Hopfield neural network with delays and reaction-diffusion terms are investigated. By employing Lyapunov method, Poincare inequality and linear matrix inequality, some novel criteria on ultimate boundedness, weak attractor and asymptotic stability are obtained. The criteria are independent of the magnitude of the delays, and dependent on the diffusion effects and the derivative of the delays. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

Abstract: Dynamical behaviors of stochastic reaction-diffusion Hopfield neural networks with delays are investigated. By employing Lyapunov method, Hardy-Poincare inequality and linear matrix inequality, some novel criteria on ultimate boundedness and asymptotic stability are obtained. The sufficient criteria depend on the diffusion effects and are independent of the magnitude of the delays. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

Abstract: The mechanism of the intercalation/de-intercalation processes during the formation of α-Co (OH)₂ and its conversion to β-Co (OH)₂ is carefuly examined using a new non-invasive technique in a gel matrix. The incorporation of rhodamine molecules inside the interlayer gallery of α samples allows us to monitor the variation of its fluorescence intensity throughout different stages of the reactions. We show after calculating the corresponding activation energies that the formation/transformation reactions exhibit different dynamics depending on the nature of intercalated anions. Moreover, the morphological changes that are revealed from scanning electron micrographs suggest the occurence of an Ostawald ripening mechanism in which perfect and stable crystals are produced at the expense of smaller ones.

Abstract: In order to effectively improve the equipment maintenance material procurement management efficiency, improve economic efficiency of using the procurement funds, strengthen mathematical theory applications in the area of procurement, the neural network used in evaluation of organizational change is one of the most effective means. In this paper, a class of stochastic Cohen–Grossberg neural networks with reaction-diffusion terms, discrete time delay and distributed time delay is investigated. First, we describe the modeling, illuminate the significance of the system and introduce some preliminary definitions and lemmas which will be employed throughout the paper. Then, by using the Lyapunov functional method, M-matrix properties, nonnegative semimartingale convergence theorem and some inequality technique, sufficient conditions are obtained to guarantee the exponential stability of the system.

Abstract: To reduce the pseudo-Gibbs effects and the “curvelet like” aliased curves resulted from using curvelet transform for image denoising, we proposed a noise removal method which combines computational harmonic analysis and variation. Firstly, we presented a nonlinear reaction-diffusion digital filter based on Nordström energy functional. For effectively overcoming speckle noise due to the reaction-diffusion process of digital filtering and the ill-posed of diffusion coefficient, we gave an improved model by introducing curvelet smoothing operator and the new diffusion function. Numerical results show that the model is not only for images with Gaussian noise, Salt&pepper noise or Speckle noise, but also suitable for mixed noise, the denoised image has higher PSNR and good visual effect.

Abstract: We report a theoretical model to describe the spatiotemporal dynamics of a new system consisting of sul…de ions di¤using into an organic gel containing mercaptoethanol-capped cadmium ions. The product, cadmium sul…de, exhibits a faint yellow transparent propagating front starting at the gel-outer electrolyte interface. When subjected to UV light, this system reveals ‡uorescing CdS nuclei localized spatially in a narrow region (constant width), called pulse, that leads the front and propagates down the tube. The reported model is based on reaction-di¤usion equations coupled to dynamical competitive particle growth. The resulting evolution equations were solved numerically and the results are shown.

Abstract: In this paper, the iBone (Imitation Bone) model which is coupled with Turing reaction-diffusion system and FEM, is used. The numerical simulation of bone forming process by considering the osteoclasts and osteoblasts process are conducted. The results shown, that the bone mass is increased with increase of the initial load value, then fibula and femur bones are obtained respectively by keeping the required bone forming value. The different bone shapes are obtained by changing the both bone keeping value and the compressing force value. When set larger bone keeping value by keeping larger constant compressing force value, bone shape as a pipe with hole just like femur, when set smaller bone keeping value by keeping the smaller constant compressing force value, it is close to solid pillar as like fibula.

Abstract: The interfacial reactions between a solidified Fe shell and Ti were investigated within the framework of steel alloying. Ti cylinders were immersed into liquid Fe for various durations and subsequently water-quenched. An Fe shell solidifies around the Ti. At the interface between Fe and Ti a reaction zone is formed. Initially it consists of a liquid eutectic layer, though in later stages all stable phases at elevated temperature can be found in the quenched microstructure. The larger part of this reaction zone is fluid at high temperature and both Ti and Fe dissolve into it. Moreover, intermetallic compound formation and mixing of Fe and Ti generate extra heat, shortening the time required for shell melt-back. The reaction zone reaches thicknesses up to 40 % of the initial sample’s radius and when the shell has completely remolten, a discontinuity in the thickness-time profile is expected. The exact morphology of the reaction zone at high temperature remains to be determined: presence of a solid layer of Fe2Ti may impede mixing in the initial stages.