Inverse problem for the reaction diffusion system by optimization method

In this paper, we study an inverse problem of reconstructing two time independent coefficients in the reaction diffusion system from the final measurement. First the given problem is transformed into an optimization problem by using optimal control framework and the existence of the minimizer for the control functional is established. Then we prove the stability estimate for two coefficients with the upper bound given by some Sobolev norms of the final measurement.     

Structural and optical behavior of SnS2/NiFe2O4 NCs prepared via novel two-step synthesis approach for MB and RhB dye degradation under sun light irradiation

The present investigation focuses on facile two-step synthesis approach fabrication of tin sulfide (SnS₂)/ nickel ferrite (NiFe₂O₄) nanocomposites (NCs) for the first time. The crystallinity and phase purity of the prepared material was investigated in powder X-ray diffraction (PXRD) studies. The presence of functional groups (stretching and bending vibration) was primarily determined by the Fourier Transform Infrared Spectroscopy (FT-IR) analysis. As well as, optical behavior of the synthesized samples was determined in UV–Vis absorption spectroscopic studies, and the presence of surface defects was established by PL spectroscopic studies. From the FESEM analysis, sponge-like structure was attained and Ni, Fe, Sn, S and O elemental component was determined by the EDAX spectrum analysis. The as-prepared SnS₂/NiFe₂O₄ NCs exhibit superior photocatalytic performance and high stability toward the reduction of methylene blue (MB) and rhodamine B (RhB) dyes under irradiation of direct sunlight. The synthesized nanocomposites showed an efficient photocatalytic activity with a high reaction kinetic rate.

     

Effect of interfacial contact forces in radial contact wire strand

A new mathematical model has been developed to predict the behaviour of a stranded cable assembly under the influence of interfacial radial contact forces and radial contraction of the core. A single layered cable assembly with six helical wires and a straight cylindrical core, all made with the same material, Steel has been chosen to explain this phenomenon when the assembly is under the influence of core–wire radial contact. An attempt is made in this paper to model the strand with a radial (core–wire) contact and deduce its equations of equilibrium. Numerical analysis of strand force, twisting moment, strand stiffness, contact force and contact stresses is carriedout based on the equilibrium of thin rods, and the results are compared with the earlier research work. The importance of the inclusion of interfacial forces at the contact locations and their associated effects of axial and twist slip of the helical wires on the core, is highlighted. The behaviour of the stranded cable assembly due to the contact force in the radial direction and its associated effects on the axial strain of the core due to Poisson’s effect is one more additional feature incorporated in the present work.     

Stability and Hopf bifurcation of a diffusive predator–prey model with predator saturation and competition

This article discusses a predator–prey system with predator saturation and competition functional response. The local stability, existence of a Hopf bifurcation at the coexistence equilibrium and stability of bifurcating periodic solutions are obtained in the absence of diffusion. Further, we discuss the diffusion-driven instability, Hopf bifurcation for corresponding diffusion system with zero flux boundary condition and Turing instability region regarding the parameters are established. Finally, numerical simulations supporting the theoretical analysis are also included.     

Simultaneous Identification of Two Time Independent Coefficients in a Nonlinear Phase Field System

In this article, we study a simultaneous reconstruction of two time independent parameters in a nonlinear phase field system by final overdetermination data. To this end, the given problem is transformed into an optimization problem by using the optimal control framework; then the existence of the minimizer for the control functional is established. Further, we deduce the necessary condition for the minimizer of the control functional. Finally we derive the stability estimate for two coefficients with the upper bound given by some Sobolev norms of the final measurement of the solutions.     

Simultaneous identification of parameters and initial datum of reaction diffusion system by optimization method

In this paper, we study an inverse problem of reconstructing two time independent coefficients and the initial data in the linear reaction diffusion system from the arbitrary subdomain measurement and final measurement. First the given problem is transformed into an optimization problem by using optimal control framework and we establish the existence of the minimizer for the control functional. Further the necessary optimality condition is established which is the key ingredient to establish the stability estimate.     

In situ synthesis of cobalt nanocrystal hierarchies in a transmission electron microscope

We report a versatile electron beam (e-beam) synthesis method for the local fabrication of ferromagnetic nanocrystals “on demand”. A localized irradiation in a transmission electron microscope (TEM) is used to convert a raw cobalt fluoride material into ferromagnetic metal by means of formation of a short-range ordered distribution of well-defined faceted three-dimensional (3D) cobalt nanocrystals on the carbon substrate. A range of sizes and morphologies can be obtained, depending on the size, intensity, and acceleration voltage of the e-beam and on the initial size/thickness of the 3D raw fluoride materials, with 300 kV acceleration voltage and thermionic LaB₆ emission found most favorable. The nanofabrication of locally quasi-monodispersed, small sized, and well-distributed 3D nanocrystals opens up the possibility to generate particle arrays on demand with desirable magnetic properties.