Constrained Controllability of Fractional Dynamical Systems

The article deals with the controllability results for fractional dynamical systems with prescribed controls represented by the fractional integrodifferential equation in finite dimensional spaces. Sufficient conditions for the controllability results of nonlinear fractional dynamical systems are obtained using the contraction mapping principle. Examples are included to illustrate the theory.     

Grazing bifurcations in an elastic structure excited by harmonic impactor motions

In this article, non-smooth dynamics of an elastic structure excited by a harmonic impactor motion is studied through a combination of experimental, numerical, and analytical efforts. The test apparatus consists of a stainless steel cantilever structure with a tip mass that is impacted by a shaker. Soft impact between the impactor and the structure is considered, and bifurcations with respect to quasi-static variation of the shaker excitation frequency are examined. In the experiments, qualitative changes that can be associated with grazing and corner-collision bifurcations are observed. Aperiodic motions are also observed in the vicinity of the non-smooth bifurcation points. Assuming the system response to be dominated by the structure’s fundamental mode, a non-autonomous, single degree-of-freedom model is developed and used for local analysis and numerical simulations. The predicted grazing and corner-collision bifurcations are in agreement with the experimental results. To study the local bifurcation behavior at the corner-collision point and explore the mechanism responsible for the aperiodic motions, a derivation is carried out to construct local Poincaré maps of periodic orbits at a corner-collision point such as the one observed in the soft-impact oscillator.     

Fast proton conduction path in {\text{Ni}} - {\text{BaCe}}_{{0.8}} {\text{Y}}_{{0.2}} {\text{O}}_{{2.9 - \delta }} membrane

The effect of metal-to-oxide grain boundary layer in $ {\text{Ni}} - {\text{BaCe}}_{{0.8}} {\text{Y}}_{{0.2}} {\text{O}}_{{3 - \delta }} $ (BCY) cermet membrane on hydrogen permeation was studied by applying the different size of oxide grain on Ni-BCY membranes. Two types of cermet membranes having different grain size of oxide were prepared by using different starting particle size of oxide powder. The hydrogen flux of coarse-oxide-grain membrane showed higher flux than that of small-oxide-grain membrane. It was understood that the negative potential at metal-to-oxide grain boundary, reference to the bulk oxide ( $ \phi _{0} < \phi _{\infty } = 0 $ ), was developed, and the accumulation of the effectively positively charged protons may occur at the grain boundary layer (space charge layer), which may result in providing highly conductive proton path by shifting the charge neutrality condition from $ {\left[ {OH^{ \bullet }_{O} } \right]} = {\left[ {Y^{/}_{{Ce}} } \right]} $ to $ {\left[ {OH^{ \bullet }_{O} } \right]} = n $ .     

Synthesis of iron oxide nanoparticles using chitosan and starch templates

Natural polymers like chitosan and starch have been employed as templates for the preparation of iron oxide nanoparticles. The templates offer selective binding sites for Fe(II) under aqueous conditions. Controlled drying and subsequent removal of the template backbone enables the synthesis of spatially separated iron oxide nanoparticles. The crystalline character of the iron oxide and near narrow particle size distribution pattern have been confirmed through powder XRD, Photon Correlation Spectroscopy, and TEM measurements. The crystallite sizes of the particles were found to be 26–35 nm irrespective of the nature of the template.     

Stability and Hopf bifurcation of a diffusive predator‐prey model with hyperbolic mortality

The dynamics of a reaction‐diffusion predator‐prey model with hyperbolic mortality and Holling type II response effect is considered. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. We also study the spatially homogeneous and nonhomogeneous periodic solutions through all parameters of the system which are spatially homogeneous. To verify our theoretical results, some numerical simulations are also presented. © 2015 Wiley Periodicals, Inc. Complexity 21: 34–43, 2016     

Factors influencing activity of enzymes and their kinetics

The conventional chemically based method of dehairing and fiber-opening discharges an enormous amount of pollutants in the processing of skins. Hence, bioprocessing of skin through a two-step process, dehairing using protease and fiber opening using α-amylase, has been developed. However, because this process involves two steps, we characterized commercial protease and α-amylase for their optimum activity and determine the influence of one enzyme on the activity of the other, in order to develop an integrated enzymatic dehairing and fiber-opening process. The influence of various factors, substrate concentration, time, pH, and temperature, on the activity of both protease and α-amylase was determined. Furthermore, the activity of protease on mixing with α-amylase and vice versa was investigated. It was found that there was no significant change in the activity of one enzyme in the presence of the other. Lineweaver-Burk plots showed K _m and V _max values of 31.6 mg/mL and 0.0106 mg/(mL@min) for protease and 8.79 mg/mL and 0.0912 mg/(mL@min) for α-amylase. This study provides substantial evidence for integrating the enzyme-based dehairing and fiber-opening processes using both the selected protease and α-amylase in one step.     

Existence of solutions of neutral functional integrodifferential equation in Banach spaces

In this paper we prove the existence of mild solutions for neutral functional integrodifferential equation in a Banach space. The results are obtained by using the Schaefer fixed-point theorem.     

Controllability of Neutral Evolution Integrodifferential Systems with State Dependent Delay

In this paper, we address the problem of controllability of neutral evolution integrodifferential systems with state dependent delay in a Banach space. The results are obtained by using the theory of resolvent operators.