Lanthanide‐Doped Nanocrystals: Strategies for Improving the Efficiency of Upconversion Emission and Their Physical Understanding

The fundamental understanding of lanthanide‐doped upconverted nanocrystals remains a frontier area of research because of potential applications in photonics and biophotonics. Recent studies have revealed that upconversion luminescence dynamics depend on host crystal structure, size of the nanocrystals, dopant concentration, and core–shell structures, which influence site symmetry and the distribution and energy migration of the dopant ions. In this review, we bring to light the influences of doping/co‐doping concentration, crystal phase, crystal size of the host, and core–shell structure on the efficiency of upconversion emission. Furthermore, the lattice strain, due to a change in the crystal phase and by the core–shell structure, strongly influences the upconversion emission intensity. Analysis suggests that the local environment of the ion plays the most significant role in modification of radiative and nonradiative relaxation mechanisms of overall upconversion emission properties. Finally, an outlook on the prospects of this research field is given.     

Influence of Size and Shape on the Photocatalytic Properties of SnO2 Nanocrystals

Tuning the functional properties of nanocrystals is an important issue in nanoscience. Here, we are able to tune the photocatalytic properties of SnO₂ nanocrystals by controlling their size and shape. A structural analysis was carried out by using X‐ray diffraction (XRD)/Rietveld and transmission electron microscopy (TEM). The results reveal that the number of oxygen‐related defects varies upon changing the size and shape of the nanocrystals, which eventually influences their photocatalytic properties. Time‐resolved spectroscopic studies of the carrier relaxation dynamics of the SnO₂ nanocrystals further confirm that the electron–hole recombination process is controlled by oxygen/defect states, which can be tuned by changing the shape and size of the materials. The degradation of dyes (90 %) in the presence of SnO₂ nanoparticles under UV light is comparable to that (88 %) in the presence of standard TiO₂ Degussa P‐25 (P25) powders. The photocatalytic activity of the nanoparticles is significantly higher than those of nanorods and nanospheres because the effective charge separation in the SnO₂ nanoparticles is controlled by defect states leading to enhanced photocatalytic properties. The size‐ and shape‐dependent photocatalytic properties of SnO₂ nanocrystals make these materials interesting candidates for photocatalytic applications.     

Dynamic polarizability of two‐electron ions under Debye screening

The effect of plasma screening on the dynamic dipole polarizability (DPP) of two‐electron ions Be²⁺, B³⁺, and C⁴⁺ has been investigated using highly correlated exponential wave functions within the framework of pseudostate summation technique and Debye screening concept. Plasma‐screening effect on the oscillator strengths (OS) of the ultraviolet and visible series has also been investigated for the systems Li⁺, Be²⁺, B³⁺, C⁴⁺. The DPP are reported as functions of screening parameters. The OS for S‐P transitions are also reported for various screening parameters. The OS and dynamic polarizability show interesting behavior with increasing screening strength and nuclear charge. © 2015 Wiley Periodicals, Inc.     

On the detection of single bond ruptures in dynamic force spectroscopy by AFM

Force spectroscopy is a novel tool in physical chemistry and biophysics. This methodology is aimed at providing kinetic parameters of dissociation at a single-molecule level by rupturing molecular bonds subjected to different loading rates. One persistent problem in the implementation of this methodology is a question about the single-bond nature of the rupture events detected in experiments based on atomic force microscopy. Here we address this question by considering the probability that the nearly simultaneous rupture of two molecular bonds might appear as a single bond rupture in the experimental data, complicating the data analysis and contributing to systematic errors in the extracted kinetic parameters. An approximate analytical model predicts that such events might be common in experiments employing soft cantilever force sensors and short tethers to immobilize the interacting molecules. These findings are confirmed by a more elaborate numerical model providing valuable guidelines on performing single-molecule force spectroscopy experiments.     

Photoactive Ru(II) -polypyridyl complexes that display sequence selectivity and high-affinity binding to duplex DNA through groove binding

The duplex-DNA binding properties of a nonintercalating polypyridyl ruthenium(II) complex that incorporates a linear extended ligand with a catechol moiety has been probed with a variety of photo- and biophysical techniques. These studies reveal that the complex groove binds to DNA sequences biphasically, and displays binding constants equivalent to those of high-affinity metallointercalators. The complex also displays preferential binding to AT-rich sequences. Changes in the structure of the coordinated catechol ligand and the incorporation of intercalating ancillary ligands into the complex were found to modulate both the optical-binding response and binding parameters of the system, which indicates that the catechol moiety plays a crucial role in the observed enhancement to binding affinities.     

Optimal control of harvest and bifurcation of a prey-predator model with stage structure

This paper describes a prey-predator model with stage structure for prey. The adult prey and predator populations are harvested in the proposed system. The dynamic behavior of the model system is discussed. It is observed that singularity induced bifurcation phenomenon is appeared when variation of the economic interest of harvesting is taken into account. State feedback controller is incorporated to stabilize the model system in case of positive economic interest. Harvesting of prey and predator population are used as controls to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent earned from the resource. The Pontryagin’s maximum principle is used to characterize the optimal controls. The optimality system is derived and then solved numerically using an iterative method with Runge-Kutta fourth order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem.     

Observer-based synchronization scheme for a class of chaotic systems using contraction theory

In this paper, an adaptive synchronization scheme is proposed for a class of nonlinear systems. The design utilizes an adaptive observer, which is quite useful in establishing a transmitter–receiver kind of synchronization scheme. The proposed approach is based on contraction theory and provides a very simple way of establishing exponential convergence of observer states to actual system states. The class of systems addressed here has uncertain parameters, associated with the part of system dynamics that is a function of measurable output only. The explicit conditions for the stability of the observer are derived in terms of gain selection of the observer. Initially, the case without uncertainty is considered and then the results are extended to the case with uncertainty in parameters of the system. An application of the proposed approach is presented to synchronize the family of N chaotic systems which are coupled through the output variable only. The numerical results are presented for designing an adaptive observer for the chaotic Chua system to verify the efficacy of the proposed approach. Explicit bounds on observer gains are derived by exploiting the properties of the chaotic attractor exhibited by Chua’s system. Convergence of uncertain parameters is also analyzed for this case and numerical simulations depict the convergence of parameter estimates to their true value.     

A bioeconomic model of a ratio-dependent predator-prey system and optimal harvesting

This paper deals with the problem of a ratio-dependent prey-predator model with combined harvesting. The existence of steady states and their stability are studied using eigenvalue analysis. Boundedness of the exploited system is examined. We derive conditions for persistence and global stability of the system. The possibility of existence of bionomic equilibria has been considered. The problem of optimal harvest policy is then solved by using Pontryagin’s maximal principle.     

Inventory of differential items selling at two shops under single management

Inventory of differential (both good and defective) items purchased in a lot for two shops under a single management is considered here. In the primary shop, the lot is received and separated, only good units are sold and shortages are allowed which are backlogged from the good units specially purchased at the beginning of the next cycle. The separated defective units are continuously trasnsferred and sold at a reduced price from the secondary shop. This inventory model is formulated and illustrated numerically for three scenarios depending upon the time periods of the shops.