Strong phase separation in a model of sedimenting lattices

We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a one-dimensional lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels- hence the term strong phase separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.     

Quantum dot capped magnetite nanorings as high performance nanoprobe for multiphoton fluorescence and magnetic resonance imaging

In the present study, quantum dot (QD) capped magnetite nanorings (NRs) with a high luminescence and magnetic vortex core have been successfully developed as a new class of magnetic-fluorescent nanoprobe. Through electrostatic interaction, cationic polyethylenimine (PEI) capped QD have been firmly graft into negatively charged magnetite NRs modified with citric acid on the surface. The obtained biocompatible multicolor QD capped magnetite NRs exhibit a much stronger magnetic resonance (MR) T2* effect where the r2* relaxivity and r2*/r1 ratio are 4 times and 110 times respectively larger than those of a commercial superparamagnetic iron oxide. The multiphoton fluorescence imaging and cell uptake of QD capped magnetite NRs are also demonstrated using MGH bladder cancer cells. In particular, these QD capped magnetite NRs can escape from endosomes and be released into the cytoplasm. The obtained results from these exploratory experiments suggest that the cell-penetrating QD capped magnetite NRs could be an excellent dual-modality nanoprobe for intracellular imaging and therapeutic applications. This work has shown great potential of the magnetic vortex core based multifunctional nanoparticle as a high performance nanoprobe for biomedical applications.     

Zero-Sum Differential Games Involving Hybrid Controls

We study a zero-sum differential game with hybrid controls in which both players are allowed to use continuous as well as discrete controls. Discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, an autonomous jump set A or a controlled jump set C, where one controller can choose to jump or not. At each jump, the trajectory can move to a different Euclidean space. One player uses all the three types of controls, namely, continuous controls, autonomous jumps, and controlled jumps; the other player uses continuous controls and autonomous jumps. We prove the continuity of the associated lower and upper value functions V⁻ and V⁺. Using the dynamic programming principle satisfied by V⁻ and V⁺, we derive lower and upper quasivariational inequalities satisfied in the viscosity sense. We characterize the lower and upper value functions as the unique viscosity solutions of the corresponding quasivariational inequalities. Lastly, we state an Isaacs like condition for the game to have a value This work was partially supported by Grants DRDO 508 and ISRO 050 to the Non-linear Studies Group, Indian Institute of Science. The first author is a University Grant Commission Research Fellow and the financial support is gratefully acknowledged. The authors thank Prof. M.K. Ghosh, Department of Mathematics, Indian Institute of Science, for introducing the problem and thank the referee for useful suggestions.     

Dynamical signatures of ‘phase transitions’: Chaos in finite clusters

Finite clusters of atoms or molecules, typically composed of about 50 particles (and often as few as 13 or even less) have proved to be useful prototypes of systems undergoing phase transitions. Analogues of the solid-liquid melting transition, surface melting, structural phase transitions and the glass transition have been observed in cluster systems. The methods of nonlinear dynamics can be applied to systems of this size, and these have helped elucidate the nature of the microscopic dynamics, which, as a function of internal energy (or ‘temperature’) can be in a solidlike, liquidlike, or even gaseous state. The Lyapunov exponents show a characteristic behaviour as a function of energy, and provide a reliable signature of the solid-liquid melting phase transition. The behaviour of such indices at other phase transitions has only partially been explored. These and related applications are reviewed in the present article.     

18‐Crown‐6 Catalyzed Microwave‐mediated Synthesis of Symmetric Bis‐Heterocyclic Compounds under Solvent‐free Condition

An efficient, solvent‐free and 18‐crown‐6 catalyzed method for the synthesis of N‐alkyl‐4‐(4‐(5‐(2‐(alkyl‐amino)thiazol‐4‐yl)pyridin‐3‐yl)phenyl)thiazol‐2‐amine, N‐alkyl‐4‐(5‐(2‐alkyamino)thiazol‐4‐yl)pyridine‐3‐yl)thiazol‐2‐amine, and 4,4′‐bis‐{2‐[amino]‐4‐thiazolyl}biphenyl bis‐heterocyclic derivatives via microwave accelerated cyclization is presented.     

Screening the optical properties of Ag-Au alloy gradients formed by bipolar electrodeposition using surface enhanced Raman spectroscopy

We report the synthesis of Ag-Au alloy gradients on stainless steel substrates using bipolar electrodeposition (BP-ED), a technique based on the existence of a potential gradient at the interface of a bipolar electrode (BPE) and an electrolytic solution. The interfacial potential gradient causes the rates of electrodeposition of Ag and Au to vary along the length of the BPE, leading to the electrodeposition of a chemical concentration gradient. The surface morphology of the electrodeposits was characterized using scanning electron microscopy (SEM), and their chemical composition was determined using energy dispersive X-ray spectroscopy (EDX). Self-assembled monolayers of a Raman-active probe molecule (benzene thiol) were allowed to form on the surface of the alloy gradients, and confocal Raman microscopy was employed to determine the alloy composition that resulted in the maximum surface enhanced Raman scattering (SERS) intensity. An alloy composition of ca. 70% Ag/30% Au was found to be optimum for SERS excited using 514.5 nm radiation, and it is explained on the basis of composition-dependent changes in the local surface plasmon resonance (LSPR) of the electrodeposited Ag-Au alloy.