Localized coherent structures of (2+1) dimensional generalizations of soliton systems

We briefly review the recent progress in obtaining (2+1) dimensional integrable generalizations of soliton equations in (1+1) dimensions. Then, we develop an algorithmic procedure to obtain interesting classes of solutions to these systems. In particular using a Painlevé singularity structure analysis approach, we investigate their integrability properties and obtain their appropriate Hirota bilinearized forms. We identify line solitons and from which we introduce the concept of ghost solitons, which are patently boundary effects characteristic of these (2+1) dimensional integrable systems. Generalizing these solutions, we obtain exponentially localized solutions, namely the dromions which are driven by the boundaries. We also point out the interesting possibility that while the physical field itself may not be localized, either the potential or composite fields may get localized. Finally, the possibility of generating an even wider class of localized solutions is hinted by using curved solitons.     

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.     

Comparing stimulus-frequency otoacoustic emissions measured by compression, suppression, and spectral smoothing

Stimulus-frequency otoacoustic emissions (SFOAEs) have been measured in several different ways, including (1) nonlinear compression, (2) two-tone suppression, and (3) spectral smoothing. Each of the three methods exploits a different cochlear phenomenon or signal-processing technique to extract the emission. The compression method makes use of the compressive growth of emission amplitude relative to the linear growth of the stimulus. The emission is defined as the complex difference between ear-canal pressure measured at one intensity and the rescaled pressure measured at a higher intensity for which the emission is presumed negligible. The suppression method defines the SFOAE as the complex difference between the ear-canal pressure measured with and without a suppressor tone at a nearby frequency. The suppressor tone is presumed to substantially reduce or eliminate the emission. The spectral smoothing method involves convolving the complex ear-canal pressure spectrum with a smoothing function. The analysis exploits the differing latencies of stimulus and emission and is equivalent to windowing in the corresponding latency domain. Although the three methods are generally assumed to yield identical emissions, no equivalence has ever been established. This paper compares human SFOAEs measured with the three methods using procedures that control for temporal drifts, contamination of the calibration by evoked emissions, and other potential confounds. At low stimulus intensities, SFOAEs measured using all three methods are nearly identical. At higher intensities, limitations of the procedures contribute to small differences, although the general spectral shape and phase of the three SFOAEs remain similar. The near equivalence of SFOAEs measured by compression, suppression, and spectral smoothing indicates that SFOAE characteristics are not mere artifacts of measurement methodology.     

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.     

Solution-based direct readout surface enhanced Raman spectroscopic (SERS) detection of ultra-low levels of thiram with dogbone shaped gold nanoparticles

We report the use of two different sizes of dogbone shaped gold nanoparticles as colloidal substrates for surface enhanced Raman spectroscopy (SERS) based detection of ultra-low levels of thiram, a dithiocarbamate fungicide. We demonstrate the ability to use a solution based, direct readout SERS method as a quantitative tool for the detection of ultra-low levels of thiram. The two different sizes of dogbone shaped gold nanoparticles are synthesized by using the seed-mediated growth method and characterized by using UV-visible spectroscopy and transmission electron microscopy (TEM). The smaller dogbone shaped nanoparticles have an average size of 43 ± 13 nm. The larger dogbone shaped gold nanoparticles have an average size of 65 ± 15 nm. The nanoparticle concentration is 1.25 × 10(11) nanoparticles per mL for the smaller dogbone shaped gold nanoparticles and is 1.13 × 10(11) nanoparticles per mL for the larger dogbone shaped gold nanoparticles. Different concentrations of thiram are allowed to bind to the two different sizes of dogbone shaped gold nanoparticles and the SERS spectra are obtained. From the calibration curve, the limit of detection for thiram is 43.9 ± 6.2 nM when the smaller dogbone shaped gold nanoparticles are used as colloidal SERS substrates In the case of the larger dogbone shaped gold nanoparticles, the limit of detection for thiram is 11.8 ± 3.2 nM. The lower limit of detection obtained by using the larger dogbone shaped gold nanoparticles as colloidal substrates is due to the lightning rod effect, higher contributions from the electromagnetic enhancement effect, and larger number of surface sites for thiram to bind.     

Synthesis,characterization, and evaluation of antimicrobial activities of a new class of macrocyclic phosphonates

A series of a new class of phosphorus analogue macrocycles was accomplished by condensation of N‐substituted‐[bis(3,5‐dimethyl‐2‐hydroxybenzyl)]‐amines with various phosphorus dichlorides in dry toluene in the presence of triethylamine at 0–50°C. All the title compounds were evaluated for antimicrobial activity to determine their efficacy and were effective in suppressing the growth of bacteria and fungi. The chemical structures of the title products were characterized by IR, ¹H, ¹³C, ³¹P‐NMR, mass spectral studies, and elemental analysis. J. Heterocyclic Chem., (2011).     

Symmetry breaking in quantum chaotic systems

We show, using semiclassical methods, that as a symmetry is broken, the transition between universality classes for the spectral correlations of quantum chaotic systems is governed by the same parametrization as in the theory of random matrices. The theory is quantitatively verified for the kicked rotor quantum map. We also provide an explicit substantiation of the random matrix hypothesis, namely that in the symmetry-adapted basis the symmetry-violating operator is random.