Colliding gravitational plane waves and Black Hole creation

A brief review of the work done in collaboration with Irina Aref’eva and Igor Volovich in the nineties and published in Nucl. Phys. B [1] with the above title is presented on honor of the Sixty Fifth birthday of Academician Igor Volovich.     

Detection of carcinoembryonic antigen using functional magnetic and fluorescent nanoparticles in magnetic separators

We combined a sandwich immunoassay, anti-CEA/CEA/anti-CEA, with functional magnetic (~80 nm) and fluorescent (~180 nm) nanoparticles in magnetic separators to demonstrate a detection method for carcinoembryonic antigen (CEA). Determination of CEA in serum can be used in clinical diagnosis and monitoring of tumor-related diseases. The CEA concentrations in samples were deduced and determined based on the reference plot using the measured fluorescent intensity of sandwich nanoparticles from the sample. The linear range of CEA detection was from 18 ng/mL to 1.8 pg/mL. The detection limit of CEA was 1.8 pg/mL. In comparison with most other detection methods, this method had advantages of lower detection limit and wider linear range. The recovery was higher than 94%. The CEA concentrations of two serum samples were determined to be 9.0 and 55 ng/mL, which differed by 6.7% (9.6 ng/mL) and 9.1% (50 ng/mL) from the measurements of enzyme-linked immunosorbent assay (ELISA), respectively. The analysis time can be reduced to one third of ELISA. This method has good potential for other biomarker detections and biochemical applications.     

Second order elastic anomalies in barium titanate from cubic to tetragonal phase transition

The anomalies of the second order elastic constants have been derived for barium titanate for the phase transition from cubic to tetragonal. The equilibrium values of the components of the order parameter and the strain variables have been obtained from the stability conditions. The fluctuations in the order parameter have been derived from the Landau-Khalatnikov equations. Expression for the shift in the zero point energy in the tetragonal phase is obtained and is shown to be proportional to (T −T _c)². The anomalies for all the second order elastic constants have been derived and relations among them reported. It is shown that the second order elastic anomalies suffer a discontinuity at the transition temperature.     

Silicon surface modification with trialkoxysilyl‐functionalized star‐shaped polymers

The synthesis of trimethoxysilane end‐capped linear polystyrene (PS) and star‐branched PS and subsequent silicon (Si) surface modification with linear and star polymers are described. Trimethoxysilane terminated PS was synthesized using sec‐butyl lithium initiated anionic polymerization of styrene and subsequent end‐capping of the living anions with p‐chloromethylphenyl trimethoxysilane (CMPTMS). ¹H and ²⁹Si NMR spectroscopy confirmed the successful end‐capping of polystyryllithium with the trimethoxysilane functional group. The effect of a molar excess of end‐capper on the efficiency of functionalization was also investigated, and the required excess increased for higher molar mass oligomers. Acid catalyzed hydrolysis and condensation of the trimethoxysilane end‐groups resulted in star‐branched PS, and NMR spectroscopy and SEC analysis were used to characterize the star polymers. This is the first report of core‐functionalized star‐shaped polymers as surface modifiers and the first comparative study showing differences in surface topography between star and linear polymer modified surfaces. Surface‐sensitive techniques such as ellipsometry, contact angle goniometry, and AFM were used to confirm the attachment of star PS, as well as to compare the characteristics of the star and linear PS modified Si surfaces. The polymer film properties were referenced to polymer dimensions in dilute solution, which revealed that linear PS chains were in the intermediate brush regime and the star‐branched PS produced a surface with covalently attached chains in the mushroom regime. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3655–3666, 2005     

Two-loop calculation of the effective potential for the Wess-Zumino model

The effective potential for the supersymmetric Wess-Zumino model is computed off-shell to two loops. A renormalization procedure which preserves positivity of the kinetic terms in the effective action is implemented. Supersymmetry is not broken to this order.     

Novel ring enlargement of 1-aminopyrrolidines

1-Aminopyrrolidines undergo oxidative ring enlargement to 1,4,5,6-tetrahydropyridazines on treatment with silica gel in chloroform-methanol.     

Solitons in a linear lattice with defects

Solitons are generated in an anharmonic linear lattice in which neighbouring atoms interact through a Morse potential by giving either a strong initial impulse or a large displacement to an end atom. Studies on the variation of the characteristic properties of the soliton with the strength of the initial pulse show that the velocity and the amplitude of the soliton increase with the strength of the initial impulse, but below a certain critical value for the initial impulse, only an oscillatory tail is generated. It is shown that when a defect is present in the lattice, a localised mode appears at the site of the defect and additional solitons travelling forward or even backwards, are generated. When two solitons collide at a defect region, they reemerge but leave a localised mode at the site of the defect. If an initial velocity is imparted to a particular particle, synchronously with the crossing of the particle by the soliton, a localised mode emerges at the site of the particle and additional solitons are also generated. When a soliton moves from a denser to a rarer medium, a strong localised pulse is created near the region of the density discontinuity and additional solitons appear; and further a weak oscillatory tail is left behind in the denser medium. On the other hand, if a soliton moves from a rarer to a denser medium, it is reflected back and a small localised mode is generated at the site of the density discontinuity. The variation of amplitude of the soliton with the velocity of propagation is also studied.