Supersymmetric Integrable Systems in (2 + 1) Dimensions and Their Backlund Transformation

Nonlinear integrable systems in (2 + 1)dimensions which are supersymmetric are generated in twodifferent ways. In one approach the homogeneous spacesof super-Lie algebra are used, and in the other we use a different technique of extending thedimension of the system. The two sets of equations turnout to be different. The methodologies ofDarbux–Backlund transformation and gaugetransformation are used to generate the Backlund transformations ofthese equations. An important result of our analysis isthe existence of purely fermionic nonlinear systems in(2 + 1) dimensions.     

Colouring lines in projective space

Let V be a vector space of dimension v over a field of order q. The q-Kneser graph has the k-dimensional subspaces of V as its vertices, where two subspaces α and β are adjacent if and only if is the zero subspace. This paper is motivated by the problem of determining the chromatic numbers of these graphs. This problem is trivial when k=1 (and the graphs are complete) or when v<2k (and the graphs are empty). We establish some basic theory in the general case. Then specializing to the case k=2, we show that the chromatic number is q²+q when v=4 and (q^v-1-1)/(q-1) when v>4. In both cases we characterise the minimal colourings.     

K isomers in 254No: probing single-particle energies and pairing strengths in the heaviest nuclei

We have identified two isomers in 254No, built on two- and four-quasiparticle excitations, with quantum numbers K pi = 8- and (14+), as well as a low-energy 2-quasiparticle Kpi = 3+ state. The occurrence of isomers establishes that K is a good quantum number and therefore that the nucleus has an axial prolate shape. The 2-quasiparticle states probe the energies of the proton levels that govern the stability of superheavy nuclei, test 2-quasiparticle energies from theory, and thereby check their predictions of magic gaps.     

Ion acoustic solitons in a streaming relativistic plasma with negative ions

We analyze the effect of a nonzero streaming velocity of both positive and negative ions on the formation of solitary waves in a relativistic plasma. The thermodynamic situation is considered to be isothermal. For various values ofu _0/C andn _o/nowe obtain the variations of the amplitude and the width of the solitary wave.     

Domain growth in the three-dimensional dilute Ising model

We investigate the kinetics of domain growth in the three-dimensional Ising model with quenched random site dilution, using Monte Carlo simulation technique. A crossover from the power law growth regime to a much slower growth observed in our simulation is interpreted through the roughening of the interfaces by the quenched impurities. The results are also compared with the corresponding results in two dimensions.     

Site-specific hydration status of an amphipathic peptide in AOT reverse micelles

Reverse micelles formed by sodium bis(2-ethylhexyl) sulfosuccinate (AOT) in isooctane (IO) and water have long been used as a means to provide a confined aqueous environment for various applications. In particular, AOT reverse micelles have often been used as a template to mimic membrane-water interfaces. While earlier studies have shown that membrane-binding peptides can indeed be incorporated into the polar cavity of AOT reverse micelles where they mostly fold into an alpha-helical structure, the underlying interactions leading to the ordered conformation are however not well understood. Herein, we have used circular dichroism (CD) and infrared (IR) spectroscopies in conjunction with a local IR marker (i.e., the CN group of a non-natural amino acid, p-cyano-phenylalanine) and a global IR reporter (i.e., the amide I' band of the peptide backbone) to probe the conformation as well as the hydration status of an antimicrobial peptide, mastoparan x (MPx), in AOT reverse micelles of different water contents. Our results show that at, w0=6, MPx adopts an alpha-helical conformation with both the backbone and hydrophobic side chains mostly dehydrated, whereas its backbone becomes partially hydrated at w0=20. In addition, our results suggest that the amphipathic alpha-helix so formed orients itself in such a manner that its positively charged, lysine-rich, hydrophilic face points toward the negatively charged AOT head groups, while its hydrophobic face is directed toward the polar interior of the water pool. This picture is in marked contrast to that observed for the binding of MPx to phospholipid bilayers wherein the hydrophobic surface of the bound alpha-helix is buried deeper into the membrane interior.