Linear and nonlinear properties of Rao-dust-Alfv\'en waves in magnetized plasmas

The linear and nonlinear properties of the Rao-dust-magnetohydrodynamic (R-D-MHD) waves in a dusty magnetoplasma are studied. By employing the inertialess electron equation of motion, inertial ion equation of motion, Amp\`ere's law, Faraday's law, and the continuity equation in a plasma with immobile charged dust grains, the linear and nonlinear propagation of two-dimensional R-D-MHD waves are investigated. In the linear regime, the existence of immobile dust grains produces the Rao cutoff frequency, which is proportional to the dust charge density and the ion gyrofrequency. On the other hand, the dynamics of an amplitude modulated R-D-MHD waves is governed by the cubic nonlinear Schroedinger equation. The latter has been derived by using the reductive perturbation technique and the two-timescale analysis which accounts for the harmonic generation nonlinearity in plasmas. The stability of the modulated wave envelope against non-resonant perturbations is studied. Finally, the possibility of localized envelope excitations is discussed.Comment: 30 pages, 8 figures, to appear in Physics of Plasma

Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form $\phi(r)$ and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed $v_0$. Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.Comment: 21 pages, 12 figures, to appear in Eur. Phys. J.

Modulational instability in asymmetric coupled wave functions

The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and the GVD terms) and the nonlinearity and coupling coefficients, on which no assumption is made. A generalized dispersion relation is obtained, relating the frequency and wave-number of a small perturbation around a coupled monochromatic (Stokes') wave solution. Explicitly stability criteria are obtained. The analysis reveals a number of possibilities. Two (individually) stable systems may be destabilized due to coupling. Unstable systems may, when coupled, present an enhanced instability growth rate, for an extended wave number range of values. Distinct unstable wavenumber windows may arise simultaneously.Comment: NEXT Sigma-Phi Statistical Physics Conference (2005, Kolymbari, Greece) Proceedings, submitted; v.2 is a shorter version of the text in v.1 (more detailed and somehow more explanatory, yet abbreviated due to submission regulations); some typos corrected as wel

Nonlinear modulation of transverse dust lattice waves in complex plasma crystals

The occurrence of the modulational instability (MI) in transverse dust lattice waves propagating in a one-dimensional dusty plasma crystal is investigated. The amplitude modulation mechanism, which is related to the intrinsic nonlinearity of the sheath electric field, is shown to destabilize the carrier wave under certain conditions, possibly leading to the formation of localized envelope excitations. Explicit expressions for the instability growth rate and threshold are presented and discussed.Comment: 5 pages, no figures; submitted to Physics of Plasma

A prelude report on molecular docking of HER2 protein towards comprehending anti-cancer properties of saponins from Solanum tuberosum

Saponins are extensively known for many biological activities e.g. antimicrobial, anti-palatability, anti-cancer and hemolytic. As cancer cells have a more cholesterol-like compound in their membrane structure the saponins bind cholesterol due to their natural affinity to bind cancer cell membrane. This prevents them from entering the body through the intestinal tract, where they have the ability to attach themselves to vital organs and grow. This study reports the effective use of lower dose saponins like immunotoxin so that they can inhibit the proliferation of cancerous pancreatic cells. The investigation of pancreatic cancer metabolic pathway it was found that proteins 3H3B produced by genes HER-2 are involved in the enhancement of this type of cancer. Further docking studies showed that there is an effective interaction between saponins and cancer cells. The glide score of the saponin analogue compound with CID 21573770 (Pubchem) was -6.30 followed by score of -6.05 and -5.29 for 5-Florouracil and gemcitabine respectively. The interaction was observed in the GLU and GLN rich region, saponins made H-bonds with GLU-188, GLN-119, VAL-72 and GLN-71. This study indicates an effective way towards leading newer prospects for developing saponin analogue based cancer-fighting drugs with improved cancer cell inhibition property without killing normal cells