Ion-Acoustic Solitons in Bi-Ion Dusty Plasma

The propagation of ion-acoustic solitons in a warm dusty plasma containing two ion species is investigated theoretically. Using an approach based on the Korteveg-de-Vries equation, it is shown that the critical value of the negative ion density that separates the domains of existence of compressi- on and rarefaction solitons depends continuously on the dust density. A modified Korteveg-de Vries equation for the critical density is derived in the higher order of the expansion in the small parameter. It is found that the nonlinear coefficient of this equation is positive for any values of the dust density and the masses of positive and negative ions. For the case where the negative ion density is close to its critical value, a soliton solution is found that takes into account both the quadratic and cubic nonlinearities. The propagation of a solitary wave of arbitrary amplitude is investigated by the quasi-potential method. It is shown that the range of the dust densities around the critical value within which solitary waves with positive and negative potentials can exist simultaneously is relatively wide.Comment: 17 pages, 5 figure

New results on group classification of nonlinear diffusion-convection equations

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient $(1+1)$-dimensional nonlinear diffusion-convection equations of the general form $f(x)u_t=(D(u)u_x)_x+K(u)u_x.$ We obtain new interesting cases of such equations with the density $f$ localized in space, which have large invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local trasformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.Comment: LaTeX2e, 19 page

RfaH Suppresses Small RNA MicA Inhibition of fimB Expression in Escherichia coli K-12

The phase variation (reversible on-off switching) of the type 1 fimbrial adhesin of Escherichia coli involves a DNA inversion catalyzed by FimB (switching in either direction) or FimE (on-to-off switching). Here, we demonstrate that RfaH activates expression of a FimB-LacZ protein fusion while having a modest inhibitory effect on a comparable fimB-lacZ operon construct and on a FimE-LacZ protein fusion, indicating that RfaH selectively controls fimB expression at the posttranscriptional level. Further work demonstrates that loss of RfaH enables small RNA (sRNA) MicA inhibition of fimB expression even in the absence of exogenous inducing stress. This effect is explained by induction of σE , and hence MicA, in the absence of RfaH. Additional work con- firms that the procaine-dependent induction of micA requires OmpR, as reported previously (A. Coornaert et al., Mol. Microbiol. 76:467–479, 2010, doi:10.1111/j.1365-2958.2010.07115.x), but also demonstrates that RfaH inhibition of fimB transcription is enhanced by procaine independently of OmpR. While the effect of procaine on fimB transcription is shown to be independent of RcsB, it was found to require SlyA, another known regulator of fimB transcription. These results demonstrate a complex role for RfaH as a regulator of fimB expression

Plasma with two-negative ions and immobile dust particles: planar and non-planar ion-acoustic wave propagation

By using the hydrodynamic equations of positive and two negative ions, Boltzmann electron density distribution, and Poisson equation with immobile positive/negative dust particles, a cylindrical Korteweg-de Vries (CKdV) equation is derived for small but finite amplitude ion-acoustic waves. At the critical total negative ion concentration and/or the critical density rate of the second-negative ions, the pulses collapse at this limit as nonlinearity fails to balance dispersion. Then the CKdV equation is not appropriate to describe the system. Therefore, the modified CKdV (MCKdV) and extended CKdV (ECKdV) equations are derived at the critical plasma compositions and in the vicinity of the critical plasma compositions, respectively. The physical parameters of two plasma environments (e.g., Xe+–F-–SF$_{6}^{-}$ and Ar+–F-–SF$_{6}^{-}$ plasmas) are examined on the wave phase velocity and the nonlinear localized pulse profile. The latter should satisfy necessary condition to exist. The localized pulse of Ar+–F-–SF$_{6}^{-}$ plasma is much spiky than Xe+–F-–SF$_{6}^{-}$ plasma. Thus, the mass ratio of the negative-to-positive ions is focused upon and it emphasizes to play an important role on the pulse profile. Dependence of the geometrical divergence on the pulse profile is also investigated, which indicates that the localized pulse damps with time. The implications of our results agrees with the experimental observations