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

Solitary Dust--Acoustic Waves in a Plasma with Two-Temperature Ions and Distributed Grain Size

The propagation of weakly nonlinear dust--acoustic waves in a dusty plasma containing two ion species with different temperatures is explored. The nonlinear equations describing both the quadratic and cubic plasma nonlinearities are derived. It is shown that the properties of dust--acoustic waves depend substantially on the grain size distribution. In particular, for solitary dust--acoustic waves with a positive potential to exist in a plasma with distributed grain size, it is necessary that the difference between the temperatures of two ion species be large that that in the case of unusized grains.Comment: 16 pages, 6 figure

Stepwise inverse consistent Euler’s scheme for diffeomorphic image registration

Abstract. Theoretically, inverse consistency in an image registration problem can be achieved by employing a diffeomorphic scheme that uses transformations parametrized by stationary velocity fields (SVF). The displacement from a given SVF, formulated as a series of self composi-tions of a transformation function, can be obtained by Euler integration in the time domain. However in practice, the discrete time integration produces results that are inverse inconsistent, and inverse consistency in the final solution needs to be explicitly ensured. One way of achieving this is to penalize the endpoint displacement offset obtained by evaluating a composition of the transformation with its inverse at an arbitrary point. In this paper, we propose a variation in which the displacement penaliza-tion is required only in the first composition step of the transformation thereby bringing down the computational complexity. We compare these two ways of enforcing inverse consistency by applying the registration framework on four pairs of brain magnetic resonance images. We ob-serve that the proposed stepwise scheme maintains both precision and level of inverse consistency similar to the endpoint scheme.