Semi-analytical method of calculating the electrostatic interaction of colloidal solutions

We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis functions such as spherical harmonic function and cylinder function. The expansion coefficients can be obtained by solving the equations of the boundary conditions, combining an analytical translation transform of the coordinates and a numerical multipoint collection method. The precise electrostatic potential and the interaction energy are then obtained automatically. The method is available not only for the uniformly charged colloids but also for nonuniformly charged ones. We have successfully applied it to unconfined diluted colloid system and some confined systems such as the long cylinder wall confinement, the air–water interfacial confinement and porous membrane confinement. The consistence checks of our calculations with some known analytical cases have been made for all our applications. In theory, the method is applicable to any dilute colloid solutions with an arbitrary distribution of the surface charge on the colloidal particle under a regular solid confinement, such as spherical cavity confinement and lamellar confinement.

Propagation properties of foreshock cavitons: Cluster observations

Foreshock cavitons are transient phenomena observed in the terrestrial foreshock region.They are characterized by a simultaneous depression of magnetic field magnitude and plasma density,which are bounded with enhancements of these two parameters and surrounded by ultralow frequency(ULF)waves.Previous studies focused on the interplanetary magnetic field(IMF)conditions,solar wind(SW)conditions,and the growth of the foreshock waves related to the generation of foreshock cavitons.Previously,a multipoint spacecraft analysis method using Cluster data was applied to analyze only two foreshock cavitons,and this method did not consider uncertainties.In this study,multipoint spacecraft analysis methods,including the timing method,the minimum directional derivative(MDD)method,and the spatiotemporal difference(STD)method are applied to determine the velocity in both spacecraft and solar wind frames.The propagation properties show good agreement with previous results from simulations and observations that most cavitons move sunward in the solar wind frame,with the velocities larger than the Alfvén speed.The propagation properties of foreshock cavitons support the formation mechanism of cavitons in previous simulations,which suggested that cavitons are formed due to the nonlinear evolution of compressive ULF waves.We find that there is clear decreasing trend between the size of cavitons and their velocity in the solar wind frame.In addition,the timing method considering errors has been applied to study the evolution properties by comparing the velocities with errors of the leading and trailing edges,and we identify three stable cavitons and one contracting caviton,which has not been studied before.Most cavitons should remain stable when they travel toward the Earth’s bow shock.The relationship between the size of foreshock cavitons and their distance from the bow shock is also discussed.