For two fermion fields y l ( x ) and yz(z) interacting with the electromagnetic field via the minimal and Pauli-couplings we introduce a composite field @(q, x2). The total action can be rewritten in terms of @ and its time derivatives if we use the physical retarded Green's functions P e t (corresponding to an effective to (1/2)(Dret + D&dV) = 6 ) between two particles). The variation of the action with respect to @ gives then exact covariant two-body, one-time, equations with relativistic potentials. The center of motion can be covariantly separated leading to an infinite component wave equation for the composite system, which reduces to the well-known covariant wave equation for the moving H-atom in the limit mz -+ ca.
Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a "backward flow" is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.