Gas and dust dynamics in $γ$ Cephei-type disks
(Abridged) Giant planets are observed orbiting the primary stars of close binary systems. Such planets may have formed in compact circumprimary disks, under conditions much different than those around single stars. To quantify the effects of the strong gravitational perturbations exerted on circumprimary disk material, the 3D dynamics of gas and dust in orbit around the primary star of a compact and eccentric binary was modeled by using gamma Cephei as a representative of a class of close binary systems. Circumprimary gas was approximated as an Eulerian viscous and compressible fluid. Dust grains were modeled as Lagrangean particles, subjected to gravity and drag forces. Some models also include a giant planet. Models show that spiral density waves excited around pericenter passage propagate toward the inner disk boundary, through a few pressure scaleheights from the midplane, inducing radial and vertical mixing in the gas. However, perturbations imparted to gas, both in terms of eccentricity and precession, are far weaker than previously estimated by 2D simulations. Models predict small eccentricities, <~ 0.03, and slow retrograde precession. The addition of a giant planet does not change the low eccentricity state of the disk. The parameters applied to the disk would lead to the formation of a planet many times the mass of Jupiter, in agreement with some observations. Micron to mm-size dust grains are well coupled to the gas, resulting in similar dynamics and statistically similar distributions of orbital elements. The planet only affects the dust distributions locally. In agreement with results of recent 2D models, the lifetime of an isolated circumprimary disk would be brief, ~1e5 years, due to its compact nature, requiring a long-term external supply of mass to allow for the in situ formation of a giant planet.