  Overdamped motion of Brownian particles in tilted piecewise linear periodic
potentials is considered. Explicit algebraic expressions for the diffusion
coefficient, current, and coherence level of Brownian transport are derived.
Their dependencies on temperature, tilting force, and the shape of the
potential are analyzed. The necessary and sufficient conditions for the
non-monotonic behavior of the diffusion coefficient as a function of
temperature are determined. The diffusion coefficient and coherence level are
found to be extremely sensitive to the asymmetry of the potential. It is
established that at the values of the external force, for which the enhancement
of diffusion is most rapid, the level of coherence has a wide plateau at low
temperatures with the value of the Peclet factor 2. An interpretation of the
amplification of diffusion in comparison with free thermal diffusion in terms
of probability distribution is proposed.
