Ratchet-like transport of the self-ordered fronts generated by the similarly shaped rate functions: high-efficiency deterministic front-ratchet

The ratchet-like transport of the self-ordered fronts joining two states of different stability in a bistable system of the reaction-diffusion type is considered within the cubic polynomial and piecewise linear models of the system. We approximate the rate function in the governing equation of the 'bistable' front (BF) by the cubic polynomial dependence and its piecewise linear emulations, all of these satisfying the same symmetry properties. The unforced drift transport of BFs under the differently shaped zero-mean ac forces of the different spectral content, namely, the single-harmonic and rectangular one, is considered. By using both the numerical and analytic tools we show that (i) the unforced drift transport is much more pronounced in a low-frequency range of the driving forces, when the period of the force significantly exceeds the characteristic relaxation time of the system; the average drift velocity of the ac-driven BF rapidly decreases with the decreasing period of the force and practically vanishes when the period of the force becomes lesser if compared to the characteristic relaxation time of the system, (ii) the unforced drift transport generated by the square-pulse force is more pronounced if compared to that being derived by the single-harmonic force, (iii) the oscillatory rectangular driver is of the highest 'efficiency' in terms of the 'speed rectification' of the ac-driven front; the absolutely maximal shift of the mean drift velocity of the ac-driven BF is achieved with the square-pulse force when the period of the force tends to infinity and (iv) the average characteristics of the ratchet-like transport generated by the similarly shaped rate functions are similarly shaped and close to each other