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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Retarding accelerations and ratchet-like transport of the self-ordered front in a bistable system of reaction-diffusion type
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Retarding accelerations and ratchet-like transport of the self-ordered front in a bistable system of reaction-diffusion type

机译：反应扩散型双稳态系统中有序加速的自减速前沿加速和棘轮状传输

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摘要

Front dynamics with time delays in a reaction-diffusion equation with the piecewise linear rate function is studied by considering the response of the self-ordered front to the rapidly varying force. More specifically, the retarding accelerations of the bistable front (BF) joining two states of different stability in the system are examined. Two cases of differently shaped forcing functions are studied. In examining the 'size' of the retardation, namely, the lag time between the propagation velocity of the front and the driving force we approximate the forcing function by the step-like dependence of the flexible steepness. The lag time is found to be sensitive to both the rate (steepness) of the driving force and the characteristic parameters of the rate function. A significant retardation effect occurred when the steepness of the force exceeded the characteristic relaxation rate of the system; the lag time monotonically increases with increasing steepness and approaches the maximal value depending on the relaxation time of the system, when the driving force becomes extremely steep. The influence of delays on the ratchet-like transport of the self-ordered front is studied by considering the response of BF to the periodically oscillating square-pulse force. The average characteristics of the unforced dc motion of BFs are presented. The occurrence of delays, as shown, significantly reduces the unforced dc motion of BE The ratchet-like transport is highly suppressed if the period of the ac force becomes low compared to the characteristic relaxation time of the system.
机译：通过考虑自序前沿对快速变化力的响应，研究了具有分段线性速率函数的反应扩散方程中具有时间延迟的前沿动力学。更具体地说，检查了连接系统中不同稳定性的两个状态的双稳态前缘（BF）的延迟加速度。研究了两种形状不同的强迫函数。在检查延迟的“大小”时，即前部的传播速度与驱动力之间的滞后时间，我们通过柔性陡度的阶梯状相关性来逼近强迫函数。发现滞后时间对驱动力的速率（陡度）和速率函数的特征参数均敏感。当力的陡度超过系统的特征松弛率时，会产生明显的延迟效果。当驱动力变得非常陡峭时，滞后时间会随着陡度的增加而单调增加，并且会随着系统的松弛时间而接近最大值。通过考虑BF对周期振荡方波力的响应，研究了延迟对自序前沿棘轮状传输的影响。给出了高炉无强迫直流运动的平均特性。如图所示，延迟的发生极大地降低了BE的无力dc运动如果与系统的特征驰豫时间相比，交流力的周期变短，则棘轮状的传输将受到高度抑制。

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