Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel.
Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia.
Phys Rev E. 2016 Mar;93(3):032216. doi: 10.1103/PhysRevE.93.032216. Epub 2016 Mar 15.
We describe and explore accelerating oscillatory fronts in sonic vacua with nonlocal interactions. As an example, a chain of particles oscillating in the plane and coupled by linear springs, with fixed ends, is considered. When one end of this system is harmonically excited in the transverse direction, one observes accelerated propagation of the excitation front, accompanied by an almost monochromatic oscillatory tail. Position of the front obeys the scaling law l(t) ∼ t(4/3). The frequency of the oscillatory tail remains constant, and the wavelength scales as λ ∼ t(1/3). These scaling laws result from the nonlocal effects; we derive them analytically (including the scaling coefficients) from a continuum approximation. Moreover, a certain threshold excitation amplitude is required in order to initiate the front propagation. The initiation threshold is evaluated on the basis of a simplified discrete model, further reduced to a completely integrable nonlinear system. Given their simplicity, nonlinear sonic vacua of the type considered herein should be common in periodic lattices.
我们描述并探索了具有非局部相互作用的声波真空中的加速振荡前沿。 作为一个例子，考虑了一个在平面上振动并通过线性弹簧连接的粒子链，其两端固定。 当此系统的一端在横向方向上受到谐振动激励时，观察到激励前沿的加速传播，同时伴随着几乎单色的振荡尾迹。 前沿的位置遵循标度律 l(t)∼t(4/3)。 振荡尾迹的频率保持不变，波长的标度为 λ∼t(1/3)。 这些标度律源于非局部效应；我们从连续体近似中对此进行了分析推导（包括标度系数）。 此外，为了启动前沿传播，需要一定的起始激励幅度。 根据简化的离散模型评估了起始阈值，进一步简化为完全可积的非线性系统。 鉴于它们的简单性，本文考虑的这种类型的非线性声波真空中应该在周期性晶格中很常见。
