Abstract Transmission line displaying non-locality effects is modelled by considering the magnetic coupling of inductors in the series branch of Heaviside’s elementary circuit, so that the magnetic flux is obtained as a superposition of local and constitutively given non-local magnetic flux through the cross-inductivity kernel. Non-local telegrapher’s equations are derived as the continuum limit of corresponding Kirchhoff’s laws and solved for prescribed external excitation analytically by the means of integral transforms method and also numerically. Numerical examples of the mollified impulse responses illustrate the non-local behavior of signal propagation in case of power, exponential, and Gauss type cross-inductivity kernels.

中文翻译：

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外地电报员方程作为传输线模型

摘要 通过考虑 Heaviside 基本电路串联支路中电感器的磁耦合对显示非局域效应的传输线进行建模，从而获得磁通量为局部和本构给定的非局部磁通量通过交叉点的叠加。电感内核。非本地电报方程作为相应基尔霍夫定律的连续极限推导出来，并通过积分变换方法和数值方法对规定的外部激励进行解析求解。缓和脉冲响应的数值示例说明了在功率、指数和高斯型交叉电感核的情况下信号传播的非局部行为。