Electric Circuit Analogs of First-Order Dual-Phase-Lag Diffusion

Abstract

The dual-phase-lag (DPL) model of nonclassical diffusion plays an expanding role for applications involving transient heat, mass, and momentum transfer. To open a new realm of applications for the model, the work reported here introduces RLC-type (resistor–inductor–capacitor) and RCC-type (resistor–capacitor–capacitor) electric circuits that behave as discrete analogs of first-order, continuum DPL diffusion. Importantly, the phase lags are two time-scales representing departures from classical diffusion that define the wave-like and over-diffusive regimes of DPL behavior. Expressions for these phase lags arise while deriving the difference–differential equations that govern the circuits. Furthermore, simulations exhibit DPL behavior for simple, one-dimensional ladder circuits subjected to step increases in boundary voltages. In particular, the subsequent voltage disturbances in the circuits propagate faster in the over-diffusive regime than in the wave-like regime. The simulations also show that DPL behavior stems from transient divisions of current between RL components in the wave-like circuit and between RC components in the over-diffusive circuit. Consequently, adopting the DPL perspective in the design of electronic systems may inspire novel applications that take advantage of DPL behavior. Finally, the circuits introduced here may lead to the study of DPL diffusion in analogous scenarios of heat, mass, and momentum transfer that are difficult to access experimentally.