Corrector estimates for the homogenization of a locally-periodic medium with areas of low and high diffusivity

We prove an upper bound for the convergence rate of the homogenization limit $\epsilon\to 0$ for a linear transmission problem for a advection-diffusion(-reaction) system posed in areas with low and high diffusivity, where $\epsilon$ is a suitable scale parameter. On this way, we justify the formal homogenization asymptotics obtained by us earlier by proving an upper bound for the convergence rate (a corrector estimate). The main ingredients of the proof of the corrector estimate include integral estimates for rapidly oscillating functions with prescribed average, properties of the macroscopic reconstruction operators, energy bounds and extra two-scale regularity estimates. The whole procedure essentially relies on a good understanding of the analysis of the limit two-scale problem.Comment: 19 pages, 1 figur

D-Jogger: Syncing Music with Walking

(Abstract to follow

Modern Problems of Metabolism.

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Homogenization of a locally-periodic medium with areas of low and high diffusivity

We aim at understanding transport in porous materials including regions with both high and low diffusivities. For such scenarios, the transport becomes structured (here: micro- macro). The geometry we have in mind includes regions of low diffusivity arranged in a locally-periodic fashion. We choose a prototypical advection-diffusion system (of minimal size), discuss its formal homogenization (the heterogenous medium being now assumed to be made of zones with circular areas of low diffusivity of x-varying sizes), and prove the weak solvability of the limit two-scale reaction-diffusion model. A special feature of our analysis is that most of the basic estimates (positivity, L^inf-bounds, uniqueness, energy inequality) are obtained in x-dependent Bochner spaces. Keywords: Heterogeneous porous materials, homogenization, micro-macro transport, two-scale model, reaction-diffusion system, weak solvability

A new circuitry model for electric double layer capacitor

A new circuitry model, which consists of constant phase elements is proposed to simply describe the charge storage mechanism of an electric double layer capacitor (EDLC). The model is developed based on previously reported experimental data of cellulose- and glass wool-based capacitors measured by electrochemical impedance spectroscopy. As a result, with a considerably small normalized error, the proposed model fitted the experimental data well for the whole frequency range (from mHz to kHz). The model is capable of providing beneficial information on the charge storage mechanism inside the tested capacitors for each frequency region; low, medium and high frequency region separately. Interestingly, the fitted parameters from the model are consistent with the static EDLC parameters; in particular, the specific capacitance (corresponds to double layer capacitance) and internal resistance values attained from dc properties characterization