Compact nonlinear model of an implantable electrode array for spinal cord stimulation (SCS)

We describe the construction of a model of the electrode-electrolyte interface and surrounding electrolyte in the case of a platinum-electrode array intended for spinal-cord stimulation (SCS) application. We show that a finite, two dimensional, resistor array provides a satisfactory model of the bulk electrolyte, and we identify the complexity required of that resistor array. The electrode-electrolyte interface is modelled in a fashion suitable for commonly-available, compact simulators using a nonlinear extension of the model of Franks et al. that incorporates diodes and a memristor. The electrode-electrolyte interface model accounts for the nonlinear current-overpotential characteristic and diffusion-limiting effects. We characterise a commercial, implantable, electrode array, fit the model to it, and show that the model successfully predicts subtle operational characteristics

Quantum phase transition of dynamical resistance in a mesoscopic capacitor

We study theoretically dynamic response of a mesoscopic capacitor, which consists of a quantum dot connected to an electron reservoir via a point contact and capacitively coupled to a gate voltage. A quantum Hall edge state with a filling factor nu is realized in a strong magnetic field applied perpendicular to the two-dimensional electron gas. We discuss a noise-driven quantum phase transition of the transport property of the edge state by taking into account an ohmic bath connected to the gate voltage. Without the noise, the charge relaxation for nu>1/2 is universally quantized at R_q=h/(2e^2), while for nu<1/2, the system undergoes the Kosterlitz-Thouless transtion, which drastically changes the nature of the dynamical resistance. The phase transition is facilitated by the noisy gate voltage, and we see that it can occur even for an integer quantum Hall edge at nu=1. When the dissipation by the noise is sufficiently small, the quantized value of R_q is shifted by the bath impedance.Comment: 5 pages, 2 figures, proceeding of the 19th International Conference on the Application of High Magnetic Fields in Semiconductor Physics and Nanotechnology (HMF-19

A Coherent RC Circuit

We review the first experiment on dynamic transport in a phase-coherent quantum conductor. In our discussion, we highlight the use of time-dependent transport as a means of gaining insight into charge relaxation on a mesoscopic scale. For this purpose, we studied the ac conductance of a model quantum conductor, i.e. the quantum RC circuit. Prior to our experimental work, M. B\"{u}ttiker, H. Thomas and A. Pr\^{e}tre first worked on dynamic mesoscopic transport in the 1990s. They predicted that the mesoscopic RC circuit can be described by a quantum capacitance related to the density of states in the capacitor and a constant charge relaxation resistance value equal to half of the resistance quantum h/2e^2, when a single mode is transmitted between the capacitance and a reservoir. By applying a microwave excitation to a gate located on top of a coherent submicronic quantum dot that is coupled to a reservoir, we validate this theoretical prediction on the ac conductance of the quantum RC circuit. Our study demonstrates that the ac conductance is directly related to the dwell time of electrons in the capacitor. Thereby, we observed a counterintuitive behavior of a quantum origin: as the transmission of the single conducting mode decreases, the resistance of the quantum RC circuit remains constant while the capacitance oscillates.Comment: 30 page

Various analytical models for supercapacitors: a mathematical study

Supercapacitors (SCs) are used extensively in high-power potential energy applications like renewable energy systems, electric vehicles, power electronics, and many other industrial applications. This is due to SCs containing high-power density and the ability to respond spontaneously with fast charging and discharging demands. Advancements in material and fabrication techniques have induced a scope for research to improve the application of SCs. Many researchers have studied various SC properties and their effects on energy storage and management performance. In this paper, various fractional calculus-based SC models are summarized, with emphasis on analytical studies from derived classical SC models. Study prevails such parameterized resistor- capacitor networks have simplified the representation of electrical behavior of SCs to deal with the complicated internal structure. Fractional calculus has been used to develop SC models with the aim of understanding their complicated structure. Finally, the properties of different SC models utilized by various researchers to understand the behavior of SCs are listed using an equivalent circuit

Analogue circuit realisation of surface-confined redox reaction kinetics

The literature on voltammetry and electrochemical impedance spectroscopy (EIS) recognises the importance of using large-amplitude sinusoidal perturbations to better characterise electrochemical systems. To identify the parameters of a given reaction, various electrochemical models with different sets of values are simulated and compared against the experimental data to determine the best-fit set of parameters. However, the process of solving these nonlinear models is computationally expensive. This paper proposes analogue circuit elements for synthesising surface-confined electrochemical kinetics at the electrode interface. The resultant analogue model could be used as a solver to compute reaction parameters as well as a tracker for ideal biosensor behaviour. The performance of the analogue model was verified against numerical solutions to theoretical and experimental electrochemical models. Results show that the proposed analogue model has a high accuracy of at least 97% and a wide bandwidth of up to 2 kHz. The circuit consumed an average power of 9 μW