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We report a study on modeling carbon nanotube (CNT) ultracapacitor performance, utilizing molecular dynamics to obtain solutions of Poisson's equation within the capacitor cell. For a given voltage, the total current is computed based on the electric field generated from the nanotube electrodes and the friction caused by the motion of the electrolyte ions, yielding the frequency-dependent impedance. From the current and impedance behavior at a given frequency, we extract the Nyquist and Cyclic-Voltammetry plots for the simulated ultracapacitor. These plots compare well with existing experimental data. The behavior of the capacitor is further analyzed based on simulated spatial distributions of electrolyte ions.