An RF Circuit Model for Carbon Nanotubes

We develop an rf circuit model for single walled carbon nanotubes for both dc and capacitively contacted geometries. By modeling the nanotube as a nano-transmission line with distributed kinetic and magnetic inductance as well as distributed quantum and electrostatic capacitance, we calculate the complex, frequency dependent impedance for a variety of measurement geometries. Exciting voltage waves on the nano-transmission line is equivalent to directly exciting the yet-to-be observed one dimensional plasmons, the low energy excitation of a Luttinger liquid.Comment: 4 pages, 4 figures. To be published in the proceedings of IEEE-NANO 200

A combined R-matrix eigenstate basis set and finite-differences propagation method for the time-dependent Schr\"{od}dinger equation: the one-electron case

In this work we present the theoretical framework for the solution of the time-dependent Schr\"{o}dinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron's coordinates separated over two regions, that is regions $I$ and $II$. In region $I$ the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wavefunction. In region $II$ a grid representation of the wavefunction is considered and propagation in space and time is obtained through the finite-differences method. It appears this is the first time a combination of basis set and grid methods has been put forward for tackling multi-region time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multi-electron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely that beyond a certain distance (encompassing region $I$) a single ejected electron is distinguishable from the other electrons of the multi-electron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.Comment: 13 pages, 6 figures, submitte

Microwave Nanotube Transistor Operation at High Bias

We measure the small signal, 1 GHz source-drain dynamical conductance of a back-gated single-walled carbon nanotube field effect transistor at both low and high dc bias voltages. At all bias voltages, the intrinsic device dynamical conductance at 1 GHz is identical to the low frequency dynamical conductance, consistent with the prediction of a cutoff frequency much higher than 1 GHz. This work represents a significant step towards a full characterization of a nanotube transistor for RF and microwave amplifiers.Comment: 3 pages, 4 figure

On the quasi-steady state assumption applied to Michaelis-Menten and suicide substrate reactions with diffusion

We consider a recent extension to the validity of the quasi-steady-state assumption (QSSA) which includes the case where the ratio of the initial enzyme to substrate concentration is not necessarily small. We extend the analysis to include diffusion of substrate, in which case the initial enzyme to substrate ratio is spatially dependent and no longer constant. We show that the region in which the QSSA holds depends on the nature of the enzyme-substrate reaction: if the enzyme is inactivated by the substrate then the QSSA holds in a growing disc; if the enzyme is unchanged after reaction then the QSSA holds in a ring travelling through space

Suicide substrate reaction-diffusion equations: varying the source

The suicide substrate reaction is a model for certain enzyme-inhibiting drugs. This reaction system is examined assuming that the substrate diffuses freely while the enzyme remains fixed. Two sets of initial and boundary conditions are examined: one modelling an instantaneous point source, akin to an injection of substrate, the other, a continuous point source, akin to a continuing influx, or intravenous drip, of substrate. The quasi-steady-state assumption is applied to obtain analytical solutions for a limited parameter space. Finally, further applications of numerical and analytical experimentation on pharmaceutical mechanisms are described

On the kinetics of suicide substrates

We consider a realistic suicide substrate reaction which can be represented by four rate equations for the concentrations of the various molecules as functions of time. We present a general procedure to obtain accurate, approximate solutions analytically in terms of the rate equation parameters. This systematic technique provides more accurate approximations to the exact (numerical) solutions than other approximate methods which have been proposed based on a pseudo-steady state hypothesis

Microwave Transport in Metallic Single-Walled Carbon Nanotubes

The dynamical conductance of electrically contacted single-walled carbon nanotubes is measured from dc to 10 GHz as a function of source-drain voltage in both the low-field and high-field limits. The ac conductance of the nanotube itself is found to be equal to the dc conductance over the frequency range studied for tubes in both the ballistic and diffusive limit. This clearly demonstrates that nanotubes can carry high-frequency currents at least as well as dc currents over a wide range of operating conditions. Although a detailed theoretical explanation is still lacking, we present a phenomenological model of the ac impedance of a carbon nanotube in the presence of scattering that is consistent with these results.Comment: Added reference