Convective Instability in Superposed Fluid and Porous Layers with Vertical Throughflow

A closed form solution to the convective instability in a composite system of fluid and porous layers with vertical throughflow is presented. The boundaries are considered to be rigid-permeable and insulating to temperature perturbations. Flow in the porous layer is governed by Darcy–Forchheimer equation and the Beavers–Joseph condition is applied at the interface between the fluid and the porous layer. In contrast to the single-layer system, it is found that destabilization due to throughflow arises, and the ratio of fluid layer thickness to porous layer thickness, , too, plays a crucial role in deciding the stability of the system depending on the Prandtl number.     

Convergence analysis of the Wolf method for Coulombic interactions

A rigorous proof for convergence of the Wolf method (Wolf et al., 1999 [9]) for calculating electrostatic energy of a periodic lattice is presented. In particular, we show that for an arbitrary lattice of unit cells, the lattice sum obtained via Wolf method converges to the one obtained via Ewald method.     

Switchable ErSc2N rotor within a C80 fullerene cage: an electron paramagnetic resonance and photoluminescence excitation study

Motivated by the possibility of observing photoluminescence and electron paramagnetic resonance from the same species located within a fullerene molecule, we initiated an EPR study of Er3+ in ErSc2N@C80. Two orientations of the ErSc2N rotor within the C80 fullerene are observed in EPR, consistent with earlier studies using photoluminescence excitation (PLE) spectroscopy. For some crystal field orientations, electron spin relaxation is driven by an Orbach process via the first excited electronic state of the 4I(15/2) multiplet. We observe a change in the relative populations of the two ErSc2N configurations upon the application of 532 nm illumination, and are thus able to switch the majority cage symmetry. This photoisomerization, observable by both EPR and PLE, is metastable, lasting many hours at 20 K.     

On the existence of chaotic circumferential waves in spinning disks

We use a third-order perturbation theory and Melnikov's method to prove the existence of chaos in spinning circular disks subject to a lateral point load. We show that the emergence of transverse homoclinic and heteroclinic points lead, respectively, to a random reversal in the traveling direction of circumferential waves and a random phase shift of magnitude pi for both forward and backward wave components. These long-term phenomena occur in imperfect low-speed disks sufficiently far from fundamental resonances.     

Toward controlled spacing in one-dimensional molecular chains: alkyl-chain-functionalized fullerenes in carbon nanotubes

A range of fullerenes (C60) functionalized with long alkyl chains have been synthesized and inserted into single-walled carbon nanotubes. The impact of the alkyl chain length and of the type of linker between the addend and the fullerene cage on the geometry of molecular arrays in nanotube has been studied by high-resolution transmission electron microscopy. In the presence of functional groups the mean interfullerene separations are significantly increased by 2-8 nm depending on the length of the alkyl chain, but the periodicity of the fullerene arrays is disrupted due to the conformational flexibility of the alkyl groups.     

Davies electron-nuclear double resonance revisited: enhanced sensitivity and nuclear spin relaxation

Over the past 50 years, electron-nuclear double resonance (ENDOR) has become a fairly ubiquitous spectroscopic technique, allowing the study of spin transitions for nuclei which are coupled to electron spins. However, the low spin number sensitivity of the technique continues to pose serious limitations. Here we demonstrate that signal intensity in a pulsed Davies ENDOR experiment depends strongly on the nuclear relaxation time T(1n), and can be severely reduced for long T(1n). We suggest a development of the original Davies ENDOR sequence that overcomes this limitation, thus offering dramatically enhanced signal intensity and spectral resolution. Finally, we observe that the sensitivity of the original Davies method to T(1n) can be exploited to measure nuclear relaxation, as we demonstrate for phosphorous donors in silicon and for endohedral fullerenes N@C(60) in CS(2).     

High fidelity single qubit operations using pulsed electron paramagnetic resonance

Systematic errors in spin rotation operations using simple rf pulses place severe limitations on the usefulness of the pulsed magnetic resonance methods in quantum computing applications. In particular, the fidelity of quantum logic operations performed on electron spin qubits falls well below the threshold for the application of quantum algorithms. Using three independent techniques, we demonstrate the use of composite pulses to improve this fidelity by several orders of magnitude. The observed high-fidelity operations are limited by pulse phase errors, but nevertheless fall within the limits required for the application of quantum error correction.     

Configuration-selective spectroscopic studies of Er3+ centers in ErSc2N@C80 and Er2ScN@C80 fullerenes

Low temperature photoluminescence (PL) and photoluminescence excitation (PLE) spectroscopy of high purity ErSc(2)N@C(80) and Er(2)ScN@C(80) fullerenes reveal at least two metastable configurations of the Er(3+) ion within the cage, consistent with previous observations from x-ray diffraction. Using PLE measurements at a number of different emission wavelengths we have characterized the ground state, (4)I(152), and the first excited state, (4)I(132), of the various Er(3+) configurations and their crystal-field splitting. We present detailed energy level diagrams for the ground and excited states of the two dominant configurations of ErSc(2)N@C(80) and Er(2)ScN@C(80).