A new vision in multidimensional statistics is proposed impacting severalareas of application. In these applications, a set of noisy measurementscharacterizing the repeatable response of a process is known as a realizationand can be seen as a single
point in $mathbb{R}^N$. The projections of thispoint on the N axes correspond to the N measurements. The contemporary visionof a diffuse cloud of realizations distributed in $mathbb{R}^N$ is replaced bya cloud in the shape of a shell surrounding a topological manifold. Thismanifold corresponds to the processs stabilized-response domain observedwithout the measurement noise. The measurement noise, which accumulates overseveral dimensions, distances each realization from the manifold. Theprobability density function (PDF) of the realization-to-manifold distancecreates the shell. Considering the central limit theorem as the number ofdimensions increases, the PDF tends toward the normal distribution N($mu$,$sigma$^2) where $mu$ fixes the center shell location and $sigma$fixes the shell thickness. In vision, the likelihood of a realization is afunction of the realization-to-shell distance rather than therealization-to-manifold distance. The demonstration begins with the work ofClaude Shannon followed by the introduction of the shell manifold and ends withpractical applications to monitoring equipment.
We present many-body textit{ab initio} calculations of the electronic and optical properties of semiconducting zigzag carbon nanotubes under uniaxial strain. The GW approach is utilized to obtain the quasiparticle bandgaps and is combined with the Be
the-Salpeter equation to obtain the optical absorption spectrum. We find that the dependence of the electronic bandgaps on strain is more complex than previously predicted based on tight-binding models or density-functional theory. In addition, we show that the exciton energy and exciton binding energy depend significantly on strain, with variations of tens of meVs per percent strain, but that despite these strong changes the absorbance is found to be nearly independent of strain. Our results provide new guidance for the understanding and design of optomechanical systems based on carbon nanotubes.
The thermoelectric efficiency of semiconductors is usually considered in the ohmic electronic transport regime, which is achieved through high doping. Here we consider the opposite regime of low doping where the current-voltage characteristics are no
nlinear and dominated by space-charge-limited transport. We show that in this regime, the thermoelectric efficiency can be described by a single figure of merit, in analogy with the ohmic case. Efficiencies for bulk, thin film, and nanowire materials are discussed, and it is proposed that nanowires are the most promising to take advantage of space-charge-limited transport for thermoelectrics.
The electronic properties of heterojunction electron gases formed in GaN/AlGaN core/shell nanowires with hexagonal and triangular cross-sections are studied theoretically. We show that at nanoscale dimensions, the non-polar hexagonal system exhibits
degenerate quasi-one-dimensional electron gases at the hexagon corners, which transition to a core-centered electron gas at lower doping. In contrast, polar triangular core/shell nanowires show either a non-degenerate electron gas on the polar face or a single quasi-one-dimensional electron gas at the corner opposite the polar face, depending on the termination of the polar face. More generally, our results indicate that electron gases in closed nanoscale systems are qualitatively different from their bulk counterparts.
The temperature distribution in nanowires due to Joule heating is studied analytically using a continuum model and a Greens function approach. We show that the temperatures reached in nanowires can be much lower than that predicted by bulk models of
Joule heating, due to heat loss at the nanowire surface that is important at nanoscopic dimensions, even when the thermal conductivity of the environment is relatively low. In addition, we find that the maximum temperature in the nanowire scales weakly with length, in contrast to the bulk system. A simple criterion is presented to assess the importance of these effects. The results have implications for the experimental measurements of nanowire thermal properties, for thermoelectric applications, and for controlling thermal effects in nanowire electronic devices.
The current-voltage characteristics of thin wires are often observed to be nonlinear, and this behavior has been ascribed to Schottky barriers at the contacts. We present electronic transport measurements on GaN nanorods and demonstrate that the nonl
inear behavior originates instead from space-charge-limited current. A theory of space-charge-limited current in thin wires corroborates the experiments, and shows that poor screening in high aspect ratio materials leads to a dramatic enhancement of space-charge limited current, resulting in new scaling in terms of the aspect ratio.
