Automated Engineering Design (AED); An approach to automated documentation

The automated engineering design (AED) is reviewed, consisting of a high level systems programming language, a series of modular precoded subroutines, and a set of powerful software machine tools that effectively automate the production and design of new languages. AED is used primarily for development of problem and user-oriented languages. Software production phases are diagramed, and factors which inhibit effective documentation are evaluated

Band-structure topologies of graphene: spin-orbit coupling effects from first principles

The electronic band structure of graphene in the presence of spin-orbit coupling and transverse electric field is investigated from first principles using the linearized augmented plane-wave method. The spin-orbit coupling opens a gap at the $K(K')$-point of the magnitude of 24 $\mu$eV (0.28 K). This intrinsic splitting comes 96% from the usually neglected $d$ and higher orbitals. The electric field induces an additional (extrinsic) Bychkov-Rashba-type splitting of 10 $\mu$eV (0.11 K) per V/nm, coming from the $\sigma$-$\pi$ mixing. A 'mini-ripple' configuration with every other atom is shifted out of the sheet by less than 1% differs little from the intrinsic case.Comment: 4 pages, 4 figure

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense to be precised. In a first part, we generalize the Hausdorff dimension by defining a family of bi-Lipschitz invariants, called critical parameters, that measure largeness for infinite-dimensional metric spaces. Basic properties of these invariants are given, and they are estimated for a naturel set of spaces generalizing the usual Hilbert cube. In a second part, we estimate the value of these new invariants in the case of some Wasserstein spaces, as well as the dynamical complexity of push-forward maps. The lower bounds rely on several embedding results; for example we provide bi-Lipschitz embeddings of all powers of any space inside its Wasserstein space, with uniform bound and we prove that the Wasserstein space of a d-manifold has "power-exponential" critical parameter equal to d.Comment: v2 Largely expanded version, as reflected by the change of title; all part I on generalized Hausdorff dimension is new, as well as the embedding of Hilbert cubes into Wasserstein spaces. v3 modified according to the referee final remarks ; to appear in Journal of Topology and Analysi

Shot Noise in Graphene

We report measurements of current noise in single- and multi-layer graphene devices. In four single-layer devices, including a p-n junction, the Fano factor remains constant to within +/-10% upon varying carrier type and density, and averages between 0.35 and 0.38. The Fano factor in a multi-layer device is found to decrease from a maximal value of 0.33 at the charge-neutrality point to 0.25 at high carrier density. These results are compared to theoretical predictions for shot noise in ballistic and disordered graphene.Comment: related papers available at http://marcuslab.harvard.ed

Distinct Signatures For Coulomb Blockade and Aharonov-Bohm Interference in Electronic Fabry-Perot Interferometers

Two distinct types of magnetoresistance oscillations are observed in two electronic Fabry-Perot interferometers of different sizes in the integer quantum Hall regime. Measuring these oscillations as a function of magnetic field and gate voltages, we observe three signatures that distinguish the two types. The oscillations observed in a 2.0 square micron device are understood to arise from the Coulomb blockade mechanism, and those observed in an 18 square micron device from the Aharonov-Bohm mechanism. This work clarifies, provides ways to distinguish, and demonstrates control over, these distinct physical origins of resistance oscillations seen in electronic Fabry-Perot interferometers.Comment: related papers at http://marcuslab.harvard.ed

Tunable Noise Cross-Correlations in a Double Quantum Dot

We report measurements of the cross-correlation between current noise fluctuations in two capacitively coupled quantum dots in the Coulomb blockade regime. The sign of the cross-spectral density is found to be tunable by gate voltage and source-drain bias. Good agreement is found with a model of sequential tunneling through the dots in the presence of inter-dot capacitive coupling.Comment: related papers available at http://marcuslab.harvard.ed

Evidence for Steep Luminosity Functions in Clusters of Galaxies

Luminosity Functions have been obtained for very faint dwarf galaxies in the cores of four rich clusters of galaxies (Abell 2052, 2107, 2199 and 2666). It is found that the luminosity function of dwarf galaxies rises very steeply in these clusters, with a power-law slope of \alpha -2.2 (down to absolute limiting magnitudes M_I = -13 and M_B = -11 for H_0 = 75 km/s/Mpc). A steepening of the luminosity function at faint magnitudes may in fact be a common feature of both cluster and field populations. Such a result may explain the observed excess counts of faint, intermediate redshift galaxies in the Universe, without resorting to more exotic phenomena. An alternate explanation is that star formation in dwarf galaxies is less affected by gas loss in the richest clusters, because of the dense, hot intracluster medium found in such environments.Comment: 15 pages, 2 figures (attached). Uuencoded compressed Postscript tarfile. Accepted by the Astrophysical Journal