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A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional systems. The drift and diffusion coefficients of the ROM are inferred from state observations by solving appropriate least-squares problems. The closeness of the ROM obtained by the presented approach to the intrusive ROM obtained by the proper orthogonal decomposition (POD) method is investigated. Two generalisations of the snapshot-based dominant subspace construction to the stochastic case are presented. Numerical experiments are provided to compare the developed approach to POD.

We use two-color pump-probe spectroscopy to study Rydberg excitons in Cu$_2$O in the presence of free carriers injected by above-band-gap excitation. Already at plasma densities $\rho_\text{eh}$ below one hundredth electron-hole pair per \textmu m$^{3}$, the Rydberg exciton absorption lines are bleached while their energies remain constant, until they finally disappear, starting from the highest observed principal quantum number $n_\text{max}$. As confirmed by calculations, the band gap is reduced by many-particle effects caused by free carriers scaling as $\rho_\text{eh}^{1/2}$. An exciton line looses oscillator strength when the band edge approaches the exciton energy vanishing completely at the crossing point. We quantitatively describe this plasma blockade by introducing an effective Bohr radius that determines the energy distance to the shifted band edge. In combination with the negligible associated decoherence this opens the possibility to control the Rydberg exciton absorption through the plasma-induced band gap modulation.

Rydberg atoms have attracted considerable interest due to their huge interaction among each other and with external fields. They demonstrate characteristic scaling laws in dependence on the principal quantum number $n$ for features such as the magnetic field for level crossing. While bearing striking similarities to Rydberg atoms, fundamentally new insights may be obtained for Rydberg excitons, as the crystal environment gives easy optical access to many states within an exciton multiplet. Here we study experimentally and theoretically the scaling of several characteristic parameters of Rydberg excitons with $n$. From absorption spectra in magnetic field we find for the first crossing of levels with adjacent principal quantum numbers a $B_r \propto n^{-4}$ dependence of the resonance field strength, $B_r$, due to the dominant paramagnetic term unlike in the atomic case where the diamagnetic contribution is decisive. By contrast, in electric field we find scaling laws just like for Rydberg atoms. The resonance electric field strength scales as $E_r \propto n^{-5}$. We observe anticrossings of the states belonging to multiplets with different principal quantum numbers. The energy splittings at the avoided crossings scale as $n^{-4}$ which we relate to the crystal specific deviation of the exciton Hamiltonian from the hydrogen model. We observe the exciton polarizability in the electric field to scale as $n^7$. In magnetic field the crossover field strength from a hydrogen-like exciton to a magnetoexciton dominated by electron and hole Landau level quantization scales as $n^{-3}$. The ionization voltages demonstrate a $n^{-4}$ scaling as for atoms. The width of the absorption lines remains constant before dissociation for high enough $n$, while for small $n \lesssim 12$ an exponential increase with the field is found. These results are in excellent agreement with theoretical calculations., Comment: 16 pages, 13 figures

We have used high resolution transmission spectroscopy to study the exciton level spectrum in Cu$_2$O subject to a longitudinal external electric field, i.e., in the geometry where the transmitted light is propagating along the field direction. Different experimental configurations given by the field orientation relative to the crystal and the light polarization have been explored. We focus on the range of small principal quantum numbers $n \leq 7$. The number of exciton states belonging to a particular principal quantum number increases with $n$, leading to an enhanced complexity of the spectra. Still, in particular for $n = 3 \ldots 5$ a spectral separation of the different lines is feasible and identification as well as assignment of the dominant state character are possible. We find a strong dependence of the spectra on the chosen light propagation direction and polarization configuration, reflecting the inadequacy of the hydrogen model for describing the excitons. With increasing the field excitonic states with different parity become mixed, leading to optical activation of states that are dark in zero field. As compared with atoms, due to the reduced Rydberg energy states with different $n$ can be brought into resonance in the accessible electric field strength range. When this occurs, we observe mostly crossing of levels within the experimental accuracy showing that the electron and hole motion remains regular. The observed features are well described by detailed calculations accounting for the spin-orbit coupling, the cubic anisotropy effects, and the symmetry-imposed optical selection rules., Comment: 16 pages, 13 figures

The last century has seen enormous progress in our understanding of the Universe. We know the life cycles of stars, the structure of galaxies, the remnants of the big bang, and have a general understanding of how the Universe evolved. We have come remarkably far using electromagnetic radiation as our tool for observing the Universe. However, gravity is the engine behind many of the processes in the Universe, and much of its action is dark. Opening a gravitational window on the Universe will let us go further than any alternative. Gravity has its own messenger: Gravitational waves, ripples in the fabric of spacetime. They travel essentially undisturbed and let us peer deep into the formation of the first seed black holes, exploring redshifts as large as z ~ 20, prior to the epoch of cosmic re-ionisation. Exquisite and unprecedented measurements of black hole masses and spins will make it possible to trace the history of black holes across all stages of galaxy evolution, and at the same time constrain any deviation from the Kerr metric of General Relativity. eLISA will be the first ever mission to study the entire Universe with gravitational waves. eLISA is an all-sky monitor and will offer a wide view of a dynamic cosmos using gravitational waves as new and unique messengers to unveil The Gravitational Universe. It provides the closest ever view of the early processes at TeV energies, has guaranteed sources in the form of verification binaries in the Milky Way, and can probe the entire Universe, from its smallest scales around singularities and black holes, all the way to cosmological dimensions., Comment: 20 pages; submitted to the European Space Agency on May 24th, 2013 for the L2/L3 selection of ESA's Cosmic Vision program

In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction in terms of the component proportions p and the total number of components N. These formulae correctly identify both the percolation limits and also the emergent power law behaviour between the percolation limits and show the interplay between the size of the network and the deviation of the proportion from the critical value of p = 1/2. The results compare excellently with a large number of numerical simulations.

We consider whether stellar collisions can explain the observed depletion of red giants in the Galactic center. We model the stellar population with two different IMFs: 1) the Miller-Scalo and 2) a much flatter IMF. In the former case, low-mass main-sequence stars dominate the population, and collisions are unable to remove red giants out to 0.4 pc although brighter red giants much closer in may be depleted via collisions with stellar-mass black holes. For a much flatter IMF, the stellar population is dominated by compact remnants (i.e. black holes, white dwarfs and neutron stars). The most common collisions are then those between main-sequence stars and compact remnants. Such encounters are likely to destroy the main-sequence stars and thus prevent their evolution into red giants. In this way, the red-giant population could be depleted out to 0.4 pc matching observations. If this is the case, it implies the Galactic center contains a much larger population of stellar-mass black holes than would be expected from a regular IMF. This may in turn have implications for the formation and growth of the central supermassive black hole., Comment: To appear in "The Galactic Center: A Window on the Nuclear Environment of Disk Galaxies", ed. Mark Morris, Daniel Q. Wang and Feng Yuan

A near-field scanning optical microscope is used to locally induce photocurrent in a graphene transistor with high spatial resolution. By analyzing the spatially resolved photo-response, we find that in the n-type conduction regime a p-n-p structure forms along the graphene device due to the doping of the graphene by the metal contacts. The modification of the electronic structure is not limited only underneath the metal electrodes, but extends 0.2-0.3 um into the graphene channel. The asymmetric conduction behavior of electrons and holes that is commonly observed in graphene transistors is discussed in light of the potential profiles obtained from this photocurrent imaging approach. Furthermore, we show that photocurrent imaging can be used to probe single- / multi-layer graphene interfaces.

First we present a recently developed 3D chemodynamical code for galaxy evolution from the K**2 collaboration. It follows the evolution of all components of a galaxy such as dark matter, stars, molecular clouds and diffuse interstellar matter (ISM). Dark matter and stars are treated as collisionless N-body systems. The ISM is numerically described by a smoothed particle hydrodynamics (SPH) approach for the diffuse (hot) gas and a sticky particle scheme for the (cool) molecular clouds. Physical processs such as star formation, stellar death or condensation and evaporation processes of clouds interacting with the ISM are described locally. An example application of the model to a star forming dwarf galaxy will be shown for comparison with other codes. Secondly we will discuss new kinds of exotic chemodynamical processes, as they occur in dense gas-star systems in galactic nuclei, such as non-standard ``drag''-force interactions, destructive and gas producing stellar collisions. Their implementation in 1D dynamical models of galactic nuclei is presented. Future prospects to generalize these to 3D are work in progress and will be discussed., Comment: 4 pages, 4 figures, "The 5th Workshop on Galactic Chemodynamics" - Swinburne University (9-11 July 2003). To be published in the Publications of the Astronomical Society of Australia in 2004 (B.K. Gibson and D. Kawata, eds.). Accepted version, minor changes relative to original

This is a summary paper of MODEST-2, a workshop held at the Astronomical Institute ``Anton Pannekoek'' in Amsterdam, 16-17 December 2002. MODEST is a loose collaboration of people interested in MOdelling DEnse STellar systems, particularly those interested in modelling these systems using all the available physics (stellar dynamics, stellar evolution, hydrodynamics and the interplay between the three) by defining interfaces between different codes. In this paper, we summarize 1) the main advances in this endeavour since MODEST-1; 2) the main science goals which can be and should be addressed by these types of simulations; and 3) the most pressing theoretical and modelling advances that we identified., Comment: Accepted by New Astronomy

We have fabricated air-stable n-type, ambipolar carbon nanotube field effect transistors (CNFETs), and used them in nanoscale memory cells. N-type transistors are achieved by annealing of nanotubes in hydrogen gas and contacting them by cobalt electrodes. Scanning gate microscopy reveals that the bulk response of these devices is similar to gold-contacted p-CNFETs, confirming that Schottky barrier formation at the contact interface determines accessibility of electron and hole transport regimes. The transfer characteristics and Coulomb Blockade (CB) spectroscopy in ambipolar devices show strongly enhanced gate coupling, most likely due to reduction of defect density at the silicon/silicon-dioxide interface during hydrogen anneal. The CB data in the ``on''-state indicates that these CNFETs are nearly ballistic conductors at high electrostatic doping. Due to their nanoscale capacitance, CNFETs are extremely sensitive to presence of individual charge around the channel. We demonstrate that this property can be harnessed to construct data storage elements that operate at the few-electron level., Comment: 6 pages text, 3 figures and 1 table of content graphic; available as NanoLetters ASAP article on the web

We use conducting-tip atomic force microscopy (AFM) to measure local electronic properties of single wall carbon nanotube (SWNT) circuits on insulating substrates. When a voltage is applied to the tip and AFM feedback is used to position the tip, images formed from the tip-sample tunnel current have single tube resolution (near 1 nm diameter), more than an order of magnitude better than simultaneously acquired topographic AFM images. By finding points where the tip-sample current is zero, it is possible to measure the electrochemical potential within the circuit, again with nanometer resolution. Such measurements provide compelling evidence that nanotubes within a bundle have only weak electronic coupling. Finally the AFM tip is used as a local electrostatic gate, and the gating action can be correlated with the structure of the SWNT bundle sample. This technique should be useful for a broad range of circuits containing SWNTs and other molecules., Comment: to appear in Physical Review B, Rapid Communications