Moduli spaces of coherent systems of small slope on algebraic curves

Let $C$ be an algebraic curve of genus $g\ge2$. A coherent system on $C$ consists of a pair $(E,V)$, where $E$ is an algebraic vector bundle over $C$ of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of the space of sections of $E$. The stability of the coherent system depends on a parameter $\alpha$. We study the geometry of the moduli space of coherent systems for $0<d\le2n$. We show that these spaces are irreducible whenever they are non-empty and obtain necessary and sufficient conditions for non-emptiness.Comment: 27 pages; minor presentational changes and typographical correction

Dynamics of active membranes with internal noise

We study the time-dependent height fluctuations of an active membrane containing energy-dissipating pumps that drive the membrane out of equilibrium. Unlike previous investigations based on models that neglect either curvature couplings or random fluctuations in pump activities, our formulation explores two new models that take both of these effects into account. In the first model, the magnitude of the nonequilibrium forces generated by the pumps is allowed to fluctuate temporally. In the second model, the pumps are allowed to switch between "on" and "off" states. We compute the mean squared displacement of a membrane point for both models, and show that they exhibit distinct dynamical behaviors from previous models, and in particular, a superdiffusive regime specifically arising from the shot noise.Comment: 7 pages, 4 figure

Modelling and Nonlinear Model Predictive Control of a Twin Screw Feeder

In this work, a dynamic model of a twin screw feeder, for continuous tablet manufacturing, has been developed. In particular, a First Order Plus Dead Time (FOPDT) model has been suggested. The delayed dynamics depends on operating conditions, equipment design and physical properties of the bulk solid. Model parameters are estimated by fitting the model to experimental data. Due to the nonlinear input-output relationships and the time delays involved, a Nonlinear Model Predictive Control (NMPC) is investigated to maintain an accurate mass flow rate, with the ultimate goal to improve product homogeneity in an inherently complex process. The performance of the designed control system is found to be satisfactory in a wide operating range and its potential use in a continuous manufacturing process is worth being investigated in the future

Ionized and neutral gas in the peculiar star/cluster complex in NGC 6946

The characteristics of ionized and HI gas in the peculiar star/cluster complex in NGC 6946, obtained with the 6-m telescope (BTA) SAO RAS, the Gemini North telescope, and the Westerbork Synthesis Radio Telescope (WSRT), are presented. The complex is unusual as hosting a super star cluster, the most massive known in an apparently non-interacting giant galaxy. It contains a number of smaller clusters and is bordered by a sharp C-shaped rim. We found that the complex is additionally unusual in having peculiar gas kinematics. The velocity field of the ionized gas reveals a deep oval minimum, ~300 pc in size, centered 7" east of the supercluster. The Vr of the ionized gas in the dip center is 100 km/s lower than in its surroundings, and emission lines within the dip appear to be shock excited. This dip is near the center of an HI hole and a semi-ring of HII regions. The HI (and less certainly, HII) velocity fields reveal expansion, with the velocity reaching ~30 km/s at a distance about 300 pc from the center of expansion, which is near the deep minimum position. The super star cluster is at the western rim of the minimum. The sharp western rim of the whole complex is plausibly a manifestation of a regular dust arc along the complex edge. Different hypotheses about the complex and the Vr depression origins are discussed, including a HVC/dark mini-halo impact, a BCD galaxy merging, and a gas outflow due to release of energy from the supercluster stars.Comment: MN RAS, accepte

Negative differential resistance in molecular junctions: application to graphene ribbon junctions

Using self-consistent calculations based on Non-Equilibrium Green's Function (NEGF) formalism, the origin of negative differential resistance (NDR) in molecular junctions and quantum wires is investigated. Coupling of the molecule to electrodes becomes asymmetric at high bias due to asymmetry between its highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels. This causes appearance of an asymmetric potential profile due to a depletion of charge and reduction of screening near the source electrode. With increasing bias, this sharp potential drop leads to an enhanced localization of the HOMO and LUMO states in different parts of the system. The reduction in overlap, caused by localization, results in a significant reduction in the transmission coefficient and current with increasing bias. An atomic chain connected to two Graphene ribbons was investigated to illustrate these effects. For a chain substituting a molecule, an even-odd effect is also observed in the NDR characteristics.Comment: 8 pages, 8 figure