On the rational subset problem for groups

We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN extensions with finite associated subgroups. We provide a simple proof of a result of Grunschlag showing that the decidability of this problem is a virtual property. We prove further that the problem is decidable for a direct product of a group G with a monoid M if and only if membership is uniformly decidable for G-automata subsets of M. It follows that a direct product of a free group with any abelian group or commutative monoid has decidable rational subset membership.Comment: 19 page

Magneto-transport through graphene nano-ribbons

We investigate magneto-transport through graphene nano-ribbons as a function of gate and bias voltage, and temperature. We find that a magnetic field systematically leads to an increase of the conductance on a scale of a few tesla. This phenomenon is accompanied by a decrease in the energy scales associated to charging effects, and to hopping processes probed by temperature-dependent measurements. All the observations can be interpreted consistently in terms of strong-localization effects caused by the large disorder present, and exclude that the insulating state observed in nano-ribbons can be explained solely in terms of a true gap between valence and conduction band.Comment: 4 pages, 5 figure

Darboux Transformations, Infinitesimal Symmetries and Conservation Laws for Nonlocal Two-Dimensional Toda Lattice

The technique of Darboux transformation is applied to nonlocal partner of two-dimensional periodic A_{n-1} Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear systems with quantized spectral parameter. The generalization of the Darboux transformation technique on linear equations of such a kind is given. The connections between the solutions of overdetermined linear systems and their expansions in series at singular points neighborhood are presented. The solutions of the nonlocal Toda lattice and infinite hierarchies of the infinitesimal symmetries and conservation laws are obtained.Comment: 12 pages, infinitesimal symmetries and conservation laws are adde

Fluid structure in the immediate vicinity of an equilibrium three-phase contact line and assessment of disjoining pressure models using density functional theory

We examine the nanoscale behavior of an equilibrium three-phase contact line in the presence of long-ranged intermolecular forces by employing a statistical mechanics of fluids approach, namely density functional theory (DFT) together with fundamental measure theory (FMT). This enables us to evaluate the predictive quality of effective Hamiltonian models in the vicinity of the contact line. In particular, we compare the results for mean field effective Hamiltonians with disjoining pressures defined through (I) the adsorption isotherm for a planar liquid film, and (II) the normal force balance at the contact line. We find that the height profile obtained using (I) shows good agreement with the adsorption film thickness of the DFT-FMT equilibrium density profile in terms of maximal curvature and the behavior at large film heights. In contrast, we observe that while the height profile obtained by using (II) satisfies basic sum rules, it shows little agreement with the adsorption film thickness of the DFT results. The results are verified for contact angles of 20, 40 and 60 degrees

Improved and Perfect Actions in Discrete Gravity

We consider the notion of improved and perfect actions within Regge calculus. These actions are constructed in such a way that they - although being defined on a triangulation - reproduce the continuum dynamics exactly, and therefore capture the gauge symmetries of General Relativity. We construct the perfect action in three dimensions with cosmological constant, and in four dimensions for one simplex. We conclude with a discussion about Regge Calculus with curved simplices, which arises naturally in this context.Comment: 28 pages, 2 figure

Faraday Instability in a Surface-Frozen Liquid

Faraday surface instability measurements of the critical acceleration, a_c, and wavenumber, k_c, for standing surface waves on a tetracosanol (C_24H_50) melt exhibit abrupt changes at T_s=54degC above the bulk freezing temperature. The measured variations of a_c and k_c vs. temperature and driving frequency are accounted for quantitatively by a hydrodynamic model, revealing a change from a free-slip surface flow, generic for a free liquid surface (T>T_s), to a surface-pinned, no-slip flow, characteristic of a flow near a wetted solid wall (T < T_s). The change at T_s is traced to the onset of surface freezing, where the steep velocity gradient in the surface-pinned flow significantly increases the viscous dissipation near the surface.Comment: 4 pages, 3 figures. Physical Review Letters (in press

Propulsion Powertrain Real-Time Simulation Using Hardware-in-the-Loop (HIL) for Aircraft Electric Propulsion System

It is essential to design a propulsion powertrain real-time simulator using the hardware-in-the-loop (HIL) system that emulates an electrified aircraft propulsion (EAP) systems power grid. This simulator would enable us to facilitate in-depth understanding of the system principles, to validate system model analysis and performance prediction, and to demonstrate the proof-of-concept of the EAP electrical system. This paper describes how subscale electrical machines with their controllers can mimic the power components in an EAP powertrain. In particular, three powertrain emulations are presented to mimic 1) a gas turbo-=shaft engine driving a generator, consisting of two permanent magnet (PM) motors with brushless motor drives, coupled by a shaft, 2) a motor driving a propulsive fan, and 3) a turbo-shaft engine driven fan (turbofan engine) operation. As a first step towards the demonstration, experimental dynamic characterization of the two motor drive systems, coupled by a mechanical shaft, were performed. The previously developed analytical motor models1 were then replaced with the experimental motor models to perform the real-time demonstration in the predefined flight path profiles. This technique can convert the plain motor system into a unique EAP power grid emulator that enables rapid analysis and real-time simulation performance using hardware-in-the-loop (HIL)

Multiscale Analysis of Discrete Nonlinear Evolution Equations

The method of multiscale analysis is constructed for dicrete systems of evolution equations for which the problem is that of the far behavior of an input boundary datum. Discrete slow space variables are introduced in a general setting and the related finite differences are constructed. The method is applied to a series of representative examples: the Toda lattice, the nonlinear Klein-Gordon chain, the Takeno system and a discrete version of the Benjamin-Bona-Mahoney equation. Among the resulting limit models we find a discrete nonlinear Schroedinger equation (with reversed space-time), a 3-wave resonant interaction system and a discrete modified Volterra model.Comment: published in J. Phys. A : Math. Gen. 32 (1999) 927-94

Whitham method for Benjamin-Ono-Burgers equation and dispersive shocks in internal waves in deep fluid

The Whitham modulation equations for the parameters of a periodic solution are derived using the generalized Lagrangian approach for the case of damped Benjamin-Ono equation. The structure of the dispersive shock in internal wave in deep water is considered by this method.Comment: 8 pages, 4 figure

The Dust Content of Galaxy Clusters

We report on the detection of reddening toward z ~ 0.2 galaxy clusters. This is measured by correlating the Sloan Digital Sky Survey cluster and quasar catalogs and by comparing the photometric and spectroscopic properties of quasars behind the clusters to those in the field. We find mean E(B-V) values of a few times 10^-3 mag for sight lines passing ~Mpc from the clusters' center. The reddening curve is typical of dust but cannot be used to distinguish between different dust types. The radial dependence of the extinction is shallow near the cluster center suggesting that most of the detected dust lies at the outskirts of the clusters. Gravitational magnification of background z ~ 1.7 sources seen on Mpc (projected) scales around the clusters is found to be of order a few per cent, in qualitative agreement with theoretical predictions. Contamination by different spectral properties of the lensed quasar population is unlikely but cannot be excluded.Comment: 4 pages, 3 figure