Scaling of the Thue-Morse diffraction measure

We revisit the well-known and much studied Riesz product representation of the Thue-Morse diffraction measure, which is also the maximal spectral measure for the corresponding dynamical spectrum in the complement of the pure point part. The known scaling relations are summarised, and some new findings are explained

Spinorial cohomology and maximally supersymmetric theories

Fields in supersymmetric gauge theories may be seen as elements in a spinorial cohomology. We elaborate on this subject, specialising to maximally supersymmetric theories, where the superspace Bianchi identities, after suitable conventional constraints are imposed, put the theories on shell. In these cases, the spinorial cohomologies describe in a unified manner gauge transformations, fields and possible deformations of the models, e.g. string-related corrections in an alpha' expansion. Explicit cohomologies are calculated for super-Yang-Mills theory in D=10, for the N=(2,0) tensor multiplet in D=6 and for supergravity in D=11, in the latter case from the point of view of both the super-vielbein and the super-3-form potential. The techniques may shed light on some questions concerning the alpha'-corrected effective theories, and result in better understanding of the role of the 3-form in D=11 supergravity.Comment: 23 pp, plain tex. v2: Minor changes, references adde

Rotating binary Bose-Einstein condensates and vortex clusters in quantum droplets

Quantum droplets may form out of a gaseous Bose-Einstein condensate, stabilized by quantum fluctuations beyond mean field. We show that multiple singly-quantized vortices may form in these droplets at moderate angular momenta in two dimensions. Droplets carrying these precursors of an Abrikosov lattice remain self-bound for certain timescales after switching off an initial harmonic confinement. Furthermore, we examine how these vortex-carrying droplets can be formed in a more pertubation-resistant setting, by starting from a rotating binary Bose-Einstein condensate and inducing a metastable persistent current via a non-monotonic trapping potential.Comment: 5 page, 4 figure

The interaction between the Moon and the solar wind

We study the interaction between the Moon and the solar wind using a three-dimensional hybrid plasma solver. The proton fluxes and electromagnetical fields are presented for typical solar wind conditions with different magnetic field directions. We find two different wake structures for an interplanetary magnetic field that is perpendicular to the solar wind flow, and for one that is parallell to the flow. The wake for intermediate magnetic field directions will be a mix of these two extreme conditions. Several features are consistent with a fluid interaction, e.g., the presence of a rarefaction cone, and an increased magnetic field in the wake. There are however several kinetic features of the interaction. We find kinks in the magnetic field at the wake boundary. There are also density and magnetic field variations in the far wake, maybe from an ion beam instability related to the wake refill. The results are compared to observations by the WIND spacecraft during a wake crossing. The model magnetic field and ion velocities are in agreement with the measurements. The density and the electron temperature in the central wake are not as well captured by the model, probably from the lack of electron physics in the hybrid model.Comment: Accepted for publication in Earth, Planets and Spac

Uni-directional polymerization leading to homochirality in the RNA world

The differences between uni-directional and bi-directional polymerization are considered. The uni-directional case is discussed in the framework of the RNA world. Similar to earlier models of this type, where polymerization was assumed to proceed in a bi-directional fashion (presumed to be relevant to peptide nucleic acids), left-handed and right-handed monomers are produced via an autocatalysis from an achiral substrate. The details of the bifurcation from a racemic solution to a homochiral state of either handedness is shown to be remarkably independent of whether the polymerization in uni-directional or bi-directional. Slightly larger differences are seen when dissociation is allowed and the dissociation fragments are being recycled into the achiral substrate.Comment: 9 pages, 4 figures, submitted to Astrobiolog

Intermittent Connectivity for Exploration in Communication-Constrained Multi-Agent Systems

Motivated by exploration of communication-constrained underground environments using robot teams, we study the problem of planning for intermittent connectivity in multi-agent systems. We propose a novel concept of information-consistency to handle situations where the plan is not initially known by all agents, and suggest an integer linear program for synthesizing information-consistent plans that also achieve auxiliary goals. Furthermore, inspired by network flow problems we propose a novel way to pose connectivity constraints that scales much better than previous methods. In the second part of the paper we apply these results in an exploration setting, and propose a clustering method that separates a large exploration problem into smaller problems that can be solved independently. We demonstrate how the resulting exploration algorithm is able to coordinate a team of ten agents to explore a large environment

Temperature dependence of the Laminar burning velocity of methanol flames

To better understand and predict the combustion behavior of methanol in engines, sound knowledge of the effect of the pressure, unburned mixture temperature, and composition on the laminar burning velocity is required. Because many of the existing experimental data for this property are compromised by the effects of flame stretch and instabilities, this study was aimed at obtaining new, accurate data for the laminar burning velocity of methanol–air mixtures. Non-stretched flames were stabilized on a perforated plate burner at 1 atm. The heat flux method was used to determine burning velocities under conditions when the net heat loss from the flame to the burner is zero. Equivalence ratios and initial temperatures of the unburned mixture ranged from 0.7 to 1.5 and from 298 to 358 K, respectively. Uncertainties of the measurements were analyzed and assessed experimentally. The overall accuracy of the burning velocities was estimated to be better than ±1 cm/s. In lean conditions, the correspondence with recent literature data was very good, whereas for rich mixtures, the deviation was larger. The present study supports the higher burning velocities at rich conditions, as predicted by several chemical kinetic mechanisms. The effects of the unburned mixture temperature on the laminar burning velocity of methanol were analyzed using the correlation uL = uL0(Tu/Tu0)α. Several published expressions for the variation of the power exponent α with the equivalence ratio were compared against the present experimental results and calculations using a detailed oxidation kinetic model. Whereas most existing expressions assume a linear decrease of α with an increasing equivalence ratio, the modeling results produce a minimum in α for slightly rich mixtures. Experimental determination of α was only possible for lean to stoichiometric mixtures and a single data point at equivalence ratio= 1.5. For these conditions, the measurement data agree with the modeling results

Lifting Grobner bases from the exterior algebra

In the article "Non-commutative Grobner bases for commutative algebras", Eisenbud-Peeva-Sturmfels proved a number of results regarding Grobner bases and initial ideals of those ideals in the free associative algebra which contain the commutator ideal. We prove similar results for ideals which contains the anti-commutator ideal (the defining ideal of the exterior algebra). We define one notion of generic initial ideals in the free assoicative algebra, and show that gin's of ideals containing the commutator ideal, or the anti-commutator ideal, are finitely generated.Comment: 6 pages, LaTeX2