Large distance asymptotic behavior of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain

Using its multiple integral representation, we compute the large distance asymptotic behavior of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain in the massless regime.Comment: LPENSL-TH-10, 8 page

Graded integral closures

It is investigated how graded variants of integral and complete integral closures behave under coarsening functors and under formation of group algebras.Comment: to appear in Beitr\"age Algebra Geom.; typos correcte

Pattern formation in binary fluid mixtures induced by short-range competing interactions

Molecular dynamics simulations and integral equation calculations of a simple equimolar mixture of diatomic molecules and monomers interacting via attractive and repulsive short-range potentials show the existence of pattern formation (microheterogeneity), mostly due to depletion forces away from the demixing region. Effective site-site potentials extracted from the pair correlation functions using an inverse Monte Carlo approach and an integral equation inversion procedure exhibit the features characteristic of a short-range attractive and long-range repulsive potential. When charges are incorporated into the model, this becomes a coarse grained representation of a room temperature ionic liquid, and as expected, intermediate range order becomes more pronounced and stable

On the inconsistency between the estimates of cosmic star formation rate and stellar mass density of high redshift galaxies

There are mainly two different approaches to measure the cosmic star formation history: direct star formation rate density (SFRD) and stellar mass density rhostar as functions of redshift. Compilations of current observations seem to show a disparity in the two quantities, in the sense that the integral of SFRD is higher than the observed rhostar (after considering gas recycling). Using cosmological smoothed particle hydrodynamics simulations based on the concordance Lambda cold dark matter model, we show that the two quantities become more consistent with each other when we consider the observed galaxy mass limit. The comparison between simulations and (dust corrected) observed cosmic SFRD shows a good agreement, while the observed rhostar is significantly lower than the simulation results. This can be reconciled if the current high-$z$ galaxy surveys are missing faint low-mass galaxies due to their flux limit. Our simulated GSMFs have steep low-mass end slopes of alpha 3, and when these numerous low-mass galaxies are included, the total rhostar matches with the integral of SFRD.Comment: 6 pages, 1 table, and 2 figures, accepted for publication in MNRA

Bearing-Based Formation Maneuvering

This paper studies the problem of multi-agent formation maneuver control where both of the centroid and scale of a formation are required to track given velocity references while maintaining the formation shape. Unlike the conventional approaches where the target formation is defined by inter-neighbor relative positions or distances, we propose a bearing-based approach where the target formation is defined by inter-neighbor bearings. Due to the invariance of the bearings, the bearing-based approach provides a natural solution to formation scale control. We assume the dynamics of each agent as a single integrator and propose a globally stable proportional-integral formation maneuver control law. It is shown that at least two leaders are required to collaborate in order to control the centroid and scale of the formation whereas the followers are not required to have access to any global information, such as the velocities of the leaders.Comment: To appear in the 2015 IEEE Multi-Conference on Systems and Control (MSC2015); this is the final versio