Less than 50% sublattice polarization in an insulating S=3/2 kagome' antiferromagnet at low T

We have found weak long range antiferromagnetic order in the quasi-two-dimensional insulating oxide $KCr_3(OD)_6(SO_4)_2$ which contains Cr$^{3+}$ S=3/2 ions on a kagom\'{e} lattice. In a sample with $\approx$ 76% occupancy of the chromium sites the ordered moment is 1.1(3)$\mu_B$ per chromium ion which is only one third of the N\'{e}el value $g\mu_BS=3\mu_B$. The magnetic unit cell equals the chemical unit cell, a situation which is favored by inter-plane interactions. Gapless quantum spin-fluctuations ($\Delta/k_B >$T_N$= 1.6K are the dominant contribution to the spin correlation function,$S(Q,\omega)$ in the ordered phase.Comment: 18 pages, RevTex/Latex, with 6 figure

Corresponding States of Structural Glass Formers

The variation with respect to temperature T of transport properties of 58 fragile structural glass forming liquids (68 data sets in total) are analyzed and shown to exhibit a remarkable degree of universality. In particular, super-Arrhenius behaviors of all super-cooled liquids appear to collapse to one parabola for which there is no singular behavior at any finite temperature. This behavior is bounded by an onset temperature To above which liquid transport has a much weaker temperature dependence. A similar collapse is also demonstrated, over the smaller available range, for existing numerical simulation data.Comment: 6 pages, 2 figures. Updated References, Table Values, Submitted for Publicatio

Ectropy of diversity measures for populations in Euclidean space

Measures to evaluate the diversity of a set of points (population) in Euclidean space play an important role in a variety of areas of science and engineering. Well-known measures are often used without a clear insight into their quality and many of them do not appropriately penalize populations with a few distant groups of collocated or closely located points. To the best of our knowledge, there is a lack of rigorous criteria to compare diversity measures and help select an appropriate one. In this work we define a mathematical notion of ectropy for classifying diversity measures in terms of the extent to which they tend to penalize point collocation, we investigate the advantages and disadvantages of several known measures and we propose some novel ones that exhibit a good ectropic behavior. In particular, we introduce a quasi-entropy measure based on a geometric covering problem, three measures based on discrepancy from uniform distribution and one based on Euclidean minimum spanning trees. All considered measures are tested and compared on a large set of random and structured populations. Special attention is also devoted to the complexity of computing the measures. Most of the novel measures compare favorably with the classical ones in terms of ectropy. The measure based on Euclidean minimum spanning trees turns out to be the most promising one in terms of the tradeoff between the ectropic behavior and the computational complexity

Safety-oriented path planning for articulated robots

SUMMARYThis work presents an approach to motion planning for robotic manipulators that aims at improving path quality in terms of safety. Safety is explicitly assessed using the quantity calleddanger field. The measure of safety can easily be embedded into a heuristic function that guides the exploration of the free configuration space. As a result, the resulting path is likely to have substantially higher safety margin when compared to one obtained by regular planning algorithms. To this end, four planning algorithms have been proposed. The first planner is based on volume trees comprised of bubbles of free configuration space, while the remaining ones represent modifications of classical sampling-based algorithms. Several numerical case studies are carried out to validate and compare the performance of the presented algorithms with respect to classical planners. The results indicate significantly lower danger metric for paths obtained by safety-oriented planners even with some decrease in running time.</jats:p

Towards the Exact Solution for Speed and Separation Monitoring for Improved Human-Robot Collaboration

In this paper, we approach the problem of ensuring safety requirements within human-robot collaborative scenarios. The safety requirements considered herein are consistent with the paradigm of speed and separation monitoring. In such a setup, safety guarantees for human operators usually imply limited robot velocities and/or significant distance margins, which in turn may have adverse effects regarding the productivity of the robot. In this paper, we propose a novel approach that minimally affects the productivity while being consistent with such a safety prescription. A comprehensive simulation study shows that our method outperforms the current state of the art algorithm