Streamers in air splitting into three branches

We investigate the branching of positive streamers in air and present the first systematic investigation of splitting into more than two branches. We study discharges in 100 mbar artificial air that is exposed to voltage pulses of 10 kV applied to a needle electrode 160 mm above a grounded plate. By imaging the discharge with two cameras from three angles, we establish that about every 200th branching event is a branching into three. Branching into three occurs more frequently for the relatively thicker streamers. In fact, we find that the surface of the total streamer cross-sections before and after a branching event is roughly the same.Comment: 6 pages, 7 figure

Positive and negative streamers in ambient air: measuring diameter, velocity and dissipated energy

Positive and negative streamers are studied in ambient air at 1 bar; they emerge from a needle electrode placed 40 mm above a planar electrode. The amplitudes of the applied voltage pulses range from 5 to 96 kV; most pulses have rise times of 30 ns or shorter. Diameters, velocities and energies of the streamers are measured. Two regimes are identified; a low voltage regime where only positive streamers appear and a high voltage regime where both positive and negative streamers exist. Below 5 kV, no streamers emerge. In the range from 5 to 40 kV, positive streamers form, while the negative discharges only form a glowing cloud at the electrode tip, but no streamers. For 5 to 20 kV, diameters and velocities of the positive streamers have the minimal values of d=0.2 mm and v \approx 10^5 m/s. For 20 to 40 kV, their diameters increase by a factor 6 while the voltage increases only by a factor 2. Above the transition value of 40 kV, streamers of both polarities form; they strongly resemble each other, though the positive ones propagate further; their diameters continue to increase with applied voltage. For 96 kV, positive streamers attain diameters of 3 mm and velocities of 4*10^6 m/s, negative streamers are about 20 % slower and thinner. An empirical fit formula for the relation between velocity v and diameter d is v=0.5 d^2/(mm ns) for both polarities. Streamers of both polarities dissipate energies of the order of several mJ per streamer while crossing the gap.Comment: 20 pages, 9 figures, accepted for J. Phys.

Beyond Worst-Case Analysis for Joins with Minesweeper

We describe a new algorithm, Minesweeper, that is able to satisfy stronger runtime guarantees than previous join algorithms (colloquially, `beyond worst-case guarantees') for data in indexed search trees. Our first contribution is developing a framework to measure this stronger notion of complexity, which we call {\it certificate complexity}, that extends notions of Barbay et al. and Demaine et al.; a certificate is a set of propositional formulae that certifies that the output is correct. This notion captures a natural class of join algorithms. In addition, the certificate allows us to define a strictly stronger notion of runtime complexity than traditional worst-case guarantees. Our second contribution is to develop a dichotomy theorem for the certificate-based notion of complexity. Roughly, we show that Minesweeper evaluates $\beta$-acyclic queries in time linear in the certificate plus the output size, while for any $\beta$-cyclic query there is some instance that takes superlinear time in the certificate (and for which the output is no larger than the certificate size). We also extend our certificate-complexity analysis to queries with bounded treewidth and the triangle query.Comment: [This is the full version of our PODS'2014 paper.

Answering Conjunctive Queries under Updates

We consider the task of enumerating and counting answers to $k$-ary conjunctive queries against relational databases that may be updated by inserting or deleting tuples. We exhibit a new notion of q-hierarchical conjunctive queries and show that these can be maintained efficiently in the following sense. During a linear time preprocessing phase, we can build a data structure that enables constant delay enumeration of the query results; and when the database is updated, we can update the data structure and restart the enumeration phase within constant time. For the special case of self-join free conjunctive queries we obtain a dichotomy: if a query is not q-hierarchical, then query enumeration with sublinear$^\ast$ delay and sublinear update time (and arbitrary preprocessing time) is impossible. For answering Boolean conjunctive queries and for the more general problem of counting the number of solutions of k-ary queries we obtain complete dichotomies: if the query's homomorphic core is q-hierarchical, then size of the the query result can be computed in linear time and maintained with constant update time. Otherwise, the size of the query result cannot be maintained with sublinear update time. All our lower bounds rely on the OMv-conjecture, a conjecture on the hardness of online matrix-vector multiplication that has recently emerged in the field of fine-grained complexity to characterise the hardness of dynamic problems. The lower bound for the counting problem additionally relies on the orthogonal vectors conjecture, which in turn is implied by the strong exponential time hypothesis. $^\ast)$ By sublinear we mean $O(n^{1-\varepsilon})$ for some $\varepsilon>0$, where $n$ is the size of the active domain of the current database

Inception and propagation of positive streamers in high-purity nitrogen: effects of the voltage rise-rate

Controlling streamer morphology is important for numerous applications. Up to now, the effect of the voltage rise rate was only studied across a wide range. Here we show that even slight variations in the voltage rise can have significant effects. We have studied positive streamer discharges in a 16 cm point-plane gap in high-purity nitrogen 6.0, created by 25 kV pulses with a duration of 130 ns. The voltage rise varies by a rise rate from 1.9 kV/ns to 2.7 kV/ns and by the first peak voltage of 22 to 28 kV. A structural link is found between smaller discharges with a larger inception cloud caused by a faster rising voltage. This relation is explained by the greater stability of the inception cloud due to a faster voltage rise, causing a delay in the destabilisation. Time-resolved measurements show that the inception cloud propagates slower than an earlier destabilised, more filamentary discharge. This explains that the discharge with a faster rising voltage pulse ends up to be shorter. Furthermore, the effect of remaining background ionisation in a pulse sequence has been studied, showing that channel thickness and branching rate are locally affected, depending on the covered volume of the previous discharge.Comment: 16 pages, 9 figure

Power laws and self-similar behavior in negative ionization fronts

We study anode-directed ionization fronts in curved geometries. When the magnetic effects can be neglected, an electric shielding factor determines the behavior of the electric field and the charged particle densities. From a minimal streamer model, a Burgers type equation which governs the dynamics of the electric shielding factor is obtained. A Lagrangian formulation is then derived to analyze the ionization fronts. Power laws for the velocity and the amplitude of streamer fronts are observed numerically and calculated analytically by using the shielding factor formulation. The phenomenon of geometrical diffusion is explained and clarified, and a universal self-similar asymptotic behavior is derived.Comment: 25 pages, 9 figure

Full Elite Sets for Multi-Objective Optimisation

Copyright © 2002 Springer. The final publication is available at link.springer.com5th International Conference on Adaptive Computing in Design and Manufacture (ACDM 2002), Exeter, UK, 16-18 April, 2002Multi-objective evolutionary algorithms frequently use an archive of non-dominated solutions to approximate the Pareto front. We show that the truncation of this archive to a limited number of solutions can lead to oscillating and shrinking estimates of the Pareto front. New data structures to permit efficient query and update of the full archive are proposed, and the superior quality of frontal estimates found using the full archive is illustrated on test problems

Probing photo-ionization: Experiments on positive streamers in pure gasses and mixtures

Positive streamers are thought to propagate by photo-ionization whose parameters depend on the nitrogen:oxygen ratio. Therefore we study streamers in nitrogen with 20%, 0.2% and 0.01% oxygen and in pure nitrogen, as well as in pure oxygen and argon. Our new experimental set-up guarantees contamination of the pure gases to be well below 1 ppm. Streamers in oxygen are difficult to measure as they emit considerably less light in the sensitivity range of our fast ICCD camera than the other gasses. Streamers in pure nitrogen and in all nitrogen/oxygen mixtures look generally similar, but become somewhat thinner and branch more with decreasing oxygen content. In pure nitrogen the streamers can branch so much that they resemble feathers. This feature is even more pronounced in pure argon, with approximately 10^2 hair tips/cm^3 in the feathers at 200 mbar; this density could be interpreted as the free electron density creating avalanches towards the streamer stem. It is remarkable that the streamer velocity is essentially the same for similar voltage and pressure in all nitrogen/oxygen mixtures as well as in pure nitrogen, while the oxygen concentration and therefore the photo-ionization lengths vary by more than five orders of magnitude. Streamers in argon have essentially the same velocity as well. The physical similarity of streamers at different pressures is confirmed in all gases; the minimal diameters are smaller than in earlier measurements.Comment: 28 pages, 14 figures. Major differences with v1: - appendix and spectra removed - subsection regarding effects of repetition frequency added - many more smaller change