On the complexity of the chip-firing reachability problem

In this paper, we study the complexity of the chip-firing reachability problem. We show that for Eulerian digraphs, the reachability problem can be decided in strongly polynomial time, even if the digraph has multiple edges. We also show a special case when the reachability problem can be decided in polynomial time for general digraphs: if the target distribution is recurrent restricted to each strongly connected component. As a further positive result, we show that the chip-firing reachability problem is in co-NP for general digraphs. We also show that the chip-firing halting problem is in co-NP for Eulerian digraphs

Strongly trapped two-dimensional quantum walks

Discrete time quantum walks (DTQWs) are nontrivial generalizations of random walks with a broad scope of applications. In particular, they can be used as computational primitives, and they are suitable tools for simulating other quantum systems. DTQWs usually spread ballistically due to their quantumness. In some cases, however, they can remain localized at their initial state (trapping). The trapping and other fundamental properties of DTQWs are determined by the choice of the coin operator. We introduce and analyze an up to now uncharted type of walks driven by a coin class leading to strong trapping, complementing the known list of walks. This class of walks exhibit a number of exciting properties with the possible applications ranging from light pulse trapping in a medium to topological effects and quantum search.Comment: 5 pages, 4 figures, Accepted for publication in Physical Review

The formation of carbonaceous layer from ethylene over various transition metal catalysts – an FT-IR study

The ethylene-derived carbonaceous overlayers were studied over silica-supported Pt, Pd, Rh and Cu catalysts by FT-IR spectroscopy under desorption conditions. As a general feature it was observed over all catalysts that upon increasing the desorption temperature the overlayer gradually became poor in hydrogen. The structure of the overlayers was similar over the silica-supported Pt, Pd and Rh. On increasing the reaction temperature the σ-adsorbed half-hydrogenated species are transformed to adsorbed ethylidyne. On the Cu catalyst prepared with ion exchange a similar picture emerged, while on those prepared with precipitation ethylidyne soon became the predominant species. Hydrogen swept off the carbonaceous species from the transition metals, however, copper retained large portions of it

Discrete time quantum walks on percolation graphs

Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear and disappear randomly in each step during the time evolution. The resulting open system dynamics is hard to treat numerically in general. We shortly review the literature on this problem. We then present our method to solve the evolution on finite percolation graphs in the long time limit, applying the asymptotic methods concerning random unitary maps. We work out the case of one dimensional chains in detail and provide a concrete, step by step numerical example in order to give more insight into the possible asymptotic behavior. The results about the case of the two-dimensional integer lattice are summarized, focusing on the Grover type coin operator.Comment: 22 pages, 3 figure

New approach for estimation of incident energy on high voltage level

Abstract The purpose of this paper is to show a new calculation model, which is able to calculate the incident energy in any places near an electric arc in case of high voltage, without neglecting of length and position of the electric arc. This method is developed especially for the electric transmission network above 35 kV and several meters of gap distances. It would be used to estimate the thermal load of a power line worker close an initiated electric arc during live-line maintenance by bare-hand and hot stick method as well

Motion planning algorithms for stratified kinematic systems with application to the hexapod robot

The paper addresses the motion planning problem of legged robots. Kinematic models of these robots are stratified, i.e. the equations of motion differ on different strata. An improved version of the motion planning algorithm proposed in the literature is compared with two alternative solutions via the example of the six-legged (hexapod) robot. The first alternative solution uses explicit integration of the vector fields while the second one exploits the flatness of a restricted subsystem

Noninteracting control of a steering system

This paper describes the modeling and control of a novel steering system which makes it possible to achieve a steer-by-wire like operation with the maintenance of the mechanical contact between the steering wheel and the steered wheels. First the derivation of the dynamical model is given where linear and nonlinear holonomic constraints are introduced by two elements of the steering system, namely by a harmonic drive and a universal joint. The flatness property of the nonlinear model is shown, but, since the controlled variables are not the linearizing outputs, we give another noninteracting control algorithm for the linearized model and show the tolerance of the closed-loop performance to nonlinearities

Moments of the superdiffusive elephant random walk with general step distribution

We consider the elephant random walk with general step distribution. We calculate the first four moments of the limiting distribution of the position rescaled by $n^\alpha$ in the superdiffusive regime where $\alpha$ is the memory parameter. This extends the results obtained by Bercu.Comment: 11 page