Stopping paramagnetic supersonic beams: the advantage of a co-moving magnetic trap decelerator

The long standing goal of chemical physics is finding a convenient method to create slow and cold beams intense enough to observe chemical reactions in the temperature range of a few Kelvin. We present an extensive numerical analysis of our moving magnetic trap decelerator showing that a 3D confinement throughout the deceleration process enables deceleration of almost all paramagnetic particles within the original supersonic expansion to stopping velocities. We show that the phase space region containing the decelerating species is larger by two orders of magnitude as compared to other available deceleration methods.     

Chasing a Fast Robber on Planar Graphs and Random Graphs

We consider a variant of the Cops and Robber game, in which the robber has unbounded speed, that is, can take any path from her vertex in her turn, but she is not allowed to pass through a vertex occupied by a cop. Let denote the number of cops needed to capture the robber in a graph G in this variant, and let denote the treewidth of G. We show that if G is planar then , and there is a polynomial‐time constant‐factor approximation algorithm for computing . We also determine, up to constant factors, the value of of the Erd?s–Rényi random graph for all admissible values of p, and show that when the average degree is ω(1), is typically asymptotic to the domination number.     

Biased games on random boards

In this paper we analyze biased Maker‐Breaker games and Avoider‐Enforcer games, both played on the edge set of a random board . In Maker‐Breaker games there are two players, denoted by Maker and Breaker. In each round, Maker claims one previously unclaimed edge of G and Breaker responds by claiming b previously unclaimed edges. We consider the Hamiltonicity game, the perfect matching game and the k‐vertex‐connectivity game, where Maker's goal is to build a graph which possesses the relevant property. Avoider‐Enforcer games are the reverse analogue of Maker‐Breaker games with a slight modification, where the two players claim at least 1 and at least b previously unclaimed edges per move, respectively, and Avoider aims to avoid building a graph which possesses the relevant property. Maker‐Breaker games are known to be “bias‐monotone”, that is, if Maker wins the (1,b) game, he also wins the game. Therefore, it makes sense to define the critical bias of a game, b ^*, to be the “breaking point” of the game. That is, Maker wins the (1,b) game whenever and loses otherwise. An analogous definition of the critical bias exists for Avoider‐Enforcer games: here, the critical bias of a game b ^* is such that Avoider wins the (1,b) game for every , and loses otherwise. We prove that, for every is typically such that the critical bias for all the aforementioned Maker‐Breaker games is asymptotically . We also prove that in the case , the critical bias is . These results settle a conjecture of Stojakovi? and Szabó. For Avoider‐Enforcer games, we prove that for , the critical bias for all the aforementioned games is . © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 46,651–676, 2015     

Quasi-periodic and random quasi-phase matching of high harmonic generation

Quasi-phase matching schemes employing quasi-periodic or random spatial modulations, previously applied to perturbative nonlinear optics, are demonstrated theoretically for the extreme nonlinear optical process of high harmonic generation. We show that quasi-periodic quasi-phase matching of high harmonic generation can be used for simultaneous enhancement of arbitrarily chosen spectral regions. We also demonstrate enhancement of a single extremely wide bandwidth using random quasi-phase matching.