Strong Ramsey games: Drawing on an infinite board

Consider the following strong Ramsey game. Two players take turns in claiming a previously unclaimed edge of the complete graph on n vertices until all edges have been claimed. The first player to build a copy of K5 is declared the winner of the game. If none of the players win, then the game ends in a draw. A simple strategy stealing argument shows that the second player cannot expect to ever win this game. Moreover, for sufficiently large n, it follows from Ramsey’s Theorem that the game cannot end in a draw and is thus a first player win. A famous question of Beck asks whether the minimum number of moves needed for the first player to win this game on Kn grows with n. This seems unlikely but is still wide open. A striking equivalent formulation of this question is whether the same game played on the infinite complete graph is a first player win or a draw. The target graph of the strong Ramsey game does not have to be K5, it can be any predetermined fixed graph. In fact, it can even be a k-uniform hypergraph (and then the game is played on the infinite k-uniform hypergraph). Since strategy stealing and Ramsey’s Theorem still apply, one can ask the same question: is this game a first player win or a draw? The same intuition which lead most people (including the authors) to believe that the K5 strong Ramsey game on the infinite board is a first player win, would also lead one to believe that the H strong Ramsey game on the infinite board is a first player win for any uniform hypergraph H. However, in this paper we construct a 5-uniform hypergraph for which the corresponding game is a draw

Controlling the quality factor of a tuning-fork resonance between 9 K and 300 K for scanning-probe microscopy

We study the dynamic response of a mechanical quartz tuning fork in the temperature range from 9 K to 300 K. Since the quality factor Q of the resonance strongly depends on temperature, we implement a procedure to control the quality factor of the resonance. We show that we are able to dynamically change the quality factor and keep it constant over the whole temperature range. This procedure is suitable for applications in scanning probe microscopy.Comment: 5 pages, 6 figure

Nanoscale piezoelectric response across a single antiparallel ferroelectric domain wall

Surprising asymmetry in the local electromechanical response across a single antiparallel ferroelectric domain wall is reported. Piezoelectric force microscopy is used to investigate both the in-plane and out-of- plane electromechanical signals around domain walls in congruent and near-stoichiometric lithium niobate. The observed asymmetry is shown to have a strong correlation to crystal stoichiometry, suggesting defect-domain wall interactions. A defect-dipole model is proposed. Finite element method is used to simulate the electromechanical processes at the wall and reconstruct the images. For the near-stoichiometric composition, good agreement is found in both form and magnitude. Some discrepancy remains between the experimental and modeling widths of the imaged effects across a wall. This is analyzed from the perspective of possible electrostatic contributions to the imaging process, as well as local changes in the material properties in the vicinity of the wall

Damping of optomechanical disks resonators vibrating in air

We report on miniature GaAs disk optomechanical resonators vibrating in air in the radiofrequency range. The flexural modes of the disks are studied by scanning electron microscopy and optical interferometry, and correctly modeled with the elasticity theory for annular plates. The mechanical damping is systematically measured, and confronted with original analytical models for air damping. Formulas are derived that correctly reproduce both the mechanical modes and the damping behavior, and can serve as design tools for optomechanical applications in fluidic environment

Local probing of ionic diffusion by electrochemical strain microscopy: spatial resolution and signal formation mechanisms

Electrochemical insertion-deintercalation reactions are typically associated with significant change of molar volume of the host compound. This strong coupling between ionic currents and strains underpins image formation mechanisms in electrochemical strain microscopy (ESM), and allows exploring the tip-induced electrochemical processes locally. Here we analyze the signal formation mechanism in ESM, and develop the analytical description of operation in frequency and time domains. The ESM spectroscopic modes are compared to classical electrochemical methods including potentiostatic and galvanostatic intermittent titration (PITT and GITT), and electrochemical impedance spectroscopy (EIS). This analysis illustrates the feasibility of spatially resolved studies of Li-ion dynamics on the sub-10 nanometer level using electromechanical detection.Comment: 49 pages, 17 figures, 4 tables, 3 appendices, to be submitted to J. Appl. Phys

Strong Ramsey games: drawing on an infinite board

We consider the strong Ramsey-type game R(k)(H,ℵ0), played on the edge set of the infinite complete k-uniform hypergraph KkN. Two players, called FP (the first player) and SP (the second player), take turns claiming edges of K^k_N with the goal of building a copy of some finite predetermined k-uniform hypergraph H. The first player to build a copy of H wins. If no player has a strategy to ensure his win in finitely many moves, then the game is declared a draw. In this paper, we construct a 5-uniform hypergraph H such that R(5)(H,ℵ0) is a draw. This is in stark contrast to the corresponding finite game R(5)(H,n), played on the edge set of K5n. Indeed, using a classical game-theoretic argument known as \emph{strategy stealing} and a Ramsey-type argument, one can show that for every k-uniform hypergraph G, there exists an integer n0 such that FP has a winning strategy for R(k)(G,n) for every n≥n0

Production of antihydrogen at reduced magnetic field for anti-atom trapping

We have demonstrated production of antihydrogen in a 1$,$T solenoidal magnetic field. This field strength is significantly smaller than that used in the first generation experiments ATHENA (3$,$T) and ATRAP (5$,$T). The motivation for using a smaller magnetic field is to facilitate trapping of antihydrogen atoms in a neutral atom trap surrounding the production region. We report the results of measurements with the ALPHA (Antihydrogen Laser PHysics Apparatus) device, which can capture and cool antiprotons at 3$,$T, and then mix the antiprotons with positrons at 1$,$T. We infer antihydrogen production from the time structure of antiproton annihilations during mixing, using mixing with heated positrons as the null experiment, as demonstrated in ATHENA. Implications for antihydrogen trapping are discussed

A novel antiproton radial diagnostic based on octupole induced ballistic loss

We report results from a novel diagnostic that probes the outer radial profile of trapped antiproton clouds. The diagnostic allows us to determine the profile by monitoring the time-history of antiproton losses that occur as an octupole field in the antiproton confinement region is increased. We show several examples of how this diagnostic helps us to understand the radial dynamics of antiprotons in normal and nested Penning-Malmberg traps. Better understanding of these dynamics may aid current attempts to trap antihydrogen atoms

Alpha Antihydrogen Experiment

ALPHA is an experiment at CERN, whose ultimate goal is to perform a precise test of CPT symmetry with trapped antihydrogen atoms. After reviewing the motivations, we discuss our recent progress toward the initial goal of stable trapping of antihydrogen, with some emphasis on particle detection techniques.Comment: Invited talk presented at the Fifth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 28-July 2, 201

Abnormal phenomena in a one-dimensional periodic structure containing left-handed materials

The explicit dispersion equation for a one-dimensional periodic structure with alternative layers of left-handed material (LHM) and right-handed material (RHM) is given and analyzed. Some abnormal phenomena such as spurious modes with complex frequencies, discrete modes and photon tunnelling modes are observed in the band structure. The existence of spurious modes with complex frequencies is a common problem in the calculation of the band structure for such a photonic crystal. Physical explanation and significance are given for the discrete modes (with real values of wave number) and photon tunnelling propagation modes (with imaginary wave numbers in a limited region).Comment: 10 pages, 4 figure