On the zero of the fermion zero mode

We argue that the fermionic zero mode in non-trivial gauge field backgrounds must have a zero. We demonstrate this explicitly for calorons where its location is related to a constituent monopole. Furthermore a topological reasoning for the existence of the zero is given which therefore will be present for any non-trivial configuration. We propose the use of this property in particular for lattice simulations in order to uncover the topological content of a configuration.Comment: 6 pages, 3 figures in 5 part

Instanton constituents in the O(3) model at finite temperature

It is shown that instantons in the O(3) model at finite temperature consist of fractional charge constituents and the (topological) properties of the latter are discussed.Comment: 5 pages, 12 plots in 3 figure

Quantitative comparison of filtering methods in lattice QCD

We systematically compare filtering methods used to extract topological excitations (like instantons, calorons, monopoles and vortices) from lattice gauge configurations, namely APE-smearing and spectral decompositions based on lattice Dirac and Laplace operators. Each of these techniques introduces ambiguities, which can invalidate the interpretation of the results. We show, however, that all these methods, when handled with care, reveal very similar topological structures. Hence, these common structures are free of ambiguities and faithfully represent infrared degrees of freedom in the QCD vacuum. As an application we discuss an interesting power-law for the clusters of filtered topological charge.Comment: 6 pages, 18 plots in 5 figures; final version as published in EPJ A; section 4 was adde

Calorons with non-trivial holonomy on and off the lattice

We discuss recent solutions for SU(2) calorons with non-trivial holonomy at higher charge, both through analytic means and using cooling, as well as extensive lattice studies for SU(3).Comment: 12 pages, 16 figures in 34 parts, 4 talks presented at Lattice 2004(topology

Probing for Instanton Quarks with epsilon-Cooling

We use epsilon-cooling, adjusting at will the order a^2 corrections to the lattice action, to study the parameter space of instantons in the background of non-trivial holonomy and to determine the presence and nature of constituents with fractional topological charge at finite and zero temperature for SU(2). As an additional tool, zero temperature configurations were generated from those at finite temperature with well-separated constituents. This is achieved by "adiabatically" adjusting the anisotropic coupling used to implement finite temperature on a symmetric lattice. The action and topological charge density, as well as the Polyakov loop and chiral zero-modes are used to analyse these configurations. We also show how cooling histories themselves can reveal the presence of constituents with fractional topological charge. We comment on the interpretation of recent fermion zero-mode studies for thermalized ensembles at small temperatures.Comment: 26 pages, 14 figures in 33 part

Cautionary remarks on the moduli space metric for multi-dyon simulations

We perform a detailed numerical investigation of the approximate moduli space metric proposed by Diakonov and Petrov [arXiv:0704.3181] for a confining model of dyons. Our findings strongly indicate that only for a small number of dyons at sufficiently low density this metric is positive definite - and, therefore, a valid moduli space metric - throughout a considerable part of configuration space. This poses strong limitations on results obtained by an unrestricted integration over collective coordinates in this model. It also indicates that strong correlations between collective coordinates will be essential for the physical content of a dyon model, which could be exhibited by a suitable simulation algorithm.Comment: 20 pages, 6 figure

Photometric reverberation mapping of 3C120

We present the results of a five month monitoring campaign of the local active galactic nuclei (AGN) 3C120. Observations with a median sampling of two days were conducted with the robotic 15cm telescope VYSOS-6 located near Cerro Armazones in Chile. Broad band (B,V) and narrow band (NB) filters were used in order to measure fluxes of the AGN and the H_beta broad line region (BLR) emission line. The NB flux is constituted by about 50% continuum and 50% H_beta emission line. To disentangle line and continuum flux, a synthetic H_beta light curve was created by subtracting a scaled V-band light curve from the NB light curve. Here we show that the H_beta emission line responds to continuum variations with a rest frame lag of 23.6 +/- 1.69 days. We estimate a virial mass of the central black hole M_BH = 57 +/- 27 * 10^6 solar masses, by combining the obtained lag with the velocity dispersion of a single contemporaneous spectrum. Using the flux variation gradient (FVG) method, we determined the host galaxy subtracted rest frame 5100A luminosity at the time of our monitoring campaign with an uncertainty of 10% (L_AGN = 6.94 +/- 0.71* 10^43 ergs^-1). Compared with recent spectroscopic reverberation results, 3C120 shifts in the R_BLR - L_AGN diagram remarkably close to the theoretically expected relation of R-L^0.5. Our results demonstrate the performance of photometric AGN reverberation mapping, in particular for efficiently determining the BLR size and the AGN luminosityComment: 11 pages, 11 figures, Published in Astronomy and Astrophysic

Rest-to-Rest Trajectory Planning for Underactuated Cable-Driven Parallel Robots

This article studies the trajectory planning for underactuated cable-driven parallel robots (CDPRs) in the case of rest-to-rest motions, when both the motion time and the path geometry are prescribed. For underactuated manipulators, it is possible to prescribe a control law only for a subset of the generalized coordinates of the system. However, if an arbitrary trajectory is prescribed for a suitable subset of these coordinates, the constraint deficiency on the end-effector leads to the impossibility of bringing the system at rest in a prescribed time. In addition, the behavior of the system may not be stable, that is, unbounded oscillatory motions of the end-effector may arise. In this article, we propose a novel trajectory-planning technique that allows the end effector to track a constrained geometric path in a specified time, and allows it to transition between stable static poses. The design of such a motion is based on the solution of a boundary value problem, aimed at a finding solution to the differential equations of motion with constraints on position and velocity at start and end times. To prove the effectiveness of such a method, the trajectory planning of a six-degrees-of-freedom spatial CDPR suspended by three cables is investigated. Trajectories of a reference point on the moving platform are designed so as to ensure that the assigned path is tracked accurately, and the system is brought to a static condition in a prescribed time. Experimental validation is presented and discussed