Stochastic Perturbations of Periodic Orbits with Sliding

Vector fields that are discontinuous on codimension-one surfaces are known as Filippov systems and can have attracting periodic orbits involving segments that are contained on a discontinuity surface of the vector field. In this paper we consider the addition of small noise to a general Filippov system and study the resulting stochastic dynamics near such a periodic orbit. Since a straight-forward asymptotic expansion in terms of the noise amplitude is not possible due to the presence of discontinuity surfaces, in order to quantitatively determine the basic statistical properties of the dynamics, we treat different parts of the periodic orbit separately. Dynamics distant from discontinuity surfaces is analyzed by the use of a series expansion of the transitional probability density function. Stochastically perturbed sliding motion is analyzed through stochastic averaging methods. The influence of noise on points at which the periodic orbit escapes a discontinuity surface is determined by zooming into the transition point. We combine the results to quantitatively determine the effect of noise on the oscillation time for a three-dimensional canonical model of relay control. For some parameter values of this model, small noise induces a significantly large reduction in the average oscillation time. By interpreting our results geometrically, we are able to identify four features of the relay control system that contribute to this phenomenon.Comment: 44 pages, 9 figures, submitted to: J Nonlin. Sc

Propositional Dynamic Logic for Message-Passing Systems

We examine a bidirectional propositional dynamic logic (PDL) for finite and infinite message sequence charts (MSCs) extending LTL and TLC-. By this kind of multi-modal logic we can express properties both in the entire future and in the past of an event. Path expressions strengthen the classical until operator of temporal logic. For every formula defining an MSC language, we construct a communicating finite-state machine (CFM) accepting the same language. The CFM obtained has size exponential in the size of the formula. This synthesis problem is solved in full generality, i.e., also for MSCs with unbounded channels. The model checking problem for CFMs and HMSCs turns out to be in PSPACE for existentially bounded MSCs. Finally, we show that, for PDL with intersection, the semantics of a formula cannot be captured by a CFM anymore

Optics Calibration at the MLS and at BESSY II

In this paper we present the results of our studies employing LOCO and MML for optics calibration at the MLS and at the BESSY II storage rings. Both the standard user modes and dedicated low alpha modes are analyze

Modifications to the Machine Optics of BESSY II Necessitated by the EMIL Project

The Helmholtz Zentrum Berlin and the Max Planck Society are going to build a new dedicated X ray beam line at the synchrotron light source BESSY II which will be used for analyzing materials for renewable energy generation. The new large scale project has been dubbed EMIL. In this document we present the modifications to the machine optics and to what extent these changes affect the performance of BESSY I

The Isomorphism Relation Between Tree-Automatic Structures

An $\omega$-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for $\omega$-tree-automatic structures. We prove first that the isomorphism relation for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is neither a $\Sigma_2^1$-set nor a $\Pi_2^1$-set

Trees over Infinite Structures and Path Logics with Synchronization

We provide decidability and undecidability results on the model-checking problem for infinite tree structures. These tree structures are built from sequences of elements of infinite relational structures. More precisely, we deal with the tree iteration of a relational structure M in the sense of Shelah-Stupp. In contrast to classical results where model-checking is shown decidable for MSO-logic, we show decidability of the tree model-checking problem for logics that allow only path quantifiers and chain quantifiers (where chains are subsets of paths), as they appear in branching time logics; however, at the same time the tree is enriched by the equal-level relation (which holds between vertices u, v if they are on the same tree level). We separate cleanly the tree logic from the logic used for expressing properties of the underlying structure M. We illustrate the scope of the decidability results by showing that two slight extensions of the framework lead to undecidability. In particular, this applies to the (stronger) tree iteration in the sense of Muchnik-Walukiewicz.Comment: In Proceedings INFINITY 2011, arXiv:1111.267

Monitoring the exhaust air of a compost pile as a process variable with an e-nose

In this paper, the monitoring of the composting process with an e-nose is presented. An emission chamber is developed for this purpose and put on a household waste compost pile. A lab-made e-nose with metal oxide sensors is located at the exit of this chamber. Simultaneously to the e-nose measurements, air sampling on sorbent tubes as well as physico-chemical analysis are realised. The adsorbed air samples are analysed in the lab by gas chromatography coupled to mass spectrometry (GC-MS). In addition, some parameters of the composting process are collected (compost temperature, age of the pile, date of the aeration). Correlation between the sensors and 14 chemical families is determined by principal component analysis (PCA). By canonical analysis, two models are developed and calibrated by the proportion of each chemical family and in function of the compost process events. Thanks to these models, monitoring of various kinds of compost process events is possible with only one measurement device. © 2004 Elsevier B.V. All rights reserved

Automatic structures of bounded degree revisited

The first-order theory of a string automatic structure is known to be decidable, but there are examples of string automatic structures with nonelementary first-order theories. We prove that the first-order theory of a string automatic structure of bounded degree is decidable in doubly exponential space (for injective automatic presentations, this holds even uniformly). This result is shown to be optimal since we also present a string automatic structure of bounded degree whose first-order theory is hard for 2EXPSPACE. We prove similar results also for tree automatic structures. These findings close the gaps left open in a previous paper of the second author by improving both, the lower and the upper bounds.Comment: 26 page

Fast Orbit Feedback at BESSY II Performance and Operational Experiences

At the 3rd generation light source BESSY II the first phase of a fast orbit feedback system has been completed and put into operation in 2012. In this first phase the aim was to achieve noise suppression in the 1Hz to several 10Hz range, mostly avoiding expensive upgrades to existing hardware, such as beam position monitors and the CAN based setpoint transmission to the power supplies. Only the power supplies were replaced with newer, faster versions. This paper describes the capability of the phase I FOFB with respect to beam motion transient suppression, low frequency damping and high frequency noise generation as well as aspects of operational integration and stabilit