Model Checking Markov Chains with Actions and State Labels

In the past, logics of several kinds have been proposed for reasoning about discrete- or continuous-time Markov chains. Most of these logics rely on either state labels (atomic propositions) or on transition labels (actions). However, in several applications it is useful to reason about both state-properties and action-sequences. For this purpose, we introduce the logic asCSL which provides powerful means to characterize execution paths of Markov chains with actions and state labels. asCSL can be regarded as an extension of the purely state-based logic asCSL (continuous stochastic logic). \ud In asCSL, path properties are characterized by regular expressions over actions and state-formulas. Thus, the truth value of path-formulas does not only depend on the available actions in a given time interval, but also on the validity of certain state formulas in intermediate states.\ud We compare the expressive power of CSL and asCSL and show that even the state-based fragment of asCSL is strictly more expressive than CSL if time intervals starting at zero are employed. Using an automaton-based technique, an asCSL formula and a Markov chain with actions and state labels are combined into a product Markov chain. For time intervals starting at zero we establish a reduction of the model checking problem for asCSL to CSL model checking on this product Markov chain. The usefulness of our approach is illustrated by through an elaborate model of a scalable cellular communication system for which several properties are formalized by means of asCSL-formulas, and checked using the new procedure

Partially-shared zero-suppressed multi-terminal BDDs: concept, algorithms and applications

Multi-Terminal Binary Decision Diagrams (MTBDDs) are a well accepted technique for the state graph (SG) based quantitative analysis of large and complex systems specified by means of high-level model description techniques. However, this type of Decision Diagram (DD) is not always the best choice, since finite functions with small satisfaction sets, and where the fulfilling assignments possess many 0-assigned positions, may yield relatively large MTBDD based representations. Therefore, this article introduces zero-suppressed MTBDDs and proves that they are canonical representations of multi-valued functions on finite input sets. For manipulating DDs of this new type, possibly defined over different sets of function variables, the concept of partially-shared zero-suppressed MTBDDs and respective algorithms are developed. The efficiency of this new approach is demonstrated by comparing it to the well-known standard type of MTBDDs, where both types of DDs have been implemented by us within the C++-based DD-package JINC. The benchmarking takes place in the context of Markovian analysis and probabilistic model checking of systems. In total, the presented work extends existing approaches, since it not only allows one to directly employ (multi-terminal) zero-suppressed DDs in the field of quantitative verification, but also clearly demonstrates their efficienc

The Nonlinear Dynamic Conversion of Analog Signals into Excitation Patterns

Local periodic perturbations induce frequency-dependent propagation waves in an excitable spatio-temporally chaotic system. We show how segments of noise-contaminated and chaotic perturbations induce characteristic sequences of excitations in the model system. Using a set of tuned excitable systems, it is possible to characterize signals by their spectral composition of excitation pattern. As an example we analyze an epileptic spike-and-wave time series.Comment: 14 pages, 5 figure

Hard photon production rate of a quark-gluon plasma at finite quark chemical potential

We compute the photon production rate of a quark-gluon plasma (QGP) at finite quark chemical potential $\mu$ using the Braaten-Pisarski method, thus continuing the work of Kapusta, Lichard, and Seibert who did the calculation for $\mu =0$.Comment: 9 pages, revtex, no figures, error in soft part corrected, figures available at ftp://theorie.physik.uni-giessen.de/usr/users/ftp/photon

Hard Thermal Photon Production in Relativistic Heavy Ion Collisions

The recent status of hard thermal photon production in relativistic heavy ion collisions is reviewed and the current rates are presented with emphasis on corrected bremsstrahlung processes in the quark-gluon plasma (QGP) and quark-hadron duality. Employing Bjorken hydrodynamics with an EOS supporting the phase transition from QGP to hot hadron gas (HHG), thermal photon spectra are computed. For SPS 158 GeV Pb+Pb collisions, comparison with other theoretical results and the WA98 direct photon data indicates significant contributions due to prompt photons. Extrapolating the presented approach to RHIC and LHC experiments, predictions of the thermal photon spectrum show a QGP outshining the HHG in the high-pT-region.Comment: 20 pages with 8 figures. v3: Erratum to [Phys. Lett. B 510 (2001) 98] with correctly labeled Figs. 2, 4, and 5 adde

Assessment and verification of mean effective diameter of internal channels fabricated by laser powder bed fusion

Abstract Channels with small diameters, used for example in conformal cooling, can nowadays be fabricated by laser powder bed fusion. Measurements of the mean effective diameter and surface topography are important to quantify the flow capabilities through the channel. In this paper, a new method using X-ray computed tomography is developed to obtain the mean effective diameter and mean surface topography height. The developed method is verified by determining the mean effective diameter using incompressible turbulent fluid flow simulations, whereupon the determined mean surface topography height is fed as an input to the simulation. The method is proved to offer a non-destructive and relatively fast approach to measure the mean effective diameter and mean surface topography height in circular channels

Bremsstrahlung from an Equilibrating Quark-Gluon Plasma

The photon production rate from a chemically equilibrating quark-gluon plasma likely to be produced at RHIC (BNL) and LHC (CERN) energies is estimated taking into account bremsstrahlung. The plasma is assumed to be in local thermal equilibrium, but with a phase space distribution that deviates from the Fermi or Bose distribution by space-time dependent factors (fugacities). The photon spectrum is obtained by integrating the photon rate over the space-time history of the plasma, adopting a boost invariant cylindrically symmetric transverse expansion of the system with different nuclear profile functions. Initial conditions obtained from a self-screened parton cascade calculation and, for comparison, from the HIJING model are used. Compared to an equilibrated plasma at the same initial energy density, taken from the self-screened parton cascade, a moderate suppression of the photon yield by a factor of one to five depending on the collision energy and the photon momentum is observed. The individual contributions to the photon production, however, are completely different in the both scenarios.Comment: 14 pages, 4 figures, shortened version to be published in Phys. Rev.

Braaten-Pisarski Method at Finite Chemical Potential

The effective perturbation theory developed by Braaten and Pisarski for gauge theories at finite temperature is extended to finite chemical potential. As a first application the collisional energy loss of a heavy quark propagating through a quark-gluon plasma with non-vanishing quark chemical potential is considered. Assuming $\mu /T\simeq 1$, motivated by numerical simulations of heavy ion collisions at RHIC energies, we find that the effect of the quark chemical potential is rather small, unless the energy density instead of the temperature is fixed.Comment: 14 pages, REVTEX, 6 postscript figures appended, UGI-94-1

Collisional Energy Loss of Fast Charged Particles in Relativistic Plasmas

Following an argument by Kirzhnits we rederive an exact expression for the energy loss of a fast charged particle in a relativistic plasma using the quantum field theoretical language. We compare this result to perturbative calculations of the collisional energy loss of an energetic electron or muon in an electron-positron plasma and of an energetic parton in the quark-gluon plasma.Comment: 9 pages, LATEX, 2 PostScript figure