Fragmentation Phase Transition in Atomic Clusters II - Coulomb Explosion of Metal Clusters -

We discuss the role and the treatment of polarization effects in many-body systems of charged conducting clusters and apply this to the statistical fragmentation of Na-clusters. We see a first order microcanonical phase transition in the fragmentation of $Na^{Z+}_{70}$ for Z=0 to 8. We can distinguish two fragmentation phases, namely evaporation of large particles from a large residue and a complete decay into small fragments only. Charging the cluster shifts the transition to lower excitation energies and forces the transition to disappear for charges higher than Z=8. At very high charges the fragmentation phase transition no longer occurs because the cluster Coulomb-explodes into small fragments even at excitation energy $\epsilon^* = 0$.Comment: 19 text pages +18 *.eps figures, my e-mail adress: [email protected] submitted to Z. Phys.

Tropically convex constraint satisfaction

A semilinear relation S is max-closed if it is preserved by taking the componentwise maximum. The constraint satisfaction problem for max-closed semilinear constraints is at least as hard as determining the winner in Mean Payoff Games, a notorious problem of open computational complexity. Mean Payoff Games are known to be in the intersection of NP and co-NP, which is not known for max-closed semilinear constraints. Semilinear relations that are max-closed and additionally closed under translations have been called tropically convex in the literature. One of our main results is a new duality for open tropically convex relations, which puts the CSP for tropically convex semilinaer constraints in general into NP intersected co-NP. This extends the corresponding complexity result for scheduling under and-or precedence constraints, or equivalently the max-atoms problem. To this end, we present a characterization of max-closed semilinear relations in terms of syntactically restricted first-order logic, and another characterization in terms of a finite set of relations L that allow primitive positive definitions of all other relations in the class. We also present a subclass of max-closed constraints where the CSP is in P; this class generalizes the class of max-closed constraints over finite domains, and the feasibility problem for max-closed linear inequalities. Finally, we show that the class of max-closed semilinear constraints is maximal in the sense that as soon as a single relation that is not max-closed is added to L, the CSP becomes NP-hard.Comment: 29 pages, 2 figure

Solving order constraints in logarithmic space.

We combine methods of order theory, finite model theory, and universal algebra to study, within the constraint satisfaction framework, the complexity of some well-known combinatorial problems connected with a finite poset. We identify some conditions on a poset which guarantee solvability of the problems in (deterministic, symmetric, or non-deterministic) logarithmic space. On the example of order constraints we study how a certain algebraic invariance property is related to solvability of a constraint satisfaction problem in non-deterministic logarithmic space

Linking Dynamical and Thermal Models of Ultrarelativistic Nuclear Scattering

To analyse ultrarelativistic nuclear interactions, usually either dynamical models like the string model are employed, or a thermal treatment based on hadrons or quarks is applied. String models encounter problems due to high string densities, thermal approaches are too simplistic considering only average distributions, ignoring fluctuations. We propose a completely new approach, providing a link between the two treatments, and avoiding their main shortcomings: based on the string model, connected regions of high energy density are identified for single events, such regions referred to as quark matter droplets. Each individual droplet hadronizes instantaneously according to the available n-body phase space. Due to the huge number of possible hadron configurations, special Monte Carlo techniques have been developed to calculate this disintegration.Comment: Complete paper enclosed as postscript file (uuencoded

Microcanonical Treatment of Hadronizing the Quark-Gluon Plasma

We recently introduced a completely new way to study ultrarelativistic nuclear scattering by providing a link between the string model approach and a statistical description. A key issue is the microcanonical treatment of hadronizing individual quark matter droplets. In this paper we describe in detail the hadronization of these droplets according to n-body phase space, by using methods of statistical physics, i.e. constructing Markov chains of hadron configurations.Comment: Complete paper enclosed as postscript file (uuencoded

Cluster Editing: Kernelization based on Edge Cuts

Kernelization algorithms for the {\sc cluster editing} problem have been a popular topic in the recent research in parameterized computation. Thus far most kernelization algorithms for this problem are based on the concept of {\it critical cliques}. In this paper, we present new observations and new techniques for the study of kernelization algorithms for the {\sc cluster editing} problem. Our techniques are based on the study of the relationship between {\sc cluster editing} and graph edge-cuts. As an application, we present an ${\cal O}(n^2)$-time algorithm that constructs a $2k$ kernel for the {\it weighted} version of the {\sc cluster editing} problem. Our result meets the best kernel size for the unweighted version for the {\sc cluster editing} problem, and significantly improves the previous best kernel of quadratic size for the weighted version of the problem

Fully Dynamic Maintenance of Arc-Flags in Road Networks

International audienceThe problem of finding best routes in road networks can be solved by applying Dijkstra's shortest paths algorithm. Unfortunately, road networks deriving from real-world applications are huge yielding unsustainable times to compute shortest paths. For this reason, great research efforts have been done to accelerate Dijkstra's algorithm on road networks. These efforts have led to the development of a number of speed-up techniques, as for example Arc-Flags, whose aim is to compute additional data in a preprocessing phase in order to accelerate the shortest paths queries in an on-line phase. The main drawback of most of these techniques is that they do not work well in dynamic scenarios. In this paper we propose a new algorithm to update the Arc-Flags of a graph subject to edge weight decrease operations. To check the practical performances of the new algorithm we experimentally analyze it, along with a previously known algorithm for edge weight increase operations, on real-world road networks subject to fully dynamic sequences of operations. Our experiments show a significant speed-up in the updating phase of the Arc-Flags, at the cost of a small space and time overhead in the preprocessing phase

The level set method for the two-sided eigenproblem

We consider the max-plus analogue of the eigenproblem for matrix pencils Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible values of lambda), which is a finite union of intervals, can be computed in pseudo-polynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introduction of a spectral function, which we interpret in terms of the least Chebyshev distance between Ax and lambda Bx. The spectrum is obtained as the zero level set of this function.Comment: 34 pages, 4 figures. Changes with respect to the previous version: we explain relation to mean-payoff games and discrete event systems, and show that the reconstruction of spectrum is pseudopolynomia

A Testpart for Interdisciplinary Analyses in Micro Production Engineering

AbstractIn 2011, a round robin test was initiated within the group of CIRP Research Affiliates. The aim was to establish a platform for linking interdisciplinary research in order to share the expertise and experiences of participants all over the world. This paper introduces a testpart which has been designed to allow an analysis of different manufacturing technologies, simulation methods, machinery and metrology as well as process and production planning aspects. Current investigations are presented focusing on the machining and additive processes to produce the geometry, simulation approaches, machine analysis, and a comparison of measuring technologies. Challenges and limitations regarding the manufacturing and evaluation of the testpart features by the applied methods are discussed.Video abstrac