Quark-Gluon-Plasma Formation at SPS Energies?

By colliding ultrarelativistic ions, one achieves presently energy densities close to the critical value, concerning the formation of a quark-gluon-plasma. This indicates the importance of fluctuations and the necessity to go beyond the investigation of average events. Therefore, we introduce a percolation approach to model the final stage ($\tau > 1$ fm/c) of ion-ion collisions, the initial stage being treated by well-established methods, based on strings and Pomerons. The percolation approach amounts to finding high density domains, and treating them as quark-matter droplets. In this way, we have a {\bf realistic, microscopic, and Monte--Carlo based model which allows for the formation of quark matter.} We find that even at SPS energies large quark-matter droplets are formed -- at a low rate though. In other words: large quark-matter droplets are formed due to geometrical fluctuation, but not in the average event.Comment: 7 Pages, HD-TVP-94-6 (1 uuencoded figure

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.

Density of critical points for a Gaussian random function

Critical points of a scalar quantitiy are either extremal points or saddle points. The character of the critical points is determined by the sign distribution of the eigenvalues of the Hessian matrix. For a two-dimensional homogeneous and isotropic random function topological arguments are sufficient to show that all possible sign combinations are equidistributed or with other words, the density of the saddle points and extrema agree. This argument breaks down in three dimensions. All ratios of the densities of saddle points and extrema larger than one are possible. For a homogeneous Gaussian random field one finds no longer an equidistribution of signs, saddle points are slightly more frequent.Comment: 11 pages 1 figure, changes in list of references, corrected typo

On Sparsification for Computing Treewidth

We investigate whether an n-vertex instance (G,k) of Treewidth, asking whether the graph G has treewidth at most k, can efficiently be made sparse without changing its answer. By giving a special form of OR-cross-composition, we prove that this is unlikely: if there is an e > 0 and a polynomial-time algorithm that reduces n-vertex Treewidth instances to equivalent instances, of an arbitrary problem, with O(n^{2-e}) bits, then NP is in coNP/poly and the polynomial hierarchy collapses to its third level. Our sparsification lower bound has implications for structural parameterizations of Treewidth: parameterizations by measures that do not exceed the vertex count, cannot have kernels with O(k^{2-e}) bits for any e > 0, unless NP is in coNP/poly. Motivated by the question of determining the optimal kernel size for Treewidth parameterized by vertex cover, we improve the O(k^3)-vertex kernel from Bodlaender et al. (STACS 2011) to a kernel with O(k^2) vertices. Our improved kernel is based on a novel form of treewidth-invariant set. We use the q-expansion lemma of Fomin et al. (STACS 2011) to find such sets efficiently in graphs whose vertex count is superquadratic in their vertex cover number.Comment: 21 pages. Full version of the extended abstract presented at IPEC 201

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

Optimal Route Assignment in Large Scale Micro-Simulations

Traffic management and route guidance are optimization problems by nature. In this article, we consider algorithms for centralized route guidance and discuss fairness aspects for the individual user resulting from optimal route guidance policies. The first part of this article deals with the mathematical aspects of these optimization problems from the viewpoint of network flow theory. We present algorithms which solve the constrained multicommodity minimum cost flow problem (CMCF) to optimality. A feasible routing is given by a flow x, and the cost of flow x is the total travel time spent in the network. The corresponding optimum is a restricted system optimum with a globally controlled constrained or fairness factor . This approach implements a compromise between user equilibrium and system optimum. The goal is to find a route guidance strategy which minimizes global and community criteria with individual needs as constraints. The fairness factor L restricts the set of all feasible routes to the subset of acceptable routes. This might include the avoidance of routes which are much longer than shortest routes, the exclusion of certain streets, preferences for scenic paths, or restrictions on the number of turns to be taken. Most remarkably is that the subset of acceptable routes can also be interpreted as a mental map of routes. ()cx1L> In the second part we apply our CMCF algorithms in a large scale multi-agent transportation simulation toolkit, which is called MATSIM-T. We use as initial routes the ones computed by our CMCF algorithms. This choice of initial routes makes it possible to exploit the optimization potential within the simulation much better then it was done before. The result is a speed up of the iteration process in the simulation. We compare the existing simulation toolkit with the new integration of CMCF to proof our results

Molecular dynamics approach: from chaotic to statistical properties of compound nuclei

Statistical aspects of the dynamics of chaotic scattering in the classical model of $\alpha$-cluster nuclei are studied. It is found that the dynamics governed by hyperbolic instabilities which results in an exponential decay of the survival probability evolves to a limiting energy distribution whose density develops the Boltzmann form. The angular distribution of the corresponding decay products shows symmetry with respect to $\pi/2$ angle. Time estimated for the compound nucleus formation ranges within the order of $10^{-21}$s.Comment: 11 pages, LaTeX, non

Linear MIM-Width of Trees

We provide an $O(n \log n)$ algorithm computing the linear maximum induced matching width of a tree and an optimal layout.Comment: 19 pages, 7 figures, full version of WG19 paper of same nam

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