The SILCC (SImulating the LifeCycle of molecular Clouds) project: I. Chemical evolution of the supernova-driven ISM

The SILCC project (SImulating the Life-Cycle of molecular Clouds) aims at a more self-consistent understanding of the interstellar medium (ISM) on small scales and its link to galaxy evolution. We simulate the evolution of the multi-phase ISM in a 500 pc x 500 pc x 10 kpc region of a galactic disc, with a gas surface density of $\Sigma_{_{\rm GAS}} = 10 \;{\rm M}_\odot/{\rm pc}^2$. The Flash 4.1 simulations include an external potential, self-gravity, magnetic fields, heating and radiative cooling, time-dependent chemistry of H$_2$ and CO considering (self-) shielding, and supernova (SN) feedback. We explore SN explosions at different (fixed) rates in high-density regions (peak), in random locations (random), in a combination of both (mixed), or clustered in space and time (clustered). Only random or clustered models with self-gravity (which evolve similarly) are in agreement with observations. Molecular hydrogen forms in dense filaments and clumps and contributes 20% - 40% to the total mass, whereas most of the mass (55% - 75%) is in atomic hydrogen. The ionised gas contributes <10%. For high SN rates (0.5 dex above Kennicutt-Schmidt) as well as for peak and mixed driving the formation of H$_2$ is strongly suppressed. Also without self-gravity the H$_2$ fraction is significantly lower ($\sim$ 5%). Most of the volume is filled with hot gas ($\sim$90% within $\pm$2 kpc). Only for random or clustered driving, a vertically expanding warm component of atomic hydrogen indicates a fountain flow. Magnetic fields have little impact on the final disc structure. However, they affect dense gas ($n\gtrsim 10\;{\rm cm}^{-3}$) and delay H$_2$ formation. We highlight that individual chemical species, in particular atomic hydrogen, populate different ISM phases and cannot be accurately accounted for by simple temperature-/density-based phase cut-offs.Comment: 30 pages, 23 figures, submitted to MNRAS. Comments welcome! For movies of the simulations and download of selected Flash data see the SILCC website: http://www.astro.uni-koeln.de/silc

The SILCC project: III. Regulation of star formation and outflows by stellar winds and supernovae

We study the impact of stellar winds and supernovae on the multi-phase interstellar medium using three-dimensional hydrodynamical simulations carried out with FLASH. The selected galactic disc region has a size of (500 pc)$^2$ x $\pm$ 5 kpc and a gas surface density of 10 M$_{\odot}$/pc$^2$. The simulations include an external stellar potential and gas self-gravity, radiative cooling and diffuse heating, sink particles representing star clusters, stellar winds from these clusters which combine the winds from indi- vidual massive stars by following their evolution tracks, and subsequent supernova explosions. Dust and gas (self-)shielding is followed to compute the chemical state of the gas with a chemical network. We find that stellar winds can regulate star (cluster) formation. Since the winds suppress the accretion of fresh gas soon after the cluster has formed, they lead to clusters which have lower average masses (10$^2$ - 10$^{4.3}$ M$_{\odot}$) and form on shorter timescales (10$^{-3}$ - 10 Myr). In particular we find an anti-correlation of cluster mass and accretion time scale. Without winds the star clusters easily grow to larger masses for ~5 Myr until the first supernova explodes. Overall the most massive stars provide the most wind energy input, while objects beginning their evolution as B-type stars contribute most of the supernova energy input. A significant outflow from the disk (mass loading $\gtrsim$ 1 at 1 kpc) can be launched by thermal gas pressure if more than 50% of the volume near the disc mid-plane can be heated to T > 3x10$^5$ K. Stellar winds alone cannot create a hot volume-filling phase. The models which are in best agreement with observed star formation rates drive either no outflows or weak outflows.Comment: 23 pages; submitted to MNRA

Ground-State Roughness of the Disordered Substrate and Flux Line in d=2

We apply optimization algorithms to the problem of finding ground states for crystalline surfaces and flux lines arrays in presence of disorder. The algorithms provide ground states in polynomial time, which provides for a more precise study of the interface widths than from Monte Carlo simulations at finite temperature. Using $d=2$ systems up to size $420^2$, with a minimum of $2 \times 10^3$ realizations at each size, we find very strong evidence for a $\ln^2(L)$ super-rough state at low temperatures.Comment: 10 pages, 3 PS figures, to appear in PR

Statistical Topography of Glassy Interfaces

Statistical topography of two-dimensional interfaces in the presence of quenched disorder is studied utilizing combinatorial optimization algorithms. Finite-size scaling is used to measure geometrical exponents associated with contour loops and fully packed loops. We find that contour-loop exponents depend on the type of disorder (periodic ``vs'' non-periodic) and they satisfy scaling relations characteristic of self-affine rough surfaces. Fully packed loops on the other hand are unaffected by disorder with geometrical exponents that take on their pure values.Comment: 4 pages, REVTEX, 4 figures included. Further information can be obtained from [email protected]

Simulation of the Zero Temperature Behavior of a 3-Dimensional Elastic Medium

We have performed numerical simulation of a 3-dimensional elastic medium, with scalar displacements, subject to quenched disorder. We applied an efficient combinatorial optimization algorithm to generate exact ground states for an interface representation. Our results indicate that this Bragg glass is characterized by power law divergences in the structure factor $S(k)\sim A k^{-3}$. We have found numerically consistent values of the coefficient $A$ for two lattice discretizations of the medium, supporting universality for $A$ in the isotropic systems considered here. We also examine the response of the ground state to the change in boundary conditions that corresponds to introducing a single dislocation loop encircling the system. Our results indicate that the domain walls formed by this change are highly convoluted, with a fractal dimension $d_f=2.60(5)$. We also discuss the implications of the domain wall energetics for the stability of the Bragg glass phase. As in other disordered systems, perturbations of relative strength $\delta$ introduce a new length scale $L^* \sim \delta^{-1/\zeta}$ beyond which the perturbed ground state becomes uncorrelated with the reference (unperturbed) ground state. We have performed scaling analysis of the response of the ground state to the perturbations and obtain $\zeta = 0.385(40)$. This value is consistent with the scaling relation $\zeta=d_f/2- \theta$, where $\theta$ characterizes the scaling of the energy fluctuations of low energy excitations.Comment: 20 pages, 13 figure

The SILCC (SImulating the LifeCycle of molecular Clouds) project - I. Chemical evolution of the supernova-driven ISM

The SILCC (SImulating the Life-Cycle of molecular Clouds) project aims to self-consistently understand the small-scale structure of the interstellar medium (ISM) and its link to galaxy evolution. We simulate the evolution of the multiphase ISM in a (500pc)2×±5kpc region of a galactic disc, with a gas surface density of $\Sigma _{_{\rm GAS}} = 10 \;{\rm M}_{\odot }\,{\rm pc}^{-2}$. The flash 4 simulations include an external potential, self-gravity, magnetic fields, heating and radiative cooling, time-dependent chemistry of H2 and CO considering (self-) shielding, and supernova (SN) feedback but omit shear due to galactic rotation. We explore SN explosions at different rates in high-density regions (peak), in random locations with a Gaussian distribution in the vertical direction (random), in a combination of both (mixed), or clustered in space and time (clus/clus2). Only models with self-gravity and a significant fraction of SNe that explode in low-density gas are in agreement with observations. Without self-gravity and in models with peak driving the formation of H2 is strongly suppressed. For decreasing SN rates, the H2 mass fraction increases significantly from<10 per cent for high SN rates, i.e. 0.5 dex above Kennicutt-Schmidt, to 70-85 per cent for low SN rates, i.e. 0.5 dex below KS. For an intermediate SN rate, clustered driving results in slightly more H2 than random driving due to the more coherent compression of the gas in larger bubbles. Magnetic fields have little impact on the final disc structure but affect the dense gas (n≳10 cm−3) and delay H2 formation. Most of the volume is filled with hot gas (∼80 per cent within ±150pc). For all but peak driving a vertically expanding warm component of atomic hydrogen indicates a fountain flow. We highlight that individual chemical species populate different ISM phases and cannot be accurately modelled with temperature-/density-based phase cut-off

Fuzzy-logic controlled genetic algorithm for the rail-freight crew-scheduling problem

AbstractThis article presents a fuzzy-logic controlled genetic algorithm designed for the solution of the crew-scheduling problem in the rail-freight industry. This problem refers to the assignment of train drivers to a number of train trips in accordance with complex industrial and governmental regulations. In practice, it is a challenging task due to the massive quantity of train trips, large geographical span and significant number of restrictions. While genetic algorithms are capable of handling large data sets, they are prone to stalled evolution and premature convergence on a local optimum, thereby obstructing further search. In order to tackle these problems, the proposed genetic algorithm contains an embedded fuzzy-logic controller that adjusts the mutation and crossover probabilities in accordance with the genetic algorithm’s performance. The computational results demonstrate a 10% reduction in the cost of the schedule generated by this hybrid technique when compared with a genetic algorithm with fixed crossover and mutation rates

Rail-freight crew scheduling with a genetic algorithm

peer reviewedThis article presents a novel genetic algorithm designed for the solution of the Crew Scheduling Problem (CSP) in the rail-freight industry. CSP is the task of assigning drivers to a sequence of train trips while ensuring that no driver’s schedule exceeds the permitted working hours, that each driver starts and finishes their day’s work at the same location, and that no train routes are left without a driver. Real-life CSPs are extremely complex due to the large number of trips, opportunities to use other means of transportation, and numerous government regulations and trade union agreements. CSP is usually modelled as a set-covering problem and solved with linear programming methods. However, the sheer volume of data makes the application of conventional techniques computationally expensive, while existing genetic algorithms often struggle to handle the large number of constraints. A genetic algorithm is presented that overcomes these challenges by using an indirect chromosome representation and decoding procedure. Experiments using real schedules on the UK national rail network show that the algorithm provides an effective solution within a faster timeframe than alternative approaches

A multiobjective model for passive portfolio management: an application on the S&P 100 index

This is an author's accepted manuscript of an article published in: “Journal of Business Economics and Management"; Volume 14, Issue 4, 2013; copyright Taylor & Francis; available online at: http://dx.doi.org/10.3846/16111699.2012.668859Index tracking seeks to minimize the unsystematic risk component by imitating the movements of a reference index. Partial index tracking only considers a subset of the stocks in the index, enabling a substantial cost reduction in comparison with full tracking. Nevertheless, when heterogeneous investment profiles are to be satisfied, traditional index tracking techniques may need different stocks to build the different portfolios. The aim of this paper is to propose a methodology that enables a fund s manager to satisfy different clients investment profiles but using in all cases the same subset of stocks, and considering not only one particular criterion but a compromise between several criteria. For this purpose we use a mathematical programming model that considers the tracking error variance, the excess return and the variance of the portfolio plus the curvature of the tracking frontier. The curvature is not defined for a particular portfolio, but for all the portfolios in the tracking frontier. This way funds managers can offer their clients a wide range of risk-return combinations just picking the appropriate portfolio in the frontier, all of these portfolios sharing the same shares but with different weights. An example of our proposal is applied on the S&P 100.García García, F.; Guijarro Martínez, F.; Moya Clemente, I. (2013). A multiobjective model for passive portfolio management: an application on the S&P 100 index. Journal of Business Economics and Management. 14(4):758-775. doi:10.3846/16111699.2012.668859S758775144Aktan, B., Korsakienė, R., & Smaliukienė, R. (2010). TIME‐VARYING VOLATILITY MODELLING OF BALTIC STOCK MARKETS. 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V., & Stasytyte, V. (s. f.). Decision Making Strategies in Global Exchange and Capital Markets. Advances and Innovations in Systems, Computing Sciences and Software Engineering, 17-22. doi:10.1007/978-1-4020-6264-3_4Tabata, Y., & Takeda, E. (1995). Bicriteria Optimization Problem of Designing an Index Fund. Journal of the Operational Research Society, 46(8), 1023-1032. doi:10.1057/jors.1995.139Teresienė, D. (2009). LITHUANIAN STOCK MARKET ANALYSIS USING A SET OF GARCH MODELS. Journal of Business Economics and Management, 10(4), 349-360. doi:10.3846/1611-1699.2009.10.349-36