Equilibrium Configurations of Homogeneous Fluids in General Relativity

By means of a highly accurate, multi-domain, pseudo-spectral method, we investigate the solution space of uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies. It turns out that this space can be divided up into classes of solutions. In this paper, we present two new classes including relativistic core-ring and two-ring solutions. Combining our knowledge of the first four classes with post-Newtonian results and the Newtonian portion of the first ten classes, we present the qualitative behaviour of the entire relativistic solution space. The Newtonian disc limit can only be reached by going through infinitely many of the aforementioned classes. Only once this limiting process has been consummated, can one proceed again into the relativistic regime and arrive at the analytically known relativistic disc of dust.Comment: 8 pages, colour figures, v3: minor additions including one reference, accepted by MNRA

Adding a new station and a road link to a road-rail network in the presence of modal competition

In this paper we study the problem of locating a new station on an existing rail corridor and a new junction on an existing road network, and connecting them with a new road segment under a budget constraint. We consider three objective functions and the corresponding optimization problems, which are modeled by means of mixed integer non-linear programs. For small instances, the models can be solved directly by a standard solver. For large instances, an enumerative algorithm based on a discretization of the problem is proposed. Computational experiments show that the latter approach yields high quality solutions within short computing times.This research was done while one of the co-authors (Federico Perea) was enjoying a research stay funded by the Spanish Ministerio de Educacion y Ciencia, under program Jose Castillejo. This research was partially funded by the Canadian Natural Sciences and Engineering Research Council under grant 39682-10, by the Spanish Ministerio de Educacion, Ciencia e Innovacion/FEDER under grant MTM2009-14243, by the Spanish Ministerio de Economia y Competitividad/FEDER under grant MTM2012-37048, and by the Junta de Andalucia/FEDER under grants P09-TEP-5022 and FQM-5849. This support is gratefully acknowledged. Special thanks are due to the referees for their valuable comments and to Javier Fernandez and Lorenzo jaro, from the Spanish railway infrastructure management company ADIF, for providing some of the necessary data for the case study.Perea Rojas Marcos, F.; Mesa López-Colmenar, JA.; Laporte, G. (2014). Adding a new station and a road link to a road-rail network in the presence of modal competition. Transportation Research Part B: Methodological. 68:1-16. https://doi.org/10.1016/j.trb.2014.05.015S1166

Restoring betatron phase coherence in a beam-loaded laser-wakefield accelerator

Matched beam loading in laser wakefield acceleration (LWFA), characterizing the state of flattening of the acceleration electric field along the bunch, leads to the minimization of energy spread at high bunch charges. Here, we demonstrate by independently controlling injected charge and acceleration gradients, using the self-truncated ionization injection scheme, that minimal energy spread coincides with a reduction of the normalized beam divergence. With the simultaneous confirmation of a constant beam radius at the plasma exit, deduced from betatron radiation spectroscopy, we attribute this effect to the reduction of chromatic betatron decoherence. Thus, beam loaded LWFA enables highest longitudinal and transverse phase space densities

Delay management including capacities of stations

The question of delay management (DM) is whether trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the capacity constraints of the tracks making sure that no two trains can use the same piece of track at the same time. While these capacity constraints have been included in integer programming formulations for DM, the capacity constraints of the stations (only offering a limited number of platforms) have been neglected so far. This can lead to highly infeasible solutions. In order to overcome this problem we suggest two new formulations for DM both including the stations' capacities. We present numerical results showing that the assignment-based formulation is clearly superior to the packing formulation. We furthermore propose an iterative algorithm in which we improve the platform assignment with respect to the current delays of the trains at each station in each step. We will show that this subproblem asks for coloring the nodes of a graph with a given number of colors while minimizing the weight of the conflicts. We show that the graph to be colored is an interval graph and that the problem can be solved in polynomial time by presenting a totally unimodular IP formulation

Delay Management including Capacities of Stations

The question of delay management is whether trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the available capacity of the railway infrastructure. While the limited capacity of the tracks has been considered in delay management models, the limited capacity of the stations has been neglected so far. In this paper, we develop a model for the delay management problem that includes the stations’ capacities. This model allows to reschedule the platform assignment dynamically. Furthermore, we propose an iterative algorithm in which we first solve the delay management model with a fixed platform assignment and then improve this platform assignment in each step. We show that the latter problem can be solved in polynomial time by presenting a totally unimodular IP formulation. Finally, we present an extension of the model that balances the delay of the passengers on the one hand and the number of changes in the platform assignment on the other. All models are evaluated on real-world instances from Netherlands Railways

Delay Management with Re-Routing of Passengers

The question of delay management is whether trains should wait for a delayed feeder train or should depart on time. In classical delay management models passengers always take their originally planned route. In this paper, we propose a model where re-routing of passengers is incorporated. To describe the problem we represent it as an event-activity network similar to the one used in classical delay management, with some additional events to incorporate origin and destination of the passengers. We present an integer programming formulation of this problem. Furthermore, we discuss the variant in which we assume fixed costs for maintaining connections and we present a polynomial algorithm for the special case of only one origin-destination pair. Finally, computational experiments based on real-world data from Netherlands Railways show that significant improvements can be obtained by taking the re-routing of passengers into account in the model

Mesostructured ZnO/Au nanoparticle composites with enhanced photocatalytic activity

Ease of catalyst separation from reaction mixtures represents a significant advantage in heterogeneous photocatalytic wastewater treatment. However, the activity of the catalyst strongly depends on its surface-to-volume ratio. Here, we present an approach based on cylindrical polybutadiene-block-poly(2-vinylpyridine) polymer brushes as template, which can be simultaneously loaded with zinc oxide (ZnO) and gold (Au) nanoparticles. Pyrolytic template removal of the polymer yields in mesostructured ZnO/Au composites, showing higher efficiencies in the photocatalytic degradation of ciprofloxacin and levofloxacin (generic antibiotics present in clinical wastewater) as compared to neat mesostructured ZnO. Upscaling of the presented catalyst is straightforward promising high technical relevance

The continuous stop location problem in public transportation networks

In this paper we consider the location of stops along the edges of an already existing public transportation network. This can be the introduction of bus stops along some given bus routes, or of railway stations along the tracks in a railway network. The positive effect of new stops is given by the better access of the potential customers to their closest station, while the increasement of travel time caused by the additional stopping activities of the trains leads to a negative effect. The goal is to cover all given demand points with a minimal amount of additional traveling time, where covering may be defined with respect to an arbitrary norm (or even a gauge). Unfortunately, this problem is NP-hard, even if only the Euclidean distance is used. In this paper, we give a reduction to a finite candidate set leading to a discrete set covering problem. Moreover, we identify network structures in which the coefficient matrix of the resulting set covering problem is totally unimodular, and use this result to derive efficient solution approaches. Various extensions of the problem are also discussed

Min-ordering and max-ordering scalarization methods for multi-objective robust optimization

Several robustness concepts for multi-objective uncertain optimization have been developed during the last years, but not many solution methods. In this paper we introduce two methods to find min–max robust efficient solutions based on scalarizations: the min-ordering and the max-ordering method. We show that all point-based min–max robust weakly efficient solutions can be found with the max-ordering method and that the min-ordering method finds set-based min–max robust weakly efficient solutions, some of which cannot be found with formerly developed scalarization based methods. We then show how the scalarized problems may be approached for multi-objective uncertain combinatorial optimization problems with special uncertainty sets. We develop compact mixed-integer linear programming formulations for multi-objective extensions of bounded uncertainty (also known as budgeted or Γ-uncertainty). For interval uncertainty, we show that the resulting problems reduce to well-known single-objective problems