This paper deals with intersections' modeling for vehicular traffic flow governed by the Lighthill $\&$ Whitham [24] and Richards [26] model. We present a straightforward reformulation of recent intersections' models, introduced in [19] and [4], using a description in terms of supply and demand functions [22, 6]. This formulation is used to state the new model which takes into account a possible storage capacity of an intersection as seen in roundabouts or highway on-ramps. We discuss the Riemann problem at the junction and present numerical simulations.

We have developed a new hybrid model for an heterogeneous traffic flow, based on a coupling of the Lighthill — Whitham and Richards (LWR) macroscopic model and the kinetic model. On the highways of a road network, we consider the macroscopic description of the traffic flow and switch to the kinetic model to compute the mass flux through a junction. This new model reproduces the capacity drop phenomenon at a merge junction, for instance, without imposing any priority rule. We present some numerical simulations in which we compare the results of the hybrid model with those given by the fully macroscopic model. Furthermore, we illustrate the consequences of the velocity distribution on the flow through a merging junction.

Background: It is generally acknowledged that a functional understanding of a biological system can only be obtained by an understanding of the collective of molecular interactions in form of biological networks. Protein networks are one particular network type of special importance, because proteins form the functional base units of every biological cell. On a mesoscopic level of protein networks, modules are of significant importance because these building blocks may be the next elementary functional level above individual proteins allowing to gain insight into fundamental organizational principles of biological cells. Results: In this paper, we provide a comparative analysis of five popular and four novel module detection algorithms. We study these module prediction methods for simulated benchmark networks as well as 10 biological protein interaction networks (PINs). A particular focus of our analysis is placed on the biological meaning of the predicted modules by utilizing the Gene Ontology (GO) database as gold standard for the definition of biological processes. Furthermore, we investigate the robustness of the results by perturbing the PINs simulating in this way our incomplete knowledge of protein networks. Conclusions: Overall, our study reveals that there is a large heterogeneity among the different module prediction algorithms if one zooms-in the biological level of biological processes in the form of GO terms and all methods are severely affected by a slight perturbation of the networks. However, we also find pathways that are enriched in multiple modules, which could provide important information about the hierarchical organization of the system.

Subsurface physical barriers are amongst the most effective methods to mitigate seawater intrusion in coastal aquifers. The main objective of this study was to examine the impact of cutoff walls on saltwater upconing using laboratory and numerical modelling experiments. Physical experiments were first completed to reproduce the saltwater upconing process in a laboratory-scale coastal aquifer model incorporating an impermeable cutoff wall. Numerical modelling was used for validation purposes and to perform additional simulations to explore the protective effect of cutoff walls against saltwater upconing. The results suggest that the cutoff wall did not substantially delay the saltwater upconing mechanism in the investigated configurations. Laboratory and numerical observations showed the existence of some residual saline water, which remained on the upper part of the aquifer on the seaward side of the wall following the retreat of the saltwater. The protective effect of cutoff walls was noticeably sensitive to the design parameters. Specifically, cutoff walls installed close to the pumping well enabled the implementation of higher pumping rates, therefore a more optimal use of the freshwater, especially for deeper wells. The results highlighted that the penetration depth of the cutoff walls may not necessarily need to exceed the depth of the pumping well to ensure effectiveness, which is of great importance from construction and economic perspectives.

In this paper, we introduce a macroscopic model for road traffic accidents along highway sections. We discuss the motivation and the derivation of such a model, and we present its mathematical properties. The results are presented by means of examples where a section of a crowded one-way highway contains in the middle a cluster of drivers whose dynamics are prone to road traffic accidents. We discuss the coupling conditions and present some existence results of weak solutions to the associated Riemann Problems. Furthermore, we illustrate some features of the proposed model through some numerical simulations.

Image analysis is a useful tool for visualising flow through laboratory-scale aquifers but existing methods of converting image light intensity to concentration can be labour intensive and time consuming. The new approach proposed in this study utilises the Random Forest machine learning technique to build a calibration model to replace the requirement for unique calibrations of each test aquifer. Calibration images from a previous experimental study were used to train the Random Forest model and the output was compared to the results from a high resolution pixel-wise methodology. The Random Forest model provided a trade-off in accuracy with increased efficiency and reduced sensitivity to image desynchronisation when compared to the pixel-wise method. The reduced accuracy was attributed in part to non-linear lighting distribution across the sandbox, which could be corrected by orientating the backlights effectively. Time savings of around 35% were achieved for this experimental study and this is expected to increase for larger scale studies. The new calibration approach exhibits some promising features in terms of its robustness to experimental error and its ability to process efficiently large-scale experiments in a shorter time frame.