Influence of a slow moving vehicle on traffic: Well-posedness and approximation for a mildly non-local model

In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a non-local constraint on the flux. The constraint level depends on the trajectory of the slower vehicle which is given by an ODE depending on the downstream traffic density. After proving well-posedness, we first build a finite volume scheme and prove its convergence, and then investigate numerically this model by performing a series of tests. In particular, the link with the limit local problem of [M.L. Delle Monache and P. Goatin, J. Differ. Equ. 257(11), 4015-4029 (2014)] is explored numerically

Initial Data Identication in Space Dependent Conservation Laws and Hamilton-Jacobi Equations

Consider a Conservation Law and a Hamilton-Jacobi equation with a ux/Hamiltonian depending also on the space variable. We characterize rst the attainable set of the two equations and, second, the set of initial data evolving at a prescribed time into a prescribed prole. An explicit example then shows the deep dierences between the cases of x-independent and x-dependent uxes/Hamiltonians

High order numerical schemes for transport equations on bounded domains

This article is an account of the NABUCO project achieved during the summer camp CEMRACS 2019 devoted to geophysical fluids and gravity flows. The goal is to construct finite difference approximations of the transport equation with nonzero incoming boundary data that achieve the best possible convergence rate in the maximum norm. We construct, implement and analyze the so-called inverse Lax-Wendroff procedure at the incoming boundary. Optimal convergence rates are obtained by combining sharp stability estimates for extrapolation boundary conditions with numerical boundary layer expansions. We illustrate the results with the Lax-Wendroff and O3 schemes

Robust late twenty-first century shift in the regional monsoons in RegCM-CORDEX simulations

AbstractWe use an unprecedented ensemble of regional climate model (RCM) projections over seven regional CORDEX domains to provide, for the first time, an RCM-based global view of monsoon changes at various levels of increased greenhouse gas (GHG) forcing. All regional simulations are conducted using RegCM4 at a 25 km horizontal grid spacing using lateral and lower boundary forcing from three General Circulation Models (GCMs), which are part of the fifth phase of the Coupled Model Inter-comparison Project (CMIP5). Each simulation covers the period from 1970 through 2100 under two Representative Concentration Pathways (RCP2.6 and RCP8.5). Regional climate simulations exhibit high fidelity in capturing key characteristics of precipitation and atmospheric dynamics across monsoon regions in the historical period. In the future period, regional monsoons exhibit a spatially robust delay in the monsoon onset, an increase in seasonality, and a reduction in the rainy season length at higher levels of radiative forcing. All regions with substantial delays in the monsoon onset exhibit a decrease in pre-monsoon precipitation, indicating a strong connection between pre-monsoon drying and a shift in the monsoon onset. The weakening of latent heat driven atmospheric warming during the pre-monsoon period delays the overturning of atmospheric subsidence in the monsoon regions, which defers their transitioning into deep convective states. Monsoon changes under the RCP2.6 scenario are mostly within the baseline variability

Minimally invasive surgery and cancer: controversies part 1

Perhaps there is no more important issue in the care of surgical patients than the appropriate use of minimally invasive surgery (MIS) for patients with cancer. Important advances in surgical technique have an impact on early perioperative morbidity, length of hospital stay, pain management, and quality of life issues, as clearly proved with MIS. However, for oncology patients, historically, the most important clinical questions have been answered in the context of prospective randomized trials. Important considerations for MIS and cancer have been addressed, such as what are the important immunologic consequences of MIS versus open surgery and what is the role of laparoscopy in the staging of gastrointestinal cancers? This review article discusses many of the key controversies in the minimally invasive treatment of cancer using the pro–con debate format

BioVeL : a virtual laboratory for data analysis and modelling in biodiversity science and ecology

Background: Making forecasts about biodiversity and giving support to policy relies increasingly on large collections of data held electronically, and on substantial computational capability and capacity to analyse, model, simulate and predict using such data. However, the physically distributed nature of data resources and of expertise in advanced analytical tools creates many challenges for the modern scientist. Across the wider biological sciences, presenting such capabilities on the Internet (as "Web services") and using scientific workflow systems to compose them for particular tasks is a practical way to carry out robust "in silico" science. However, use of this approach in biodiversity science and ecology has thus far been quite limited. Results: BioVeL is a virtual laboratory for data analysis and modelling in biodiversity science and ecology, freely accessible via the Internet. BioVeL includes functions for accessing and analysing data through curated Web services; for performing complex in silico analysis through exposure of R programs, workflows, and batch processing functions; for on- line collaboration through sharing of workflows and workflow runs; for experiment documentation through reproducibility and repeatability; and for computational support via seamless connections to supporting computing infrastructures. We developed and improved more than 60 Web services with significant potential in many different kinds of data analysis and modelling tasks. We composed reusable workflows using these Web services, also incorporating R programs. Deploying these tools into an easy-to-use and accessible 'virtual laboratory', free via the Internet, we applied the workflows in several diverse case studies. We opened the virtual laboratory for public use and through a programme of external engagement we actively encouraged scientists and third party application and tool developers to try out the services and contribute to the activity. Conclusions: Our work shows we can deliver an operational, scalable and flexible Internet-based virtual laboratory to meet new demands for data processing and analysis in biodiversity science and ecology. In particular, we have successfully integrated existing and popular tools and practices from different scientific disciplines to be used in biodiversity and ecological research.Peer reviewe

Hétérogénéité dans les lois de conservation scalaires : approximation et applications

This thesis is devoted to the treatment of heterogeneity in scalar conservation laws. We call heterogeneous a conservation law which is not invariant by space translation. These equations arise for instance in traffic flow dynamics modeling. The presence of traffic lights or roads that have a variable maximum speed limit are examples of mechanisms which lead to heterogeneous conservation laws. Considering such equations is a way to expand macroscopic traffic flow models. We tackle three classes of inhomogeneous problems for which we extend the mathematical framework for both the theoretical analysis and the numerical approximation. We fully investigate the treatment of heterogeneity when one or several moving interfaces are added in the classic LWR model for traffic flow. Flux constraints are attached to each interfaces. The resulting class of models can be used to take into account the presence of slow moving vehicles that reduce the road capacity and thus generates moving bottlenecks for the surrounding traffic flow. They can also describe the regulating effect of autonomous vehicles. In this framework, the interfaces and the constraints are linked in a nonlocal way to the traffic density and/or to an orderliness marker describing the state of the drivers. The description of the heterogeneity caused by the variations in the drivers' organization leads to the analysis of a so-called second order model. The numerical aspect plays a central role in the analysis of these traffic flow models. We construct robust numerical schemes and establish specific techniques to obtain compactness of the approximate solutions. Proving the convergence of these schemes lead to existence results.Finally, with the space-dependent LWR traffic flow model in mind, we theoretically analyze a class of scalar conservation laws with explicit space dependency. Classical results such as well-posedness or the link to the associated Hamilton-Jacobi equation are obtained under a set of assumptions more fitting with the modeling hypothesis. With applications that go beyond traffic modeling in mind, we aim to tackle initial data identification problems.Dans cette thèse, on traite la prise en compte de l'hétérogénéité dans les lois de conservation scalaires, c'est-à-dire les lois de conservation non invariantes par translation en espace. Ces équations apparaissent notamment dans les modèles de trafic. Par exemple, les mécanismes suivants introduisent de l'hétérogénéité : la présence de feux de circulation, des portions de route où la vitesse maximale est limitée, la variabilité de l'état de la route, etc... La prise en compte de l'hétérogénéité permet d'enrichir les modèles de trafic. On aborde trois classes de problèmes inhomogènes pour lesquelles on complète et approfondit le cadre mathématique pour l'analyse théorique et l'approximation numérique.Nous explorons en détail le cadre où l'hétérogénéité est matérialisée par l'ajout d'une ou plusieurs interfaces mobiles. Le long des interfaces, on impose une condition de majoration sur le flux de la loi de conservation. Cette classe de modèles permet de tenir compte de la présence d'un petit nombre de véhicules encombrants et lents (ou alors, de véhicules autonomes qui ont pour rôle la régulation du trafic). Dans ce cadre, l'évolution des interfaces et des contraintes est couplée de façon non locale à l'état du trafic et/ou à des paramètres spécifiant l'état du véhicule ou du conducteur. En outre, nous élaborons une description de l'hétérogénéité du trafic résultant des variations du degré d'organisation des conducteurs, dans le cadre des modèles dits "du second ordre". L'aspect numérique est prépondérant pour les modèles de trafic que nous étudions. On construit des schémas numériques robustes et on élabore des techniques de compacité spécifiques. La convergence de ces schémas conduit à des résultats d'existence.Enfin, en lien avec le modèle décrivant l'évolution d'une densité de véhicules sur une route hétérogène, on étudie théoriquement une loi de conservation dans laquelle la dépendance spatiale du flux est explicite. Des résultats classiques sur le caractère bien posé ou la correspondance avec l'équation de Hamilton-Jacobi associée sont obtenus sous des hypothèses plus en adéquation avec la modélisation que celles rencontrées dans la littérature. Les applications allant au-delà de la description du trafic, on se donne pour objectif l'analyse approfondie des problèmes d'identification de données initiales

A LWR model with constraints at moving interfaces

39 pages, 7 fig., 24 ref.We propose a mathematical framework to the study of scalar conservation laws with moving interfaces. This framework is developed on a LWR model with constraint on the flux along these moving interfaces. Existence is proved by means of a finite volume scheme. The originality lies in the local modification of the mesh and in the treatment of the crossing points of the trajectories

Influence of a slow moving vehicle on traffic: Well-posedness and approximation for a mildly nonlocal model

In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a non-local constraint on the flux. The constraint level depends on the trajectory of the slower vehicle which is given by an ODE depending on the downstream traffic density. After proving well-posedness, we first build a finite volume scheme and prove its convergence, and then investigate numerically this model by performing a series of tests. In particular, the link with the limit local problem of [M.L. Delle Monache and P. Goatin, J. Differ. Equ. 257(11), 4015-4029 (2014)] is explored numerically