Related papers: Nash Flows Over Time with Tolls
We consider traffic flow dynamics for a network of signalized intersections, where the outflow from every link is constrained to be equal to a given capacity function if the queue length is positive, and equal to the minimum of cumulative…
A simple analytical model for a turbulent flow is proposed, which considers the flow as a collection of localized spatial structures that are composed of elementary "cells" in which the state of the particles (atoms or molecules) is…
The mathematical approaches for modeling dynamic traffic can roughly be divided into two categories: discrete packet routing models and continuous flow over time models. Despite very vital research activities on models in both categories,…
A bottleneck can largely deteriorate the flow, such as a traffic light or an on-ramp at a road. To alleviate bottleneck situations, one of the important strategies is to control the input rate to suit the state of the road. In this study,…
We consider a curve with boundary points free to move on a line in $\mathbb R^2$, which evolves by the $L^2$--gradient flow of the elastic energy, that is a linear combination of the Willmore and the length functional. For such planar…
Many transitional wall-bounded shear flows are characterised by the coexistence in state-space of laminar and turbulent regimes. Probing the edge boundary between the two attractors has led in the last decade to the numerical discovery of…
Modeling transition-continuum hypersonic flows poses significant challenges due to thermodynamic nonequilibrium and the associated breakdown of the continuum assumption. Standard continuum models such as the Navier-Stokes equations are…
We numerically study a model convection system of a suspension of self-propelled particles, motivated by recent experimental findings of localized and bistable bioconvection pattern, being distinct from classical Rayleigh--B\'{e}nard…
The problem Orienteering asks whether there exists a walk which visits a number of sites without exceeding some fuel budget. In the variant of the problem we consider, the cost of each edge in the walk is dependent on the time we depart one…
This paper presents a novel methodology for the direct numerical modeling and simulation of turbulent flows. The kinetic model equation is firstly extended to turbulent flow with the account of coupled evolution of kinetic, thermal, and…
We introduce temporal flows on temporal networks, i.e., networks the links of which exist only at certain moments of time. Such networks are ephemeral in the sense that no link exists after some time. Our flow model is new and differs from…
Network games are widely used as a model for selfish resource-allocation problems. In the classical model, each player selects a path connecting her source and target vertices. The cost of traversing an edge depends on the {\em load};…
We consider a game of decentralized timing of jobs to a single server (machine) with a penalty for deviation from a due date, and no delay costs. The jobs' sizes are homogeneous and deterministic. Each job belongs to a single decision…
Flows over time generalize classical network flows by introducing a notion of time. Each arc is equipped with a transit time that specifies how long flow takes to traverse it, while flow rates may vary over time within the given edge…
We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper…
Traveling waves are ubiquitous in nature and control the speed of many important dynamical processes, including chemical reactions, epidemic outbreaks, and biological evolution. Despite their fundamental role in complex systems, traveling…
Sadeghi et al. considered a bottleneck system with periodic inflow rate, and proved that a constant-rate input maximizes the time-averaged output rate among all periodic inflow rates. Here we provide a short and elementary proof of this…
In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is not convex in the usual sense in general but it turns out…