Related papers: Continuous-time link-based kinematic wave model: f…
The kinematic wave theory, originally proposed by (Lighthill and Whitham, 1955b; Richards, 1956), has been a good candidate for studying vehicular traffic. In this dissertation, we study kinematic wave models of network traffic, which are…
The link transmission model (LTM) has great potential for simulating traffic flow in large-scale networks since it is much more efficient and accurate than the Cell Transmission Model (CTM). However, there lack general continuous…
Accurate dynamic modeling of power systems is essential to assess the stability of electrical power systems when faced with disturbances, which can trigger cascading failures leading to blackouts. A continuum model proves to be effective in…
Visual navigation requires agents to reach goals in complex environments through perception and planning. World models address this task by simulating action-conditioned state transitions to predict future observations. Current navigation…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
Merging junctions are important network bottlenecks, and a better understanding of merging traffic dynamics has both theoretical and practical implications. In this paper, we present continuous kinematic wave models of merging traffic flow…
Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator…
Dynamic user equilibrium (DUE) is the most widely studied form of dynamic traffic assignment, in which road travelers engage in a non-cooperative Nash-like game with departure time and route choices. DUE models describe and predict the…
We analyze the Drinfeld-Sokolob-Wilson system, which features a dispersive, KdV type evolution with a dispersionless conservation law. We establish well-posedness with low regularity initial data $L^2({\mathbb T})\times L^2({\mathbb T})$…
In this work, a methodology is proposed for formulating general dynamical equations in mechanics under the umbrella of the principle of energy conservation. It is shown that Lagrange's equation, Hamilton's canonical equations, and…
The existence of random dynamical systems for McKean--Vlasov SDEs is established. This is approached by considering the joint dynamics of the corresponding nonlinear Fokker-Planck equation governing the law of the system and the underlying…
This paper establishes the continuity of the path delay operators for dynamic network loading (DNL) problems based on the Lighthill-Whitham-Richards model, which explicitly capture vehicle spillback. The DNL describes and predicts the…
We consider a coupled system composed of a linear differential-algebraic equation (DAE) and a linear large-scale system of ordinary differential equations where the latter stands for the dynamics of numerous identical particles. Replacing…
A fluid queuing network constitutes one of the simplest models in which to study flow dynamics over a network. In this model we have a single source-sink pair and each link has a per-time-unit capacity and a transit time. A dynamic…
A wide variety of real-world data, such as sea measurements, e.g., temperatures collected by distributed sensors and multiple unmanned aerial vehicles (UAV) trajectories, can be naturally represented as graphs, often exhibiting…
The paper considers a coupled system of linear Boltzmann transport equations (BTE), and its Continuous Slowing Down Approximation (CSDA). This system can be used to model the relevant transport of particles used e.g. in dose calculation in…
We study evolution equations on networks that can be modeled by means of hyperbolic systems. We extend our previous findings in \cite{KraMugNic20} by discussing well-posedness under rather general transmission conditions that might be…
We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the…
Dynamical systems governed by priority rules appear in the modeling of emergency organizations and road traffic. These systems can be modeled by piecewise linear time-delay dynamics, specifically using Petri nets with priority rules. A…
This work studies a macroscopic traffic flow model driven by a system of nonlinear hyperbolic partial differential equations. Using Lie symmetry analysis, we determine the infinitesimal generators and construct an optimal system of…