Related papers: On the Stability of Dynamical Multi-Commodity Flow…
We investigate the percentage of delivering capacities that are actually consumed in a typical traffic dynamics where the capacities are uniformly assigned over a scale-free network. Theoretical analysis, as well as simulations, reveal that…
This paper studies the problem of output agreement in networks of nonlinear dynamical systems under time-varying disturbances. Necessary and sufficient conditions for output agreement are derived for the class of incrementally passive…
It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal…
We develop and analyze a measure-valued fluid model keeping track of parking and charging requirements of electric vehicles in a local distribution grid. We show how this model arises as an accumulation point of an appropriately scaled…
We introduce a class of stochastic advection problems amenable to analysis of turbulent transport. The statistics of the flow field are represented as a continuous time Markov process, a choice that captures the intuitive notion of…
We propose a macroscopic modeling framework for a network of roads and multi-commodity traffic. The proposed framework is based on the Lighthill-Whitham-Richards kinematic wave theory; more precisely, on its discretization, the Cell…
During a financial crisis, the capital markets network frequently exhibits a high correlation between returns. We developed a network analysis framework based on daily returns from 42 countries to determine systemic stability. Our network…
We study the mixing in the presence of convective flow in a porous medium. Convection is characterized by the formation of vortices and stagnation points, where the fluid interface is stretched and compressed enhancing mixing. We analyze…
We study flow driven through a finite-length planar rigid channel by a fixed upstream flux, where a segment of one wall is replaced by a pre-stressed elastic beam subject to uniform external pressure. The steady and unsteady systems are…
Dynamic network flows, sometimes called flows over time, extend the notion of network flows to include a transit time for each edge. While Ford and Fulkerson showed that certain dynamic flow problems can be solved via a reduction to static…
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…
In transportation systems (e.g. highways, railways, airports), traffic flows with distinct origin-destination pairs usually share common facilities and interact extensively. Such interaction is typically stochastic due to natural…
We consider the capacity problem for wireless networks. Networks are modeled as random unit-disk graphs, and the capacity problem is formulated as one of finding the maximum value of a multicommodity flow. In this paper, we develop a proof…
We consider a multi-class single server queueing network as a model of a packet switching network. The rates packets are sent into this network are controlled by queues which act as congestion windows. By considering a sequence of…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
Water distribution networks are hydraulic infrastructures that aim to meet water demands at their various nodes. Water flows through pipes in the network create nonlinear dynamics on networks. A desirable feature of water distribution…
We study a simple transport model driven out of equilibrium by reservoirs at the boundaries, corresponding to the hydrodynamic limit of the symmetric simple exclusion process. We show that a nonlocal transformation of densities and currents…
Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…
Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch,…
Urban transportation networks face significant challenges due to traffic congestion, leading to adverse environmental and socioeconomic impacts. Vehicular admission control (VAC) strategies have emerged as a promising solution to alleviate…