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Optimal power flow (OPF) is a critical optimization problem that allocates power to the generators in order to satisfy the demand at a minimum cost. Solving this problem exactly is computationally infeasible in the general case. In this…

Traditional communication theory focuses on minimizing transmit power. However, communication links are increasingly operating at shorter ranges where transmit power can be significantly smaller than the power consumed in decoding. This…

Motivated by the need to localise faults along electrical power lines, this paper adopts a frequency-domain approach to parameter estimation for an infinite-dimensional linear dynamical system with one spatial variable. Since the time of…

Motivated by an increase of renewable energy sources we propose a distributed optimal Load Frequency Control scheme achieving frequency regulation and economic dispatch. Based on an energy function of the power network we derive an…

Transmission line failures in power systems propagate non-locally, making the control of the resulting outages extremely difficult. In this work, we establish a mathematical theory that characterizes the patterns of line failure propagation…

We consider navigation schemes on planar diluted lattices and semi lattices with one discrete and one continuous component. More precisely, nodes that survive inhomogeneous Bernoulli site percolation, or are placed as inhomogeneous Poisson…

We derive novel results on the ergodic theory of irreducible, aperiodic Markov chains. We show how to optimally steer the network flow to a stationary distribution over a finite or infinite time horizon. Optimality is with respect to an…

Analytical models describing the motion of colloidal particles in given velocity fields are presented. In addition to local approaches, leading to well known master equations such as the Langevin and the Fokker-Planck equations, a global…

We construct a minimal two-chain random walk model and study the information that fluctuations of the flux and higher cumulants can reveal about the model: its structure, parameters, and whether it operates under nonequilibrium conditions.…

We study a single-lane traffic model that is based on human driving behavior. The outflow from a traffic jam self-organizes to a critical state of maximum throughput. Small perturbations of the outflow far downstream create emergent traffic…

Uncertainty in renewable energy generation has the potential to adversely impact the operation of electric networks. Numerous approaches to manage this impact have been proposed, ranging from stochastic and chance-constrained programming to…

In this paper, we consider a chance-constrained formulation of the optimal power flow problem to handle uncertainties resulting from renewable generation and load variability. We propose a tuning method that iterates between solving an…

A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…

Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random…

We explore the properties of run-and-tumble particles moving in a piecewise-linear "ratchet" potential by deriving analytic results for the system's steady-state probability density, current, entropy production rate, extractable power, and…

The property of limiting fragmentation of various observables such as rapidity distributions ($dN/dy$), elliptic flow ($v_{2}$), average transverse momentum ($\langle p_{T} \rangle$) etc. of charged particles is observed when they are…

We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average…

We study the electrical distribution network reconfiguration problem, defined as follows. We are given an undirected graph with a root vertex, demand at each non-root vertex, and resistance on each edge. Then, we want to find a spanning…

In nonlinear systems, small perturbations are conventionally attributed to negligible nonlinearity, justifying linear approximations. Here, we uncover a notable exception to this paradigm in an electrokinetic (EK) flow. Using a novel dual…

We derive a conservation law on a network made of two incoming branches and a single outgoing one from a discrete traffic flow model. The continuous model is obtained from the discrete one by letting the number of vehicles tend to infinity…