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We introduce an optimum principle for a vehicular traffic network with road bottlenecks. This network breakdown minimization (BM) principle states that the network optimum is reached, when link flow rates are assigned in the network in such…
The water uptake by roots of plants is examined for an ideal situation, with an approximation that resembles plants growing in pots, meaning that the total soil volume is fixed. We propose a coupled water uptake-root growth model. A…
We propose a many-particle-inspired theory for granular outflows from a hopper and for the escape dynamics through a bottleneck based on a continuity equation in polar coordinates. If the inflow is below the maximum outflow, we find an…
Power system components, particularly electrical substations, may be severely damaged due to flooding, resulting in prolonged power outages and resilience degradation. This problem is more severe in low-elevated regions such as Louisiana.…
The mathematical modelling of species transport in the turbulent boundary layer of fluids that precipitate on the wall, is an important topic at the heart of one of the biggest challenges in efficient energy utilization in all process…
Reinforced elastic sheets surround us in daily life, from concrete shell buildings to biological structures such as the arthropod exoskeleton or the venation network of dicotyledonous plant leaves. Natural structures are often highly…
Vascular networks exhibit a remarkable diversity of architectures and transport mechanisms across biological systems. Inspired by embolism propagation in plant xylem, where air invades water-filled conduits under negative pressure, we study…
In most settings, from international pipelines to home water supplies, the drag caused by turbulence raises pumping costs many times higher than if the flow were laminar. Drag reduction has therefore long been an aim of high priority. In…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
In this paper, we study the problem of traffic management in highways facing stochastic perturbations. To model the macroscopic traffic flow under perturbations, we use cell-transmission model with Markovian capacities. The decision…
Recent experiments proposed to use confined bacteria in order to generate flows near surfaces. We develop a mathematical and a computational model of this fluid transport using a linear superposition of fundamental flow singularities. The…
Modeling heterogeneous and multi-lane traffic flow is essential for understanding and controlling complex transportation systems. In this work, we consider three vehicle populations: two classes of human-driven vehicles (cars and trucks)…
A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…
Trapping and manipulation of small particles underlies many scientific and technological applications. Recently, the precise manipulation of multiple small particles was demonstrated using a Stokes trap that relies only on fluid flow…
A case study in bifurcation and stability analysis is presented, in which reduced dynamical system modelling yields substantial new global and predictive information about the behaviour of a complex system. The first smooth pathway, free of…
We develop a general transfer-matrix formalism for determining the growth rate of the Rayleigh-Taylor instability in a fluid system with spatially varying density and viscosity. We use this formalism to analytically and numerically treat…
Leaf venation is a pervasive example of a complex biological network, endowing leaves with a transport system and mechanical resilience. Transport networks optimized for efficiency have been shown to be trees, i.e. loopless. However,…
The transport phenomena of Lennard-Jones molecules through a structural bottleneck driven by an external force are investigated by molecular dynamics simulations. We observe two distinct molecular flow regimes distinguished by a critical…
Zermelo's navigation problem seeks the trajectory of minimal travel time between two points in a fluid flow. We address this problem for an agent -- such as a micro-robot or active particle -- that is advected by a two-dimensional flow,…