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We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell ---consisting of the…
This paper considers the dynamics of edges in a network. The Dynamic Bond Percolation (DBP) process models, through stochastic local rules, the dependence of an edge $(a,b)$ in a network on the states of its neighboring edges. Unlike…
We consider non-stationary free and forced transverse oscillation of an infinite taut string on the Winkler foundation subjected to a discrete mass-spring system non-uniformly moving at a given sub-critical speed. The speed of the…
Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…
By event-driven molecular dynamics simulations we investigate magneto-transport in a two-dimensional model with randomly distributed scatterers close to the field-induced localization transition. This transition is generated by percolating…
A positive rate of entropy production at steady state is a distinctive feature of truly non-equilibrium processes. Exact results, while being often limited to simple models, offer a unique opportunity to explore the thermodynamic features…
We develop a theory of edge excitations of fractonic systems in two dimensions, and elucidate their connections to bulk transport properties and quantum statistics of bulk excitations. The system we consider has immobile point charges,…
The cytoskeleton is an important subsystem of cells that is involved for example in cell division and locomotion. It consists of filaments that are cross-linked by molecular motors that can induce relative sliding between filaments and…
We investigate a 2D dynamical absorbing state model of monodisperse disks, in which rich phase behavior arises from interactions consisting solely of repulsive displacements between overlapping particles. The phase diagram reveals several…
We consider two minimal models of active fluid droplets that exhibit complex dynamics including steady motion, deformation, rotation and oscillating motion. First we consider a droplet with a concentration of active contractile matter…
We consider a phenomenological continuum theory for an extensile, overdamped active nematic liquid crystal, applicable in the dense regime. Constructed from general principles, the theory is universal, with parameters independent of any…
Metastability, i.e., partial relaxation to long-lived, quasi-stationary states before true asymptotic equilibrium sets in, emerges ubiquitously in classical and quantum dynamical systems as a result of timescales separation. In open quantum…
Active filaments, such as microtubules with attached cargo-carrying motor proteins, are important dynamic structures for fluid transport in and around living cells. The mathematical models of active filaments appearing in the literature…
Two data-driven modal analysis approaches, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are applied to analyze the unsteady flow obtained by solving the Reynolds-averaged Navier-Stokes (RANS) equations in a…
Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…
We study the onset of spontaneous dynamics in the follower force model of an active filament, wherein a slender elastic filament in a viscous liquid is clamped normal to a wall at one end and subjected to a tangential compressive force at…
Spatial self-similarity is a hallmark of critical phenomena. We study the dynamic process of percolation, in which bonds are incrementally added to an initially empty lattice until the system becomes fully occupied. By tracking the gap --…
The statistical properties of turbulent flows are fundamentally different from those of systems at equilibrium due to the presence of an energy flux from the scales of injection to those where energy is dissipated by the viscous forces: a…
We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square-displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As…
We study the dynamics of small fluctuations about the uniform state of a crystal moving through a dissipative medium, e.g. a sedimenting colloidal crystal or a moving flux lattice, using a set of continuum equations for the displacement…