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We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are…
We study low Reynolds number turbulence in a suspension of polar, extensile, self-propelled inertial swimmers. We review the bend and splay mechanisms that destabilize an ordered flock. The suspension is always unstable to bend…
This paper presents a novel methodology for the direct numerical modeling and simulation of turbulent flows. The kinetic model equation is firstly extended to turbulent flow with the account of coupled evolution of kinetic, thermal, and…
Forecasting the number of trips in bike-sharing systems and its volatility over time is crucial for planning and optimizing such systems. This paper develops timeseries models to forecast hourly count timeseries data, and estimate its…
A new method for the study of resonant behavior - using wave-packet dynamics - is presented, based on the powerful window operator technique. The method is illustrated and quantified by application to the astrophysically-important example…
We study the statistical properties of the convex hull of a planar run-and-tumble particle (RTP), also known as the "persistent random walk", where the particle/walker runs ballistically between tumble events at which it changes its…
We study a nonlinear PDE problem motivated by the peculiar patterns arising in myxobacteria, namely counter-migrating cell density waves. We rigorously prove the existence of Hopf bifurcations for some specific values of the parameters of…
Emerging wireless communication systems will be characterized by a tight coupling between communication and positioning. This is particularly apparent in millimeter-wave (mm-wave) communications, where devices use a large number of antennas…
The persistent motion of bacteria produces clusters with a stationary cluster size distribution (CSD). Here we develop a minimal model for bacteria in a narrow channel to assess the relative importance of motility diversity (i.e.…
Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the…
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of…
Resonant electron interaction with whistler-mode chorus waves is recognized as one of the main drivers of radiation belt dynamics. For moderate wave intensity, this interaction is well described by quasi-linear theory. However, recent…
We elaborate and validate a generalization of the renowned transition-path-sampling algorithm for a paradigmatic model of active particles, namely the Run-and-Tumble particles. Notwithstanding the non-equilibrium character of these…
In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density…
A non-perturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line…
We simulate the dynamics of a single circle microswimmer exploring a disordered array of fixed obstacles. The interplay of two different types of randomness, quenched disorder and stochastic noise, is investigated to unravel their impact on…
When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy…
A unique pattern selection in the absolutely unstable regime of driven, nonlinear, open-flow systems is reviewed. It has recently been found in numerical simulations of propagating vortex structures occuring in Taylor-Couette and…
In this work, nonlinear variational optimization is used for obtaining minimal seeds for the formation of turbulent bands in channel flow. Using nonlinear optimization together with energy bisection, we have found that the minimal energy…