Related papers: On the relation between linear stability analysis …
A major transition in modern power systems is the replacement of conventional generation units with renewable sources of energy. The latter results in lower rotational inertia which compromises the stability of the power system, as…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
Neuronal networks alternate between high- and low-activity regimes, known as up and down states. They also display rhythmic patterns essential for perception, memory consolidation, and sensory processing. Despite their importance, the…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
Wake and force characteristics of an oscillating cylinder in inline steady currents are investigated numerically over a wide parameter space of dimensionless oscillation amplitude ($A^* = 0.01 - 0.50$) and wavelength ($\lambda^* = 0.4 -…
An initial-value problem for arbitrary small 3D vorticity perturbations imposed on a free shear flow is considered. The viscous perturbation equations are then combined in terms of the vorticity and velocity, and are solved by means of a…
In this work, we introduce the novel application of the adaptive mesh refinement (AMR) technique in the global stability analysis of incompressible flows. The design of an accurate mesh for transitional flows is crucial. Indeed, an…
Willems' fundamental lemma enables data-driven analysis and control by characterizing an unknown system's behavior directly in terms of measured data. In this work, we extend a recent frequency-domain variant of this result--previously…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
The nonlinear response of noisy bistable systems driven by strong amplitude periodical force is investigated by physical experiment. The new phenomenon of locking of the mean switching frequency between states of bistable system is found.…
We analyze the role of the relative phasing in the nonlinear saturation of the unstable Mack modes in a hypersonic parallel flow boundary layer in two dimensions (2D). As the linearly unstable Mack modes extract energy from the mean flow,…
We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is…
Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
Despite the nonlinear nature of wall turbulence, there is evidence that the mechanism underlying the energy transfer from the mean flow to the turbulent fluctuations can be ascribed to linear processes. One of the most acclaimed linear…
When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common…
A streamwise-constant model is presented to investigate the basic mechanisms responsible for the change in mean flow occuring during pipe flow transition. Using a single forced momentum balance equation, we show that the shape of the…
Coriolis force effects on shear flows are important in geophysical and astrophysical contexts. We here report a study on the linear stability and the transient energy growth of the plane Couette flow with system rotation perpendicular to…
This paper analyzes how power injections affect frequency quality in power systems. We first derive a general expression linking active and reactive power injections at buses to the system's frequency. This formulation explicitly considers…