Related papers: Beyond optimal disturbances: a statistical framewo…
The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the 'bypass' path…
We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…
How can a microorganism adapt to a variety of environmental conditions despite there exists a limited number of signal transduction machineries? We show that for any growing cells whose gene expression is under stochastic fluctuations,…
Transient energy growth suppression is a common control objective for feedback flow control aimed at delaying transition to turbulence. A prevailing control approach in this context is observer-based feedback, in which a full-state feedback…
How predictable are turbulent flows? Here we use theoretical estimates and shell model simulations to argue that Eulerian spontaneous stochasticity, a manifestation of the non-uniqueness of the solutions to the Euler equation that is…
We look into the fluctuations caused by disturbances in power systems. In the linearized system of the power systems, the disturbance is modeled by a Brownian motion process, and the fluctuations are described by the covariance matrix of…
We investigate the effect of turbulence on the combined condensational and collisional growth of cloud droplets by means of high resolution direct numerical simulations of turbulence and a superparticle approximation for droplet dynamics…
Direct numerical simulations of a Couette Poiseuille flow were performed near the transition to turbulence to investigate the nonlinear relationship between streak waviness and rolls. This relationship is a key step in Waleffe's model for a…
Ruelle predicted that the maximal amplification of perturbations in homogeneous isotropic turbulence is exponential $e^{\sigma \sqrt{Re} t}$ (where $\sigma \sqrt{Re}$ is the maximal Liapunov exponent). In our earlier works, we predicted…
To better understand the temporal characteristics and the lifetime of fluctuations in stochastic processes in networks, we investigated diffusive persistence in various graphs. Global diffusive persistence is defined as the fraction of…
Dissipation is a ubiquitous phenomenon in dynamical systems encountered in nature because no finite system is fully isolated from its environment. In optical systems, a key challenge facing any technological application has traditionally…
Transient instability in nonlinear stochastic dynamical systems is a fundamental limitation in safety-critical aerospace applications, particularly during powered descent and landing where failure is driven by finite-time excursions rather…
We study gravitationally unstable, transient, diffusive boundary layers in porous media using modal and nonmodal stability methods. Using nonmodal stability theory, we demonstrate that both the onset of linear instabilities and the shape of…
To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the…
We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby…
A comprehensive study of the effect of wall heating or cooling on the linear, transient and secondary growth of instability in channel flow is conducted. The effect of viscosity stratification, heat diffusivity and of buoyancy are estimated…
Statistical solutions of incompressible Euler describe turbulent dynamics as time-parameterized laws on $L^2$ whose multi-point correlations satisfy an infinite hierarchy of weak identities. Modern generative samplers for PDE forecasting…
We consider the problem of an overdamped Brownian particle moving in multiscale potential with N + 1 characteristic length scales: the macroscale and N separated microscales. We show that the coarse-grained dynamics is given by an…
Bounding energetic growth of gyrokinetic instabilities is a complementary approach to linear instability analyses involving normal eigenmodes. Previous work has focused on upper bounds which are valid linearly and nonlinearly. However, if…
Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may…