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The dynamics of inertial particles in $2-d$ incompressible flows can be modeled by $4-d$ bailout embedding maps. The density of the inertial particles, relative to the density of the fluid, is a crucial parameter which controls the…
We study uncertainty in the dynamics of time-dependent flows by identifying barriers and enhancers to stochastic transport. This topological segmentation is closely related to the theory of Lagrangian coherent structures and is based on a…
This work introduces RedEigCD, the first self-adaptive timestepping technique specifically tailored for reduced-order models (ROMs) of the incompressible Navier-Stokes equations. Building upon linear stability concepts, the method adapts…
Self-healing slip pulses are major spatiotemporal failure modes of frictional systems, featuring a characteristic size $L(t)$ and a propagation velocity $c_{\rm p}(t)$ ($t$ is time). Here, we develop a theory of slip pulses in realistic…
We study dynamic network flows with uncertain input data under a robust optimization perspective. In the dynamic maximum flow problem, the goal is to maximize the flow reaching the sink within a given time horizon $T$, while flow requires a…
In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…
A transition to unsteadiness of a flow inside a cubic diagonally lid-driven cavity with no-slip boundaries is numerically investigated by a series of direct numerical simulations (DNS) performed on 100^3 and 200^3 stretched grids. It is…
Mixing in numerous medical and chemical applications, involving overly long microchannels, can be enhanced by inducing flow instabilities. The channel length, is thus shortened in the inertial microfluidics regime due to the enhanced…
Highly stratified shear layers are rendered unstable even at high stratifications by Holmboe instabilities when the density stratification is concentrated in a small region of the shear layer. These instabilities may cause mixing in highly…
In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the…
Traditional theories of optimization cannot describe the dynamics of optimization in deep learning, even in the simple setting of deterministic training. The challenge is that optimizers typically operate in a complex, oscillatory regime…
The low-frequency modal and non-modal stability characteristics of an incompressible, pressure-gradient-induced turbulent separation bubble (TSB) are investigated with the objective of studying the mechanism responsible for the…
In this paper, we show that the quasi-one-dimensional flow of an ideal inviscid fluid in a corrugated pipe is parametrically unstable in certain frequency bands. First-order perturbation theory is used to analyze the stability of the flow,…
It was shown previously that the current-carrying state of a Field Effect Transistor with asymmetric source and drain boundary conditions may become unstable against spontaneous generation of plasma waves [1]. By extending the analysis to…
In this article we use analytical and numerical modeling to describe parallel viscous two-phase flows in microchannels. The focus is on idealized two-dimensional geometries, with a view to validating the various methodologies for future…
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…
Motivated by the need to better understand flow unsteadiness in hydraulic turbines, we perform a local linear stability and adjoint-based sensitivity analysis of the turbulent swirling jet at the outlet of a Francis turbine. We use measured…
Tilted lattice potentials with periodic driving play a crucial role in the study of artificial gauge fields and topological phases with ultracold quantum gases. However, driving-induced heating and the growth of phonon modes restrict their…
The non-modal transient growth of perturbations in horizontal and inclined channel flows of two immiscible fluids is studied. 3D perturbations are examined in order to find the optimal perturbations that attain the maximum amplification of…
We study stability of unidirectional flows for the linearized 2D $\alpha$-Euler equations on the torus. The unidirectional flows are steady states whose vorticity is given by Fourier modes corresponding to a vector $\mathbf p \in \mathbb…