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This paper is concerned with the basic model for compressible and incompressible two phase flows with phase transitions The flows are separated by nearly flat interface represented as a graph over the $N-1$ dimensional Euclidean space…
Nonlinear wave propagation in parity-time ($\mathcal{PT}$) symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex…
The dynamics of perturbations to large-amplitude Internal Solitary Waves (ISW) in two-layered flows with thin interfaces is analyzed by means of linear optimal transient growth methods. Optimal perturbations are computed through…
We prove the well-posedness results, i.e. existence, uniqueness, and stability, of the solutions to a class of nonlocal fully nonlinear parabolic partial differential equations (PDEs), where there is an external time parameter $t$ on top of…
We describe ideal incompressible hydrodynamics on the hyperbolic plane which is an infinite surface of constant negative curvature. We derive equations of motion, general symmetries and conservation laws, and then consider turbulence with…
The instability of pipe flow has been a subject of extensive research, yet a significant gap remains between experimental observations and theoretical predictions. This study revisits the classical problem of kinetic energy instability of…
Managing power grids with the increasing presence of variable renewable energy-based (distributed) generation involves solving high-dimensional optimization tasks at short intervals. Linearizing the AC power flow (PF) constraints is a…
The growing reliance of electric power systems on gas-fired generation to balance intermittent sources of renewable energy has increased the variation and volume of flows through natural gas transmission pipelines. Adapting pipeline…
We consider a system of two linear and linearly coupled oscillators with ideal impact constraints. Primary resonant energy exchange is investigated by analysis of the slow-flow using the action-angle (AA) formalism. Exact inversion of the…
We derive a microscopic theory of glassy dynamics based on the transport of voids by micro-string motions, each of which involves particles arranged in a line hopping simultaneously displacing one another. Disorder is modeled by a random…
We consider a one dimensional infinite chain of har- monic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to…
Effective power flow (PF) modeling critically affects the solution accuracy and computational complexity of large-scale grid optimization problems. Especially for grid optimization involving flexible topology to enhance resilience,…
Pressure-driven flow of a dilute polymer solution has been numerically observed to possess a form of elastic turbulence which is organised around the interactions of localised versions of 2-dimensional `arrowhead' travelling waves (Page et…
The dynamics of transitional flows are governed by an interplay between the non-normal linear dynamics and quadratic nonlinearity in the incompressible Navier-Stokes equations. In this work, we propose a framework for nonlinear stability…
We study optimal and strategic extraction of a renewable resource that is distributed over a network, migrates mass-conservatively across nodes, and evolves under nonlinear (concave) growth. A subset of nodes hosts extractors while the…
For wall-bounded turbulent flows, Townsend's attached eddy hypothesis proposes that the logarithmic layer is populated by a set of energetic and geometrically self-similar eddies. These eddies scale with a single length scale, their…
The energy cascade and diverse turbulence properties of active-grid-generated turbulence were studied in a wind tunnel via hot-wire anemometry. To this aim, two active grid protocols were considered. The first protocol is the standard…
In this paper, we are concerned with the global existence and optimal rates of strong solutions for three-dimensional compressible viscoelastic flows. We prove the global existence of the strong solutions by the standard energy method under…
As the penetration level of transmission-scale time-intermittent renewable generation resources increases, control of flexible resources will become important to mitigating the fluctuations due to these new renewable resources. Flexible…
We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of…