336 citations · 1.5k across the 38 of their papers we have counts for
12 papers · 1 filter
Slow Manifold Reduction for Inertial Particles with Quadratic Drag
Mathew Angel, Mohammad Farazmand
We consider the dynamics of inertial particles in unsteady fluid flows. At low Reynolds numbers, where the drag force is linear in the relative velocity, it is well-known that the…
Fisher information and shape-morphing modes for solving the Fokker-Planck equation in higher dimensions
William Anderson, Mohammad Farazmand
The Fokker-Planck equation describes the evolution of the probability density associated with a stochastic differential equation. As the dimension of the system grows, solving this…
Fast and scalable computation of shape-morphing nonlinear solutions with application to evolutional neural networks
William Anderson, Mohammad Farazmand
We develop fast and scalable methods for computing reduced-order nonlinear solutions (RONS). RONS was recently proposed as a framework for reduced-order modeling of time-dependent…
Shape-morphing reduced-order models for nonlinear Schrodinger equations
William Anderson, Mohammad Farazmand
We consider reduced-order modeling of nonlinear dispersive waves described by a class of nonlinear Schrodinger (NLS) equations. We compare two nonlinear reduced-order modeling meth…
Mitigation of rare events in multistable systems driven by correlated noise
Konstantinos Mamis, Mohammad Farazmand
We consider rare transitions induced by colored noise excitation in multistable systems. We show that undesirable transitions can be mitigated by a simple time-delay feedback contr…
Data-driven prediction of multistable systems from sparse measurements
Bryan Chu, Mohammad Farazmand
We develop a data-driven method, based on semi-supervised classification, to predict the asymptotic state of multistable systems when only sparse spatial measurements of the system…
Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems
Mohammad Farazmand, Themistoklis Sapsis
Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coo…
Attraction-Based Computation of Hyperbolic Lagrangian Coherent Structures
Daniel Karrasch, Mohammad Farazmand, George Haller
Recent advances enable the simultaneous computation of both attracting and repelling families of Lagrangian Coherent Structures (LCS) at the same initial or final time of interest.…
How coherent are the vortices of two-dimensional turbulence?
Mohammad Farazmand, George Haller
We use recent developments in the theory of finite-time dynamical systems to objectively locate the material boundaries of coherent vortices in two-dimensional Navier--Stokes turbu…
The Maxey-Riley Equation: Existence, Uniqueness and Regularity of Solutions
Mohammad Farazmand, George Haller
The Maxey--Riley equation describes the motion of an inertial (i.e., finite-size) spherical particle in an ambient fluid flow. The equation is a second-order, implicit integro-diff…
Shearless transport barriers in unsteady two-dimensional flows and maps
Mohammad Farazmand, Daniel Blazevski, George Haller
We develop a variational principle that extends the notion of a shearless transport barrier from steady to general unsteady two-dimensional flows and maps defined over a finite tim…
Attracting and repelling Lagrangian coherent structures from a single computation
Mohammad Farazmand, George Haller
Hyperbolic Lagrangian Coherent Structures (LCSs) are locally most repelling or most attracting material surfaces in a finite-time dynamical system. To identify both types of hyperb…