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A variational theory of hyperbolic Lagrangian coherent structures
We develop a mathematical theory that clarifies the relationship between observable
Lagrangian Coherent Structures (LCSs) and invariants of the Cauchy–Green strain tensor …
Lagrangian Coherent Structures (LCSs) and invariants of the Cauchy–Green strain tensor …
A new mixing diagnostic and Gulf oil spill movement
Chaotic advection has served as the paradigm for mixing in fluid flows with simple time
dependence. Its skeletal structure is based on analysis of invariant attracting and repelling …
dependence. Its skeletal structure is based on analysis of invariant attracting and repelling …
Distinguishing between deterministic oscillations and noise
Time-dependent dynamics is ubiquitous in the natural world and beyond. Effectively
analysing its presence in data is essential to our ability to understand the systems from …
analysing its presence in data is essential to our ability to understand the systems from …
Finite-time Lagrangian transport analysis: stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents
We consider issues associated with the Lagrangian characterisation of flow structures
arising in aperiodically time-dependent vector fields that are only known on a finite time …
arising in aperiodically time-dependent vector fields that are only known on a finite time …
Hyperbolicity and invariant manifolds for planar nonautonomous systems on finite time intervals
The method of invariant manifolds was originally developed for hyperbolic rest points of
autonomous equations. It was then extended from fixed points to arbitrary solutions and from …
autonomous equations. It was then extended from fixed points to arbitrary solutions and from …
[ספר][B] Barriers and transport in unsteady flows: a Melnikov approach
S Balasuriya - 2016 - SIAM
Over the past several years, there has been an explosion of interest in analyzing flow
barriers in fluids. This has been driven by a variety of reasons. One is a concern for our …
barriers in fluids. This has been driven by a variety of reasons. One is a concern for our …
Finite-time attractivity and bifurcation for nonautonomous differential equations
The aim of this article is to introduce nonautonomous and finite-time versions of central
concepts from the theory of dynamical systems such as attractivity and bifurcation. The …
concepts from the theory of dynamical systems such as attractivity and bifurcation. The …
[HTML][HTML] Stabilization of cyclic processes by slowly varying forcing
We introduce a new mathematical framework for the qualitative analysis of dynamical
stability, designed particularly for finite-time processes subject to slow-timescale external …
stability, designed particularly for finite-time processes subject to slow-timescale external …
Areas of attraction for nonautonomous differential equations on finite time intervals
In this article, new concepts of (exponential) attractivity for nonautonomous differential
equations on a finite time interval are introduced. Due to nonuniqueness of finite-time …
equations on a finite time interval are introduced. Due to nonuniqueness of finite-time …
A definition of spectrum for differential equations on finite time
Hyperbolicity of an autonomous rest point is characterised by its linearization not having
eigenvalues on the imaginary axis. More generally, hyperbolicity of any solution which exists …
eigenvalues on the imaginary axis. More generally, hyperbolicity of any solution which exists …