523 citations · 1.6k across the 17 of their papers we have counts for
19 papers
Integral theorems for the gradient of a vector field, with a fluid dynamical application
Jonathan M. Lilly, Joel Feske, Baylor Fox-Kemper +1
The familiar divergence and Kelvin-Stokes theorem are generalized by a tensor-valued identity that relates the volume integral of the gradient of a vector field to the integral ove…
Kinematics of a Fluid Ellipse in a Linear Flow
J. M. Lilly
A four-parameter kinematic model for the position of a fluid parcel in a time-varying ellipse is introduced. For any ellipse advected by an arbitrary linear two-dimensional flow, t…
Element analysis: a wavelet-based method for analyzing time-localized events in noisy time series
J. M. Lilly
A method is derived for the quantitative analysis of signals that are composed of superpositions of isolated, time-localized "events". Here these events are taken to be well repres…
Analysis of nonstationary modulated time series with applications to oceanographic flow measurements
Arthur P. Guillaumin, Adam M. Sykulski, Sofia C. Olhede +2
We propose a new class of univariate nonstationary time series models, using the framework of modulated time series, which is appropriate for the analysis of rapidly-evolving time…
The De-Biased Whittle Likelihood
Adam M. Sykulski, Sofia C. Olhede, Arthur P. Guillaumin +2
The Whittle likelihood is a widely used and computationally efficient pseudo-likelihood. However, it is known to produce biased parameter estimates for large classes of models. We…
Fractional Brownian motion, the Matern process, and stochastic modeling of turbulent dispersion
J. M. Lilly, A. M. Sykulski, J. J Early +1
Stochastic process exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm). In particular, the spectral slope at high fr…
A Widely Linear Complex Autoregressive Process of Order One
Adam M. Sykulski, Sofia C. Olhede, Jonathan M. Lilly
We propose a simple stochastic process for modeling improper or noncircular complex-valued signals. The process is a natural extension of a complex-valued autoregressive process, e…
A Power Variance Test for Nonstationarity in Complex-Valued Signals
Thomas E. Bartlett, Adam M. Sykulski, Sofia C. Olhede +2
We propose a novel algorithm for testing the hypothesis of nonstationarity in complex-valued signals. The implementation uses both the bootstrap and the Fast Fourier Transform such…
Lagrangian Time Series Models for Ocean Surface Drifter Trajectories
Adam M. Sykulski, Sofia C. Olhede, Jonathan M. Lilly +1
This paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely-drifting satellite-tracked instruments. The proposed time series models ar…
Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals
Adam M. Sykulski, Sofia C. Olhede, Jonathan M. Lilly +1
There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signal…
Generalized Morse Wavelets as a Superfamily of Analytic Wavelets
Jonathan M. Lilly, Sofia C. Olhede
The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct typ…
The unity of instantaneous spectral moments and physical moments
Jonathan M. Lilly
A modulated oscillation in two or three dimensions can be represented as the trajectory traced out in space by a particle orbiting an ellipse, the properties of which vary as a fun…
Extracting waves and vortices from Lagrangian trajectories
Jonathan M. Lilly, Richard K. Scott, Sofia C. Olhede
A method for extracting time-varying oscillatory motions from time series records is applied to Lagrangian trajectories from a numerical model of eddies generated by an unstable eq…
Direct observations of formation and propagation of subpolar eddies into the subtropical North Atlantic
Amy S. Bower, Ross M. Hendry, Daniel E. Amrhein +1
Subsurface float and moored observations are presented to show for the first time the formation and propagation of anticyclonic submesoscale coherent vortices that transport relati…
Analysis of Modulated Multivariate Oscillations
Jonathan M. Lilly, Sofia C. Olhede
The concept of a common modulated oscillation spanning multiple time series is formalized, a method for the recovery of such a signal from potentially noisy observations is propose…
Modulated Oscillations in Three Dimensions
Jonathan M. Lilly
The analysis of the fully three-dimensional and time-varying polarization characteristics of a modulated trivariate, or three-component, oscillation is addressed. The use of the an…
Bivariate Instantaneous Frequency and Bandwidth
Jonathan M. Lilly, Sofia C. Olhede
The generalizations of instantaneous frequency and instantaneous bandwidth to a bivariate signal are derived. These are uniquely defined whether the signal is represented as a pair…
Higher-Order Properties of Analytic Wavelets
J. M. Lilly, S. C. Olhede
The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified.…
On the Analytic Wavelet Transform
Jonathan M. Lilly, Sofia C. Olhede
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and freq…