Related papers: Periodic eigendecomposition and its application to…
In this paper, we investigate the spectral stability of periodic traveling waves for a cubic-quintic and double dispersion equation. Using the quadrature method we find explict periodic waves and we also present a characterization for all…
It is known that, if a locally perturbed periodic self-adjoint operator on a combinatorial or quantum graph admits an eigenvalue embedded in the continuous spectrum, then the associated eigenfunction is compactly supported--that is, if the…
The self-healing diffusion Monte Carlo algorithm (SHDMC) [Reboredo, Hood and Kent, Phys. Rev. B {\bf 79}, 195117 (2009); Reboredo, {\it ibid.} {\bf 80}, 125110 (2009)] is extended to study the ground and excited states of magnetic and…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
Using the new periodicity concept based on shifts, we construct a unified Floquet theory for homogeneous and nonhomogeneous hybrid periodic systems on domains having continuous, discrete or hybrid structure. New periodicity concept based on…
Travelling wavepackets are key coherent features contributing to the dynamics of several advective flows. This work introduces the Hilbert proper orthogonal decomposition (HPOD) to distil these features from flow field data, leveraging…
We study the intermediate statistics of the spectrum of quasi-energies and of the eigenfunctions in the kicked rotator, in the case when the corresponding system is fully chaotic while quantally localized. As for the eigenphases, we find…
We employ the framework of the Koopman operator and dynamic mode decomposition to devise a computationally cheap and easily implementable method to detect transient dynamics and regime changes in time series. We argue that typically…
This paper develops data-driven methods to identify eigenfunctions of the Koopman operator associated to a dynamical system and subspaces that are invariant under the operator. We build on Extended Dynamic Mode Decomposition (EDMD), a…
We consider the Laplacian on a periodic metric graph and obtain its decomposition into a direct fiber integral in terms of the corresponding discrete Laplacian. Eigenfunctions and eigenvalues of the fiber metric Laplacian are expressed…
We present a version of the classical Floquet-Lyapunov theorem for $\omega-$periodic nonautonomous linear (impulsive and non-impulsive) differential equations with piecewise constant arguments of generalized type (in short, IDEPCAG or…
In this work, we consider a general time-periodic linear transport equation with integral source term. We prove the existence of a Floquet principal eigenvalue, namely a real number such that the equation rescaled by this number admits…
The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to It\^o diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the…
A numerical method is proposed for computing time-periodic and relative time-periodic solutions in dissipative wave systems. In such solutions, the temporal period, and possibly other additional internal parameters such as the propagation…
The Floquet exponents of periodic field lines are studied through the variations of the magnetic action on the magnetic axis, which is assumed to be elliptical. The near-axis formalism developed by Mercier, Solov'ev and Shafranov is…
This study presents a comprehensive spatial eigenanalysis of fully-discrete discontinuous spectral element methods, now generalizing previous spatial eigenanalysis that did not include time integration errors. The influence of discrete time…
A variational principle enabling one to compute individual Floquet states of a periodically time-dependent quantum system is formulated, and successfully tested against the benchmark system provided by the analytically solvable model of a…
The Kuramoto-Sivashinsky equation is a prototypical chaotic nonlinear partial differential equation (PDE) in which the size of the spatial domain plays the role of a bifurcation parameter. We investigate the changing dynamics of the…
A new approach is presented to compute the seismic normal modes of a fully heterogeneous, rotating planet. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core. The relevant…
In this paper, we employed linear algebra and functional analysis to determine necessary and sufficient conditions for oscillation-free and stable solutions to linear and nonlinear parabolic partial differential equations. We applied…