Related papers: Modal Extraction in Spatially Extended Systems
We describe a method to extract from experimental data the important dynamical modes in spatio-temporal patterns in a system driven out of thermodynamic equilibrium. Using a novel optical technique for controlling fluid flow, we create an…
We demonstrate that the spatial profiles of both propagating and evanescent Bloch-modes in a periodic structure can be extracted from a single measurement of electric field at the specified optical wavelength. We develop a systematic…
The objective of the present paper is to develop a two-step methodology integrating system identification and numerical continuation for the experimental extraction of nonlinear normal modes (NNMs) under broadband forcing. The first step…
Slow extraction of beam from synchrotrons or storage rings as required by many fixed target experiments is performed by controlled excitation and feeding of a structural lattice resonance. Due to the sensitive nature of this resonant…
This paper discusses the application of Dynamic Mode Decomposition (DMD) to the extraction of modal properties of linear mechanical systems, i.e., experimental modal analysis (EMA). First, theoretical background of the DMD is briefly…
Reduced Bloch mode expansion is presented for fast periodic media band structure calculations. The expansion employs a natural basis composed of a selected reduced set of Bloch eigenfunctions. The reduced basis is selected within the…
Methods for reconstructing the spectral density of a vibrational environment from experimental data can yield key insights into the impact of the environment on molecular function. Although such experimental methods exist, they generally…
Modal analysis has long been consolidated as a basic tool to interpret dynamics and build low-order models of mechanical, thermal, and fluid systems. Eigenmodes arising from the spectral decomposition of the underlying linearized dynamics…
The evolution of the scanning modules for scanning transmission electron microscopes (STEM) has realized the possibility to generate arbitrary scan pathways, an approach currently explored to improve acquisition speed and to reduce electron…
Let a measurement consist of a linear combination of damped complex exponential modes, plus noise. The problem is to estimate the parameters of these modes, as in line spectrum estimation, vibration analysis, speech processing, system…
An external description for aperiodically sampled MIMO linear systems has been developed. Emphasis is on the sampling period sequence, included among the variables to be handled. The computational procedure is simple and no use of…
Modal methods are a long-standing approach to physical modelling synthesis. Extensions to nonlinear problems are possible, leading to coupled nonlinear systems of ordinary differential equations. Recent work in scalar auxiliary variable…
Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and…
Models of physics beyond the Standard Model often contain a large number of parameters. These form a high-dimensional space that is computationally intractable to fully explore. Experimental constraints project onto a subspace of viable…
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
Modal decomposition techniques, such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Singular Spectrum Analysis (SSA), have advanced time-frequency signal analysis since the early 21st century. These methods…
Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…
We present the applications of wavelet analysis methods in constrained variational framework to calculation of dynamical aperture. We construct represention via exact nonlinear high-localized periodic eigenmodes expansions, which allows to…