Related papers: On decomposing mixed-mode oscillations and their r…
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…
We address the problem of estimating time and frequency shifts of a known waveform in the presence of multiple measurement vectors (MMVs). This problem naturally arises in radar imaging and wireless communications. Specifically, a signal…
We adapt Vertex models to understand the physical origin of the formation of long-range ordered structures in repulsive soft particles. The model incorporates contributions from the volume and surface area of each particle. Sampling using…
Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest neighbor interactions,…
We use a simple yet Earth-like atmospheric model to propose a new framework for understanding the mathematics of blocking events. Analysing error growth rates along a very long model trajectory, we show that blockings are associated with…
The much-studied Morse oscillator (MO) is couched here in the context of an open quantum system, in which the interaction with the quantum environment, however, is taken to commute with the subsystem Hamiltonian. The result is decoherence…
This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…
The traditional approach to analyzing mean motion resonances is through canonical perturbation theory. While this is a powerful method, its generality leads to complicated combinations of variables that are challenging to interpret and…
A numerical method is presented to compute the eigenmodes supported by three dimensional (3D) metamaterials using the Method of Moments (MoM). The method relies on interstitial equivalent currents between layers. First, a parabolic…
Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low order models of complex phenomena. In this work, we analyze the…
We present a new method for generating robust guesses for unstable periodic orbits (UPOs) by post-processing turbulent data using dynamic mode decomposition (DMD). The approach relies on the identification of near-neutral, repeated…
Like the ordinary power spectrum, higher-order spectra (HOS) describe signal properties that are invariant under translations in time. Unlike the power spectrum, HOS retain phase information from which details of the signal waveform can be…
Amorphous solids form an enormous and underutilized class of materials. In order to drive the discovery of new useful amorphous materials further we need to achieve a closer convergence between computational and experimental methods. In…
We propose a new hybrid modelling approach that combines a mechanistic model with a machine-learnt model to predict the limit cycle oscillations of physical systems with a Hopf bifurcation. The mechanistic model is an ordinary differential…
We study the oscillations of neutrinos in a model in which the neutrino is coupled to a localized, idealized source and detector. By varying the spatial and temporal resolution of the source and detector we are able to model the full range…
This paper introduces the concept of a bi-scale metric for use in the cooperative phase of the self-organizing map (SOM) algorithm. Use of a bi-scale metric allows segmentation of the map into a number of regions, corresponding to…
Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…
Quantum oscillations (QO) are a well-established probe of Fermi-surface (FS) geometry and in the presence of long-range density wave order can display new QO frequencies from reconstructed FS pockets. We show that such reconstructed…
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
We study a two-dimensional Kolmogorov system when its two parameters vary in a small neighbourhood of the value $0.$ The local behavior of the system is described in terms of bifurcation diagrams.