Related papers: Discovering multiscale and self-similar structure …
This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated…
This study aims to extract and characterize structures in fully developed pipe flow at a friction Reynolds number of $\text{Re}_\tau = 12\,400$. To do so, we employ data-driven wavelet decomposition (DDWD) [D.~Floryan and M.~D.~Graham, PNAS…
A study of correlations in tractable multiparticle cascade models in terms of wavelets reveals many promising features. The selfsimilar construction of the wavelet basis functions and their multiscale localization properties provide a new…
The geometrical structure is among the most fundamental ingredients in understanding complex systems. Is there any systematic approach in defining structures quantitatively, rather than illustratively? If yes, what are the basic principles…
Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
A number of micro-scale biological flows are characterized by spatio-temporal chaos. These include dense suspensions of swimming bacteria, microtubule bundles driven by motor proteins, and dividing and migrating confluent layers of cells. A…
In turbulent flows, energy production is associated with highly organized structures, known as coherent structures. Since these structures are three-dimensional, their detection remains challenging in the most common situation, when…
Plasma turbulence at scales of the order of the ion inertial length is mediated by several mechanisms, including linear wave damping, magnetic reconnection, formation and dissipation of thin current sheets, stochastic heating. It is now…
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…
High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…
Turbulence is ubiquitous in plasmas, leading to rich dynamics characterized by irregularity, irreversibility, energy fluctuations across many scales, and energy transfer across many scales. Another fundamental and generic feature of…
It is important to accurately model materials' properties at lower length scales (micro-level) while translating the effects to the components and/or system level (macro-level) can significantly reduce the amount of experimentation required…
We propose a statistical tool to compare the scaling behaviour of turbulence in pairs of molecular cloud maps. Using artificial maps with well defined spatial properties, we calibrate the method and test its limitations to ultimately apply…
We present a detailed review of large-scale structure (LSS) study using the discrete wavelet transform (DWT). After describing how one constructs a wavelet decomposition we show how this bases can be used as a complete statistical…
Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on…
Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…
A methodology is developed to quantify the transfer and transport of kinetic energy of specific scales associated with coherent structures. Coherent motions are characterized by the triple decomposition of a multi-scale flow and used to…
For the last 140 years, the mechanisms of transport and dissipation of energy in a turbulent flow have not been completely understood. Previous research has focused on analyzing the so-called coherent structures, organized flow patterns…
Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed…