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Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality…
Harmonic drive systems (HDS) are high-precision robotic transmissions featuring compact size and high gear ratios. However, issues like kinematic transmission errors hamper their precision performance. This article focuses on data-driven…
We present our ongoing work aimed at accelerating a particle-resolved direct numerical simulation model designed to study aerosol-cloud-turbulence interactions. The dynamical model consists of two main components - a set of fluid dynamics…
We consider dimensional reduction techniques for the Liouville-von Neumann equation for the evaluation of the expectation values in a mixed quantum system. In applications such as nuclear spin dynamics the main goal for simulations is being…
This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…
A new approach to turbulence simulation, based on a combination of large-eddy simulation (LES) for the whole flow and an array of non-space-filling quasi-direct numerical simulations (QDNS), which sample the response of near-wall turbulence…
Consider a continuous dynamical system for which partial information about its current state is observed at a sequence of discrete times. Discrete data assimilation inserts these observational measurements of the reference dynamical system…
Real-time control of pumps can be an infeasible task in water distribution systems (WDSs) because the calculation to find the optimal pump speeds is resource-intensive. The computational need cannot be lowered even with the capabilities of…
A novel algorithm for the direct numerical simulation of the variable-density, low-Mach Navier-Stokes equations extending the method of Kim, Moin, and Moser (1987) for incompressible flow is presented here. A Fourier representation is…
We apply the Direct Simulation Monte Carlo (DSMC) method, developed originally to calculate rarefied gas dynamical problems, to study the gas flow in an accretion disc in a close binary system. The method involves viscosity and thermal…
Modern technological advances have expanded the scope of applications requiring analysis of large-scale datastreams that comprise multiple indefinitely long time series. There is an acute need for statistical methodologies that perform…
A new slow growth formulation for DNS of wall-bounded turbulent flow is developed and demonstrated to enable extension of slow growth modeling concepts to complex boundary layer flows. As in previous slow growth approaches, the formulation…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
We present results of three-dimensional Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of turbulent gravity currents with a Discontinuous Galerkin (DG) Finite Elements method. In particular, we consider the…
An efficient representation of observed data has many benefits in various domains of engineering and science. Representing static data sets, such as images, is a living branch in machine learning and eases downstream tasks, such as…
In-air microfluidics became a new method for technical production processes with ultra-high throughput formerly performed in micro channels. Direct Numerical Simulations (DNS) provide a valuable contribution for the fundamental…
The perspective of statistical state dynamics (SSD) has recently been applied to the study of mechanisms underlying turbulence in various physical systems. An example implementation of SSD is the second order closure referred to as…
The aim of this work is to investigate the use of Incrementally Input-to-State Stable ($\delta$ISS) deep Long Short Term Memory networks (LSTMs) for the identification of nonlinear dynamical systems. We show that suitable sufficient…
We put forward a new type of spectral method for the direct numerical simulation of flows where anisotropy or very fine boundary layers are present. The mean idea is to take advantage of the fact that such structures are dissipative and…
We introduce Density sketches (DS): a succinct online summary of the data distribution. DS can accurately estimate point wise probability density. Interestingly, DS also provides a capability to sample unseen novel data from the underlying…