296 citations · 399 across the 15 of their papers we have counts for
17 papers
Prevalence of Delay Embeddings with a Fixed Observation Function
Raymundo Navarrete, Divakar Viswanath
Let , , be a dynamical system with being a diffeomorphism. Although the state vector is often unobservable, the dynamics can b…
Delay Embedding of Periodic Orbits Using a Fixed Observation Function
Raymundo Navarrete, Divakar Viswanath
Delay coordinates are a widely used technique to pass from observations of a dynamical system to a representation of the dynamical system as an embedding in Euclidean space. Curren…
Prediction of Dynamical time Series Using Kernel Based Regression and Smooth Splines
Raymundo Navarrete, Divakar Viswanath
Prediction of dynamical time series with additive noise using support vector machines or kernel based regression has been proved to be consistent for certain classes of discrete dy…
Error Analysis of Finite Differences and the Mapping Parameter in Spectral Differentiation
Divakar Viswanath
The Chebyshev points are commonly used for spectral differentiation in non-periodic domains. The rounding error in the Chebyshev approximation to the -the derivative increases a…
Intermittency at Fine Scales and Complex Singularities of Turbulent Couette Flow
Andre Souza, Divakar Viswanath
Fine scales of turbulent velocity fields, beyond the inertial range and well into the dissipative range, are highly intermittent. It has been hypothesized that complex plane singul…
Accuracy and stability of inversion of power series
Raymundo Navarrete, Divakar Viswanath
This article considers the numerical inversion of the power series to compute the inverse series satisfying . Numerical inversi…
Navier-Stokes solver using Green's functions II: spectral integration of channel flow and plane Couette flow
Divakar Viswanath
The Kleiser-Schumann algorithm has been widely used for the direct numerical simulation of turbulence in rectangular geometries. At the heart of the algorithm is the solution of li…
Spectral integration of linear boundary value problems
Divakar Viswanath
Spectral integration was deployed by Orszag and co-workers (1977, 1980, 1981) to obtain stable and efficient solvers for the incompressible Navier-Stokes equation in rectangular ge…
Navier-Stokes solver using Green's functions I: channel flow and plane Couette flow
Divakar Viswanath, Ian Tobasco
Numerical solvers of the incompressible Navier-Stokes equations have reproduced turbulence phenomena such as the law of the wall, the dependence of turbulence intensities on the Re…
Barycentric Hermite Interpolation
Burhan Sadiq, Divakar Viswanath
Let be distinct grid points. If is the prescribed value of a function at the grid point , and the prescribed value of the \foreig…
Finite Difference Weights, Spectral Differentiation, and Superconvergence
Burhan Sadiq, Divakar Viswanath
Let be a sequence of distinct grid points. A finite difference formula approximates the -th derivative as , with …
Metric Entropy and the Optimal Prediction of Chaotic Signals
Divakar Viswanath, Xuan Liang, Kirill Serkh
Suppose we are given a time series or a signal for . We consider the problem of predicting the signal in the interval from a knowledge of it…
Complex Singularities and the Lorenz Attractor
Divakar Viswanath, Sonmez Sahutoglu
The Lorenz attractor is one of the best known examples of applied mathematics. However, much of what is known about it is a result of numerical calculations and not of mathematical…
Exact and Asymptotic Conditions on Traveling Wave Solutions of the Navier-Stokes Equations
Y. Charles Li, Divakar Viswanath
We derive necessary conditions that traveling wave solutions of the Navier-Stokes equations must satisfy in the pipe, Couette, and channel flow geometries. Some conditions are exac…
Heteroclinic connections in plane Couette flow
Jonathan Halcrow, John F. Gibson, Predrag Cvitanović +1
Plane Couette flow transitions to turbulence for Re~325 even though the laminar solution with a linear profile is linearly stable for all Re (Reynolds number). One starting point f…
Recurrent motions within plane Couette turbulence
D. Viswanath
The phenomenon of bursting, in which streaks in turbulent boundary layers oscillate and then eject low speed fluid away from the wall, has been studied experimentally, theoreticall…
Convergence of numerical ODE solvers and Lyapunov's theory of stability
Divakar Viswanath
For the ordinary differential equation (ODE) , , , , assume to be at least continuous in and locally Lipshitz in , an…