We investigate the response of energy flux in isotropic turbulence to step-function like perturbation in external forcing at large length scales. From both physical experiments and direct numerical simulations, we measured the evolution of the Eulerian velocity structure functions, such as DLL(r), DNN (r), before and after the perturbation in forcing. In both cases, we observed the cascade of t...

Using the language of pseudospectra, we study the behavior of matrix eigenvalues under two scales of matrix perturbation. First, we relate Lidskii’s analysis of small perturbations to a recent result of Karow on the growth rate of pseudospectra. Then, considering larger perturbations, we follow recent work of Alam and Bora in characterizing the distance from a given matrix to the set of matrice...

By efforts of several reserchers, it is recently established that the dynamical behavior of the cosmological perturbation on superhorizon scales is well approximated in terms of that in the long wavelength limit, and that the latter can be constructed from the evolution of corresponding exactly homogeneous universe. Using these facts, we investigate the evolution of the cosmological perturbatio...