47 citations · 178 across the 21 of their papers we have counts for
23 papers
Sparsity of Fourier mass of passively advected scalars in the Batchelor regime
Alex Blumenthal, Manh Khang Huynh
In 1959, Batchelor gave a prediction for the power spectral density of a passive scalar advected by an incompressible fluid exhibiting shear-straining, a mechanism for the creation…
On the norm equivalence of Lyapunov exponents for regularizing linear evolution equations
Alex Blumenthal, Sam Punshon-Smith
We consider the top Lyapunov exponent associated to a dissipative linear evolution equation posed on a separable Hilbert or Banach space. In many applications in partial differenti…
Exponential mixing for random dynamical systems and an example of Pierrehumbert
Alex Blumenthal, Michele Coti Zelati, Rishabh S. Gvalani
We consider the question of exponential mixing for random dynamical systems on arbitrary compact manifolds without boundary. We put forward a robust, dynamics-based framework that…
Noise induced order for skew-products over a non-uniformly expanding base
Alex Blumenthal, Isaia Nisoli
Noise-induced order is the phenomenon by which the chaotic regime of a deterministic system is destroyed in the presence of noise. In this manuscript, we establish noise-induced or…
Lower bounds on the Lyapunov exponents of stochastic differential equations
Jacob Bedrossian, Alex Blumenthal, Sam Punshon-Smith
In this article, we review our recently introduced methods for obtaining strictly positive lower bounds on the top Lyapunov exponent of high-dimensional, stochastic differential eq…
On the pitchfork bifurcation for the Chafee-Infante equation with additive noise
Alex Blumenthal, Maximilian Engel, Alexandra Neamtu
We investigate pitchfork bifurcations for a stochastic reaction diffusion equation perturbed by an infinite-dimensional Wiener process. It is well-known that the random attractor i…