16 citations · 91 across the 25 of their papers we have counts for
34 papers
On the wave turbulence theory for the beam wave equation
Gigliola Staffilani, Minh-Binh Tran
Starting from the beam wave equation, which has a Schrödinger structure, on a hypercubic lattice of size , with weak nonlinearity of strength , we show that the two point cor…
On the wave turbulence theory for a stochastic KdV type equation -- Generalization for the inhomogeneous kinetic limit
Amirali Hannani, Matthew Rosenzweig, Gigliola Staffilani +1
Starting from a stochastic Zakharov-Kuznetsov (ZK) equation on a lattice, the previous work [ST21] by the last two authors gave a derivation of the homogeneous 3-wave kinetic equat…
A Deep Learning Approximation of Non-Stationary Solutions to Wave Kinetic Equations
Steven Walton, Minh-Binh Tran, Alain Bensoussan
We present a deep learning approximation, stochastic optimization based, method for wave kinetic equations. To build confidence in our approach, we apply the method to a Smoluchows…
Wave turbulence and collective behavior models for wave equations with short- and long-range interactions
Alejandro Aceves, Ricardo Alonso, Minh-Binh Tran
In this work, we discuss a situation which could lead to both wave turbulence and collective behavior kinetic equations. The wave turbulence kinetic models appear in the kinetic li…
A Numerical Scheme for Wave Turbulence: 3-Wave Kinetic Equations
Steven Walton, Minh-Binh Tran
We introduce a finite volume scheme to solve a special case of isotropic 3-wave kinetic equations. We test our numerical solution against theoretical results concerning the long ti…
On the wave turbulence theory: ergodicity for the elastic beam wave equation
Benno Rumpf, Avy Soffer, Minh-Binh Tran
We analyse a 3-wave kinetic equation, derived from the elastic beam wave equation on the lattice. The ergodicity condition states that two distinct wavevectors are supposed to be c…