43 citations · 166 across the 17 of their papers we have counts for
17 papers
Symplectic Isospectral Runge--Kutta Methods as Lie group methods
Paolo Cifani, Klas Modin, Cecilia Pagliantini +1
We compare three approaches for structure preserving numerical integration of isospectral flows on quadratic Lie algebras. Such flows originate from Hamiltonian dynamics on the cot…
A brief introduction to matrix hydrodynamics
Klas Modin, Milo Viviani
This survey gives a basic demonstration of matrix hydrodynamics; the field pioneered by V. Zeitlin, where 2-D incompressible fluids are spatially discretized via quantization theor…
Two-dimensional fluids via matrix hydrodynamics
Klas Modin, Milo Viviani
Two-dimensional (2-D) incompressible, inviscid fluids produce fascinating patterns of swirling motion. How and why the patterns emerge are long-standing questions, first addressed…
Zero-Noise Selection for Point Vortex Dynamics after Collapse
Francesco Grotto, Marco Romito, Milo Viviani
The continuation of point vortex dynamics after a vortex collapse is investigated by means of a regularization procedure consisting in introducing a small stochastic diffusive term…
Data-driven stochastic spectral modeling for coarsening of the two-dimensional Euler equations on the sphere
Sagy Ephrati, Paolo Cifani, Milo Viviani +1
A resolution-independent data-driven stochastic parametrization method for subgrid-scale processes in coarsened fluid descriptions is proposed. The method enables the inclusion of…
Sparse-stochastic model reduction for 2D Euler equations
Paolo Cifani, Sagy Ephrati, Milo Viviani
The 2D Euler equations are a simple but rich set of non-linear PDEs that describe the evolution of an ideal inviscid fluid, for which one dimension is negligible. Solving numerical…
An efficient geometric method for incompressible hydrodynamics on the sphere
Paolo Cifani, Milo Viviani, Klas Modin
We present an efficient and highly scalable geometric method for two-dimensional ideal fluid dynamics on the sphere. The starting point is Zeitlin's finite-dimensional model of hyd…
On the infinite dimension limit of invariant measures and solutions of Zeitlin's 2D Euler equations
Franco Flandoli, Umberto Pappalettera, Milo Viviani
In this work we consider a finite dimensional approximation for the 2D Euler equations on the sphere, proposed by V. Zeitlin, and show their convergence towards a solution to Euler…
Casimir preserving spectrum of two-dimensional turbulence
Paolo Cifani, Milo Viviani, Erwin Luesink +2
We present predictions of the energy spectrum of forced two-dimensional turbulence obtained by employing a structure-preserving integrator. In particular, we construct a finite-mod…
Solving cubic matrix equations arising in conservative dynamics
Michele Benzi, Milo Viviani
In this paper we consider the spatial semi-discretization of conservative PDEs. Such finite dimensional approximations of infinite dimensional dynamical systems can be described as…
Turbulent magneto-genesis in a collisionless plasma
F. Pucci, M. Viviani, F. Valentini +3
We investigate an efficient mechanism for generating magnetic fields in turbulent, collisionless plasmas. By using fully kinetic, particle-in-cell simulations of an initially non-m…
An algebraic approach to the spontaneous formation of spherical jets
Milo Viviani
The global structure of the atmosphere and the oceans is a continuous source of intriguing challenges in geophysical fluid dynamics (GFD). Among these, jets are determinant in the…
Canonical scale separation in two-dimensional incompressible hydrodynamics
Klas Modin, Milo Viviani
A two-dimensional inviscid incompressible fluid is governed by simple rules. Yet, to characterise its long-time behaviour is a knotty problem. The fluid evolves according to Euler'…
Integrability of point-vortex dynamics via symplectic reduction: a survey
Klas Modin, Milo Viviani
Point-vortex dynamics describe idealized, non-smooth solutions to the incompressible Euler equations on 2-dimensional manifolds. Integrability results for few point-vortices on var…
A minimal-variable symplectic method for isospectral flows
Milo Viviani
Isospectral flows are abundant in mathematical physics; the rigid body, the the Toda lattice, the Brockett flow, the Heisenberg spin chain, and point vortex dynamics, to mention bu…
A Casimir preserving scheme for long-time simulation of spherical ideal hydrodynamics
Klas Modin, Milo Viviani
The incompressible 2D Euler equations on a sphere constitute a fundamental model in hydrodynamics. The long-time behaviour of solutions is largely unknown; statistical mechanics pr…
Lie-Poisson methods for isospectral flows
Klas Modin, Milo Viviani
The theory of isospectral flows comprises a large class of continuous dynamical systems, particularly integrable systems and Lie--Poisson systems. Their discretization is a classic…