## 11 Citations

### Normal stability of slow manifolds in nearly periodic Hamiltonian systems

- MathematicsJournal of Mathematical Physics
- 2021

M. Kruskal showed that each nearly-periodic dynamical system admits a formal U(1) symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly-invariant manifolds of…

### Slow manifolds of classical Pauli particle enable structure-preserving geometric algorithms for guiding center dynamics

- PhysicsComput. Phys. Commun.
- 2021

### Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

- MathematicsNonlinear Dynamics
- 2021

This paper aims at reviewing nonlinear methods for model order reduction in structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory.…

### Asymptotically preserving particle methods for strongly magnetizedplasmas in a torus

- Computer ScienceJ. Comput. Phys.
- 2023

### Slow manifold reduction as a systematic tool for revealing the geometry of phase space

- Physics, MathematicsPhysics of Plasmas
- 2022

Many non-dissipative reduced plasma models can be derived from more fundamental non-dissipative models by restricting to an approximate invariant manifold. I present a general systematic procedure…

### Approximation of nearly-periodic symplectic maps via structure-preserving neural networks

- MathematicsArXiv
- 2022

. A continuous-time dynamical system with parameter ε is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as ε approaches 0. Nearly-periodic maps are…

### On a large-stepsize integrator for charged-particle dynamics

- PhysicsBIT Numerical Mathematics
- 2023

Xiao and Qin (Comput Phys Commun 265:107981, 2021) recently proposed a remarkably simple modification of the Boris algorithm to compute the guiding centre of the highly oscillatory motion of a…

### Nearly Periodic Maps and Geometric Integration of Noncanonical Hamiltonian Systems

- MathematicsJournal of Nonlinear Science
- 2023

M. Kruskal showed that each continuous-time nearly periodic dynamical system admits a formal U(1)-symmetry, generated by the so-called roto-rate. When the nearly periodic system is also Hamiltonian,…

### Geometric Methods for Adjoint Systems

- Mathematics, Computer ScienceArXiv
- 2022

It is shown that the adjoint variational quadratic conservation laws, which are key to adjoint sensitivity analysis, arise from (pre)symplecticity of such adjoint systems, and structure-preserving numerical methods for such systems using Galerkin Hamiltonian variational integrators (Leok and Zhang) are developed.

### Hamiltonian reduction of Vlasov–Maxwell to a dark slow manifold

- MathematicsJournal of Plasma Physics
- 2021

We show that non-relativistic scaling of the collisionless Vlasov–Maxwell system implies the existence of a formal invariant slow manifold in the infinite-dimensional Vlasov–Maxwell phase space.…

## References

SHOWING 1-10 OF 101 REFERENCES

### Initialization and the quasi-geostrophic slow manifold

- Environmental Science
- 2003

Atmospheric dynamics span a range of time-scales. The projection of measured data to a slow manifold, ${\cal M}$, removes fast gravity waves from the initial state for numerical simulations of the…

### Extending the zero-derivative principle for slow–fast dynamical systems

- Mathematics
- 2015

Slow–fast systems often possess slow manifolds, that is invariant or locally invariant sub-manifolds on which the dynamics evolves on the slow time scale. For systems with explicit timescale…

### Guiding center dynamics as motion on a formal slow manifold in loop space

- PhysicsJournal of Mathematical Physics
- 2020

Since the late 1950's, the dynamics of a charged particle's ``guiding center" in a strong, inhomogeneous magnetic field have been understood in terms of near-identity coordinate transformations. The…

### Constraint-Defined Manifolds: a Legacy Code Approach to Low-Dimensional Computation

- Computer ScienceJ. Sci. Comput.
- 2005

This paper demonstrates that with the knowledge only of a set of “slow” variables that can be used to parameterize the slow manifold, one can conveniently compute, using a legacy simulator, on a nearby manifold.

### On the Nonexistence of a Slow Manifold

- Mathematics
- 1986

Abstract We identify the slow manifold of a primitive-equation system with the set of all solutions that are completely devoid of gravity-wave activity. We construct a five-variable model describing…

### Variational nonlinear WKB in the Eulerian frame

- Physics
- 2019

Nonlinear WKB is a multiscale technique for studying locally-plane-wave solutions of nonlinear partial differential equations (PDE). Its application comprises two steps: (1) replacement of the…

### Magnetohydrodynamic motion of a two-fluid plasma

- Physics, Mathematics
- 2017

The two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell's equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled…

### A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

- Computer ScienceJ. Comput. Phys.
- 2016

### Hamiltonian structure of the guiding center plasma model

- Physics
- 2017

The guiding center plasma model (also known as kinetic MHD) is a rigorous sub-cyclotron-frequency closure of the Vlasov-Maxwell system. While the model has been known for decades, and it plays a…