Model reduction via parametrized locally invariant manifolds: Some examples
نویسندگان
چکیده
A method for model reduction in non-linear ODE systems is demonstrated through computational examples. The method does not require an implicit separation of time-scales in the fine dynamics to be effective. From the computational standpoint, the method has the potential of serving as a subgrid modeling tool. From the physical standpoint, it provides a model for interpreting and describing history dependence in coarse-grained response of an autonomous system. 2006 Elsevier B.V. All rights reserved.
منابع مشابه
Statistical cosymplectic manifolds and their submanifolds
In this paper, we introduce statistical cosymplectic manifolds and investigate some properties of their tensors. We define invariant and anti-invariant submanifolds and study invariant submanifolds with normal and tangent structure vector fields. We prove that an invariant submanifold of a statistical cosymplectic manifold with tangent structure vector field is a cosymplectic and minimal...
متن کاملReduction for Locally Conformal Symplectic Manifolds
It is shown how one can do symplectic reduction for locally conformal symplectic manifolds, especially with an action of a Lie group. This generalizes well known procedures for symplectic manifolds to the slightly larger class of locally conformal symplectic manifolds. The whole setting is very conformally invariant.
متن کاملOn Positive Solutions to Semi-linear Conformally Invariant Equations on Locally Conformally Flat Manifolds
In this paper we study the existence and compactness of positive solutions to a family of conformally invariant equations on closed locally conformally flat manifolds. The family of conformally covariant operators Pα were introduced via the scattering theory for Poincaré metrics associated with a conformal manifold (Mn, [g]). We prove that, on a closed and locally conformally flat manifold with...
متن کاملLocal Rigidity of Hyperbolic 3-manifolds after Dehn Surgery
It is well known that some lattices in SO(n, 1) can be nontrivially deformed when included in SO(n+1, 1) (e.g., via bending on a totally geodesic hypersurface); this contrasts with the (super) rigidity of higher rank lattices. M. Kapovich recently gave the first examples of lattices in SO(3, 1) which are locally rigid in SO(4, 1) by considering closed hyperbolic 3-manifolds obtained by Dehn fil...
متن کاملOptimal Low-Thrust, Invariant Manifold Trajectories via Attainable Sets
A method to incorporate low-thrust propulsion into the invariant manifolds technique is presented in this paper. The low-thrust propulsion is introduced by means of special attainable sets that are used in conjunction with invariant manifolds to define a first guess solution. This is later optimized in a more refined model where an optimal control formalism is used. Planar low-energy, low-thrus...
متن کامل