A symplectic integration method for elastic filaments
نویسندگان
چکیده
منابع مشابه
A symplectic integration method for elastic filaments.
A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integra...
متن کاملThe split integration symplectic method.
r 0 H H H + = where 0 H is the pure harmonic part and r H is the remaining part. This splitting, incorporated in the second order generalized leapfrog scheme, gives the following approximation for the solution operator of the Hamiltonian system ( ) ( ) ( ) 0 0 r 0 0 t H 2 t H H 2 t t t | x L exp L t exp L exp | x r r ∆ ∆ ∆ + ∆ ≈ which prescribes how to propagate from one point in the phase spac...
متن کاملFree expansion of elastic filaments.
The dynamics of an elastic polymer filament undergoing contour length expansion is studied using computer simulation. The expansion occurs by development of transverse buckling waves that grow through a coarsening process. The growing buckles locally organize into a helical structure with a characteristic persistence length. The helical domain boundaries are eliminated from the relaxing structu...
متن کاملFourth-order Symplectic Integration*
In this paper we present an explicit fourth-order method for the integration of Hamilton’s Equations. This method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state. That is, the integration step is an explicit symplectic map. Although the result is first derived for a specific type of Hamiltonian, it ...
متن کاملEquivariant Constrained Symplectic Integration
We use recent results on symplectic integration of Hamiltonian systems with constraints to construct symplectic integrators on cotangent bundles of manifolds by embedding the manifold in a linear space. We also prove that these methods are equivariant under cotangent lifts of a symmetry group acting linearly on the ambient space and consequently preserve the corresponding momentum. These result...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Journal of Chemical Physics
سال: 2009
ISSN: 0021-9606,1089-7690
DOI: 10.1063/1.3077863