Forecasting The Ocean Wave Heights Using Linear Genetic Programming

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Variations of moduli of parabolic bundles

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46243/1/208_2005_Article_BF01446645.pd

Colision but no pair formation from A geometric framework for dynamics with unilateral constraints and friction, illustrated by an example of self-organized locomotion

If θ_l - θ_h is large enough, then the two dumbbells collide but do not form a stable pair, as formation of a pair involves an alignment of their headings

Formation of left handed dyads from A geometric framework for dynamics with unilateral constraints and friction, illustrated by an example of self-organized locomotion

If θ_h < θ_l ≤ 0, then the dumbbells usually form a stable pair, which is left-handed

Supplementary Information from A geometric framework for dynamics with unilateral constraints and friction, illustrated by an example of self-organized locomotion

We present a geometric framework to deal with mechanical systems which have unilateral constraints, and are subject to damping/friction, which cannot be treated within usual classical mechanics. In this new framework, the dynamical evolution of the system takes place on a multidimensional curvilinear polyhedron, and energetics near the corners of the polyhedron leads to qualitative behaviour such as stable entrapment and bifurcation. We illustrate this by an experiment in which dumbbells, placed inside a tilted hollow cylindrical drum that rotates slowly around its axis, climb uphill by forming dynamically stable pairs, seemingly against the pull of gravity

Formation of right handed dyads from A geometric framework for dynamics with unilateral constraints and friction, illustrated by an example of self-organized locomotion

If 0 ≤ θ_h < θ_l then the dumbbells will usually form a stable pair, which is right-handed