20 Solving dynamic user equilibrium by mean field routing game with explicit conges 48:09 Understanding data and agents' interaction patterns in large networks using GNNs 50:22 Weak solutions to the master equation of a potential mean field game 57:26 Controlling Human Microbiota 48:56 Describing ...
For the particular case of n=4, such homoclinic cycles have been classified as of type A, B and C on the basis of the action of the symmetry group. It has been also suggested that type C cycles have an even number of equilibrium points.In this paper we investigate the number of ...
In the special case of statical equilibrium without body forces, the number of different categories for the isotropic points in a stress distribution reduces to four and there is a close analogy with the umbilic points of a surface, but for strain the number remains six.doi:10.1080/...
Mineral - Classification, Properties, Types: Since the middle of the 19th century, minerals have been classified on the basis of their chemical composition. Under this scheme, they are divided into classes according to their dominant anion or anionic gro
In particular, we consider orbits about equilibrium points in the Earth-sun rotating frame, which are high above the... T Waters,CR Mcinnes 被引量: 23发表: 2007年 Invariant manifolds of L_3 and horseshoe motion in the restricted three-body problem In this paper, we consider horseshoe ...
of equilibrium points, owing to the large number of different kinds of possible topologies of large scale networks. Instead of theoretical proofs, often simulation and experimentation based proofs have been provided. One of the most important findings of this category of approaches is the lack of ...
The classification results are stated separately for nonequilibrium and equilibrium points. The functional invariants which appear in the normal form have a direct interpretation in terms of singular, time-extremal trajectories of the systems. We show that, roughly, the singular extremals determine the...
For a saddle equilibrium point of a dynamical system, the relation between its stable and unstable manifolds usually has three cases: separation, transversal intersection, and homoclinic tangency.The case of separation is trivial. It is well-known that for transversal intersection infinitely many saddle...
Much is understood about 1-dimensional spin chains in terms of entanglement properties, physical phases, and integrability. However, the Lie algebraic properties of the Hamiltonians describing these systems remain largely unexplored. In this work, we pro
In previous chapters, we were dealing with equilibrium of objects modeled either as particles (points) or rigid bodies depending on their size and loading conditions. As we already know the actual geodoi:10.1007/978-1-4939-2101-0_7Emri, IgorVoloshin, ArkadySpringer New York...