Deformation of geometry and bifurcations of vortex rings
نویسندگان
چکیده
We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a necessary tool.
منابع مشابه
A New Technique for the Calculation of Colliding Vortex Rings
The present study involves a novel computational technique, regarding simultaneous use of the pseudo particle method, Poisson integral method and a special-purpose computer originally designed for molecular dynamics simulations (MDGRAPE-3). In the present calculations, the dynamics of two colliding vortex rings have been studied using the vortex method. The present acceleration technique allows...
متن کاملNumerical Investigation of Vortex Interaction in Pipe Flow
To discover the nonlinear characteristics of pipe flow, we simulated the flow as a sum of many vortex rings. As a first step, we investigated the nonlinear interaction among a maximum of three vortex rings. The pipe wall was replaced by many bound vortices. A free vortex ring moves right or left according to the radius, and that of a particular radius keeps the initial position. The energy of a...
متن کاملGrazing Bifurcations and Chaos of a Hydraulic Engine Mount
The constitutive relationships of the rubber materials that act as the main spring of a hydraulic engine mount are nonlinear. In addition to material induced nonlinearity, further nonlinearities may be introduced by mount geometry, turbulent fluid behavior, temperature, boundary conditions, decoupler action, and hysteretic behavior. In this research all influence the behavior of the system only...
متن کاملSimulation study of Hemodynamic in Bifurcations for Cerebral Arteriovenous Malformation using Electrical Analogy
Background and Objective: Cerebral Arteriovenous Malformation (CAVM) hemodynamic is disease condition, results changes in the flow and pressure level in cerebral blood vessels. Measuring flow and pressure without catheter intervention along the vessel is big challenge due to vessel bifurcations/complex bifurcations in Arteriovenous Malformation patients. The vessel geometry in CAVM patients are...
متن کاملNew geometry for TCP: severe plastic deformation of tubes
Since tubes are widely used for different industrial applications, processing of tubes by the Severe Plastic Deformation (SPD) method has been the target of different attempts. Among these attempts, development of SPD processes for tubes based on Equal Channel Angular Pressing (ECAP) has been more successful. As an illustration, Tube Channel Pressing (TCP) has been presented as an attractive SP...
متن کامل