The EPDiff equation (or dispersionless Camassa-Holm equation in 1D) is a well known example of geodesic motion on the Diff group of smooth invertible maps (diffeomorphisms). Its recent two-component extension governs geodesic motion on the semidirect product Diff sF , where F denotes the space of scalar functions. This paper generalizes the second construction to consider geodesic motion on Dif...

this paper investigates the lateral vibration of single-layered graphene sheets based on a new theory called doublet mechanics with a length scale parameter. after a brief reviewing of doublet mechanics fundamentals, a sixth order partial differential equation that governs the lateral vibration of single-layered graphene sheets is derived. using doublet mechanics, the relation between natural f...

We investigate the dynamical behavior of finite rings of classical spin vectors interacting via nearest-neighbor isotropic exchange in an external magnetic field. Our approach is to utilize the solutions of a continuum version of the discrete spin equations of motion (EOM) which we derive by assuming continuous modulations of spin wave solutions of the EOM for discrete spins. This continuum EOM...

The particle-hole continuum in the Dirac sea of graphene has a unique window underneath, which in principle leaves room for bound state formation in the triplet particle-hole channel (Baskaran and Jafari 2002 Phys. Rev. Lett. 89 016402). In this work, we construct appropriate triplet particle-hole operators and, using a repulsive Hubbard-type effective interaction, we employ equations of motio...

Dirac equation for the finite dipole potential is solved by the method of the join of the asymptotics. The formulas for the near continuum state energy term of a relativistic electron-dipole system are obtained analytically. Two cases are considered: Z < 137 and Z > 137 Dirac equation for Z > 137 is solved by usual method of cut-off potential at small distances.

: Investigations on control and optimization of continuum manipulators have resulted in a number of kinematic and dynamic modeling approaches each having their own advantages and limitations in various applications. In this paper, a comparative study of five main methods in the literature for kinematic, static and dynamic modeling of continuum manipulators is presented in a unified mathematical...

In this paper, we present a new control strategy for continuous backbone (continuum) ”trunk and tentacle” robots. Control of this emerging new class of robots has proved difficult due to the inherent complexity of their dynamics. Using a recently established full dynamic model, we introduce a new nonlinear model-based control strategy for continuum robots. The approach is applicable to continuu...

Until now, we have developed continuum models for the dynamics of electrolytes at the macroscopic scale, much larger than typical length scales for intermolecular forces. In particular, we have used principles of nonequlibrium thermodynamics, to arrive at general models of interfacial voltage (Nernst equation), reaction kinetics (Butler-Volmer equation), and transport (Poisson-Nernst-Planck equ...

We propose a differential difference equation in R × Z and study it by Hirota’s bilinear method. This equation has a singular continuum limit into a system which admits the reduction to the Davey-Stewartson equation. The solutions of this discrete DS system are characterized by Casorati and Grammian determinants. Based on the bilinear form of this discrete DS system, we construct the bilinear B...