This paper elaborates how the time update of the continuous-discrete extended Kalman-Filter (EKF) can be computed in the most efficient way. The specific structure of the EKF-moment differential equations leads to a new Taylor-Heun-approximation of the nonlinear vector field. Furthermore, the order of consistency and stability behavior of the outlined procedure is investigated. The results are ...

Since electrons in a ballistic regime perceive carbon nanotube or graphene layer structure as continuous medium, we can use the study of quantum dynamics one electron constrained to curve surface obtain qualitative description conduction electrons’ behavior. The confinement process particle leads us, so-called confining potential formalism, geometry-induced effective Schrödinger equation. With ...

The behaviour of a particle with a spin 1/2 and a dipole magnetic moment in a time-varying magnetic field in the form (h0cn(ωt, k), h0sn(ωt, k),H0dn(ωt, k)), where ω is the driving field frequency, t is the time, h0 and H0 are the field amplitudes, cn, sn, dn are Jacobi elliptic functions, k is the modulus of the elliptic functions has been considered. The variation parameter k from zero to 1 g...

We consider the problem of three identical charged particles on a plane under a perpendicular magnetic field and interacting through Coulomb repulsion. This problem is treated within Taut's framework, in the limit of vanishing center of mass vector R → 0, which corresponds to the strong magnetic field limit, occuring for example in the Fractional Quantum Hall Effect. Using the solutions of the ...

The Rajeev–Ranken (RR) model is a Hamiltonian system describing screw-type nonlinear waves of wavenumber k in scalar field theory pseudodual to the 1 + 1D SU(2) principal chiral model. Classically, RR Liouville integrable. Here, we interpret as novel 3D cylindrically symmetric quartic oscillator with an additional rotational energy. quantum has two dimensionless parameters. Upon separating vari...