Linear instability of Vlasov-Maxwell systems revisited-A Hamiltonian approach

<p style='text-indent:20px;'>We consider linear stability of steady states of 1<inline-formula><tex-math id="M1">\begin{document}$ \frac{1}{2} $\end{document}</tex-math></inline-formula> and 3DVlasov-Maxwell systems for collisionless plasmas. The linearized systems canbe written as separable Hamiltonian systems with constraints. By using ageneral theory for separable Hamiltonian systems, we recover the sharp linearstability criteria obtained previously by different approaches. Moreover, weobtain the exponential trichotomy estimates for the linearized Vlasov-Maxwellsystems in both relativistic and nonrelativistic cases.</p>

Polarization in Quasirelativistic Graphene Model with Topologically Non-Trivial Charge Carriers

Within the earlier developed high-energy-k→·p→-Hamiltonian approach to describe graphene-like materials, the simulations of band structure, non-Abelian Zak phases and the complex conductivity of graphene have been performed. The quasi-relativistic graphene model with a number of flavors (gauge fields) NF=3 in two approximations (with and without a pseudo-Majorana mass term) has been utilized as a ground for the simulations. It has been shown that Zak-phases set for the non-Abelian Majorana-like excitations (modes) in graphene represent the cyclic Z12 and this group is deformed into a smaller one Z8 at sufficiently high momenta due to a deconfinement of the modes. Simulations of complex longitudinal low-frequency conductivity have been performed with a focus on effects of spatial dispersion. A spatial periodic polarization in the graphene models with the pseudo Majorana charge carriers is offered.

Effect of asymmetries of stiffness and mass on parametric instabilities of hollow rotor system

The present work aims to understand the influence of the asymmetries on the dynamics of the hollow rotor system. The study comprises the analytical study through the extended Lagrangian Hamiltonian approach and validation conducted with the simulation study through the bond graphs. This study involves an investigation of the dynamics of the hollow rotor system through two case studies. First case study considers a hollow rotor system with small asymmetry in stiffness while another study considers a hollow rotor system with asymmetry in mass. The lumped analysis involves the development of a mathematical model by considering the symmetry breaking of a hollow rotor caused by mass or stiffness. The study shows good agreement in simulation and analytical results.