Trapped Particle Stability for the Kinetic Stabilizer

A kinetically stabilized axially symmetric tandem mirror (KSTM) uses the momentum flux of low-energy, unconfined particles that sample only the outer end-regions of the mirror plugs, where large favorable field-line curvature exists. The window of operation is determined for achieving MHD stability with tolerable energy drain from the kinetic stabilizer. Then MHD stable systems are analyzed for stability of the trapped particle mode. This mode is characterized by the detachment of the central-cell plasma from the kinetic stabilizer region without inducing field-line bending. Stability of the trapped particle mode is sensitive to the electron connection between the stabilizer and the end plug. It is found that the stability condition for the trapped particle mode is more constraining than the stability condition for the MHD mode, and it is challenging to satisfy the required power constraint. Furthermore a severe power drain may arise from the necessary connection of low-energy electrons in the kinetic stabilizer to the central region

Effect of kinetic resonances on the stability of Resistive Wall Mode in Reversed Field Pinch

The kinetic effects, due to the mode resonance with thermal particle drift motions in the reversed field pinch (RFP) plasmas, are numerically investigated for the stability of the resistive wall mode, using a non-perturbative MHD-kinetic hybrid formulation. The kinetic effects are generally found too weak to substantially change the mode growth rate, or the stability margin, re-enforcing the fact that the ideal MHD model is rather adequate for describing the RWM physics in RFP experiments.Comment: Submitted to: Plasma Phys. Control. Fusio

Topological Stability of Kinetic kk-Centers

We study the $k$-center problem in a kinetic setting: given a set of continuously moving points $P$ in the plane, determine a set of $k$ (moving) disks that cover $P$ at every time step, such that the disks are as small as possible at any point in time. Whereas the optimal solution over time may exhibit discontinuous changes, many practical applications require the solution to be stable: the disks must move smoothly over time. Existing results on this problem require the disks to move with a bounded speed, but this model is very hard to work with. Hence, the results are limited and offer little theoretical insight. Instead, we study the topological stability of $k$-centers. Topological stability was recently introduced and simply requires the solution to change continuously, but may do so arbitrarily fast. We prove upper and lower bounds on the ratio between the radii of an optimal but unstable solution and the radii of a topologically stable solution---the topological stability ratio---considering various metrics and various optimization criteria. For $k = 2$ we provide tight bounds, and for small $k > 2$ we can obtain nontrivial lower and upper bounds. Finally, we provide an algorithm to compute the topological stability ratio in polynomial time for constant $k$

Energy stability analysis for a hybrid fluid-kinetic plasma model

In plasma physics, a hybrid fluid-kinetic model is composed of a magnetohydrodynamics (MHD) part that describes a bulk fluid component and a Vlasov kinetic theory part that describes an energetic plasma component. While most hybrid models in the plasma literature are non-Hamiltonian, this paper investigates a recent Hamiltonian variant in its two-dimensional configuration. The corresponding Hamiltonian structure is described along with its Casimir invariants. Then, the energy-Casimir method is used to derive explicit sufficient stability conditions, which imply a stable spectrum and suggest nonlinear stability

Density controls the kinetic stability of ultrastable glasses

We use a swap Monte Carlo algorithm to numerically prepare bulk glasses with kinetic stability comparable to that of glass films produced experimentally by physical vapor deposition. By melting these systems into the liquid state, we show that some of our glasses retain their amorphous structures longer than 10^5 times the equilibrium structural relaxation time. This exceptional kinetic stability cannot be achieved experimentally for bulk materials. We perform simulations at both constant volume and constant pressure to demonstrate that the density mismatch between the ultrastable glass and the equilibrium liquid accounts for a major part of the observed kinetic stability.Comment: 7 Pages, 6 Figures. Figures 4b) and 5b) updated, revisions to text to improve discussion, missing page numbers added to references, typos correcte

A comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flows

We consider a kinetic model, which describes the sedimentation of rod-like particles in dilute suspensions under the influence of gravity. This model has recently been derived by Helzel and Tzavaras in \cite{HT2015}. Here we restrict our considerations to shear flow and consider a simplified situation, where the particle orientation is restricted to the plane spanned by the direction of shear and the direction of gravity. For this simplified kinetic model we carry out a linear stability analysis and we derive two different macroscopic models which describe the formation of clusters of higher particle density. One of these macroscopic models is based on a diffusive scaling, the other one is based on a so-called quasi-dynamic approximation. Numerical computations, which compare the predictions of the macroscopic models with the kinetic model, complete our presentation.Comment: Keywords: rod-like particles, sedimentation, linear stability, moment closure, quasi-dynamic approximation, diffusive scalin

Finding complex balanced and detailed balanced realizations of chemical reaction networks

Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not "encoded" in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability of the underlying reaction kinetic system when further conditions are also fulfilled. In this paper, efficient numerical procedures are given for finding complex balanced or detailed balanced realizations of mass action type chemical reaction networks or kinetic dynamical systems in the framework of linear programming. The procedures are illustrated on numerical examples.Comment: submitted to J. Math. Che