Criticality in a Vlasov-Poisson system - a fermionic universality class

A model Vlasov--Poisson system is simulated close the point of marginal stability, thus assuming only the wave-particle resonant interactions are responsible for saturation, and shown to obey the power--law scaling of a second-order phase transition. The set of critical exponents analogous to those of the Ising universality class is calculated and shown to obey the Widom and Rushbrooke scaling and Josephson's hyperscaling relations at the formal dimensionality $d=5$ below the critical point at nonzero order parameter. However, the two-point correlation function does not correspond to the propagator of Euclidean quantum field theory, which is the Gaussian model for the Ising universality class. Instead it corresponds to the propagator for the fermionic {\it vector} field and to the {\it upper critical dimensionality} $d_c=2$. This suggests criticality of collisionless Vlasov-Poisson systems as representative of the {\it universality class} of critical phenomena of {\it a fermionic} quantum field description.Comment: 10 pages, 6 figures, Submitted to Phys. Rev.

Universal trapping scaling on the unstable manifold for a collisionless electrostatic mode

An amplitude equation for an unstable mode in a collisionless plasma is derived from the dynamics on the two-dimensional unstable manifold of the equilibrium. The mode amplitude $\rho(t)$ decouples from the phase due to the spatial homogeneity of the equilibrium, and the resulting one-dimensional dynamics is analyzed using an expansion in $\rho$. As the linear growth rate $\gamma$ vanishes, the expansion coefficients diverge; a rescaling $\rho(t)\equiv\gamma^2\,r(\gamma t)$ of the mode amplitude absorbs these singularities and reveals that the mode electric field exhibits trapping scaling $|E_1|\sim\gamma^2$ as $\gamma\rightarrow0$. The dynamics for $r(\tau)$ depends only on the phase $e^{i\xi}$ where $d\epsilon_{{k}} /dz=|{\epsilon_{{k}}}|e^{-i\xi/2}$ is the derivative of the dielectric as $\gamma\rightarrow0$.Comment: 11 pages (Latex/RevTex), 2 figures available in hard copy from the Author ([email protected]); paper accepted by Physical Review Letter

Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling

The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $\rho(t)$ is studied using an expansion in $\rho$; in particular, in the limit $\gamma\rightarrow0^+$, the singularities in the expansion coefficients are analyzed to predict the asymptotic dependence of the electric field on the linear growth rate $\gamma$. Generically $|E_k|\sim \gamma^{5/2}$, as $\gamma\rightarrow0^+$, but in the limit of infinite ion mass or for instabilities in reflection-symmetric systems due to real eigenvalues the more familiar trapping scaling $|E_k|\sim \gamma^{2}$ is predicted.Comment: 13 pages (Latex/RevTex), 4 postscript encapsulated figures which are included using the utility "uufiles". They should be automatically included with the text when it is downloaded. Figures also available in hard copy from the authors ([email protected]

Multigrid particle-in-cell simulations of plasma microturbulence

A new scheme to accurately retain kinetic electron effects in particle-in-cell (PIC) simulations for the case of electrostatic drift waves is presented. The splitting scheme, which is based on exact separation between adiabatic and on adiabatic electron responses, is shown to yield more accurate linear growth rates than the standard df scheme. The linear and nonlinear elliptic problems that arise in the splitting scheme are solved using a multi-grid solver. The multi-grid particle-in-cell approach offers an attractive path, both from the physics and numerical points of view, to simulate kinetic electron dynamics in global toroidal plasmas

Adaptive thrust vector control during on-orbit servicing

On-orbit servicing missions often include a final propulsive phase where a spacecraft pushes the other one towards a different orbit. Specifically this is the case of the debris grasping mission where the chaser, after capturing the target by means of robotic arms, has to perform a de-orbit operation. The large thrust involved needs a perfect alignment with respect to the center of mass or the system composed by chaser and target, in order to avoid attitude changes. Such accurate alignment is quite difficult to achieve especially when the characteristics of the target are not perfectly known. A procedure is proposed in this paper, allowing a complete estimation of the center of mass position and of the moments of inertia of the system, starting from the data obtained by the gyros mounted on board of the spacecraft. The output is used to design a maneuver for correcting the target and chaser relative position by moving the robotic arms. Numerical simulations show the proficiency and the applicability of the estimation algorithm and of re-alignment maneuver to a selected mission scenario

Design and validation of exoskeleton actuated by soft modules towards neurorehabilitation - vision-based control for precise reaching motion of upper limb

We demonstrated the design, production, and functional properties of the Exoskeleton Actuated by the Soft Modules (EAsoftM). Integrating the 3D printed exoskeleton with passive joints to compensate gravity and with active joints to rotate the shoulder and elbow joints resulted in ultra-light system that could assist planar reaching motion by using the vision-based control law. The EAsoftM can support the reaching motion with compliance realised by the soft materials and pneumatic actuation. In addition, the vision-based control law has been proposed for the precise control over the target reaching motion within the millimeter scale. % Aiming at rehabilitation exercise for individuals, typically soft actuators have been developed for relatively small motions, such as grasping motion, and one of the challenges has been to extend their use for a wider range reaching motion. The proposed EAsoftM presented one possible solution for this challenge by transmitting the torque effectively along the anatomically aligned with a human body exoskeleton. % The proposed integrated systems will be an ideal solution for neurorehabilitation where affordable wearable and portable systems are required to be customised for individuals with specific motor impairments

An Overview of Kinematic and Calibration Models Using Internal/External Sensors or Constraints to Improve the Behavior of Spatial Parallel Mechanisms

This paper presents an overview of the literature on kinematic and calibration models of parallel mechanisms, the influence of sensors in the mechanism accuracy and parallel mechanisms used as sensors. The most relevant classifications to obtain and solve kinematic models and to identify geometric and non-geometric parameters in the calibration of parallel robots are discussed, examining the advantages and disadvantages of each method, presenting new trends and identifying unsolved problems. This overview tries to answer and show the solutions developed by the most up-to-date research to some of the most frequent questions that appear in the modelling of a parallel mechanism, such as how to measure, the number of sensors and necessary configurations, the type and influence of errors or the number of necessary parameters