Robust and Resilient State-dependent Control of Continuous-time Nonlinear Systems with General Performance Criteria

A novel state-dependent control approach for continuous-time nonlinear systems with general performance criteria is presented in this paper. This controller is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state-dependent linear matrix inequality at each time, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control. The efficacy of the proposed technique is demonstrated by numerical simulations of the nonlinear control of the inverted pendulum on a cart system

Mini-jet thermalization and diffusion of transverse momentum correlation in high-energy heavy-ion collisions

Transverse momentum correlation in azimuthal angle of produced hadrons due to mini-jets are studied first within the HIJING Monte Carlo model in high-energy heavy-ion collisions. Jet quenching in the early stage of thermalization is shown to lead to significant diffusion (broadening) of the correlation. Evolution of the transverse momentum density fluctuation that gives rise to such correlation in azimuthal angle in the later stage of heavy-ion collisions is further investigated within a linearized diffusion-like equation and is shown to be determined by the shear viscosity of the evolving dense matter. Such a diffusion equation for the transverse momentum fluctuation is solved with initial values given by HIJING and together with the hydrodynamic equation for the bulk medium. The final transverse momentum correlation in azimuthal angle is calculated along the freeze-out hyper-surface and is found further diffused for larger values of shear viscosity to entropy density ratio $\eta/s \sim 0.2-0.4$. Therefore the final transverse momentum correlation in azimuthal angle can be used to study the thermalization of mini-jets in the early stage of heavy-ion collisions and the viscous effect in the hydrodynamic evolution of the strongly coupled quark gluon plasma.Comment: RevTex 4, 4 pages and 2 figures, the method to determine the fluctuation in transverse fluid velocity in the initial time of the hydro evolution has been improved. The relevant parts have been rewritten with some discussions and references adde

Vortical fluid and Λ\Lambda spin correlations in high-energy heavy-ion collisions

Fermions become polarized in a vortical fluid due to spin-vorticity coupling. The spin polarization density is proportional to the local fluid vorticity at the next-to-leading order of a gradient expansion in a quantum kinetic theory. Spin correlations of two $\Lambda$-hyperons can therefore reveal the vortical structure of the dense matter in high-energy heavy-ion collisions. We employ a (3+1)D viscous hydrodynamic model with event-by-event fluctuating initial conditions from A MultiPhase Transport (AMPT) model to calculate the vorticity distributions and $\Lambda$ spin correlations. The azimuthal correlation of the transverse spin is shown to have a cosine form plus an offset due to a circular structure of the transverse vorticity around the beam direction and global spin polarization. The longitudinal spin correlation shows a structure of vortex-pairing in the transverse plane due to the convective flow of hot spots in the radial direction. The dependence on colliding energy, rapidity, centrality and sensitivity to the shear viscosity are also investigated.Comment: 5 pages in Latex, 3 figure

Effects of jet-induced medium excitation in γ\gamma-hadron correlation in A+A collisions

Coupled Linear Boltzmann Transport and hydrodynamics (CoLBT-hydro) is developed for co-current and event-by-event simulations of jet transport and jet-induced medium excitation (j.i.m.e.) in high-energy heavy-ion collisions. This is made possible by a GPU parallelized (3+1)D hydrodynamics that has a source term from the energy-momentum deposition by propagating jet shower partons and provides real time update of the bulk medium evolution for subsequent jet transport. Hadron spectra in $\gamma$-jet events of A+A collisions at RHIC and LHC are calculated for the first time that include hadrons from both the modified jet and j.i.m.e.. CoLBT-hydro describes well experimental data at RHIC on the suppression of leading hadrons due to parton energy loss. It also predicts the enhancement of soft hadrons from j.i.m.e. The onset of soft hadron enhancement occurs at a constant transverse momentum due to the thermal nature of soft hadrons from j.i.m.e. which also have a significantly broadened azimuthal distribution relative to the jet direction. Soft hadrons in the $\gamma$ direction are, on the other hand, depleted due to a diffusion wake behind the jet.Comment: 4 pages, 4 figures in LaTeX, final version published in PL

Magnetic resonance imaging and computerised tomography findings in an intraspinal extradural hydatid cyst mimicking tuberculous spondylitis: a case report

Spinal hydatid cyst with thoracic vertebra involvement is rare but serious condition. We present a 63-year old woman with spinal hydatid disease mimicking tuberculous spondylitis. A case study with Computerised Tomography and Magnetic Resonance Imaging diagnostic findings and surgical treatment is reported in this article. Primary spinal hydatid disease should be considered in the differential diagnosis of tuberculous spondylitis in endemic area. Familiarity with typical imaging appearances of spinal hydatid disease may be helpful in making a correct diagnosis and treatment