Stabilization of Traffic Flow With a Leading Autonomous Vehicle

This paper develops boundary control law for autonomous vehicles to stabilize the stop-and-go traffic on freeway. The macroscopic traffic dynamics is described by the Aw-Rascle-Zhang (ARZ) model in a time and state dependent domain. The leading autonomous vehicle aims to regulate the traffic behind it to uniform equilibrium and the domain length of the traffic to a setpoint. The traffic density and speed is governed by second-order, nonlinear hyperbolic partial differential equations (PDEs), coupled with a state-dependent ODE for the leading autonomous vehicle. The actuation is the speed of autonomous vehicle at the moving front boundary of the domain. We linearize the system around a uniform velocity and density reference and certain physical properties are discussed for the model validity. The linearized model describes the dynamics of deviations of density and velocity from the reference. By transforming the linearized system in a moving coordinate, we obtain a domain with a fixed boundary at one end and a state-dependent moving boundary at the other end. The well-posedness of the system is proved and the linear instability of open-loop system is shown. We further map the system to Riemann variables and based on it, propose the boundary feedback control law actuated by the leading autonomous vehicle. The exponential stability of state variables in L2 norm and convergence to the setpoint domain length is achieved for the closed-loop system.

Synchrotron FTIR imaging of OH in quartz mylonites

Previous measurements of water in deformed quartzites using conventional Fourier transform infrared spectroscopy (FTIR) instruments have shown that water contents of larger grains vary from one grain to another. However, the non-equilibrium variations in water content between neighboring grains and within quartz grains cannot be interrogated further without greater measurement resolution, nor can water contents be measured in finely recrystallized grains without including absorption bands due to fluid inclusions, films, and secondary minerals at grain boundaries.Synchrotron infrared (IR) radiation coupled to a FTIR spectrometer has allowed us to distinguish and measure OH bands due to fluid inclusions, hydrogen point defects, and secondary hydrous mineral inclusions through an aperture of 10 µm for specimens > 40 µm thick. Doubly polished infrared (IR) plates can be prepared with thicknesses down to 4–8 µm, but measurement of small OH bands is currently limited by strong interference fringes for samples < 25 µm thick, precluding measurements of water within individual, finely recrystallized grains. By translating specimens under the 10 µm IR beam by steps of 10 to 50 µm, using a software-controlled x − y stage, spectra have been collected over specimen areas of nearly 4.5 mm2. This technique allowed us to separate and quantify broad OH bands due to fluid inclusions in quartz and OH bands due to micas and map their distributions in quartzites from the Moine Thrust (Scotland) and Main Central Thrust (Himalayas).Mylonitic quartzites deformed under greenschist facies conditions in the footwall to the Moine Thrust (MT) exhibit a large and variable 3400 cm−1 OH absorption band due to molecular water, and maps of water content corresponding to fluid inclusions show that inclusion densities correlate with deformation and recrystallization microstructures. Quartz grains of mylonitic orthogneisses and paragneisses deformed under amphibolite conditions in the hanging wall to the Main Central Thrust (MCT) exhibit smaller broad OH bands, and spectra are dominated by sharp bands at 3595 to 3379 cm−1 due to hydrogen point defects that appear to have uniform, equilibrium concentrations in the driest samples. The broad OH band at 3400 cm−1 in these rocks is much less common. The variable water concentrations of MT quartzites and lack of detectable water in highly sheared MCT mylonites challenge our understanding of quartz rheology. However, where water absorption bands can be detected and compared with deformation microstructures, OH concentration maps provide information on the histories of deformation and recovery, evidence for the introduction and loss of fluid inclusions, and water weakening processes.

A Stability Analysis of Thermostatically Controlled Loads for Power System Frequency Control

Thermostatically controlled loads (TCLs) are a flexible demand resource with the potential to play a significant role in supporting electricity grid operation. We model a large number of identical TCLs acting autonomously according to a deterministic control scheme to provide frequency response as a population of coupled oscillators. We perform stability analysis to explore the danger of the TCL temperature cycles synchronising: an emergent phenomenon often found in populations of coupled oscillators and predicted in this type of demand response scheme. We take identical TCLs as it can be assumed to be the worst case. We find that the uniform equilibrium is stable and the fully synchronised periodic cycle is unstable, suggesting that synchronisation might not be as serious a danger as feared. Then detailed simulations are performed to study the effects of a population of frequency-sensitive TCLs acting under real system conditions using historic system data. The potential reduction in frequency response services required from other providers is determined, for both homogeneous and heterogeneous populations. For homogeneous populations, we find significant synchronisation, but very minimal diversity removes the synchronisation effects. In summary, we combine dynamical systems stability analysis with large-scale simulations to offer new insights into TCL switching behaviour.

A PLANKTON ALLELOPATHIC MODEL DESCRIBED BY A DELAYED QUASILINEAR PARABOLIC SYSTEM

The quasilinear parabolic system has been applied to a variety of physical and engineering problems. However, most works lack effective techniques to deal with the asymptotic stability. This paper is concerned with the existence and stability of solutions for a plankton allelopathic model described by a quasilinear parabolic system, in which the diffusions are density-dependent. By the coupled upper and lower solutions and its associated monotone iterations, it is shown that under some parameter conditions the positive uniform equilibrium is asymptotically stable. Some biological interpretations for our results are given.

GLOBAL SMOOTH FLOWS FOR THE COMPRESSIBLE EULER–MAXWELL SYSTEM: THE RELAXATION CASE

The Euler–Maxwell system regarded as a hydrodynamic model for plasma physics describes the dynamics of 'compressible electrons' in a constant, charged, non-moving ion background. A global smooth flow with small amplitude is constructed here in three space dimensions when the electron velocity relaxation is taken into account. The speed of the electron flow tending to a uniform equilibrium, and the pointwise behavior of solutions to the linearized homogeneous system in the frequency space are investigated in detail.

Channel and shoal development in a short tidal embayment: an idealized model study

In many tidal embayments, complex patterns of channels and shoals are observed. To gain a better understanding of these features, an idealized model, that describes the interaction of water motion, sediment transport and bed evolution in a semi-enclosed, rectangular basin, is developed and analysed. To explain the initial formation of channels and shoals, two-dimensional perturbations superposed on a laterally uniform equilibrium bottom are studied. These perturbations evolve due to convergences of various residual suspended sediment fluxes: a diffusive flux, a flux related to the bed topography, an advective flux resulting from internally generated overtides and an advective flux due to externally prescribed overtides. For most combinations of these fluxes, perturbations start to grow if the bottom friction is strong enough. Their growth is mainly a result of convergences of diffusive and topographically induced sediment fluxes. Advective contributions due to internally generated overtides enhance this growth. If only diffusive sediment fluxes are considered, the underlying equilibrium is always unstable. This can be traced back to the depth dependence of the deposition parameter. Contrary to the results of previous idealized models, the channels and shoals always initiate in the shallow, landward areas. This is explained by the enhanced generation (compared to that in previous models) of frictional torques in shallow regions. The resulting initial channel–shoal formation compares well with results found in complex numerical model studies. The instability mechanism and the location of the initial formation of bottom patterns do not change qualitatively when varying parameters. Changes are mainly related to differences in the underlying equilibrium profile due to parameter variations.