Condensation of Eigen Microstate in Statistical Ensemble and Phase Transition

In a statistical ensemble with $M$ microstates, we introduce an $M \times M$ correlation matrix with the correlations between microstates as its elements. Using eigenvectors of the correlation matrix, we can define eigen microstates of the ensemble. The normalized eigenvalue by $M$ represents the weight factor in the ensemble of the corresponding eigen microstate. In the limit $M \to \infty$, weight factors go to zero in the ensemble without localization of microstate. The finite limit of weight factor when $M \to \infty$ indicates a condensation of the corresponding eigen microstate. This indicates a phase transition with new phase characterized by the condensed eigen microstate. We propose a finite-size scaling relation of weight factors near critical point, which can be used to identify the phase transition and its universality class of general complex systems. The condensation of eigen microstate and the finite-size scaling relation of weight factors have been confirmed by the Monte Carlo data of one-dimensional and two-dimensional Ising models.Comment: 9 pages, 16 figures, accepted for publication in Sci. China-Phys. Mech. Astro

Cost-optimal energy management of hybrid electric vehicles using fuel cell/battery health-aware predictive control

Energy management is an enabling technology for increasing the economy of fuel cell/battery hybrid electric vehicles. Existing efforts mostly focus on optimization of a certain control objective (e.g., hydrogen consumption), without sufficiently considering the implications for on-board power sources degradation. To address this deficiency, this article proposes a cost-optimal, predictive energy management strategy, with an explicit consciousness of degradation of both fuel cell and battery systems. Specifically, we contribute two main points to the relevant literature, with the purpose of distinguishing our study from existing ones. First, a model predictive control framework, for the first time, is established to minimize the total running cost of a fuel cell/battery hybrid electric bus, inclusive of hydrogen cost and costs caused by fuel cell and battery degradation. The efficacy of this framework is evaluated, accounting for various sizes of prediction horizon and prediction uncertainties. Second, the effects of driving and pricing scenarios on the optimized vehicular economy are explored

Thermoelectric effect in high mobility single layer epitaxial graphene

The thermoelectric response of high mobility single layer epitaxial graphene on silicon carbide substrates as a function of temperature and magnetic field have been investigated. For the temperature dependence of the thermopower, a strong deviation from the Mott relation has been observed even when the carrier density is high, which reflects the importance of the screening effect. In the quantum Hall regime, the amplitude of the thermopower peaks is lower than a quantum value predicted by theories, despite the high mobility of the sample. A systematic reduction of the amplitude with decreasing temperature suggests that the suppression of the thermopower is intrinsic to Dirac electrons in graphene.Comment: 5 pages, 4 figure

Filtering driving cycles for assessment of electrified vehicles

We present a method for pre-filtering driving cycles that are to be used for assessment of electrified vehicles. The method ensures that the vehicle may exactly follow the filtered velocity demanded by the driving cycle. Employing convex optimization, the method also allows optimal velocity shaping that minimizes the amount of wasted energy. We illustrate the method by an example of performance assessment of a hybrid electric bus in a series powertrain topology

Pontryagin's Minimum Principle based model predictive control of energy management for a plug-in hybrid electric bus

To improve computational efficiency of energy management strategies for plug-in hybrid electric vehicles (PHEVs), this paper proposes a stochastic model predictive controller (MPC) based on Pontryagin’s Minimum Principle (PMP), which differs from widely used dynamic programming (DP)-based predictive methods. First, short-time speed forecasting is achieved using a Markov chain model, based on real-world driving cycles. The PMP- and DP-based MPCs are compared under four preview horizons (5 s, 10 s, 15 s and 20 s), and the results show that the computational time of the DP-MPC is almost four times of that in the PMP-MPC. Moreover, the influence of predication horizon length on computational time and energy consumption is examined. Given a preview horizon of 5 s, the PMP-MPC holds a total energy consumption cost of 7.80 USD and computational time per second of 0.0130 s. When the preview horizon increases to 20 s, the total cost is 7.77 USD with the computational time per second increasing to 0.0502 s. Finally, DP, PMP, and rule-based strategies are contrasted to the PMP-MPC method, further demonstrating the promising performance and computational efficiency of the proposed methodology