Examples of Discontinuity of Lyapunov Exponent in Smooth Quasi-Periodic Cocycles

We study the regularity of the Lyapunov exponent for quasi-periodic cocycles $(T_\omega, A)$ where $T_\omega$ is an irrational rotation $x\to x+ 2\pi\omega$ on \SS^1 and A\in {\cal C}^l(\SS^1, SL(2,\mathbb{R})), $0\le l\le \infty$. For any fixed $l=0, 1, 2, \cdots, \infty$ and any fixed $\omega$ of bounded-type, we construct D_{l}\in {\cal C}^l(\SS^1, SL(2,\mathbb{R})) such that the Lyapunov exponent is not continuous at $D_{l}$ in ${\cal C}^l$-topology. We also construct such examples in a smaller Schr\"odinger class.Comment: 43pages, 2 figure

su(2) and su(1,1) displaced number states and their nonclassical properties

We study su(2) and su(1,1) displaced number states. Those states are eigenstates of density-dependent interaction systems of quantized radiation field with classical current. Those states are intermediate states interpolating between number and displaced number states. Their photon number distribution, statistical and squeezing properties are studied in detail. It is show that these states exhibit strong nonclassical properties.Comment: 10 pages, 3 figure

Winding number, density of states and acceleration

Winding number and density of states are two fundamental physical quantities for non-self-adjoint quasi-periodic Schr\"odinger operators, which reflect the asymptotic distribution of zeros of the characteristic determinants of the truncated operators under Dirichlet boundary condition, with respect to complexified phase and the energy respectively. We will prove that the winding number is in fact Avila's acceleration and it is also closely related to the density of states by a generalized Thouless formula for non-self-adjoint Schr\"odinger operators and Avila's global theory

Investigating the critical characteristics of thermal runaway process for LiFePO4/graphite batteries by a ceased segmented method

Lithium-ion batteries (LIBs) are widely used as the energy carrier in our daily life. However, the higher energy density of LIBs results in poor safety performance. Thermal runaway (TR) is the critical problem which hinders the further application of LIBs. Clarifying the mechanism of TR evolution is beneficial to safer cell design and safety management. In this paper, liquid nitrogen spray is proved to be an effective way to stop the violent reaction of LIBs during the TR process. Based on extended-volume accelerating rate calorimetry, the liquid nitrogen ceasing combined with non-atmospheric exposure analysis is used to investigate the TR evolution about LiFePO4/graphite batteries at critical temperature. Specifically, the geometrical shape, voltage, and impedance change are monitored during the TR process on the cell level. The morphologies/constitution of electrodes and separators are presented on the component level. Utilizing the gas analysis, the failure mechanism of the prismatic LiFePO4/graphite battery is studied comprehensively

Realization of high-dynamic-range broadband magnetic-field sensing with ensemble nitrogen-vacancy centers in diamond

We present a new magnetometry method integrating an ensemble of nitrogen-vacancy (NV) centers in a single-crystal diamond with an extended dynamic range for monitoring the fast changing magnetic-field. The NV-center spin resonance frequency is tracked using a closed-loop frequency locked technique with fast frequency hopping to achieve a 10 kHz measurement bandwidth, thus, allowing for the detection of fast changing magnetic signals up to 0.723 T/s.This technique exhibits an extended dynamic range subjected to the working bandwidth of the microwave source. This extended dynamic range can reach up to 4.3 mT, which is 86 times broader than the intrinsic dynamic range. The essential components for NV spin control and signal processing such as signal generation, microwave frequency control, data processing and readout are integrated in a board-level system. With this platform, we demonstrate broadband magnetometry with an optimized sensitivity of 4.2 nT-Hz-1/2. This magnetometry method has the potential to be implemented in a multichannel frequency locked vector magnetometer suitable for a wide range of practical applications such as magnetocardiography and high-precision current sensors.Comment: 18 pages, 9 figure

A unified multi-step wind speed forecasting framework based on numerical weather prediction grids and wind farm monitoring data

Wind speed forecasting is the basis of wind farm operation, which provides a reference for the future operation status evaluation of wind farms. For the wind speed forecast of wind turbines in the whole wind farm, a strategy combining unified forecast and single site error correction is proposed in this paper. The unified forecast framework is composed of a unified forecast model and multiple single site error correction models, which combines the forecasted grids of numerical weather prediction (NWP) with the monitoring data of wind farms. The proposed unified forecast model is called spatiotemporal conversion deep predictive network (STC-DPN), which is composed of temporal convolution network (TCN) and 2D convolution long short-term memory network (ConvLSTM). Firstly, the NWP forecasted grids are interpolated to the fan location, and the sequence matrix is composed of the NWP data and the monitored data of each wind turbine according to the time series, which is entered into the TCN network for time sequence feature extraction. Then, the output of the TCN network is converted into a regular spatio-temporal data matrix, which is entered into the ConvLSTM network for joint learning of spatio-temporal features to obtain the wind speed sequence forecasted in the whole wind farm. Finally, an independent TCN-LSTM error correction model is added for each site. Variational modal decomposition (VMD) is used to process data series, and different processing methods are adopted in unified forecast and single site error correction. In the 96 steps forecast test of a wind farm from Jining City, China, the proposed method is superior to several baseline methods and has important practical application value

Data-driven capacity estimation of commercial lithium-ion batteries from voltage relaxation

Accurate capacity estimation is crucial for the reliable and safe operation of lithium-ion batteries. In particular, exploiting the relaxation voltage curve features could enable battery capacity estimation without additional cycling information. Here, we report the study of three datasets comprising 130 commercial lithium-ion cells cycled under various conditions to evaluate the capacity estimation approach. One dataset is collected for model building from batteries with LiNi$_{0.86}$Co$_{0.11}$Al$_{0.03}$O$_{2}$-based positive electrodes. The other two datasets, used for validation, are obtained from batteries with LiNi$_{0.83}$Co$_{0.11}$Mn$_{0.07}$O$_{2}$-based positive electrodes and batteries with the blend of Li(NiCoMn)O$_{2}$ - Li(NiCoAl)O$_{2}$ positive electrodes. Base models that use machine learning methods are employed to estimate the battery capacity using features derived from the relaxation voltage profiles. The best model achieves a root-mean-square error of 1.1% for the dataset used for the model building. A transfer learning model is then developed by adding a featured linear transformation to the base model. This extended model achieves a root-mean-square error of less than 1.7% on the datasets used for the model validation, indicating the successful applicability of the capacity estimation approach utilizing cell voltage relaxation

Adiponectin Protects Against Cerebral Ischemic Injury Through AdipoR1/AMPK Pathways

Excitotoxicity induced by excessive N-methyl-D-aspartate (NMDA) receptor activation underlies the pathology of ischemic injury. Adiponectin (APN) is an adipocyte-derived protein hormone that modulates a number of metabolic processes. APN exerts a wide range of biological functions in the central nervous system. However, the role of APN and its receptors in cerebral ischemia/reperfusion (I/R)-induced injury and the related mechanisms remain to be clarified. Here, we found that APN and APN receptor agonist AdipoRon (APR) were protective against excitotoxicity induced by oxygen and glucose deprivation/reperfusion (OGD/R) and NMDA in primary neurons. Adiponectin receptor 1 (AdipoR1) knockdown reversed the protection conferred by either APN or APR. Moreover, the protective effects offered by both APN and APR were compromised by compound C, an inhibitor of amp-activated protein kinase (AMPK) phosphorylation. Both APN and APR protected the dissipation of the ΔΨm caused by OGD/R. They also up-regulated the PGC-1α expression, which was reversed by compound C. Furthermore, both APN and APR ameliorated but APN knockout aggravated the infarct volume and neurological deficient induced by transient middle cerebral artery occlusion (tMCAO) in vivo. Taken together, these findings show that APN and APR protect against ischemic injury in vitro and in vivo. The protective mechanism is mainly related to AdipoR1-dependent AMPK phosphorylation and PGC-1α up-regulation