The finite-distance gravitational deflection of massive particles in stationary spacetime: a Jacobi metric approach

In this paper, we study the weak gravitational deflection of relativistic massive particles for a receiver and source at finite distance from the lens in stationary, axisymmetric and asymptotically flat spacetimes. For this purpose, we extend the generalized optical metric method to the generalized Jacobi metric method by using the Jacobi-Maupertuis Randers-Finsler metric. More specifically,we apply the Gauss-Bonnet theorem to the generalized Jacobi metric space and then obtain an expression for calculating the deflection angle, which is related to Gaussian curvature of generalized optical metric and geodesic curvature of particles orbit. In particular, the finite-distance correction to the deflection angle of signal with general velocity in the the Kerr black hole and Teo wormhole spacetimes are considered. Our results cover the previous work of the deflection angle of light, as well as the deflection angle of massive particles in the limit for the receive and source at infinite distance from the lens object. In Kerr black hole spacetime, we compared the effects due to the black hole spin, the finite-distance of source or receiver, and the relativistic velocity in microlensings and lensing by galaxies. It is found in these cases, the effect of BH spin is usually a few orders larger than that of the finite-distance and relativistic velocity, while the relative size of the latter two could vary according to the particle velocity, source or observer distance and other lensing parameters.Comment: 16 pages, 4 figure

Deflection of charged signals in a dipole magnetic field in Schwarzschild background using Gauss-Bonnet theorem

This paper studies the deflection of charged particles in a dipole magnetic field in Schwarzschild spacetime background in the weak field approximation. To calculate the deflection angle, we use Jacobi metric and Gauss-Bonnet theorem. Since the corresponding Jacobi metric is a Finsler metric of Randers type, we use both the osculating Riemannian metric method and generalized Jacobi metric method. The deflection angle up to fourth order is obtained and the effect of the magnetic field is discussed. It is found that the magnetic dipole will increase (or decrease) the deflection angle of a positively charged signal when its rotation angular momentum is parallel (or antiparallel) to the magnetic field. It is argued that the difference in the deflection angles of different rotation directions can be viewed as a Finslerian effect of the non-reversibility of the Finsler metric. The similarity of the deflection angle in this case with that for the Kerr spacetime allows us to directly use the gravitational lensing results in the latter case. The dependence of the apparent angles on the magnetic field suggests that by measuring these angles the magnetic dipole might be constrained.Comment: 13 pages, 3 figure

The deflection of charged massive particles by a 4-Dimensional charged Einstein-Gauss-Bonnet black hole

Based on the Jacobi metric method, this paper studies the deflection of a charged massive particle by a novel 4-dimensional charged Einstein-Gauss-Bonnet black hole. We focus on the weak-filed approximation and consider the deflection angle with finite-distance effects, i.e. the source and observer at finite distances from the black hole. To this end, we use a geometric and topological method, which is to apply the Gauss-Bonnet theorem to the Jacobi-metric surface to calculate the deflection angle. We find that the deflection angle contains a pure gravitational contribution $\delta_g$, a pure electrostatic one $\delta_c$ and a gravitational-electrostatic coupling term $\delta_{gc}$. We also show that the electrostatic contribution $\delta_c$ can also be computed by the Jacobi-metric method using the GB theorem to a charge in a Minkowski flat spacetime background. We find that the deflection angle increases(decreases) if the Gauss-Bonnet coupling constant $\alpha$ is negative(positive). Furthermore, the effects of the BH charge, the particle charge-to-mass ratio and the particle velocity on the deflection angle are analyzed.Comment: 11 pages, 5 Figures; conclusion part improved and reference adde

Model-based State-of-energy Estimation of Lithium-ion Batteries in Electric Vehicles

AbstractWith the increasing application of lithium-ion batteries, the function of battery management system (BMS) comes to be more sophisticated. The state-of-energy (SOE) of lithium-ion batteries is a critical index for energy optimization and management in electric vehicles. The conventional power integral methods are easy to cause accumulated error due to current or voltage drift of sensors. Therefore the EKF method is employed in this study. A data-driven model is established to describe the relationship between the open-circuit voltage (OCV) and SOE based on the experimental data of a Li(Ni1/3Co1/3Mn1/3)O2 battery. The dynamic urban driving schedule of Wuhui city in China has been conducted on the lithium-ion battery to verify the accuracy of the proposed method. The results show that accurate SOE estimation results can be obtained by the proposed method

Free serum cortisol during the postoperative acute phase response determined by equilibrium dialysis liquid chromatography-tandem mass spectrometry

In severely ill patients low concentrations of the corticosteroid binding globulin are typically found; the aim of this study was to quantify directly free bioactive cortisol concentrations in the sera of postoperative cardiosurgical patients. Serum samples of 12 consecutive patients undergoing aortocoronary bypass surgery taken preoperatively and on the postoperative days 1 to 4 were analyzed. Total serum cortisol was quantified using liquid chromatographytandem mass spectrometry with an online sample extraction system and trideuterated cortisol as the internal standard, and free serum cortisol was measured after overnight equilibrium dialysis. Whereas on the first postoperative day, the median total serum cortisol concentration was approximately twofold increased compared to preoperative samples (preoperatively, 245 nmol/l (interquartile range (IQR) 203293 nmol/l); first postoperative day, 512 nmol/l (IQR 410611 nmol/l)), median dialyzable free cortisol concentration was almost sevenfold increased (preoperatively, 14.2 nmol/l (IQR 10.920.7 nmol/l); first postoperative day, 98.3 nmol/l (IQR 81.3134 nmol/l)). On the fourth postoperative day, median free cortisol was still significantly increased compared to baseline sampling (p < 0.05), whereas median total cortisol was not. A median of 5.7% (IQR 5.47.0%) of total cortisol was found as free cortisol on the preoperative day, 21.2% (IQR 18.9 23.5%) on the first postoperative day and 10.5% (IQR 9.814.0%) on the fourth postoperative day. It is concluded that during the postoperative period the freeto bound ratio of cortisol is highly variable and that during the acute phase response direct quantification of free bioactive cortisol concentrations seems to be biologically more appropriate than the measurement of total cortisol concentrations