Magnification relations of quad lenses and applications on Einstein crosses

In this work, we mainly study the magnification relations of quad lens models for cusp, fold and cross configurations. By dividing and ray-tracing in different image regions, we numerically derive the positions and magnifications of the four images for a point source lying inside of the astroid caustic. Then, based on the magnifications, we calculate the signed cusp and fold relations for the singular isothermal elliptical lenses. The signed fold relation map has positive and negative regions, and the positive region is usually larger than the negative region as has been confirmed before. It can also explain that for many observed fold image pairs, the fluxes of the Fermat minimum images are apt to be larger than those of the saddle images. We define a new quantity cross relation which describes the magnification discrepancy between two minimum images and two saddle images. Distance ratio is also defined as the ratio of the distance of two saddle images to that of two minimum images. We calculate the cross relations and distance ratios for nine observed Einstein crosses. In theory, for most of the quad lens models, the cross relations decrease as the distance ratios increase. In observation, the cross relations of the nine samples do not agree with the quad lens models very well, nevertheless, the cross relations of the nine samples do not give obvious evidence for anomalous flux ratio as the cusp and fold types do. Then, we discuss several reasons for the disagreement, and expect good consistencies for more precise observations and better lens models in the future.Comment: 12 pages, 11 figures, accepted for publication in MNRA

An Inductive Sensor for Real Time Measurement of Plantar Normal and Shear Forces Distribution

Goal: The objective of this article is to demonstrate a multiplexed inductive force sensor for simultaneously measuring normal force and shear forces on a foot. Methods: The sensor measures the normal force and shear forces by monitoring the inductance changes of three planar sensing coils. Resonance frequency division multiplexing was applied to signals from the multiple sensing coils, making it feasible to simultaneously measure the three forces (normal force, shear forces in x and y axis) on a foot using only one set of measurement electronics with high sensitivity and resolution. Results: The testing results of the prototype sensor have shown that the sensor is capable of measuring normal force ranging from 0 to 800 N and shear forces ranging from 0 to 130 N in real time. Conclusion: With its high resolution, high sensitivity and the capability of monitoring forces at different positions of a foot simultaneously, this sensor can be potentially used for real time measurement of plantar normal force and shear forces distribution on diabetes patient’s foot. Significance: Real time monitoring of the normal force and shear forces on diabetes patient’s foot can provide useful information for physicians and diabetes patients to take actions in preventing foot ulceration

Distributed Robust Learning-Based Backstepping Control Aided with Neurodynamics for Consensus Formation Tracking of Underwater Vessels

This paper addresses distributed robust learning-based control for consensus formation tracking of multiple underwater vessels, in which the system parameters of the marine vessels are assumed to be entirely unknown and subject to the modeling mismatch, oceanic disturbances, and noises. Towards this end, graph theory is used to allow us to synthesize the distributed controller with a stability guarantee. Due to the fact that the parameter uncertainties only arise in the vessels' dynamic model, the backstepping control technique is then employed. Subsequently, to overcome the difficulties in handling time-varying and unknown systems, an online learning procedure is developed in the proposed distributed formation control protocol. Moreover, modeling errors, environmental disturbances, and measurement noises are considered and tackled by introducing a neurodynamics model in the controller design to obtain a robust solution. Then, the stability analysis of the overall closed-loop system under the proposed scheme is provided to ensure the robust adaptive performance at the theoretical level. Finally, extensive simulation experiments are conducted to further verify the efficacy of the presented distributed control protocol

Expressions of Hippocampal Mineralocorticoid Receptor (MR) and Glucocorticoid Receptor (GR) in the Single-Prolonged Stress-Rats

Post-traumatic stress disorder (PTSD) is a stress-related mental disorder caused by traumatic experience. Single-prolonged stress (SPS) is one of the animal models proposed for PTSD. Rats exposed to SPS showed enhanced inhibition of the hypothalamo-pituitary-adrenal (HPA) axis, which has been reliably reproduced in patients with PTSD. Mineralocorticoid receptor (MR) and glucocorticoid receptor (GR) in the hippocampus regulate HPA axis by glucocorticoid negative feedback. Abnormalities in negative feedback are found in PTSD, suggesting that GR and MR might be involved in the pathophysiology of these disorders

Distributed Neurodynamics-Based Backstepping Optimal Control for Robust Constrained Consensus of Underactuated Underwater Vehicles Fleet

Robust constrained formation tracking control of underactuated underwater vehicles (UUVs) fleet in three-dimensional space is a challenging but practical problem. To address this problem, this paper develops a novel consensus based optimal coordination protocol and a robust controller, which adopts a hierarchical architecture. On the top layer, the spherical coordinate transform is introduced to tackle the nonholonomic constraint, and then a distributed optimal motion coordination strategy is developed. As a result, the optimal formation tracking of UUVs fleet can be achieved, and the constraints are fulfilled. To realize the generated optimal commands better and, meanwhile, deal with the underactuation, at the lower-level control loop a neurodynamics based robust backstepping controller is designed, and in particular, the issue of "explosion of terms" appearing in conventional backstepping based controllers is avoided and control activities are improved. The stability of the overall UUVs formation system is established to ensure that all the states of the UUVs are uniformly ultimately bounded in the presence of unknown disturbances. Finally, extensive simulation comparisons are made to illustrate the superiority and effectiveness of the derived optimal formation tracking protocol.Comment: This paper is accepted by IEEE Transactions on Cybernetic

Recent progress in antiferromagnetic dynamics

Spintronics, since its inception, has mainly focused on ferromagnetic materials for manipulating the spin degree of freedom in addition to the charge degree of freedom, whereas much less attention has been paid to antiferromagnetic materials. Thanks to the advances of micro-nano-fabrication techniques and the electrical control of the N\'eel order parameter, antiferromagnetic spintronics is booming as a result of abundant room temperature materials, robustness against external fields and dipolar coupling, and rapid dynamics in the terahertz regime. For the purpose of applications of antiferromagnets, it is essential to have a comprehensive understanding of the antiferromagnetic dynamics at the microscopic level. Here, we first review the general form of equations that govern both antiferromagnetic and ferrimagnetic dynamics. This general form unifies the previous theories in the literature. We also provide a survey for the recent progress related to antiferromagnetic dynamics, including the motion of antiferromagnetic domain walls and skyrmions, the spin pumping and quantum antiferromagnetic spintronics. In particular, open problems in several topics are outlined. Furthermore, we discuss the development of antiferromagnetic quantum magnonics and its potential integration with modern information science and technology.Comment: 7 pages, 2 figure

Entanglement in spin-1/2 dimerized Heisenberg systems

We study entanglement in dimerized Heisenberg systems. In particular, we give exact results of ground-state pairwise entanglement for the four-qubit model by identifying a Z_2 symmetry. Although the entanglements cannot identify the critical point of the system, the mean entanglement of nearest-neighbor qubits really does, namely, it reaches a maximum at the critical point.Comment: Four pages, three figures, accepted in Communications in Theoretical Physic