Lorentz transformation of three dimensional gravitational wave tensor

Recently there are more and more interest on the gravitational wave of moving sources. This introduces a Lorentz transformation problem of gravitational wave. Although Bondi-Metzner-Sachs (BMS) theory has in principle already included the Lorentz transformation of gravitational wave, the transformation of the three dimensional gravitational wave tensor has not been explicitly calculated before. Within four dimensional spacetime, gravitational wave have property of `boost weight zero' and `spin weight 2'. This fact makes the Lorentz transformation of gravitational wave difficult to understand. In the current paper we adopt the traditional three dimensional tensor description of gravitational wave. Such a transverse-traceless tensor describes the gravitational wave freedom directly. We derive the explicit Lorentz transformation of the gravitational wave tensor. The transformation is similar to the Lorentz transformation for electric field vector and magnetic field vector which are three dimensional vectors. Based on the deduced Lorentz transformation of the gravitational wave three dimensional tensor, we can construct the gravitational waveform of moving source with any speed if only the waveform of the corresponding rest waveform is given. As an example, we apply our method to the effect of kick velocity of binary black hole. The adjusted waveform by the kick velocity is presented.Comment: 17 pages, 8 figure

Iterative learning control for multi-agent systems with impulsive consensus tracking

In this paper, we adopt D-type and PD-type learning laws with the initial state of iteration to achieve uniform tracking problem of multi-agent systems subjected to impulsive input. For the multi-agent system with impulse, we show that all agents are driven to achieve a given asymptotical consensus as the iteration number increases via the proposed learning laws if the virtual leader has a path to any follower agent. Finally, an example is illustrated to verify the effectiveness by tracking a continuous or piecewise continuous desired trajectory

Iterative learning control for impulsive multi-agent systems with varying trial lengths

In this paper, we introduce iterative learning control (ILC) schemes with varying trial lengths (VTL) to control impulsive multi-agent systems (I-MAS). We use domain alignment operator to characterize each tracking error to ensure that the error can completely update the control function during each iteration. Then we analyze the system’s uniform convergence to the target leader. Further, we use two local average operators to optimize the control function such that it can make full use of the iteration error. Finally, numerical examples are provided to verify the theoretical results

The effect of the gravitational constant variation on the propagation of gravitational waves

Since the first detection of gravitational waves, they have been used to investigate various fundamental problems, including the variation of physical constants. Regarding the gravitational constant, previous works focused on the effect of the gravitational constant variation on the gravitational wave generation. In this paper, we investigate the effect of the gravitational constant variation on the gravitational wave propagation. The Maxwell-like equation that describes the propagation of gravitational waves is extended in this paper to account for situations where the gravitational constant varies. Based on this equation, we find that the amplitude of gravitational waves will be corrected. Consequently the estimated distance to the gravitational wave source without considering such a correction may be biased. Applying our correction result to the well known binary neutron star coalescence event GW170817, we get a constraint on the variation of the gravitational constant. Relating our result to the Yukawa deviation of gravity, we for the first time get the constraint of the Yukawa parameters in 10Mpc scale. This scale corresponds to a graviton mass $m_g\sim10^{-31}$eV

In vivo tracing of the ascending vagal projections to the brain with manganese enhanced magnetic resonance imaging

IntroductionThe vagus nerve, the primary neural pathway mediating brain-body interactions, plays an essential role in transmitting bodily signals to the brain. Despite its significance, our understanding of the detailed organization and functionality of vagal afferent projections remains incomplete.MethodsIn this study, we utilized manganese-enhanced magnetic resonance imaging (MEMRI) as a non-invasive and in vivo method for tracing vagal nerve projections to the brainstem and assessing their functional dependence on cervical vagus nerve stimulation (VNS). Manganese chloride solution was injected into the nodose ganglion of rats, and T1-weighted MRI scans were performed at both 12 and 24 h after the injection.ResultsOur findings reveal that vagal afferent neurons can uptake and transport manganese ions, serving as a surrogate for calcium ions, to the nucleus tractus solitarius (NTS) in the brainstem. In the absence of VNS, we observed significant contrast enhancements of around 19–24% in the NTS ipsilateral to the injection side. Application of VNS for 4 h further promoted nerve activity, leading to greater contrast enhancements of 40–43% in the NTS.DiscussionThese results demonstrate the potential of MEMRI for high-resolution, activity-dependent tracing of vagal afferents, providing a valuable tool for the structural and functional assessment of the vagus nerve and its influence on brain activity