Phase Difference Research Articles

Self-adjoint Phase Difference Operator and Its Uncertainty Relation with Number Difference Operator

Self-adjoint Phase Difference Operator and Its Uncertainty Relation with Number Difference Operator

The influence of timescales and data injection schemes for reservoir computing using spin-VCSELs

AbstractReservoir computing with photonic systems promises fast and energy efficient computations. Vertical emitting semiconductor lasers with two spin-polarized charge-carrier populations (spin-VCSEL), are good candidates for high-speed reservoir computing. With our work, we highlight the role of the internal dynamic coupling on the prediction performance. We present numerical evidence for the critical impact of different data injection schemes and internal timescales. A central finding is that the internal dynamics of all dynamical degrees of freedom can only be utilized if an appropriate perturbation via the input is chosen as data injection scheme. If the data is encoded via an optical phase difference, the internal spin-polarized carrier dynamics is not addressed but instead a faster data injection rate is possible. We find strong correlations of the prediction performance with the system response time and the underlying delay-induced bifurcation structure, which allows to transfer the results to other physical reservoir computing systems.

Non-Hermitian phase-biased Josephson junctions

We study non-Hermitian Josephson junctions formed by superconductors with a finite phase difference under non-Hermiticity, which naturally appears due to coupling to normal reservoirs. Depending on the structure of non-Hermiticity, captured in terms of retarded self-energies, the low-energy spectrum hosts topologically stable exceptional points either at zero or finite real energies as a function of the superconducting phase difference. Interestingly, the corresponding phase-biased supercurrents may acquire divergent profiles at such exceptional points. This instance is a natural and unique non-Hermitian effect that signals a possible way to enhance the sensitivity of Josephson junctions. Our work opens a way for realizing unique non-Hermitian phenomena due to the interplay between non-Hermitian topology and the Josephson effect. Published by the American Physical Society 2024

Proton bunch monitors for the clinical translation of prompt gamma-ray timing

Objective. Prompt gamma-ray timing is an emerging technology in the field of particle therapy treatment verification. This system measures the arrival times of gamma rays produced in the patient body and uses the cyclotron radio frequency signal as time reference for the beam micro-bunches. Its translation into clinical practice is currently hindered by observed instabilities in the phase relation between the cyclotron radio frequency and the measured arrival time of prompt gamma rays. To counteract this, two proton bunch monitors are presented, integrated into the prompt gamma-ray timing workflow and evaluated.Approach. The two monitors are (a) a diamond detector placed at the beam energy degrader, and (b) a cyclotron monitor signal measuring the phase difference between dee current and voltage. First, the two proton bunch monitors as well as their mutual correlation were characterized. Then, a prompt gamma-ray timing measurement was performed aiming to quantify the present magnitude of the phase instabilities and to evaluate the ability of the proton bunch monitors to correct for these instabilities.Main results. It was found that the two new monitors showed a very high correlation for intermediate proton energies after the first second of irradiation, and that they were able to reduce fluctuations in the detected phase of prompt gamma rays. Furthermore, the amplitude of the phase instabilities had intrinsically decreased from about 700 ps to below 100 ps due to cyclotron upgrades.Significance. The uncertainty of the prompt gamma-ray timing method for proton treatment verification was reduced. For routine clinical application, challenges remain in accounting for detector load effects, temperature drifts and throughput limitations.

DESIGN OF MULIFREQUENCY ELECTRICAL IMPEDANCE TOMOGRAPHY (MfEIT) BASED ON ANALOG DISCOVERY TO DETECT BREAST CANCER

This study aims to design Multifrequency Electrical Impedance Tomography (MfEIT) based on Analog Discovery to detect breast cancer. The MfEIT was built from Analog Discovery which can be used as a signal generator, power supply, voltage control and measuring voltage and phase difference. Other complementary modules are Multiplexer, Instrument amplifier, Voltage Constant Current Source (VCCS), and High Pass Filter (HPF). The MfEIT performance test was carried out on a phantom object made of agar with a certain conductivity that represents breast and cancer tissue. The MfEIT performance testing at a frequency of 10 kHz, 40 kHz, and 80 kHz. The reconstruction from both potential and phase difference data, it shown that are in accordance with the phantom condition, both in number, size and position of anomalies. The reconstruction from the voltage data shown fine at all frequencies, but the phase data produces a good reconstruction image when frequencies was less than 80 kHz.

Long-term Simultaneous Monitoring Observations of SiO and H2O Masers toward the Mira Variable WX Serpentis

We present the results from long-term simultaneous monitoring observations of SiO and H2O masers toward the Mira variable star WX Serpentis. This study has been conducted with 21 m single-dish radio telescopes of the Korean VLBI Network from 2009 June to 2021 June. Five maser lines were considered: SiO v = 1, 2, J = 1−0; SiO v = 1, J = 2−1, 3−2; and H2O 61,6–52,3 transitions, with the SiO maser lines distributed near the stellar velocity and the H2O maser exhibiting an asymmetric line profile with five to six peaked components. Intense H2O maser emissions suddenly appeared in 2019 September, indicating flaring. The intensity variations of SiO and H2O masers are strongly correlated with the optical light curve (OLC) of the central star, with individual phase lags; the phase lag of the H2O maser relative to the OLC is larger than that of the SiO masers. The consequent phase difference between the SiO masers and the H2O maser likely indicates that their formation regions and main driving mechanisms are different from each other. The SiO masers in WX Ser exhibit a dominant single-peak velocity distribution, similar to other Mira variable stars. However, the H2O maser displays distinct morphological features, showing a radial acceleration and preferential intensity dominance at blueshifted velocities. This suggests that the H2O maser clouds of WX Ser are moving outward, thereby developing an asymmetric outflow owing to nonuniform material ejection from the stellar atmosphere. The findings confirm that an initial asymmetric outflow structure emerged during the thermally pulsing asymptotic giant branch phase, specifically in the Mira variable star stage.

What is the difference between shooting technique and pointer kinematics in novice athletes? A study on the sport of Petanque

Petanque, as a sport, requires proficiency in shooting techniques and pointing kinematic movements. Understanding the distinctions between these two skills is crucial for novice athletes to excel in the sport. This study aimed to assess the kinematic motion of children practicing petanque pointing and shooting techniques. Employing a quantitative approach with a comparative design, the study utilized purposive sampling to select 21 male novice petanque athletes. Kinematic analysis using Kinovea Software 0.9.4 was conducted to observe throwing success in the sagittal plane. The kinematic data collected for both pointing and shooting techniques were categorized into four stages: backswing, zero position, release, and advanced throwing position. Results indicated significant differences in the backswing phase, particularly in shoulder extension and ball height (α < 0.05). Several variables differed significantly between the two techniques across various phases. Shooting exhibited higher speed (10.94 ± 13.34 m/s) compared to pointing (5.290 ± 0.44 m/s). At the release stage, variables such as ball height, speed, and release angle differed significantly (α < 0.05), with pointing generally resulting in higher ball height (92.53 ± 9.69 m) but slower speed (6.46 ± 0.43 m/s) compared to shooting (80.19 ± 10.74 m and 16.09 ± 5.18 m/s, respectively). Moreover, pointing involved a wider release angle (42.38 ± 5.85 o) compared to shooting (35.31 ± 7.26 o). Significant differences in body and knee flexion, maximum ball height, and ball speed were observed during the follow-through phase (α < 0.05). Notably, ball speed during pointing was slower (4.90 ± 2.35 m/s) than shooting (13.01 ± 5.36 m/s). The study suggests that specific techniques in shooting and pointing can be tailored to enhance training methods for children, thereby improving their performance outcomes. Deep comprehension of the disparities between these techniques enables novice athletes to develop their skills effectively in petanque. Further research exploring various age groups and genders could provide additional insights into petanque throwing techniques.

Fingerprinting‐Based Indoor Localization in a 3 × 3 Meter Grid Using OFDM Signals at Sub‐6 GHz

ABSTRACTAccurately determining the indoor location of mobile devices has garnered significant interest due to the complex challenges posed by non‐line‐of‐sight (NLOS) propagation and multipath effects. To address this challenge, this paper proposes a new approach to indoor positioning that utilises channel state information (CSI) and machine learning (ML) techniques to improve accuracy. The proposed method extracts the amplitude and phase differences of the subcarriers from the CSI data to create fingerprints. ML algorithms and network architecture are utilised to train the CSI data from two antennas, in the form of phase and amplitude. Experiments conducted in a standard indoor environment demonstrate the effectiveness of the proposed method.

Epsilon negative dynamic coded THz metamaterial beamformer for digital information encryption

Light propagation facilitates digital information encryption by utilizing Epsilon Negative (ENG) metamaterials as a medium. Achieving the desired encryption hinges on synchronizing two pivotal features: the phase difference and the epsilon shifting of the metamaterials. The proposed metamaterial is intricately designed to represent digital bit 1 (states 0 and 1), contingent upon the arrangement of material multilayers within the metamaterial device. Specifically, state 1 is fashioned through a combination of Graphene and Gold, while state 0 is solely represented by Graphene on a metamaterial structure. The developed structure exhibits right hand metamaterial (epsilon of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:+$$\\end{document}7.20) for state 0 and plasma metamaterial (epsilon \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:-$$\\end{document}6.94) for state 1 at 8.6 THz. Notably, the phase difference between 0 and 1 states is around \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:90^\\circ\\:$$\\end{document}. Primarily leveraging the synchronized combination phase and epsilon as the key design parameters for the metamaterial array, the beamforming pattern enables beam steering within the angular range of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:+30^\\circ\\:$$\\end{document} to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:-30^\\circ\\:$$\\end{document}. Secondly, employing a sophisticated material addition strategy involving Gallium Arsenide (GaAs) systematically manipulates the sidelobe in specific directions, thereby providing a mechanism to modulate the sidelobe and concurrently augment spatial resolution. After preparing the metamaterial coded (MC) lens, the source, lens and receiver strategically encrypt the scanning image, employing techniques including Doppler compression and 2D discrete Fourier transform. The proposed MC lens offers applicability like image encryption, security scanning, conveyor systems, hyperlenses and modern cryptography.

Transport-of-intensity phase imaging using commercially available confocal microscope.

Confocal microscopy is an indispensable tool for biologists to observe samples and is useful for fluorescence imaging of living cells with high spatial resolution. Recently, phase information induced by the sample has been attracting attention because of its applicability such as the measurability of physical parameters and wavefront compensation. However, commercially available confocal microscopy has no phase imaging function. We reborn an off-the-shelf confocal microscope as a phase measurement microscope. This is a milestone in changing the perspective of researchers in this field. We would meet the demand of biologists if only they had measured the phase with their handheld microscopes. We proposed phase imaging based on the transport of intensity equation (TIE) in commercially available confocal microscopy. The proposed method requires no modification using a bright field imaging module of a commercially available confocal microscope. The feasibility of the proposed method is confirmed by evaluating the phase difference of a microlens array and living cells of the moss Physcomitrium patens and living mammalian cultured cells. In addition, multi-modal imaging of fluorescence and phase information is demonstrated. TIE-based quantitative phase imaging (QPI) using commercially available confocal microscopy is proposed. We evaluated the feasibility of the proposed method by measuring the microlens array, plant, and mammalian cultured cells. The experimental result indicates that QPI can be realized in commercially available confocal microscopy using the TIE technique. This method will be useful for measuring dry mass, viscosity, and temperature of cells and for correcting phase fluctuation to cancel aberration and scattering caused by an object in the future.

Meta-structure of amorphous-inspired 65.1Co28.2Cr5.3Mo lattices augmented by artificial intelligence

A hatching-distance-controlled lattice of 65.1Co28.2Cr5.3Mo is additively manufactured via laser powder bed fusion with a couple of periodic and aperiodic arrangements of nodes and struts. Thus, the proposed lattice has an amorphous-inspired structure in the short- and long-range orders. From the structural perspective, an artificial intelligence algorithm is used to effectively align lattices with various hatching distances. Then, the metastable lattice combination exhibits an unexpectedly high specific compression strength that is only slightly below that of a solid structure. From the microstructural perspective, the nodes in the newly designed lattice, where the thermal energy from laser irradiation is mainly concentrated, exhibit an equiaxial microstructure. By contrast, the struts exhibit a columnar microstructure, thereby allowing the thermal energy to pass through the narrow ligaments. The heterogeneous phase differences between the nodal and strut areas explain the strength-deteriorating mechanism, owing to the undesirable multi-phase development in the as-built state. However, solid-solution heat treatment to form a homogeneous phase bestows even higher specific compression strength. Furthermore, electrochemical leaching leads to the formation of nanovesicles on the surface of the microporous lattice system, thereby leading to a large surface area. A more advanced valve cage for use in a power plant is designed by using artificial intelligence both to (i) effectively preserve its mechanical stiffness and (ii) actively dissipate the generated stress through the large surface area provided by the nanovesicles.

Underground XLPE coaxial cable length calculation and fault detection based on broadband impedance spectroscopy

Abstract Accurately determining the tested cable's total length is important in cable fault detection and localization. Therefore, an iterative method of relative propagation coefficients based on broadband impedance spectroscopy (BIS) is proposed to solve the actual length of the cable and a phase difference integral transform method for fault detection. First, the overall detection process framework is designed. Then, the cable distribution parameter model and the characteristics of the input impedance spectroscopy are analyzed. The calculation methods for determining the cable length and propagation coefficients are explained, followed by a demonstration of the fault localization process. Finally, the model LCR1000A impedance analyzer is used to measure cable length and actual faults in cables with lengths of 35 m, 100 m, and 500 m. The final fault location error is less than 0.67%, proving that the method can calculate the length of cables and various fault point locations.

Design of polarization-independent multilayer dielectric gratings: a reflection-phase threaded approach

We present a method to design polarization-independent multilayer dielectric gratings. In this method the reflection phases in TE and TM polarizations of the multilayer stack thread surface-relief grating at the top and the multilayer stack at the bottom together, allowing the two parts first to be designed separately and efficiently, and then to be combined to achieve simultaneously high diffraction efficiency and large fabrication tolerance. We find numerically that in general a periodic stack is unable to provide the top-grating-demanded phase difference between TM and TE polarizations; adequate aperiodic layers atop of a periodic stack are needed. The analytic diffraction efficiency formula of a recent work [J. Opt. Soc. Am. A 41, 252 (2024)] is used at various places of the presented optimization algorithm to save computation time. An example grating with rectangular surface-relief profile and another with trapezoidal profile were successfully designed, validating the effectiveness of this design method.

The resonance effect for the CP asymmetry associated with the process $\omega \rightarrow \pi^{+}\pi^{-}\pi^{0}$

Abstract The direct CP asymmetry in the weak decay process of hadrons is commonly attributed to the weak phase of the CKM matrix and the indeterminate strong phase. We propose a method to generate a significant phase difference through the interference between $\rho$ and $\omega$ mesons, taking into account the G-parity allowed decay process of $\omega \rightarrow \pi^{+}\pi^{-}\pi^{0}$ and the G-parity suppressed decay process of $\rho^{0} \rightarrow \pi^{+}\pi^{-}\pi^{0}$ in B meson decays. 
It can lead to a significant CP asymmetry changes in the interference region. 
Besides, we also calculate the integral results of different phase space regions for the four-body decay process. We hope that our work can offer valuable theoretical guidance for future experimental investigations on CP asymmetry in these decays.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

In-depth hemodynamic assessment in acute mild stroke patients with large vessel occlusion or stenosis

ObjectiveAcute treatment in mild stroke patients with acute anterior circulation large vessel occlusion/stenosis (AACLVO/S) had limited evidence. Hemodynamic play an important role in neurological deterioration. We aimed to investigate predictor value of hemodynamic assessment for clinical outcome predicting and guiding individual therapeutic decisions in those patients.MethodsWe retrospectively analyze the stroke database in our stroke center. We recruited patients with mild stroke, defined by National Institutes of Health Stroke Scale (NIHSS) score ≤ 5, caused by AACLVO/S treated with just medical management (MT). They all received cerebral autoregulation (CA) assessments within 72 h after stroke onset. The primary end point was clinical outcome at 90-day after stroke.ResultsLogistic regression analysis showed that bilateral higher baseline phase difference (PD) were independent variables related to favorable 90-day outcome, (OR 0.963, 95% CI 0.936–0.991, p = 0.040; OR 0.943, 95% CI 0.970–0.997; p = 0.008, respectively). The optimal cutoff value of bilateral PD was > 34.97º and > 14.29º respectively.ConclusionCA evaluation can provide hemodynamic status in mild stroke patients with AACLVO/S.

Trade-Off Between Growth Regimes in Chlorella vulgaris: Impact on Carotenoid Production

With the increasing awareness of socio-environmental issues, a global trend has emerged emphasizing the valorization of natural ingredients that promote health and well-being within sustainable production systems, such as microalgae-based carotenoids. Currently, little is understood about the correlation between biomass productivity and carotenoid content, which is a fundamental parameter for facilitating the immediate expansion of microalgae bioprocesses and ensuring the availability and industrial viability of these compounds. In this context, this study aims to investigate the carotenoid profile of Chlorella vulgaris through growth curve experiments conducted under photoautotrophic and heterotrophic regimes. Additionally, a trade-off analysis was performed for the production of carotenoids from microalgae. Carotenoids were quantified using high-performance liquid chromatography coupled with diode array and mass spectrometry detectors (HPLC-PDA-MS/MS). The performance of kinetic phases and energy demands across growth regimes was assessed to provide insights into production trade-offs. The results indicated that a total of 22 different carotenoids were identified in all the extracts. The all-trans-lutein and all-trans-β-carotene were the majority compounds. The total carotenoid content of Chlorella vulgaris revealed significant differences in the kinetic phases of carotenoid production, indicating that carotenoid volumetric production is only viable if the cultures are conducted until the log and stationary phases, based on the function of the biomass volumetric production (weight.volume−1). Therefore, the best trade-off for the process was to provide photoautotrophic growth until the exponential phase (log). Under this condition, the maximum carotenoid and lutein content was 2921.70 µg.L−1, reaching a maximum cell biomass of 1.46 g.L−1. From an environmental/economic point of view, the energy demand was 7.74 kWh.L−1. Finally, the scientific advances achieved in this study provide a holistic view of the influence of the main cultivation methods on the production of microalgae carotenoids, suggesting a viable initial direction for different industrial applications.

A Physics- and Data-Driven Study on the Ground Effect on the Propulsive Performance of Tandem Flapping Wings

In this paper, we present a physics- and data-driven study on the ground effect on the propulsive performance of tandem flapping wings. With numerical simulations, the impact of the ground effect on the aerodynamic force, energy consumption, and efficiency is analyzed, revealing a unique coupling effect between the ground effect and the wing–wing interference. It is found that, for smaller phase differences between the front and rear wings, the thrust is higher, and the boosting effect due to the ground on the rear wing (maximum of 12.33%) is lower than that on a single wing (maximum of 43.83%) For a larger phase difference, a lower thrust is observed, and it is also found that the boosting effect on the rear wing is above that on a single wing. Further, based on the bidirectional gate recurrent units (BiGRUs) time-series neural network, a surrogate model is further developed to predict the unsteady aerodynamic characteristics of tandem flapping wings under the ground effect. The surrogate model exhibits high predictive precision for aerodynamic forces, energy consumption, and efficiency. On the test set, the relative errors of the time-averaged values range from −4% to 2%, while the root mean squared error of the transient values is less than 0.1. Meanwhile, it should be pointed out that the established surrogate model also demonstrates strong generalization capability. The findings contribute to a comprehensive understanding of the ground effect mechanism and provide valuable insights for the aerodynamic design of tandem flapping-wing air vehicles operating near the ground.

An independent continuously scannable dual-beam liquid crystal phased array antenna for Ku-band

ABSTRACT An independent continuously scannable dual-beam liquid crystal (LC) phased array antenna (DBLCPA) operating in the Ku-band is proposed for the first time in this article. Eight right-hand circularly polarised microstrip patch antennas (RHCPMPAs), four 90° hybrid couplers, eight liquid crystal phase shifters (LCPSs), and two power dividers form the proposed array antenna, which utilises the dynamic phase difference between LCPSs and the inherent phase difference of the 90° hybrid coupler to achieve scannable dual-beam driving. The proposed DBLCPA can be conceptualised as two one-dimensional phased array systems. By adjusting the phase difference of each group of LCPSs respectively, the two independent scannable beams can be achieved simultaneously. The S-parameters and far-field pattern of the fabricated antenna array are measured and analysed. The measured S 11 and S 22 of the DBLCPA is below −10 dB and the isolation is better than 10 dB at 11.5–12.5 GHz. The two beams can achieve independent continuous scanning in E-plane, in which the left beam is scannable between 0° and 40°, and the right beam is scannable among 0° to −40°. The measured maximum dual-beam gain of the antenna array is 11.3 dBi, while the axial ratio is less than 3 dB.

Investigation of the aerodynamic performance of the dragonfly-inspired tandem wings considering the coupling between the stroke plane and phase difference

The dragonfly's tandem wings can make full use of the interference of various spatial vortices to obtain efficient flight capability. The complex coupling among multiple motion parameters will have an important influence on the interference between the forewing (FW) and hindwing (HW). In this paper, the aerodynamic performance of the dragonfly-inspired tandem wings is analyzed using the Computational Fluid Dynamics (CFD) method considering the coupling effect of the stroke plane and phase difference. The variation of the force coefficient, vortex structure and aerodynamic efficiency of the tandem wings in forward flight are analyzed, respectively. The results show that the stroke plane angle affects the distribution of the leading edge vortex (LEV) and trailing edge vortex (TEV), which primarily controls the trend of horizontal force variation. The phase difference of tandem wings will change the fluctuation of the horizontal force coefficient curve by affecting the meeting time of the forewing and hindwing. However, with the increase of stroke plane angle, the fluctuation of aerodynamic coefficient caused by phase difference will decrease. The propulsion efficiency(η) and power loading(PL) can be improved through increasing the stroke plane angle and selecting a reasonable phase difference. The conclusion can provide theoretical guidance for the design of the dragonfly-inspired tandem flapping wing aircraft (DTFWA) and the choice of motion parameters.

Bounds on the charge of the graviton using gravitational wave observations

If the graviton possesses a non-zero charge qg , gravitational waves (GW) originating from astrophysical sources would experience an additional time delay due to intergalactic magnetic fields. This would result in a modification of the phase evolution of the observed GW signal similar to the effect induced by a massive graviton. As a result, we can reinterpret the most recent upper limits on the graviton's mass as constraints on the joint mass-charge parameter space, finding |qg |/e < 3 × 10-34 where e represents the charge of an electron. Additionally, we illustrate that a charged graviton would introduce a constant phase difference in the gravitational waves detected by two spatially separated GW detectors due to the Aharonov-Bohm effect. Using the non-observation of such a phase difference for the GW event GW190814, we establish a mass-independent constraint |qg |/e < 2 × 10-26. To the best of our knowledge, our results constitute the first-ever bounds on the charge of the graviton. We also discuss various caveats involved in our measurements and prospects for strengthening these bounds with future GW observations.