Time Delay Measurements Research Articles

Observational tests of asymptotically flat R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {R}}}^{2}$$\\end{document} spacetimes

A novel class of Buchdahl-inspired metrics with closed-form expressions was recently obtained based on Buchdahl’s seminal work on searching for static, spherically symmetric metrics in R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {R}}}^{2}$$\\end{document} gravity in vacuo. Buchdahl-inspired spacetimes provide an interesting framework for testing predictions of R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {R}}}^{2}$$\\end{document} gravity models against observations. To test these Buchdahl-inspired spacetimes, we consider observational constraints imposed on the deviation parameter, which characterizes the deviation of the asymptotically flat Buchdahl-inspired metric from the Schwarzschild spacetime. We utilize several recent solar system experiments and observations of the S2 star in the galactic center and the black hole shadow. By calculating the effects of Buchdahl-inspired spacetimes on astronomical observations both within and outside of the solar system, including the deflection angle of light by the Sun, gravitational time delay, perihelion advance, shadow, and geodetic precession, we determine observational constraints on the corresponding deviation parameters by comparing theoretical predictions with the most recent observations. Among these constraints, we find that the tightest one comes from the Cassini mission’s measurement of gravitational time delay.

Time delay and nonadiabatic calibration of the attoclock. Multiphoton process versus tunneling in strong field interaction

The measurement of the tunneling time delay in attosecond experiments, termed attoclock, sparked a heated debate about tunneling time and the role of time in quantum mechanics. We show a model that explains the experimental result of the attoclock in the nonadiabatic field calibration, where we find good agreement with the experimental data of Hofmann et al. (J. Mod. Opt. 66, 1052, 2019). We confirm our result with the numerical integration of the time-dependent Schrödinger equation. We also found that at a field strength F≤Fa (Fa is the atomic field strength), the model always predicts a time delay with respect to the quantum (lower) limit τa at F=Fa. For an adiabatic tunneling, the saturation at the limit (F=Fa) explains the well-known Hartman effect or Hartman paradox.

Ultrafast and High-Precision Time Delay Measurement Based on Complementary Frequency-Swept Light and Frequency-Shifted Dechirping

Ultrafast and High-Precision Time Delay Measurement Based on Complementary Frequency-Swept Light and Frequency-Shifted Dechirping

Guided Lamb Wave Array Time-Delay-Based MUSIC Algorithm for Impact Imaging.

Composite materials, valued in aerospace for their stiffness, strength and lightness, require impact monitoring for structural health, especially against low-velocity impacts. The MUSIC algorithm, known for efficient directional scanning and easy sensor deployment, is gaining prominence in this area. However, in practical engineering applications, the broadband characteristics of impact response signals and the time delay errors in array elements' signal reception lead to inconsistencies between the steering vector and the actual signal subspace, affecting the precision of the MUSIC impact localization method. Furthermore, the anisotropy of composite materials results in time delay differences between array elements in different directions. If the MUSIC algorithm uses a fixed velocity value, this also introduces time delay errors, further reducing the accuracy of localization. Addressing these challenges, this paper proposes an innovative MUSIC algorithm for impact imaging using a guided Lamb wave array, with an emphasis on time delay management. This approach focuses on the extraction of high-energy, single-frequency components from impact response signals, ensuring accurate time delay measurement across array elements and enhancing noise resistance. It also calculates the average velocity of single-frequency components in varying directions for an initial impact angle estimation. This estimated angle then guides the selection of a specific single-frequency velocity, culminating in precise impact position localization. The experimental evaluation, employing equidistantly spaced array elements to capture impact response signals, assessed the effectiveness of the proposed method in accurately determining array time delays. Furthermore, impact localization tests on reinforced composite structures were conducted, with the results indicating high precision in pinpointing impact locations.

Modulation Transfer between Microwave Beams: Asymptotic Evaluation of Integrals with Pole Singularities near a First-Order Saddle Point

Experimental results of delay-time measurements in the transfer of modulation between microwave beams, as reported in previous articles, were interpreted on a competition (interference) between two waves, one of which is modulated and the other is a continuous wave (c.w.). The creation of one of these waves was attributed to a saddle-point contribution, while the other was attributed to pole singularities. In this paper, such an assumption is justified by a quantitative field-amplitude analysis in order to make the modeling plausible. In particular, two ways of calculating field amplitudes are considered. These lead to results that are quantitatively markedly different, although qualitatively similar.

Light Curves of Lensed Components and Time Delay Measurements in the Binary Gravtationally Lensed Quasars SDSS J2124$$+$$1632 and SDSS J0806$$+$$2006

Light Curves of Lensed Components and Time Delay Measurements in the Binary Gravtationally Lensed Quasars SDSS J2124$$+$$1632 and SDSS J0806$$+$$2006

A Reverberation Mapping Study of a Highly Variable Active Galactic Nucleus 6dFGS gJ022550.0-060145

We use LCOGT observations (MJD 59434−59600) with a total exposure time of ≃50 hr and a median cadence of 0.5 day to measure the interband time delays (with respect to u) in the g, r, and i continua of a highly variable active galactic nucleus (AGN), 6dFGS gJ022550.0-060145. We also calculate the expected time delays of the X-ray reprocessing of a static Shakura–Sunyaev disk according to the source's luminosity and virial black hole mass; the two parameters are measured from the optical spectrum of our spectroscopic observation via the Lijiang 2.4 m telescope. It is found that the ratio of the measured time delays to the predicted ones is 2.6−1.3+1.3 . With optical light curves (MJD 53650–59880) from our new LCOGT and archival Zwicky Transient Facility, Pan-STARRS, Catalina Sky Survey, and ATLAS observations, and Wide-field Infrared Survey Explorer (WISE) data (MJD 55214−59055), we also measured time delays between WISE W1/W2 and the optical emission. W1 and W2 have time delays (with respect to V), 9.6−1.6+2.9×102 days and 1.18−0.10+0.13×103 days in the rest frame, respectively; hence, the dusty torus of 6dFGS gJ022550.0-060145 should be compact. The time delays of the W1 and W2 bands are higher than the dusty torus size–luminosity relationship of Lyu et al. By comparing the infrared and optical variability amplitude, we find that the dust-covering factors of the W1 and W2 emission regions are 0.7 and 0.6, respectively. Future broad emission-line reverberation mapping of this target and the results of this work enable us to determine the sizes of the AGN main components simultaneously.

Time Delay Study of Ultrasonic Gas Flowmeters Based on VMD-Hilbert Spectrum and Cross-Correlation.

The accuracy of ultrasonic flowmeter time delay measurement is directly affected by the processing method of the ultrasonic echo signal. This paper proposes a method for estimating the time delay of the ultrasonic gas flowmeter based on the Variational Mode Decomposition (VMD)-Hilbert Spectrum and Cross-Correlation (CC). The method improves the accuracy of the ultrasonic gas flowmeter by enhancing the quality of the echo signal. To denoise forward and reverse ultrasonic echo signals collected at various wind speeds, a Butterworth filter is initially used. The ultrasonic echo signals are then analyzed by Empirical Mode De-composition (EMD) and VMD analysis to obtain the Intrinsic Mode Function (IMF) containing distinct center frequencies, respectively. The Hilbert spectrum time-frequency diagram is used to evaluate the results of the VMD and EMD decompositions. It is found that the IMF decomposed by VMD has a better filtering performance and better anti-interference performance. Therefore, the IMF with a better effect is selected for signal reconstruction. The ultrasonic time delay is then calculated using the Cross-Correlation algorithm. The self-developed ultrasonic gas flowmeter was tested on the experimental platform of the gas flow standard devices using this signal processing method. The results show a maximum indication error of 0.84% within the flow range of 60-606 m3/h, with a repeatability of no more than 0.29%. These results meet the 1-level accuracy requirements as outlined in the national ultrasonic flowmeters calibration regulation JJG1030-2007.

Reevaluating LSST’s Capability for Time Delay Measurements in Quasar Accretion Disks

The Legacy Survey of Space and Time at the Vera C. Rubin Observatory is poised to observe thousands of quasars using the Deep Drilling Fields (DDF) across six broadband filters over a decade. Understanding quasar accretion disk (AD) time delays is pivotal for probing the physics of these distant objects. Pozo Nuñez et al. has recently demonstrated the feasibility of recovering AD time delays with accuracies ranging from 5% to 20%, depending on the quasar’s redshift and time sampling intervals. Here we reassess the potential for measuring AD time delays under the current DDF observing cadence, which is placeholder until a final cadence is decided. We find that contrary to prior expectations, achieving reliable AD time delay measurements for quasars is significantly more challenging, if not unfeasible, due to the limitations imposed by the current observational strategies.

Enhanced ignition and combustion performance of boron-based energetic materials through surface modification and titanium dioxides coating

The present study focuses on the removal of ineffective hydroxyl surface (B–OH) of the shell of pristine boron (B) particles, followed by its modification using a low-cost, eco-friendly, and non-hazardous ethylene glycol (EG). Subsequently, very small-sized titanium dioxide (TiO2) particles are coated onto the boron surface by adding titanium tetraisopropoxide (TTIP) precursors at room temperature. Characterization techniques were employed to investigate the structure and morphology of these materials. FTIR, XPS, and TEM analysis reveal that EG effectively removes ineffective boron hydroxyl surfaces and modifies the surface through passivation by its surface functionalities. Furthermore, EG assists in the coating very small-sized TiO2 particles on the boron surface. Thermal stability tests show that the modified boron surface and TiO2-coated boron surface exhibit earlier oxidation of the core boron compared to pristine boron. This enhanced capability for earlier oxidation of core boron was further investigated in the shock tube and bomb calorimeter for measurement of ignition delay time and heat of combustion. The findings demonstrate that room temperature synthesized TiO2-coated B particles (ignition delay time of ∼181 μs and heat of combustion of ∼17.3 kJ/g) outperform pristine B particles (ignition delay time of ∼284 μs and heat of combustion of ∼13.2 kJ/g). This improvement is attributed to the removal of ineffective boron hydroxyl surfaces, surface modification, uniform coating with very small TiO2 particles, the catalytic effect of TiO2 on oxygen diffusion, and effective oxidation of core boron. This study suggests that efficient energetic material can be achieved at room temperature with no potential harm to the environment.

Ignition Delay and Reaction Time Measurements of Hydrogen–Air Mixtures at High Temperatures

Induction and reaction times of hydrogen–air mixtures (ϕ = 0.5–2) have been measured behind reflected shock waves at temperatures of 1000–1600 K, pressures of 0.1, 0.3, 0.6 MPa in the domain of the extended second explosion limit. The measurements were performed in the shock tube with a completely transparent test section of 0.5 m long, which provides pressure, ion current, OH and high-speed chemiluminescence observations. The experimental induction time plots demonstrate a clear increasing of the global activation energy from high- to low temperature post-shock conditions. This trend is strongly pronounced at higher post-shock pressures. For a high-temperature range of T > 1200 K, induction time measurements show an activation energy for the global reaction rate of hydrogen oxidation of 64–83 kJ/mole. Detected reaction times exhibit a big scatter and a weak temperature dependence. The minimum reaction time value was nearly 2 µs. Obtained induction time data were compared with calculations carried out in accordance with the known kinetic mechanisms. For current and former shock-tube experiments within a pressure range of 0.1–2 MPa, critical temperatures required for strong (1000–1100 K), transient and weak auto-ignition modes behind reflected shock waves were identified by means of the pressure and ion-probe measurements in stoichiometric hydrogen-air mixture. The transfer from the strong volumetric self-ignition near the reflecting wall to the hot spot ignition (transient) was established and visualized below <1200 K with a post-shock temperature decreasing.

Augmenting the power of time-delay cosmography in lens galaxy clusters by probing their member galaxies

We present a novel approach to measuring the expansion rate and the geometry of the Universe, which combines time-delay cosmography in lens galaxy clusters with pure samples of ‘cosmic chronometers’ by probing the member galaxies. The former makes use of the measured time delays between the multiple images of time-varying sources strongly lensed by galaxy clusters, while the latter exploits the most massive and passive cluster member galaxies to measure the differential time evolution of the Universe. We applied two different statistical techniques, adopting realistic errors on the measured quantities, to assess the accuracy and the gain in precision on the values of the cosmological parameters. We demonstrate that the proposed combined method allows for a robust and accurate measurement of the value of the Hubble constant. In addition, this provides valuable information on the other cosmological parameters thanks to the complementarity between the two different probes in breaking parameter degeneracies. Finally, we showcased the immediate observational feasibility of the proposed joint method by taking advantage of the existing high-quality spectro-photometric data for several lens galaxy clusters.

Chemical Kinetic Analysis of High-Pressure Hydrogen Ignition and Combustion toward Green Aviation

In the framework of the “Multidisciplinary Optimization and Regulations for Low-boom and Environmentally Sustainable Supersonic aviation” project, pursued by a consortium of European government and academic institutions, coordinated by Politecnico di Torino under the European Commission Horizon 2020 financial support, the Italian Aerospace Research Centre is computationally investigating the high-pressure hydrogen/air kinetic combustion in the operative conditions typically encountered in supersonic aeronautic ramjet engines. This task is being carried out starting from the zero-dimensional and one-dimensional chemical kinetic assessment of the complex and strongly pressure-sensitive ignition behavior and flame propagation characteristics of hydrogen combustion through the validation against experimental shock tube and laminar flame speed measurements. The 0D results indicate that the kinetic mechanism by Politecnico di Milano and the scheme formulated by Kéromnès et al. provide the best matching with the experimental ignition delay time measurements carried out in high-pressure shock tube strongly argon-diluted reaction conditions. Otherwise, the best behavior in terms of laminar flame propagation is achieved by the Mueller scheme, while the other investigated kinetic mechanisms fail to predict the flame speeds at elevated pressures. This confirms the non-linear and intensive pressure-sensitive behavior of hydrogen combustion especially in the critical high-pressure and low-temperature region which is hard to be described by a single all-encompassing chemical model.

Determining cosmological-model-independent H0 and post-Newtonian parameter with time-delay lenses and supernovae

ABSTRACT Strong gravitational lensing provides a natural opportunity to test general relativity (GR). We propose a model-independent method for simultaneous constraining on Hubble constant (H0) and post-Newtonian parameter (γPPN) using strong lensing systems and observational Type Ia supernovae. The time-delay measurements from strong lensing can directly determine the Hubble constant, and the lens distance inferred from the spectroscopic measurement of the stellar kinematics of the deflector galaxy can help us to constrain the post-Newtonian parameter. We seek the Pantheon data set and reconstruct unanchored distances using Gaussian process regression to achieve the cosmological-model-independent GR testing instead of assuming a specific model, which can reduce possible bias on GR testing and measurement of Hubble constant. Combining the reconstructed unanchored distances and the four H0LiCOW lens data sets, our results are $H_0=72.9^{+2.0}_{-2.3} \, \mathrm{km \, s^{-1} \, Mpc^{-1}}$ and $\gamma _{\rm {PPN}}=0.89^{+0.17}_{-0.15}$. All the lenses show that there is no obvious evidence to support GR deviation within observational uncertainties. In the subsequent analysis, we consider a ratio of distance ${D_{\Delta t}}/{D^{^{\prime }}_{\mathrm{ d}}}$ method to further avoid the influence of H0 on GR testing. The results show that, except J1206 within the ∼1.2σ observational uncertainty, the remaining three lenses support that GR holds within the 1σ observational uncertainties.

Allylic-alkylic C-C bond decomposition in 1-butene and 1-pentene

1-Butene and 1-pentene are critical intermediates in the oxidation and pyrolysis of larger alkanes and alcohols. Their thermal decomposition plays important role in fuel consumption under combustion conditions, yet seldom investigated. In this work, we studied the title reactions behind reflected shock waves over temperatures of 1178 – 1416 K and pressures near 1.2 bar. We monitored absorbance time-history of the product allyl radicals by employing a sensitive UV diagnostic scheme at a wavelength of 220 nm. We extracted the target rate coefficients by simulating the measured absorbance profiles with detailed kinetic models. Our determined rate coefficients of 1-butene (k1) and 1-pentene (k2) thermal decomposition may be expressed as (unit s−1):k1(1C4H8→CH3+aC3H5)=1.52×1016e(−37937T)k2(1C5H10→C2H5+aC3H5)=3.84×1014e(−31434T)We believe the current work provides the first direct measurements of these reactions. Our 1-butene thermal decomposition rate coefficients exhibit a positive Arrhenius temperature dependence. Around 1350 K and 1 bar, 1-butene decomposition proceeds ∼ 4.5 times faster than n-butane, and ∼ 66 times faster than 1,3-butadiene. Our work extends the literature measurements of 1-butene decomposition to temperatures higher than 1310 K. Literature measurements above 1000 K underestimate our rate coefficients by ∼ 20 %. Additionally, our 1-butene rate coefficients provide an analogy to bio-derived molecules containing similar allylic-alkylic C-C bonds, such as methyl-3-hexenoate. For 1-pentene thermal decomposition, we observed the product allyl radicals starting from 1178 K compared to 1213 K in 1-butene measurements. Thus 1-pentene decomposition proceeds 2 – 6 times faster than 1-butene, and shows a gentler Arrhenius temperature dependence. The current literature models exhibit a range of rate values that vary by an order of magnitude, resulting in noticeable discrepancies. Our study addresses this issue by providing much-needed clarity and precision. Furthermore, we implemented our rate coefficients in literature kinetic models and evaluated their influence on ignition delay time (IDT) and speciation measurements. The results indicate that our rate coefficients generally improved the model performance.

Low-temperature ignition and oxidation mechanisms of tetrahydropyran

Cyclic ethers are relevant as next-generation biofuels and are also combustion intermediates that follow directly from unimolecular decomposition of hydroperoxyalkyl radicals. Accordingly, cyclic ether reactions are crucial to understanding low-temperature oxidation for advanced compression-ignition applications in combustion where peroxy radials are central to degenerate chain-branching pathways. Reaction mechanisms relevant to low-temperature ignition of cyclic ethers contain intrinsic complexities due to competing reactions of carbon-centered radicals formed in the initiation step undergoing either ring-opening or reactions with O2. To gain insight into mechanisms describing tetrahydropyran combustion, ignition delay time and speciation measurements were conducted. The present work integrates measurements below 1000 K of ignition delay times and species profiles in rapid compression machine experiments from 5 – 20 bar, spanning several equivalence ratios, with jet-stirred reactor experiments at 1 bar and stoichiometric conditions. The experiments are complemented with the development of the first chemical kinetics mechanism for tetrahydropyran that includes peroxy radical reactions, including O2-addition to tetrahydropyranyl (Ṙ), HOȮ-elimination from tetrahydropyranylperoxy (ROȮ) and hydroperoxytetrahydropyranyl (Q˙OOH), bi-cyclic ether formation, β-scission of Q˙OOH, and ketohydroperoxide formation.Negative-temperature coefficient (NTC) behavior is exhibited in the experiments and is reflected in the model predictions, which were within experimental uncertainty for several conditions. Disparities between the model predictions and experiments were analyzed via sensitivity analysis to identify contributing factors from elementary reactions. The analyses examine the role of ring-opening products of tetrahydropyranyl and hydroperoxytetrahydropyranyl isomers to identify reaction mechanisms that may contribute to model uncertainties. The detection of 66 species in the JSR experiments indicates that tetrahydropyran undergoes complex reaction networks, which includes interconnected reactions of aldehyde radicals and alkyl radicals. Primary radicals pentanal-5-yl and butanal-4-yl are derived from ring-opening reactions of tetrahydropyran-1-yl and undergo subsequent decarbonylation to form alkyl radicals (1-butyl and 1-propyl) that undergo reaction with O2 and may contribute to chain-branching, in addition to pathways involving tetrahydropyran-derived ketohydroperoxides.

Notice of Violation of IEEE Publication Principles:Consensus-Based Distributed Anti-Disturbance Control of DC Microgrids Over Fading Channels

This paper develops a novel consensus-based distributed anti-disturbance control scheme that can achieve current sharing of distributed generations (DG) and voltage restoration of DC bus in mean square subject to multiplicative measurement noises and communication delays over fading networks. Since the cyber channels are exposed to inherent communication delays, the measurement information exchange with noise interferences among multiple and cooperative DGs may be disturbed in fading communication networks, where fading may either be due to noises, delays, and shadowing from obstacles affecting the wave propagation. As a result, fading makes every DG receives incomplete/imprecise information from its neighbors. To dispel the adverse influences of measurement noises and time delays over fading networks, a washout filter-based distributed anti-disturbance control algorithm is developed for DC microgrids, in which only the current state variable is exchanged among DGs with the local decentralized voltage controller. By introducing stochastic theory and Lyapunov stability function, the criteria for the stability analysis and delays boundedness considering noise interferences is derived to ensure the stability operation of the whole closed-loop DC network. The obtained results show the effectiveness of the proposed strategy by a tested DC microgrid in OPAL-RT real-time simulator.

A Model-independent Method to Determine H 0 Using Time-delay Lensing, Quasars, and Type Ia Supernovae

Absolute distances from strong lensing can anchor Type Ia Supernovae (SNe Ia) at cosmological distances giving a model-independent inference of the Hubble constant (H 0). Future observations could provide strong lensing time-delay distances with source redshifts up to z ≃ 4, which are much higher than the maximum redshift of SNe Ia observed so far. In order to make full use of time-delay distances measured at higher redshifts, we use quasars as a complementary cosmic probe to measure cosmological distances at redshifts beyond those of SNe Ia and provide a model-independent method to determine H 0. In this work, we demonstrate a model-independent, joint constraint of SNe Ia, quasars, and time-delay distances from strong lensed quasars. We first generate mock data sets of SNe Ia, quasar, and time-delay distances based on a fiducial cosmological model. Then, we calibrate the quasar parameters model independently using Gaussian process (GP) regression with mock SNe Ia data. Finally, we determine the value of H 0 model-independently using GP regression from mock quasars and time-delay distances from strong lensing systems. As a comparison, we also show the H 0 results obtained from mock SNe Ia in combination with time-delay lensing systems whose redshifts overlap with SNe Ia. Our results show that quasars at higher redshifts show great potential to extend the redshift coverage of SNe Ia and thus enable the full use of strong lens time-delay distance measurements from ongoing cosmic surveys and improve the accuracy of the estimation of H 0 from 2.1% to 1.3% when the uncertainties of the time-delay distances are 5% of the distance values.

Multistatic Target Localization in Absence of Transmitter Position Using Differential Time Delay Measurements

Multistatic Target Localization in Absence of Transmitter Position Using Differential Time Delay Measurements

Distributed phase-matching measurement for dynamic strain and temperature sensing based on stimulated Brillouin scattering enhanced four-wave mixing

A Brillouin dynamic grating (BDG) can be used for distributed birefringence measurement in optical fibers, offering high sensitivity and spatial resolution for sensing applications. However, it is quite a challenge to simultaneously achieve dynamic measurements with both high accuracy and high spatial resolution. In this work, we propose a sensing mechanism to achieve distributed phase-matching measurement using a chirped pulse as a probe signal. In BDG reflection, the peak reflection corresponds to the highest four-wave mixing (FWM) conversion efficiency, and it requires the Brillouin frequency in the fast and slow axes to be equal, which is called the phase-matching condition. This condition changes at different fiber positions, which requires a range of frequency injection for the probe wave. The proposed method uses a chirped pulse as a probe wave to cover this frequency range associated with distributed birefringence inhomogeneity. This allows us to detect distributed phase matching for birefringence changes that are introduced by temperature and strain variations. Thanks to the single shot and direct time delay measurement capability, the acquisition rate in our system is only limited by the fiber length. Notably, unlike conventional BDG spectrum recovery-based systems, the spatial resolution here is determined by both the frequency chirping rate of the probe pulse and the birefringence profile of the fiber. In the experiments, an acquisition rate of 1 kHz (up to fiber length limits) and a spatial resolution of 10 cm using a 20 ns probe pulse width are achieved. The minimum detectable temperature and strain variation are 5.6 mK and 0.37 με along a 2 km long polarization-maintaining fiber (PMF).