An extensive review of past work on relativistic gravimetry, gradiometry and chronometric geodesy is given. Then, general theoretical tools are presented and applied for the case of a stationary parameterized post-Newtonian metric. The special case of a stationary clock on the surface of the Earth is studied.

Context. Several space missions that will use atomic clocks on board of an Earth-orbiting satellite are planned for the near future, such as the Atomic Clock Ensemble in Space (ACES) or the Space Optical Clock on the International Space Station (I-SOC). The increasing accuracies of the developed clocks and of the links connecting them with ground stations impose corresponding accuracy requirements for theoretical models of electromagnetic signal propagation through the atmosphere of Earth and for the related time and frequency transfer corrections. For example, the fractional frequency accuracy of the optical lattice clock for the I-SOC project is about 10⁻¹⁷. Aims. We develop a relativistic model of one- and two-way time and frequency transfer. In addition to the gravitational effects, it also includes the effects of atmospheric refractivity and atmospheric flows within the relativistic framework. Methods. The model is based on an analytical solution of the equation of motion of a light ray in spacetime filled with a medium: the null geodesic equation of Gordon’s optical metric. Results. Explicit formulas for one- and two-way time and frequency transfer corrections are given using realistic fields of the gravitational potential, the refractive index, and the wind speed, taking nonstationarity and deviations from spherical symmetry into account. Numerical examples are provided that focus on two-way ground-to-satellite transfer, with satellite parameters similar to those of the International Space Station. The effect of the atmospheric refractive index increases as the satellite position moves from zenith to horizon, and it is shown that the effect ranges from 0 ps to 5 ps for two-way time transfer and from 10⁻¹⁷ to 10⁻¹³ for two-way frequency transfer, with a steep increase as the satellite approaches the horizon. The effect of the wind contribution is well below 1 ps for the two-way time transfer for normal atmospheric conditions, but for the two-way frequency transfer, the effect can be significant: A contribution of 10⁻¹⁷ is possible for a horizontal wind field with a velocity magnitude of about 11 m s⁻¹. Conclusions. The atmospheric effects including the effect of wind should be considered in the forthcoming clock-on-satellite experiments such as ACES or I-SOC.

Main text: Supplementary interlaboratory comparison between European low air speed calibration facilities. Two thermal anemometers have been used as transfer standards and circulated between five participants. The transfer standards selection was based on stable behaviour and sensitivity at very low air speeds. The first anemometer was calibrated by the participants at nominal velocities from 0.05 m/s to 1.0 m/s. The second anemometer was calibrated at nominal velocities from 0.15 m/s to 1 m/s. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database https://www.bipm.org/kcdb/. The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Hydrodynamic resistance is a critical parameter in microfluidics, affecting device functionality and performance. However, quantifying hydrodynamic resistance in microfluidics is a challenge due to many influencing factors and the difficulties associated with the precise measurements of low flow rates (< 10 L/min) and pressure drops (< 5 kPa). This article presents a simple experimental test method for assessing hydrodynamic resistance, correlating with theoretical and numerical calculations. The results demonstrate good agreement between benchtop and theoretical data, suggesting a potential standardized method for assessing hydrodynamic resistance in microfluidic devices.

We derive relativistic corrections for one-way and two-way time and frequency transfer over optical fibres neglecting no terms that exceed 1 ps in time and $10^{-18}$ in fractional frequency, and estimate their magnitude in typical fibre links. We also provide estimates of the uncertainties in the evaluation of the relativistic corrections due to imperfect knowledge of parameters like the coordinates of the fibre and stations, Earth rotation, or thermal effects of the fibre index and length. The links between Teddington(UK) and Paris(F) as well as Braunschweig(D) and Paris(F), that are currently under construction, are studied as specific examples.