We report the first results of the LISA Pathfinder in-flight experiment. The results demonstrate that two free-falling reference test masses, such as those needed for a space-based gravitational wave ...observatory like LISA, can be put in free fall with a relative acceleration noise with a square root of the power spectral density of 5.2 +/- 0.1 fm s(exp -2)/square root of Hz, or (0.54 +/- 0.01) x 10(exp -15) g/square root of Hz, with g the standard gravity, for frequencies between 0.7 and 20 mHz. This value is lower than the LISA Pathfinder requirement by more than a factor 5 and within a factor 1.25 of the requirement for the LISA mission, and is compatible with Brownian noise from viscous damping due to the residual gas surrounding the test masses. Above 60 mHz the acceleration noise is dominated by interferometer displacement readout noise at a level of (34.8 +/- 0.3) fm square root of Hz, about 2 orders of magnitude better than requirements. At f less than or equal to 0.5 mHz we observe a low-frequency tail that stays below 12 fm s(exp -2)/square root of Hz down to 0.1 mHz. This performance would allow for a space-based gravitational wave observatory with a sensitivity close to what was originally foreseen for LISA.
We report a test of the universality of free fall by comparing the gravity acceleration of the ^{87}Rb atoms in m_{F}=+1 versus those in m_{F}=-1, of which the corresponding spin orientations are ...opposite. A Mach-Zehnder-type atom interferometer is exploited to alternately measure the free fall acceleration of the atoms in these two magnetic sublevels, and the resultant Eötvös ratio is η_{S}=(0.2±1.2)×10^{-7}. This also gives an upper limit of 5.4×10^{-6} m^{-2} for a possible gradient field of the spacetime torsion. The interferometer using atoms in m_{F}=±1 is highly sensitive to the magnetic field inhomogeneity. A double differential measurement method is developed to alleviate the inhomogeneity influence, of which the effectiveness is validated by a magnetic field modulating experiment.
We present a new general model for the prediction of the drag coefficient of non-spherical solid particles of regular and irregular shapes falling in gas or liquid valid for sub-critical particle ...Reynolds numbers (i.e. Re<3×105). Results are obtained from experimental measurements on 300 regular and irregular particles in the air and analytical solutions for ellipsoids. Depending on their size, irregular particles are accurately characterized with a 3D laser scanner or SEM micro-CT method. The experiments are carried out in settling columns with height of 0.45 to 3.60m and in a 4m-high vertical wind tunnel. In addition, 881 additional experimental data points are also considered that are compiled from the literature for particles of regular shapes falling in liquids. New correlation is based on the particle Reynolds number and two new shape descriptors defined as a function of particle flatness, elongation and diameter. New shape descriptors are easy-to-measure and can be more easily characterized than sphericity. The new correlation has an average error of ~10%, which is significantly lower than errors associated with existing correlations. Additional aspects of particle sedimentation are also investigated. First, it is found that particles falling in dense liquids, in particular at Re>1000, tend to fall with their maximum projection area perpendicular to their falling direction, whereas in gases their orientation is random. Second, effects of small-scale surface vesicularity and roughness on the drag coefficient of non-spherical particles found to be <10%. Finally, the effect of particle orientation on the drag coefficient is discussed and additional correlations are presented to predict the end members of drag coefficient due to change in the particle orientation.
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•Drag coefficient, CD, of non-spherical particles are measured at Re<3×105.•The effects of particle orientation and density ratio on CD are discussed in detail.•Flatness and elongation were found to be the most influential parameters on CD.•Particle to fluid density ratio can significantly affect CD at Re>103.•New shape descriptors and correlations for predicting CD are presented.
We extend the concept of dynamical decoupling from spin to mechanical degrees of freedom of macroscopic objects, for application in interferometry. In this manner, the superposition of matter waves ...can be made resilient to many important sources of noise when these are driven along suitable paths in space. As a concrete implementation, we present the case of levitated (or free falling) nanodiamonds hosting a color center in a magnetic field gradient. We point out that these interferometers are inherently affected by diamagnetic forces, which restrict the separation of the superposed states to distances that scale with the inverse of the magnetic field gradient. Periodic forcing of the mechanical degree of freedom is shown to overcome this limitation, achieving a linear-in-time growth of the separation distance independent of the magnetic field gradient, while simultaneously protecting the coherence of the superposition from environmental perturbations.
Atom interferometry tests of universality of free fall based on the differential measurement of two different atomic species provide a useful complement to those based on macroscopic masses. However, ...when striving for the highest possible sensitivities, gravity gradients pose a serious challenge. Indeed, the relative initial position and velocity for the two species need to be controlled with extremely high accuracy, which can be rather demanding in practice and whose verification may require rather long integration times. Furthermore, in highly sensitive configurations gravity gradients lead to a drastic loss of contrast. These difficulties can be mitigated by employing wave packets with narrower position and momentum widths, but this is ultimately limited by Heisenberg's uncertainty principle. We present a promising scheme that overcomes these problems by compensating the effects of the gravity gradients and circumvents the fundamental limitations due to Heisenberg's uncertainty principle. Furthermore, it relaxes the experimental requirements on initial colocation by several orders of magnitude.
Abstract
This research is based on the usefulness of mobile phones as a tool for students to learn about uniform rectilinear motion in vertical free fall, based on experimental practice. To evaluate ...whether these mobile devices allow better learning on the subject, a pre-test/post-test design was carried out with 43 students participating in the 9th grade in natural sciences. McNemar and Stuart-Maxwell non-parametric tests were applied. The proposal on the experimental practice gave satisfactory results when comparing the pre-test and post-test, in the analysis of the particular and global form of the answers.
A Bose-Einstein condensate is used as an atomic source for a high precision sensor. A 5×10^{6} atom F=1 spinor condensate of ^{87}Rb is released into free fall for up to 750 ms and probed with a ...T=130 ms Mach-Zehnder atom interferometer based on Bragg transitions. The Bragg interferometer simultaneously addresses the three magnetic states |m_{f}=1,0,-1⟩, facilitating a simultaneous measurement of the acceleration due to gravity with a 1000 run precision of Δg/g=1.45×10^{-9} and the magnetic field gradient to a precision of 120 pT/m.
Abstract The free fall of a sphere was studied by considering air buoyancy and resistance. After selecting the reasonable drag coefficient formula recommended by the literature, partial differential ...formulas on the motion of balls falling in the Leaning Tower of Pisa are solved. The variation process of acceleration, velocity and displacement over time during the falling process of two spheres is obtained. The research results indicate that the kinematics of free fall considering air resistance is different from that neglecting air resistance. Air Resistance must be considered in the free fall of the solid ball after 0.3005 seconds. In the free fall of the leaning tower, air resistance makes the solid ball land at 0.4418 seconds which is earlier than the hollow. The variation of the acceleration of a solid ball with time can be described by a second-order function a =- 0.115t 2 - 0.022t + 9.801 . Velocity does not satisfy the product of acceleration and time but can be described as a polynomial function of the velocity variation with time v = c 1 t 2 + c 2 t + c 3 . About the relationship between displacement and time, for a solid sphere, displacement is proportional to 1.9526 power of time h = 5.4945t 1.9526 , while for a hollow sphere, it cannot be expressed by a function. The relationship between air resistance and velocity during the falling process of an iron ball satisfies a polynomial function F d = c 1 v 2 - c 2 v + c 3 rather than a simple relationship where air resistance is directly proportional to the first or second power of speed, which was used in many papers as a reasonable assumption.
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