Comparison of GOCE-GPS gravity fields derived by different approaches

Several techniques have been proposed to exploit GNSS-derived kinematic orbit information for the determination of long-wavelength gravity field features. These methods include the (i) celestial mechanics approach, (ii) short-arc approach, (iii) point-wise acceleration approach, (iv) averaged acceleration approach, and (v) energy balance approach. Although there is a general consensus that—except for energy balance—these methods theoretically provide equivalent results, real data gravity field solutions from kinematic orbit analysis have never been evaluated against each other within a consistent data processing environment. This contribution strives to close this gap. Target consistency criteria for our study are the input data sets, period of investigation, spherical harmonic resolution, a priori gravity field information, etc. We compare GOCE gravity field estimates based on the aforementioned approaches as computed at the Graz University of Technology, the University of Bern, the University of Stuttgart/Austrian Academy of Sciences, and by RHEA Systems for the European Space Agency. The involved research groups complied with most of the consistency criterions. Deviations only occur where technical unfeasibility exists. Performance measures include formal errors, differences with respect to a state-of-the-art GRACE gravity field, (cumulative) geoid height differences, and SLR residuals from precise orbit determination of geodetic satellites. We found that for the approaches (i) to (iv), the cumulative geoid height differences at spherical harmonic degree 100 differ by only ≈10 % ; in the absence of the polar data gap, SLR residuals agree by ≈96 % . From our investigations, we conclude that real data analysis results are in agreement with the theoretical considerations concerning the (relative) performance of the different approaches.

Development of a balanced experimental–computational approach to understanding the mechanics of proximal femur fractures

The majority of people who sustain hip fractures after a fall to the side would not have been identified using current screening techniques such as areal bone mineral density. Identifying them, however, is essential so that appropriate pharmacological or lifestyle interventions can be implemented. A protocol, demonstrated on a single specimen, is introduced, comprising the following components; in vitro biofidelic drop tower testing of a proximal femur; high-speed image analysis through digital image correlation; detailed accounting of the energy present during the drop tower test; organ level finite element simulations of the drop tower test; micro level finite element simulations of critical volumes of interest in the trabecular bone. Fracture in the femoral specimen initiated in the superior part of the neck. Measured fracture load was 3760 N, compared to 4871 N predicted based on the finite element analysis. Digital image correlation showed compressive surface strains as high as 7.1% prior to fracture. Voxel level results were consistent with high-speed video data and helped identify hidden local structural weaknesses. We found using a drop tower test protocol that a femoral neck fracture can be created with a fall velocity and energy representative of a sideways fall from standing. Additionally, we found that the nested explicit finite element method used allowed us to identify local structural weaknesses associated with femur fracture initiation.

The AEgIS experiment at CERN for the measurement of antihydrogen gravity acceleration

The Antihydrogen Experiment: Gravity, Interferometry, Spectroscopy (AEgIS) experiment is conducted by an international collaboration based at CERN whose aim is to perform the first direct measurement of the gravitational acceleration of antihydrogen in the local field of the Earth, with Δg/g = 1% precision as a first achievement. The idea is to produce cold (100 mK) antihydrogen ( ¯H) through a pulsed charge exchange reaction by overlapping clouds of antiprotons, from the Antiproton Decelerator (AD) and positronium atoms inside a Penning trap. The antihydrogen has to be produced in an excited Rydberg state to be subsequently accelerated to form a beam. The deflection of the antihydrogen beam can then be measured by using a moir´e deflectometer coupled to a position sensitive detector to register the impact point of the anti-atoms through the vertex reconstruction of their annihilation products. After being approved in late 2008, AEgIS started taking data in a commissioning phase in 2012. This paper presents an outline of the experiment with a brief overview of its physics motivation and of the state-of-the-art of the g measurement on antimatter. Particular attention is given to the current status of the emulsion-based position detector needed to measure the ¯H sag in AEgIS.

Supersymmetric quantum mechanics on the lattice: II. Exact results

Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper – the second in a series of three – we present such an investigation for N=2 supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.

Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms

In the fermion loop formulation the contributions to the partition function naturally separate into topological equivalence classes with a definite sign. This separation forms the basis for an efficient fermion simulation algorithm using a fluctuating open fermion string. It guarantees sufficient tunnelling between the topological sectors, and hence provides a solution to the fermion sign problem affecting systems with broken supersymmetry. Moreover, the algorithm shows no critical slowing down even in the massless limit and can hence handle the massless Goldstino mode emerging in the supersymmetry broken phase. In this paper – the third in a series of three – we present the details of the simulation algorithm and demonstrate its efficiency by means of a few examples.

GRAIL gravity field determination using the Celestial Mechanics Approach

The NASA mission GRAIL (Gravity Recovery and Interior Laboratory) inherited its concept from the GRACE (Gravity Recovery and Climate Experiment) mission to determine the gravity field of the Moon. We present lunar gravity fields based on the data of GRAIL’s primary mission phase. Gravity field recovery is realized in the framework of the Celestial Mechanics Approach, using a development version of the Bernese GNSS Software along with Ka-band range-rate data series as observations and the GNI1B positions provided by NASA JPL as pseudo-observations. By comparing our results with the official level-2 GRAIL gravity field models we show that the lunar gravity field can be recovered with a high quality by adapting the Celestial Mechanics Approach, even when using pre-GRAIL gravity field models as a priori fields and when replacing sophisticated models of non-gravitational accelerations by appropriately spaced pseudo-stochastic pulses (i.e., instantaneous velocity changes). We present and evaluate two lunar gravity field solutions up to degree and order 200 – AIUB-GRL200A and AIUB-GRL200B. While the first solution uses no gravity field information beyond degree 200, the second is obtained by using the official GRAIL field GRGM900C up to degree and order 660 as a priori information. This reduces the omission errors and demonstrates the potential quality of our solution if we resolved the gravity field to higher degree.

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

A New Approach for Automatic Removal of Movement Artifacts in Near-Infrared Spectroscopy Time Series by Means of Acceleration Data

Abstract: Near-infrared spectroscopy (NIRS) enables the non-invasive measurement of changes in hemodynamics and oxygenation in tissue. Changes in light-coupling due to movement of the subject can cause movement artifacts (MAs) in the recorded signals. Several methods have been developed so far that facilitate the detection and reduction of MAs in the data. However, due to fixed parameter values (e.g., global threshold) none of these methods are perfectly suitable for long-term (i.e., hours) recordings or were not time-effective when applied to large datasets. We aimed to overcome these limitations by automation, i.e., data adaptive thresholding specifically designed for long-term measurements, and by introducing a stable long-term signal reconstruction. Our new technique (“acceleration-based movement artifact reduction algorithm”, AMARA) is based on combining two methods: the “movement artifact reduction algorithm” (MARA, Scholkmann et al. Phys. Meas. 2010, 31, 649–662), and the “accelerometer-based motion artifact removal” (ABAMAR, Virtanen et al. J. Biomed. Opt. 2011, 16, 087005). We describe AMARA in detail and report about successful validation of the algorithm using empirical NIRS data, measured over the prefrontal cortex in adolescents during sleep. In addition, we compared the performance of AMARA to that of MARA and ABAMAR based on validation data.