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Jürgen Müller

Publications and source records attributed to Jürgen Müller.

At least 37 records · Page 2Linked to original sources
arXiv2023

The Graph Database Interface: Scaling Online Transactional and Analytical Graph Workloads to Hundreds of Thousands of Cores

Graph databases (GDBs) are crucial in academic and industry applications. The key challenges in developing GDBs are achieving high performance, scalability, programmability, and portability. To tackle these challenges, we harness established practices from the HPC landscape to build a system that outperforms all past GDBs presented in the literature by orders of magnitude, for both OLTP and OLAP workloads. For this, we first identify and crystallize performance-critical building blocks in the GDB design, and abstract them into a portable and programmable API specification, called the Graph Database Interface (GDI), inspired by the best practices of MPI. We then use GDI to design a GDB for distributed-memory RDMA architectures. Our implementation harnesses one-sided RDMA communication and collective operations, and it offers architecture-independent theoretical performance guarantees. The resulting design achieves extreme scales of more than a hundred thousand cores. Our work will facilitate the development of next-generation extreme-scale graph databases.

cs.DB↗
arXiv2022

Equivalence of Active and Passive Gravitational Mass Tested with Lunar Laser Ranging

LLR measures the distance between observatories on Earth and retro-reflectors on Moon since 1969. In this paper, we study the possible violation of the equality of passive and active gravitational mass ($m_{a}/m_{p}$), for Aluminium (Al) and Iron (Fe), using LLR data. Our new limit of $3.9\cdot10^{-14}$ is about 100 times better than that of Bartlett and Van Buren [1986] reflecting the benefit of the many years of LLR data.

gr-qc↗
arXiv2022

A Fourier integral formula for logarithmic energy

A formula which expresses logarithmic energy of Borel measures on R^n in terms of the Fourier transforms of the measures is established and some applications are given. In addition, using similar techniques a (known) formula for Riesz energy is reinvented.

math.CA↗
arXiv2022

GENESIS: Co-location of Geodetic Techniques in Space

Improving and homogenizing time and space reference systems on Earth and, more directly, realizing the Terrestrial Reference Frame (TRF) with an accuracy of 1mm and a long-term stability of 0.1mm/year are relevant for many scientific and societal endeavors. The knowledge of the TRF is fundamental for Earth and navigation sciences. For instance, quantifying sea level change strongly depends on an accurate determination of the geocenter motion but also of the positions of continental and island reference stations, as well as the ground stations of tracking networks. Also, numerous applications in geophysics require absolute millimeter precision from the reference frame, as for example monitoring tectonic motion or crustal deformation for predicting natural hazards. The TRF accuracy to be achieved represents the consensus of various authorities which has enunciated geodesy requirements for Earth sciences. Today we are still far from these ambitious accuracy and stability goals for the realization of the TRF. However, a combination and co-location of all four space geodetic techniques on one satellite platform can significantly contribute to achieving these goals. This is the purpose of the GENESIS mission, proposed as a component of the FutureNAV program of the European Space Agency. The GENESIS platform will be a dynamic space geodetic observatory carrying all the geodetic instruments referenced to one another through carefully calibrated space ties. The co-location of the techniques in space will solve the inconsistencies and biases between the different geodetic techniques in order to reach the TRF accuracy and stability goals endorsed by the various international authorities and the scientific community. The purpose of this white paper is to review the state-of-the-art and explain the benefits of the GENESIS mission in Earth sciences, navigation sciences and metrology.

physics.ins-det↗
arXiv2022

Mixing operators with prescribed unimodular eigenvectors

For arbitrary closed countable subsets $Z$ of the unit circle examples of topologically mixing operators on Hilbert spaces are given which have a densely spanning set of unimodular eigenvectors with eigenvalues restricted to $Z$. In particular, these operators cannot be ergodic in the Gaussian sense.

math.DS↗
arXiv2021

Earth rotation parameter estimation from LLR and impact of non-tidal station loading

LLR measures the distance between observatories on Earth and retro-reflectors on Moon since 1969. In this paper, we estimate the Earth Rotation Parameters (ERP; terrestrial pole offsets, $x_p$ and $y_p$, and Earth rotation phase, $Δ$UT) using LLR data. We estimate the values of $Δ$UT, and the pole offsets separately. For the pole offsets, we estimate the values of $x_p$ and $y_p$ together and separately. Overall, the uncertainties of ERP from the new LLR data (after 2000.0) have significantly improved, staying less than 20 $μ$s for $Δ$UT, less than 2.5 mas for $x_p$, and less than 3 mas for $y_p$ for nights selected from subsets of the LLR time series which have 10 and 15 normal points obtained per night. Furthermore, we add the non-tidal loading effect provided by the IMLS, as observation level corrections of the LLR observatories in the analysis. This effect causes deformations of the Earth surface up to the centimetre level. Its addition in the Institute of Geodesy (IfE) LLR model, leads to a marginal improvement in the uncertainties (3-$σ$ values) of about 1% for both, $Δ$UT and the pole offsets.

physics.geo-ph↗
arXiv2020

Benefit of New High-Precision LLR Data for the Determination of Relativistic Parameters

Since 1969, Lunar Laser Ranging (LLR) data have been collected by various observatories and analysed by different analysis groups. In the recent years, observations with bigger telescopes (APOLLO) and at infra-red wavelength (OCA) are carried out, resulting in a better distribution of precise LLR data over the lunar orbit and the observed retro-reflectors on the Moon. This is a great advantage for various investigations in the LLR analysis. The aim of this study is to evaluate the benefit of the new LLR data for the determination of relativistic parameters. Here we show current results for relativistic parameters like a possible temporal variation of the gravitational constant $\dot{G}/G_0 = (-5.0 \pm 9.6) \times 10^{-15} \, \mathrm{yr}^{-1}$, the equivalence principle with $Δ\left(m_g/m_i\right)_{\mathrm{EM}} = (-2.1 \pm 2.4)\times10^{-14}$ and the PPN parameters $β-1 = (6.2 \pm 7.2) \times 10^{-5}$ and $γ-1 = (1.7 \pm 1.6) \times 10^{-4}$. The results show a significant improvement in the accuracy of the various parameters, mainly due to better coverage of the lunar orbit, better distribution of measurements over the lunar retro-reflectors, and last but not least, higher accuracy of the data. Within the estimated accuracies, no violation of Einstein's theory is found and the results set improved limits for the different effects.

gr-qc↗
arXiv2020

Impact of non-tidal station loading in LLR

Lunar Laser Ranging (LLR) measures the distance between observatories on Earth and retro-reflectors on Moon since 1970. In this paper, we study the effect of non-tidal station loading (NTSL) in the analysis of LLR data. We add the non-tidal loading effect provided by three data centres: the German Research Centre for Geosciences (GFZ), the International Mass Loading Service (IMLS) and EOST loading service of University of Strasbourg in France, as observation level corrections of the LLR observatories in our analysis. This effect causes deformations of the Earth surface up to the centimetre level. Its addition in the Institute of Geodesy (IfE) LLR model, it leads to a change in the uncertainties (3-sigma values) of the station coordinates resulting in up to a 0.60% improvement, an improvement in the post-fit LLR residuals of up to 9%, and a decrease in the power of the annual signal in the LLR post-fit residuals of up to 57%.

physics.geo-ph↗
arXiv2020

Gravity field modelling for the Hannover 10m atom interferometer

Absolute gravimeters (AG) are used in geodesy, geophysics, and physics for a wide spectrum of applications. Stable gravimetric measurements over timescales from several days to decades are required to provide relevant insight into geophysical processes. Users of AGs participate in comparisons with a metrological reference in order to monitor the temporal stability of the instruments and determine the bias to that reference. However, since no measurement standard of higher-order accuracy currently exists, users of AGs participate in key comparisons led by the CIPM. These comparisons provide the reference values of highest accuracy compared to the calibration against a single AG. The construction of stationary, large scale atom interferometers paves the way towards a new measurement standard in absolute gravimetry used as a reference with a potential stability up to 1 nm/s$^2$ at 1 s integration time. At the Leibniz University Hannover, we are currently building such a very long baseline atom interferometer with a 10 m long interaction zone. The knowledge of local gravity and its gradient along and around the baseline is required to establish the instrument's uncertainty budget and enable transfers of gravimetric measurements to nearby devices for comparison and calibration purposes. We therefore established a control network for relative gravimeters and repeatedly measured its connections during the construction of the atom interferometer. We additionally developed a 3D model of the host building to investigate the self-attraction effect and studied the impact of mass changes due to groundwater hydrology on the gravity field around the reference instrument. The gravitational effect from the building 3D model is in excellent agreement with the latest gravimetric measurement campaign which opens the possibility to transfer gravity values with an uncertainty below the 10 nm/s$^2$ level.

physics.ins-det↗
arXiv2020

Extending Science from Lunar Laser Ranging

The Lunar Laser Ranging (LLR) experiment has accumulated 50 years of range data of improving accuracy from ground stations to the laser retroreflector arrays (LRAs) on the lunar surface. The upcoming decade offers several opportunities to break new ground in data precision through the deployment of the next generation of single corner-cube lunar retroreflectors and active laser transponders. This is likely to expand the LLR station network. Lunar dynamical models and analysis tools have the potential to improve and fully exploit the long temporal baseline and precision allowed by millimetric LLR data. Some of the model limitations are outlined for future efforts. Differential observation techniques will help mitigate some of the primary limiting factors and reach unprecedented accuracy. Such observations and techniques may enable the detection of several subtle signatures required to understand the dynamics of the Earth-Moon system and the deep lunar interior. LLR model improvements would impact multi-disciplinary fields that include lunar and planetary science, Earth science, fundamental physics, celestial mechanics and ephemerides.

astro-ph.IM↗
arXiv2020

The Relativistic Geoid: Gravity Potential and Relativistic Effects

The Earth's geoid is one of the most essential and fundamental concepts to provide a gravity field-related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to consistently interpret high-precision measurements without any doubt, a relativistic treatment of geodetic notions (including the geoid) within Einstein's theory of General Relativity is inevitable. Building on the theoretical construction of isochronometric surfaces and the so-called redshift potential for clock comparison, we define a relativistic gravity potential as a generalization of (post-)Newtonian notions. This potential exists in any stationary configuration with rigidly co-rotating observers, and it is the same as realized by local plumb lines. In a second step, we employ the gravity potential to define the relativistic geoid in direct analogy to the Newtonian understanding. In the respective limit, the framework allows to recover well-known (post-) Newtonian results. For a better illustration and proper interpretation of the general relativistic gravity potential and geoid, some particular examples are considered. Explicit results are derived for exact vacuum solutions to Einstein's field equation as well as a parametrized post-Newtonian model. Comparing the Earth's Newtonian geoid to its relativistic generalization is a very subtle problem, but of high interest. An isometric embedding into Euclidean three-dimensional space is an appropriate solution and allows a genuinely intrinsic comparison. With this method, the leading-order differences are determined, which are at the mm-level.

gr-qc↗
arXiv2020

Dynamics of the Taylor shift on Bergman spaces

The Taylor (backward) shift on Bergman spaces $A^p(\om)$ for general open sets $\om$ in the extended complex plane shows rich variety concerning its dynamical behaviour. Different aspects are worked out, where in the case $p<2$ a recent result of Bayart and Matheron plays a central role.

math.DS↗
arXiv2018

Regular orbits of sporadic simple groups

Given a finite group $G$ and a faithful irreducible $FG$-module $V$ where $F$ has prime order, does $G$ have a regular orbit on $V$? This problem is equivalent to determining which primitive permutation groups of affine type have a base of size 2. Let $G$ be a covering group of an almost simple group whose socle $T$ is sporadic, and let $V$ be a faithful irreducible $FG$-module where $F$ has prime order dividing $|G|$. We classify the pairs $(G,V)$ for which $G$ has no regular orbit on $V$, and determine the minimal base size of $G$ in its action on $V$. To obtain this classification, for each non-trivial $g\in G/Z(G)$, we compute the minimal number of $T$-conjugates of $g$ generating $\langle T,g\rangle$.

math.RT↗
arXiv2017

Invariant bilinear forms on $W$-graph representations and linear algebra over integral domains

Lie-theoretic structures of type $E_8$ (e.g., Lie groups and algebras, Hecke algebras and Kazhdan-Lusztig cells, ...) are considered to serve as a `gold standard' when it comes to judging the effectiveness of a general algorithm for solving a computational problem in this area. Here, we address a problem that occurred in our previous work on decomposition numbers of Iwahori-Hecke algebras, namely, the computation of invariant bilinear forms on so-called $W$-graph representations. We present a new algorithmic solution which makes it possible to produce and effectively use the main results in further applications.

math.RT↗
arXiv2017

A structured description of the genus spectrum of abelian $p$-groups

The genus spectrum of a finite group $G$ is the set of all $g$ such that $G$ acts faithfully on a compact Riemann surface of genus $g$. It is an open problem to find a general description of the genus spectrum of the groups in interesting classes, such as the abelian $p$-groups. Motivated by the work of Talu for odd primes $p$, we develop a general combinatorial machinery, for arbitrary primes, to obtain a structured description of the so-called reduced genus spectrum of abelian $p$-groups. We have a particular view towards how to generally find the reduced minimum genus in this class of groups, determine the complete genus spectrum for a large subclass of abelian $p$-groups, consisting of those groups in a certain sense having `large' defining invariants, and use this to construct infinitely many counterexamples to Talu's Conjecture, saying that an abelian $p$-group is recoverable from its genus spectrum. Finally, we indicate the effectiveness of our combinatorial approach by applying it to quite a few explicit examples.

math.GR↗
arXiv2016

Erdmessung mit Quanten und Relativität

Recent developments in fundamental physics (in theory as well as in technology) provide novel capabilities for geodetic applications such as refined observations of the Earth`s gravity field. We will focus on two new concepts: one applies atomic interferometry for (satellite) gravimetry, the other uses clock measurements for observing potential values. In the first case, gravity anomalies are determined by observing free-falling atoms (quantum gravimetry), such technique can also be applied for future gradiometric measurements in space. In the second case according to Einstein`s theory of general relativity, frequency comparisons of highly precise optical clocks give access to differences of the gravity potential, even over long distances (relativistic geodesy). Also laser interferometry between test masses in space with nanometer accuracy belongs to these novel concepts. For the latter, technology developed for gravitational wave detection and successfully tested in the LISA/pathfinder mission is being prepared for geodetic measurements. Those concepts are recently elaborated in close cooperation between physicists and geodesists at the University of Hannover under the umbrella of the Collaborative Research Center SFB 1128 Relativistic geodesy and gravimetry with quantum sensors (geo-Q). We will give a few examples where geodesy will potentially benefit from these novel developments and show future perspectives.

physics.geo-ph↗
arXiv2016

On low-degree representations of the symmetric group

The aim of the present paper is to obtain a classification of all the irreducible modular representations of the symmetric group on $n$ letters of dimension at most $n^3$, including dimension formulae. This is achieved by improving an idea, originally due to G. James, to get hands on dimension bounds, by building on the current knowledge about decomposition numbers of symmetric groups and their associated Iwahori-Hecke algebras, and by employing a mixture of theory and computation.

math.RT↗