Realtime magnetic field sensing and imaging using a single spin in diamond

The Zeeman splitting of a localized single spin can be used to construct a magnetometer allowing high precision measurements of magnetic fields with almost atomic spatial resolution. While sub-{\mu}T sensitivity can in principle be obtained using pulsed techniques and long measurement times, a fast and easy-to-use method without laborious data post-processing is desirable for a scanning-probe approach with high spatial resolution. In order to measure the resonance frequency in realtime, we applied a field-frequency lock to the continuous wave ODMR signal of a single electron spin in a nanodiamond. In our experiment, we achieved a sampling rate of up to 100 readings per second with a sensitivity of 6 {\mu}T/$\sqrt{Hz}$. Using this method we have imaged the microscopic field distribution around a magnetic wire. Images with \sim 30 {\mu}T resolution and 4096 sub-micron sized pixels were acquired in 10 minutes. By measuring the field response of multiple spins on the same object we were able to partly reconstruct the orientation of the field

Structural quantities of quasi-two-dimensional fluids

Quasi-two-dimensional fluids can be generated by confining a fluid between two parallel walls with narrow separation. Such fluids exhibit an inhomogeneous structure perpendicular to the walls due to the loss of translational symmetry. Taking the transversal degrees of freedom as a perturbation to an appropriate 2D reference fluid we provide a systematic expansion of the $m$-particle density for arbitrary $m$. To leading order in the slit width this density factorizes into the densities of the transversal and lateral degrees of freedom. Explicit expressions for the next-to-leading order terms are elaborated analytically quantifying the onset of inhomogeneity. The case $m=1$ yields the density profile with a curvature given by an integral over the pair-distribution function of the corresponding 2D reference fluid, which reduces to its 2D contact value in the case of pure excluded-volume interactions. Interestingly, we find that the 2D limit is subtle and requires stringent conditions on the fluid-wall interactions. We quantify the rapidity of convergence for various structural quantities to their 2D counterparts.Comment: 12 page

Mode-coupling theory of the glass transition for confined fluids

We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.Comment: 16 pages; to be published in PR

Counting and Algorithmic Generalization with Transformers

Algorithmic generalization in machine learning refers to the ability to learn the underlying algorithm that generates data in a way that generalizes out-of-distribution. This is generally considered a difficult task for most machine learning algorithms. Here, we analyze algorithmic generalization when counting is required, either implicitly or explicitly. We show that standard Transformers are based on architectural decisions that hinder out-of-distribution performance for such tasks. In particular, we discuss the consequences of using layer normalization and of normalizing the attention weights via softmax. With ablation of the problematic operations, we demonstrate that a modified transformer can exhibit a good algorithmic generalization performance on counting while using a very lightweight architecture.Comment: 10 pages, 9 figures, submitted to AAAI 202

Die Trümmereisenerze von Damme (Grube Damme und benachbarte Vorkommen) : mit 4 Tabellen

Bei Damme, Gehrde und Rieste, 30 km nordöstlich von Osnabrück, kommt ein marin-sedimentäres, stratiformes Eisenerzlager vor, das aus Brauneisenerz-Geröllen und mergelig-glaukonitischer Matrix besteht und meist 2-7 m mächtig ist. Dieses Erzlager tritt in fünf unterschiedlich großen, linsenförmigen Zonen auf, die in 70-400 m Tiefe unter Gelände auf den flach einfallenden Flügeln einer 35 km langen und 10km breiten Oberkreide-Mulde liegen. Es gehört stratigraphisch dem Oberen Unter-Campan an und transgrediert auf tonige Gesteine der Unterkreide. In seinem Hangenden liegen Sedimentgesteine des Ober-Campan, Tertiär und Quartär. Das Erzlager entstand als marine Seife durch Abtragung, Umlagerung und Oxidation von Siderit-Konkretionen aus den tonigen Gesteinen der Unterkreide im Liegenden und in der Umgebung des Erzvorkommens. Von 1944-1967 ist das Erzlager in der jetzt auflässigen Grube Damme abgebaut worden. Dort erzeugte man aus Roherz mit 30-32 % Fe und 0,6-0,7% P durch naßmechanische Aufbereitung ein Konzentrat (versandfertiges Produkt) mit 46-47 % Fe und 0,8% P, das im Ruhrgebiet verhüttet wurde. Insgesamt wurden rund 9,2 Mio. t Roherz gefördert und 5,1 Mio. t Konzentrat erzeugt. Die Grube Damme ist aus wirtschaftlichen Gründen stillgelegt worden. Das Erz ist gegenwärtig nicht abbauwürdig. Deshalb sind die Erzvorräte noch nicht vollständig erkundet

Analysis of Memory Latencies in Multi-Processor Systems

Predicting timing behavior is key to efficient embedded real-time system design and verification. Current approaches to determine end-to-end latencies in parallel heterogeneous architectures focus on performance analysis either on task or system level. Especially memory accesses, basic operations of embedded application, cannot be accurately captured on a single level alone: While task level methods simplify system behavior, system level methods simplify task behavior. Both perspectives lead to overly pessimistic estimations. To tackle these complex interactions we integrate task and system level analysis. Each analysis level is provided with the necessary data to allow precise computations, while adequate abstraction prevents high time complexity