Topology counts: force distributions in circular spring networks

Filamentous polymer networks govern the mechanical properties of many biological materials. Force distributions within these networks are typically highly inhomogeneous and, although the importance of force distributions for structural properties is well recognized, they are far from being understood quantitatively. Using a combination of probabilistic and graph-theoretical techniques we derive force distributions in a model system consisting of ensembles of random linear spring networks on a circle. We show that characteristic quantities, such as mean and variance of the force supported by individual springs, can be derived explicitly in terms of only two parameters: (i) average connectivity and (ii) number of nodes. Our analysis shows that a classical mean-field approach fails to capture these characteristic quantities correctly. In contrast, we demonstrate that network topology is a crucial determinant of force distributions in an elastic spring network.Comment: 5 pages, 4 figures. Missing labels in Fig. 4 added. Reference fixe

Magnetic fabric in ilmeniterich norites of the Bjerkreimer-Sokndal Layered Intrusion, Norway

The Bjerkreim-Sokndal (BKS) is a layered intrusion, located in the Mid- Proterozoic Egersund anorthosite-norite province within the Sveconorwegian province of the Baltic Shield, south Norway. The layered intrusion formed by influxes of more primitive magma into more evolved magma to produce six Megacyclic units (MCU), each of which can be divided into up to six subunits. From bottom to top in each megacycle the rocks consist of early plagioclase-rich norites, intermediate hemo-ilmenite-rich norites and later magnetite-rich norites. Aeromagnetic maps over the intrusion show large negative and positive anomalies. A negative anomaly with amplitude to - 13000 nT at 60m above ground is associated with hemo-ilmenite-rich norite layer MCU Ive. This layer IVe contains plagioclase, orthopyroxene, hemoilmenite, magnetite, and minor clinopyroxene, biotite, apatite and sulfides. Multi-domain (MD) magnetite makes up 2–3% of the rock. The negative magnetic anomaly associated with MCU IVe reaches its most negative value on the east limb of the Bjerkreim Lobe near Heskestad. The anomaly at Heskestad is part of a longer negative anomaly, which follows MCU IVe for more than 20 km around a large syncline. The average NRM intensity decreases from 25AM−1 along the east fold limb to 10AM−1 towards the hinge area to 7AM−1 at the hinge. The BKS has a penetrative deformation fabric within the syncline with the weakest deformation found in the hinge area and the strongest on the east limb. Electron backscatter diffraction (EBSD) was used to determine the lattice-preferred orientation (LPO) of orthopyroxene and ilmenite. The (100)-planes of the orthopyroxenes are found to lie parallel to a foliation in the rock, which is subparallel to the cumulate layering. Orthopyroxene c-axes form the steep lineation within the foliation plane. The anisotropy of magnetic susceptibility (AMS) was measured for samples that were taken at five locations from the eastern limb to the hinge area of the syncline to investigate if the change in NRM intensity could be related to magnetic fabric.conferenc

Optomechanical circuits for nanomechanical continuous variable quantum state processing

We propose and analyze a nanomechanical architecture where light is used to perform linear quantum operations on a set of many vibrational modes. Suitable amplitude modulation of a single laser beam is shown to generate squeezing, entanglement, and state-transfer between modes that are selected according to their mechanical oscillation frequency. Current optomechanical devices based on photonic crystals may provide a platform for realizing this scheme.Comment: 11 pages, 5 figure

Dust survival rates in clumps passing through the Cas A reverse shock -- II. The impact of magnetic fields

Dust grains form in the clumpy ejecta of core-collapse supernovae where they are subject to the reverse shock, which is able to disrupt the clumps and destroy the grains. Important dust destruction processes include thermal and kinetic sputtering as well as fragmentation and grain vaporization. In the present study, we focus on the effect of magnetic fields on the destruction processes. We have performed magneto-hydrodynamical simulations using AstroBEAR to model a shock wave interacting with an ejecta clump. The dust transport and destruction fractions are computed using our post-processing code Paperboats in which the acceleration of grains due to the magnetic field and a procedure that allows partial grain vaporization have been newly implemented. For the oxygen-rich supernova remnant Cassiopeia A we found a significantly lower dust survival rate when magnetic fields are aligned perpendicular to the shock direction compared to the non-magnetic case. For a parallel field alignment, the destruction is also enhanced but at a lower level. The survival fractions depend sensitively on the gas density contrast between the clump and the ambient medium and on the grain sizes. For a low-density contrast of $100$, e.g., $5\,$nm silicate grains are completely destroyed while the survival fraction of $1\,\mu$m grains is $86\,$per cent. For a high-density contrast of $1000$, $95\,$per cent of the $5\,$nm grains survive while the survival fraction of $1\,\mu$m grains is $26\,$per cent. Alternative clump sizes or dust materials (carbon) have non-negligible effects on the survival rate but have a lower impact compared to density contrast, magnetic field strength, and grain size.Comment: Accepted by MNRAS. Author accepted manuscript. Accepted on 23/01/2023. 24 pages, 21 Figure

Atomistic defect states as quantum emitters in monolayer MoS2_2

Quantum light sources in solid-state systems are of major interest as a basic ingredient for integrated quantum device technologies. The ability to tailor quantum emission through deterministic defect engineering is of growing importance for realizing scalable quantum architectures. However, a major difficulty is that defects need to be positioned site-selectively within the solid. Here, we overcome this challenge by controllably irradiating single-layer MoS$_{2}$ using a sub-nm focused helium ion beam to deterministically create defects. Subsequent encapsulation of the ion bombarded MoS$_{2}$ flake with high-quality hBN reveals spectrally narrow emission lines that produce photons at optical wavelengths in an energy window of one to two hundred meV below the neutral 2D exciton of MoS$_{2}$. Based on ab-initio calculations we interpret these emission lines as stemming from the recombination of highly localized electron-hole complexes at defect states generated by the helium ion bombardment. Our approach to deterministically write optically active defect states in a single transition metal dichalcogenide layer provides a platform for realizing exotic many-body systems, including coupled single-photon sources and exotic Hubbard systems.Comment: Main: 9 pages, 3 figures + SI: 19 pages, 10 figure

Impact of the rpoS genotype for acid resistance patterns of pathogenic and probiotic Escherichia coli

BACKGROUND: Enterohemorrhagic E. coli (EHEC), a subgroup of Shiga toxin (Stx) producing E. coli (STEC), may cause severe enteritis and hemolytic uremic syndrome (HUS) and is transmitted orally via contaminated foods or from person to person. The infectious dose is known to be very low, which requires most of the bacteria to survive the gastric acid barrier. Acid resistance therefore is an important mechanism of EHEC virulence. It should also be a relevant characteristic of E. coli strains used for therapeutic purposes such as the probiotic E. coli Nissle 1917 (EcN). In E. coli and related enteric bacteria it has been extensively demonstrated, that the alternative sigma factor σ(S), encoded by the rpoS gene, acts as a master regulator mediating resistance to various environmental stress factors. METHODS: Using rpoS deletion mutants of a highly virulent EHEC O26:H11 patient isolate and the sequenced prototype EHEC EDL933 (ATCC 700927) of serotype O157:H7 we investigated the impact of a functional rpoS gene for orchestrating a satisfactory response to acid stress in these strains. We then functionally characterized rpoS of probiotic EcN and five rpoS genes selected from STEC isolates pre-investigated for acid resistance. RESULTS: First, we found out that ATCC isolate 700927 of EHEC EDL933 has a point mutation in rpoS, not present in the published sequence, leading to a premature stop codon. Moreover, to our surprise, one STEC strain as well as EcN was acid sensitive in our test environment, although their cloned rpoS genes could effectively complement acid sensitivity of an rpoS deletion mutant. CONCLUSION: The attenuation of sequenced EHEC EDL933 might be of importance for anyone planning to do either in vitro or in vivo studies with this prototype strain. Furthermore our data supports recently published observations, that individual E. coli isolates are able to significantly modulate their acid resistance phenotype independent of their rpoS genotype

Topology Counts: Force Distributions in Circular Spring Networks

Filamentous polymer networks govern the mechanical properties of many biological materials. Force distributions within these networks are typically highly inhomogeneous, and, although the importance of force distributions for structural properties is well recognized, they are far from being understood quantitatively. Using a combination of probabilistic and graph-theoretical techniques, we derive force distributions in a model system consisting of ensembles of random linear spring networks on a circle. We show that characteristic quantities, such as the mean and variance of the force supported by individual springs, can be derived explicitly in terms of only two parameters: (i) average connectivity and (ii) number of nodes. Our analysis shows that a classical mean-field approach fails to capture these characteristic quantities correctly. In contrast, we demonstrate that network topology is a crucial determinant of force distributions in an elastic spring network. Our results for 1D linear spring networks readily generalize to arbitrary dimensions

Topology determines force distributions in one-dimensional random spring networks

Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N,z). Despite the universal properties of such (N,z) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks