Curie Temperature for Small World Ising Systems of Different Dimensions

For Small World Ising systems of different dimensions, "concentration" dependencies T_C(p) of the Curie temperature upon the fraction p of long-range links have been derived on a basis of simple physical considerations. We have found T_C(p) ~ 1/ln|p| for 1D, T_C(p) ~ p^{1/2} for 2D, and T_C(p) ~ p^{2/3} for 3D.Comment: 3 pages, 2 figure

An assessment of the precise products on static Precise Point Positioning using Multi-Constellation GNSS

Precise point positioning (PPP) is highly dependent on the precise ephemerides and satellite clock products that are used. Different ephemeris and clock products are available from a variety of different organizations. The aim of this paper is to assess the achievable static positioning accuracy and precision when using different precise ephemerides from three analysis centres Natural Resources Canada (EMX), European Space Agency (ESA) and GeoForschungsZentrum (GFZ), using GPS alone, GLONASS alone, and GPS and GLONASS combined. It will be shown in this paper that the precise products are significantly affected by the time-base of the reference stations, and that this is propagated through to all the estimated satellite clocks. In order to overcome the combined biases in the estimated satellite clock, in the PPP processing, these clocks errors need to be handled with an appropriate variation in the estimated receiver clock. It will also be shown that the precise coordinates of the satellites differ between the analysis centres, and this affects the PPP position estimation at the millimetre level. However, all those products will be shown to result in the same level of precision for all coordinate components and are equivalent to the horizontal precision from a Global Double Difference (GDD) solution. For the horizontal coordinate component, the level of agreement between the PPP solutions, and with the GDD solution, is at the millimetre level. There is a notable, but small, bias in the north coordinate components of the PPP solutions, from the corresponding north component of the GDD solutions. It is shown that this difference is due to the different strategy adopted for the GDD and PPP solutions, with PPP being more affected by the changing satellite systems. The precision of the heights of the receiver sites will be shown to be almost the same across all the PPP scenarios, with all three products. Finally, it will be concluded that accuracy of the height component is system dependent and is related to the behaviour of antenna phase centre with the different constellation type

Study of Neutron-Induced Ionization in Helium and Argon Chamber Gases

Ion chambers used to monitor the secondary hadron and tertiary muon beam in the NuMI neutrino beamline will be exposed to background particles, including low energy neutrons produced in the beam dump. To understand these backgrounds, we have studied Helium- and Argon-filled ionization chambers exposed to intense neutron fluxes from PuBe neutron sources ($E_n=1-10$ MeV). The sources emit about 10$^8$ neutrons per second. The number of ion pairs in the chamber gas volume per incident neutron is derived. While limited in precision because of a large gamma ray background from the PuBe sources, our results are consistent with the expectation that the neutrons interact purely elastically in the chamber gas.Comment: accepted for publication in NIM

Role of dipolar and exchange interactions in the positions and widths of EPR transitions for the single-molecule magnets Fe8 and Mn12

We examine quantitatively the temperature dependence of the linewidths and line shifts in electron paramagnetic resonance experiments on single crystals of the single-molecule magnets Fe$_8$ and Mn$_{12}$, at fixed frequency, with an applied magnetic field along the easy axis. We include inter-molecular spin-spin interactions (dipolar and exchange) and distributions in both the uniaxial anisotropy parameter $D$ and the Land\'{e} $g$-factor. The temperature dependence of the linewidths and the line shifts are mainly caused by the spin-spin interactions. For Fe$_8$ and Mn$_{12}$, the temperature dependence of the calculated line shifts and linewidths agrees well with the trends of the experimental data. The linewidths for Fe$_8$ reveal a stronger temperature dependence than those for Mn$_{12}$, because for Mn$_{12}$ a much wider distribution in $D$ overshadows the temperature dependence of the spin-spin interactions. For Fe$_8$, the line-shift analysis suggests two competing interactions: a weak ferromagnetic exchange coupling between neighboring molecules and a longer-ranged dipolar interaction. This result could have implications for ordering in Fe$_8$ at low temperatures.Comment: published versio

On the practicality of time-optimal two-qubit Hamiltonian simulation

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer and Cirac [Phys. Rev. Lett. 88 (2002) 237902] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.Comment: 9 pages, 2 figure

Systematic investigation of imprinted gene expression and 1 enrichment in the mouse brain explored at single-cell resolution

BACKGROUND: Although a number of imprinted genes are known to be highly expressed in the brain, and in certain brain regions in particular, whether they are truly over-represented in the brain has never been formally tested. Using thirteen single-cell RNA sequencing datasets we systematically investigated imprinted gene over-representation at the organ, brain region, and cell-specific levels. RESULTS: We established that imprinted genes are indeed over-represented in the adult brain, and in neurons particularly compared to other brain cell-types. We then examined brain-wide datasets to test enrichment within distinct brain regions and neuron subpopulations and demonstrated over-representation of imprinted genes in the hypothalamus, ventral midbrain, pons and medulla. Finally, using datasets focusing on these regions of enrichment, we identified hypothalamic neuroendocrine populations and the monoaminergic hindbrain neurons as specific hotspots of imprinted gene expression. CONCLUSIONS: These analyses provide the first robust assessment of the neural systems on which imprinted genes converge. Moreover, the unbiased approach, with each analysis informed by the findings of the previous level, permits highly informed inferences about the functions on which imprinted gene expression converges. Our findings indicate the neuronal regulation of motivated behaviours such as feeding and sleep, alongside the regulation of pituitary function, as functional hotspots for imprinting. This adds statistical rigour to prior assumptions and provides testable predictions for novel neural and behavioural phenotypes associated with specific genes and imprinted gene networks. In turn, this work sheds further light on the potential evolutionary drivers of genomic imprinting in the brain. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12864-022-08986-8

Soap Bubbles in Outer Space: Interaction of a Domain Wall with a Black Hole

We discuss the generalized Plateau problem in the 3+1 dimensional Schwarzschild background. This represents the physical situation, which could for instance have appeared in the early universe, where a cosmic membrane (thin domain wall) is located near a black hole. Considering stationary axially symmetric membranes, three different membrane-topologies are possible depending on the boundary conditions at infinity: 2+1 Minkowski topology, 2+1 wormhole topology and 2+1 black hole topology. Interestingly, we find that the different membrane-topologies are connected via phase transitions of the form first discussed by Choptuik in investigations of scalar field collapse. More precisely, we find a first order phase transition (finite mass gap) between wormhole topology and black hole topology; the intermediate membrane being an unstable wormhole collapsing to a black hole. Moreover, we find a second order phase transition (no mass gap) between Minkowski topology and black hole topology; the intermediate membrane being a naked singularity. For the membranes of black hole topology, we find a mass scaling relation analogous to that originally found by Choptuik. However, in our case the parameter $p$ is replaced by a 2-vector $\vec{p}$ parametrizing the solutions. We find that $Mass\propto|\vec{p}-\vec{p}_*|^\gamma$ where $\gamma\approx 0.66$. We also find a periodic wiggle in the scaling relation. Our results show that black hole formation as a critical phenomenon is far more general than expected.Comment: 15 pages, Latex, 4 figures include

Semiconductive and Photoconductive Properties of the Single Molecule Magnets Mn12_{12}-Acetate and Fe8_8Br8_8

Resistivity measurements are reported for single crystals of Mn$_{12}$-Acetate and Fe$_8$Br$_8$. Both materials exhibit a semiconductor-like, thermally activated behavior over the 200-300 K range. The activation energy, $E_a$, obtained for Mn$_{12}$-Acetate was 0.37 $\pm$ 0.05 eV, which is to be contrasted with the value of 0.55 eV deduced from the earlier reported absorption edge measurements and the range of 0.3-1 eV from intramolecular density of states calculations, assuming $2E_a$= $E_g$, the optical band gap. For Fe$_8$Br$_8$, $E_a$ was measured as 0.73 $\pm$ 0.1 eV, and is discussed in light of the available approximate band structure calculations. Some plausible pathways are indicated based on the crystal structures of both lattices. For Mn$_{12}$-Acetate, we also measured photoconductivity in the visible range; the conductivity increased by a factor of about eight on increasing the photon energy from 632.8 nm (red) to 488 nm (blue). X-ray irradiation increased the resistivity, but $E_a$ was insensitive to exposure.Comment: 7 pages, 8 figure

Low Background Micromegas in CAST

Solar axions could be converted into x-rays inside the strong magnetic field of an axion helioscope, triggering the detection of this elusive particle. Low background x-ray detectors are an essential component for the sensitivity of these searches. We report on the latest developments of the Micromegas detectors for the CERN Axion Solar Telescope (CAST), including technological pathfinder activities for the future International Axion Observatory (IAXO). The use of low background techniques and the application of discrimination algorithms based on the high granularity of the readout have led to background levels below 10$^{-6}$ counts/keV/cm$^2$/s, more than a factor 100 lower than the first generation of Micromegas detectors. The best levels achieved at the Canfranc Underground Laboratory (LSC) are as low as 10$^{-7}$ counts/keV/cm$^2$/s, showing good prospects for the application of this technology in IAXO. The current background model, based on underground and surface measurements, is presented, as well as the strategies to further reduce the background level. Finally, we will describe the R&D paths to achieve sub-keV energy thresholds, which could broaden the physics case of axion helioscopes.Comment: 6 pages, 3 figures, Large TPC Conference 2014, Pari

An assessment of static Precise Point Positioning using GPS only, GLONASS only, and GPS plus GLONASS

The aim of this paper is to look into the achievable repeatability and accuracy from Precise Point Positioning (PPP) daily solutions when using GPS only (PPP GPS), GLONASS only (PPP GLO), and GPS plus GLONASS (PPP GPS+GLO) for static positioning. As part of the assessment, a comparison with global double difference (DD) GPS daily solutions is presented. It is shown, therefore, that all of the PPP daily solutions can achieve millimetric level repeatability, similar to the global DD GPS solutions. Furthermore, the mean of the biases between the PPP daily solutions and the global DD GPS daily solutions are constellation type dependent, while an improvement is found in the vertical component for PPP GPS+GLO over PPP GLO, as the latter may be more affected by any imperfections in the models for GLONASS antenna phase centre variations. It is concluded that PPP GLO daily solutions have the ability to be used as independent solutions to PPP GPS daily solutions for static positioning, and as an alternative to PPP GPS+GLO or global DD GPS daily solutions