Wigner function of noninteracting trapped fermions

We study analytically the Wigner function $W_N({\bf x},{\bf p})$ of $N$ noninteracting fermions trapped in a smooth confining potential $V({\bf x})$ in $d$ dimensions. At zero temperature, $W_N({\bf x},{\bf p})$ is constant over a finite support in the phase space $({\bf x},{\bf p})$ and vanishes outside. Near the edge of this support, we find a universal scaling behavior of $W_N({\bf x},{\bf p})$ for large $N$. The associated scaling function is independent of the precise shape of the potential as well as the spatial dimension $d$. We further generalize our results to finite temperature $T>0$. We show that there exists a low temperature regime $T \sim e_N/b$ where $e_N$ is an energy scale that depends on $N$ and the confining potential $V({\bf x})$, where the Wigner function at the edge again takes a universal scaling form with a $b$-dependent scaling function. This temperature dependent scaling function is also independent of the potential as well as the dimension $d$. Our results generalize to any $d\geq 1$ and $T \geq 0$ the $d=1$ and $T=0$ results obtained by Bettelheim and Wiegman [Phys. Rev. B ${\bf 84}$, 085102 (2011)].Comment: 16 pages, 4 figure

New Baryons in the Delta eta and Delta omega Channels

The decays of excited nonstrange baryons into the final states Delta eta and Delta omega are examined in a relativized quark pair creation model. The wavefunctions and parameters of the model are fixed by previous calculations of N pi and N pi pi, etc., decays through various quasi-two body channels including N eta and N omega. Our results show that the combination of thresholds just below the region of interest and the isospin selectivity of these channels should allow the discovery of several new baryons in such experiments.Comment: 10 pages, RevTe

Weak local rules for planar octagonal tilings

We provide an effective characterization of the planar octagonal tilings which admit weak local rules. As a corollary, we show that they are all based on quadratic irrationalities, as conjectured by Thang Le in the 90s.Comment: 23 pages, 6 figure

Good Learning and Implicit Model Enumeration

MathSBML is an open-source, freely-downloadable Mathematica package that facilitates working with Systems Biology Markup Language (SBML) models. SBML is a toolneutral,computer-readable format for representing models of biochemical reaction networks, applicable to metabolic networks, cell-signaling pathways, genomic regulatory networks, and other modeling problems in systems biology that is widely supported by the systems biology community. SBML is based on XML, a standard medium for representing and transporting data that is widely supported on the internet as well as in computational biology and bioinformatics. Because SBML is tool-independent, it enables model transportability, reuse, publication and survival. In addition to MathSBML, a number of other tools that support SBML model examination and manipulation are provided on the sbml.org website, including libSBML, a C/C++ library for reading SBML models; an SBML Toolbox for MatLab; file conversion programs; an SBML model validator and visualizer; and SBML specifications and schemas. MathSBML enables SBML file import to and export from Mathematica as well as providing an API for model manipulation and simulation

Competing interactions in artificial spin chains

The low-energy magnetic configurations of artificial frustrated spin chains are investigated using magnetic force microscopy and micromagnetic simulations. Contrary to most studies on two-dimensional artificial spin systems where frustration arises from the lattice geometry, here magnetic frustration originates from competing interactions between neighboring spins. By tuning continuously the strength and sign of these interactions, we show that different magnetic phases can be stabilized. Comparison between our experimental findings and predictions from the one-dimensional Anisotropic Next-Nearest-Neighbor Ising (ANNNI) model reveals that artificial frustrated spin chains have a richer phase diagram than initially expected. Besides the observation of several magnetic orders and the potential extension of this work to highly-degenerated artificial spin chains, our results suggest that the micromagnetic nature of the individual magnetic elements allows observation of metastable spin configurations.Comment: 5 pages, 4 figure

Exploring the origin of ice-filled craters in the north polar region of Mars

We investigate the origins of enigmatic ice-filled craters in the north polar region of Mars. We test several explanations for their origin, namely: (1) as polar cap remnants (2) accumulation independently of the polar cap, and (3) upwelling of subsurface water, analogous to either aufice or pingo formation on Earth. Each of these hypotheses has a significant impact on our understanding of Mars’ recent geological and climatic history and the behaviour of water and water ice at high latitudes. We used several lines of evidence to assess the most likely formation mechanism. We first performed a crater survey based on THEMIS visual data and MOLA elevation data to identify any craters that had domal central lumps which were different from normal central peaks. From this survey we identified 17 craters for further study. These include Louth, Korolev, Dokka and other unnamed craters. Using data from orbiting spectrometers; OMEGA on ESA’s Mars Express and CRISM on NASA’s Mars Reconnaissance Orbiter; we verified that the composition of the exposed central domes was predominantly water ice. We found the domes fell into three groups: (1) those completely covered by dunes, (2) those partially covered by dunes and (3) those with no dunes. We investigated the morphology and the relative position of the domes using MOLA elevation data. We found that the domes are always asymmetrically placed within the craters. However, this asymmetry could not easily be linked to wind directions as revealed by dune slip-faces [2]. The domes often have a moat-like structure and in some cases do not cover the entire crater floor, e.g. Louth Crater. From image data, we identified six craters which possessed internal stratigraphy, in the form of regularly spaced layers, and of these we have inspected three in detail. We found that the layers possess both strong sinuosity and high angle unconformities. We interpret the internal stratigraphy as representing a sequence of regular cyclic accumulations, which produced the layers, followed by asymmetric ablation and subsequent resumption of accumulation, to produce the unconformities. Hence, the present-day shape of the domes indicates that they are in a phase of ablation.We attribute the colour contrasts between layers to different levels of dust, or particulate content. This could form a source for the dunes, which are often located on the summits of these domes. We find that this sequence is best explained by a model of atmospheric condensation. Our measurements of internal layer spacing and observations of layer stratigraphy argues that these deposits are not linked directly to a former, more extensive polar cap

The Input Signal Step Function (ISSF), a Standard Method to Encode Input Signals in SBML Models with Software Support, Applied to Circadian Clock Models

LetterThis is the final version of the article. Available from SAGE Publications via the DOI in this record.Time-dependent light input is an important feature of computational models of the circadian clock. However, publicly available models encoded in standard representations such as the Systems Biology Markup Language (SBML) either do not encode this input or use different mechanisms to do so, which hinders reproducibility of published results as well as model reuse. The authors describe here a numerically continuous function suitable for use in SBML for models of circadian rhythms forced by periodic light-dark cycles. The Input Signal Step Function (ISSF) is broadly applicable to encoding experimental manipulations, such as drug treatments, temperature changes, or inducible transgene expression, which may be transient, periodic, or mixed. It is highly configurable and is able to reproduce a wide range of waveforms. The authors have implemented this function in SBML and demonstrated its ability to modify the behavior of publicly available models to accurately reproduce published results. The implementation of ISSF allows standard simulation software to reproduce specialized circadian protocols, such as the phase-response curve. To facilitate the reuse of this function in public models, the authors have developed software to configure its behavior without any specialist knowledge of SBML. A community-standard approach to represent the inputs that entrain circadian clock models could particularly facilitate research in chronobiology.K.S. was supported by the UK BBSRC grant BB/E015263/1. SynthSys Edinburgh is a Centre for Integrative Systems Biology (CISB) funded by BBSRC and EPSRC, reference BB/D019621/1

On the Kramers-Kronig transform with logarithmic kernel for the reflection phase in the Drude model

We use the Kramers-Kronig transform (KKT) with logarithmic kernel to obtain the reflection phase and, subsequently, the complex refractive index of a bulk mirror from reflectance. However, there remains some confusion regarding the formulation for this analysis. Assuming the damped Drude model for the dielectric constant and the oblique incidence case, we calculate the additional terms: phase at zero frequency and Blashke factor and we propose a reformulated KKT within this model. Absolute reflectance in the s-polarization case of a gold film is measured between 40 and 350 eV for various glancing angles using synchrotron radiation and its complex refractive index is deduced using the reformulated KKT that we propose. The results are discussed with respect to the data available in the literature.Comment: 18 pages, piblished in j. Mod. Opt. 57, 1504 (2010