Local Anisotropy of Fluids using Minkowski Tensors

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\leq \beta_\nu^{a,b}\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from $\beta_\nu^{a,b}\approx 0.3$ for vapor phases to $\beta_\nu^{a,b}\to 1$ for ordered solids. We find that for fluids, local anisotropy decreases monotonously with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices $\beta_\nu^{a,b}$ are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs

Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

Second order analysis of geometric functionals of Boolean models

This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second version mainly resolves minor LaTeX problems.

Predictive value of fear avoidance in developing chronic neck pain disability: consequences for clinical decision making

Objective\ud To improve clinical decision making in posttraumatic neck pain by investigating the additional value of fear-avoidance variables in predicting chronic neck pain disability.\ud \ud Design\ud An inception cohort with baseline assessment 1 week posttrauma and outcome assessment 24 weeks posttrauma. Predictive factors include pain intensity, Neck Disability Index (NDI), catastrophizing, fear of movement (Tampa Scale for Kinesiophobia [TSK]), and avoidance muscle behavior.\ud \ud Setting\ud Hospital emergency department of a general hospital.\ud \ud Participants\ud A consecutive sample of 90 people reporting of pain in neck or head region after a motor vehicle collision. Eighty-two subjects (91.1%) of the sample provided 24-week follow-up on the outcome.\ud \ud Interventions\ud Not applicable.\ud \ud Main outcome measure\ud The NDI assessing physical disability of subjects with neck pain.\ud \ud Results\ud By using a combination of the baseline NDI and TSK, it appears to be possible to predict chronic disability with a probability of 54.3% (95% confidence interval [CI], 35.2%–72.3%) after entering the NDI (cutoff, 15) as a first test, and with a probability of 83.3% (95% CI, 70.3%–91.3%) after entering the TSK (cutoff, 40) in a second test.\ud \ud Conclusions\ud A simple rating of baseline neck pain disability within a week of the trauma, separately or in combination with a test for fear of movement, can be used to predict future outcome. Patients showing fear of movement can be offered an intervention that focuses on reduction of this fear.\ud \u

Turbulence Time Series Data Hole Filling using Karhunen-Loeve and ARIMA methods

Measurements of optical turbulence time series data using unattended instruments over long time intervals inevitably lead to data drop-outs or degraded signals. We present a comparison of methods using both Principal Component Analysis, which is also known as the Karhunen--Loeve decomposition, and ARIMA that seek to correct for these event-induced and mechanically-induced signal drop-outs and degradations. We report on the quality of the correction by examining the Intrinsic Mode Functions generated by Empirical Mode Decomposition. The data studied are optical turbulence parameter time series from a commercial long path length optical anemometer/scintillometer, measured over several hundred metres in outdoor environments.Comment: 8 pages, 9 figures, submitted to ICOLAD 2007, City University, London, U

First measurement of the Head-Tail directional nuclear recoil signature at energies relevant to WIMP dark matter searches

We present first evidence for the so-called Head-Tail asymmetry signature of neutron-induced nuclear recoil tracks at energies down to 1.5 keV/amu using the 1m^3 DRIFT-IIc dark matter detector. This regime is appropriate for recoils induced by Weakly Interacting Massive Particle (WIMPs) but one where the differential ionization is poorly understood. We show that the distribution of recoil energies and directions induced here by Cf-252 neutrons matches well that expected from massive WIMPs. The results open a powerful new means of searching for a galactic signature from WIMPs.Comment: 4 pages, 6 figures, 1 tabl

An examination of the psychometric structure of the Multidimensional Pain Inventory in temporomandibular disorder patients: a confirmatory factor analysis

BACKGROUND: This paper seeks to analyse the psychometric and structural properties of the Multidimensional Pain Inventory (MPI) in a sample of temporomandibular disorder patients. METHODS: The internal consistency of the scales was obtained. Confirmatory Factor Analysis was carried out to test the MPI structure section by section in a sample of 114 temporomandibular disorder patients. RESULTS: Nearly all scales obtained good reliability indexes. The original structure could not be totally confirmed. However, with a few adjustments we obtained a satisfactory structural model of the MPI which was slightly different from the original: certain items and the Self control scale were eliminated; in two cases, two original scales were grouped in one factor, Solicitous and Distracting responses on the one hand, and Social activities and Away from home activities, on the other. CONCLUSION: The MPI has been demonstrated to be a reliable tool for the assessment of pain in temporomandibular disorder patients. Some divergences to be taken into account have been clarified

Resolving the Formation of Protogalaxies. II. Central Gravitational Collapse

Numerous cosmological hydrodynamic studies have addressed the formation of galaxies. Here we choose to study the first stages of galaxy formation, including non-equilibrium atomic primordial gas cooling, gravity and hydrodynamics. Using initial conditions appropriate for the concordance cosmological model of structure formation, we perform two adaptive mesh refinement simulations of ~10^8 M_sun galaxies at high redshift. The calculations resolve the Jeans length at all times with more than 16 cells and capture over 14 orders of magnitude in length scales. In both cases, the dense, 10^5 solar mass, one parsec central regions are found to contract rapidly and have turbulent Mach numbers up to 4. Despite the ever decreasing Jeans length of the isothermal gas, we only find one site of fragmentation during the collapse. However, rotational secular bar instabilities transport angular momentum outwards in the central parsec as the gas continues to collapse and lead to multiple nested unstable fragments with decreasing masses down to sub-Jupiter mass scales. Although these numerical experiments neglect star formation and feedback, they clearly highlight the physics of turbulence in gravitationally collapsing gas. The angular momentum segregation seen in our calculations plays an important role in theories that form supermassive black holes from gaseous collapse.Comment: Replaced with accepted version. To appear in ApJ v681 (July 1

Minkowski tensors and local structure metrics: Amorphous and crystalline sphere packings

Robust and sensitive tools to characterise local structure are essential for investigations of granular or particulate matter. Often local structure metrics derived from the bond network are used for this purpose, in particular Steinhardt's bond-orientational order parameters ql . Here we discuss an alternative method, based on the robust characterisation of the shape of the particles' Voronoi cells, by Minkowski tensors and derived anisotropy measures. We have successfully applied these metrics to quantify structural changes and the onset of crystallisation in random sphere packs. Here we specifically discuss the expectation values of these metrics for simple crystalline unimodal packings of spheres, consisting of single spheres on the points of a Bravais lattice. These data provide an important reference for the discussion of anisotropy values of disordered structures that are typically of relevance in granular systems. This analysis demonstrates that, at least for sufficiently high packing fractions above φ > 0.61, crystalline sphere packs exist whose Voronoi cells are more anisotropic with respect to a volumetric moment tensor than the average value of Voronoi cell anisotropy in random sphere packs