427 research outputs found
Simplicial Quantum Gravity on a Randomly Triangulated Sphere
We study 2D quantum gravity on spherical topologies employing the Regge
calculus approach with the dl/l measure. Instead of the normally used fixed
non-regular triangulation we study random triangulations which are generated by
the standard Voronoi-Delaunay procedure. For each system size we average the
results over four different realizations of the random lattices. We compare
both types of triangulations quantitatively and investigate how the difference
in the expectation value of the squared curvature, , for fixed and random
triangulations depends on the lattice size and the surface area A. We try to
measure the string susceptibility exponents through finite-size scaling
analyses of the expectation value of an added -interaction term, using two
conceptually quite different procedures. The approach, where an ultraviolet
cut-off is held fixed in the scaling limit, is found to be plagued with
inconsistencies, as has already previously been pointed out by us. In a
conceptually different approach, where the area A is held fixed, these problems
are not present. We find the string susceptibility exponent in
rough agreement with theoretical predictions for the sphere, whereas the
estimate for appears to be too negative. However, our results
are hampered by the presence of severe finite-size corrections to scaling,
which lead to systematic uncertainties well above our statistical errors. We
feel that the present methods of estimating the string susceptibilities by
finite-size scaling studies are not accurate enough to serve as testing grounds
to decide about a success or failure of quantum Regge calculus.Comment: LaTex, 29 pages, including 9 figure
Volume fluctuations and geometrical constraints in granular packs
Structural organization and correlations are studied in very large packings
of equally sized acrylic spheres, reconstructed in three-dimensions by means of
X-ray computed tomography. A novel technique, devised to analyze correlations
among more than two spheres, shows that the structural organization can be
conveniently studied in terms of a space-filling packing of irregular
tetrahedra. The study of the volume distribution of such tetrahedra reveals an
exponential decay in the region of large volumes; a behavior that is in very
good quantitative agreement with theoretical prediction. I argue that the
system's structure can be described as constituted of two phases: 1) an
`unconstrained' phase which freely shares the volume; 2) a `constrained' phase
which assumes configurations accordingly with the geometrical constraints
imposed by the condition of non-overlapping between spheres and mechanical
stability. The granular system exploits heterogeneity maximizing freedom and
entropy while constraining mechanical stability.Comment: 5 pages, 4 figure
New insight into cataract formation -- enhanced stability through mutual attraction
Small-angle neutron scattering experiments and molecular dynamics simulations
combined with an application of concepts from soft matter physics to complex
protein mixtures provide new insight into the stability of eye lens protein
mixtures. Exploring this colloid-protein analogy we demonstrate that weak
attractions between unlike proteins help to maintain lens transparency in an
extremely sensitive and non-monotonic manner. These results not only represent
an important step towards a better understanding of protein condensation
diseases such as cataract formation, but provide general guidelines for tuning
the stability of colloid mixtures, a topic relevant for soft matter physics and
industrial applications.Comment: 4 pages, 4 figures. Accepted for publication on Phys. Rev. Let
Identification of structure in condensed matter with the topological cluster classification
We describe the topological cluster classification (TCC) algorithm. The TCC
detects local structures with bond topologies similar to isolated clusters
which minimise the potential energy for a number of monatomic and binary simple
liquids with particles. We detail a modified Voronoi bond detection
method that optimizes the cluster detection. The method to identify each
cluster is outlined, and a test example of Lennard-Jones liquid and crystal
phases is considered and critically examined.Comment: 28 pages, 28 figure
New Monte Carlo method for planar Poisson-Voronoi cells
By a new Monte Carlo algorithm we evaluate the sidedness probability p_n of a
planar Poisson-Voronoi cell in the range 3 \leq n \leq 1600. The algorithm is
developed on the basis of earlier theoretical work; it exploits, in particular,
the known asymptotic behavior of p_n as n\to\infty. Our p_n values all have
between four and six significant digits. Accurate n dependent averages, second
moments, and variances are obtained for the cell area and the cell perimeter.
The numerical large n behavior of these quantities is analyzed in terms of
asymptotic power series in 1/n. Snapshots are shown of typical occurrences of
extremely rare events implicating cells of up to n=1600 sides embedded in an
ordinary Poisson-Voronoi diagram. We reveal and discuss the characteristic
features of such many-sided cells and their immediate environment. Their
relevance for observable properties is stressed.Comment: 35 pages including 10 figures and 4 table
Gravitational Wilson Loop and Large Scale Curvature
In a quantum theory of gravity the gravitational Wilson loop, defined as a
suitable quantum average of a parallel transport operator around a large
near-planar loop, provides important information about the large-scale
curvature properties of the geometry. Here we shows that such properties can be
systematically computed in the strong coupling limit of lattice regularized
quantum gravity, by performing a local average over rotations, using an assumed
near-uniform measure in group space. We then relate the resulting quantum
averages to an expected semi-classical form valid for macroscopic observers,
which leads to an identification of the gravitational correlation length
appearing in the Wilson loop with an observed large-scale curvature. Our
results suggest that strongly coupled gravity leads to a positively curved (De
Sitter-like) quantum ground state, implying a positive effective cosmological
constant at large distances.Comment: 22 pages, 6 figure
Asymptotic statistics of the n-sided planar Voronoi cell: II. Heuristics
We develop a set of heuristic arguments to explain several results on planar
Poisson-Voronoi tessellations that were derived earlier at the cost of
considerable mathematical effort. The results concern Voronoi cells having a
large number n of sides. The arguments start from an entropy balance applied to
the arrangement of n neighbors around a central cell. It is followed by a
simplified evaluation of the phase space integral for the probability p_n that
an arbitrary cell be n-sided. The limitations of the arguments are indicated.
As a new application we calculate the expected number of Gabriel (or full)
neighbors of an n-sided cell in the large-n limit.Comment: 22 pages, 10 figure
The perimeter of large planar Voronoi cells: a double-stranded random walk
Let be the probability for a planar Poisson-Voronoi cell to have
exactly sides. We construct the asymptotic expansion of up to
terms that vanish as . We show that {\it two independent biased
random walks} executed by the polar angle determine the trajectory of the cell
perimeter. We find the limit distribution of (i) the angle between two
successive vertex vectors, and (ii) the one between two successive perimeter
segments. We obtain the probability law for the perimeter's long wavelength
deviations from circularity. We prove Lewis' law and show that it has
coefficient 1/4.Comment: Slightly extended version; journal reference adde
Asymptotic statistics of the n-sided planar Poisson-Voronoi cell. I. Exact results
We achieve a detailed understanding of the -sided planar Poisson-Voronoi
cell in the limit of large . Let be the probability for a cell to
have sides. We construct the asymptotic expansion of up to
terms that vanish as . We obtain the statistics of the lengths of
the perimeter segments and of the angles between adjoining segments: to leading
order as , and after appropriate scaling, these become independent
random variables whose laws we determine; and to next order in they have
nontrivial long range correlations whose expressions we provide. The -sided
cell tends towards a circle of radius (n/4\pi\lambda)^{\half}, where
is the cell density; hence Lewis' law for the average area of
the -sided cell behaves as with . For
the cell perimeter, expressed as a function of the polar
angle , satisfies , where is known Gaussian
noise; we deduce from it the probability law for the perimeter's long
wavelength deviations from circularity. Many other quantities related to the
asymptotic cell shape become accessible to calculation.Comment: 54 pages, 3 figure
Triceps Insufficiency After Total Elbow Arthroplasty:A Systematic Review.
Copyright © 2021 by The Journal of Bone and Joint Surgery, Incorporated.BACKGROUND: The incidence of triceps insufficiency after total elbow arthroplasty (TEA) varies in the literature, and a consensus on treatment strategy is lacking. We review the incidence, the risk factors, the clinical presentation, and the diagnosis and treatment of triceps insufficiency after TEA. Based on this information, we have formulated recommendations for clinical practice. METHODS: We performed a systematic review of the literature from January 2003 to April 2020 to identify studies that investigated triceps function following TEA by searching the PubMed, Cochrane, and Embase databases. Eligible studies (1) reported on triceps function following primary or revision TEA for every indication, regardless of technique (e.g., bone grafts), (2) included ≥6 adult patients, (3) had the full-text article available, and (4) had a minimum follow-up of 1 year. RESULTS: Eighty studies with a total of 4,825 TEAs were included. The quality was low in 15 studies, moderate in 64 studies, and high in 1 study. The mean incidence of triceps insufficiency was 4.5%. The rates were highest in patients after revision TEA (22%), in those with posttraumatic arthritis as an indication for surgery (10.2%), and after a triceps-reflecting approach (4.9%). Most studies used the Medical Research Council scale to score triceps function, although cutoff points and the definition of triceps insufficiency differed among studies. Surgical treatment showed favorable results with anconeus tendon transfer and Achilles allograft repair when compared with direct repair. CONCLUSIONS: The incidence of triceps insufficiency varies greatly, probably due to a lack of consensus on the definition of the term. Therefore, we recommend the guidelines for clinical practice that are presented in this article. These guidelines assist clinicians in providing the best possible treatment strategy for their patients and help researchers optimize their future study designs in order to compare outcomes. LEVEL OF EVIDENCE: Therapeutic Level IV. See Instructions for Authors for a complete description of levels of evidence
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