1,198 research outputs found
Geometric partition functions of cellular systems: Explicit calculation of the entropy in two and three dimensions
A method is proposed for the characterisation of the entropy of cellular
structures, based on the compactivity concept for granular packings.
Hamiltonian-like volume functions are constructed both in two and in three
dimensions, enabling the identification of a phase space and making it possible
to take account of geometrical correlations systematically. Case studies are
presented for which explicit calculations of the mean vertex density and
porosity fluctuations are given as functions of compactivity. The formalism
applies equally well to two- and three-dimensional granular assemblies.Comment: 14 pages, 4 figures, to appear in The European Physical Journal E -
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An Efficient Spectral Dynamical Core for Distributed Memory Computers
The practical question of whether the classical spectral transform method, widely used in atmospheric modeling, can be efficiently implemented on inexpensive commodity clusters is addressed. Typically, such clusters have limited cache and memory sizes. To demonstrate that these limitations can be overcome, the authors have built a spherical general circulation model dynamical core, called BOB (“Built on Beowulf”), which can solve either the shallow water equations or the atmospheric primitive equations in pressure coordinates.
That BOB is targeted for computing at high resolution on modestly sized and priced commodity clusters is reflected in four areas of its design. First, the associated Legendre polynomials (ALPs) are computed “on the fly” using a stable and accurate recursion relation. Second, an identity is employed that eliminates the storage of the derivatives of the ALPs. Both of these algorithmic choices reduce the memory footprint and memory bandwidth requirements of the spectral transform. Third, a cache-blocked and unrolled Legendre transform achieves a high performance level that resists deterioration as resolution is increased. Finally, the parallel implementation of BOB is transposition-based, employing load-balanced, one-dimensional decompositions in both latitude and wavenumber.
A number of standard tests is used to compare BOB's performance to two well-known codes—the Parallel Spectral Transform Shallow Water Model (PSTSWM) and the dynamical core of NCAR's Community Climate Model CCM3. Compared to PSTSWM, BOB shows better timing results, particularly at the higher resolutions where cache effects become important. BOB also shows better performance in its comparison with CCM3's dynamical core. With 16 processors, at a triangular spectral truncation of T85, it is roughly five times faster when computing the solution to the standard Held–Suarez test case, which involves 18 levels in the vertical. BOB also shows a significantly smaller memory footprint in these comparison tests
From one cell to the whole froth: a dynamical map
We investigate two and three-dimensional shell-structured-inflatable froths,
which can be constructed by a recursion procedure adding successive layers of
cells around a germ cell. We prove that any froth can be reduced into a system
of concentric shells. There is only a restricted set of local configurations
for which the recursive inflation transformation is not applicable. These
configurations are inclusions between successive layers and can be treated as
vertices and edges decorations of a shell-structure-inflatable skeleton. The
recursion procedure is described by a logistic map, which provides a natural
classification into Euclidean, hyperbolic and elliptic froths. Froths tiling
manifolds with different curvature can be classified simply by distinguishing
between those with a bounded or unbounded number of elements per shell, without
any a-priori knowledge on their curvature. A new result, associated with
maximal orientational entropy, is obtained on topological properties of natural
cellular systems. The topological characteristics of all experimentally known
tetrahedrally close-packed structures are retrieved.Comment: 20 Pages Tex, 11 Postscript figures, 1 Postscript tabl
On Random Bubble Lattices
We study random bubble lattices which can be produced by processes such as
first order phase transitions, and derive characteristics that are important
for understanding the percolation of distinct varieties of bubbles. The results
are relevant to the formation of topological defects as they show that infinite
domain walls and strings will be produced during appropriate first order
transitions, and that the most suitable regular lattice to study defect
formation in three dimensions is a face centered cubic lattice. Another
application of our work is to the distribution of voids in the large-scale
structure of the universe. We argue that the present universe is more akin to a
system undergoing a first-order phase transition than to one that is
crystallizing, as is implicit in the Voronoi foam description. Based on the
picture of a bubbly universe, we predict a mean coordination number for the
voids of 13.4. The mean coordination number may also be used as a tool to
distinguish between different scenarios for structure formation.Comment: several modifications including new abstract, comparison with froth
models, asymptotics of coordination number distribution, further discussion
of biased defects, and relevance to large-scale structur
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
Topological correlations in soap froths
Correlation in two-dimensional soap froth is analysed with an effective
potential for the first time. Cells with equal number of sides repel (with
linear correlation) while cells with different number of sides attract (with
NON-bilinear) for nearest neighbours, which cannot be explained by the maximum
entropy argument. Also, the analysis indicates that froth is correlated up to
the third shell neighbours at least, contradicting the conventional ideas that
froth is not strongly correlated.Comment: 10 Pages LaTeX, 6 Postscript figure
Validity and responsiveness of the French version of the Örebro musculoskeletal pain screening questionnaire in chronic low back pain
The assessment of a broad range of biopsychosocial aspects is important in the rehabilitation of patients with chronic low back pain (CLBP) for the prediction of outcome as well as for evaluation. The objective of this study was to test the responsiveness, construct validity and predictive value of the A-rebro Musculoskeletal Pain Screening Questionnaire (OMPSQ) compared to other instruments widely used to assess biopsychosocial aspects in patients with CLBP.
111 patients with CLBP admitted to an inpatient rehabilitation completed a set of questionnaires on biopsychosocial aspects at baseline and at discharge. Ninety-eight patients responded at three months for an assessment of the return to work status. Responsiveness of the OMPSQ, the ability to detect change in the construct of interest, was investigated by a set of hypotheses on correlations with widely used questionnaires. We tested the hypothesis that the changes in the OMPSQ would vary along with the responses in the Patient's Global Impression of Change. Prediction of disability at discharge, work status at three months and time to return to work was evaluated with linear, logistic and cox regression models.
The OMPSQ showed good predictive values for disability and return to work and construct validity of the instrument was corroborated. Seventy-nine percent of our hypotheses for responsiveness could be confirmed, with the OMPSQ showing the second highest change during the rehabilitation.
The OMPSQ can also be applied in patients with CLBP, but for the assessment of change in psychosocial variables one should add specific questionnaires
Process algebra modelling styles for biomolecular processes
We investigate how biomolecular processes are modelled in process algebras, focussing on chemical reactions. We consider various modelling styles and how design decisions made in the definition of the process algebra have an impact on how a modelling style can be applied. Our goal is to highlight the often implicit choices that modellers make in choosing a formalism, and illustrate, through the use of examples, how this can affect expressability as well as the type and complexity of the analysis that can be performed
The Suprafroth (Superconducting Froth)
The structure and dynamics of froths have been subjects of intense interest
due to the desire to understand the behaviour of complex systems where
topological intricacy prohibits exact evaluation of the ground state. The
dynamics of a traditional froth involves drainage and drying in the cell
boundaries, thus it is irreversible. We report a new member to the froths
family: suprafroth, in which the cell boundaries are superconducting and the
cell interior is normal phase. Despite very different microscopic origin,
topological analysis of the structure of the suprafroth shows that statistical
von Neumann and Lewis laws apply. Furthermore, for the first time in the
analysis of froths there is a global measurable property, the magnetic moment,
which can be directly related to the suprafroth structure. We propose that this
suprafroth is a new, model system for the analysis of the complex physics of
two-dimensional froths
Space-time defects and teleparallelism
We consider the class of space-time defects investigated by Puntigam and
Soleng. These defects describe space-time dislocations and disclinations
(cosmic strings), and are in close correspondence to the actual defects that
arise in crystals and metals. It is known that in such materials dislocations
and disclinations require a small and large amount of energy, respectively, to
be created. The present analysis is carried out in the context of the
teleparallel equivalent of general relativity (TEGR). We evaluate the
gravitational energy of these space-time defects in the framework of the TEGR
and find that there is an analogy between defects in space-time and in
continuum material systems: the total gravitational energy of space-time
dislocations and disclinations (considered as idealized defects) is zero and
infinit, respectively.Comment: 22 pages, no figures, to appear in the Class. Quantum Gravit
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