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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 (âBuilt on Beowulfâ), 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 âon the flyâ 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 codesâthe 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 HeldâSuarez test case, which involves 18 levels in the vertical. BOB also shows a significantly smaller memory footprint in these comparison tests
The effect of 'Astressin', a novel antagonist of corticotropin releasing hormone (CRH), on CRH-induced seizures in the infant rat: comparison with two other antagonists.
Corticotropin releasing hormone (CRH) has both neuroendocrine effects, promoting ACTH release from the anterior pituitary, and neurotransmitter properties, acting on specific neuronal populations. A recently designed CRH analogue has been shown to be highly potent in preventing activation of pituitary CRH receptors. The efficacy of this compound, 'Astressin', in blocking the effects of CRH in the central nervous system (CNS) has not been determined. CRH induces prolonged amygdala-origin seizures in neonatal and infant rats. This model was used in the current study, to compare Astressin to alpha-helical CRH-(9-41), and to [D-Phe12, Nle21.38, C-MeLeu37]CRH-(12-41), i.e. D-Phe-CRH-(12-41). Astressin (3 or 10 micrograms) was infused into the cerebral ventricles of infant rats prior to CRH infusion. Both doses of the analogue significantly delayed the onset of CRH-induced seizures when given 15, but not 30 min before CRH. No effect of the lower Astressin dose on seizure duration was demonstrated; the higher dose prevented seizures in 2/12 rats, and delayed seizure onset in the others (22.7 +/- 5 min vs 10.1 +/- 1.3 min). In the same paradigm, 10 micrograms of alpha-helical CRH-(9-41) and 5 micrograms of D-Phe-CRH-(12-41) had comparable effects on seizure latency and duration. Electroencephalograms confirmed the behavioral effects of Astressin. Therefore, in a CNS model of CRH-mediated neurotransmission, the potency of Astressin is not substantially higher than that of alpha-helical CRH (9-41) and D-Phe-CRH-(12-41)
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
Statistical Mechanics of Two-dimensional Foams
The methods of statistical mechanics are applied to two-dimensional foams
under macroscopic agitation. A new variable -- the total cell curvature -- is
introduced, which plays the role of energy in conventional statistical
thermodynamics. The probability distribution of the number of sides for a cell
of given area is derived. This expression allows to correlate the distribution
of sides ("topological disorder") to the distribution of sizes ("geometrical
disorder") in a foam. The model predictions agree well with available
experimental data
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
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
Analysis of signalling pathways using continuous time Markov chains
We describe a quantitative modelling and analysis approach for signal transduction networks.
We illustrate the approach with an example, the RKIP inhibited ERK pathway [CSK+03]. Our models are high level descriptions of continuous time Markov chains: proteins are modelled by synchronous processes and reactions by transitions. Concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis such as what is the probability that if a concentration reaches a certain level, it will remain at that level thereafter? or how does varying a given reaction rate affect that probability? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable
Analysis of Dislocation Mechanism for Melting of Elements
The melting of elemental solids is modelled as a dislocation-mediated
transition on a lattice. Statistical mechanics of linear defects is used to
obtain a new relation between melting temperature, crystal structure, atomic
volume, and shear modulus that is accurate to 17% for at least half of the
Periodic Table.Comment: 8 pages, LaTeX, to appear in Solid State Com
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
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