808 research outputs found
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
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
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
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
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
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
2C-B: A New Psychoactive Phenylethylamine Recently Discovered in Ecstasy Tablets Sold on the Swiss Black Market
This study sought to identify, by means of several analytical methods (GC-MS, HPLC-DAD, CE-DAD, FTIR, and NMR), 4-bromo-2,5-dimethoxyphenethylamine (2C-B), which was found in two sets of tablets obtained from the Swiss black market. Unequivocal identification of 2C-B was only achieved by a combination of mass spectrometric and NMR analysis. Quantitation of 2C-B was performed by HPLC-DAD and CE-DAD. The amounts of 2C-B found in the tablets (3-8 mg) were in the range of the minimum quantity required to induce the effects characteristic of this dru
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 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
The frustration-based approach of supercooled liquids and the glass transition: a review and critical assessment
One of the most spectacular phenomena in physics in terms of dynamical range
is the glass transition and the associated slowing down of flow and relaxation
with decreasing temperature. That it occurs in many different liquids seems to
call for a "universal" theory. In this article, we review one such theoretical
approach which is based on the concept of "frustration". Frustration in this
context describes an incompatibility between extension of the locally preferred
order in a liquid and tiling of the whole space. We provide a critical
assessment of what has been achieved within this approach and we discuss the
relation with other theories of the glass transition.Comment: 48 pages, 13 figures, submitted to J. Phys : Cond. Matte
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