62 research outputs found
Corrections to scaling for percolative conduction: anomalous behavior at small L
Recently Grassberger has shown that the correction to scaling for the
conductance of a bond percolation network on a square lattice is a nonmonotonic
function of the linear lattice dimension with a minimum at , while this
anomalous behavior is not present in the site percolation networks. We perform
a high precision numerical study of the bond percolation random resistor
networks on the square, triangular and honeycomb lattices to further examine
this result. We use the arithmetic, geometric and harmonic means to obtain the
conductance and find that the qualitative behavior does not change: it is not
related to the shape of the conductance distribution for small system sizes. We
show that the anomaly at small L is absent on the triangular and honeycomb
networks. We suggest that the nonmonotonic behavior is an artifact of
approximating the continuous system for which the theory is formulated by a
discrete one which can be simulated on a computer. We show that by slightly
changing the definition of the linear lattice size we can eliminate the minimum
at small L without significantly affecting the large L limit.Comment: 3 pages, 4 figures;slightly expanded, 2 figures added. Accepted for
publishing in Phys. Rev.
Critical Percolation in High Dimensions
We present Monte Carlo estimates for site and bond percolation thresholds in
simple hypercubic lattices with 4 to 13 dimensions. For d<6 they are
preliminary, for d >= 6 they are between 20 to 10^4 times more precise than the
best previous estimates. This was achieved by three ingredients: (i) simple and
fast hashing which allowed us to simulate clusters of millions of sites on
computers with less than 500 MB memory; (ii) a histogram method which allowed
us to obtain information for several p values from a single simulation; and
(iii) a new variance reduction technique which is especially efficient at high
dimensions where it reduces error bars by a factor up to approximately 30 and
more. Based on these data we propose a new scaling law for finite cluster size
corrections.Comment: 5 pages including figures, RevTe
Universal features of the order-parameter fluctuations : reversible and irreversible aggregation
We discuss the universal scaling laws of order parameter fluctuations in any
system in which the second-order critical behaviour can be identified. These
scaling laws can be derived rigorously for equilibrium systems when combined
with the finite-size scaling analysis. The relation between order parameter,
criticality and scaling law of fluctuations has been established and the
connexion between the scaling function and the critical exponents has been
found. We give examples in out-of-equilibrium aggregation models such as the
Smoluchowski kinetic equations, or of at-equilibrium Ising and percolation
models.Comment: 19 pages, 10 figure
Universality and Critical Phenomena in String Defect Statistics
The idea of biased symmetries to avoid or alleviate cosmological problems
caused by the appearance of some topological defects is familiar in the context
of domain walls, where the defect statistics lend themselves naturally to a
percolation theory description, and for cosmic strings, where the proportion of
infinite strings can be varied or disappear entirely depending on the bias in
the symmetry. In this paper we measure the initial configurational statistics
of a network of string defects after a symmetry-breaking phase transition with
initial bias in the symmetry of the ground state. Using an improved algorithm,
which is useful for a more general class of self-interacting walks on an
infinite lattice, we extend the work in \cite{MHKS} to better statistics and a
different ground state manifold, namely , and explore various different
discretisations. Within the statistical errors, the critical exponents of the
Hagedorn transition are found to be quite possibly universal and identical to
the critical exponents of three-dimensional bond or site percolation. This
improves our understanding of the percolation theory description of defect
statistics after a biased phase transition, as proposed in \cite{MHKS}. We also
find strong evidence that the existence of infinite strings in the Vachaspati
Vilenkin algorithm is generic to all (string-bearing) vacuum manifolds, all
discretisations thereof, and all regular three-dimensional lattices.Comment: 62 pages, plain LaTeX, macro mathsymb.sty included, figures included.
also available on
http://starsky.pcss.maps.susx.ac.uk/groups/pt/preprints/96/96011.ps.g
Instability of vortex array and transitions to turbulent states in rotating helium II
We consider superfluid helium inside a container which rotates at constant
angular velocity and investigate numerically the stability of the array of
quantized vortices in the presence of an imposed axial counterflow. This
problem was studied experimentally by Swanson {\it et al.}, who reported
evidence of instabilities at increasing axial flow but were not able to explain
their nature. We find that Kelvin waves on individual vortices become unstable
and grow in amplitude, until the amplitude of the waves becomes large enough
that vortex reconnections take place and the vortex array is destabilized. The
eventual nonlinear saturation of the instability consists of a turbulent tangle
of quantized vortices which is strongly polarized. The computed results compare
well with the experiments. Finally we suggest a theoretical explanation for the
second instability which was observed at higher values of the axial flow
Molecular interactions of the plasma membrane calcium ATPase 2 at pre- and post-synaptic sites in rat cerebellum.
The plasma membrane calcium extrusion mechanism, PMCA (plasma membrane calcium ATPase) isoform 2 is richly expressed in the brain and particularly the cerebellum. Whilst PMCA2 is known to interact with a variety of proteins to participate in important signalling events [Strehler EE, Filoteo AG, Penniston JT, Caride AJ (2007) Plasma-membrane Ca(2+) pumps: structural diversity as the basis for functional versatility. Biochem Soc Trans 35 (Pt 5):919-922], its molecular interactions in brain synapse tissue are not well understood. An initial proteomics screen and a biochemical fractionation approach identified PMCA2 and potential partners at both pre- and post-synaptic sites in synapse-enriched brain tissue from rat. Reciprocal immunoprecipitation and GST pull-down approaches confirmed that PMCA2 interacts with the post-synaptic proteins PSD95 and the NMDA glutamate receptor subunits NR1 and NR2a, via its C-terminal PDZ (PSD95/Dlg/ZO-1) binding domain. Since PSD95 is a well-known partner for the NMDA receptor this raises the exciting possibility that all three interactions occur within the same post-synaptic signalling complex. At the pre-synapse, where PMCA2 was present in the pre-synapse web, reciprocal immunoprecipitation and GST pull-down approaches identified the pre-synaptic membrane protein syntaxin-1A, a member of the SNARE complex, as a potential partner for PMCA2. Both PSD95-PMCA2 and syntaxin-1A-PMCA2 interactions were also detected in the molecular and granule cell layers of rat cerebellar sagittal slices by immunohistochemistry. These specific molecular interactions at cerebellar synapses may allow PMCA2 to closely control local calcium dynamics as part of pre- and post-synaptic signalling complexes
Noisy random resistor networks: renormalized field theory for the multifractal moments of the current distribution
We study the multifractal moments of the current distribution in randomly
diluted resistor networks near the percolation treshold. When an external
current is applied between to terminals and of the network, the
th multifractal moment scales as , where is the correlation length exponent of
the isotropic percolation universality class. By applying our concept of master
operators [Europhys. Lett. {\bf 51}, 539 (2000)] we calculate the family of
multifractal exponents for to two-loop order. We find
that our result is in good agreement with numerical data for three dimensions.Comment: 30 pages, 6 figure
Various Models for Pion Probability Distributions from Heavy-Ion Collisions
Various models for pion multiplicity distributions produced in relativistic
heavy ion collisions are discussed. The models include a relativistic
hydrodynamic model, a thermodynamic description, an emitting source pion laser
model, and a description which generates a negative binomial description. The
approach developed can be used to discuss other cases which will be mentioned.
The pion probability distributions for these various cases are compared.
Comparison of the pion laser model and Bose-Einstein condensation in a laser
trap and with the thermal model are made. The thermal model and hydrodynamic
model are also used to illustrate why the number of pions never diverges and
why the Bose-Einstein correction effects are relatively small. The pion
emission strength of a Poisson emitter and a critical density
are connected in a thermal model by , and this fact
reduces any Bose-Einstein correction effects in the number and number
fluctuation of pions. Fluctuations can be much larger than Poisson in the pion
laser model and for a negative binomial description. The clan representation of
the negative binomial distribution due to Van Hove and Giovannini is discussed
using the present description. Applications to CERN/NA44 and CERN/NA49 data are
discussed in terms of the relativistic hydrodynamic model.Comment: 12 pages, incl. 3 figures and 4 tables. You can also download a
PostScript file of the manuscript from
http://p2hp2.lanl.gov/people/schlei/eprint.htm
Rotating inclined cylinder and the effect of the tilt angle on vortices
We study numerically some possible vortex configurations in a rotating
cylinder that is tilted with respect to the rotation axis and where different
numbers of vortices can be present at given rotation velocity. In a long
cylinder at small tilt angles the vortices tend to align along the cylinder
axis and not along the rotation axis. We also show that the axial flow along
the cylinder axis, caused by the tilt, will result in the Ostermeier-Glaberson
instability above some critical tilt angle. When the vortices become unstable
the final state often appears to be a dynamical steady state, which may contain
turbulent regions where new vortices are constantly created. These new vortices
push other vortices in regions with laminar flow towards the top and bottom
ends of the cylinder where they finally annihilate. Experimentally the inclined
cylinder could be a convenient environment to create long lasting turbulence
with a polarization which can be adjusted with the tilt angle.Comment: 10 pages, 10 figure
Highly optimized tolerance in epidemic models incorporating local optimization and regrowth
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