1,937 research outputs found
Planar lattice gases with nearest-neighbour exclusion
We discuss the hard-hexagon and hard-square problems, as well as the
corresponding problem on the honeycomb lattice. The case when the activity is
unity is of interest to combinatorialists, being the problem of counting binary
matrices with no two adjacent 1's. For this case we use the powerful corner
transfer matrix method to numerically evaluate the partition function per site,
density and some near-neighbour correlations to high accuracy. In particular
for the square lattice we obtain the partition function per site to 43 decimal
places.Comment: 16 pages, 2 built-in Latex figures, 4 table
Comment on `Series expansions from the corner transfer matrix renormalization group method: the hard-squares model'
Earlier this year Chan extended the low-density series for the hard-squares
partition function to 92 terms. Here we analyse this extended
series focusing on the behaviour at the dominant singularity which lies
on on the negative fugacity axis. We find that the series has a confluent
singularity of order 2 at with exponents and
. We thus confirm that the exponent has the exact
value as observed by Dhar.Comment: 5 pages, 1 figure, IoP macros. Expanded second and final versio
Family intentions of women with one child : an Armidale study
This study is concerned with the family intentions of married
women in Armidale, a medium sized country town in northern New
South Wales. The surveyed women had their first baby in 1976, a
year when the two child family was the preference of a majority of
Australian women. Previously recorded differentials in family
size such as religion, age at marriage and education had narrowed
to the point where they were barely measurable. The study focuses
on fertility in an extra metropolitan area, the timing of the first
birth after marriage as a life cycle event, the spacing of further
children and the ultimate family size anticipated
A study of logarithmic corrections and universal amplitude ratios in the two-dimensional 4-state Potts model
Monte Carlo (MC) and series expansion (SE) data for the energy, specific
heat, magnetization and susceptibility of the two-dimensional 4-state Potts
model in the vicinity of the critical point are analysed. The role of
logarithmic corrections is discussed and an approach is proposed in order to
account numerically for these corrections in the determination of critical
amplitudes. Accurate estimates of universal amplitude ratios ,
, and are given, which arouse
new questions with respect to previous works
Particle motion and stain removal during simulated abrasive tooth cleaning
Stain removal from teeth is important both to prevent decay and for appearance. This is usually achieved using a filament-based toothbrush with a toothpaste consisting of abrasive particles in a carrier fluid. This work has been carried out to examine how these abrasive particles interact with the filaments and cause material removal from a stain layer on the surface of a tooth. It is important to understand this mechanism as while maximum cleaning efficiency is required, this must not be accompanied by damage to the enamel or dentine substrate. In this work simple abrasive scratch tests were used to investigate stain removal mechanism of two abrasive particles commonly used in tooth cleaning, silica and perlite. Silica particles are granular in shape and very different to perlite particles, which are flat and have thicknesses many times smaller than their width. Initially visualisation studies were carried out with perlite particles to study how they are entrained into a filament/counterface contact. Results were compared with previous studies using silica. Reciprocating scratch tests were then run to study how many filaments have a particle trapped at one moment and are involved in the cleaning process. Stain removal tests were then carried out in a similar manner to establish cleaning rates with the two particle types. Perlite particles were found to be less abrasive than silica. This was because of their shape and how they were entrained into the filament contacts and loaded against a counterface. With both particles subsurface damage during stain removal was found to be minimal. A simple model was built to predict stain removal rates with silica particles, which gave results that correlated well with the experimental data
Universal ratios of critical amplitudes in the Potts model universality class
Monte Carlo (MC) simulations and series expansions (SE) data for the energy,
specific heat, magnetization, and susceptibility of the three-state and
four-state Potts model and Baxter-Wu model on the square lattice are analyzed
in the vicinity of the critical point in order to estimate universal
combinations of critical amplitudes. We also form effective ratios of the
observables close to the critical point and analyze how they approach the
universal critical-amplitude ratios. In particular, using the duality relation,
we show analytically that for the Potts model with a number of states ,
the effective ratio of the energy critical amplitudes always approaches unity
linearly with respect to the reduced temperature. This fact leads to the
prediction of relations among the amplitudes of correction-to-scaling terms of
the specific heat in the low- and high-temperature phases. It is a common
belief that the four-state Potts and the Baxter-Wu model belong to the same
universality class. At the same time, the critical behavior of the four-state
Potts model is modified by logarithmic corrections while that of the Baxter-Wu
model is not. Numerical analysis shows that critical amplitude ratios are very
close for both models and, therefore, gives support to the hypothesis that the
critical behavior of both systems is described by the same renormalization
group fixed point.Comment: Talk presented at CCP 2008, Ouro Preto, 5-9 August 200
Spanning tree generating functions and Mahler measures
We define the notion of a spanning tree generating function (STGF) , which gives the spanning tree constant when evaluated at and gives
the lattice Green function (LGF) when differentiated. By making use of known
results for logarithmic Mahler measures of certain Laurent polynomials, and
proving new results, we express the STGFs as hypergeometric functions for all
regular two and three dimensional lattices (and one higher-dimensional
lattice). This gives closed form expressions for the spanning tree constants
for all such lattices, which were previously largely unknown in all but one
three-dimensional case. We show for all lattices that these can also be
represented as Dirichlet -series. Making the connection between spanning
tree generating functions and lattice Green functions produces integral
identities and hypergeometric connections, some of which appear to be new.Comment: 26 pages. Dedicated to F Y Wu on the occasion of his 80th birthday.
This version has additional references, additional calculations, and minor
correction
Directed Branched Polymer near an Attractive Line
We study the adsorption-desorption phase transition of directed branched
polymer in dimensions in contact with a line by mapping it to a
dimensional hard core lattice gas at negative activity. We solve the model
exactly in 1+1 dimensions, and calculate the crossover exponent related to
fraction of monomers adsorbed at the critical point of surface transition, and
we also determine the density profile of the polymer in different phases. We
also obtain the value of crossover exponent in 2+1 dimensions and give the
scaling function of the sticking fraction for 1+1 and 2+1 dimensional directed
branched polymer.Comment: 19 pages, 4 figures, accepted for publication in J. Phys. A:Math. Ge
Thermodynamics of a finite system of classical particles with short and long range interactions and nuclear fragmentation
We describe a finite inhomogeneous three dimensional system of classical
particles which interact through short and (or) long range interactions by
means of a simple analytic spin model. The thermodynamic properties of the
system are worked out in the framework of the grand canonical ensemble. It is
shown that the system experiences a phase transition at fixed average density
in the thermodynamic limit. The phase diagram and the caloric curve are
constructed and compared with numerical simulations. The implications of our
results concerning the caloric curve are discussed in connection with the
interpretation of corresponding experimental data.Comment: 11pages, LaTeX, 6 figures. Major change : A new section dealing with
numerical simulations in the framework of a cellular model has been adde
Identification of a functionally essential amino acid for Arabidopsis cyclic nucleotide gated ion channels using the chimeric AtCNGC11/12 gene
We used the chimeric Arabidopsis cyclic nucleotide-gated ion channel AtCNGC11/12 to conduct a structure-function study of plant cyclic nucleotide-gated ion channels (CNGCs). AtCNGC11/12 induces multiple pathogen resistance responses in the Arabidopsis mutant constitutive expresser of PR genes 22 (cpr22). A genetic screen for mutants that suppress cpr22-conferred phenotypes identified an intragenic mutant, #73, which has a glutamate to lysine substitution (E519K) at the beginning of the eighth β-sheet of the cyclic nucleotide-binding domain in AtCNGC11/12. The #73 mutant is morphologically identical to wild-type plants and has lost cpr22-related phenotypes including spontaneous cell death and enhanced pathogen resistance. Heterologous expression analysis using a K+-uptake-deficient yeast mutant revealed that this Glu519 is important for AtCNGC11/12 channel function, proving that the occurrence of cpr22 phenotypes requires active channel function of AtCNGC11/12. Additionally, Glu519 was also found to be important for the function of the wild-type channel AtCNGC12. Computational structural modeling and in vitro cAMP-binding assays suggest that Glu519 is a key residue for the structural stability of AtCNGCs and contributes to the interaction of the cyclic nucleotide-binding domain and the C-linker domain, rather than the binding of cAMP. Furthermore, a mutation in the α-subunit of the human cone receptor CNGA3 that causes total color blindness aligned well to the position of Glu519 in AtCNGC11/12. This suggests that AtCNGC11/12 suppressors could be a useful tool for discovering important residues not only for plant CNGCs but also for CNGCs in general. © 2008 The Authors
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