208 research outputs found
Minimal knotted polygons in cubic lattices
An implementation of BFACF-style algorithms on knotted polygons in the simple
cubic, face centered cubic and body centered cubic lattice is used to estimate
the statistics and writhe of minimal length knotted polygons in each of the
lattices. Data are collected and analysed on minimal length knotted polygons,
their entropy, and their lattice curvature and writhe
The Compressibility of Minimal Lattice Knots
The (isothermic) compressibility of lattice knots can be examined as a model
of the effects of topology and geometry on the compressibility of ring
polymers. In this paper, the compressibility of minimal length lattice knots in
the simple cubic, face centered cubic and body centered cubic lattices are
determined. Our results show that the compressibility is generally not
monotonic, but in some cases increases with pressure. Differences of the
compressibility for different knot types show that topology is a factor
determining the compressibility of a lattice knot, and differences between the
three lattices show that compressibility is also a function of geometry.Comment: Submitted to J. Stat. Mec
Paediatric cardiac anaesthesia in sickle cell disease : a case series
Sickle cell disease (SCD) is the most common inherited haematological disorder, producing a mutation of the haemoglobin molecule known as haemoglobin S (HbS). The presence of HbS in the erythrocyte makes it prone to sickling - a process which may lead to vaso-occlusive injury, haemolysis and a hypercoagulable state. Sickling is precipitated by dehydration, hypoxia, hypothermia, acidosis and low flow states. Over time, multi-organ damage develops with significant morbidity and mortality. Paediatric patients with SCD and congenital heart defects may require anaesthesia for corrective cardiac surgery on cardiopulmonary bypass (CPB). During the perioperative period these high-risk patients may suffer significant complications when exposed to the conditions that favour erythrocyte sickling. This case series details our experience of four paediatric patients with SCD patients who underwent corrective cardiac surgery at Red Cross War Memorial Children’s Hospital. The pathophysiology is discussed and the perioperative management of transfusion, cardiopulmonary bypass and temperature regulation is highlighted
Partially directed paths in a wedge
The enumeration of lattice paths in wedges poses unique mathematical
challenges. These models are not translationally invariant, and the absence of
this symmetry complicates both the derivation of a functional recurrence for
the generating function, and solving for it. In this paper we consider a model
of partially directed walks from the origin in the square lattice confined to
both a symmetric wedge defined by , and an asymmetric wedge defined
by the lines and Y=0, where is an integer. We prove that the
growth constant for all these models is equal to , independent of
the angle of the wedge. We derive functional recursions for both models, and
obtain explicit expressions for the generating functions when . From these
we find asymptotic formulas for the number of partially directed paths of
length in a wedge when .
The functional recurrences are solved by a variation of the kernel method,
which we call the ``iterated kernel method''. This method appears to be similar
to the obstinate kernel method used by Bousquet-Melou. This method requires us
to consider iterated compositions of the roots of the kernel. These
compositions turn out to be surprisingly tractable, and we are able to find
simple explicit expressions for them. However, in spite of this, the generating
functions turn out to be similar in form to Jacobi -functions, and have
natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT
A simple model of a vesicle drop in a confined geometry
We present the exact solution of a two-dimensional directed walk model of a
drop, or half vesicle, confined between two walls, and attached to one wall.
This model is also a generalisation of a polymer model of steric stabilisation
recently investigated. We explore the competition between a sticky potential on
the two walls and the effect of a pressure-like term in the system. We show
that a negative pressure ensures the drop/polymer is unaffected by confinement
when the walls are a macroscopic distance apart
Forcing Adsorption of a Tethered Polymer by Pulling
We present an analysis of a partially directed walk model of a polymer which
at one end is tethered to a sticky surface and at the other end is subjected to
a pulling force at fixed angle away from the point of tethering. Using the
kernel method, we derive the full generating function for this model in two and
three dimensions and obtain the respective phase diagrams.
We observe adsorbed and desorbed phases with a thermodynamic phase transition
in between. In the absence of a pulling force this model has a second-order
thermal desorption transition which merely gets shifted by the presence of a
lateral pulling force. On the other hand, if the pulling force contains a
non-zero vertical component this transition becomes first-order.
Strikingly, we find that if the angle between the pulling force and the
surface is beneath a critical value, a sufficiently strong force will induce
polymer adsorption, no matter how large the temperature of the system.
Our findings are similar in two and three dimensions, an additional feature
in three dimensions being the occurrence of a reentrance transition at constant
pulling force for small temperature, which has been observed previously for
this model in the presence of pure vertical pulling. Interestingly, the
reentrance phenomenon vanishes under certain pulling angles, with details
depending on how the three-dimensional polymer is modeled
Incidence of heat-labile enterotoxin-producing Escherichia coli detected by means of polymerase chain reaction amplification
CITATION: Winterbach, R. et al. 1994. Incidence of heat-labile enterotoxin-producing Escherichia coli detected by means of polymerase chain reaction amplification. South African Medical Journal, 84:85-87.The original publication is available at http://www.samj.org.zaDiarrhoea can be caused by many different organisms, some of which are notoriously difficult to identify. One of these is enterotoxin-producing Escherichia coli. Recently a new diagnostic technique that uses polymerase chain reaction DNA amplification was developed for detection of the 'A' subunit of the labile enterotoxin-producing E. coli gene. This technique was used to evaluate the incidence of heat-labile (LT+) enterotoxin-producing E. coli in the causation of diarrhoea. The results from this study showed that LT+ E. coli is a cause of diarrhoea in the western Cape and that 5,3% of non-diagnosed diarrhoea patients in Tygerberg Hospital were infected with this pathogen. This represented less than 1% of the total number of cases of diarrhoea investigated in this hospital. The peak coincides with the wetter months in this locality and the infection rate is lower than that reported in most other countries. Given the low incidence of occurrence of this organism we do not recommend routine implementation of the diagnostic procedure. However, this test may be useful at times, e.g. to ascertain the source of a diarrhoea epidemic.Publisher’s versio
Fresh look at randomly branched polymers
We develop a new, dynamical field theory of isotropic randomly branched
polymers, and we use this model in conjunction with the renormalization group
(RG) to study several prominent problems in the physics of these polymers. Our
model provides an alternative vantage point to understand the swollen phase via
dimensional reduction. We reveal a hidden Becchi-Rouet-Stora (BRS) symmetry of
the model that describes the collapse (-)transition to compact
polymer-conformations, and calculate the critical exponents to 2-loop order. It
turns out that the long-standing 1-loop results for these exponents are not
entirely correct. A runaway of the RG flow indicates that the so-called
-transition could be a fluctuation induced first order
transition.Comment: 4 page
Collapsing lattice animals and lattice trees in two dimensions
We present high statistics simulations of weighted lattice bond animals and
lattice trees on the square lattice, with fugacities for each non-bonded
contact and for each bond between two neighbouring monomers. The simulations
are performed using a newly developed sequential sampling method with
resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used
for linear chain polymers. We determine with high precision the line of second
order transitions from an extended to a collapsed phase in the resulting
2-dimensional phase diagram. This line includes critical bond percolation as a
multicritical point, and we verify that this point divides the line into two
different universality classes. One of them corresponds to the collapse driven
by contacts and includes the collapse of (weakly embeddable) trees, but the
other is {\it not yet} bond driven and does not contain the Derrida-Herrmann
model as special point. Instead it ends at a multicritical point where a
transition line between two collapsed phases (one bond-driven and the other
contact-driven) sparks off. The Derrida-Herrmann model is representative for
the bond driven collapse, which then forms the fourth universality class on the
transition line (collapsing trees, critical percolation, intermediate regime,
and Derrida-Herrmann). We obtain very precise estimates for all critical
exponents for collapsing trees. It is already harder to estimate the critical
exponents for the intermediate regime. Finally, it is very difficult to obtain
with our method good estimates of the critical parameters of the
Derrida-Herrmann universality class. As regards the bond-driven to
contact-driven transition in the collapsed phase, we have some evidence for its
existence and rough location, but no precise estimates of critical exponents.Comment: 11 pages, 16 figures, 1 tabl
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