1,613 research outputs found
Monte Carlo computation of correlation times of independent relaxation modes at criticality
We investigate aspects of universality of Glauber critical dynamics in two
dimensions. We compute the critical exponent and numerically corroborate
its universality for three different models in the static Ising universality
class and for five independent relaxation modes. We also present evidence for
universality of amplitude ratios, which shows that, as far as dynamic behavior
is concerned, each model in a given universality class is characterized by a
single non-universal metric factor which determines the overall time scale.
This paper also discusses in detail the variational and projection methods that
are used to compute relaxation times with high accuracy
Who Receives Specialist Palliative Care in Western Australia - and Who Misses Out
Our research describes the provision of palliative care services at a time of transition.Typically, palliative care has offered a holistic, non-curative focus with an emphasis on improving the quality of life of people with life-limiting conditions. Traditionally it has aimed to improve the conditions of people who were dying of cancer. Palliative care now seeks to extend a holistic, team-based and family-centred approach to people with other life-limiting conditions. Until now the degree to which this aim was reflected in the actual provision of health services has been unclear. There has been a paucity of population-based data on which to base equitable healthcare decision-making regarding the extension of palliative care topeople suffering from a range of life-limiting, complex and painful conditions. Our study provides such data for Western Australia and provides an insight into who is missing out on palliative care services in the last year of life
Exact critical points of the O() loop model on the martini and the 3-12 lattices
We derive the exact critical line of the O() loop model on the martini
lattice as a function of the loop weight .A finite-size scaling analysis
based on transfer matrix calculations is also performed.The numerical results
coincide with the theoretical predictions with an accuracy up to 9 decimal
places. In the limit , this gives the exact connective constant
of self-avoiding walks on the martini lattice. Using
similar numerical methods, we also study the O() loop model on the 3-12
lattice. We obtain similarly precise agreement with the exact critical points
given by Batchelor [J. Stat. Phys. 92, 1203 (1998)].Comment: 4 pages, 3 figures, 2 table
Improved Phenomenological Renormalization Schemes
An analysis is made of various methods of phenomenological renormalization
based on finite-size scaling equations for inverse correlation lengths, the
singular part of the free energy density, and their derivatives. The analysis
is made using two-dimensional Ising and Potts lattices and the
three-dimensional Ising model. Variants of equations for the phenomenological
renormalization group are obtained which ensure more rapid convergence than the
conventionally used Nightingale phenomenological renormalization scheme. An
estimate is obtained for the critical finite-size scaling amplitude of the
internal energy in the three-dimensional Ising model. It is shown that the
two-dimensional Ising and Potts models contain no finite-size corrections to
the internal energy so that the positions of the critical points for these
models can be determined exactly from solutions for strips of finite width. It
is also found that for the two-dimensional Ising model the scaling finite-size
equation for the derivative of the inverse correlation length with respect to
temperature gives the exact value of the thermal critical exponent.Comment: 14 pages with 1 figure in late
Numerical Studies of the Two Dimensional XY Model with Symmetry Breaking Fields
We present results of numerical studies of the two dimensional XY model with
four and eight fold symmetry breaking fields. This model has recently been
shown to describe hydrogen induced reconstruction on the W(100) surface. Based
on mean-field and renormalization group arguments,we first show how the
interplay between the anisotropy fields can give rise to different phase
transitions in the model. When the fields are compatible with each other there
is a continuous phase transition when the fourth order field is varied from
negative to positive values. This transition becomes discontinuous at low
temperatures. These two regimes are separated by a multicritical point. In the
case of competing four and eight fold fields, the first order transition at low
temperatures opens up into two Ising transitions. We then use numerical methods
to accurately locate the position of the multicritical point, and to verify the
nature of the transitions. The different techniques used include Monte Carlo
histogram methods combined with finite size scaling analysis, the real space
Monte Carlo Renormalization Group method, and the Monte Carlo Transfer Matrix
method. Our numerical results are in good agreement with the theoretical
arguments.Comment: 29 pages, HU-TFT-94-36, to appear in Phys. Rev. B, Vol 50, November
1, 1994. A LaTeX file with no figure
Conformal invariance and linear defects in the two-dimensional Ising model
Using conformal invariance, we show that the non-universal exponent eta_0
associated with the decay of correlations along a defect line of modified bonds
in the square-lattice Ising model is related to the amplitude A_0=xi_n/n of the
correlation length \xi_n(K_c) at the bulk critical coupling K_c, on a strip
with width n, periodic boundary conditions and two equidistant defect lines
along the strip, through A_0=(\pi\eta_0)^{-1}.Comment: Old paper, for archiving. 5 pages, 4 figures, IOP macro, eps
Wetting of a symmetrical binary fluid mixture on a wall
We study the wetting behaviour of a symmetrical binary fluid below the
demixing temperature at a non-selective attractive wall. Although it demixes in
the bulk, a sufficiently thin liquid film remains mixed. On approaching
liquid/vapour coexistence, however, the thickness of the liquid film increases
and it may demix and then wet the substrate. We show that the wetting
properties are determined by an interplay of the two length scales related to
the density and the composition fluctuations. The problem is analysed within
the framework of a generic two component Ginzburg-Landau functional
(appropriate for systems with short-ranged interactions). This functional is
minimized both numerically and analytically within a piecewise parabolic
potential approximation. A number of novel surface transitions are found,
including first order demixing and prewetting, continuous demixing, a
tricritical point connecting the two regimes, or a critical end point beyond
which the prewetting line separates a strongly and a weakly demixed film. Our
results are supported by detailed Monte Carlo simulations of a symmetrical
binary Lennard-Jones fluid at an attractive wall.Comment: submitted to Phys. Rev.
Measuring elastic nonlinearity in a soft solid using a tilted acoustic radiation force for shear wave excitation
Excitation of multiple wave modes using shear wave elastography can result in additional information about the tissue's material characteristics and, potentially, improve disease diagnosis. Theoretically, tilting the acoustic radiation force excitation axis with respect to the material's symmetry axis should excite several wave modes in the material. In this work, we have experimentally demonstrated proof of concept in a uniaxially stretched phantom, while increasing the stretch level. Tilted acoustic radiation force experiments showed a clearly visible second wave mode across the stretch direction for larger stretches (>160%)
Monte Carlo Determination of Multiple Extremal Eigenpairs
We present a Monte Carlo algorithm that allows the simultaneous determination
of a few extremal eigenpairs of a very large matrix without the need to compute
the inner product of two vectors or store all the components of any one vector.
The new algorithm, a Monte Carlo implementation of a deterministic one we
recently benchmarked, is an extension of the power method. In the
implementation presented, we used a basic Monte Carlo splitting and termination
method called the comb, incorporated the weight cancellation method of Arnow
{\it et al.}, and exploited a new sampling method, the sewing method, that does
a large state space sampling as a succession of small state space samplings. We
illustrate the effectiveness of the algorithm by its determination of the two
largest eigenvalues of the transfer matrices for variously-sized
two-dimensional, zero field Ising models. While very likely useful for other
transfer matrix problems, the algorithm is however quite general and should
find application to a larger variety of problems requiring a few dominant
eigenvalues of a matrix.Comment: 22 pages, no figure
On the Symmetry of Universal Finite-Size Scaling Functions in Anisotropic Systems
In this work a symmetry of universal finite-size scaling functions under a
certain anisotropic scale transformation is postulated. This transformation
connects the properties of a finite two-dimensional system at criticality with
generalized aspect ratio to a system with . The symmetry
is formulated within a finite-size scaling theory, and expressions for several
universal amplitude ratios are derived. The predictions are confirmed within
the exactly solvable weakly anisotropic two-dimensional Ising model and are
checked within the two-dimensional dipolar in-plane Ising model using Monte
Carlo simulations. This model shows a strongly anisotropic phase transition
with different correlation length exponents parallel
and perpendicular to the spin axis.Comment: RevTeX4, 4 pages, 3 figure
- …