1,532 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
Universal Dynamics of Independent Critical Relaxation Modes
Scaling behavior is studied of several dominant eigenvalues of spectra of
Markov matrices and the associated correlation times governing critical slowing
down in models in the universality class of the two-dimensional Ising model. A
scheme is developed to optimize variational approximants of progressively
rapid, independent relaxation modes. These approximants are used to reduce the
variance of results obtained by means of an adaptation of a quantum Monte Carlo
method to compute eigenvalues subject to errors predominantly of statistical
nature. The resulting spectra and correlation times are found to be universal
up to a single, non-universal time scale for each model
Collaborating With Parents of Children With Chronic Conditions and Professionals to Design, Develop and Pre-pilot PLAnT (the Parent Learning Needs and Preferences Assessment Tool)
© 2017 Elsevier Inc. Purpose This study aimed to design, develop and pre-pilot an assessment tool (PLAnT) to identify parents' learning needs and preferences when carrying out home-based clinical care for their child with a chronic condition. Design and Methods A mixed methods, two-phased design was used. Phase 1: a total of 10 parents/carers and 13 professionals from six UK's children's kidney units participated in qualitative interviews. Interview data were used to develop the PLAnT. Eight of these participants subsequently took part in an online survey to refine the PLAnT. Phase 2: thirteen parents were paired with one of nine professionals to undertake a pre-pilot evaluation of PLAnT. Data were analyzed using the Framework approach. Results A key emergent theme identifying parents' learning needs and preferences was identified. The importance of professionals being aware of parents' learning needs and preferences was recognised. Participants discussed how parents' learning needs and preferences should be identified, including: the purpose for doing this, the process for doing this, and what would the outcome be of identifying parents' needs. Conclusions The evidence suggests that asking parents directly about their learning needs and preferences may be the most reliable way for professionals to ascertain how to support individual parents' learning when sharing management of their child's chronic condition. Practice Implications With the increasing emphasis on parent-professional shared management of childhood chronic conditions, professionals can be guided by PLAnT in their assessment of parents' learning needs and preferences, based on identified barriers and facilitators to parental learning
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
Critical line of an n-component cubic model
We consider a special case of the n-component cubic model on the square
lattice, for which an expansion exists in Ising-like graphs. We construct a
transfer matrix and perform a finite-size-scaling analysis to determine the
critical points for several values of n. Furthermore we determine several
universal quantities, including three critical exponents. For n<2, these
results agree well with the theoretical predictions for the critical O(n)
branch. This model is also a special case of the () model of
Domany and Riedel. It appears that the self-dual plane of the latter model
contains the exactly known critical points of the n=1 and 2 cubic models. For
this reason we have checked whether this is also the case for 1<n<2. However,
this possibility is excluded by our numerical results
The Dynamic Exponent of the Two-Dimensional Ising Model and Monte Carlo Computation of the Sub-Dominant Eigenvalue of the Stochastic Matrix
We introduce a novel variance-reducing Monte Carlo algorithm for accurate
determination of autocorrelation times. We apply this method to two-dimensional
Ising systems with sizes up to , using single-spin flip dynamics,
random site selection and transition probabilities according to the heat-bath
method. From a finite-size scaling analysis of these autocorrelation times, the
dynamical critical exponent is determined as (12)
Critical temperature of a fully anisotropic three-dimensional Ising model
The critical temperature of a three-dimensional Ising model on a simple cubic
lattice with different coupling strengths along all three spatial directions is
calculated via the transfer matrix method and a finite size scaling for L x L
oo clusters (L=2 and 3). The results obtained are compared with available
calculations. An exact analytical solution is found for the 2 x 2 oo Ising
chain with fully anisotropic interactions (arbitrary J_x, J_y and J_z).Comment: 17 pages in tex using preprint.sty for IOP journals, no figure
Automotive Stirling Engine Development Program
Development test activities on Mod I engines directed toward evaluating technologies for potential inclusion in the Mod II engine are summarized. Activities covered include: test of a 12-tube combustion gas recirculation combustor; manufacture and flow-distribution test of a two-manifold annular heater head; piston rod/piston base joint; single-solid piston rings; and a digital air/fuel concept. Also summarized are results of a formal assessment of candidate technologies for the Mod II engine, and preliminary design work for the Mod II. The overall program philosophy weight is outlined, and data and test results are presented
Potts and percolation models on bowtie lattices
We give the exact critical frontier of the Potts model on bowtie lattices.
For the case of , the critical frontier yields the thresholds of bond
percolation on these lattices, which are exactly consistent with the results
given by Ziff et al [J. Phys. A 39, 15083 (2006)]. For the Potts model on
the bowtie-A lattice, the critical point is in agreement with that of the Ising
model on this lattice, which has been exactly solved. Furthermore, we do
extensive Monte Carlo simulations of Potts model on the bowtie-A lattice with
noninteger . Our numerical results, which are accurate up to 7 significant
digits, are consistent with the theoretical predictions. We also simulate the
site percolation on the bowtie-A lattice, and the threshold is
. In the simulations of bond percolation and site
percolation, we find that the shape-dependent properties of the percolation
model on the bowtie-A lattice are somewhat different from those of an isotropic
lattice, which may be caused by the anisotropy of the lattice.Comment: 18 pages, 9 figures and 3 table
Hyperuniversality of Fully Anisotropic Three-Dimensional Ising Model
For the fully anisotropic simple-cubic Ising lattice, the critical
finite-size scaling amplitudes of both the spin-spin and energy-energy inverse
correlation lengths and the singular part of the reduced free-energy density
are calculated by the transfer-matrix method and a finite-size scaling for
cyclic L x L x oo clusters with L=3 and 4. Analysis of the data obtained shows
that the ratios and the directional geometric means of above amplitudes are
universal.Comment: RevTeX 3.0, 24 pages, 2 figures upon request, accepted for
publication in Phys. Rev.
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