2,008 research outputs found
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
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
Surface and bulk transitions in three-dimensional O(n) models
Using Monte Carlo methods and finite-size scaling, we investigate surface
criticality in the O models on the simple-cubic lattice with , 2, and
3, i.e. the Ising, XY, and Heisenberg models. For the critical couplings we
find and . We
simulate the three models with open surfaces and determine the surface magnetic
exponents at the ordinary transition to be ,
, and for , 2, and 3, respectively. Then we vary
the surface coupling and locate the so-called special transition at
and , where
. The corresponding surface thermal and magnetic exponents are
and for the Ising
model, and and for
the XY model. Finite-size corrections with an exponent close to -1/2 occur for
both models. Also for the Heisenberg model we find substantial evidence for the
existence of a special surface transition.Comment: TeX paper and 10 eps figure
Scaling in the vicinity of the four-state Potts fixed point
We study a self-dual generalization of the Baxter-Wu model, employing results
obtained by transfer matrix calculations of the magnetic scaling dimension and
the free energy. While the pure critical Baxter-Wu model displays the critical
behavior of the four-state Potts fixed point in two dimensions, in the sense
that logarithmic corrections are absent, the introduction of different
couplings in the up- and down triangles moves the model away from this fixed
point, so that logarithmic corrections appear. Real couplings move the model
into the first-order range, away from the behavior displayed by the
nearest-neighbor, four-state Potts model. We also use complex couplings, which
bring the model in the opposite direction characterized by the same type of
logarithmic corrections as present in the four-state Potts model. Our
finite-size analysis confirms in detail the existing renormalization theory
describing the immediate vicinity of the four-state Potts fixed point.Comment: 19 pages, 7 figure
Transfer-Matrix Monte Carlo Estimates of Critical Points in the Simple Cubic Ising, Planar and Heisenberg Models
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm
are discussed. Enhancements of this algorithm are illustrated by applications
to several phase transitions in lattice spin models. We demonstrate how the
statistical noise can be reduced considerably by a similarity transformation of
the transfer matrix using a variational estimate of its leading eigenvector, in
analogy with a common practice in various quantum Monte Carlo techniques. Here
we take the two-dimensional coupled -Ising model as an example.
Furthermore, we calculate interface free energies of finite three-dimensional
O() models, for the three cases , 2 and 3. Application of finite-size
scaling to the numerical results yields estimates of the critical points of
these three models. The statistical precision of the estimates is satisfactory
for the modest amount of computer time spent
Optimal Levels of Inputs to Control Listeria monocytogenes Contamination at a Smoked Fish Plant
Reducing the incidence of listeriosis from contaminated food has significant social health benefits, but reduction requires the use of additional or higher quality inputs at higher costs. We estimate the impact of three inputs in a food processing plant on the prevalence of L. monocytogenes contaminated finished cold smoked salmon. These three inputs were non-contamination of the raw fish fillets, non-contamination of the plant environment, and rate of glove changes on workers. We then estimate the levels of these inputs to use such that the marginal cost of these inputs become equal to the increased social health benefit of reduction in human listeriosis. Since the costs of these inputs are borne by the food processing plant, which may not be able to secure a higher product price because of asymmetric information, we show how social sub-optimal use of these inputs may result.Food Consumption/Nutrition/Food Safety,
Automotive Stirling Engine Development Program
Activities performed on Mod I engine testing and test results; the manufacture, assembly, and test of a Mod I engine in the United States; design initiation of the Mod I-A engine system; transient performance testing; Stirling reference engine manufacturing and reduced size studies; components and subsystems; and the study and test of low cost alloys are summarized
High-growth firms: introduction to the special section
High-growth firms (HGFs) have attracted considerable attention recently, as academics and policymakers have increasingly recognized the highly skewed nature of many metrics of firm performance. A small number of HGFs drives a disproportionately large amount of job creation, while the average firm has a limited impact on the economy. This article explores the reasons for this increased interest, summarizes the existing literature, and highlights the methodological considerations that constrain and bias research. This special section draws attention to the importance of HGFs for future industrial performance, explores their unusual growth trajectories and strategies, and highlights the lack of persistence of high growth. Consequently, while HGFs are important for understanding the economy and developing public policy, they are unlikely to be useful vehicles for public policy given the difficulties involved in predicting which firms will grow, the lack of persistence in high growth levels, and the complex and often indirect relationship between firm capability, high growth, and macro-economic performance
Specific heat of the simple-cubic Ising model
We provide an expression quantitatively describing the specific heat of the
Ising model on the simple-cubic lattice in the critical region. This expression
is based on finite-size scaling of numerical results obtained by means of a
Monte Carlo method. It agrees satisfactorily with series expansions and with a
set of experimental results. Our results include a determination of the
universal amplitude ratio of the specific-heat divergences at both sides of the
critical point.Comment: 20 pages, 3 figure
Automotive Stirling Engine Development Program
Mod I engine testing and test results, the test of a Mod I engine in the United States, Mod I engine characterization and analysis, Mod I Transient Test Bed fuel economy, Mod I-A engine performance are discussed. Stirling engine reference engine manufacturing and reduced size studies, components and subsystems, and the study and test of low-cost casting alloys are also covered. The overall program philosophy is outlined, and data and results are presented
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