27,943 research outputs found
Clusters and Recurrence in the Two-Dimensional Zero-Temperature Stochastic Ising Model
We analyze clustering and (local) recurrence of a standard Markov process
model of spatial domain coarsening. The continuous time process, whose state
space consists of assignments of +1 or -1 to each site in , is the
zero-temperature limit of the stochastic homogeneous Ising ferromagnet (with
Glauber dynamics): the initial state is chosen uniformly at random and then
each site, at rate one, polls its 4 neighbors and makes sure it agrees with the
majority, or tosses a fair coin in case of a tie. Among the main results
(almost sure, with respect to both the process and initial state) are: clusters
(maximal domains of constant sign) are finite for times , but the
cluster of a fixed site diverges (in diameter) as ; each of the
two constant states is (positive) recurrent. We also present other results and
conjectures concerning positive and null recurrence and the role of absorbing
states.Comment: 16 pages, 1 figur
Two-Dimensional Scaling Limits via Marked Nonsimple Loops
We postulate the existence of a natural Poissonian marking of the double
(touching) points of SLE(6) and hence of the related continuum nonsimple loop
process that describes macroscopic cluster boundaries in 2D critical
percolation. We explain how these marked loops should yield continuum versions
of near-critical percolation, dynamical percolation, minimal spanning trees and
related plane filling curves, and invasion percolation. We show that this
yields for some of the continuum objects a conformal covariance property that
generalizes the conformal invariance of critical systems. It is an open problem
to rigorously construct the continuum objects and to prove that they are indeed
the scaling limits of the corresponding lattice objects.Comment: 25 pages, 5 figure
Interfaces (and Regional Congruence?) in Spin Glasses
We present a general theorem restricting properties of interfaces between
thermodynamic states and apply it to the spin glass excitations observed
numerically by Krzakala-Martin and Palassini-Young in spatial dimensions d=3
and 4. We show that such excitations, with interface dimension smaller than d,
cannot yield regionally congruent thermodynamic states. More generally, zero
density interfaces of translation-covariant excitations cannot be pinned (by
the disorder) in any d but rather must deflect to infinity in the thermodynamic
limit. Additional consequences concerning regional congruence in spin glasses
and other systems are discussed.Comment: 4 pages (ReVTeX); 1 figure; submitted to Physical Review Letter
The Economic Returns to Membership of a Dairy Discussion Group: Evidence from the Irish National Farm Survey
In December 2009 the Irish Department of Agriculture launched the Dairy Efficiency Programme. The Programme, which is operated through a series of discussion groups, is designed to promote technology transfer to dairy farmers. Drawing on National Farm Survey data from 2009, the purpose of this paper is to quantify the economic return to membership of dairy discussion groups. An endogenous switching regression model is specified for over 300 dairy farms to assess the impact of discussion group participation on farm gross margins. The results indicate self-selection into discussion groups, suggesting that âbetterâ farmers tend to participate. Generally, younger farmers who operate larger farms are more likely to join discussion groups. Discussion group members have higher gross margins than non-members, but non-members could increase their gross margins if they join discussion groups. Overall, the findings confirm positive returns to discussion group membership, thus supporting the Dairy Efficiency Programme.Endogenous switching regression model, Discussion group membership, Dairy Efficiency Programme, Livestock Production/Industries,
The design and development of transonic multistage compressors
The development of the transonic multistage compressor is reviewed. Changing trends in design and performance parameters are noted. These changes are related to advances in compressor aerodynamics, computational fluid mechanics and other enabling technologies. The parameters normally given to the designer and those that need to be established during the design process are identified. Criteria and procedures used in the selection of these parameters are presented. The selection of tip speed, aerodynamic loading, flowpath geometry, incidence and deviation angles, blade/vane geometry, blade/vane solidity, stage reaction, aerodynamic blockage, inlet flow per unit annulus area, stage/overall velocity ratio, and aerodynamic losses are considered. Trends in these parameters both spanwise and axially through the machine are highlighted. The effects of flow mixing and methods for accounting for the mixing in the design process are discussed
The role of financing frictions in agricultural investment decisions: an analysis pre and post financial crisis
This paper uses a fundamental Q model of investment to consider the role played by financing frictions in agricultural investment decisions, controlling econometrically for censoring, heterogeneity and errors-in-variables. Our findings suggest that farmer's investment decisions are not driven by market fundamentals. We find some evidence that debt overhang restricts investment but investment is not dependent on liquidity or internal funds. The role of financing frictions in determining investment decisions changes in the post-financial crisis period when debt overhang becomes a significant impediment to farm investment. The evidence suggests that farmers increasingly rely on internal liquidity to drive investment. Finally, we find no evidence that farmers use on-farm capital to fund on-farm investment.Credit Constraints, Firm Level Investment, Tobin's Q, Debt, Agricultural Finance, G31, G32, F34,
The Effect of Pure State Structure on Nonequilibrium Dynamics
Motivated by short-range Ising spin glasses, we review some rigorous results
and their consequences for the relation between the number/nature of
equilibrium pure states and nonequilibrium dynamics. Two of the consequences
for spin glass dynamics following a deep quench to a temperature with broken
spin flip symmetry are: (1) Almost all initial configurations lie on the
boundary between the basins of attraction of multiple pure states. (2) Unless
there are uncountably many pure states with almost all pairs having zero
overlap, there can be no equilibration to a pure state as time goes to
infinity. We discuss the relevance of these results to the difficulty of
equilibration of spin glasses. We also review some results concerning the
``nature vs. nurture'' problem of whether the large-time behavior of both
ferromagnets and spin glasses following a deep quench is determined more by the
initial configuration or by the dynamics realization.Comment: 20 page
Assembling thefacebook: Using heterogeneity to understand online social network assembly
Online social networks represent a popular and diverse class of social media
systems. Despite this variety, each of these systems undergoes a general
process of online social network assembly, which represents the complicated and
heterogeneous changes that transform newly born systems into mature platforms.
However, little is known about this process. For example, how much of a
network's assembly is driven by simple growth? How does a network's structure
change as it matures? How does network structure vary with adoption rates and
user heterogeneity, and do these properties play different roles at different
points in the assembly? We investigate these and other questions using a unique
dataset of online connections among the roughly one million users at the first
100 colleges admitted to Facebook, captured just 20 months after its launch. We
first show that different vintages and adoption rates across this population of
networks reveal temporal dynamics of the assembly process, and that assembly is
only loosely related to network growth. We then exploit natural experiments
embedded in this dataset and complementary data obtained via Internet
archaeology to show that different subnetworks matured at different rates
toward similar end states. These results shed light on the processes and
patterns of online social network assembly, and may facilitate more effective
design for online social systems.Comment: 13 pages, 11 figures, Proceedings of the 7th Annual ACM Web Science
Conference (WebSci), 201
Matching Kasteleyn Cities for Spin Glass Ground States
As spin glass materials have extremely slow dynamics, devious numerical
methods are needed to study low-temperature states. A simple and fast
optimization version of the classical Kasteleyn treatment of the Ising model is
described and applied to two-dimensional Ising spin glasses. The algorithm
combines the Pfaffian and matching approaches to directly strip droplet
excitations from an excited state. Extended ground states in Ising spin glasses
on a torus, which are optimized over all boundary conditions, are used to
compute precise values for ground state energy densities.Comment: 4 pages, 2 figures; minor clarification
Mean-field solution of the small-world network model
The small-world network model is a simple model of the structure of social
networks, which simultaneously possesses characteristics of both regular
lattices and random graphs. The model consists of a one-dimensional lattice
with a low density of shortcuts added between randomly selected pairs of
points. These shortcuts greatly reduce the typical path length between any two
points on the lattice. We present a mean-field solution for the average path
length and for the distribution of path lengths in the model. This solution is
exact in the limit of large system size and either large or small number of
shortcuts.Comment: 14 pages, 2 postscript figure
- âŠ