Overlap and activity glass transitions in plaquette spin models with hierarchical dynamics

We consider thermodynamic and dynamic phase transitions in plaquette spin models of glasses. The thermodynamic transitions involve coupled (annealed) replicas of the model. We map these coupled-replica systems to a single replica in a magnetic field, which allows us to analyse the resulting phase transitions in detail. For the triangular plaquette model (TPM), we find for the coupled-replica system a phase transition between high- and low-overlap phases, occuring at a coupling eps*(T), which vanishes in the low-temperature limit. Using computational path sampling techniques, we show that a single TPM also displays space-time transitions between active and inactive dynamical phases. These first-order dynamical transitions occur at a critical counting field s_c(T)>=0 that appears to vanish at zero temperature, in a manner reminiscent of the thermodynamic overlap transition. In order to extend the ideas to three dimensions we introduce the square pyramid model which also displays both overlap and activity transitions. We discuss a possible common origin of these various phase transitions, based on long-lived (metastable) glassy states.Comment: 12 pages, 9 fig

Productivity differences: the importance of intra-state black-white schooling differences across the United States, 1840-2000

Using newly created data containing real output per worker, real physical capital per worker, and human capital per worker for US states from 1840 to 2000, Turner et. al (2007) analyze the growth rates of aggregate inputs and total factor productivity (TFP). We continue this line of work by documenting the importance of TFP differences in explaining cross sectional variation in the levels of (log) output. We construct plausible upper bounds on the fraction of the variance in output levels that can be explained by TFP and inputs. Similar to the growth rate analysis, we find that TFP can, on average, explain nearly 90% of output variance while inputs can explain up to only 50% of output variance. We then consider the possibility that one major institutional difference across states, the extent to which blacks were denied access to formal education, might explain TFP differences across states. To this end, we generate and present a years of schooling measures, by race, at the state level from 1840 to 2000. While directly exploiting this series has very little impact on the upper bound of the fraction of output variation that can be explained by inputs, we do find that the size of the gap between white and black years of schooling is negatively related to TFP in the period from 1840 to 1950. We also consider the extent to which time-varying rates of return on education alters the upper bound on the fraction of output variation that can be explained by inputs, finding that time-varying rates have little impact. Finally, we find some evidence for external effects of higher education and physical capital.black-white schooling differences; state productivity differences

Prediction of the thermal environment and thermal response of simple panels exposed to radiant heat

A method of predicting the radiant heat flux distribution produced by a bank of tubular quartz heaters was applied to a radiant system consisting of a single unreflected lamp irradiating a flat metallic incident surface. In this manner, the method was experimentally verified for various radiant system parameter settings and used as a source of input for a finite element thermal analysis. Two finite element thermal analyses were applied to a thermal system consisting of a thin metallic panel exposed to radiant surface heating. A two-dimensional steady-state finite element thermal analysis algorithm, based on Galerkin's Method of Weighted Residuals (GFE), was formulated specifically for this problem and was used in comparison to the thermal analyzers of the Engineering Analysis Language (EAL). Both analyses allow conduction, convection, and radiation boundary conditions. Differences in the respective finite element formulation are discussed in terms of their accuracy and resulting comparison discrepancies. The thermal analyses are shown to perform well for the comparisons presented here with some important precautions about the various boundary condition models. A description of the experiment, corresponding analytical modeling, and resulting comparisons are presented

The prior training and experience of the supervising elementary school principal in Massachusetts and Rhode Island

Thesis (Ed.M.)--Boston Universit

Fluctuating observation time ensembles in the thermodynamics of trajectories

The dynamics of stochastic systems, both classical and quantum, can be studied by analysing the statistical properties of dynamical trajectories. The properties of ensembles of such trajectories for long, but fixed, times are described by large-deviation (LD) rate functions. These LD functions play the role of dynamical free-energies: they are cumulant generating functions for time-integrated observables, and their analytic structure encodes dynamical phase behaviour. This "thermodynamics of trajectories" approach is to trajectories and dynamics what the equilibrium ensemble method of statistical mechanics is to configurations and statics. Here we show that, just like in the static case, there is a variety of alternative ensembles of trajectories, each defined by their global constraints, with that of trajectories of fixed total time being just one of these. We show that an ensemble of trajectories where some time-extensive quantity is constant (and large) but where total observation time fluctuates, is equivalent to the fixed-time ensemble, and the LD functions that describe one ensemble can be obtained from those that describe the other. We discuss how the equivalence between generalised ensembles can be exploited in path sampling schemes for generating rare dynamical trajectories.Comment: 12 pages, 5 figure