5,946 research outputs found
Automated Transit Networks (ATN): A Review of the State of the Industry and Prospects for the Future, MTI Report 12-31
The concept of Automated Transit Networks (ATN) - in which fully automated vehicles on exclusive, grade-separated guideways provide on-demand, primarily non-stop, origin-to-destination service over an area network – has been around since the 1950s. However, only a few systems are in current operation around the world. ATN does not appear “on the radar” of urban planners, transit professionals, or policy makers when it comes to designing solutions for current transit problems in urban areas. This study explains ATN technology, setting it in the larger context of Automated Guideway Transit (AGT); looks at the current status of ATN suppliers, the status of the ATN industry, and the prospects of a U.S.-based ATN industry; summarizes and organizes proceedings from the seven Podcar City conferences that have been held since 2006; documents the U.S./Sweden Memorandum of Understanding on Sustainable Transport; discusses how ATN could expand the coverage of existing transit systems; explains the opportunities and challenges in planning and funding ATN systems and approaches for procuring ATN systems; and concludes with a summary of the existing challenges and opportunities for ATN technology. The study is intended to be an informative tool for planners, urban designers, and those involved in public policy, especially for urban transit, to provide a reference for history and background on ATN, and to use for policy development and research
Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model
In this paper we give a complete analysis of the phase transitions in the
mean-field Blume-Emery-Griffiths lattice-spin model with respect to the
canonical ensemble, showing both a second-order, continuous phase transition
and a first-order, discontinuous phase transition for appropriate values of the
thermodynamic parameters that define the model. These phase transitions are
analyzed both in terms of the empirical measure and the spin per site by
studying bifurcation phenomena of the corresponding sets of canonical
equilibrium macrostates, which are defined via large deviation principles.
Analogous phase transitions with respect to the microcanonical ensemble are
also studied via a combination of rigorous analysis and numerical calculations.
Finally, probabilistic limit theorems for appropriately scaled values of the
total spin are proved with respect to the canonical ensemble. These limit
theorems include both central-limit-type theorems, when the thermodynamic
parameters are not equal to critical values, and noncentral-limit-type
theorems, when these parameters equal critical values.Comment: Published at http://dx.doi.org/10.1214/105051605000000421 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
RG/Pade Estimate of the Three-Loop Contribution to the QCD Static Potential Function
The three renormalization-group-accessible three-loop coefficients of powers
of logarithms within the \bar{MS} series momentum-space for the QCD static
potential are calculated and compared to values obtained via asymptotic
Pad\'e-approximant methods. The leading and next-to-leading logarithmic
coefficients are both found to be in exact agreement with their asymptotic
Pad\'e-predictions. The predicted value for the third RG-accessible coefficient
is found to be within 7% relative |error| of its true value for n_f leq 6, and
is shown to be in exact agreement with its true value in the n_f \to \infty
limit. Asymptotic Pad\'e estimates are also obtained for the remaining
(RG-inaccessible) three-loop coefficient. Comparison is also made with recent
estimates of the three-loop contribution to the configuration-space
static-potential function.Comment: 13 pages, LaTeX, additional discussion on the result
Asymptotic behavior of the finite-size magnetization as a function of the speed of approach to criticality
The main focus of this paper is to determine whether the thermodynamic
magnetization is a physically relevant estimator of the finite-size
magnetization. This is done by comparing the asymptotic behaviors of these two
quantities along parameter sequences converging to either a second-order point
or the tricritical point in the mean-field Blume--Capel model. We show that the
thermodynamic magnetization and the finite-size magnetization are asymptotic
when the parameter governing the speed at which the sequence
approaches criticality is below a certain threshold . However, when
exceeds , the thermodynamic magnetization converges to 0
much faster than the finite-size magnetization. The asymptotic behavior of the
finite-size magnetization is proved via a moderate deviation principle when
.
To the best of our knowledge, our results are the first rigorous confirmation
of the statistical mechanical theory of finite-size scaling for a mean-field
model.Comment: Published in at http://dx.doi.org/10.1214/10-AAP679 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Ginzburg-Landau Polynomials and the Asymptotic Behavior of the Magnetization Near Critical and Tricritical Points
For the mean-field version of an important lattice-spin model due to Blume
and Capel, we prove unexpected connections among the asymptotic behavior of the
magnetization, the structure of the phase transitions, and a class of
polynomials that we call the Ginzburg-Landau polynomials. The model depends on
the parameters n, beta, and K, which represent, respectively, the number of
spins, the inverse temperature, and the interaction strength. Our main focus is
on the asymptotic behavior of the magnetization m(beta_n,K_n) for appropriate
sequences (beta_n,K_n) that converge to a second-order point or to the
tricritical point of the model and that lie inside various subsets of the
phase-coexistence region. The main result states that as (beta_n,K_n) converges
to one of these points (beta,K), m(beta_n,K_n) ~ c |beta - beta_n|^gamma --> 0.
In this formula gamma is a positive constant, and c is the unique positive,
global minimum point of a certain polynomial g that we call the Ginzburg-Landau
polynomial. This polynomial arises as a limit of appropriately scaled
free-energy functionals, the global minimum points of which define the
phase-transition structure of the model. For each sequence (beta_n,K_n) under
study, the structure of the global minimum points of the associated
Ginzburg-Landau polynomial mirrors the structure of the global minimum points
of the free-energy functional in the region through which (beta_n,K_n) passes
and thus reflects the phase-transition structure of the model in that region.
The properties of the Ginzburg-Landau polynomials make rigorous the predictions
of the Ginzburg-Landau phenomenology of critical phenomena, and the asymptotic
formula for m(beta_n,K_n) makes rigorous the heuristic scaling theory of the
tricritical point.Comment: 70 pages, 8 figure
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