Improved Bounds on the Phase Transition for the Hard-Core Model in 2-Dimensions

For the hard-core lattice gas model defined on independent sets weighted by an activity $\lambda$, we study the critical activity $\lambda_c(\mathbb{Z}^2)$ for the uniqueness/non-uniqueness threshold on the 2-dimensional integer lattice $\mathbb{Z}^2$. The conjectured value of the critical activity is approximately $3.796$. Until recently, the best lower bound followed from algorithmic results of Weitz (2006). Weitz presented an FPTAS for approximating the partition function for graphs of constant maximum degree $\Delta$ when $\lambda<\lambda_c(\mathbb{T}_\Delta)$ where $\mathbb{T}_\Delta$ is the infinite, regular tree of degree $\Delta$. His result established a certain decay of correlations property called strong spatial mixing (SSM) on $\mathbb{Z}^2$ by proving that SSM holds on its self-avoiding walk tree $T_{\mathrm{saw}}^\sigma(\mathbb{Z}^2)$ where $\sigma=(\sigma_v)_{v\in \mathbb{Z}^2}$ and $\sigma_v$ is an ordering on the neighbors of vertex $v$. As a consequence he obtained that $\lambda_c(\mathbb{Z}^2)\geq\lambda_c( \mathbb{T}_4) = 1.675$. Restrepo et al. (2011) improved Weitz's approach for the particular case of $\mathbb{Z}^2$ and obtained that $\lambda_c(\mathbb{Z}^2)>2.388$. In this paper, we establish an upper bound for this approach, by showing that, for all $\sigma$, SSM does not hold on $T_{\mathrm{saw}}^\sigma(\mathbb{Z}^2)$ when $\lambda>3.4$. We also present a refinement of the approach of Restrepo et al. which improves the lower bound to $\lambda_c(\mathbb{Z}^2)>2.48$.Comment: 19 pages, 1 figure. Polished proofs and examples compared to earlier versio

Plasma formation from ultracold Rydberg gases

Recent experiments have demonstrated the spontaneous evolution of a gas of ultracold Rydberg atoms into an expanding ultracold plasma, as well as the reverse process of plasma recombination into highly excited atomic states. Treating the evolution of the plasma on the basis of kinetic equations, while ionization/excitation and recombination are incorporated using rate equations, we have investigated theoretically the Rydberg-to-plasma transition. Including the influence of spatial correlations on the plasma dynamics in an approximate way we find that ionic correlations change the results only quantitatively but not qualitatively

A Study of Bus Stop Accessibility: Public Health Students Working in Partnership with the Center for Independent Living

Over 54 million U.S. citizens report living with at least one disability. The Americans with Disabilities Act stipulates legislation that prohibits the discrimination of persons on the basis of disability. Rather than riding the bus in areas that offer a fixed-route bus system, individuals with disabilities often rely on expensive and limited paratransit services, or on family and friends. It has been proposed that with improvements in bus accessibility, riders with disabilities could use the fixed-route system more often and increase their options for independence and community participation. During their 2008 spring semester, participants in the University of Florida College of Public Health and Health Professions’ course, Assessment and Surveillance, partnered with the Center for Independent Living (CIL) of North Central Florida to conduct an accessibility study of the Gainesville, Florida fixed-route bus system. Students focused on factors that make bus stops user-friendly for persons with disabilities. This paper presents the rationale, methods, and findings from this accessibility study and efforts undertaken to forge a mutually beneficial partnership among UF-PHHP students and the CIL

Modelling Urban Housing Stocks for Building Energy Simulation using CityGML EnergyADE

Understanding the energy demand of a city’s housing stock is an important focus for local and national administrations to identify strategies for reducing carbon emissions. Building energy simulation offers a promising approach to understand energy use and test plans to improve the efficiency of residential properties. As part of this, models of the urban stock must be created that accurately reflect its size, shape and composition. However, substantial effort is required in order to generate detailed urban scenes with the appropriate level of attribution suitable for spatially explicit simulation of large areas. Furthermore, the computational complexity of microsimulation of building energy necessitates consideration of approaches that reduce this processing overhead. We present a workflow to automatically generate 2.5D urban scenes for residential building energy simulation from UK mapping datasets. We describe modelling the geometry, the assignment of energy characteristics based upon a statistical model and adopt the CityGML EnergyADE schema which forms an important new and open standard for defining energy model information at the city-scale. We then demonstrate use of the resulting urban scenes for estimating heating demand using a spatially explicit building energy microsimulation tool, called CitySim+, and evaluate the effects of an off-the-shelf geometric simplification routine to reduce simulation computational complexity

Magnetic trapping of metastable 3P2^3P_2 atomic strontium

We report the magnetic trapping of metastable $^3P_2$ atomic strontium. Atoms are cooled in a magneto-optical trap (MOT) operating on the dipole allowed $^1S_0-^1P_1$ transition at 461 nm. Decay via $^1P_1\to {^1D_2}\to {^3P_2}$ continuously loads a magnetic trap formed by the quadrupole magnetic field of the MOT. Over $10^8$ atoms at a density of $8 \times 10^9$ cm$^{-3}$ and temperature of 1 mK are trapped. The atom temperature is significantly lower than what would be expected from the kinetic and potential energy of atoms as they are transferred from the MOT. This suggests that thermalization and evaporative cooling are occurring in the magnetic trap.Comment: This paper has been accepted by PR

Probing Primordial Non-Gaussianity with Large-Scale Structure

We consider primordial non-Gaussianity due to quadratic corrections in the gravitational potential parametrized by a non-linear coupling parameter fnl. We study constraints on fnl from measurements of the galaxy bispectrum in redshift surveys. Using estimates for idealized survey geometries of the 2dF and SDSS surveys and realistic ones from SDSS mock catalogs, we show that it is possible to probe |fnl|~100, after marginalization over bias parameters. We apply our methods to the galaxy bispectrum measured from the PSCz survey, and obtain a 2sigma-constraint |fnl|< 1800. We estimate that an all sky redshift survey up to z~1 can probe |fnl|~1. We also consider the use of cluster abundance to constrain fnl and find that in order to be sensitive to |fnl|~100, cluster masses need to be determined with an accuracy of a few percent, assuming perfect knowledge of the mass function and cosmological parameters.Comment: 15 pages, 7 figure

An entomocentric view of the Janzen-Connell hypothesis

In 1987, in the first issue of Conservation Biology, Edward O. Wilson wrote about the “little things that run the world” – the importance and conservation of insects (Wilson, 1987). Readers of Insect Conservation and Diversity will no doubt be very familiar with the concept. Sadly, however, this perception is not as widely shared among the rest of the scientific community as it should be, and insects are still comparatively neglected as a prime focus of scientific investigations

Ω-Arithmetization of Ellipses

International audienceMulti-resolution analysis and numerical precision problems are very important subjects in fields like image analysis or geometrical modeling. In the continuation of our previous works, we propose to apply the method of Ω-arithmetization to ellipses. We obtain a discrete multi-resolution representation of arcs of ellipses. The corresponding algorithms are completely constructive and thus, can be exactly translated into functional computer programs. Moreover, we give a global condition for the connectivity of the discrete curves generated by the method at every scale

Finite Temperature Properties of Quantum Antiferromagnets in a Uniform Magnetic Field in One and Two Dimensions

Consider a $d$-dimensional antiferromagnet with a quantum disordered ground state and a gap to bosonic excitations with non-zero spin. In a finite external magnetic field, this antiferromagnet will undergo a phase transition to a ground state with non-zero magnetization, describable as the condensation of a dilute gas of bosons. The finite temperature properties of the Bose gas in the vicinity of this transition are argued to obey a hypothesis of ZERO SCALE-FACTOR UNIVERSALITY for $d < 2$, with logarithmic violations in $d=2$. Scaling properties of various experimental observables are computed in an expansion in $\epsilon=2-d$, and exactly in $d=1$.Comment: 27 pages, REVTEX 3.0, 8 Postscript figures appended, YCTP-xyz