Do Binary Hard Disks Exhibit an Ideal Glass Transition?

We demonstrate that there is no ideal glass transition in a binary hard-disk mixture by explicitly constructing an exponential number of jammed packings with densities spanning the spectrum from the accepted ``amorphous'' glassy state to the phase-separated crystal. Thus the configurational entropy cannot be zero for an ideal amorphous glass, presumed distinct from the crystal in numerous theoretical and numerical estimates in the literature. This objection parallels our previous critique of the idea that there is a most-dense random (close) packing for hard spheres [Torquato et al, Phys. Rev. Lett., 84, 2064 (2000)].Comment: Submitted for publicatio

Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator

In this and subsequent paper arXiv:1011.5185 we develop a recursive approach for calculating the short-time expansion of the propagator for a general quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used to substantially speed up numerical Monte Carlo simulations for path integrals, or to set up various analytic approximation techniques to study properties of quantum systems in time-dependent potentials. The analytically derived results are numerically verified by treating several simple models.Comment: 29 pages, 5 figure

Fermat's principle of least time in the presence of uniformly moving boundaries and media

The refraction of a light ray by a homogeneous, isotropic and non-dispersive transparent material half-space in uniform rectilinear motion is investigated theoretically. The approach is an amalgamation of the original Fermat's principle and the fact that an isotropic optical medium at rest becomes optically anisotropic in a frame where the medium is moving at a constant velocity. Two cases of motion are considered: a) the material half-space is moving parallel to the interface; b) the material half-space is moving perpendicular to the interface. In each case, a detailed analysis of the obtained refraction formula is provided, and in the latter case, an intriguing backward refraction of light is noticed and thoroughly discussed. The results confirm the validity of Fermat's principle when the optical media and the boundaries between them are moving at relativistic speeds.Comment: 11 pages, 6 figures, RevTeX 4, comments welcome; V2: revised, Fig. 7 added; V3: several typos corrected, accepted for publication in European Journal of Physics (online at: http://stacks.iop.org/EJP/28/933

Efficient Reactive Brownian Dynamics

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and disassociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion, and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as Reaction-Diffusion Master Equation (RDME) algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction- and diffusion-limited irreversible association in three dimensions. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. We find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.Comment: To appear in J. Chem. Phy

Alloy*: A Higher-Order Relational Constraint Solver

The last decade has seen a dramatic growth in the use of constraint solvers as a computational mechanism, not only for analysis and synthesis of software, but also at runtime. Solvers are available for a variety of logics but are generally restricted to first-order formulas. Some tasks, however, most notably those involving synthesis, are inherently higher order; these are typically handled by embedding a first-order solver (such as a SAT or SMT solver) in a domain-specific algorithm. Using strategies similar to those used in such algorithms, we show how to extend a first-order solver (in this case Kodkod, a model finder for relational logic used as the engine of the Alloy Analyzer) so that it can handle quantifications over higher-order structures. The resulting solver is sufficiently general that it can be applied to a range of problems; it is higher order, so that it can be applied directly, without embedding in another algorithm; and it performs well enough to be competitive with specialized tools on standard benchmarks. Although the approach is demonstrated for a particular relational logic, the principles behind it could be applied to other first-order solvers. Just as the identification of first-order solvers as reusable backends advanced the performance of specialized tools and simplified their architecture, factoring out higher-ordersolvers may bring similar benefits to a new class of tools

Time trend and clinical pattern of extrapulmonary tuberculosis in Serbia, 1993-2007

Background/Aim. Increased incidence of extrapulmonary tuberculosis (XPTB) is reported worldwide. Serbia is a country in socio-economic transition period with lowmiddle HIV prevalence and intermediate-to-low tuberculosis (TB) incidence rate, 100% directly observed treatment (DOT) coverage, and mandatory BCG vaccination at birth. The aim of the study was to examine the incidence trend and clinical features of XPTB in Serbia during a 15-year period. Methods. This retrospective observational study included XPTB cases diagnosed in the period between 1st January 1993 and 31st Decembre 2007, according to the reports of the National Referral Institute of Lung Diseases and Tuberculosis in Belgrade and Central Tuberculosis Register. Population estimates with extrapolations were based on 1991 and 2002 census data. Results. While the overall TB incidence rate showed a slight, not significant decreasing trend (p = 0.535), a significant increase was found for XPTB (y = 1.7996 + 0.089x; R2 = 0.4141; p = 0.01). A total of 2,858 XPTB cases (newly diagnosed and 10% relapses) gave an average age specific incidence rate of 2.51/100,000 population (95% confidence interval, SD = 0.6182) with 8.9% annual increase. The male-to-female ratio was 0.54. Lymph nodes were most frequently affected site (48.5%) followed by genitourinary (20.5%), pleural (12%), and osseo-arthicular (10.3%) TB. Treatment outcome was successful in 88.29% of patients (cured and completed), 3.64% died, 5.18% interrupted, 0.57% displaced, and 2.3% unknown. Conclusion. Increasing trend of XPTB incidence rate may be a result of increased morbidity due to still present risk factors, possible higher detection rate in Serbia and better notification. A high coverage of newborns with BCG vaccination at birth might contribute to a decreased number and rare XPTB cases in children

Dependent Types for Pragmatics

This paper proposes the use of dependent types for pragmatic phenomena such as pronoun binding and presupposition resolution as a type-theoretic alternative to formalisms such as Discourse Representation Theory and Dynamic Semantics.Comment: This version updates the paper for publication in LEU

A spectral density approach for modelling continuous vertical forces on pedestrian structures due to walking

Existing walking models used for vibration serviceability assessment of structures carrying pedestrians are typically based on measurements of single footfalls replicated at precise intervals. This assumed perfect periodicity allows walking forces to be modelled as a Fourier series based on the walking pace and its integer multiples. This paper examines real continuous walking forces obtained from an instrumented treadmill and the effect of their random imperfections through time simulations of structural response and shows that there are significant differences between responses due to the imperfect real walking forces and the equivalent perfectly periodic simulation. These differences are most significant for higher harmonics where the simulated vibration response is overestimated. As a realistic representation of imperfect walking is an auto-spectral density function, the random character naturally leads to a stochastic approach to treatment of pedestrian loading applied in the frequency domain. The approach can be used for single pedestrians as well as crowd loading where correlation between pedestrians as well as statistics of their pacing rates is used