A unified framework for Schelling's model of segregation

Schelling's model of segregation is one of the first and most influential models in the field of social simulation. There are many variations of the model which have been proposed and simulated over the last forty years, though the present state of the literature on the subject is somewhat fragmented and lacking comprehensive analytical treatments. In this article a unified mathematical framework for Schelling's model and its many variants is developed. This methodology is useful in two regards: firstly, it provides a tool with which to understand the differences observed between models; secondly, phenomena which appear in several model variations may be understood in more depth through analytic studies of simpler versions.Comment: 21 pages, 3 figure

Multiple Hard Partonic Collisions with Correlations in Proton-Proton Scattering

We propose a simple method for incorporating correlations into the impact parameter space description of multiple (semi-)hard partonic collisions in high energy hadron-hadron scattering. The perturbative QCD input is the standard factorization theorem for inclusive dijet production with a lower cutoff on transverse momentum. The width of the transverse distribution of hard partons is fixed by parameterizations of the two-gluon form factor. We then reconstruct the hard contribution to the total inelastic profile function and obtain corrections due to correlations to the more commonly used eikonal description. Estimates of the size of double correlation corrections are based on the rate of double collisions measured at the Tevatron. We find that, if typical values for the lower transverse momentum cutoff are used in the calculation of the inclusive hard dijet cross section, then the correlation corrections are necessary for maintaining consistency with expectations for the total inelastic proton-proton cross section at LHC energies.Comment: Typos fixed, Figures 2,9 and 10 added, matches version published in Phys. Rev.

Observational signatures of convectively driven waves in massive stars

We demonstrate observational evidence for the occurrence of convectively driven internal gravity waves (IGW) in young massive O-type stars observed with high-precision CoRoT space photometry. This evidence results from a comparison between velocity spectra based on 2D hydrodynamical simulations of IGW in a differentially-rotating massive star and the observed spectra.We also show that the velocity spectra caused by IGW may lead to detectable line-profile variability and explain the occurrence of macroturbulence in the observed line profiles of OB stars. Our findings provide predictions that can readily be tested by including a sample of bright slowly and rapidly rotating OB-type stars in the scientific programme of the K2 mission accompanied by high-precision spectroscopy and their confrontation with multi-dimensional hydrodynamic simulations of IGW for various masses and ages.Comment: 4 pages, 3 figures, accepted for publication in The Astrophysical Journal Letter

The Response of Normal Shocks in Diffusers

The frequency response of a normal shock in a diverging channel is calculated for application to problems of pressure oscillations in ramjet engines. Two limits of a linearized analysis arc discussed: one represents isentropic flow on both sides of a shock wave; the other may be a crude appr'l'I;imation to the influence of flow separation induced hy the wave. Numerical results arc given, and the influences of the shock wave on oscillations in the engine are discus,ed

Gauge links, TMD-factorization, and TMD-factorization breaking

In this section, we discuss some basic features of transverse momentum dependent, or unintegrated, parton distribution functions. In particular, when these correlation functions are combined in a factorization formulae with hard processes beyond the simplest cases, there are basic problems with universality and factorization. We discuss some of these problems as well as the opportunities that they offer.Comment: 9 pages, 10 figures Gluons and the quark sea at high energies: distributions, polarization, tomograph

Modeling pressure oscillations in Ramjets

Pressure oscillations in ramjet engines are approximated as one-dimensional motions and treated within linear acoustics. The exhaust nozzle is represented by the admittance function for a short choked nozzle. New results have been obtained for the quasi-steady response of a normal shock wave in the diffuser. Acoustic fields in the inlet region and in the combustion chamber are matched to provide an analytical expression of the criterion for linear stability. Combustion processes are accommodated but not treated in detail. As examples, data are discussed for two liquid-fueled engines, one having axial dump and one having side dumps

On the Tidal Dissipation of Obliquity

We investigate tidal dissipation of obliquity in hot Jupiters. Assuming an initial random orientation of obliquity and parameters relevant to the observed population, the obliquity of hot Jupiters does not evolve to purely aligned systems. In fact, the obliquity evolves to either prograde, retrograde or 90^{o} orbits where the torque due to tidal perturbations vanishes. This distribution is incompatible with observations which show that hot jupiters around cool stars are generally aligned. This calls into question the viability of tidal dissipation as the mechanism for obliquity alignment of hot Jupiters around cool stars.Comment: 6 pages, 4 figures, accepted at ApJ

Multivariable Repetitive-predictive Controllers using Frequency Decomposition

Repetitive control is a methodology for the tracking of a periodic reference signal. This paper develops a new approach to repetitive control systems design using receding horizon control with frequency decomposition of the reference signal. Moreover, design and implementation issues for this form of repetitive predictive control are investigated from the perspectives of controller complexity and the effects of measurement noise. The analysis is supported by a simulation study on a multi-input multi-output robot arm where the model has been constructed from measured frequency response data, and experimental results from application to an industrial AC motor