Stochastic switching circuit synthesis

Shannon in his 1938 Masterpsilas Thesis demonstrated that any Boolean function can be realized by a switching relay circuit, leading to the development of deterministic digital logic. Here, we replace each classical switch with a probabilistic switch (pswitch). We present algorithms for synthesizing circuits closed with a desired probability, including an algorithm that generates optimal size circuits for any binary fraction. We also introduce a new duality property for series-parallel stochastic switching circuits. Finally, we construct a universal probability generator which maps deterministic inputs to arbitrary probabilistic outputs. Potential applications exist in the analysis and design of stochastic networks in biology and engineering

Higgs-Boson Production at Small Transverse Momentum

Using methods from effective field theory, we have recently developed a novel, systematic framework for the calculation of the cross sections for electroweak gauge-boson production at small and very small transverse momentum q_T, in which large logarithms of the scale ratio m_V/q_T are resummed to all orders. This formalism is applied to the production of Higgs bosons in gluon fusion at the LHC. The production cross section receives logarithmically enhanced corrections from two sources: the running of the hard matching coefficient and the collinear factorization anomaly. The anomaly leads to the dynamical generation of a non-perturbative scale q_* ~ m_H e^{-const/\alpha_s(m_H)} ~ 8 GeV, which protects the process from receiving large long-distance hadronic contributions. We present detailed numerical predictions for the transverse-momentum spectrum of the Higgs boson, finding that it is quite insensitive to hadronic effects.Comment: 18 pages, 5 figures; v2: published version, includes a correction in (8) and (22

Massive Boson Production at Small q_T in Soft-Collinear Effective Theory

We study the differential cross sections for electroweak gauge-boson and Higgs production at small and very small transverse-momentum q_T. Large logarithms are resummed using soft-collinear effective theory. The collinear anomaly generates a non-perturbative scale q_*, which protects the processes from receiving large long-distance hadronic contributions. A numerical comparison of our predictions with data on the transverse-momentum distribution in Z-boson production at the Tevatron and LHC is given.Comment: PDF LaTeX, 4 pages, 7 pdf figures. To appear in the proceedings of the 16th International Conference in Quantum ChromoDynamics (QCD12), 2-6 July 2012, Montpellie

Slow blow-up solutions for the H^1(R^3) critical focusing semi-linear wave equation in R^3

We prove the existence of energy solutions of the energy critical focusing wave equation in R^3 which blow up exactly at x=t=0. They decompose into a bulk term plus radiation term. The bulk is a rescaled version of the stationary "soliton" type solution of the NLW. The construction depends crucially on the renormalization procedure of the "soliton" which we introduced in our companion paper on the wave map problem.Comment: 38 page

Circumbinary discs: Numerical and physical behaviour

We study the evolution of circumbinary disks under the gravitational influence of the binary using two-dimensional hydrodynamical simulations to investigate the impact of disk and binary parameters on the dynamical aspects of the disk. To distinguish between physical and numerical effects we apply three hydrodynamical codes. First we analyse in detail numerical issues concerning the conditions at the boundaries and grid resolution. We then perform a series of simulations with different binary (eccentricity, mass ratio) and disk parameters (viscosity, aspect ratio) starting from a reference model with Kepler-16 parameters. Concerning the numerical aspects we find that the inner grid radius must be of the order of the binary semi-major axis, with free outflow conditions applied such that mass can flow onto the central binary. A closed inner boundary leads to unstable evolutions. We find that the inner disk turns eccentric and precesses for all investigated physical parameters. The precession rate is slow with periods ($T_\mathrm{prec}$) starting at around 500 binary orbits ($T_\mathrm{bin}$) for high viscosity and large $H/R$ where the inner hole is smaller and more circular. Reducing $\alpha$ and $H/R$ increases the gap size and $T_\mathrm{prec}$ reaches 2500 $T_\mathrm{bin}$. For varying binary mass ratios $q_\mathrm{bin}$ the gap size remains constant whereas $T_\mathrm{prec}$ decreases for increasing $q_\mathrm{bin}$. For varying binary eccentricities $e_\mathrm{bin}$ we find two separate branches in the gap size and eccentricity diagram. The bifurcation occurs at around $e_\mathrm{crit} \approx 0.18$ where the gap is smallest with the shortest $T_\mathrm{prec}$. For $e_\mathrm{bin}$ smaller and larger than $e_\mathrm{crit}$ the gap size and $T_\mathrm{prec}$ increase. Circular binaries create the most eccentric disks.Comment: 20 pages, 25 figures, published in A&A, language edited versio

Performance Assessment of BIM in University Facilities Management Organisations : Exploring industry perceptions in Australia and Sweden

This thesis explores methodologies for assessing BIM performance in Facilities Management organisations. Limited previous research in this field initiated case studies focussing industry managers of university buildings in Australia and Sweden and their readiness (organisational, capability) for handling BIM in a whole-of-life context. Furthermore, it identifies critical factors affecting their capabilities to implement and effectively use BIM in their operations