Modelling vortex formation in an unbaffled stirred tank reactors

Agitating liquids in unbaffled stirred tank leads to the formation of a vortex in the region of the impeller shaft when operating in the turbulent flow regime. A numerical model is presented here that captures such a vortex. The volume of fluid model, a multiphase flow model was employed in conjunction with a multiple reference frame model and the shear stress turbulence model. The dimensions of the tank considered here, were 0.585 m for the liquid depth and tank diameter with a 0.2925 m diameter impeller at a height of 0.2925 m. The impeller considered was an eight-bladed paddle type agitator that was rotating with an angular velocity of 7.54 rad s (72 rpm) giving a Reynolds number of 10 and Froude number of 0.043. Preliminary results of a second investigation into the effect of liquid phase properties on the vortex formed are also presented

The Higgs resonance shape in gluon fusion: Heavy Higgs effects

We study the influence of two--loop radiative corrections of enhanced electroweak strength on Higgs production at the LHC. We consider Higgs production by the gluon fusion mechanism, with the subsequent decay of the Higgs boson into a pair of Z bosons, and incorporate the resonance shape corrections up to order $(g^2 \, m_H^2 / m_W^2)^2$. We take into account the full $g g \rightarrow Z Z$ process and the $q \bar{q} \rightarrow Z Z$ background, as well as the subsequent decay of the Z pair into leptons. We also discuss the theoretical uncertainty related to the use of the equivalence theorem in this process

Planar box diagram for the (N_F = 1) 2-loop QED virtual corrections to Bhabha scattering

In this paper we present the master integrals necessary for the analytic calculation of the box diagrams with one electron loop (N_{F}=1) entering in the 2-loop (\alpha^3) QED virtual corrections to the Bhabha scattering amplitude of the electron. We consider on-shell electrons and positrons of finite mass m, arbitrary squared c.m. energy s, and momentum transfer t; both UV and soft IR divergences are regulated within the continuous D-dimensional regularization scheme. After a brief overview of the method employed in the calculation, we give the results, for s and t in the Euclidean region, in terms of 1- and 2-dimensional harmonic polylogarithms, of maximum weight 3. The corresponding results in the physical region can be recovered by analytical continuation. For completeness, we also provide the analytic expression of the 1-loop scalar box diagram including the first order in (D-4).Comment: Misprints in Eqs. (36), (38), (39), and (B.9) have been corrected. The results are now available at http://pheno.physik.uni-freiburg.de/~bhabha, as FORM input file

Two-Loop N_F =1 QED Bhabha Scattering: Soft Emission and Numerical Evaluation of the Differential Cross-section

Recently, we evaluated the virtual cross-section for Bhabha scattering in pure QED, up to corrections of order alpha^4 (N_F =1). This calculation is valid for arbitrary values of the squared center of mass energy s and momentum transfer t; the electron and positron mass m was considered a finite, non vanishing quantity. In the present work, we supplement the previous calculation by considering the contribution of the soft photon emission diagrams to the differential cross-section, up to and including terms of order alpha^4 (N_F=1). Adding the contribution of the real corrections to the renormalized virtual ones, we obtain an UV and IR finite differential cross-section; we evaluate this quantity numerically for a significant set of values of the squared center of mass energy s.Comment: 24 pages, 15 figures. Formulas in Appendix B corrected, changes in Section 3, references adde

Two-Loop N_F=1 QED Bhabha Scattering Differential Cross Section

We calculate the two-loop virtual, UV renormalized corrections at order \alpha^4 (N_F=1) in QED to the Bhabha scattering differential cross section, for arbitrary values of the squared c.m. energy s and momentum transfer t, and on-shell electrons and positrons of finite mass m. The calculation is carried out within the dimensional regularization scheme; the remaining IR divergences appear as polar singularities in (D-4). The result is presented in terms of 1- and 2-dimensional harmonic polylogarithms, of maximum weight 3.Comment: 61 pages, 4 figures. Overall sign mistakes in some formulas in appendix corrected, references adde

Genomic differentiation during speciation-with-gene-flow: Comparing geographic and host-related variation in divergent life history adaptation in rhagoletis pomonella

A major goal of evolutionary biology is to understand how variation within populations gets partitioned into differences between reproductively isolated species. Here, we examine the degree to which diapause life history timing, a critical adaptation promoting population divergence, explains geographic and host-related genetic variation in ancestral hawthorn and recently derived apple-infesting races of Rhagoletis pomonella. Our strategy involved combining experiments on two different aspects of diapause (initial diapause intensity and adult eclosion time) with a geographic survey of genomic variation across four sites where apple and hawthorn flies co-occur from north to south in the Midwestern USA. The results demonstrated that the majority of the genome showing significant geographic and host-related variation can be accounted for by initial diapause intensity and eclosion time. Local genomic differences between sympatric apple and hawthorn flies were subsumed within broader geographic clines; allele frequency differences within the races across the Midwest were two to three-fold greater than those between the races in sympatry. As a result, sympatric apple and hawthorn populations displayed more limited genomic clustering compared to geographic populations within the races. The findings suggest that with reduced gene flow and increased selection on diapause equivalent to that seen between geographic sites, the host races may be recognized as different genotypic entities in sympatry, and perhaps species, a hypothesis requiring future genomic analysis of related sibling species to R. pomonella to test. Our findings concerning the way selection and geography interplay could be of broad significance for many cases of earlier stages of divergence-with-gene flow, including (1) where only modest increases in geographic isolation and the strength of selection may greatly impact genetic coupling and (2) the dynamics of how spatial and temporal standing variation is extracted by selection to generate differences between new and discrete units of biodiversity

Interstellar MHD Turbulence and Star Formation

This chapter reviews the nature of turbulence in the Galactic interstellar medium (ISM) and its connections to the star formation (SF) process. The ISM is turbulent, magnetized, self-gravitating, and is subject to heating and cooling processes that control its thermodynamic behavior. The turbulence in the warm and hot ionized components of the ISM appears to be trans- or subsonic, and thus to behave nearly incompressibly. However, the neutral warm and cold components are highly compressible, as a consequence of both thermal instability in the atomic gas and of moderately-to-strongly supersonic motions in the roughly isothermal cold atomic and molecular components. Within this context, we discuss: i) the production and statistical distribution of turbulent density fluctuations in both isothermal and polytropic media; ii) the nature of the clumps produced by thermal instability, noting that, contrary to classical ideas, they in general accrete mass from their environment; iii) the density-magnetic field correlation (or lack thereof) in turbulent density fluctuations, as a consequence of the superposition of the different wave modes in the turbulent flow; iv) the evolution of the mass-to-magnetic flux ratio (MFR) in density fluctuations as they are built up by dynamic compressions; v) the formation of cold, dense clouds aided by thermal instability; vi) the expectation that star-forming molecular clouds are likely to be undergoing global gravitational contraction, rather than being near equilibrium, and vii) the regulation of the star formation rate (SFR) in such gravitationally contracting clouds by stellar feedback which, rather than keeping the clouds from collapsing, evaporates and diperses them while they collapse.Comment: 43 pages. Invited chapter for the book "Magnetic Fields in Diffuse Media", edited by Elisabete de Gouveia dal Pino and Alex Lazarian. Revised as per referee's recommendation

LHC sensitivity to the resonance spectrum of a minimal strongly interacting electroweak symmetry breaking sector

We present a unified analysis of the two main production processes of vector boson pairs at the LHC, VV-fusion and qqbar annihilation, in a minimal strongly interacting electroweak symmetry breaking sector. Using a unitarized electroweak chiral Lagrangian formalism and modeling the final V_L V_L strong rescattering effects by a form factor, we describe qqbar annihilation processes in terms of the two chiral parameters that govern elastic V_L V_L scattering. Depending on the values of these two chiral parameters, the unitarized amplitudes may present resonant enhancements in different angular momentum-isospin channels. Scanning this two parameter space, we generate the general resonance spectrum of a minimal strongly interacting electroweak symmetry breaking sector and determine the regions that can be probed at the LHC.Comment: Final version to appear in Phys. Rev. D, including a more detailed exposition and a few more references. Conclusions and results unchanged. 14 pages, 5 figure

DETERMINATION OF THE ELECTROWEAK CHIRAL-LAGRANGIAN PARAMETERS AT THE LHC

In this work we report on the results obtained in a detailed and systematical study of the possibility to measure the parameters appearing in the electroweak chiral lagrangian. The main novelty of our approach is that we do not use the Equivalence Theorem and therefore we work explicitly with all the gauge boson degrees of freedom.Comment: 59 pages,latex, figures available on reques

The Problem of Patent Thickets in Convergent Technologies

Patent thickets are unintentionally dense webs of overlapping intellectual property rights owned by different companies that can retard progress. This article begins with a review of existing research on patent thickets, focusing in particular on the problem of patent thickets in nanotechnology, or nanothickets. After presenting visual evidence of the presence of nanothickets using a network analytic technique, it discusses potential organizational responses to patent thickets. It then reviews the existing research on patent pools and discusses pool formation in the shadow of antitrust enforcement. Based on recent research on patent pool formation, it examines the divergent fate of two recent pools and discusses the prospects for the future formation of nanotechnology patent pools, or nanopools.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72678/1/annals.1382.014.pd