Forks, Noodles and the Burau representation for n=4n=4

\begin{abstract} The reduced Burau representation is a natural action of the braid group $B_n$ on the first homology group $H_1({\tilde{D}}_n;\mathbb{Z})$ of a suitable infinite cyclic covering space ${\tilde{D}}_n$ of the $n$--punctured disc $D_n$. It is known that the Burau representation is faithful for $n\le 3$ and that it is not faithful for $n\ge 5$. We use forks and noodles homological techniques and Bokut--Vesnin generators to analyze the problem for $n=4$. We present a Conjecture implying faithfulness and a Lemma explaining the implication. We give some arguments suggesting why we expect the Conjecture to be true. Also, we give some geometrically calculated examples and information about data gathered using a C\texttt{++} program.Comment: 24 pages, 21 figure

Generalized breakup and coalescence models for population balance modelling of liquid-liquid flows

Population balance framework is a useful tool that can be used to describe size distribution of droplets in a liquid-liquid dispersion. Breakup and coalescence models provide closures for mathematical formulation of the population balance equation (PBE) and are crucial for accu- rate predictions of the mean droplet size in the ow. Number of closures for both breakup and coalescence can be identi ed in the literature and most of them need an estimation of model parameters that can di er even by several orders of magnitude on a case to case basis. In this paper we review the fundamental assumptions and derivation of breakup and coalescence ker- nels. Subsequently, we rigorously apply two-stage optimization over several independent sets of experiments in order to identify model parameters. Two-stage identi cation allows us to estab- lish new parametric dependencies valid for experiments that vary over large ranges of important non-dimensional groups. This be adopted for optimization of parameters in breakup and co- alescence models over multiple cases and we propose a correlation based on non-dimensional numbers that is applicable to number of di erent ows over wide range of Reynolds numbers

Search for Z-primes and Randall-Sundrum Gravitons with dimuons in CMS

This paper presents results from studies on observability of Z' particles and Randall-Sundrum gravitons in the dimuon channel in the CMS detector. Full detector simulation and reconstruction were carried out to derive both the discovery potential and results for model discrimination. Effects of systematic uncertainties on the expected reach of the CMS experiment are also presented

Knots and algebras

This paper gives a skein-theoretic construction of the Hecke algebras based on oriented tangles and the Homfly relations. A similar approach with unoriented tangles and Kauffman's Dubrovnik relations then gives a construction of the Birman-Wenzl algebra

Charged particle multiplicities in pp interactions at √s = 0.9, 2.36, and 7 TeV

Measurements of primary charged hadron multiplicity distributions are presented for non-single-diractive events in proton-proton collisions at centre-of-mass energies of √s = 0.9, 2.36, and 7 TeV, in five pseudorapidity ranges from |η| < 0.5 to |η| < 2.4. The data were collected with the minimum-bias trigger of the CMS experiment during the LHC commissioning runs in 2009 and the 7 TeV run in 2010. The multiplicity distribution at √s = 0.9 TeV is in agreement with previous measurements. At higher energies the increase of the mean multiplicity with √s is underestimated by most event generators. The average transverse momentum as a function of the multiplicity is also presented. The measurement of higher-order moments of the multiplicity distribution confirms the violation of Koba-Nielsen-Olesen scaling that has been observed at lower energies

Two Graviton Production at e+e−e^+e^- and Hadron Hadron Colliders in the Randall-Sundrum Model

We compute the pair production cross section of two Kaluza Klein modes in the Randall-Sundrum model at $e^+e^-$ and hadron hadron colliders. These processes are interesting because they get dominant contribution from the graviton interaction at next to leading order. Hence they provide a nontrivial test of the low scale gravity models. All the Feynman rules at next to leading order are also presented. These rules may be useful for many phenomenological applications including the computation of higher order loop corrections.Comment: 24 pages, 11 figures, some typos correcte

Search for physics beyond the standard model using multilepton signatures in pp collisions at √s=7 TeV

A search for physics beyond the standard model in events with at least three leptons and any number of jets is presented. The data sample corresponds to 35 pb^(−1) of integrated luminosity in pp collisions at √s=7 TeV collected by the CMS experiment at the LHC. A number of exclusive multileptonic channels are investigated and standard model backgrounds are suppressed by requiring sufficient missing transverse energy, invariant mass inconsistent with that of the Z boson, or high jet activity. Control samples in data are used to ascertain the robustness of background evaluation techniques and to minimise the reliance on simulation. The observations are consistent with background expectations. These results constrain previously unexplored regions of supersymmetric parameter space