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# Scholarly Works - Applied Mathematics and Theoretical Physics

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Item Accepted version Open Access Cylinders out of a top hat: Counts-in-cells for projected densities(Oxford University Press, 2018-06-21) Uhlemann, C; Pichon, C; Codis, S; L'Huillier, B; Kim, J; Bernardeau, F; Park, C; Prunet, S; Uhlemann, Cora [0000-0001-7831-1579]Show more © 2017 The Authors. Large deviation statistics is implemented to predict the statistics of cosmic densities in cylinders applicable to photometric surveys. It yields few per cent accurate analytical predictions for the one-point probability distribution function (PDF) of densities in concentric or compensated cylinders; and also captures the density dependence of their angular clustering (cylinder bias). All predictions are found to be in excellent agreement with the cosmological simulation Horizon Run 4 in the quasi-linear regime where standard perturbation theory normally breaks down. These results are combined with a simple local bias model that relates dark matter and tracer densities in cylinders and validated on simulated halo catalogues. This formalism can be used to probe cosmology with existing and upcoming photometric surveys like DES, Euclid or WFIRST containing billions of galaxies.Show more Item Published version Open Access Dark Energy Survey Year 1 Results: Photometric Data Set for Cosmology(IOP Publishing, 2018) Drlica-Wagner, A; Sevilla-Noarbe, I; Rykoff, ES; Gruendl, RA; Yanny, B; Tucker, DL; Hoyle, B; Rosell, A Carnero; Bernstein, GM; Bechtol, K; Becker, MR; Benoit-Levy, A; Bertin, E; Kind, M Carrasco; Davis, C; Vicente, J de; Diehl, HT; Gruen, D; Hartley, WG; Leistedt, B; Li, TS; Marshall, JL; Neilsen, E; Rau, MM; Sheldon, E; Smith, J; Troxel, MA; Wyatt, S; Zhang, Y; Abbott, TMC; Abdalla, FB; Allam, S; Banerji, M; Brooks, D; Buckley-Geer, E; Burke, DL; Capozzi, D; Carretero, J; Cunha, CE; D'Andrea, CB; Costa, LN da; DePoy, DL; Desai, S; Dietrich, JP; Doel, P; Evrard, AE; Neto, A Fausti; Flaugher, B; Fosalba, P; Frieman, J; Garcia-Bellido, J; Gerdes, DW; Giannantonio, T; Gschwend, J; Gutierrez, G; Honscheid, K; James, DJ; Jeltema, T; Kuehn, K; Kuhlmann, S; Kuropatkin, N; Lahav, O; Lima, M; Lin, H; Maia, MAG; Martini, P; McMahon, RG; Melchior, P; Menanteau, F; Miquel, R; Nichol, RC; Ogando, RLC; Plazas, AA; Romer, AK; Roodman, A; Sanchez, E; Scarpine, V; Schindler, R; Schubnell, M; Smith, M; Smith, RC; Soares-Santos, M; Sobreira, F; Suchyta, E; Tarle, G; Vikram, V; Walker, AR; Wechsler, RH; Zuntz, J; Banerji, Manda [0000-0002-0639-5141]; Giannantonio, Tommaso [0000-0002-9865-0436]; McMahon, Richard [0000-0001-8447-8869]Show more We describe the creation, content, and validation of the Dark Energy Survey (DES) internal year-one cosmology data set, Y1A1 GOLD, in support of upcoming cosmological analyses. The Y1A1 GOLD data set is assembled from multiple epochs of DES imaging and consists of calibrated photometric zero-points, object catalogs, and ancillary data products—e.g., maps of survey depth and observing conditions, star–galaxy classification, and photometric redshift estimates—that are necessary for accurate cosmological analyses. The Y1A1 GOLD wide-area object catalog consists of $\sim 137$ million objects detected in co-added images covering $\sim 1800\,{\deg }^{2}$ in the DES grizY filters. The 10σ limiting magnitude for galaxies is $g=23.4$, $r=23.2$, $i=22.5$, $z=21.8$, and $Y=20.1$. Photometric calibration of Y1A1 GOLD was performed by combining nightly zero-point solutions with stellar locus regression, and the absolute calibration accuracy is better than 2% over the survey area. DES Y1A1 GOLD is the largest photometric data set at the achieved depth to date, enabling precise measurements of cosmic acceleration at z lesssim 1.Show more Item Accepted version Open Access Analytic solutions for reduced leading-edge noise aerofoils(American Institute of Aeronautics and Astronautics, 2018-06-25) Ayton, LJ; Paruchuri, C; Ayton, Lorna [0000-0001-6280-9460]Show more This paper presents an analytic solution for the sound generated by an unsteady gust interacting with a semi-infinite flat plate with a piecewise linear periodic leading edge. The Wiener-Hopf method is used in conjunction with a non-orthogonal coordinate transformation and separation of variables to allow analytical progress. A fully analytic solution is obtained in terms of a modal expansion for the far-field noise which is obtained by summing only a finite number of cuton modes, allowing very quick evaluation. The analytic solution is compared to experimental results for five test case leading-edge geometries. Good agreement is seen indicating the analytic model is capturing the key features of the interaction such as the destructive interference from the tip and root. In four of the five test cases the serrated edges show large reductions of noise compared to the straight edge at mid and high frequencies, however the square wave geometry is seen to be ineffective at noise reduction for high frequencies.Show more Item Published version Open Access An affine model of the dynamics of astrophysical discs(Oxford University Press (OUP), 2018) Ogilvie, GI; Ogilvie, Gordon [0000-0002-7756-1944]Show more © 2018 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. Thin astrophysical discs are very often modelled using the equations of 2D hydrodynamics. We derive an extension of this model that describes more accurately the behaviour of a thin disc in the absence of self-gravity, magnetic fields, and complex internal motions. The ideal fluid theory is derived directly from Hamilton's Principle for a 3D fluid after making a specific approximation to the deformation gradient tensor. We express the equations in Eulerian form after projection on to a reference plane. The disc is thought of as a set of fluid columns, each of which is capable of a time-dependent affine transformation, consisting of a translation together with a linear transformation in three dimensions. Therefore, in addition to the usual 2D hydrodynamics in the reference plane, the theory allows for a deformation of the mid-plane (as occurs in warped discs) and for the internal shearing motions that accompany such deformations. It also allows for the vertical expansions driven in non-circular discs by a variation of the vertical gravitational field around the horizontal streamlines, or by a divergence of the horizontal velocity. The equations of the affine model embody conservation laws for energy and potential vorticity, even for non-planar discs.We verify that they reproduce exactly the linear theories of 3D warped and eccentric discs in a secular approximation. However, the affine model does not rely on any secular or small-amplitude assumptions and should be useful in more general circumstances.Show more Item Accepted version Open Access A lower bound on the positive semidefinite rank of convex bodies(Society for Industrial and Applied Mathematics, 2018) Fawzi, Hamza; Din, Mohab Safey El; Fawzi, Hamza [0000-0001-6026-4102]Show more The positive semidefinite rank of a convex body $C$ is the size of its smallest positive semidefinite formulation. We show that the positive semidefinite rank of any convex body $C$ is at least $\sqrt{\log d}$ where $d$ is the smallest degree of a polynomial that vanishes on the boundary of the polar of $C$. This improves on the existing bound which relies on results from quantifier elimination. The proof relies on the B\'ezout bound applied to the Karush-Kuhn-Tucker conditions of optimality. We discuss the connection with the algebraic degree of semidefinite programming and show that the bound is tight (up to constant factor) for random spectrahedra of suitable dimension.Show more Item Accepted version Open Access Relativistic magnetised perturbations: Magnetic pressure versus magnetic tension(IOP Publishing, 2018) Tseneklidou, D; Tsagas, CG; Barrow, JD; Tseneklidou, D [0000-0003-2582-1705]; Tsagas, CG [0000-0002-8527-0418]; Barrow, JD [0000-0002-6083-9751]Show more We study the linear evolution of magnetised cosmological perturbations in the post-recombination epoch. Using full general relativity and adopting the ideal magnetohydrodynamic approximation, we refine and extend the previous treatments. More specifically, this is the first relativistic study that accounts for the effects of the magnetic tension, in addition to those of the field's pressure. Our solutions show that on sufficiently large scales, larger than the (purely magnetic) Jeans length, the perturbations evolve essentially unaffected by the magnetic presence. The magnetic pressure dominates on small scales, where it forces the perturbations to oscillate and decay. Close to the Jeans length, however, the field's tension takes over and leads to a weak growth of the inhomogeneities. These solutions clearly demonstrate the opposing action of the aforementioned two magnetic agents, namely of the field's pressure and tension, on the linear evolution of cosmological density perturbations.Show more Item Published version Open Access Gauge Mediation in the NMSSM with a Light Singlet: Sparticles within the Reach of LHC Run II(2015-10-12) Allanach, Ben; Badziak, Marcin; Hugonie, Cyril; Ziegler, Robert; Allanach, Benjamin [0000-0003-4635-6830]Show more Relatively light stops in gauge mediation models are usually made compatible with the Higgs mass of 125 GeV by introducing direct Higgs-messenger couplings. We show that such couplings are not necessary in a simple and predictive model that combines minimal gauge mediation and the next-to-minimal supersymmetric standard model (NMSSM). We show that one can obtain a 125 GeV Standard Model-like Higgs boson with stops as light as 1.1 TeV, thanks to the mixing of the Higgs with a singlet state at ${\cal O}(90-100)$ GeV that can explain the LEP excess. In this scenario the singlet-higgs-higgs superfields coupling $\lambda$ is small and $\tan\beta$ large. Sparticle searches at the LHC may come with additional $b-$jets or taus and may involve displaced vertices. The sparticle production cross-section at the 13 TeV LHC can be ${\mathcal O}(10-100)$ fb, leading to great prospects for discovery in the early phase of LHC Run II.Show more Item Accepted version Open Access Interpreting the CMS ℓ+ ℓ-jj+ missing transverse energy excess with a leptoquark model(American Physical Society (APS), 2015) Allanach, B; Alves, A; Queiroz, FS; Sinha, K; Strumia, A; Allanach, Benjamin [0000-0003-4635-6830]Show more Motivated by excesses in $ee jj$ and $e\nu jj$ channels observed by the CMS collaboration, in 8 TeV LHC data, a model of lepto-quarks with mass around 500 GeV was proposed in the literature. In order to reproduce the claimed event rate, lepto-quarks were assumed to have a significant partial branching ratio into an extra sector, taken to be Dark Matter, other than the canonical $ej$. We here show that the decay channel of lepto-quark into Dark Matter can fit another excess claimed by CMS, in $\ell^+\ell^- jj E\!\!\!\!/_{\rm T}$: the event rate, the distribution in di-lepton invariant mass and the rapidity range are compatible with the data. We provide predictions for the forthcoming Run II of the 14 TeV LHC and discuss aspects of dark matter detection.Show more Item Accepted version Open Access Z′ models for the LHCb and g-2 muon anomalies(American Physical Society (APS), 2016) Allanach, B; Queiroz, FS; Strumia, A; Sun, S; Allanach, Benjamin [0000-0003-4635-6830]Show more We revisit a class of Z' explanations of the anomalies found by the LHCb collaboration in $B$ decays, and show that the scenario is tightly constrained by a combination of constraints: (i) LHC searches for di-muon resonances, (ii) pertubativity of the Z' couplings; (iii) the $B_s$ mass difference, and (iv) and electro-weak precision data. Solutions are found by suppressing the Z' coupling to electrons and to light quarks and/or by allowing for a Z' decay width into dark matter. We also present a simplified framework where a TeV-scale Z' gauge boson that couples to standard leptons as well as to new heavy vector-like leptons, can simultaneously accommodate the LHCb anomalies and the muon g-2 anomaly.Show more Item Accepted version Open Access Wormhole throats in*R*gravity^{m}(IOP Publishing, 2005-01-21) Furey, N; DeBenedictis, A; Furey, Nichol [0000-0002-8695-2904]Show more Item Published version Open Access ADHM and the 4d quantum Hall effect(Springer Science and Business Media LLC, 2018) Barns-Graham, A; Dorey, N; Lohitsiri, N; Tong, D; Turner, C; Tong, David [0000-0001-9120-2174]; Turner, Carl [0000-0001-7202-5731]Show more Yang-Mills instantons are solitonic particles in d=4+1 dimensional gauge theories. We construct and analyse the quantum Hall states that arise when these particles are restricted to the lowest Landau level. We describe the ground state wavefunctions for both Abelian and non-Abelian quantum Hall states. Although our model is purely bosonic, we show that the excitations of this 4d quantum Hall state are governed by the Nekrasov partition function of a certain five dimensional supersymmetric gauge theory with Chern-Simons term. The partition function can also be interpreted as a variant of the Hilbert series of the instanton moduli space, counting holomorphic sections rather than holomorphic functions. It is known that the Hilbert series of the instanton moduli space can be rewritten using mirror symmetry of 3d gauge theories in terms of Coulomb branch variables. We generalise this approach to include the effect of a five dimensional Chern-Simons term. We demonstrate that the resulting Coulomb branch formula coincides with the corresponding Higgs branch Molien integral which, in turn, reproduces the standard formula for the Nekrasov partition function.Show more Item Accepted version Open Access Towards the european strategy for particle physics: The briefing book(Springer Science and Business Media LLC, 2007) Åkesson, T; Aleksan, R; Allanach, B; Bertolucci, S; Blondel, A; Butterworth, J; Cavalli-Sforza, M; Cervera, A; De Naurois, M; Desch, K; Egede, U; Heuer, R; Hoecker, A; Huber, P; Jungmann, K; Linde, F; Lombardi, A; Mangano, M; Mezzetto, M; Onderwater, G; Palanque-Delabrouille, N; Peach, K; Polosa, A; Rondio, E; Webber, B; Weiglein, G; Womersley, J; Allanach, Benjamin [0000-0003-4635-6830]; Webber, Bryan [0000-0001-7474-0990]Show more This document was prepared as part of the briefing material for the Workshop of the CERN Council Strategy Group, held in DESY Zeuthen from 2nd to 6th May 2006. It gives an overview of the physics issues and of the technological challenges that will shape the future of the field, and incorporates material presented and discussed during the Symposium on the European Strategy for Particle Physics, held in Orsay from 30th January to 2nd February 2006, reflecting the various opinions of the European community as recorded in written submissions to the Strategy Group and in the discussions at the Symposium.Show more Item Accepted version Open Access The quasi-fixed Minimal Supersymmetric Standard Model(Elsevier BV, 1997-12-25) Abel, SA; Allanach, BC; Allanach, Benjamin [0000-0003-4635-6830]Show more The infra-red fixed points are determined for all the parameters of the MSSM. They dominate the renormalisation group running when the top-Yukawa is in the quasi-fixed point regime (i.e. large at the GUT scale). We examine this behaviour analytically, by solving the full set of one-loop renormalisation group equations in the approximation that the electroweak contributions are negligible, and also numerically. We find the quasi-fixed points for the top-quark trilinear couplings; A_{U_{\alpha 3}} = A_{U_{3\alpha}}=-0.59 m_g independently of the input parameters at the unification scale. All the remaining parameters are significantly focused towards their true fixed points at the weak scale. We examine how this increases the predictivity of the MSSM in this regime.Show more Item Accepted version Open Access The calculation of sparticle and Higgs decays in the minimal and next-to-minimal supersymmetric standard models: SOFTSUSY4.0(Elsevier BV, 2017) Allanach, BC; Cridge, T; Allanach, BC [0000-0003-4635-6830]Show more We describe a major extension of the SOFTSUSY spectrum calculator to include the calculation of the decays, branching ratios and lifetimes of sparticles into lighter sparticles, covering the next-to-minimal supersymmetric standard model (NMSSM) as well as the minimal supersymmetric standard model (MSSM). This document acts as a manual for the new version of SOFTSUSY, which includes the calculation of sparticle decays. We present a comprehensive collection of explicit expressions used by the program for the various partial widths of the different decay modes in the appendix.Show more Item Published version Open Access The case for future hadron colliders from B -> K-(*) mu(+)mu(-) decays(Springer Nature, 2018-03-06) Allanach, BC; Gripaios, Ben; You, Tevong; Allanach, Benjamin [0000-0003-4635-6830]; Gripaios, Ben [0000-0003-2835-2713]Show more Recent measurements in B → K(*)μ+μ− decays are somewhat discrepant with Standard Model predictions. They may be harbingers of new physics at an energy scale potentially accessible to direct discovery. We estimate the sensitivity of future hadron colliders to the possible new particles that may be responsible for the anomalies at tree-level: leptoquarks or Z′s. We consider luminosity upgrades for a 14 TeV LHC, a 33 TeV LHC, and a 100 TeV pp collider such as the FCC-hh. In the most conservative and pessimistic models, for narrow particles with perturbative couplings, Z′ masses up to 20 TeV and leptoquark masses up to 41 TeV may in principle explain the anomalies. Coverage of Z′ models is excellent: a 33 TeV 1 ab−1 LHC is expected to cover most of the parameter space up to 8 TeV in mass, whereas the 100 TeV FCC-hh with 10 ab−1 will cover all of it. A smaller portion of the leptoquark parameter space is covered by future colliders: for example, in a μ+μ−jj di-leptoquark search, a 100 TeV 10 ab−1 collider has a projected sensitivity up to leptoquark masses of 12 TeV (extendable to 21 TeV with a strong coupling for single leptoquark production).Show more Item Accepted version Open Access Inhomogeneous initial data and small-field inflation(IOP Publishing, 2018) Marsh, MCD; Barrow, JD; Ganguly, C; Marsh, David [0000-0001-7271-4115]; Barrow, John [0000-0002-6083-9751]Show more We consider the robustness of small-field inflation in the presence of scalar field inhomo- geneities. Previous numerical work has shown that if the scalar potential is flat only over a narrow in- terval, such as in commonly considered inflection-point models, even small-amplitude inhomogeneities present at the would-be onset of inflation at τ = τi can disrupt the accelerated expansion. In this paper, we parametrise and evolve the inhomogeneities from an earlier time τIC at which the initial data were imprinted, and show that for a broad range of inflationary and pre-inflationary models, inflection-point inflation withstands initial inhomogeneities. We consider three classes of perturbative pre-inflationary solutions (corresponding to energetic domination by the scalar field kinetic term, a relativistic fluid, and isotropic negative curvature), and two classes of exact solutions to Einstein’s equations with large inhomogeneities (corresponding to a stiff fluid with cylindrical symmetry, and anisotropic negative curvature). We derive a stability condition that depends on the Hubble scales H(τi) and H(τIC), and a few properties of the pre-inflationary cosmology. For initial data imprinted at the Planck scale, the absence of an inhomogeneous initial data problem for inflection-point inflation leads to a novel, lower limit on the tensor-to-scalar ratio.Show more Item Published version Open Access Spiral density waves and vertical circulation in protoplanetary discs(Oxford University Press, 2018-06-01) Latter, HN; Riols, AntoineShow more Spiral density waves dominate several facets of accretion disc dynamics – planet-disc interactions and gravitational instability (GI) most prominently. Though they have been examined thoroughly in two-dimensional simulations, their vertical structures in the non-linear regime are somewhat unexplored. This neglect is unwarranted given that any strong vertical motions associated with these waves could profoundly impact dust dynamics, dust sedimentation, planet formation, and the emissivity of the disc surface. In this paper, we combine linear calculations and shearing box simulations in order to investigate the vertical structure of spiral waves for various polytropic stratifications and wave amplitudes. For sub-adiabatic profiles, we find that spiral waves develop a pair of counter-rotating poloidal rolls. Particularly strong in the non-linear regime, these vortical structures issue from the baroclinicity supported by the background vertical entropy gradient. They are also intimately connected to the disc's g modes which appear to interact non-linearly with the density waves. Furthermore, we demonstrate that the poloidal rolls are ubiquitous in gravitoturbulence, emerging in the vicinity of GI spiral wakes, and potentially transporting grains off the disc mid-plane. Other than hindering sedimentation and planet formation, this phenomena may bear on observations of the disc's scattered infrared luminosity. The vortical features could also impact on the turbulent dynamo operating in young protoplanetary discs subject to GI, or possibly even galactic discs.Show more Item Published version Open Access Submesoscale Rossby waves on the Antarctic circumpolar current.(American Association for the Advancement of Science (AAAS), 2018-03) Taylor, John R; Bachman, Scott; Stamper, Megan; Hosegood, Phil; Adams, Katherine; Sallee, Jean-Baptiste; Torres, Ricardo; Taylor, John R [0000-0002-1292-3756]; Stamper, Megan [0000-0001-5400-0063]; Hosegood, Phil [0000-0002-4415-7152]; Adams, Katherine [0000-0003-1478-5235]; Torres, Ricardo [0000-0002-9035-2637]Show more The eastward-flowing Antarctic circumpolar current (ACC) plays a central role in the global ocean overturning circulation and facilitates the exchange of water between the ocean surface and interior. Submesoscale eddies and fronts with scales between 1 and 10 km are regularly observed in the upper ocean and are associated with strong vertical circulations and enhanced stratification. Despite their importance in other locations, comparatively little is known about submesoscales in the Southern Ocean. We present results from new observations, models, and theories showing that submesoscales are qualitatively changed by the strong jet associated with the ACC in the Scotia Sea, east of Drake Passage. Growing submesoscale disturbances develop along a dense filament and are transformed into submesoscale Rossby waves, which propagate upstream relative to the eastward jet. Unlike their counterparts in slower currents, the submesoscale Rossby waves do not destroy the underlying frontal structure. The development of submesoscale instabilities leads to strong net subduction of water associated with a dense outcropping filament, and later, the submesoscale Rossby waves are associated with intense vertical circulations.Show more Item Published version Open Access A Variational Model for Joint Motion Estimation and Image Reconstruction(Society for Industrial and Applied Mathematics, 2018-01) Burger, Martin; Dirks, Hendrik; Schönlieb, Carola-BibianeShow more The aim of this paper is to derive and analyze a variational model for the joint estimation of motion and reconstruction of image sequences, which is based on a time-continuous Eulerian motion model. The model can be set up in terms of the continuity equation or the brightness constancy equation. The analysis in this paper focuses on the latter for robust motion estimation on sequences of twodimensional images. We rigorously prove the existence of a minimizer in a suitable function space setting. Moreover, we discuss the numerical solution of the model based on primal-dual algorithms and investigate several examples. Finally, the benefits of our model compared to existing techniques, such as sequential image reconstruction and motion estimation, are shown.Show more Item Open Access An elliptic regularity theorem for fractional partial differential operators(Springer Science and Business Media LLC, 2018) Fernandez, A; Fernandez, A [0000-0002-1491-1820]Show more We present and prove a version of the elliptic regularity theorem for partial differential equations involving fractional Riemann-Liouville derivatives. In this case, regularity is defined in terms of Sobolev spaces $H^s(X)$: if the forcing of a linear elliptic fractional PDE is in one Sobolev space, then the solution is in the Sobolev space of increased order corresponding to the order of the derivatives. We also mention a few applications and potential extensions of this result.Show more