arXiv subjects

Martin Bauer

Publications and source records attributed to Martin Bauer.

At least 127 records · Page 7Linked to original sources

arXiv2017

Diffeomorphic random sampling using optimal information transport

In this article we explore an algorithm for diffeomorphic random sampling of nonuniform probability distributions on Riemannian manifolds. The algorithm is based on optimal information transport (OIT)---an analogue of optimal mass transport (OMT). Our framework uses the deep geometric connections between the Fisher-Rao metric on the space of probability densities and the right-invariant information metric on the group of diffeomorphisms. The resulting sampling algorithm is a promising alternative to OMT, in particular as our formulation is semi-explicit, free of the nonlinear Monge--Ampere equation. Compared to Markov Chain Monte Carlo methods, we expect our algorithm to stand up well when a large number of samples from a low dimensional nonuniform distribution is needed.

math.NA↗

arXiv2017

Fractional Sobolev metrics on spaces of immersed curves

Motivated by applications in the field of shape analysis, we study reparametrization invariant, fractional order Sobolev-type metrics on the space of smooth regular curves $\operatorname{Imm}(S^1,\mathbb{R}^d)$ and on its Sobolev completions $\mathcal{I}^{q}(S^1,\mathbb{R}^{d})$. We prove local well-posedness of the geodesic equations both on the Banach manifold $\mathcal{I}^{q}(S^1,\mathbb{R}^{d})$ and on the Fréchet-manifold $\operatorname{Imm}(S^1,\mathbb{R}^d)$ provided the order of the metric is greater or equal to one. In addition we show that the $H^s$-metric induces a strong Riemannian metric on the Banach manifold $\mathcal{I}^{s}(S^1,\mathbb{R}^{d})$ of the same order $s$, provided $s>\frac 32$. These investigations can be also interpreted as a generalization of the analysis for right invariant metrics on the diffeomorphism group.

math.AP↗

arXiv2017

Towards the next generation of simplified Dark Matter models

This White Paper is an input to the ongoing discussion about the extension and refinement of simplified Dark Matter (DM) models. Based on two concrete examples, we show how existing simplified DM models (SDMM) can be extended to provide a more accurate and comprehensive framework to interpret and characterise collider searches. In the first example we extend the canonical SDMM with a scalar mediator to include mixing with the Higgs boson. We show that this approach not only provides a better description of the underlying kinematic properties that a complete model would possess, but also offers the option of using this more realistic class of scalar mixing models to compare and combine consistently searches based on different experimental signatures. The second example outlines how a new physics signal observed in a visible channel can be connected to DM by extending a simplified model including effective couplings. This discovery scenario uses the recently observed excess in the high-mass diphoton searches of ATLAS and CMS for a case study to show that such a pragmatic approach can aid the experimental search programme to verify/falsify a potential signal and to study its underlying nature. In the next part of the White Paper we outline other interesting options for SDMM that could be studied in more detail in the future. Finally, we discuss important aspects of supersymmetric models for DM and how these could help to develop of more complete SDMM.

hep-ex↗

arXiv2016

On the Validity of Dark Matter Effective Theory

An effective theory of dark matter offers an attractive framework for global analyses of dark matter. In the light of global fits we test the validity of the link between the non-relativistic dark matter annihilation, or the predicted relic density, and LHC signatures. Specifically, we study how well the effective theory describes the main features of simple models with s-channel and t-channel mediators coupling to the Standard Model at tree level or through one-loop diagrams. Our results indicate that global dark matter analyses in terms of effective Lagrangians are highly non-trivial to interpret in term of actual models.

hep-ph↗

arXiv2016

Moving Charged Particles in Lattice Boltzmann-Based Electrokinetics

The motion of ionic solutes and charged particles under the influence of an electric field and the ensuing hydrodynamic flow of the underlying solvent is ubiquitous in aqueous colloidal suspensions. The physics of such systems is described by a coupled set of differential equations, along with boundary conditions, collectively referred to as the electrokinetic equations. Capuani et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for solving this system of equations, which builds upon the lattice Boltzmann algorithm for the simulation of hydrodynamic flow and exploits computational locality. However, thus far, a description of how to incorporate moving boundary conditions into the Capuani scheme has been lacking. Moving boundary conditions are needed to simulate multiple arbitrarily-moving colloids. In this paper, we detail how to introduce such a particle coupling scheme, based on an analogue to the moving boundary method for the pure LB solver. The key ingredients in our method are mass and charge conservation for the solute species and a partial-volume smoothing of the solute fluxes to minimize discretization artifacts. We demonstrate our algorithm's effectiveness by simulating the electrophoresis of charged spheres in an external field; for a single sphere we compare to the equivalent electro-osmotic (co-moving) problem. Our method's efficiency and ease of implementation should prove beneficial to future simulations of the dynamics in a wide range of complex nanoscopic and colloidal systems that was previously inaccessible to lattice-based continuum algorithms.

cond-mat.soft↗

arXiv2016

A Numerical Framework for Sobolev Metrics on the Space of Curves

Statistical shape analysis can be done in a Riemannian framework by endowing the set of shapes with a Riemannian metric. Sobolev metrics of order two and higher on shape spaces of parametrized or unparametrized curves have several desirable properties not present in lower order metrics, but their discretization is still largely missing. In this paper, we present algorithms to numerically solve the geodesic initial and boundary value problems for these metrics. The combination of these algorithms enables one to compute Karcher means in a Riemannian gradient-based optimization scheme and perform principal component analysis and clustering. Our framework is sufficiently general to be applicable to a wide class of metrics. We demonstrate the effectiveness of our approach by analyzing a collection of shapes representing HeLa cell nuclei.

math.DG↗

arXiv2016

Analyzing the CP Nature of a New Scalar Particle via S->Zh Decay

Scalar particles $S$ which are singlets under the Standard Model gauge group are generic features of many models of fundamental physics, in particular as possible mediators to a hidden sector. We show that the decay $S\to Zh$ provides a powerful probe of the CP nature of the scalar, because it is allowed only if $S$ has CP-odd interactions. We perform a model-independent analysis of this decay using an effective Lagrangian and compute the relevant Wilson coefficients arising from integrating out heavy fermions to one-loop order.

hep-ph↗

arXiv2016

Extreme Scale-out SuperMUC Phase 2 - lessons learned

In spring 2015, the Leibniz Supercomputing Centre (Leibniz-Rechenzentrum, LRZ), installed their new Peta-Scale System SuperMUC Phase2. Selected users were invited for a 28 day extreme scale-out block operation during which they were allowed to use the full system for their applications. The following projects participated in the extreme scale-out workshop: BQCD (Quantum Physics), SeisSol (Geophysics, Seismics), GPI-2/GASPI (Toolkit for HPC), Seven-League Hydro (Astrophysics), ILBDC (Lattice Boltzmann CFD), Iphigenie (Molecular Dynamic), FLASH (Astrophysics), GADGET (Cosmological Dynamics), PSC (Plasma Physics), waLBerla (Lattice Boltzmann CFD), Musubi (Lattice Boltzmann CFD), Vertex3D (Stellar Astrophysics), CIAO (Combustion CFD), and LS1-Mardyn (Material Science). The projects were allowed to use the machine exclusively during the 28 day period, which corresponds to a total of 63.4 million core-hours, of which 43.8 million core-hours were used by the applications, resulting in a utilization of 69%. The top 3 users were using 15.2, 6.4, and 4.7 million core-hours, respectively.

cs.DC↗

arXiv2016

Diphoton Resonance from a Warped Extra Dimension

We argue that extensions of the Standard Model (SM) with a warped extra dimension, which successfully address the hierarchy and flavor problems of elementary particle physics, can provide an elegant explanation of the 750 GeV diphoton excess recently reported by ATLAS and CMS. A gauge-singlet bulk scalar with ${\cal O}(1)$ couplings to fermions is identified as the new resonance $S$, and the vector-like Kaluza-Klein excitations of the SM quarks and leptons mediate its loop-induced couplings to photons and gluons. The electroweak gauge symmetry almost unambiguously dictates the bulk matter content and hence the hierarchies of the $S\to γγ$, $WW$, $ZZ$, $Zγ$, $t\bar t$ and dijet decay rates. We find that the $S\to Zγ$ decay mode is strongly suppressed, such that $\mbox{Br}(S\to Zγ)/\mbox{Br}(S\toγγ)<0.1$. The hierarchy problem for the new scalar boson is solved in analogy with the Higgs boson by localizing it near the infrared brane. The infinite sums over the Kaluza-Klein towers of fermion states are finite and can be calculated in closed form with a remarkably simple result. Reproducing the observed $pp\to S\toγγ$ signal requires Kaluza-Klein masses in the multi-TeV range, consistent with bounds from flavor physics and electroweak precision observables. Useful side products of our analysis, which can be adapted to almost any model for the diphoton resonance, are the calculation of the gluon-fusion production cross section $σ(pp\to S)$ at NNLO in QCD, an exact expression for the inclusive $S\to gg$ decay rate at N$^3$LO, a study of the $S\to t\bar t h$ three-body decay and a phenomenological analysis of portal couplings connecting $S$ with the Higgs field.

hep-ph↗

arXiv2016

Learning from the New Higgs-like Scalar before It Vanishes

Motivated by a di-photon anomaly observed by ATLAS and CMS we develop an SFitter analysis for a combined electroweak-Higgs sector, and a scalar portal at the LHC. The theoretical description is based on the linear effective Lagrangian for the Higgs and gauge fields, combined with an additional singlet scalar. The key feature is the extraction of reliable information on the portal structure of the combined scalar potential. For the specific di-photon anomaly we find that the new state might well form such a Higgs portal. To obtain more conclusive results we define and test the connection of the Wilson coefficients in the Higgs and heavy scalar sectors, as suggested by a portal setup.

hep-ph↗

arXiv2016

The "forgotten" decay S -> Z+h as a CP analyzer

Scalar particles $S$ which are gauge singlets under the Standard Model are generic features of many models of fundamental physics, in particular as possible mediators to a hidden or dark sector. We show that the decay $S\to Zh$ provides a powerful probe of the CP nature of the scalar, because it is allowed only if $S$ has CP-odd interactions. We perform a model-independent analysis of this decay in the context of an effective Lagrangian and compute the relevant Wilson coefficients arising from integrating out heavy fermions to one-loop order. We illustrate our findings with the example of the 750 GeV diphoton resonance seen by ATLAS and CMS and show that the $S\to Zh$ decay rate could naturally be of similar magnitude or larger than the diphoton rate.

hep-ph↗

arXiv2016

Flavor Anomalies, the Diphoton Excess and a Dark Matter Candidate

We argue that the diphoton excess recently reported by ATLAS and CMS can be explained, along with several anomalies seen in the flavor sector, in models where a Standard-Model singlet scalar resonance with mass $M \approx 750$ GeV is produced in gluon fusion via loops containing a scalar color- triplet leptoquark $ϕ$. For a leptoquark mass $M_ϕ\lesssim$ 1 TeV, the production cross section is naturally in the 10 fb range. A large $S \to γγ$ branching ratio can be obtained by coupling the scalar S to new color-singlet fermions $χ$ with electroweak scale masses, which can be part of an $SU(2)_L$ multiplet, whose neutral component has the right mass and quantum numbers to be a dark matter candidate. Our model reveals a connection between flavor anomalies, the nature of dark matter and a new scalar, which acts as a mediator to the dark sector. The loop-mediated decay $S \to τ^+τ^-$ could be a striking signature of this model.

hep-ph↗

arXiv2016

One Leptoquark to Rule Them All: A Minimal Explanation for $R_{D^{(*)}}$, $R_K$ and $(g-2)_μ$

We show that by adding a single new scalar particle to the Standard Model, a TeV-scale leptoquark with the quantum numbers of a right-handed down quark, one can explain in a natural way three of the most striking anomalies of particle physics: the violation of lepton universality in $\bar B\to\bar K\ell^+\ell^-$ decays, the enhanced $\bar B\to D^{(*)}τ\barν$ decay rates, and the anomalous magnetic moment of the muon. Constraints from other precision measurements in the flavor sector can be satisfied without fine-tuning. Our model predicts enhanced $\bar B\to\bar K^{(*)}ν\barν$ decay rates and a new-physics contribution to $B_s\!-\!\bar B_s$ mixing close to the current central fit value.

hep-ph↗

arXiv2016

Hunting the Flavon

The next generation of experiments in particle physics will for the first time systematically test flavor physics models based on flavon fields. Starting from the current quark-flavor constrains on such models we show how the new generation of lepton flavor experiments will dominate indirect searches in the coming decades. A future 100 TeV hadron collider will then be the first experiment to probe flavons as propagating degrees of freedom. Our estimate of the collider reach relies on a proper treatment of backgrounds and detector effects. Complementary searches for indirect effects in lepton flavor experiments and propagating degrees of freedom at colliders are very limited at the LHC, but will be a new feature at a 100 TeV hadron collider.

hep-ph↗

arXiv2015

Creating the Fermion Mass Hierarchies with Multiple Higgs Bosons

After the Higgs boson discovery, it is established that the Higgs mechanism explains electroweak symmetry breaking and generates the masses of all particles in the Standard Model, with the possible exception of neutrino masses. The hierarchies among fermion masses and mixing angles remain however unexplained. We propose a new class of two Higgs doublet models in which a flavor symmetry broken at the electroweak scale addresses this problem. The models are strongly constrained by electroweak precision tests and the fact that they produce modifications to Higgs couplings and flavor changing neutral currents; they are also constrained by collider searches for extra scalar bosons. The surviving models are very predictive, implying unavoidable new physics signals at the CERN Large Hadron Collider, e.g. extra Higgs Bosons with masses $M < 700$ GeV.

hep-ph↗

arXiv2015

A Python Extension for the Massively Parallel Multiphysics Simulation Framework waLBerla

We present a Python extension to the massively parallel HPC simulation toolkit waLBerla. waLBerla is a framework for stencil based algorithms operating on block-structured grids, with the main application field being fluid simulations in complex geometries using the lattice Boltzmann method. Careful performance engineering results in excellent node performance and good scalability to over 400,000 cores. To increase the usability and flexibility of the framework, a Python interface was developed. Python extensions are used at all stages of the simulation pipeline: They simplify and automate scenario setup, evaluation, and plotting. We show how our Python interface outperforms the existing text-file-based configuration mechanism, providing features like automatic nondimensionalization of physical quantities and handling of complex parameter dependencies. Furthermore, Python is used to process and evaluate results while the simulation is running, leading to smaller output files and the possibility to adjust parameters dependent on the current simulation state. C++ data structures are exported such that a seamless interfacing to other numerical Python libraries is possible. The expressive power of Python and the performance of C++ make development of efficient code with low time effort possible.

cs.DC↗

arXiv2015

Hörmander's condition for normal bundles on spaces of immersions

Several representations of geometric shapes involve quotients of mapping spaces. The projection onto the quotient space defines two sub-bundles of the tangent bundle, called the horizontal and vertical bundle. We investigate in these notes the sub-Riemannian geometries of these bundles. In particular, we show for a selection of bundles which naturally occur in applications that they are either bracket generating or integrable.

math.DG↗

arXiv2015

Geometric investigations of a vorticity model equation

This article consists of a detailed geometric study of the one-dimensional vorticity model equation $$ω_{t} + uω_{x} + 2ωu_{x} = 0, \qquad ω= H u_{x}, \qquad t\in\mathbb{R},\; x\in S^{1}\,,$$ which is a particular case of the generalized Constantin-Lax-Majda equation. Wunsch showed that this equation is the Euler-Arnold equation on $\operatorname{Diff}(S^{1})$ when the latter is endowed with the right-invariant homogeneous $\dot{H}^{1/2}$-metric. In this article we prove that the exponential map of this Riemannian metric is not Fredholm and that the sectional curvature is locally unbounded. Furthermore, we prove a Beale-Kato-Majda-type blow-up criterion, which we then use to demonstrate a link to our non-Fredholmness result. Finally, we extend a blow-up result of Castro-Córdoba to the periodic case and to a much wider class of initial conditions, using a new generalization of an inequality for Hilbert transforms due to Córdoba-Córdoba.

math.AP↗