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26 records · Page 2

Exploring gauge-fixing conditions with gradient-based optimization

Lattice gauge fixing is required to compute gauge-variant quantities, for example those used in RI-MOM renormalization schemes or as objects of comparison for model calculations. Recently, gauge-variant quantities have also been found to be more amenable to signal-to-noise optimization using contour deformations. These applications motivate systematic parameterization and exploration of gauge-fixing schemes. This work introduces a differentiable parameterization of gauge fixing which is broad enough to cover Landau gauge, Coulomb gauge, and maximal tree gauges. The adjoint state method allows gradient-based optimization to select gauge-fixing schemes that minimize an arbitrary target loss function.

Detmold, William↗

Evaluation of data obtained from atmospheric laser Doppler velocimeter

The Doppler lidar velocimeter produces a variety of kinds of data. Besides the line of sight velocity components, there are the reflected amplitudes and the Doppler widths. Computer graphics software for displaying these data was produced. Different methods of presentation are needed for the various items. A picture was produced as pictures are often the best way to gain understanding. The individual lidar scans form a crosshatch pattern. Thus one-dimensional measurements fit together to form a two-dimensional whole. A pair of velocity measurements at a point combine to form a wind measurement with direction and magnitude. This gives a forest of wind vectors. The goal is to find a recognizable pattern to these trees. Often it is necessary to show only part of the information. That is, show only the wind direction not its magnitude or reduce the wind to streamlines of air flow. In other cases data are reduced to contour plots. Just enough contour lines are included to show the picture described.

Keck, T. S.↗

A double copy from twisted (co)homology at genus one

We study the twisted (co)homology of a family of genus-one integrals — the so called Riemann-Wirtinger integrals. These integrals are closely related to one-loop string amplitudes in chiral splitting where one leaves the loop-momentum, modulus and all but one puncture un-integrated. While not actual one-loop string integrals, they share many properties and are simple enough that the associated twisted (co)homologies have been completely characterized [1]. Using intersection numbers — an inner product on the vector space of allowed differential forms — we derive the Gauss-Manin connection for two bases of the twisted cohomology providing an independent check of [2]. We also use the intersection index — an inner product on the vector space of allowed contours — to derive a double-copy formula for the closed-string analogues of Riemann-Wirtinger integrals (one-dimensional integrals over the torus). Similar to the celebrated KLT formula between open- and closed-string tree-level amplitudes, these intersection indices form a genus-one KLT-like kernel defining bilinears in meromorphic Riemann-Wirtinger integrals that are equal to their complex counterparts.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Comparison of different methods for estimating snowcover in forested, mountainous basins using LANDSAT (ERTS) images

Snow-covered areas on LANDSAT (ERTS) images of the Santiam River basin, Oregon, and other basins in Washington were measured using several operators and methods. Seven methods were used: (1) Snowline tracing followed by measurement with planimeter, (2) mean snowline altitudes determined from many locations, (3) estimates in 2.5 x 2.5 km boxes of snow-covered area with reference to snow-free images, (4) single radiance-threshold level for entire basin, (5) radiance-threshold setting locally edited by reference to altitude contours and other images, (6) two-band color-sensitive extraction locally edited as in (5), and (7) digital (spectral) pattern recognition techniques. The seven methods are compared in regard to speed of measurement, precision, the ability to recognize snow in deep shadow or in trees, relative cost, and whether useful supplemental data are produced.

Meier, M. J.↗

Loop amplitudes monodromy relations and color-kinematics duality

Color-kinematics duality is a remarkable conjectured property of gauge theory which, together with double copy, is at the heart of a wealth of new developments in scattering amplitudes. So far, its validity has been verified in most cases only empirically, with limited ab initio understanding beyond tree-level. In this paper we provide initial steps in a first-principle understanding of color-kinematics duality and double-copy at loop level, through a detailed analysis of the field-theory limit of the monodromy relations of string theory at one loop. In this limit, we dissect the type of Feynman graphs generated and the relations they obey. We find that graphs with contact-terms are unavoidable and are generated in the field theory limit of “bulk” contours which do not have a standard physical interpretation in string perturbation theory. We show how they are related to ambiguities in the definition of the loop momentum and that their role is precisely to cancel those ambiguities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Shadow of a laser beam

Light, being massless, casts no shadow; under ordinary circumstances, photons pass right through each other unimpeded. Here, we demonstrate a laser beam acting like an object — the beam casts a shadow upon a surface when the beam is illuminated by another light source. We observe a regular shadow in the sense it can be seen by the naked eye, it follows the contours of the surface it falls on, and it follows the position and shape of the object (the laser beam). Specifically, we use a nonlinear optical process involving four atomic levels of ruby. We are able to control the intensity of a transmitted laser beam by applying another perpendicular laser beam. We experimentally measure the dependence of the contrast of the shadow on the power of the laser beam, finding a maximum of approximately 22%, similar to that of a shadow of a tree on a sunny day. We provide a theoretical model that predicts the contrast of the shadow. This work opens new possibilities for fabrication, imaging, and illumination.

47 OTHER INSTRUMENTATION↗

On unitarity of tree-level string amplitudes

Four-particle tree-level scattering amplitudes in string theory are magically consistent with unitarity, reflected in the non-trivial fact that beneath the critical dimension, the residues of the amplitudes on massive poles can be expanded in partial waves with all positive coefficients. While this follows (rather indirectly) from the no-ghost theorem, the simplicity of the statement and its fundamental importance for the physical consistency of string theory begs for a more direct and elementary understanding. In this note we take a step in this direction by presenting a new expression for the partial wave coefficients of string amplitudes, given by surprisingly simple double/triple contour integrals for open/closed strings. This representation allows us to directly prove unitarity of all superstring theories in D ≤ 6 spacetime dimensions, and can also be used to determine various asymptotics of the partial waves at large mass levels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Low-Cost Aero Technology Demonstrations

The main focus of this work was to demonstrate the use of polymeric additive manufacturing (AM) to create tooling for both preforming and consolidation. Polymeric tooling was utilized where both modest and higher pressures are used for part consolidation. The key focus for the AM tooling development was for fabrication of complex structures such as ducting, C-channel stiffened skins, and airfoils where conventional male tooling would typically be trapped in the cured part. The AM tooling was evaluated for use as a tool master used to fabricate and re-shape deformable/re-formable mandrels based on SpinTech’s shape memory composite technology known as Smart Tooling. The AM tooling was also evaluated for use as a mold for composite infusion and consolidation. Key performance parameters were tracked for project schedule completion with each step comprising of “art to part” cycle time, cost, and model fidelity for dimensions, performance, and cost. The primary focus of this demonstration was to determine if a 50% cost reduction was achievable, for each AM tooling-set, as compared to conventional processes. UDRI leveraged project partner SpinTech, who manufactures tools and parts in these categories and thus provided a baseline regarding current best practices and provided valuable feedback during the entirety of this demonstration. This demonstration primarily focused on the use of AM tooling for fabrication of three composite component structures which are typically utilized in aircraft and comprise salient geometric features of broad interest. These components are often tooling intensive and have features requiring extraction of male tools which are usually trapped by the geometry. The three structures selected by the team included: 1) A one-piece airfoil shell comprised of compound contours where male tooling would be trapped unless the part were manufactured in two halves as is typically the case. 2) A one-piece duct used for air handling, comprised of compound contours where male tooling would be trapped unless the part were manufactured in two halves, or a washout mandrel were to be used. 3) A co-cured C-channel stiffened skin where typically C-channels would be individually manufactured and then bonded to a cured skin. The demonstration was comprised of three main tasks: • Task 1: AM Tool Feasibility Study – ensure the AM tooling meets the performance requirements as specified by SpinTech to match baseline performance. • Task 2: Complex Tool Demonstration – Fabricate tooling, preforms, and parts representative of an airfoil and duct. • Task 3: Large Aerostructure Fabrication Demonstration – Fabricate tooling, preforms, and part representative of a C-channel stiffened skin. With the conclusion of this project, a decision tree was developed to determine the key considerations necessary to determine if use of AM tooling for the three selected structures was able to attain the same quality as historically achieved on metallic tooling, while providing a significant cost reduction.

36 MATERIALS SCIENCE↗