The WARP Reactor Concept
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Method and apparatus for weaving curved material preforms
A method and apparatus for fabricating straight or curved planar or three-dimensional (C channel, for example) fabric for fabrication into composite structures is presented. In the first embodiment, the fill yarns are inserted between layers of warp yarns, and a canted or curved reed, depending on the desired orientation of the fill yarns, is used to compact or 'beat-up' the fill yarns. In the second embodiment, the warp yarns of the fabric are curved using a conical or a combination of conical and cylindrical rollers to effect differential fabric take-up of the warp yarns for obtaining a constant radius of curvature of the warp yarns. In a third embodiment, a clamping bar fabric take-up device is used to effect the differential fabric take-up of the warp yarns for obtaining straight warp yarns, curved warp yarns with a constant radius of curvature, curved warp yarns with a non-contant radius of curvature, or some combinations of straight and curved warp yarns. In a fourth embodiment, for forming the flanges of the curved C channel, the warp yarns are alternately inserted through adjacent dent wires of the reed to permit vertical weaving of the flanges.
Farley, Gary L.↗
Modeling approaches for addressing unrelaxable bound constraints with unconstrained optimization methods
We explore novel approaches for solving nonlinear optimization problems with unrelaxable bound constraints, which must be satisfied before the objective function can be evaluated. Our method reformulates the unrelaxable bound-constrained problem as an unconstrained optimization problem that is amenable to existing unconstrained optimization methods. The reformulation relies on a domain warping to form a merit function; the choice of the warping determines the level of exactness with which the unconstrained problem can be used to find solutions to the bound-constrained problem, as well as key properties of the unconstrained formulation such as smoothness. We develop theory when the domain warping is a multioutput sigmoidal warping, and we explore the practical elements of applying unconstrained optimization methods to the formulation. Here, we develop an algorithm that exploits the structure of the sigmoidal warping to guarantee that unconstrained optimization algorithms applied to the merit function will find a stationary point to the desired tolerance.
97 MATHEMATICS AND COMPUTING↗
The interacting pair Mkn 305/306
Direct images and spectra at different slit positions of the interacting system Mkn 305/306 are discussed. Both galaxies show starburst properties due to tidal interaction. The morphology and velocity structure of Mkn 306 reveals the strongest warp of a stellar disk so far known. The galaxies Mkn 305 and Mkn 306 form a double system with 30 arcsec separation and having a common envelope at m sub B greater than or equal to 24.5. Furthermore a small tidal tail west of Mkn 305A, an isophote twist of Mkn 305 and the near identical redshifts of the two galaxies prove that this is a physical pair. Mkn 306 itself was classified as a double nucleus galaxy (Petrosyan et al., 1978). The optical morphology of Mkn 306 has the form of an integral sign which is similar to the radio morphology of strongly warped galaxies (Bottema et al., 1987). But in the optical the warp of the stellar component is normally far weaker than in the radio for the HI-gas. Therefore the authors investigate whether the double nucleus structure of Mkn 306 is real or an artifact due to an extreme warp in the optical. The origin for the warp phenomenon is not clear yet. Direct images of the galaxy system were taken with the Calar Alto 2.2m telescope in the B-band and at La Silla in the r-band using the 2.2m telescope; low dispersion spectra (240 A/mm) as well as high dispersion spectra (56 A/mm) for studying the velocity field were taken with the Calar Alto 3.5m telescope at different position angles. Also a spectrum of Mkn 305 was taken at Calar Alto with the 3.5m telescope covering the whole spectral range (240 A/mm).
Dietrich, Matthias↗
Frame Shift/warp Compensation for the ARID Robot System
The Automatic Radiator Inspection Device (ARID) is a system aimed at automating the tedious task of inspecting orbiter radiator panels. The ARID must have the ability to aim a camera accurately at the desired inspection points, which are in the order of 13,000. The ideal inspection points are known; however, the panel may be relocated due to inaccurate parking and warpage. A method of determining the mathematical description of a translated as well as a warped surface by accurate measurement of only a few points on this surface is developed here. The method uses a linear warp model whose effect is superimposed on the rigid body translation. Due to the angles involved, small angle approximations are possible, which greatly reduces the computational complexity. Given an accurate linear warp model, all the desired translation and warp parameters can be obtained by knowledge of the ideal locations of four fiducial points and the corresponding measurements of these points on the actual radiator surface. The method uses three of the fiducials to define a plane and the fourth to define the warp. Given this information, it is possible to determine a transformation that will enable the ARID system to translate any desired inspection point on the ideal surface to its corresponding value on the actual surface.
Latino, Carl D.↗
Second harmonic generation in topological insulators under quantizing magnetic fields
We theoretically investigate the second harmonic generation (SHG) of topological insulator surface states in a perpendicular magnetic field. Our theory is based on the microscopic expression of the second-order magneto-optical conductivity developed from the density matrix formalism, taking into account hexagonal warping effects on the surface states' band structure. Using numerically exact Landau-level energies and wave functions including hexagonal warping, we calculate the spectrum of SHG conductivities under normal incidence for different values of magnetic field and chemical potential. The imaginary parts of the SHG conductivities show prominent resonant peaks corresponding to one-photon and two-photon inter-Landau-level transitions. Treating the hexagonal warping term perturbatively, these transitions are clarified analytically within a perturbation theory from which approximate selection rules for the allowable optical transitions for SHG are determined. Furthermore, our results show extremely high SHG susceptibility that is easily tunable by magnetic field and doping level for topological surface states in the far-infrared regime, exceeding that of many conventional nonlinear materials. This work highlights the key role of hexagonal warping effects in generating second-order optical responses and provides insights into the nonlinear magneto-optical properties of the topological insulators.
Landau levels↗
Weaving multi-layer fabrics for reinforcement of engineering components
The performance of interlinked, multi-layer fabrics and near net shape preforms for engineering applications, woven on a 48 shaft dobby loom using glass, aramid, and carbon continuous filament yarns is assessed. The interlinking was formed using the warp yarns. Two basic types of structure were used. The first used a single warp beam and hence each of the warp yarns followed a similar path to form four layer interlinked reinforcements and preforms. In the second two warp beams were used, one for the interlinking yarns which pass from the top to the bottom layer through-the-thickness of the fabric and vice versa, and the other to provide 'straight' yarns in the body of the structure to carry the axial loading. Fabrics up to 15mm in thickness were constructed with varying amounts of through-the-thickness reinforcement. Tapered T and I sections were also woven, with the shaping produced by progressive removal of ends during construction. These fabrics and preforms were impregnated with resin and cured to form composite samples for testing. Using these two basic types of construction, the influence of reinforcement construction and the proportion and type of interlinking yarn on the performance of the composite was assessed.
Hill, B. J.↗
Method of forming variable cross-sectional shaped three-dimensional fabrics
Method of weaving a variable cross-sectional shaped three-dimensional fabric which utilizes different weft yarn insertion from at least one side of the warp layers for selectively inserting weft yarns into different portions of the fabric cross-sectional profile defined by the warp yarn layers during the weaving process. If inserted from both sides of the warp yarn layers, the weft yarns may be inserted simultaneously or alternately from each side of the warp yarn layers. The vertical yarn is then inserted into the fabric by reciprocation of a plurality of harnesses which separate the vertical yarn into a plurality of vertical yarn systems as required by the shape of the three-dimensional fabric being formed.
Mohamed, Mansour H.↗
Functional Data Analysis of Spaceflight-Induced Changes in Coordination and Phase in Head Pitch Acceleration During Treadmill Walking
Astronauts returning from spaceflight experience neurovestibular disturbances during head movements and attempt to mitigate them by limiting head motion. Analyses to date of the head movements made during walking have concentrated on amplitude and variability measures extracted from ensemble averages of individual gait cycles. Phase shifts within each gait cycle can be determined by functional data analysis through the computation of time-warping functions. Large, localized variations in the timing of peaks in head kinematics may indicate changes in coordination. The purpose of this study was to determine timing changes in head pitch acceleration of astronauts during treadmill walking before and after flight. Six astronauts (5M/1F; age = 43.5+/-6.4yr) participated in the study. Subjects walked at 1.8 m/sec (4 mph) on a motorized treadmill while reading optotypes displayed on a computer screen 4 m in front of their eyes. Three-dimensional motion of the subject s head was recorded with an Inertial Measurement Unit (IMU) device. Data were recorded twice before flight and four times after landing. The head pitch acceleration was calculated by taking the time derivative of the pitch velocity data from the IMU. Data for each session with each subject were time-normalized into gait cycles, then registered to align significant features and create a mean curve. The mean curves of each postflight session for each subject were re-registered based on their preflight mean curve to create time-warping functions. The root mean squares (RMS) of these warping functions were calculated to assess the deviation of head pitch acceleration mean curves in each postflight session from the preflight mean curve. After landing, most crewmembers exhibited localized shifts within their head pitch acceleration regimes, with the greatest deviations in RMS occurring on landing day or 1 day after landing. These results show that the alteration of head pitch coordination due to spaceflight may be assessed using an analysis of time-warping functions.
Miller, Christopher↗
Phase transitions from the fifth dimension
We study the cosmological transition of 5D warped compactifications, from the high-temperature black-brane phase to the low-temperature Randall-Sundrum I phase. The transition proceeds via percolation of bubbles of IR-brane nucleating from the black-brane horizon. The violent bubble dynamics can be a powerful source of observable stochastic gravitational waves. While bubble nucleation is non-perturbative in 5D gravity, it is amenable to semiclassical treatment in terms of a “bounce” configuration interpolating between the two phases. We demonstrate how such a bounce configuration can be smooth enough to maintain 5D effective field theory control, and how a simple ansatz for it places a rigorous lower-bound on the transition rate in the thin-wall regime, and gives plausible estimates more generally. When applied to the Hierarchy Problem, the minimal Goldberger-Wise stabilization of the warped throat leads to a slow transition with significant supercooling. We demonstrate that a simple generalization of the Goldberger-Wise potential modifies the IR-brane dynamics so that the transition completes more promptly. Supercooling determines the dilution of any (dark) matter abundances generated before the transition, potentially at odds with data, while the prompter transition resolves such tensions. We discuss the impact of the different possibilities on the strength of the gravitational wave signals. Via AdS/CFT duality the warped transition gives a theoretically tractable holographic description of the 4D Composite Higgs (de)confinement transition. Our generalization of the Goldberger-Wise mechanism is dual to, and concretely models, our earlier proposal in which the composite dynamics is governed by separate UV and IR RG fixed points. The smooth 5D bounce configuration we introduce complements the 4D dilaton/radion dominance derivation presented in our earlier work.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo
Functional data registration is a necessary processing step for many applications. The observed data can be inherently noisy, often due to measurement error or natural process uncertainty; which most functional alignment methods cannot handle. A pair of functions can also have multiple optimal alignment solutions, which is not addressed in current literature. In this paper, a flexible Bayesian approach to functional alignment is presented, which appropriately accounts for noise in the data without any pre-smoothing required. Additionally, by running parallel MCMC chains, the method can account for multiple optimal alignments via the multi-modal posterior distribution of the warping functions. To most efficiently sample the warping functions, the approach relies on a modification of the standard Hamiltonian Monte Carlo to be well-defined on the infinite-dimensional Hilbert space. In this work, this flexible Bayesian alignment method is applied to both simulated data and real data sets to show its efficiency in handling noisy functions and successfully accounting for multiple optimal alignments in the posterior; characterizing the uncertainty surrounding the warping functions.
97 MATHEMATICS AND COMPUTING↗
Third-order Hall effect in the surface states of a topological insulator
Time reversal and inversion symmetric materials fail to yield linear and nonlinear responses since they possess net zero Berry curvature. However, higher-order Hall response can be generated in these systems upon constraining the crystalline symmetries. Motivated by the recently discovered third-order Hall (TOH) response mediated by Berry connection polarizability, namely, the variation of the Berry connection with respect to an applied electric field, here, we investigate the existence of such a Hall effect in the surface states of hexagonal warped topological insulators (e.g., Bi 2 Te 3 ) under the application of only electric field. Using the semiclassical Boltzmann formalism, we investigate the effect of tilt and hexagonal warping on the Berry connection polarizability tensor and, consequently, the TOH effect, provided the Dirac cone remains gapless. We find that the magnitude of the response increases significantly with increasing tilt strength and warping, and therefore, they can provide the tunability of this effect. In addition, we also explore the effect of chemical doping on the TOH response in this system. Interestingly, we show, based on the symmetry analysis, that the TOH can be the leading-order response in this system, which can directly be verified in experiments.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Advanced modeling of field enhanced thermionic emission
Shaped emitters are of interest to a broad range of applications in vacuum electronic devices. In particular, thermionic energy converters (TECs) take advantage of shaped emitters to increase the local surface field, thereby extracting more current for a given cathode temperature and applied voltage. However, modeling these devices is challenging; Warp [J.-L. Vay, D. P. Grote, R. H. Cohen, and A. Friedman, Comput. Sci. Discov. 5, 014019 (2012)] is a fully 3D particle-in-cell code capable of handling a wide range of physics problems and is well suited to modeling TECs. Additionally, recent improvements to Warp have enabled the accurate modeling of emitters with arbitrary curved surfaces. Specifically, the inclusion of subgrid resolution for computing the electrostatic potential and the ability to apply mesh refinement for specific areas of interest allow for a more accurate solution to the fields on these surfaces. These improvements coupled with Warp’s ability to handle variable particle weights make it an ideal candidate for simulating these complex devices. In this paper, the authors study the applicability of different subgrid configurations for simulating shaped emission surfaces and field convergence for different mesh-refinement techniques. They then implement a custom weighting algorithm that allows for uniform sampling of emission surfaces with a large variation in the surface electric field. They then use this algorithm to study emission for curved emitters in both the field-enhancement regime and the space-charge regime.
Edelen, Jonathan P. (ORCID:0000000215180652)↗
Epeirogeny and plate tectonics
This review is generated by an intensification of interest in a classical subject of geology, vertical motions of the crust and their causes. The subject was examined qualitatively for more than a century within a paradigm of a mainly static earth that merely moved up and down. The new interest derives from the fact that some aspects of vertical motion can now be explained semi‐quantitatively and also from the realization that, in the paradigm of a dynamic earth, some vertical motions are related to horizontal drifting. The fact that large regions of the earth are warped vertically has been known since the beginnings of modern geology. Lyell [1835] cites Playfair and Von Buch among others who recognized the uplift of Scandinavia. Likewise, Darwin [1842] observed that the distribution of atolls and elevated islands establishes regional warping of ocean basins. The term ‘epeirogeny’ was coined by Gilbert [1890] to describe this broad, gentle warping, which is such a common feature of the history of the whole earth.
H. W. Menard↗
Influence of the solar magnetic field on tropospheric circulation
The solar and interplanetary magnetic sector structure has its source in a large-scale photospheric magnetic field structure that is carried away from the sun by the solar wind to form a warped equatorial current sheet in the heliosphere; this current sheet makes one complete rotation past the earth in the solar rotation period of 27 days. Several advantages in using the heliospheric warped current sheet in sun-weather investigations are noted. Sun-weather analyses are described, where the time at which the warped current sheet is observed to be carried past the earth by the solar wind gives the phase information. Individual troughs crossing 180 deg longitude when the IMF is directed away from the sun are significantly larger than troughs crossing 180 deg longitude when the field is toward the sun. Possible physical mechanisms are identified, including an observed influence of the heliospheric current sheet on the vertical electric field in the troposphere.
Wilcox, J. M.↗
Effects of drift on the transport of cosmic rays. VI - A three-dimensional model including diffusion
The first results are presented from a series of computer simulations of the solar modulation of galactic cosmic rays using a full three-dimensional model which incorporates all known important effects on particle transport, particle drifts, convection with the solar wind, energy loss, and anisotropic diffusion. The model is time-independent in the coordinate frame rotating with the sun, so corotating effects can be studied. Modulation in an interplanetary magnetic field model is considered in which the current sheet separating the northern and southern solar hemispheres is warped and corotating with the sun. The amplitude of the warp is varied to simulate possible solar cycle variation of the magnetic field. Substantial effects due to the warp of the current sheet are found. Comparison of the model results with various data is presented. Among other things, it is shown that the intensity may decrease away from the current sheet for both signs of the magnetic field, as suggested by recent observations, and in contrast with inferences from earlier, more approximate calculations.
Kota, J.↗
Residual stresses and their effects in composite laminates
Residual stresses in composite laminates are caused by the anisotropy in expansional properties of constituent unidirectional plies. The effect of these residual stresses on dimensional stability is studied through the warping of unsymmetric (0 sub 4/90 sub 4)sub T graphite/epoxy laminates while their effect on ply failure is analyzed for (0/90)sub 2s Kevlar 49/epoxy laminate. The classical laminated plate theory is used to predict the warping of small and large panels. The change of warping does not indicate a noticeable stress relaxation at 75 C while it is very sensitive to moisture content and hence to environment. A prolonged gellation at the initial cure temperature reduces residual stresses while postcure does not. The matrix/interface cracking in dry (0/90)sub 2s Kevlar 49/epoxy laminate is shown to be the result of the residual stress exceeding the transverse strength.
Hahn, H. T.↗
Tapered, tubular polyester fabric
A tapered tubular polyester sleeve is described to serve as the flexible foundation for a spacesuit limb covering. The tube has a large end and a small end with a length to be determined. The ratio of taper is also determined by scale factors. All the warp yarns extend to the large end. A requisite number of warp yarns extend the full length of the sleeve. Other warp yarns extend from the large end but are terminated along the length of the sleeve. It is then woven with a filling yarn which extends in a full circle along the full length of the sleeve to thereby define the tapered sleeve. The sleeve after fabrication is then placed on a mandrel, heated in an oven, and then attached to the arm or other limb of the spacesuit.
Lapointe, Donat J. E.↗