Volterra Series Approximation for Multi-Degree of Freedom, Multi-Input, Multi-Output, Aircraft Dynamics

An analytical model of a second order system is extended from a single-axis framework, to a multi-axis, multi-degree of freedom framework for a multiple input, multiple output system. This mathematical model is built from the variational approach of the Volterra series representation of nonlinear systems. The new representation describes the second order, oscillatory natural modes of a system, and shows how to organize the Volterra terms in intuitive ways. The constructed mathematical model aims to establish an organization of the Volterra kernels to allow for analytical cause and effect type analysis on system behavior. To demonstrate the accuracy of the developed Volterra model, the model is applied to atmospheric flight dynamics. A numerical simulation of an F-16 aircraft was developed based on the experimental data collected at NASA Langley and is compared to the Volterra model. Both longitudinal and latitudinal aircraft dynamics are analyzed, and the results show that the Volterra model effectively tracks the numerical simulations and has less error than a more conventional linearized system. The results show that weak nonlinearities of a system are predicted based on this new model. The construction of the model allows for a more effective analysis to the cause and effect of the response. Individual responses of each nonlinear component are separated for analysis, and each component’s effects on the total system response are observed

Power Corrections to the Universal Heavy WIMP-Nucleon Cross Section

WIMP-nucleon scattering is analyzed at order $1/M$ in Heavy WIMP Effective Theory. The $1/M$ power corrections, where $M\gg m_W$ is the WIMP mass, distinguish between different underlying UV models with the same universal limit and their impact on direct detection rates can be enhanced relative to naive expectations due to generic amplitude-level cancellations at leading order. The necessary one- and two-loop matching calculations onto the low-energy effective theory for WIMP interactions with Standard Model quarks and gluons are performed for the case of an electroweak SU(2) triplet WIMP, considering both the cases of elementary fermions and composite scalars. The low-velocity WIMP-nucleon scattering cross section is evaluated and compared with current experimental limits and projected future sensitivities. Our results provide the most robust prediction for electroweak triplet Majorana fermion dark matter direct detection rates; for this case, a cancellation between two sources of power corrections yields a small total $1/M$ correction, and a total cross section close to the universal limit for $M \gtrsim {\rm few} \times 100\,{\rm GeV}$. For the SU(2) composite scalar, the $1/M$ corrections introduce dependence on underlying strong dynamics. Using a leading chiral logarithm evaluation, the total $1/M$ correction has a larger magnitude and uncertainty than in the fermionic case, with a sign that further suppresses the total cross section. These examples provide definite targets for future direct detection experiments and motivate large scale detectors capable of probing to the neutrino floor in the TeV mass regime.Comment: 12 pages, 4 figures; references added, XENONnT projection included, version to appear in Physics Letters

Fully anharmonic infrared cascade spectra of polycyclic aromatic hydrocarbons

The infrared (IR) emission of polycyclic aromatic hydrocarbons (PAHs) permeates our universe; astronomers have detected the IR signatures of PAHs around many interstellar objects. The IR emission of interstellar PAHs differs from their emission as seen under conditions on Earth, as they emit through a collisionless cascade down through their excited vibrational states from high internal energies. The difficulty in reproducing interstellar conditions in the laboratory results in a reliance on theoretical techniques. However, the size and complexity of PAHs requires careful consideration when producing the theoretical spectra. In this work we outline the theoretical methods necessary to lead to a fully theoretical IR cascade spectra of PAHs including: an anharmonic second order vibrational perturbation theory (VPT2) treatment; the inclusion of Fermi resonances through polyads; and the calculation of anharmonic temperature band shifts and broadenings (including resonances) through a Wang--Landau approach. We also suggest a simplified scheme to calculate vibrational emission spectra that retains the essential characteristics of the full IR cascade treatment and can directly transform low temperature absorption spectra in IR cascade spectra. Additionally we show that past astronomical models were in error in assuming a 15 cm$^{-1}$ correction was needed to account for anharmonic emission effects

Low-energy Population III supernovae and the origin of extremely metal-poor stars

Some ancient, dim, metal-poor stars may have formed in the ashes of the first supernovae (SNe). If their chemical abundances can be reconciled with the elemental yields of specific Population III (Pop III) explosions, they could reveal the properties of primordial stars. But multidimensional simulations of such explosions are required to predict their yields because dynamical instabilities can dredge material up from deep in the ejecta that would otherwise be predicted to fall back on to the central remnant and be lost in one-dimensional (1D) models. We have performed two-dimensional (2D) numerical simulations of two low-energy Pop III SNe, a 12.4 Msun explosion and a 60 Msun explosion, and find that they produce elemental yields that are a good fit to those measured in the most iron-poor star discovered to date, SMSS J031300.36-670839.3 (J031300). Fallback on to the compact remnant in these weak explosions accounts for the lack of measurable iron in J031300 and its low iron-group abundances in general. Our 2D explosions produce higher abundances of heavy elements (atomic number Z > 20) than their 1D counterparts due to dredge-up by fluid instabilities. Since almost no Ni is ejected by these weak SNe, their low luminosities will prevent their detection in the near-infrared with the James Webb Space Telescope and future 30-m telescopes on the ground. The only evidence that they ever occurred will be in the fossil abundance record.Comment: Accepted to MNRA

Thermal noise of whispering gallery resonators

By direct application of the fluctuation-dissipation theorem, we numerically calculate the fundamental dimensional fluctuations of crystalline CaF2 whispering gallery resonators in the case of structural damping, and the limit that this noise imposes on the frequency stability of such resonators at both room and cryogenic temperatures. We analyze elasto-optic noise - the effect of Brownian dimensional fluctuation on frequency via the strain-dependence of the refractive index - a noise term that has so far not been considered for whispering-gallery resonators. We find that dimensional fluctuation sets a lower limit of 1E-16 to the Allan deviation for a 10-millimeter-radius sphere at 5 K, predominantly via induced fluctuation of the refractive index.Comment: 7 pages, 3 figure

Laminations and 2-filling rays on infinite type surfaces

The loop graph of an infinite type surface is an infinite diameter hyperbolic graph first studied in detail by Juliette Bavard. An important open problem in the study of infinite type surfaces is to describe the boundary of the loop graph as a space of geodesic laminations. We approach this problem by constructing the first examples of 2-filling rays on infinite type surfaces. Such rays accumulate onto geodesic laminations which are in some sense filling, but without strong enough properties to correspond to points in the boundary of the loop graph. We give multiple constructions using both a hands-on combinatorial approach and an approach using train tracks and automorphisms of flat surfaces. In addition, our approaches are sufficiently robust to describe all 2-filling rays with certain other basic properties as well as to produce uncountably many distinct mapping class group orbits.Comment: v2: minor update, 44 pages, 37 figure

Magnetic properties of iron pnictides from spin-spiral calculations

The wave-vector (q) and doping dependences of the magnetic energy, iron moment, and effective exchange interactions in LaFeAsO, BaFe2As2, and SrFe2As2\ are studied by self-consistent LSDA calculations for co-planar spin spirals. For the undoped compounds, the calculated total energy, E(q), reaches its minimum at q corresponding to stripe anti-ferromagnetic order. In LaFeAsO, this minimum becomes flat already at low levels of electron-doping and shifts to an incommensurate q at delta=0.2, where delta is the number of additional electrons (delta>0) or holes (delta<0) per Fe. In BaFe2As2 and SrFe2As2, stripe order remains stable for hole doping down to delta=-0.3. Under electron doping, on the other hand, the E(q) minimum shifts to incommensurate q already at delta=0.1.Comment: 4 pages, 2 figures, International Conference on Magnetism, Karlsruhe, July 26 - 31, 200

A Language and Hardware Independent Approach to Quantum-Classical Computing

Heterogeneous high-performance computing (HPC) systems offer novel architectures which accelerate specific workloads through judicious use of specialized coprocessors. A promising architectural approach for future scientific computations is provided by heterogeneous HPC systems integrating quantum processing units (QPUs). To this end, we present XACC (eXtreme-scale ACCelerator) --- a programming model and software framework that enables quantum acceleration within standard or HPC software workflows. XACC follows a coprocessor machine model that is independent of the underlying quantum computing hardware, thereby enabling quantum programs to be defined and executed on a variety of QPUs types through a unified application programming interface. Moreover, XACC defines a polymorphic low-level intermediate representation, and an extensible compiler frontend that enables language independent quantum programming, thus promoting integration and interoperability across the quantum programming landscape. In this work we define the software architecture enabling our hardware and language independent approach, and demonstrate its usefulness across a range of quantum computing models through illustrative examples involving the compilation and execution of gate and annealing-based quantum programs