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While the classical methods of shadowgraph and schlieren do yield a shadow in the neighborhood of a shock, they often suffer from low power densities and the need for relatively long distances. Scanning methods may help in solving these problems. The paper describes various scanning techniques, presents experimental data obtained by mechanical scanning, and identifies conditions at which the data were taken.
SINDA '85/FLUINT handles complex problems involving pumps, valves, heat exchangers, and resistor-capacitor networks. When combining SINDA with another classic program, TRASYS II, users tackle thermal radiation problems, including shadowing by opaque or semitransparent surfaces. Utility programs automatically convert SINDA/TRASYS output to form compatible with NASTRAN-developed structures.
We introduce a technique to estimate error-mitigated expectation values on noisy quantum computers. Our technique performs shadow tomography on a logical state to produce a memory-efficient classical reconstruction of the noisy density matrix. Using efficient classical post-processing, one can mitigate errors by projecting into the codespace as in subspace expansion and taking powers of the density matrix as in virtual distillation. Relative to subspace expansion which requires Ω (2^((n-1)k) samples to estimate a Pauli observable with an [[n; k]] stabilizer code, our technique requires only Ө(2^k) samples. Relative to virtual distillation, our technique can compute powers of the density matrix without implementing additional copies of quantum states the quantum computer. We present numerical results using logical states encoded with up to sixty physical qubits and show fast convergence to error-free expectation values with only 10^5 samples under 1% depolarizing noise.
In near-term quantum applications, reducing errors and improving device reliability is an essential task. Towards these ends, various techniques have been introduced in recent literature, collectively referred to as quantum error mitigation techniques, for reducing errors in pre-fault-tolerant devices. Here, we introduce logical shadow tomography as a versatile error mitigation method. Our technique uses a stabilizer code to encode information in a logical state. Instead of doing active error correction, quantum states will be measured at the end of computation via shadow tomography and non-logical errors are projected out in the classical post-processing. Relative to quantum subspace expansion which requires O(2(M-1)L) experiments to estimate an logical Pauli observable encoded by an [[M, L, d]] code, our technique only requires 2L experiments, an important practical reduction in resources.
We study the identification of quantum phases of matter, at zero temperature, when only part of the phase diagram is known in advance. Following a supervised learning approach, we show how to use our previous knowledge to construct an observable capable of classifying the phase even in the unknown region. By using a combination of classical and quantum techniques, such as tensor networks, kernel methods, generalization bounds, quantum algorithms, and shadow estimators, we show that, in some cases, the certification of new ground states can be obtained with a polynomial number of measurements. An important application of our findings is the classification of the phases of matter obtained in quantum simulators, e.g. cold atom experiments, capable of efficiently preparing ground states of complex many-particle systems and applying simple measurements, e.g. single qubit measurements, but unable to perform a universal set of gates.
The analysis of solar sail planetocentric optimal trajectory problem is described. A computer program was produced to calculate optimal trajectories for a limited performance analysis. A square sail model is included and some consideration is given to a heliogyro sail model. Orbit to a subescape point and orbit to orbit transfer are considered. Trajectories about the four inner planets can be calculated and shadowing, oblateness, and solar motion may be included. Equinoctial orbital elements are used to avoid the classical singularities, and the method of averaging is applied to increase computational speed. Solution of the two-point boundary value problem which arises from the application of optimization theory is accomplished with a Newton procedure. Time optimal trajectories are emphasized, but a penalty function has been considered to prevent trajectories which intersect a planet's surface.
Images of Io taken by the Hubble Space Telescope (HST) Planetary Camera (PC) using filters at 7120 and 3577 A in April and May 1992 shortly after Io emerged from Jupiter's shadow have been analyzed for the effect of posteclipse brightening first report by Binder and Cruikshank (1964). The classic effect displays a 10% increase in brightening lasting for 10 to 15 min. This was not seen in any of the eclipses that were studied. A comparison of the 3577-A images with UV maps produced from images taken with Voyager 1 (McEwen 1988), showed little change in 13 years. The striking, detailed similarity of the two demonstrate that the Hubble Space Telescope Planetary Camera has the capability to monitor temporal changes on Io's surface.
We present a shadow-tomography-enhanced nonorthogonal quantum eigensolver (NOQE) for more efficient and accurate electronic structure calculations on near-term quantum devices. By integrating shadow tomography into the NOQE, the measurement cost scales linearly rather than quadratically with the number of reference states, while also reducing the required qubits and circuit depth by half. This approach enables extraction of all matrix elements via randomized measurements and classical postprocessing. We analyze its sample complexity and show that, for small systems, it remains constant in the high-precision regime, while for larger systems, it scales linearly with the system size. We further apply shadow-based error mitigation to suppress noise-induced bias without increasing quantum resources. Demonstrations on the hydrogen molecule in the strongly correlated regime achieve chemical accuracy under realistic noise, showing that our method is both resource-efficient and noise-resilient for practical quantum chemistry simulations in the near term.
We obtained HST-STIS spectra of Saturn's main rings in May 2011, using the G230L (and G430L) gratings, with final averaged radial resolution of 160 (and 330) km/pixel. The dataset filled a previous 200-330nm "spectral gap" between Cassini and ground-based spectra. The data provide radial profiles as a function of wavelength, but our most basic product at this point is a set of very low-noise spectra, radially averaged over broad regions of the rings (A, B, C, and Cassini Division). The raw spectra required special processing to remove artifacts due to extended-source grating scatter. We have modeled the spectra using a new particle surface model, which corrects for on-surface shadowing due to the likely very rough ring particle surfaces, and avoids overestimation of intra-mixed "neutral absorber". We correct for non-classical layer effects and finite ring optical depth, and relate our observed reflectivities to the spherical albedos of individual smooth particles. We model these smooth particle albedos using standard Hapke theory for regolith grain mixtures that are either homogeneous and "intramixed" (nonicy absorbers dispersed in water ice regolith grains) or heterogeneous "intimate" mixtures. As candidates for the nonicy contaminants we have considered amorphous carbon, aromatic-rich and aliphatic-rich organic tholins, silicates, hematite and iron metal. For the A and B rings, we find that iron metal (including a new theoretical estimate of the refractive indices of nanometer-sized grains of iron) is not spectrally steep enough in the 200-300nm range, and that aliphatic-rich tholins are either too steep at short wavelengths or too flat at long wavelengths. However, less than 1% by mass of aromatic-rich tholins provides a very good fit across the entire spectral range with no gratuitous "neutral absorber" needed, and a minimum of additional free parameters. The best fits require forward-scattering regolith grains. For the C Ring and Cassini Division, additional absorbers are needed (updated results will be given).
In this and companion papers, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the quantization of electromagnetism permits the existence of classical electric field states that do not obey Gauss’s law. These states are gauge invariant and their time evolution can be consistently described using the Schrödinger equation. The time evolution of these states is such that at the classical level, the full set of Maxwell’s equations would appear to hold, with the physical effects of these states being attributable to an auxiliary, static “shadow” charge density with no internal degrees of freedom. This density could affect the dynamics of charged particles in our universe and it may thus be of observational interest.
A computer code which will rapidly calculate time-optimal low thrust transfers is being developed as a mission analysis tool. The final program will apply to NEP or SEP missions and will include a variety of environmental effects. The current program assumes constant acceleration. The oblateness effect and shadowing may be included. Detailed state and costate equations are given for the thrust effect, oblateness effect, and shadowing. A simple but adequate model yields analytical formulas for power degradation due to the Van Allen radiation belts for SEP missions. The program avoids the classical singularities by the use of equinoctial orbital elements. Kryloff-Bogoliuboff averaging is used to facilitate rapid calculation. Results for selected cases using the current program are given.
Solar shadow calculations are needed in building energy modeling and performance simulation of PV systems installed on roofs or facades of buildings. We present a quantum computing approach for calculation of building surface sunlit fractions by recasting solar visibility as a binary optimization problem solved by quantum annealing. Each triangulated surface centroid is encoded as a binary qubit indicating sunlit or shaded status. Geometric visibility constraints are derived from the Möller-Trumbore intersection algorithm and converted into a constrained quadratic binary model compatible with contemporary quantum annealers. The coefficients were embedded to D-Wave quantum computer. To demonstrate feasibility, we conducted a case study in San Francisco for a target building with 52 triangles and roughly 2700 nearby triangles within 50 m evaluated at representative winter and summer solar positions. The results demonstrated that quantum annealing can reliably calculate and distinguish sunlit from shaded surfaces. Quantum samples achieved average accuracy exceeding 92.4 %, with the aggregate surface-level agreement approaching 99.9 %. The outputs of quantum computers agreed closely with classical algorithms, indicating practical feasibility and promising scalability. Finally, the hourly sunlit fractions of building surfaces can be obtained for urban energy modelling. This is the first study to apply quantum computing to the solar shadow and building surface sunlit calculation. It introduces a new paradigm that differs fundamentally from traditional approaches.
In order to obtain a measure of its responses to short circuits a large horizontal axis wind turbine generator was modeled and its performance was simulated on a digital computer. Simulation of short circuit faults on the synchronous alternator of a wind turbine generator, without resort to the classical assumptions generally made for that analysis, indicates that maximum clearing times for the system tied to an infinite bus are longer than the typical clearing times for equivalent capacity conventional machines. Also, maximum clearing times are independent of tower shadow and wind shear. Variation of circuit conditions produce the modifications in the transient response predicted by analysis.
A bulge surface, on a time reflection-symmetric Cauchy slice of a holographic spacetime, is a non-minimal extremal surface that occurs between two locally minimal surfaces homologous to a given boundary region. According to the python’s lunch conjecture of Brown et al., the bulge’s area controls the complexity of bulk reconstruction, in the sense of the amount of post-selection that needs to be overcome for the reconstruction of the entanglement wedge beyond the outermost extremal surface. We study the geometry of bulges in a variety of classical spacetimes, and discover a number of surprising features that distinguish them from more familiar extremal surfaces such as Ryu-Takayanagi surfaces: they spontaneously break spatial isometries, both continuous and discrete; they are sensitive to the choice of boundary infrared regulator; they can self-intersect; and they probe entanglement shadows, orbifold singularities, and compact spaces such as the sphere in AdS _p× S^q p × S q . These features imply, according to the python’s lunch conjecture, novel qualitative differences between complexity and entanglement in the holographic context. We also find, surprisingly, that extended black brane interiors have a non-extensive complexity; similarly, for multi-boundary wormhole states, the complexity pleateaus after a certain number of boundaries have been included.
Using the covariant phase space formalism, we construct the phase space for non-Abelian gauge theories in (d+2)-dimensional Minkowski spacetime for any d ≥ 2, including the edge modes that symplectically pair to the low energy degrees of freedom of the gauge field. Despite the fact that the symplectic form in odd and even-dimensional spacetimes appear ostensibly different, we demonstrate that both cases can be treated in a unified manner by utilizing the shadow transform. Upon quantization, we recover the algebra of the vacuum sector of the Hilbert space and derive a Ward identity that implies the leading soft gluon theorem in (d+2)-dimensional spacetime.
The basic equations of quantum scattering were translated into the Wigner representation, putting quantum mechanics in the form of a stochastic process in phase space, with real valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte-Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two body problem. Simple expressions for single and double scattering contributions to total and differential cross-sections as well as for all necessary shadow corrections are obtained.
A new computational technique, Wave Confinement (WC), is extended here to account for sound diffraction around arbitrary terrain. While diffraction around elementary scattering objects, such as a knife edge, single slit, disc, sphere, etc. has been studied for several decades, realistic environments still pose significant problems. This new technique is first validated against Sommerfeld's classical problem of diffraction due to a knife edge. This is followed by comparisons with diffraction over three-dimensional smooth obstacles, such as a disc and Gaussian hill. Finally, comparisons with flight test acoustics data measured behind a hill are also shown. Comparison between experiment and Wave Confinement prediction demonstrates that a Poisson spot occurred behind the isolated hill, resulting in significantly increased sound intensity near the center of the shadowed region.
A ray acoustics approach to fuselage scattering of rotor noise is considered. The method is based on a combination of classical geometrical acoustics and the paraxial ray approximation. The method can handle scattering by objects of arbitrary shapes and can be applied in an inhomogeneous moving medium. Applications to aeroacoustics include the scattering of blade vortex interaction (BVI) pulses by rigid scattering objects. The BVI is modeled by a rotating impulsive point force. It has been found that scattering effects of rotating sources cannot be ignored. Flow has also been found to cause a modification and displacement of the directivity pattern and the shadow zones behind scatterers.