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At least 127 records · Page 7

Higher-order moments of the elliptic flow distribution in PbPb collisions at $ \sqrt{s_{\textrm{NN}}}$ = 5.02 TeV

The hydrodynamic flow-like behavior of charged hadrons in high-energy lead-lead collisions is studied through multiparticle correlations. The elliptic anisotropy values based on different orders of multiparticle cumulants, v$_{2}${2k}, are measured up to the tenth order (k = 5) as functions of the collision centrality at a nucleon-nucleon center-of-mass energy of $ \sqrt{s_{\textrm{NN}}} $ = 5.02 TeV. The data were recorded by the CMS experiment at the LHC and correspond to an integrated luminosity of 0.607 nb$^{–1}$. A hierarchy is observed between the coefficients, with v$_{2}${2} > v$_{2}${4} ≳ v$_{2}${6} ≳ v$_{2}${8} ≳ v$_{2}${10}. Based on these results, centrality-dependent moments for the fluctuation-driven event-by-event v$_{2}$ distribution are determined, including the skewness, kurtosis and, for the first time, superskewness. Assuming a hydrodynamic expansion of the produced medium, these moments directly probe the initial-state geometry in high-energy nucleus-nucleus collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Tracking discontinuities in parameter space

We develop a geometric framework in Feynman-parameter space to determine constraints on the sequential discontinuities of Feynman integrals. Our method is based on tracking the deformation of the integration contour as external kinematics are analytically continued. This procedure imposes powerful constraints on the analytic structure of Feynman integrals, providing crucial inputs for their bootstrap. We demonstrate the usefulness of this framework by applying it to integrals in dimensional regularization, with higher propagator powers, and to examples with non-uniform transcendental weight. The method is illustrated with several one- and two-loop calculations.

Differential and Algebraic Geometry↗

Enhanced MPM framework with multipatch isogeometric analysis for geotechnical applications

Achieving stable stress solutions at large strains using the Material Point Method (MPM) is challenging due to the accumulation of errors associated with geometry discretization, cell-crossing noise, and volumetric locking. Several simplified attempts exist in the literature to mitigate these errors, including higher-order frameworks. However, the stability of the MPM solution in such frameworks has been limited to simple geometries and the single-phase formulation (i.e., neglecting pore fluid). Although never explored, multipatch isogeometric analysis offers desirable qualities to simulate complex geometries while mitigating errors in the MPM. The degree of required high-order spatial integration has also never been investigated to infer a minimum limit for the stability of the stress solution in MPM. This paper presents a general-purpose numerical framework for simulating stable stresses in porous media, capturing both near incompressibility and multiphase interactions. First, the numerical framework is presented considering Non-Uniform Rational B-splines (NURBS) to perform isogeometric analysis (IGA) in MPM. Additionally, a volumetric strain smoothing algorithm is used to alleviate errors associated with volumetric locking. Second, the manifestation of cell-crossing errors is assessed via a series of problems with orders ranging from linear to cubic interpolation functions. Third, the use of NURBS is investigated and verified for problems with circular geometries. Finally, multipatch analysis is deployed to simulate plane strain and 3D penetration in soils, considering nearly incompressible elastoplastic (total stress) analysis and fully-coupled hydro-mechanical (effective stress) analysis. The stability of the solution is also analyzed for different constitutive models. From the results, it can be concluded that the framework using cubic interpolation functions with strain smoothing is the most convenient, presenting stable stress solutions for a broad range of multiphase geotechnical applications.

58 GEOSCIENCES↗

Investigating Inherent Numerical Stabilization for the Moist, Compressible, Non‐Hydrostatic Euler Equations on Collocated Grids

This study investigates inherent numerical dissipation due to upwind fluxes and reconstruction strategies for collocated Finite-Volume integration of the Euler equations. Idealized supercell simulations are used without any explicit dissipation. Flux terms are split into: mass flux, pressure, and advected quantities. They are computed with the following upwind strategies: central, advectively upwind, and acoustically upwind. This is performed for third and ninth-order-accurate reconstructions with and without Weighted Essentially Non-Oscillatory limiting. Acoustic-only upwinding for pressure and mass flux terms and advective-only upwinding for advected quantities is the most flexible simplification found. It reduces data movement and computations. Assuming a constant speed of sound in acoustic upwinding gives similar results to using the true speed of sound. Dissipation from upwind adapts automatically to grid spacing, time step, reconstruction accuracy, and flow smoothness. While stability is maintained even at 21st-order spatial accuracy, there is a limit to the spatial order of accuracy for which upwinding alone can create a realizable solution in the conditions of this study. Convex combinations of upwind and central solutions for flux terms also reduced dissipation, but as the central proportion grows, solutions become physically unrealizable. The range of length scales of the kinetic energy spectra can be extended along k −5/3 to smaller spatial scales by reducing dissipation either with higher-order reconstructions or using convex combinations of upwind and central fluxes. However, not all extensions of the length scale range along k −5/3 exhibit physically realizable solutions, even though the spectra appear to be physical.

54 ENVIRONMENTAL SCIENCES↗

Hidden quantum criticality and entanglement in quench dynamics

Entanglement exhibits universal behavior near the ground-state critical point where correlations are long ranged and the thermodynamic entropy is vanishing. On the other hand, a quantum quench imparts extensive energy and results in a build up of entropy, hence no critical behavior is expected at long times. In this work, we present a new paradigm in the quench dynamics of integrable spin chains which exhibit a ground-state order-disorder phase transition at a critical line. Specifically, we consider a quench along the critical line which displays a volume-law behavior of the entropy and exponentially decaying correlations; however, we show that quantum criticality is hidden in higher-order correlations and becomes manifest via measures such as the mutual information and logarithmic negativity. Furthermore, we showcase the scale invariance of the Rényi mutual information between disjoint regions as further evidence for genuine critical behavior. We attribute the emergent quantum criticality to the soft mode not getting excited in spite of the quench. Moreover, the results presented here are universal to models whose low-energy or long-wavelength dynamics are well described by a free-fermionic field theory. Our results are amenable to an experimental realization on different quantum simulator platforms, particularly the Rydberg simulators. Published by the American Physical Society 2024

Paul, Sanku↗

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗

Toward Higher-order Accuracy in Self-gravitating Hydrodynamics

High-order algorithms have emerged in numerical astrophysics as a promising avenue to reduce truncation error (proportional to a power of the linear resolution Δ x ) with only a moderate increase to computational expense. Significant effort has been placed in the development of finite-volume algorithms for (magneto)hydrodynamics; however, state-of-the-art astrophysical simulations tightly couple a plenitude of physics, additionally including gravity, photon transport, cosmic-ray transport, chemistry, and/or diffusion, to name a few. Algorithms frequently operator-split this additional physics (often a first-order error in time) and/or adopt a model wherein their evaluation is limited to second-order accuracy in space. In this work, we present a fourth-order-accurate finite-volume scheme for self-gravitating hydrodynamics on a uniform Cartesian grid. The method supplies source terms for the gravitational acceleration ( ρ g ) and gravitational energy release ( ρ v · g ) associated with fourth-order-accurate solutions to the Poisson equation. Our scheme (1) guarantees the conservation of total linear momentum while (2) decreasing (in proportion to Δ x 4 ) the effects of spurious heating and/or cooling associated with truncation error in the gravity. We demonstrate expected convergence rates for the algorithm by measuring errors in test problems evolving self-gravity modified linear waves and 3D polytropic equilibria. We test robustness of the algorithm by integrating an induced “inside-out” adiabatic collapse. We also discuss a method to smoothly downgrade the solution to second-order spatial accuracy to avoid spurious overshoots near steep density and/or pressure gradients.

79 ASTRONOMY AND ASTROPHYSICS↗

A real-time approximate optimal guidance law for flight in a plane

A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.

Feeley, Timothy S.↗

On the use of residue theory for treating the subsonic flow of a compressible fluid

A new mathematical technique, due to Milne-Thomson, is used to obtain an improved form of the method of Poggi for calculating the effect of compressibility on the subsonic flow past an obstacle. By means of this new method, the difficult surface integrals of the original Poggi method can be replaced by line integrals. These line integrals are then solved by the use of residue theory. In this way an equation is obtained giving the second-order effect of compressibility on the velocity of the fluid. The method is practicable for obtaining the higher-order effects of compressibility on the velocity field. As an illustration of the general result, the flow past an elliptic cylinder is discussed.

Kaplan, Carl↗

A comparison of Lorentz, planetary gravitational, and satellite gravitational resonances

We consider a charged dust grain whose orbital motion is dominated by a planet's point-source gravity, but perturbed by higher-order terms in the planet's gravity field as well as by the Lorentz force arising from an asymmetric planetary magnetic field. Perturbations to Keplerian orbits due to a nonspherical gravity field are expressed in the traditional way: in terms of a disturbing function which can be expanded in a series of spherical harmonics (W. M. Kaula, 1966). In order to calculate the electromagnetic perturbation, we first write the Lorentz force in terms of the orbital elements and then substitute it into Gauss' perturbation equations. We use our result to derive strengths of Lorentz resonances and elucidate their properties. In particular, we compare Lorentz resonances to two types of gravitational resonances: those arising from periodic tugs of a satellite and those due to the attraction of an arbitrarily shaped planet. We find that Lorentz resonances share numerous properties with their gravitational counterparts and show, using simple physical arguments, that several of these patterns are fundamental, applying not only to our expansions, but to all quantities expressed in terms of orbital elements. Some of these patterns have been previously called 'd'Alembert rules' for satellite resonances. Other similarities arise because, to first-order in the perturbing force, the three problems share an integral of the motion. Yet there are also differences; for example, first-order inclination resonances exist for perturbations arising from planetary gravity and from the Lorentz force, but not for those due to an orbiting satellite. Finally, we provide a heuristic treatment of a particle's orbital evolution under the influence of drag and resonant forces. Particles brought into mean-motion resonances experience either trapping or resonant 'jumps,' depending on the direction from which the resonance is approached. We show that this behavior does not depend on the details of the perturbing force but rather is fundamental to all mean-motion resonances.

Hamilton, Douglas P.↗

Cooperation Among Theorem Provers

This is a final report, which supports NASA's PECSEE (Persistent Cognizant Software Engineering Environment) effort and complements the Kestrel Institute project "Inference System Integration via Logic Morphism". The ultimate purpose of the project is to develop a superior logical inference mechanism by combining the diverse abilities of multiple cooperating theorem provers. In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's, SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The PVS system (from SRI) in only automatic within decidable theories, but it has well-designed interactive capabilities: furthermore, it includes higher-order logic, not just first-order logic. The NuPRL system from Cornell University and the STeP system from Stanford University have facilities for constructive logic and temporal logic, respectively - both are interactive. It is often suggested - for example, in the anonymous "QED Manifesto"-that we should pool the resources of all these theorem provers into a single system, so that the strengths of one can compensate for the weaknesses of others, and so that effort will not be duplicated. However, there is no straightforward way of doing this, because each system relies on its own language and logic for its success. Thus. SNARK uses ordinary first-order logic with equality, PVS uses higher-order logic. and NuPRL uses constructive logic. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages. Kestrel's SPECWARE system has been the vehicle for the implementation.

Waldinger, Richard J.↗

Membrane peptides and their role in protobiological evolution

How simple membrane peptides performed such essential protocellular functions as transport of ions and organic matter across membranes separating the interior of the cell from the environment, capture and utilization of energy, and transduction of environmental signals, is a key question in protobiological evolution. On the basis of detailed, molecular-level computer simulations we explain how these peptides fold at water-membrane interfaces, insert into membranes, self-assemble into higher-order structures and acquire functions. We have investigated the interfacial behavior and folding of several peptides built of leucine and glutamine residues and have demonstrated that many of them tend to adopt ordered structures. Further, we have studied the insertion of an alpha-helical peptide containing leucine (L) and serine (S) of the form (LSLLLSL)3 into a model membrane. The transmembrane state is metastable, and approximately 15 kcal mol(-1) is required to insert the peptide into the membrane. Investigations of dimers formed by (LSLLLSL)3 and glycophorin A demonstrate how the favorable free energy of helix association can offset the unfavorable free energy of insertion, leading to self-assembly of peptide helices in the membrane. An example of a self-assembled structure is the tetrameric transmembrane pore of the influenza virus M2 protein, which is an efficient and selective voltage-gated proton channel. Our simulations explain the gating mechanism and provide guidelines how to re-engineer the channel to act as a simple proton pump. In general, emergence of integral membrane proteins appears to be quite feasible and may be easier to envision than the emergence of water-soluble proteins.

Models, Chemical↗

Advanced Small Perturbation Potential Flow Theory for Unsteady Aerodynamic and Aeroelastic Analyses

An advanced small perturbation (ASP) potential flow theory has been developed to improve upon the classical transonic small perturbation (TSP) theories that have been used in various computer codes. These computer codes are typically used for unsteady aerodynamic and aeroelastic analyses in the nonlinear transonic flight regime. The codes exploit the simplicity of stationary Cartesian meshes with the movement or deformation of the configuration under consideration incorporated into the solution algorithm through a planar surface boundary condition. The new ASP theory was developed methodically by first determining the essential elements required to produce full-potential-like solutions with a small perturbation approach on the requisite Cartesian grid. This level of accuracy required a higher-order streamwise mass flux and a mass conserving surface boundary condition. The ASP theory was further developed by determining the essential elements required to produce results that agreed well with Euler solutions. This level of accuracy required mass conserving entropy and vorticity effects, and second-order terms in the trailing wake boundary condition. Finally, an integral boundary layer procedure, applicable to both attached and shock-induced separated flows, was incorporated for viscous effects. The resulting ASP potential flow theory, including entropy, vorticity, and viscous effects, is shown to be mathematically more appropriate and computationally more accurate than the classical TSP theories. The formulaic details of the ASP theory are described fully and the improvements are demonstrated through careful comparisons with accepted alternative results and experimental data. The new theory has been used as the basis for a new computer code called ASP3D (Advanced Small Perturbation - 3D), which also is briefly described with representative results.

Batina, John T.↗

Computations of Flow Over the Hump Model Using Higher-Order Method With Turbulence Modeling

The flow over the two-dimensional hump model is computed by solving the RANS equations with kappa-omega (SST) model. The governing equations, the flow equations and the turbulent equations, are solved using the 5th order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using explicit third order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The WENO and the TVD methods and the formulas are explained in [1] and the application of ENO method to N-S equations is given in [2]. The solution method implemented in this computation is described in detail in [3].

Balakumar, P.↗

NASA Tech Briefs, May 2004

Topics include: Embedded Heaters for Joining or Separating Plastic Parts; Curing Composite Materials Using Lower-Energy Electron Beams; Aluminum-Alloy-Matrix/Alumina-Reinforcement Composites; Fibrous-Ceramic/Aerogel Composite Insulating Tiles; Urethane/Silicone Adhesives for Bonding Flexing Metal Parts; Scalable Architecture for Multihop Wireless ad Hoc Networks; Improved Thermoplastic/Iron-Particle Transformer Cores; Cooperative Lander-Surface/Aerial Microflyer Missions for Mars Exploration Dual-Frequency Airborne Scanning Rain Radar Antenna System Eight-Channel Continuous Timer Reduction of Phase Ambiguity in an Offset-QPSK Receiver Ambient-Light-Canceling Camera Using Subtraction of Frames Lightweight, Flexible, Thin, Integrated Solar-Power Packs Windows(Registered Trademark)-Based Software Models Cyclic Oxidation Behavior Software for Analyzing Sequences of Flow-Related Images Improved Ball-and-Socket Docking Mechanism Two-Stage Solenoid Ordered Nanostructures Made Using Chaperonin Polypeptides Low-Temperature Plasma Functionalization of Carbon Nanotubes Improved Cryostat for Cooling a Wide Panel Current Pulses Momentarily Enhance Thermoelectric Cooling Hand-Held Color Meters Based on Interference Filters Calculating Mass Diffusion in High-Pressure Binary Fluids Fresnel Lenses for Wide-Aperture Optical Receivers Increasing Accuracy in Computed Inviscid Boundary Conditions Higher-Order Finite Elements for Computing Thermal Radiation Radar for Monitoring Hurricanes from Geostationary Orbit Time-Transfer System for Two Orbiting Spacecraft

Source record↗

Aeroservoelastic Control Law Development for the Integrated Adaptive Wing Technology Maturation Wind-Tunnel Test

The NASA Advanced Air Transport Technology (AATT) Project seeks to “explore and develop technologies and concepts for improved energy efficiency and environmental compatibility for fixed wing subsonic transports” [1]. The IAWTM project is a subproject within AATT and is a joint Boeing/NASA effort to, in part, demonstrate the active control systems necessary to employ high-aspect ratio wings for improved aerodynamic efficiency. The aircraft configuration under study for the IAWTM project is a generic jet transport based on the NASA Common Research Model (CRM) whose wing aspect ratio has been increased to 13.5 (as opposed to nominal CRM aspect ratio of 9) and whose development is given in Ref. [2]. A semi-span model of the high-aspect-ratio CRM with 10 trailing edge control surfaces is currently being fabricated and will be delivered to the NASA Langley Transonic Dynamics Tunnel (TDT). There, several tests will be conducted to demonstrate maneuver load alleviation (MLA), gust load alleviation (GLA), active flutter suppression (AFS), and drag reduction, all at transonic conditions. A layout of the wind tunnel model is shown in Fig. 1. The wind-tunnel model is a spar/pod wing design with a relatively rigid fuselage attached to a mounting structure (seen in Fig. 1), which in turn is attached to a load balance behind the tunnel wall. Shims exist that can be attached to force the load to go through the fuselage rather than through the balance so as not to damage the balance in the event of flutter. The spar/pod design is similar to that used in the Boeing truss-braced wing aeroelastic model tested in the TDT in 2013 [3]. There is a central spar running the span of the wing to which the pods are attached that form the aerodynamic shape of the wing. The pods are constructed of ribs for attachment to the spar and skins to create the outer mold line. There are ten active control surfaces that will be used for the test objectives discussed above. Three of these (two outboard ailerons and one inboard aileron) are high-speed electrohydraulic actuators, and the remaining seven are low-speed mini-plane flaps, which have slower servo motors that will be used primarily for drag and maneuver load reductions. Control laws must be developed for each test (MLA, GLA, AFS, and drag reduction) and must be able to work in tandem when two or more control strategies are being tested simultaneously (e.g., when control laws to mitigate maneuver loads and gust loads operate simultaneously). The development of these control laws requires accurate mathematical representations of the aerodynamics, structural dynamics, and control surface dynamics of the system. Taken together, this mathematical representation—which is often in state-space form— is the ASE model. Three low-order ASE models of differing fidelities were developed for the IAWTM test and will be presented here. The differences in fidelity appeared in the aerodynamic modeling—one model assumed purely linear aerodynamics, while the other two models used different techniques to linearize the aerodynamics about a nonlinear mean. Furthermore, simple observer-based full-state feedback controllers for each test (MLA, GLA, AFS, and drag reduction) were designed from these low-order ASE models and implemented in a higher-order, nonlinear computational ASE simulation to assess the effectiveness of each controller. Observers were designed from each of the three lower-order ASE models, and each (linear) observer was then used as an estimate of the nonlinear dynamics of the system. Using the estimated states and the full-state feedback controller, control surface commands were fed back to the higher-order, nonlinear ASE system. The insight gained during this development will be applied to control law development for the physical IAWTM wind-tunnel test.

Josiah M Waite↗

Benefits of Ka-band GaN MMIC High Power Amplifiers With Wide Bandwidth and High Spectral/Power Added Efficiencies for Cognitive Radio Platforms

A cognitive radio on a future NASA near-Earth spacecraft will be capable of sensing its environment and dynamically adapting its operating parameters to provide the desired SATCOM service to the mission. A key component that can enable this type of operation is a high-power amplifier (HPA) that resides on the radio platform. In this paper, we present the RF performance characteristics of a Ka-band gallium nitride (GaN) monolithic microwave integrated circuit (MMIC) based HPA for cognitive radio platforms. These characteristics include the output power, gain, power added efficiency (PAE), RMS error vector magnitude (EVM), spectral efficiency, 3rd-order intermodulation distortion (IMD) products, spectrum, spectral regrowth, noise figure (NF), and phase noise. The data presented indicates that the HPA meets NTIA, military, and commercial spectral mask requirements. In addition, we discuss the benefits offered by the above performance characteristics toward the design and implementation of a cognitive radio platform. Furthermore, as examples, we discuss three potential use cases that apply artificial intelligence (AI) and machine learning (ML) techniques and exploit the performance characteristics discussed above to provide a knowledge-based cognitive radio platform design for SATCOM. Thus, cognitive radios with performance flexibility can enable roaming and provide seamless interoperability autonomously in the future between NASA, commercial, and other space networks owned by U.S. government agencies.

Gallium nitride↗

Diffraction by Sharp Edges of Noncanonical Shape with Mean Flow and Surface Impedance

This paper presents a study on diffraction by sharp edges of noncanonical edge shape in the presence of mean flow and surface impedance, which are important features for aircraft noise but have not been accounted for in previous studies on sharp-edge diffraction. An analytical formula for the diffracted pressure is derived by applying asymptotic analysis to the integral representation of the total pressure scattered by a geometry that contains sharp edges. The asymptotic analysis is presented as a systematic process that can be carried out to any order, if needed. An illustration is given to use a higher-order result to eliminate the singularity in the first-order result to make the solution regular in the entire parameter domain. The formula for the diffracted pressure is validated by experimental data and is applied to parametric studies to reveal the effects of noncanonical edge shape, mean flow and surface impedance, as well as the impact of these effects on the total scattered pressure in the presence of other scattering components.

Yueping Guo↗