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At least 991 records · Page 55

MO-C-17A-03: A GPU-Based Method for Validating Deformable Image Registration in Head and Neck Radiotherapy Using Biomechanical Modeling

Purpose: Deformable image registration (DIR) plays a pivotal role in head and neck adaptive radiotherapy but a systematic validation of DIR algorithms has been limited by a lack of quantitative high-resolution groundtruth. We address this limitation by developing a GPU-based framework that provides a systematic DIR validation by generating (a) model-guided synthetic CTs representing posture and physiological changes, and (b) model-guided landmark-based validation. Method: The GPU-based framework was developed to generate massive mass-spring biomechanical models from patient simulation CTs and contoured structures. The biomechanical model represented soft tissue deformations for known rigid skeletal motion. Posture changes were simulated by articulating skeletal anatomy, which subsequently applied elastic corrective forces upon the soft tissue. Physiological changes such as tumor regression and weight loss were simulated in a biomechanically precise manner. Synthetic CT data was then generated from the deformed anatomy. The initial and final positions for one hundred randomly-chosen mass elements inside each of the internal contoured structures were recorded as ground truth data. The process was automated to create 45 synthetic CT datasets for a given patient CT. For instance, the head rotation was varied between +/− 4 degrees along each axis, and tumor volumes were systematically reduced up to 30%. Finally, the original CT and deformed synthetic CT were registered using an optical flow based DIR. Results: Each synthetic data creation took approximately 28 seconds of computation time. The number of landmarks per data set varied between two and three thousand. The validation method is able to perform sub-voxel analysis of the DIR, and report the results by structure, giving a much more in depth investigation of the error. Conclusions: We presented a GPU based high-resolution biomechanical head and neck model to validate DIR algorithms by generating CT equivalent 3D volumes with simulated posture changes and physiological regression.

60 APPLIED LIFE SCIENCES↗

SU-C-213-01: 3D Printed Patient Specific Phantom Composed of Bone and Soft Tissue Substitute Plastics for Radiation Therapy

Purpose: 3D printed phantoms constructed of multiple tissue approximating materials could be useful in both clinical and research aspects of radiotherapy. This work describes a 3D printed phantom constructed with tissue substitute plastics for both bone and soft tissue; air cavities were included as well. Methods: 3D models of an anonymized nasopharynx patient were generated for air cavities, soft tissues, and bone, which were segmented by Hounsfield Unit (HU) thresholds. HU thresholds were chosen to define air-to-soft tissue boundaries of 0.65 g/cc and soft tissue-to-bone boundaries of 1.18 g/cc based on clinical HU to density tables. After evaluation of several composite plastics, a bone tissue substitute was identified as an acceptable material for typical radiotherapy x-ray energies, composed of iron and PLA plastic. PET plastic was determined to be an acceptable soft tissue substitute. 3D printing was performed on a consumer grade dual extrusion fused deposition model 3D printer. Results: MVCT scans of the 3D printed heterogeneous phantom were acquired. Rigid image registration of the patient and the 3D printed phantom scans was performed. The average physical density of the soft tissue and bone regions was 1.02 ± 0.08 g/cc and 1.39 ± 0.14 g/cc, respectively, for the patient kVCT scan. In the 3D printed phantom MVCT scan, the average density of the soft tissue and bone was 1.01 ± 0.09 g/cc and 1.44 ± 0.12 g/cc, respectively. Conclusion: A patient specific phantom, constructed of heterogeneous tissue substitute materials was constructed by 3D printing. MVCT of the 3D printed phantom showed realistic tissue densities were recreated by the 3D printing materials. Funding provided by intra-department grant by University of Minnesota Department of Radiation Oncology.

60 APPLIED LIFE SCIENCES↗

Crash Models for Advanced Automotive Batteries: A Review of the Current State of the Art

Safety is a critical aspect of lithium-ion (Li-ion) battery design. Impact/crash conditions can trigger a complex interplay of mechanical contact, heat generation and electrical discharge, which can result in adverse thermal events. The cause of these thermal events has been linked to internal contact between the opposite electrodes, i.e. internal short circuit. The severity of the outcome is influenced by the configuration of the internal short circuit and the battery state. Different loading conditions and battery states may lead to micro (soft) shorts where material burnout due to generated heat eliminates contact between the electrodes, or persistent (hard) shorts which can lead to more significant thermal events and potentially damage the entire battery system and beyond. Experimental characterization of individual battery components for the onset of internal shorts is limited, since it is impractical to canvas all possible variations in battery state of charge, operating conditions, and impact loading in a timely manner. This report provides a survey of modeling and simulation approaches and documents a project initiated and funded by DOT/NHTSA to improve modeling and simulation capabilities in order to design tests that provide leading indicators of failure in batteries. In this project, ORNL has demonstrated a computational infrastructure to conduct impact simulations of Li-ion batteries using models that resolve internal structures and electro-thermo-chemical and mechanical conditions. Initial comparisons to abuse experiments on cells and cell strings conducted at ORNL and Naval Surface Warfare Center (NSWC) at Carderock MD for parameter estimation and model validation have been performed. This research has provided insight into the mechanisms of deformation in batteries (both at cell and electrode level) and their relationship to the safety of batteries.

33 ADVANCED PROPULSION SYSTEMS↗

Quantitative micro-luminescence and related studies of fine and/or glassy lunar surface materials

Papers on Raman and soft X-ray spectroscopy of lunar glasses and electron microscopy of lunar fines are presented. Individual particles of glasses from Apollo 11, 12, 14, and 15 samples were analyzed separately. Silicon emission shifts vary between parent rock types and can be interpreted as a range of Si-O distances from 1.612 to 1.637 A. Aluminum emission shifts relate to the amount of 4- and 6-coordinated Al in the glass. Raman spectra show broadened bands. Certain bands recur in many specimens and relate to the main normative minerals for the glass bulk composition, olivine, pyroxene, and anorthite. Quantitative size and shape analyses were carried out on six Apollo 14 and 15 samples of fines by computer evaluation of scanning electron microspace images. For the size range of 0.50 to 30 micron diameter, the distributions are log-normal on a number count basis. Aspect ratios range from 0.1 to 1.0 with an average value of about 0.6. The aspect ratios and a shape complexity factor vary only slightly among the samples.

Roy, R.↗

Rapid data comparison technique development for N-ray/X-ray analysis

An operational N-ray/X-ray computer analysis system for nondestructive testing problems was realized by developing: (1) more efficient data transfer routines for use in existing image processing systems; (2) the capability to store and analyze multiple N-ray/X-ray images; (3) an efficient 2-D Fast Fourier Transform; and (4) transfer functions compensation capability to correct for distortions and nonlinearities of N-rays/X-rays. Applications of the technique are summarized for the following: thermal protection system tile with hydraulic fluid; thermal protection system tile with corrosion; thermal protection system tile debonding; stainless steel tubing corrosion; defective electrical devices; fast film restoration and deblur; corrosion tracking over time; reduction of source vignetting, and identification of materials (0 rings, Teflon parts, soft goods) via table look up.

Butterfield, R. L.↗

The two-loop five-point amplitude in $\mathcal{N}$ = 8 supergravity

We compute the symbol of the two-loop five-point amplitude in $\mathcal{N}$ = 8 supergravity. We write an ansatz for the amplitude whose rational prefactors are based on not only 4-dimensional leading singularities, but also d-dimensional ones, as the former are insufficient. Our novel d-dimensional unitarity-based approach to the systematic construction of an amplitude’s rational structures is likely to have broader applications, for example to analogous QCD calculations. We fix parameters in the ansatz by performing numerical integration-by-parts reduction of the known integrand. We find that the two-loop five-point $\mathcal{N}$ = 8 supergravity amplitude is uniformly transcendental. We then verify the soft and collinear limits of the amplitude. There is considerable similarity with the corresponding amplitude for $\mathcal{N}$ = 4 super-Yang-Mills theory: all the rational prefactors are double copies of the Yang-Mills ones and the transcendental functions overlap to a large degree. As a byproduct, we find new relations between color-ordered loop amplitudes in $\mathcal{N}$ = 4 super-Yang-Mills theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Interfractional Positional Variability of Fiducial Markers and Primary Tumors in Locally Advanced Non-Small-Cell Lung Cancer During Audiovisual Biofeedback Radiotherapy

Purpose: To evaluate implanted markers as a surrogate for tumor-based setup during image-guided lung cancer radiotherapy with audiovisual biofeedback. Methods and Materials: Seven patients with locally advanced non-small-cell lung cancer were implanted bronchoscopically with gold coils. Markers, tumor, and a reference bony structure (vertebra) were contoured for all 10 phases of the four-dimensional respiration-correlated fan-beam computed tomography and weekly four-dimensional cone-beam computed tomography. Results: The systematic/random interfractional marker-to-tumor centroid displacements were 2/3, 2/2, and 3/3 mm in the x (lateral), y (anterior-posterior), and z (superior-inferior) directions, respectively. The systematic/random interfractional marker-to-bone displacements were 2/3, 2/3, and 2/3 mm in the x, y, and z directions, respectively. The systematic/random tumor-to-bone displacements were 2/3, 2/4, and 4/4 mm in the x, y, and z directions, respectively. All displacements changed significantly over time (p < 0.0001). Conclusions: Although marker-based image guidance may decrease the risk for geometric miss compared with bony anatomy-based positioning, the observed displacements between markers and tumor centroids indicate the need for repeated soft tissue imaging, particularly in situations with large tumor volume change and large initial marker-to-tumor centroid distance.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Material separation in x-ray CT with energy resolved photon-counting detectors

Purpose: The objective of the study was to demonstrate that, in x-ray computed tomography (CT), more than two types of materials can be effectively separated with the use of an energy resolved photon-counting detector and classification methodology. Specifically, this applies to the case when contrast agents that contain K-absorption edges in the energy range of interest are present in the object. This separation is enabled via the use of recently developed energy resolved photon-counting detectors with multiple thresholds, which allow simultaneous measurements of the x-ray attenuation at multiple energies. Methods: To demonstrate this capability, we performed simulations and physical experiments using a six-threshold energy resolved photon-counting detector. We imaged mouse-sized cylindrical phantoms filled with several soft-tissue-like and bone-like materials and with iodine-based and gadolinium-based contrast agents. The linear attenuation coefficients were reconstructed for each material in each energy window and were visualized as scatter plots between pairs of energy windows. For comparison, a dual-kVp CT was also simulated using the same phantom materials. In this case, the linear attenuation coefficients at the lower kVp were plotted against those at the higher kVp. Results: In both the simulations and the physical experiments, the contrast agents were easily separable from other soft-tissue-like and bone-like materials, thanks to the availability of the attenuation coefficient measurements at more than two energies provided by the energy resolved photon-counting detector. In the simulations, the amount of separation was observed to be proportional to the concentration of the contrast agents; however, this was not observed in the physical experiments due to limitations of the real detector system. We used the angle between pairs of attenuation coefficient vectors in either the 5-D space (for non-contrast-agent materials using energy resolved photon-counting acquisition) or a 2-D space (for contrast agents using energy resolved photon-counting acquisition and all materials using dual-kVp acquisition) as a measure of the degree of separation. Compared to dual-kVp techniques, an energy resolved detector provided a larger separation and the ability to separate different target materials using measurements acquired in different energy window pairs with a single x-ray exposure. Conclusions: We concluded that x-ray CT with an energy resolved photon-counting detector with more than two energy windows allows the separation of more than two types of materials, e.g., soft-tissue-like, bone-like, and one or more materials with K-edges in the energy range of interest. Separating material types using energy resolved photon-counting detectors has a number of advantages over dual-kVp CT in terms of the degree of separation and the number of materials that can be separated simultaneously.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Toward engineering lattice structures with the material point method (MPM)

This study examines the potential of two variants of the material point method—the generalized interpolation material point (GIMP) and dual domain material point (DDMP) methods—in developing a robust computational framework for engineering lattice structures under different loading conditions. The study begins with assessing the ability of the two methods in predicting elastic buckling phenomena using column geometries with and without initial geometric imperfections. The results indicate that both methods effectively capture buckling phenomena when initial geometric imperfections are introduced. After this verification step, we create several models of tetrahedral lattice structures with varying strut diameter and orientation and subject them to quasi-static loading. We then validate the numerical results using laboratory test results. The results show that, while both methods accurately predict load–displacement curves in the pre-buckling regime, their predictive capabilities diminish in the post-buckling regime. Through visual comparison between the numerical and experimental deformed shapes, it appears that the discrepancies between model and experimental results are attributed to initial geometric imperfections in the lattices that occurred during 3D printing. We then establish a second set of lattice models where different types of initial geometric imperfections are considered. The results from these models show that imperfections have a negligible influence in the pre-buckling regime but affect the behavior considerably in the post-buckling regime. As a final step in this work, we subject the lattice models to impact loading and employ hypothetical soft and stiff materials. These results show that the lattice stiffness, which depends on material stiffness, strut diameter, and orientation, significantly influences the ability of a lattice structure to resist impact. In particular, we find that a stiffer lattice (i.e., one made with a stiff material and thicker struts) is capable of absorbing more energy than a softer one during impact. Although material nonlinearities, inelasticity, and detailed contact formulations are not considered in this study, the findings obtained herein lay the groundwork for engineering lattice structures under extreme loading conditions through a simulation-driven framework based on particle-based methods.

97 MATHEMATICS AND COMPUTING↗

Intermediate time sub-diffusion and stress relaxation in ring polymer melts

The slow dynamics of non-concatenated ring melts remains a frontier problem in polymer science with implications for many soft material environments including cellular biophysics. Here, in this work, we report large-scale simulations of model ring melts that analyze the monomer and center-of-mass (CM) mean square displacements (MSD) and stress relaxation function on intermediate time and length scales. The degree of dynamical slowing down is characterized by the maximally sub-diffusive fractional time scaling exponents. The data span an exceptionally wide range of ring degrees of polymerization and stiffnesses and are not successfully organized based on the classic measure linear chain entanglement, N/N e . Rather, we find that the crossover degree of polymerization, N D , based on ring macromolecular caging that successfully allows master curves to be constructed for the long-time CM self-diffusion constant also collapses these temporal dynamic scaling exponents. Different properties display different exponents and exhibit one or two regimes of linear variation with the logarithm of N D / N . A distinct crossover of the CM-MSD and stress relaxation exponents emerges at sufficiently large N or stiffness that is not found for the monomer MSD, indicating a novel form of dynamic decoupling. This crossover aligns with the predicted critical degree of polymerization for transitioning from a weak to strong caging regime, indicative of activated transport. The latter may reflect the emergence of an intermolecular collective contribution to stress in analogy with dense soft colloidal matter. Suggestions are made for future theoretical work to address the rich patterns of behavior discovered.

Anomalous diffusion↗

Deep Reinforcement Learning for Distribution System Restoration Using Distributed Energy Resources and Tie-Switches

Distributed energy resources (DERs), such as solar PVs and energy storage, can be used to restore distribution system critical loads after the extreme weather events to increase grid resilience. However, coordinating multiple DERs together with tie-switches for multi-step restoration process under renewable uncertainty is challenging. This paper proposes a deep reinforcement learning to control discrete actions of switching on/off tie switches and DERs for critical load restoration. The restoration problem is first cast into the Markov decision process suitable for DRL. Then, the original soft actor critic (SAC) method for continuous actions has been extended to handle discrete and continuous actions. Numerical comparison results with other stochastic optimization-based approaches on the modified IEEE 33-bus system show that the proposed method can achieve fast critical load restoration in the presence of substation power outage while maintaining system voltage limit throughout the restoration process.

active distribution systems↗

Computational self-assembly of a one-component icosahedral quasicrystal

Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. All reported IQCs are intermetallic compounds and either of face-centred-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike axially symmetric quasicrystals, IQCs have not been observed in non-atomic (that is, micellar or nanoparticle) systems, where real-space information would be directly available. Here, we show that an IQC can be assembled by means of molecular dynamics simulations from a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the third-neighbour shell. The IQC is body-centred, self-assembles from a fluid phase, and in parameter space neighbours clathrates and other tetrahedrally bonded crystals. Our findings elucidate the structure and dynamics of the IQC, and suggest routes to search for it and design it in soft matter and nanoscale systems.

36 MATERIALS SCIENCE↗

Poster — Thur Eve — 03: Application of the non-negative matrix factorization technique to [{sup 11}C]-DTBZ dynamic PET data for the early detection of Parkinson's disease

In this work, a class of non-negative matrix factorization (NMF) technique known as alternating non-negative least squares, combined with the projected gradient method, is used to analyze twenty-five [{sup 11}C]-DTBZ dynamic PET/CT brain data. For each subject, a two-factor model is assumed and two factors representing the striatum (factor 1) and the non-striatum (factor 2) tissues are extracted using the proposed NMF technique and commercially available factor analysis software “Pixies”. The extracted factor 1 and 2 curves represent the binding site of the radiotracer and describe the uptake and clearance of the radiotracer by soft tissues in the brain, respectively. The proposed NMF technique uses prior information about the dynamic data to obtain sample time-activity curves representing the striatum and the non-striatum tissues. These curves are then used for “warm” starting the optimization. Factor solutions from the two methods are compared graphically and quantitatively. In healthy subjects, radiotracer uptake by factors 1 and 2 are approximately 35–40% and 60–65%, respectively. The solutions are also used to develop a factor-based metric for the detection of early, untreated Parkinson's disease. The metric stratifies healthy subjects from suspected Parkinson's patients (based on the graphical method). The analysis shows that both techniques produce comparable results with similar computational time. The “semi-automatic” approach used by the NMF technique allows clinicians to manually set a starting condition for “warm” starting the optimization in order to facilitate control and efficient interaction with the data.

60 APPLIED LIFE SCIENCES↗

Factorization and resummation for groomed multi-prong jet shapes

Observables which distinguish boosted topologies from QCD jets are playing an increasingly important role at the Large Hadron Collider (LHC). These observables are often used in conjunction with jet grooming algorithms, which reduce contamination from both theoretical and experimental sources. In this paper we derive factorization formulae for groomed multi-prong substructure observables, focusing in particular on the groomed D 2 observable, which is used to identify boosted hadronic decays of electroweak bosons at the LHC. Our factorization formulae allow systematically improvable calculations of the perturbative D 2 distribution and the resummation of logarithmically enhanced terms in all regions of phase space using renormalization group evolution. They include a novel factorization for the production of a soft subjet in the presence of a grooming algorithm, in which clustering effects enter directly into the hard matching. We use these factorization formulae to draw robust conclusions of experimental relevance regarding the universality of the D 2 distribution in both e+e- and pp collisions. In particular, we show that the only process dependence is carried by the relative quark vs. gluon jet fraction in the sample, no non-global logarithms from event-wide correlations are present in the distribution, hadronization corrections are controlled by the perturbative mass of the jet, and all global color correlations are completely removed by grooming, making groomed D 2 a theoretically clean QCD observable even in the LHC environment. Lastly, we compute all ingredients to one-loop accuracy, and present numerical results at next-to-leading logarithmic accuracy for e + e - collisions, comparing with parton shower Monte Carlo simulations. Results for pp collisions, as relevant for phenomenology at the LHC, are presented in a companion paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Evidence for Helical Hinge Zero Modes in an Fe-Based Superconductor

Combining topology and superconductivity provides a powerful tool for investigating fundamental physics as well as a route to fault-tolerant quantum computing. There is mounting evidence that the Fe-based superconductor FeTe 0.55 Se 0.45 (FTS) may also be topologically nontrivial. Should the superconducting order be s ± , then FTS could be a higher order topological superconductor with helical hinge zero modes (HHZMs). To test the presence of these modes, we have fabricated normal-metal/superconductor junctions on different surfaces via 2D atomic crystal heterostructures. As expected, junctions in contact with the hinge reveal a sharp zero bias anomaly that is absent when tunneling purely into the c-axis. Additionally, the shape and suppression with temperature are consistent with highly coherent modes along the hinge and are incongruous with other origins of zero bias anomalies. Additional measurements with soft-point contacts in bulk samples with various Fe interstitial contents demonstrate the intrinsic nature of the observed mode. Thus, we provide evidence that FTS is indeed a higher order topological superconductor.

2D superconductor↗

Optic Nerve Sheath Mechanics and Permeability in VIIP Syndrome

Long-duration space flight carries the risk of developing Visual Impairment and Intracranial Pressure (VIIP) syndrome, a spectrum of ophthalmic changes including posterior globe flattening, choroidal folds, distension of the optic nerve sheath (ONS), optic nerve kinking and potentially permanent degradation of visual function. The slow onset of VIIP, its chronic nature, and certain clinical features strongly suggest that biomechanical factors acting on the ONS play a role in VIIP. Here we measure several relevant ONS properties needed to model VIIP biomechanics. The ONS (meninges) of fresh porcine eyes (n7) was reflected, the nerve proper was truncated near the sclera, and the meninges were repositioned to create a hollow cylinder of meningeal connective tissue attached to the posterior sclera. The distal end was cannulated, sealed, and pressure clamped (mimicking cerebrospinal fluid [CSF] pressure), while the eye was also cannulated for independent control of intraocular pressure (IOP). The meninges were inflated (CSF pressure cycling 7-50 mmHg) while ONS outer diameter was imaged. In another set of experiments (n4), fluid permeation rate across the meninges was recorded by observing the drainage of an elevated fluid reservoir (30 mmHg) connected to the meninges. The ONS showed behavior typical of soft tissues: viscoelasticity, with hysteresis in early preconditioning cycles and repeatable behavior after 4 cycles, and nonlinear stiffening, particularly at CSF pressures 15 mmHg (Figure). Tangent moduli measured from the loading curve were 372 101, 1199 358, and 2050 379 kPa (mean SEM) at CSF pressures of 7, 15 and 30 mmHg, respectively. Flow rate measurements through the intact meninges at 30mmHg gave a permeability of 1.34 0.46 lmincm2mmHg (mean SEM). The ONS is a tough, strain-stiffening connective tissue that is surprisingly permeable. The latter observation suggests that there could be significant CSF drainage through the ONS into the orbit, likely important for CSF transport in the optic nerve. These experimental measurements, extended to human eyes, are informing computational models of the pathophysiology and biomechanics of the ONS in VIIP syndrome.

biomechanics↗

Biomechanics of the Optic Nerve Sheath in VIIP Syndrome

Long-duration space flight carries the risk of developing Visual Impairment and Intracranial Pressure (VIIP) syndrome, a spectrum of ophthalmic changes including posterior globe flattening, choroidal folds, distension of the optic nerve sheath (ONS), optic nerve kinking and potentially permanent degradation of visual function. The slow onset of VIIP, its chronic nature, and certain clinical features strongly suggest that biomechanical factors acting on the ONS play a role in VIIP. Here we measure several relevant ONS properties needed to model VIIP biomechanics. The ONS (meninges) of fresh porcine eyes (n7) was reflected, the nerve proper was truncated near the sclera, and the meninges were repositioned to create a hollow cylinder of meningeal connective tissue attached to the posterior sclera. The distal end was cannulated, sealed, and pressure clamped (mimicking cerebrospinal fluid [CSF] pressure), while the eye was also cannulated for independent control of intraocular pressure (IOP). The meninges were inflated (CSF pressure cycling 7-50 mmHg) while ONS outer diameter was imaged. In another set of experiments (n4), fluid permeation rate across the meninges was recorded by observing the drainage of an elevated fluid reservoir (30 mmHg) connected to the meninges. The ONS showed behavior typical of soft tissues: viscoelasticity, with hysteresis in early preconditioning cycles and repeatable behavior after 4 cycles, and nonlinear stiffening, particularly at CSF pressures 15 mmHg (Figure). Tangent moduli measured from the loading curve were 372 101, 1199 358, and 2050 379 kPa (mean SEM) at CSF pressures of 7, 15 and 30 mmHg, respectively. Flow rate measurements through the intact meninges at 30mmHg gave a permeability of 1.34 0.46 lmincm2mmHg (mean SEM). The ONS is a tough, strain-stiffening connective tissue that is surprisingly permeable. The latter observation suggests that there could be significant CSF drainage through the ONS into the orbit, likely important for CSF transport in the optic nerve. These experimental measurements, extended to human eyes, are informing computational models of the pathophysiology and biomechanics of the ONS in VIIP syndrome.

fluid shifts↗

Finite-difference theory for sound propagation in a lined duct with uniform flow using the wave envelope concept

Finite difference equations are derived for sound propagation in a two dimensional, straight, soft wall duct with a uniform flow by using the wave envelope concept. This concept reduces the required number of finite difference grid points by one to two orders of magnitude depending on the length of the duct and the frequency of the sound. The governing acoustic difference equations in complex notation are derived. An exit condition is developed that allows a duct of finite length to simulate the wave propagation in an infinitely long duct. Sample calculations presented for a plane wave incident upon the acoustic liner show the numerical theory to be in good agreement with closed form analytical theory. Complete pressure and velocity printouts are given to some sample problems and can be used to debug and check future computer programs.

Baumeister, K. J.↗