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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1953

Impingement of water droplets on wedges and diamond airfoils at supersonic speeds

An analytical solution has been obtained for the equations of motion of water droplets impinging on a wedge in a two-dimensional supersonic flow field with a shock wave attached to the wedge. The closed-form solution yields analytical expressions for the equation of the droplet trajectory, the local rate of impingement and the impingement velocity at any point on the wedge surface, and the total rate of impingement. The analytical expressions are utilized to determine the impingement on the forward surfaces of diamond airfoils in supersonic flow fields with attached shock waves. The results presented include the following conditions: droplet diameters from 2 to 100 microns, pressure altitudes from sea level to 30,000 feet, free-stream static temperatures from 420 degrees to 460 degrees R. Also, free-stream Mach numbers from 1.1 to 2.0, semi-apex angles for the wedge from 1.14 degrees to 7.97 degrees, thickness-to-chord ratios for the diamond airfoil from 0.02 to 0.14, chord lengths from 1 to 20 feet, and angles of attack from zero to the inverse tangent of the airfoil thickness-to-chord ratio.

SURFACE CONDITIONS - WING SECTIONS↗
DOE OSTI2026

Adaptive Cybersecurity for Distributed Energy Resources (AdCyDER): Online Reinforcement Learning with Stackelberg-Optimized Defenses — Pipeline Architecture, Evaluation Methodology, and Findings from a Synthetic-Data Evaluation

This report documents the design and evaluation of an integrated online-learning pipeline developed within the AdCyDER project for Distributed Energy Resource (DER) cybersecurity. The pipeline couples a Reinforcement Learning (RL) attack classifier — which produces an attack-type probability distribution — with a Stackelberg game-theoretic (GT) defense selector that consumes those distributions alongside SME-encoded priors over (defense, attack) effectiveness pairings and perdefense costs to choose grid-health-preserving defenses. The objective is not attack classification per se but production of distributions that drive effective defense selection through the Stackelberg layer, learned from delayed grid-health feedback rather than labeled attack data. AdCyDER as a whole is broader than the work presented here; this report covers the specific RL/GT loop integration and its evaluation. We present the integrated pipeline (SCADA telemetry with Fronius inverter physics, Suricata IDS, time-windowed aggregation, per-facility LSTM classifier, Stackelberg optimizer, OpenC2 actuators), an experimental campaign of 28 eight-hour iterations across three baseline modes, and a pipeline-ordered diagnostic protocol. The protocol identifies two distinct failure modes within the loop: paired supervised ceilings on the same features establish that the deployed online RL classifier (macro F1 ≈ 0.07) sits at least 4.7× below a same-architecture supervised LSTM (≈ 0.34) and 10–11× below a linear feature-signal ceiling (≈ 0.70–0.79 depending on per-facility isolation), localizing the dominant failure to the training procedure; and the reward signal driving online updates carries weak directional coupling with classifier correctness in the methodology-expected direction (multi-lens convergent: top-decile P(true) records produce more frequent state changes and slightly larger improvements, top-vs-bot Cohen’s 𝑑 ≈ −0.19), but at effect magnitudes too small to drive gradient-based learning at the campaign sample size. The original learning hypothesis is not supported by the data. The primary contributions are the diagnostic methodology — proposed as a transferable falsification protocol for online RL/GT defense pipelines learning from delayed environmental reward — and the open, reproducible experimental infrastructure. We outline reward reformulation as the highest-priority aspirational next step given the underpowered-but-aligned Q6 reading, with hardware-in-the-loop evaluation as the broadest scope-expansion option.

Blakely, Benjamin [Argonne National Laboratory (AN↗
NASA NTRS1987

A study of multi-body aerodynamic interference at transonic Mach numbers

A wind tunnel experiment involving single, double, and triple combinations of mutually interfering generic, unfinned aircraft stores has been conducted. Each combination of stores was tested at Mach numbers from 0.60 to 1.20 and at angles of attack from 0 to 25 deg for the single store and from 0 to 6 deg for the double and triple store configurations. Extensive axial and circumferential pressure and flow visualization data at each store location were obtained. Euler solutions for each configuration at 0 deg incidence have been generated and compared with experimental data. This comparison indicates an Euler flow solver can yield accurate predictions of the location and magnitude of multibody interference provided an appropriate grid is used and the viscous effects associated with these configurations remain small. The data indicate multibody interference in the transonic region increases as the freestream Mach number approaches 1 from either direction, and subsides as the Mach number moves away from sonic conditions. This interference is characterized by a large, localized reduction in pressure on the inboard surfaces of the bodies which results in forces that draw the configuration closer together.

Cottrell, Charles J.↗
NASA NTRS1985

Wide-field shadowgraph flow visualization of tip vortices generated by a helicopter rotor

The vortex trajectory and vortex wake generated by helicopter rotors were visualized using a wide-field shadowgraph technique. Use of a retro-reflective Scotchlite screen made it possible to investigate the flow field generated by full-scale tail rotors. Tip vortex trajectories were visible in shadowgraphs for a range for tip Mach number of 0.38 - 0.60. The effect of the angle of attack was substantial. At an angle of attack greater than 8 degrees, the visibility of the vortex core was significant even at relatively low tip Mach numbers. The theoretical analysis of the visibility was carried out for a rotating blade. This analysis demonstrated that the visibility decreases with increasing dimensionless core radius (ro/c) and increases with increasing tip Mach number. Based on this investigation, it is concluded that the wide-field shadowgraph flow visualization technique should be feasible to study the flow field generated by a large main rotor in a wind tunnel and in an outdoor full-scale test stand. Of note is that the shadowgraph technique could easily be used with other on-going tests such as aerodynamic performance study, noise measurements, velocity measurements with LDV or hot-wire anemometer, local pressure measurement on the rotor surface, etc.

Parthasarathy, S. P.↗
DOE OSTI2025

Hot corrosion behavior of 304 & P91 graded composite transition joint under molten sulfate salts

A novel graded composite transition joint (GCTJ) between AISI 304 stainless steel and ASTM A335 P91 steel, has been demonstrated remarkablely superior creep performance compared to the conventional dissimilar metal weldment (DMW) under equivalent conditions. However, this advance is challenged by hot corrosion under salt deposition at elevated temperatures. Here, this study investigates the hot corrosion behavior of 304&P91 GCTJ exposed to sulfate salts at 700°C. Compared to the 304 steel, corrosion attacks initiate in the P91 triangle, where the dual-phase microstructure of ferrite and tempered martensite significantly influences pitting initiation. Anodic dissolution mainly occurs within the tempered martensite due to more vulnerable sites within the tempered martensite. With prolonged exposure, corrosion propagates across both phases, and the corrosion depth within the P91 triangle is related to the exposed surface area ratio between 304 and P91. Electrochemical analysis reveals the occurrence of galvanic corrosion between the 304 and P91, with a positive linear relationship between anodic dissolution current density (I a ) and the exposed surface area ratio between 304 and P91 in molten salts, further emphasizing the critical impact of this ratio on the corrosion severity in the P91 triangle. These findings underscore the importance of transition zone design optimization in mitigating localized corrosion.

Galvanic corrosion↗
NASA NTRS2016

Overview of the Space Launch System Ascent Aeroacoustic Environment Test Program

Characterization of accurate flight vehicle unsteady aerodynamics is critical for component and secondary structure vibroacoustic design. The Aerosciences Branch at the National Aeronautics and Space Administration (NASA) Marshall Space Flight Center has conducted a test at the NASA Ames Research Center (ARC) Unitary Plan Wind Tunnels (UPWT) to determine such ascent aeroacoustic environments for the Space Launch System (SLS). Surface static pressure measurements were also collected to aid in determination of local environments for venting, CFD substantiation, and calibration of the flush air data system located on the launch abort system. Additionally, this test supported a NASA Engineering and Safety Center study of alternate booster nose caps. Testing occurred during two test campaigns: August - September 2013 and December 2013 - January 2014. Four primary model configurations were tested for ascent aeroacoustic environment definition. The SLS Block 1 vehicle was represented by a 2.5% full stack model and a 4% truncated model. Preliminary Block 1B payload and manned configurations were also tested, using 2.5% full stack and 4% truncated models respectively. This test utilized the 11 x 11 foot transonic and 9 x 7 foot supersonic tunnel sections at the ARC UPWT to collect data from Mach 0.7 through 2.5 at various total angles of attack. SLS Block 1 design environments were developed primarily using these data. SLS Block 1B preliminary environments have also been prepared using these data. This paper discusses the test and analysis methodology utilized, with a focus on the unsteady data collection and processing.

Herron, Andrew J.↗
NASA NTRS2022

Low-Speed Performance Enhancement using Localized Active Flow Control: Program Overview and Summary (1/4)

The Boeing team executed a NASA task order, titled “Low Speed Performance Enhancement using Localized Active Flow Control”, under the BAART framework NNL16AA04B, contract number 80LARC20F0082. The project was executed from Sept. 2020 through April 2022 with the objective to explore localized active flow control (AFC) concepts on a representative commercial aircraft. A detailed literature review solidified the choice of AFC concepts to be explored, including AFC over a deflected aileron, in the leading edge region of the wing, and in the nacelle/pylon/wing region. All three concepts were investigated with numerical tools. The results were used in an integration study to assess the net benefits over the lifetime of a commercial aircraft. The aerodynamic studies concluded that AFC applied over a deflected aileron yields significant net L/D improvements (incl. the penalty of AFC system requirements) of up to potentially 5% L/D. Depending on the configuration, AFC applied in the leading edge region showed improvements in L/D of up to ~1.5%, as well as opportunities for maximum lift and increased lift at fixed angle of attack. AFC applied to the nacelle/pylon/wing region delivered 1.5% increase in L/D during take-off and ~4% increase in CLmax during landing. After considering assumed onboard sources, aspects of system integration and weight penalties, these aerodynamic improvements translate to: ~ 0.5% block fuel reduction potential for AFC over the aileron ~ 0.1% block fuel reduction potential for AFC in the LE slat region ~ 0.2% block fuel reduction potential for AFC in the nacelle/pylon/wing region considering take-off scenarios (potentially larger benefit may be realized considering the landing scenarios which haven’t been fully analyzed yet) The final report is comprised of four separate documents. The current document provides an overview and technical background. The second document details the numerical studies and the third document summarizes the integration and aircraft performance assessment. The fourth document focuses on the Common Research Model, specifically how AFC performs over a deflected aileron and how the NASA 10% scale wind tunnel model may be modified to implement an AFC equipped aileron. Each report offers significantly more detailed summaries and suggestions for future work.

Active flow control↗
NASA NTRS1988

An upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations

The two-dimensional incompressible Navier-Stokes equations are solved in a time-accurate manner in using the method of pseudocompressibility. Using this method, subiterations in pseudotime are required to satisfy the continuity equation at each time step. An upwind differencing scheme based on flux-difference splitting is used to compute the convective terms. The upwind differencing is biased based on the sign of the local eigenvalue of the Jacobian matrix. Third-order or fifth-order spatial accuracy is maintained throughout the interior grid points. The equations are solved using an implicit line-relaxation scheme. This solution scheme is stable and is capable of running at large time steps in pseudotime, leading to fast convergence for each physical time step. A variety of computed results are presented to validate the present scheme. Results for the flow over an oscillating plate are compared with the exact analytic solution, good agreement is seen. Excellent comparison is obtained between the computed solution and the analytical results for inviscid channel flow with an oscillating back pressure. Flow solutions over a circular cylinder with vortex shedding are also presented. Finally, the flow past an airfoil at -90 deg angle-of-attack is also computed.

Rogers, Stuart E.↗
DOE OSTI2022

Heinz-resistant tomato cultivars exhibit a lignin-based resistance to field dodder ( Cuscuta campestris ) parasitism

Cuscuta species (dodders) are agriculturally destructive, parasitic angiosperms. These parasitic plants use haustoria as physiological bridges to extract nutrients and water from hosts. Cuscuta campestris has a broad host range and wide geographical distribution. While some wild tomato relatives are resistant, cultivated tomatoes are generally susceptible to C. campestris infestations. However, some specific Heinz tomato (Solanum lycopersicum) hybrid cultivars exhibit resistance to dodders in the field, but their defense mechanism was previously unknown. Here, we discovered that the stem cortex in these resistant lines responds with local lignification upon C. campestris attachment, preventing parasite entry into the host. Lignin Induction Factor 1 (LIF1, an AP2-like transcription factor), SlMYB55, and Cuscuta R-gene for Lignin-based Resistance 1, a CC-NBS-LRR (CuRLR1) are identified as factors that confer host resistance by regulating lignification. SlWRKY16 is upregulated upon C. campestris infestation and potentially negatively regulates LIF1 function. Intriguingly, CuRLR1 may play a role in signaling or function as an intracellular receptor for receiving Cuscuta signals or effectors, thereby regulating lignification-based resistance. In summary, these four regulators control the lignin-based resistance response in specific Heinz tomato cultivars, preventing C. campestris from parasitizing resistant tomatoes. This discovery provides a foundation for investigating multilayer resistance against Cuscuta species and has potential for application in other essential crops attacked by parasitic plants.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2009

Vortical Flow Prediction using an Adaptive Unstructured Grid Method

A computational fluid dynamics (CFD) method has been employed to compute vortical flows around slender wing/body configurations. The emphasis of the paper is on the effectiveness of an adaptive grid procedure in "capturing" concentrated vortices generated at sharp edges or flow separation lines of lifting surfaces flying at high angles of attack. The method is based on a tetrahedral unstructured grid technology developed at the NASA Langley Research Center. Two steady-state, subsonic, inviscid and Navier-Stokes flow test cases are presented to demonstrate the applicability of the method for solving vortical flow problems. The first test case concerns vortex flow over a simple 65 delta wing with different values of leading-edge radius. Although the geometry is quite simple, it poses a challenging problem for computing vortices originating from blunt leading edges. The second case is that of a more complex fighter configuration. The superiority of the adapted solutions in capturing the vortex flow structure over the conventional unadapted results is demonstrated by comparisons with the wind-tunnel experimental data. The study shows that numerical prediction of vortical flows is highly sensitive to the local grid resolution and that the implementation of grid adaptation is essential when applying CFD methods to such complicated flow problems.

Pirzadeh, Shahyar Z.↗
NASA NTRS2003

Vortical Flow Prediction Using an Adaptive Unstructured Grid Method

A computational fluid dynamics (CFD) method has been employed to compute vortical flows around slender wing/body configurations. The emphasis of the paper is on the effectiveness of an adaptive grid procedure in "capturing" concentrated vortices generated at sharp edges or flow separation lines of lifting surfaces flying at high angles of attack. The method is based on a tetrahedral unstructured grid technology developed at the NASA Langley Research Center. Two steady-state, subsonic, inviscid and Navier-Stokes flow test cases are presented to demonstrate the applicability of the method for solving practical vortical flow problems. The first test case concerns vortex flow over a simple 65 delta wing with different values of leading-edge radius. Although the geometry is quite simple, it poses a challenging problem for computing vortices originating from blunt leading edges. The second case is that of a more complex fighter configuration. The superiority of the adapted solutions in capturing the vortex flow structure over the conventional unadapted results is demonstrated by comparisons with the wind-tunnel experimental data. The study shows that numerical prediction of vortical flows is highly sensitive to the local grid resolution and that the implementation of grid adaptation is essential when applying CFD methods to such complicated flow problems.

Pirzadeh, Shahyar Z.↗
DOE OSTI2021

Precise Timing Based on Pulsar Observation for Grid Synchronization

While Global Positioning System signals are widely used as the synchronized timing Sources for wide-area measurement systems for power grid monitoring and control, they are vulnerable to failures and malicious attacks. To address this Problem, an alternative kind of timing sources, the millisecond pulsars, were proposed to serve the power grid as they are more precise and physically indestructible. Millisecond pulsars are a kind of neutron stars that emit radio pulse signals that have extremely stable periods of milliseconds. However, the observed pulse Signals from pulsars cannot be directly used for timing because of their low signal-to-noise ratio and the dispersion effects of interstellar medium. In this paper, the precise timing method based on pulsar observation data is proposed to interpret the pulsar observation data and therefrom to generate precise timing signal for the power grid synchronization. In our proposed method,. incoherent de-dispersion is used on the observation data to mitigate the effect of interstellar medium. dispersion. Then spectrum analysis and segment folding are used to precisely estimate the local pulsar period. Finally the standard pulse per second signal is generated from. the estimated pulsar period and its precision. is analyzed. Experiments with the observation data of the pulsar based timing signal can be more accurate compared to GPS timing signals.

Luo, Xiqian↗
NASA NTRS2012

Motion-Base Simulator Evaluation of an Aircraft Using an External Vision System

Twelve air transport-rated pilots participated as subjects in a motion-base simulation experiment to evaluate the use of eXternal Vision Systems (XVS) as enabling technologies for future supersonic aircraft without forward facing windows. Three head-up flight display concepts were evaluated -a monochromatic, collimated Head-up Display (HUD) and a color, non-collimated XVS display with a field-of-view (FOV) equal to and also, one significantly larger than the collimated HUD. Approach, landing, departure, and surface operations were conducted. Additionally, the apparent angle-of-attack (AOA) was varied (high/low) to investigate the vertical field-of-view display requirements and peripheral, side window visibility was experimentally varied. The data showed that lateral approach tracking performance and lateral landing position were excellent regardless of AOA, display FOV, display collimation or whether peripheral cues were present. However, the data showed glide slope approach tracking appears to be affected by display size (i.e., FOV) and collimation. The monochrome, collimated HUD and color, uncollimated XVS with Full FOV display had (statistically equivalent) glide path performance improvements over the XVS with HUD FOV display. Approach path performance results indicated that collimation may not be a requirement for an XVS display if the XVS display is large enough and employs color. Subjective assessments of mental workload and situation awareness also indicated that an uncollimated XVS display may be feasible. Motion cueing appears to have improved localizer tracking and touchdown sink rate across all displays.

Kramer, Lynda J.↗
NASA NTRS1988

Measurement of local convective heat transfer coefficients from a smooth and roughened NACA-0012 airfoil: Flight test data

Wind tunnels typically have higher free stream turbulence levels than are found in flight. Turbulence intensity was measured to be 0.5 percent in the NASA Lewis Icing Research Tunnel (IRT) with the cloud making sprays off and around 2 percent with cloud making equipment on. Turbulence intensity for flight conditions was found to be too low to make meaningful measurements for smooth air. This difference between free stream and wing tunnel conditions has raised questions as to the validity of results obtained in the IRT. One objective of these tests was to determine the effect of free stream turbulence on convective heat transfer for the NASA Lewis LEWICE ice growth prediction code. These tests provide in-flight heat transfer data for a NASA-0012 airfoil with a 533 cm chord. Future tests will measure heat transfer data from the same airfoil in the Lewis Icing Research Tunnel. Roughness was obtained by the attachment of small, 2 mm diameter hemispheres of uniform size to the airfoil in three different patterns. Heat transfer measurements were recorded in flight on the NASA Lewis Twin Otter Icing Research Aircraft. Measurements were taken for the smooth and roughened surfaces at various aircraft speeds and angles of attack up to four degrees. Results are presented as Frossling number versus position on the airfoil for various roughnesses and angles of attack.

Newton, James E.↗
NASA NTRS1988

Measurement of local convective heat transfer coefficients from a smooth and roughened NACA-0012 airfoil - Flight test data

Wind tunnels typically have higher free stream turbulence levels than are found in flight. Turbulence intensity was measured to be 0.5 percent in the NASA Lewis Icing Research Tunnel (IRT) with the cloud making sprays off and around 2 percent with cloud making equipment on. Turbulence intensity for flight conditions was found to be too low to make meaningful measurements for smooth air. This difference between free stream and wind tunnel conditions has raised questions as to the validity of results obtained in the IRT. One objective of these tests was to determine the effect of free stream turbulence on convective heat transfer for the NASA Lewis LEWICE ice growth prediction code. These tests provide in-flight heat transfer data for a NASA-0012 airfoil with a 533 cm chord. Future tests will measure heat transfer data from the same airfoil in the Lewis Icing Research Tunnel. Roughness was obtained by the attachment of small, 2 mm diameter hemispheres of uniform size to the airfoil in three different patterns. Heat transfer measurements were recorded in flight on the NASA Lewis Twin Otter Icing Research Aircraft. Measurements were taken for the smooth and roughened surfaces at various aircraft speeds and angles of attack up to four degrees. Results are presented as Frossling number versus position on the airfoil for various roughnesses and angles of attack.

Van Fossen, G. James↗
NASA NTRS1994

Magnetocentrifugally driven flows from young stars and disks. 2: Formulation of the dynamical problem

We formulate the dynamical problem of a cool wind centrifugally driven from the magnetic interface of a young star and an adjoining Keplerian disk. We examine the situation for mildly accreting T Tauri stars that rotate slowly as well as rapidly accreting protostars that rotate near break-up. In both cases a wind can be driven from a small X-region just outside the stellar magnetopause, where the field lines assume an open geometry and are rooted to material that rotates at an angular speed equal both to the local Keplerian value and to the stellar angular speed. Assuming axial symmetry for the ideal magnetohydrodynamic flow, which requires us to postpone asking how the (lightly ionized) gas is loaded onto field lines, we can formally integrate all the governing equations analytically except for a partial equation that describes how streamlines spread in the meridional plane. Apart from the difficulty of dealing with PDEs of mixed type, finding the functional forms of the conserved quantities along streamlines - the ratio beta of magnetic field to mass flux, the specific energy H of the fluid in the rotating frame, and the total specific angular momentum J carried in the matter and the field - constitutes a standard difficulty in this kind of (Grad-Shafranov) formalism. Fortunately, because the ratio of the thermal speed of the mass-loss regions to the Keplerian speed of rotation of the interface constitutes a small parameter epsilon, we can attack the overall problem by the method of matched asymptotic expansions. This procedure leads to a natural and systematic technique for obtaining the relevant functional dependences of beta, H, and J. Moreover, we are able to solve analytically for the properties of the flow emergent from the small transsonic region driven by gas pressure without having to specify the detailed form of any of the conserved functions, beta, H, and J. This analytical solution provides inner boundary conditions for the numerical computation in a companion paper by Najita & Shu of the larger region where the main acceleration to terminal speeds occurs.

Shu, Frank H.↗
NASA NTRSDate not supplied

Effect of Geometric Fidelity on the Aerodynamics of a Swept Wing with Scalloped Ice Accretion

The effect of geometric fidelity on the aerodynamics of a swept wing with a “scallop” ice shape was studied. Three geometric fidelity versions of the ice shape were studied. The High Fidelity ice shape maintained all of the highly 3D features of the scallop shape. The 3D Smooth ice shape was smoothly lofted over the High Fidelity shape in order to eliminate all of the locally 3D feature. The third ice shape was the 3D Smooth ice shape with roughness grit attached to the surface. The two 3D Smooth versions of the ice shape exhibited a flowfield characterized by a leading edge separation bubble that rolled into spanwise running vortex. The surface pressure data showed classic leading edge separation bubbles that are observed on 2D airfoils with leading edge horn ice shapes. The High Fidelity ice shape exhibited a flowfield characterized by streamwise vortices that formed downstream of the ice shape. The streamwise vortices observed downstream of the High Fidelity ice shape appeared to reduce the size of the separation suction peak observed downstream of the 3D Smooth ice shapes. This reduced the lift for the High Fidelity ice shape, when compared to the 3D Smooth ice shapes. However, these streamwise vortices may have allowed the flow to remain attached longer and slightly increased the stall angle of attack, even though the maximum lift was lower.

Aircraft icing↗
NASA NTRS1988

Effects of surface perturbations on the asymmetric vortex flow over a slender body

An experimental investigation of the effects of surface perturbations on the asymmetric flow past a slender body has been conducted for laminar flow conditions. Beads with diameters ranging from 3/32 to 12/32 in. were attached near the apex of a cone/cylinder model having a base diameter of 3.5 in. and a cone semiapex angle of 9 deg at an angle of attack of 40 deg in an attempt to alter the sense of the asymmetric vortex flow pattern. Circumferential position as well as longitudinal location were varied to determine the most effective bead position. Whether or not the beads were effective in controlling the magnitude and direction of the vortex asymmetries was determined by 3 circumferential rows of pressure taps and by a helium-bubble flow visualization technique. The most effective circumferential position was found to be approximately 140 deg from the windward ray. While holding this circumferential position constant, the effect of bead size at three stations further along the body was also investigated. It was found that the size of the bead necessary to reverse the asymmetry increased more rapidly than the growth in cylinder radius. In general, these results indicate that discrete geometric imperfections on a body's surface can force asymmetry in a given direction if they are sufficiently large relative to the local radius.

Moskovitz, Cary A.↗