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NASA NTRS1999

Strategies and Technologies for In Situ Mineralogical Investigations on Mars

Surface landers on Mars (Viking and Pathfinder) have not revealed satisfying answers to the mineralogy and lithology of the planet's surface. In part, this results from their prime directives: Viking focused on exobiology, Pathfinder focused on technology demonstration. The analytical instruments on board the landers made admirable attempts to extract the mineralogy and geology of Mars, as did countless modeling efforts after the missions. Here we suggest a framework for elucidating martian, or any other planetary geology, through an approach that defines (a) type of information required, (b) explorational strategy harmonious with acquisition of these data, (c) interpretation approach to the data, (d) compatible mission architecture, (e) instrumentation for interrogating rocks and soil. (a) Data required: The composition of a planet is ordered at scales ranging from molecules to minerals to rocks, and from geological units to provinces to planetary-scale systems. The largest ordering that in situ compositional instruments can attempt to interrogate is rock type "aggregate" information. This is what the geologist attempts to identify first. From this, mineralogy can be either directly seen or inferred. From mineralogy can be determined elemental abundances and perhaps the state of the compounds as being crystalline or amorphous. Knowledge of rock type and mineralogy is critical for elucidating geologic process. Mars landers acquired extremely valuable elemental data, but attempted to move from elements to aggregates, but this can only be done by making many assumptions and sometimes giant leaps of faith. Data we believe essential are elements, minerals, degree of ordering of compounds, and the aggregate or rock type that these materials compose. (b) Explorational strategy: A lander should function as a surrogate geologist. Of the total landscape, a geologist sees much, but gives detailed attention to an infinitesimally small amount of what is seen. To acquire samples worth detailed scrutiny, as many samples as possible need examining at a cursory or reconnaissance level. A representative, statistically-meaningful sample number cannot be overemphasized. This maxim still applies to geological exploration of our own planet of which we have abundant knowledge. Analysis of many samples mandates low-power consumption per sample. (c) Data interpretation: No single instrument can analyze the full spectrum of the x-axis. An instrument is optimized for detecting certain material characteristics and must therefore affix itself to some point on the x-axis. Any conclusions drawn about data to the left or right of the instrument's position on this axis must necessarily be derived by inference. Hence, it seems logical to include on a mission, instruments that are not closely spaced in their x-axis-position, and if only two analytical methods are used, as shown, they should start at opposite ends of the axis and work towards the center. As examples, we depict a high-resolution camera to evaluate rock type ("aggregate" state) and mineralogy, and an x-ray diffractometer-fluorescence spectrometer (XRD-XRF) to determine elements, minerals, and the degree of order of materials. (d) Mission architecture: No instrument or suite of instruments can be relied upon to always give truly unequivocal analyses. The suite of instruments should therefore permit conclusions of one instrument to be checked against those of another through closed analytical loops. These "loops" can be structured by a combination of orbital imagery, descent imagery, broad-band site viewing/analysis, and data that cover both x and y axes. For example, the detection of a basaltic-looking rock with a microscope should be checked against the elements detected, the appearance of the rock as a lava flow from descent imagery, and so forth. (e) Instrumentation: To satisfy the above criteria, it is necessary to: (i) See the rock or soil with high resolution + magnification, (ii) Examine many samples, (iii) Consume little power per analysis, (iv) Determine elemental species, (v) Determine mineralogy directly (not inferentially) and the degree of ordering of compounds, (vi) Start analyzing from both ends of the x-axis. Every geologist wants to see the hand sample first, and apply a hand lens to its surface. This has not been the starting point for missions to Mars. Thus, our technology satisfies all these criteria . This XRD-XRF-Optical instrument currently being developed, analyses rock or soil surfaces without the need for sample acquisition or preparation; this satisfies the power criterion, and enables many analyses. The device acquires direct mineralogy and determines elemental species. The embedded endoscopic camera satisfies the critical criterion of close inspection of samples; the fiber optic cable can also be used for IR, LTV, or laser sample analysis. Additional information is contained in the original (Figures).

Marshall, J. R.↗

NASA NTRS2006

Calculation of Thermally-Induced Displacements in Spherically Domed Ion Engine Grids

An analytical method for predicting the thermally-induced normal and tangential displacements of spherically domed ion optics grids under an axisymmetric thermal loading is presented. A fixed edge support that could be thermally expanded is used for this analysis. Equations for the displacements both normal and tangential to the surface of the spherical shell are derived. A simplified equation for the displacement at the center of the spherical dome is also derived. The effects of plate perforation on displacements and stresses are determined by modeling the perforated plate as an equivalent solid plate with modified, or effective, material properties. Analytical model results are compared to the results from a finite element model. For the solid shell, comparisons showed that the analytical model produces results that closely match the finite element model results. The simplified equation for the normal displacement of the spherical dome center is also found to accurately predict this displacement. For the perforated shells, the analytical solution and simplified equation produce accurate results for materials with low thermal expansion coefficients.

Soulas, George C.↗

NASA NTRS2006

Modeling of Transient Flow Mixing of Streams Injected into a Mixing Chamber

Ignition is recognized as one the critical drivers in the reliability of multiple-start rocket engines. Residual combustion products from previous engine operation can condense on valves and related structures thereby creating difficulties for subsequent starting procedures. Alternative ignition methods that require fewer valves can mitigate the valve reliability problem, but require improved understanding of the spatial and temporal propellant distribution in the pre-ignition chamber. Current design tools based mainly on one-dimensional analysis and empirical models cannot predict local details of the injection and ignition processes. The goal of this work is to evaluate the capability of the modern computational fluid dynamics (CFD) tools in predicting the transient flow mixing in pre-ignition environment by comparing the results with the experimental data. This study is a part of a program to improve analytical methods and methodologies to analyze reliability and durability of combustion devices. In the present paper we describe a series of detailed computational simulations of the unsteady mixing events as the cold propellants are first introduced into the chamber as a first step in providing this necessary environmental description. The present computational modeling represents a complement to parallel experimental simulations' and includes comparisons with experimental results from that effort. A large number of rocket engine ignition studies has been previously reported. Here we limit our discussion to the work discussed in Refs. 2, 3 and 4 which is both similar to and different from the present approach. The similarities arise from the fact that both efforts involve detailed experimental/computational simulations of the ignition problem. The differences arise from the underlying philosophy of the two endeavors. The approach in Refs. 2 to 4 is a classical ignition study in which the focus is on the response of a propellant mixture to an ignition source, with emphasis on the level of energy needed for ignition and the ensuing flame propagation issues. Our focus in the present paper is on identifying the unsteady mixing processes that provide the propellant mixture in which the ignition source is to be placed. In particular, we wish to characterize the spatial and temporal mixture distribution with a view toward identifying preferred spatial and temporal locations for the ignition source. As such, the present work is limited to cold flow (pre-ignition) conditions

Voytovych, Dmytro M.↗

NASA NTRS1983

Geomagnetism of earth's core

Instrumentation, analytical methods, and research goals for understanding the behavior and source of geophysical magnetism are reviewed. Magsat, launched in 1979, collected global magnetometer data and identified the main terrestrial magnetic fields. The data has been treated by representing the curl-free field in terms of a scalar potential which is decomposed into a truncated series of spherical harmonics. Solutions to the Laplace equation then extend the field upward or downward from the measurement level through intervening spaces with no source. Further research is necessary on the interaction between harmonics of various spatial scales. Attempts are also being made to analytically model the main field and its secular variation at the core-mantle boundary. Work is also being done on characterizing the core structure, composition, thermodynamics, energetics, and formation, as well as designing a new Magsat or a tethered satellite to be flown on the Shuttle.

Benton, E. R.↗

NASA NTRS1995

Determining GPS average performance metrics

Analytic and semi-analytic methods are used to show that users of the GPS constellation can expect performance variations based on their location. Specifically, performance is shown to be a function of both altitude and latitude. These results stem from the fact that the GPS constellation is itself non-uniform. For example, GPS satellites are over four times as likely to be directly over Tierra del Fuego than over Hawaii or Singapore. Inevitable performance variations due to user location occur for ground, sea, air and space GPS users. These performance variations can be studied in an average relative sense. A semi-analytic tool which symmetrically allocates GPS satellite latitude belt dwell times among longitude points is used to compute average performance metrics. These metrics include average number of GPS vehicles visible, relative average accuracies in the radial, intrack and crosstrack (or radial, north/south, east/west) directions, and relative average PDOP or GDOP. The tool can be quickly changed to incorporate various user antenna obscuration models and various GPS constellation designs. Among other applications, tool results can be used in studies to: predict locations and geometries of best/worst case performance, design GPS constellations, determine optimal user antenna location and understand performance trends among various users.

Moore, G. V.↗

NASA NTRS1996

A Comparison of Tension and Compression Creep in a Polymeric Composite and the Effects of Physical Aging on Creep Behavior

Experimental and analytical methods were used to investigate the similarities and differences of the effects of physical aging on creep compliance of IM7/K3B composite loaded in tension and compression. Two matrix dominated loading modes, shear and transverse, were investigated for two load cases, tension and compression. The tests, run over a range of sub-glass transition temperatures, provided material constants, material master curves and aging related parameters. Comparing results from the short-term data indicated that although trends in the data with respect to aging time and aging temperature are similar, differences exist due to load direction and mode. The analytical model used for predicting long-term behavior using short-term data as input worked equally as well for the tension or compression loaded cases. Comparison of the loading modes indicated that the predictive model provided more accurate long term predictions for the shear mode as compared to the transverse mode. Parametric studies showed the usefulness of the predictive model as a tool for investigating long-term performance and compliance acceleration due to temperature.

Gates, Thomas S.↗

NASA NTRS1972

A method for calculating aerodynamic heating on sounding rocket tangent ogive noses

A method is presented for calculating the aerodynamic heating and shear stresses at the wall for tangent ogive noses that are slender enough to maintain an attached nose shock through that portion of flight during which heat transfer from the boundary layer to the wall is significant. The lower entropy of the attached nose shock combined with the inclusion of the streamwise pressure gradient yields a reasonable estimate of the actual flow conditions. Both laminar and turbulent boundary layers are examined and an approximation of the effects of (up to) moderate angles-of-attack is included in the analysis. The analytical method has been programmed in FORTRAN 4 for an IBM 360/91 computer.

Wing, L. D.↗

NASA NTRS1973

A method for calculating aerodynamic heating on sounding rocket tangent ogive noses.

Wing, L. D.↗

NASA NTRS1979

Testing of containers made of glass-fiber reinforced plastic with the aid of acoustic emission analysis

Acoustic emission analysis as a quasi-nondestructive test method makes it possible to differentiate clearly, in judging the total behavior of fiber-reinforced plastic composites, between critical failure modes (in the case of unidirectional composites fiber fractures) and non-critical failure modes (delamination processes or matrix fractures). A particular advantage is that, for varying pressure demands on the composites, the emitted acoustic pulses can be analyzed with regard to their amplitude distribution. In addition, definite indications as to how the damages occurred can be obtained from the time curves of the emitted acoustic pulses as well as from the particular frequency spectrum. Distinct analogies can be drawn between the various analytical methods with respect to whether the failure modes can be classified as critical or non-critical.

Wolitz, K.↗

NASA NTRS2011

Broadband Via-Less Microwave Crossover Using Microstrip-CPW Transitions

The front-to-back interface between microstrip and CPW (coplanar waveguide) typically requires complex fabrication or has high radiation loss. The microwave crossover typically requires a complex fabrication step. The prior art in microstrip-CPW transition requires a physical vias connection between the microstrip and CPW line on a separate layer. The via-less version of this transition was designed empirically and does not have a close form solution. The prior art of the micro wave crossover requires either additional substrate or wire bond as an air bridge to isolate two microwave lines at the crossing junction. The disadvantages are high radiation loss, no analytical solution to the problem, lengthy simulation time, and complex fabrication procedures to generate air bridges or via. The disadvantage of the prior crossover is a complex fabrication procedure, which also affects the device reliability and yield. This microstrip-CPW transition is visualized as two microstrip-slotline transitions combined in a way that the radiation from two slotlines cancels each other out. The invention is designed based on analytical methods; thus, it significantly reduces the development time. The crossover requires no extra layer to cross two microwave signals and has low radiation loss. The invention is simple to fabricate and design. It produces low radiation loss and can be designed with low insertion loss, with some tradeoff with signal isolation. The microstrip-CPW transition is used as an interface to connect between the device and the circuit outside the package. The via-less microwave crossover is used to allow two signals to cross without using an extra layer or fabrication processing step to enable this function. This design allows the solution to be determined entirely though analytical techniques. In addition, a planar via-less microwave crossover using this technique was proposed. The experimental results show that the proposed crossover at 5 GHz has a minimum isolation of 32 dB. It also has low in-band insertion loss and return loss of 1.2 dB and 18 dB, respectively, over more than 44 percent of bandwidth at room temperature. This microstrip-CPW transition requires the microstrip line to be split into two sections. Each section is connected to a microstrip quarter-wavelength openended stub. A slotline is also placed perpendicular to the microstrip section. The slot is connected to a grounded-end quarter-wavelength slotline and generates a microstrip-slotline transition. When two of these sections are placed in parallel and with the microstrip section combined at transition, a microstrip- CPW transition is formed. The slotline radiation is suppressed as two slots are excited with the electric field in an opposite direction, which cancels the radiation in far field. The invention on the crossover consists of the invented microstrip-CPW transitions combined back-to-back and a microstrip low-pass filter. One signal is crossed through to the microstrip layer, while the other signal is crossed through the CPW line located on the ground plane of the microstrip line. The microstrip low-pass filter produces a narrow line at the crossing point to enhance the system isolation. It also produces broadband response in the operating frequency band. The microstrip-CPW transition allows a microwave signal to travel from microstrip line to CPW line with low radiation loss. The crossover allows two microwave signals to cross with minimal parasitic coupling.

Stevenson, Thomas↗

NASA NTRS1972

Atmospheric pressure, density, temperature and wind variations between 50 and 200 km

Data on atmospheric pressure, density, temperature and winds between 50 and 200 km were collected from sources including Meteorological Rocket Network data, ROBIN falling sphere data, grenade release and pitot tube data, meteor winds, chemical release winds, satellite data, and others. These data were analyzed by a daily difference method and results on the distribution statistics, magnitude, and spatial structure of the irregular atmospheric variations are presented. Time structures of the irregular variations were determined by the analysis of residuals from harmonic analysis of time series data. The observed height variations of irregular winds and densities are found to be in accord with a theoretical relation between these two quantities. The latitude variations (at 50 - 60 km height) show an increasing trend with latitude. A possible explanation of the unusually large irregular wind magnitudes of the White Sands MRN data is given in terms of mountain wave generation by the Sierra Nevada range about 1000 km west of White Sands. An analytical method is developed which, based on an analogy of the irregular motion field with axisymmetric turbulence, allows measured or model correlation or structure functions to be used to evaluate the effective frequency spectra of scalar and vector quantities of a spacecraft moving at any speed and at any trajectory elevation angle.

Justus, C. G.↗

NASA NTRS1992

Flow analysis and design optimization methods for nozzle-afterbody of a hypersonic vehicle

This report summarizes the methods developed for the aerodynamic analysis and the shape optimization of the nozzle-afterbody section of a hypersonic vehicle. Initially, exhaust gases were assumed to be air. Internal-external flows around a single scramjet module were analyzed by solving the 3D Navier-Stokes equations. Then, exhaust gases were simulated by a cold mixture of Freon and Ar. Two different models were used to compute these multispecies flows as they mixed with the hypersonic airflow. Surface and off-surface properties were successfully compared with the experimental data. The Aerodynamic Design Optimization with Sensitivity analysis was then developed. Pre- and postoptimization sensitivity coefficients were derived and used in this quasi-analytical method. These coefficients were also used to predict inexpensively the flow field around a changed shape when the flow field of an unchanged shape was given. Starting with totally arbitrary initial afterbody shapes, independent computations were converged to the same optimum shape, which rendered the maximum axial thrust.

Baysal, O.↗

NASA NTRS1994

Computational predictive methods for fracture and fatigue

The damage-tolerant design philosophy as used by aircraft industries enables aircraft components and aircraft structures to operate safely with minor damage, small cracks, and flaws. Maintenance and inspection procedures insure that damages developed during service remain below design values. When damage is found, repairs or design modifications are implemented and flight is resumed. Design and redesign guidelines, such as military specifications MIL-A-83444, have successfully reduced the incidence of damage and cracks. However, fatigue cracks continue to appear in aircraft well before the design life has expired. The F16 airplane, for instance, developed small cracks in the engine mount, wing support, bulk heads, the fuselage upper skin, the fuel shelf joints, and along the upper wings. Some cracks were found after 600 hours of the 8000 hour design service life and design modifications were required. Tests on the F16 plane showed that the design loading conditions were close to the predicted loading conditions. Improvements to analytic methods for predicting fatigue crack growth adjacent to holes, when multiple damage sites are present, and in corrosive environments would result in more cost-effective designs, fewer repairs, and fewer redesigns. The overall objective of the research described in this paper is to develop, verify, and extend the computational efficiency of analysis procedures necessary for damage tolerant design. This paper describes an elastic/plastic fracture method and an associated fatigue analysis method for damage tolerant design. Both methods are unique in that material parameters such as fracture toughness, R-curve data, and fatigue constants are not required. The methods are implemented with a general-purpose finite element package. Several proof-of-concept examples are given. With further development, the methods could be extended for analysis of multi-site damage, creep-fatigue, and corrosion fatigue problems.

Cordes, J.↗

DOE OSTI2025

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2003

A new method to evaluate human-robot system performance

One of the key issues in space exploration is that of deciding what space tasks are best done with humans, with robots, or a suitable combination of each. In general, human and robot skills are complementary. Humans provide as yet unmatched capabilities to perceive, think, and act when faced with anomalies and unforeseen events, but there can be huge potential risks to human safety in getting these benefits. Robots provide complementary skills in being able to work in extremely risky environments, but their ability to perceive, think, and act by themselves is currently not error-free, although these capabilities are continually improving with the emergence of new technologies. Substantial past experience validates these generally qualitative notions. However, there is a need for more rigorously systematic evaluation of human and robot roles, in order to optimize the design and performance of human-robot system architectures using well-defined performance evaluation metrics. This article summarizes a new analytical method to conduct such quantitative evaluations. While the article focuses on evaluating human-robot systems, the method is generally applicable to a much broader class of systems whose performance needs to be evaluated.

Space Flight/instrumentation↗

NASA NTRS2001

Advanced Methods for Aircraft Engine Thrust and Noise Benefits: Nozzle-Inlet Flow Analysis

Three connected sub-projects were conducted under reported project. Partially, these sub-projects are directed to solving the problems conducted by the HU/FM&AL under two other NASA grants. The fundamental idea uniting these projects is to use untraditional 3D corrugated nozzle designs and additional methods for exhaust jet noise reduction without essential thrust lost and even with thrust augmentation. Such additional approaches are: (1) to add some solid, fluid, or gas mass at discrete locations to the main supersonic gas stream to minimize the negative influence of strong shock waves forming in propulsion systems; this mass addition may be accompanied by heat addition to the main stream as a result of the fuel combustion or by cooling of this stream as a result of the liquid mass evaporation and boiling; (2) to use porous or permeable nozzles and additional shells at the nozzle exit for preliminary cooling of exhaust hot jet and pressure compensation for non-design conditions (so-called continuous ejector with small mass flow rate; and (3) to propose and analyze new effective methods fuel injection into flow stream in air-breathing engines. Note that all these problems were formulated based on detailed descriptions of the main experimental facts observed at NASA Glenn Research Center. Basically, the HU/FM&AL Team has been involved in joint research with the purpose of finding theoretical explanations for experimental facts and the creation of the accurate numerical simulation technique and prediction theory for solutions for current problems in propulsion systems solved by NASA and Navy agencies. The research is focused on a wide regime of problems in the propulsion field as well as in experimental testing and theoretical and numerical simulation analysis for advanced aircraft and rocket engines. The F&AL Team uses analytical methods, numerical simulations, and possible experimental tests at the Hampton University campus. We will present some management activity and theoretical numerical simulation results obtained by the FM&AL Team in the reporting period in accordance with the schedule of the work.

Morgan, Morris H.↗

NASA NTRS2007

Aerospace Toxicology and Microbiology

Toxicology dates to the very earliest history of humanity with various poisons and venom being recognized as a method of hunting or waging war with the earliest documentation in the Evers papyrus (circa 1500 BCE). The Greeks identified specific poisons such as hemlock, a method of state execution, and the Greek word toxos (arrow) became the root of our modern science. The first scientific approach to the understanding of poisons and toxicology was the work during the late middle ages of Paracelsus. He formulated what were then revolutionary views that a specific toxic agent or "toxicon" caused specific dose-related effects. His principles have established the basis of modern pharmacology and toxicology. In 1700, Bernardo Ramazzini published the book De Morbis Artificum Diatriba (The Diseases of Workers) describing specific illnesses associated with certain labor, particularly metal workers exposed to mercury, lead, arsenic, and rock dust. Modern toxicology dates from development of the modern industrial chemical processes, the earliest involving an analytical method for arsenic by Marsh in 1836. Industrial organic chemicals were synthesized in the late 1800 s along with anesthetics and disinfectants. In 1908, Hamilton began the long study of occupational toxicology issues, and by WW I the scientific use of toxicants saw Haber creating war gases and defining time-dosage relationships that are used even today.

James, John T.↗

NASA NTRS1998

Inverse Compton Scattering in Mildly Relativistic Plasma

We investigated the effect of inverse Compton scattering in mildly relativistic static and moving plasmas with low optical depth using Monte Carlo simulations, and calculated the Sunyaev-Zel'dovich effect in the cosmic background radiation. Our semi-analytic method is based on a separation of photon diffusion in frequency and real space. We use Monte Carlo simulation to derive the intensity and frequency of the scattered photons for a monochromatic incoming radiation. The outgoing spectrum is determined by integrating over the spectrum of the incoming radiation using the intensity to determine the correct weight. This method makes it possible to study the emerging radiation as a function of frequency and direction. As a first application we have studied the effects of finite optical depth and gas infall on the Sunyaev-Zel'dovich effect (not possible with the extended Kompaneets equation) and discuss the parameter range in which the Boltzmann equation and its expansions can be used. For high temperature clusters (k(sub B)T(sub e) greater than or approximately equal to 15 keV) relativistic corrections based on a fifth order expansion of the extended Kompaneets equation seriously underestimate the Sunyaev-Zel'dovich effect at high frequencies. The contribution from plasma infall is less important for reasonable velocities. We give a convenient analytical expression for the dependence of the cross-over frequency on temperature, optical depth, and gas infall speed. Optical depth effects are often more important than relativistic corrections, and should be taken into account for high-precision work, but are smaller than the typical kinematic effect from cluster radial velocities.

Molnar, S. M.↗