THE ZENER RELAXATION AND A NEW MAGNETIC RELAXATION EFFECT IN FE-RICH FE-AL ALLOYS
Zener relaxation and a new magnetic relaxation effect in fe-rich fe-al alloys
MAGNETIC RELAXATION↗
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A relaxation function with distribution of relaxation times
Dispersion function model based on mixed second order kinetics with distributed relaxation times
Fang, P. H.↗
Simulating the Formation of Lunar Floor-Fracture Craters Using Elastoviscoplastic Relaxation
Lunar floor-fracture craters formed during the height of mare basalt emplacement. Due to a general temporal and spatial relation with the maria, these craters, numbering some 200, may be diagnostic of the thermal structure of the crust during this time. As the name suggests, these craters exhibit brittle failure, generally limited to the central floor region. That, and a shallower depth than fresh lunar craters, has led to two main theories as to their formation: laccolith emplacement under the crater and viscous relaxation. The implications of each model for the state of the Moon's crust during this time are quite different, so the viability of each model must be checked. Laccolith emplacement has been treated elsewhere. However, previous attempts to study the relaxation of the craters have assumed only a uniform, Newtonian viscous response of the near surface to the topographic driving forces, and simply postulated that the fractures resulted from tensile stresses associated with floor uplift. Here, we use a more sophisticated rheological model that includes not only non-Newtonian viscous behavior (i.e., the viscosity is stress-dependent), but also incorporates elastic behavior and a plastic component to the rheology to directly simulate the formation of the floor fractures. The results of our simulations show that while elastoviscoplastic relaxation is potentially viable for larger floor-fracture craters, it is not viable for craters with diameters < or = 60 km, the size of the majority of floor-fracture craters. We employ the finite element method, a numerical technique well suited for boundary-value problems, via the commercially available MARC software package. To test the viability of topographic relaxation, our goal is to prepare the simulations as to maximize the amount of relaxation. We take advantage of the natural axisymmetry of craters, simulating one radial plane. Initial shapes are based on data for fresh craters from Pike. To simplify implementation, a fourth order polynomial is used for the basin, while a third order inverse function is used for the rim. This form closely approximates the long-wavelength behavior of complex craters, while ignoring higher-frequency topography, save the rim. This approximation is appropriate because crater relaxation is strongly controlled by long-wavelength topography. Loading is accomplished assuming a uniform gravity field (1.62 m/s-square) and a uniform density of 2900 kg/cubic m. The initial stress state is set to be hydrostatic, with an additional pressure term to account for any overlying topography. This additional pressure term is tapered exponentially with depth. While the simulations quickly settle on a preferred stress state, and while the final solution is fairly insensitive to the choice of the e-folding depth of the taper, selecting an e-folding depth close to the diameter of the crater sets the initial stress state near the preferred state. We assume a diuranally averaged surface temperature of -20 C, and allow temperature to increase with depth at a rate of 50 K//km. Assuming a thermal conductivity of 2 W/in/K, this gradient translates to a heat flow of 100mW/square m, an extremely high value for the Moon. Temperature, of course, will not increase without bound. To maximize relaxation, we allow our temperature profile to increase linearly until it reaches the solidus (assumed to be 1200C) at a depth of 24.4 km, at which point it is kept constant. The presence of melt will drop the bulk viscosity; however, we have no rheological control for partial melts. Therefore, we make no attempt to simulate this situation. Elastoviscoplastic rheological model. In general, geologic materials can behave in three main ways: elastically, viscously (via solid-state creep), and brittly (plasticity is a continuum approach to simulate this phenomenon). We combine these three deformation mechanisms in an extended Maxwell solid, where the total strain can be broken down into a simple summation of the elastic, creep, and plastic strains. In relaxation phenomena in general, the system takes advantage of any means possible to eliminate deviatoric stresses by relaxing away the topography. Previous analyses have only modeled the viscous response. Comparatively, the elastic response in our model can augment the relaxation, to a point. This effect decreases as the elastic response becomes stiffer; indeed, in the limit of infinite elastic Young's modulus (and with no plasticity), the solution converges on the purely viscous solution. Igneous rocks common to the lunar near-surface have Young's modulii in the range of 10-100 GPa. To maximize relaxation, we use a Young's modulus of 10 GPa. (There is negligible sensitivity to the other elastic modulus, the Poisson's ratio; we use 0.25.) For the viscous response, we use a flow law for steady-state creep in thoroughly dried Columbia diabase, because the high plagioclase (about 70 vol%) and orthopyroxene (about 17 vol%) content is similar to the composition of the lunar highland crust as described by remote sensing and sample studies: noritic anorthosite. This flow law is highly non-Newtonian, i.e., the viscosity is highly stress dependent. That, and the variability with temperature, stands in strong contrast to previous examinations of lunar floor-fracture crater relaxation. To model discrete, brittle faulting, we assume "Byerlee's rule," a standard geodynamical technique. We implement this "rule" with an-angle of internal friction of about 40 deg, and a higher-than-normal cohesion of about 3.2 MPa (to approximate the breaking of unfractured rock). The actual behavior of geologic materials is more complex than in our rheological model, so the uncertainties in the plasticity do not represent the state-of-the-art error. Additional information is contained in the original.
Dombard, A. J.↗
Nonlogarithmic magnetization relaxation at the initial time intervals and magnetic field dependence of the flux creep rate in Bi2Sr2Ca(sub I)Cu2Ox single crystals
At the initial time intervals, preceding the thermally activated flux creep regime, fast nonlogarithmic relaxation is found. The fully magnetic moment Pm(t) relaxation curve is shown. The magnetic measurements were made using SQUID-magnetometer. Two different relaxation regimes exist. The nonlogarithmic relaxation for the initial time intervals may be related to the viscous Abrikosov vortices flow with j is greater than j(sub c) for high enough temperature T and magnetic field induction B. This assumption correlates with Pm(t) measurements. The characteristic time t(sub O) separating two different relaxation regimes decreases as temperature and magnetic field are lowered. The logarithmic magnetization relaxation curves Pm(t) for fixed temperature and different external magnetic field inductions B are given. The relaxation rate dependence on magnetic field, R(B) = dPm(B, T sub O)/d(1nt) has a sharp maximum which is similar to that found for R(T) temperature dependences. The maximum shifts to lower fields as temperature goes up. The observed sharp maximum is related to a topological transition in shielding critical current distribution and, consequently, in Abrikosov vortices density. The nonlogarithmic magnetization relaxation for the initial time intervals is found. This fast relaxation has almost an exponentional character. The sharp relaxation rate R(B) maximum is observed. This maximum corresponds to a topological transition in Abrikosov vortices distribution.
Moshchalcov, V. V.↗
Spectroscopic Signatures of Phonon Character in Molecular Electron Spin Relaxation
Spin–lattice relaxation constitutes a key challenge for the development of quantum technologies, as it destroys superpositions in molecular quantum bits (qubits) and magnetic memory in single molecule magnets (SMMs). Gaining mechanistic insight into the spin relaxation process has proven challenging owing to a lack of spectroscopic observables and contradictions among theoretical models. Here, we use pulse electron paramagnetic resonance (EPR) to profile changes in spin relaxation rates (T 1 ) as a function of both temperature and magnetic field orientation, forming a two-dimensional data matrix. For randomly oriented powder samples, spin relaxation anisotropy changes dramatically with temperature, delineating multiple regimes of relaxation processes for each Cu(II) molecule studied. We show that traditional T 1 fitting approaches cannot reliably extract this information. Single-crystal T 1 anisotropy experiments reveal a surprising change in spin relaxation symmetry between these two regimes. We interpret this switch through the concept of a spin relaxation tensor, enabling discrimination between delocalized lattice phonons and localized molecular vibrations in the two relaxation regimes. Variable-temperature T 1 anisotropy thus provides a unique spectroscopic method to interrogate the character of nuclear motions causing spin relaxation and the loss of quantum information.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Stress relaxation of low pressure plasma-sprayed NiCrAlY alloys
The stress relaxation behavior of three NiCrAlY alloys that are commonly used as bond coats for thermal barrier coatings (TBCs) has been directly measured. The relaxation study was conducted at temperatures of 800-1000 C and over a wide range of stresses. It was established that all three bond coat alloys relaxed quite rapidly at temperatures of 900 C and above. Since the upper use temperatures for bond coats in gas turbine engines are between 900 and 1000 C, bond coat relaxation is expected to occur in service. Therefore, relaxation of the bond coat has the potential to affect TBC life. Furthermore, the relaxation differences observed between the three alloys offers a possible explanation for the differences in TBC life observed for these bond coats. While bond coat relaxation is expected to occur for a TBC in service, the mechanism for a relaxation effect on TBC life, if it exists, is yet to be determined.
Brindley, W. J.↗
Stress relaxation of low pressure plasma-sprayed NiCrAlY alloys
The stress relaxation behavior of three NiCrAlY alloys that are commonly used as bond coats for thermal barrier coatings (TBCs) has been directly measured. The relaxation study was conducted at temperatures of 800-1000 C and over a wide range of stresses. It was established that all three bond coat alloys relaxed quite rapidly at temperatures of 900 C and above. Since the upper use temperatures for bond coats in gas turbine engines are between 900 and 1000 C, bond coat relaxation is expected to occur in service. Therefore, relaxation of the bond coat has the potential to affect TBC life. Furthermore, the relaxation differences observed between the three alloys offers a possible explanation for the differences in TBC life observed for these bond coats. While bond coat relaxation is expected to occur for a TBC in service, the mechanism for a relaxation effect on TBC life, if it exists, is yet to be determined.
Brindley, W. J.↗
Wall relaxation in growing stems: comparison of four species and assessment of measurement techniques
This study was carried out to develop improved methods for measuring in-vivo stress relaxation of growing tissues and to compare relaxation in the stems of four different species. When water uptake by growing tissue is prevented, in-vivo stress relaxation occurs because continued wall loosening reduces wall stress and cell turgor pressure. With this procedure one may measure the yield threshold for growth (Y), the turgor pressure in excess of the yield threshold (P-Y), and the physiological wall extensibility (phi). Three relaxation techniques proved useful: "turgor-relaxation", "balance-pressure" and "pressure-block". In the turgor-relaxation method, water is withheld from growing tissue and the reduction in turgor is measured directly with the pressure probe. This technique gives absolute values for P and Y, but requires tissue excision. In the balance-pressure technique, the excised growing region is sealed in a pressure chamber, and the subsequent reduction in water potential is measured as the applied pressure needed to return xylem sap to the cut surface. This method is simple, but only measures (P-Y), not the individual values of P and Y. In the pressure-block technique, the growing tissue is sealed into a pressure chamber, growth is monitored continuously, and just sufficient pressure is applied to the chamber to block growth. The method gives high-resolution kinetics of relaxation and does not require tissue excision, but only measures (P-Y). The three methods gave similar results when applied to the growing stems of pea (Pisum sativum L.), cucumber (Cucumis sativus L.), soybean (Glycine max (L.) Merr.) and zucchini (Curcubita pepo L.) seedlings. Values for (P-Y) averaged between 1.4 and 2.7 bar, depending on species. Yield thresholds averaged between 1.3 and 3.0 bar. Compared with the other methods, relaxation by pressure-block was faster and exhibited dynamic changes in wall-yielding properties. The two pressure-chamber methods were also used to measure the internal water-potential gradient (between the xylem and the epidermis) which drives water uptake for growth. For the four species it was small, between 0.3 and 0.6 bar, and so did not limit growth substantially.
NASA Program Space Biology↗
Employing Relaxed Smoothness Constraints on Imaginary Part of Refractive Index in AERONET Aerosol Retrieval Algorithm
In the Aerosol Robotic Network (AERONET) retrieval algorithm, smoothness constraints on the imaginary part of the refractive index provide control of retrieved spectral dependence of aerosol absorption by preventing the inversion code from fitting the noise in optical measurements and thus avoiding unrealistic oscillations of retrievals with wavelength. The history of implementation of the smoothness constraints in the AERONET retrieval algorithm is discussed. It is shown that the latest version of the smoothness constraints on the imaginary part of refractive index, termed standard and employed by Version 3 of the retrieval algorithm, should be modified to account for strong variability of light absorption by brown-carbon-containing aerosols in UV through mid-visible parts of the solar spectrum. In Version 3 strong spectral constraints were imposed at high values of the Ångström exponent (440–870 nm) since black carbon was assumed to be the primary absorber, while the constraints became increasingly relaxed as aerosol exponent deceased to allow for wavelength dependence of absorption for dust aerosols. The new version of the smoothness constraints on the imaginary part of the refractive index assigns different weights to different pairs of wavelengths, which are the same for all values of the Ångström exponent. For example, in the case of four-wavelength input, the weights assigned to short-wavelength pairs (440–675, 675–870 nm) are small so that smoothness constraints do not suppress natural spectral variability of the imaginary part of the refractive index. At longer wavelengths (870–1020 nm), however, the weight is 10 times higher to provide additional constraints on the imaginary part of refractive index retrievals of aerosols with a high Ångström exponent due to low sensitivity to aerosol absorption for longer channels at relatively low aerosol optical depths. The effect of applying the new version of smoothness constraints, termed relaxed, on retrievals of single-scattering albedo is analyzed for case studies of different aerosol types: black- and brown-carbon-containing fine mode aerosols, mineral dust coarse mode aerosols, and urban industrial fine mode aerosol. It is shown that for brown-carbon-containing aerosols employing the relaxed smoothness constraints resulted in significant reduction in retrieved single-scattering albedo and spectral residual errors (compared to standard) at the short wavelengths. For example, biomass burning smoke cases showed a reduction in single-scattering albedo and spectral residual error at 380 nm of ∼ 0.033 and ∼ 17 %, respectively, for the Rexburg site and ∼ 0.04 and ∼ 12.7 % for the Rimrock site, both AERONET sites in Idaho, USA. For a site with very high levels of black-carbon-containing aerosols (Mongu, Zambia), the effect of modification in the smoothness constraints was minor. For mineral dust aerosols at small Ångström exponent values (Mezaira site, UAE), the spectral constraint on the imaginary part of the refractive index was already relaxed in Version 3; therefore the new relaxed constraint results in minimal change. In the case of weakly absorbing urban industrial aerosols at the GSFC site, there are significant changes in retrieved single-scattering albedo using relaxed assumption, especially reductions at longer wavelengths: ∼ 0.016 and ∼ 0.02 at 875 and 1020 nm, respectively, for 440 nm aerosol optical depth (AOD) ∼ 0.3. The modification of smoothness constraints on the imaginary part of the refractive index has a minor effect on retrievals of other aerosol parameters such as the real part of the refractive index and parameters of the aerosol size distribution. The implementation of the relaxed smoothness constraints on the imaginary part of the refractive index in the next version of the AERONET inversion algorithm will produce significant impacts at some sites in short wavelength channels (380 and 440 nm) for some biomass burning smoke cases with significant brown carbon content and possibly in mid-visible channels (500 and 675 nm) to near-infrared channels (870 to 1020 nm) for some urban industrial aerosol types. However, most differences in single-scattering albedo retrievals between those applying the new relaxed constraint and the standard constraint will be within the uncertainty of the single-scattering albedo retrievals, depending on the level of aerosol optical depth, Ångström exponent, brown carbon content and wavelength.
Aliaksandr Siniuk↗
Molecular Dynamics Simulation and Theoretical Analysis of Structural Relaxation, Bond Exchange Dynamics, and Glass Transition in Vitrimers
Vitrimers are a class of polymer networks featuring dynamic covalent cross-links that can undergo associative bond exchange. There has been recent interest in these materials due to their promise as recyclable thermosets or self-healing polymers because of the ability of vitrimer networks to rearrange at the molecular level and undergo macroscopic flow. However, the practical use of these materials often occurs in the supercooled regime or glassy state, where the implications of dynamic bonds are complicated by the interplay between slow activated segmental dynamics, cross-link (i.e., bond-exchange) kinetics, and ultimately material properties. Here, in this paper, we combine coarse-grained molecular dynamics simulation and microscopic statistical mechanical theory to understand how cross-linking kinetics affect material dynamics and how this couples to segmental relaxation of the polymeric network strands across a spectrum of length and time scales, especially in the supercooled regime. We characterize the Kuhn segmental alpha relaxation time and bond exchange time for vitrimer systems across various cross-link densities, temperatures, and bond exchange rates. Simulation and theory both exhibit a bending-up behavior for bond exchange time upon cooling, suggesting a coupling between bond exchange dynamics and segmental relaxation that intensifies with faster bond exchange kinetics. We also found bond exchange dynamics have an impact on Kuhn segment alpha relaxation time, which is most significant at higher cross-link densities. Both these effects are most prominent when the bond exchange time is similar to the Kuhn segment alpha relaxation time, and the resulting coupling of these two relaxation processes is tied to both the probability of a free end to find a bonded pair and the time scale of the constraints imposed by the dynamic cross-links. This relationship is reflected by a cross-link dependence of a theoretical parameter which represents the quantitative degree of coupling between bond exchange and segmental dynamics. Overall, the combination of simulation and theory clarifies the intricate interaction between bond kinetics and segmental relaxation and demonstrates the ability to provide molecular-level insights into vitrimer dynamics over a wide temperature range.
dynamic relaxation↗
Strain Relaxation and Relative Defect Density with Thickness in MBE-Grown Ge 0.85 Sn 0.15 on Ge(001)
Germanium–tin (GeSn) alloys are emerging as promising materials for mid-infrared optoelectronics and silicon-compatible photonic devices, owing to their tunable direct bandgap. However, the growth of high-quality GeSn films with high Sn content remains challenging due to strain-induced defect formation. In this study, we investigate the role of film thickness on strain-induced relaxation, defect density, and Sn segregation. A series of five samples with varying thicknesses and ∼15% Sn-containing GeSn layers were grown, ranging from the critical thickness for strain relaxation to the onset of Sn segregation. All GeSn samples were analyzed using X-ray diffraction reciprocal space mapping (XRD-RSM) to explore the evolution of strain-induced relaxation as a function of thickness. Photoluminescence measurements reveal that increasing the GeSn thickness enhances strain relaxation while reducing defect-related emission, indicating a decrease in effective defect density prior to reaching the threshold thickness of GeSn layer. At a thickness of ∼150 nm, the GeSn layer shows the onset of Sn segregation, evident in the XRD-RSM spectrum, marking the threshold thickness for Sn segregation. This work defines an effective growth window in terms of thickness (35 to 150 nm) for fabricating relaxed, defect-suppressed GeSn layers with 15% Sn content. These findings emphasize the crucial role of thickness control in balancing strain relaxation and defect suppression, advancing the fabrication of high-quality, high Sn-content relaxed GeSn using molecular beam epitaxy.
Defects↗
A Spectrochemical Series for Electron Spin Relaxation
Controlling the rate of electron spin relaxation in paramagnetic molecules is essential for contemporary applications in molecular magnetism and quantum information science. However, the physical mechanisms of spin relaxation remain incompletely understood, and new spectroscopic observables play an important role in evaluating spin dynamics mechanisms and structure–property relationships. Here, we use cryogenic magnetic circular dichroism (MCD) spectroscopy and pulse electron paramagnetic resonance (EPR) in tandem to examine the impact of ligand field (d–d) excited states on spin relaxation rates. We employ a broad scope of square-planar Cu(II) compounds with varying ligand field strength, including CuS 4 , CuN 4 , CuN 2 O 2 , and CuO 4 first coordination spheres. An unexpectedly strong correlation exists between spin relaxation rates and the average d–d excitation energy (R 2 = 0.97). The relaxation rate trends as the inverse 11th power of the excited-state energies, whereas simplified theoretical models predict only an inverse second power dependence. These experimental results directly implicate ligand field excited states as playing a critical role in the ground-state spin relaxation mechanism. Furthermore, ligand field strength is revealed to be a particularly powerful design principle for spin dynamics, enabling formation of a spectrochemical series for spin relaxation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Biaxial stress relaxation in glassy polymers - Polymethylmethacrylate.
Biaxial stress relaxation studies were performed on glassy polymethylmethacrylate in combined torsion-tension strain fields using a specially designed apparatus with exceptionally high stiffness and low cross talk between the torsional and tensile load measuring transducers. It was found that at low strain levels uniaxial tension relaxation is slower than pure torsion relaxation; tensile-component relaxation rates are unaffected by the level of torsional strain; torsional-component relaxation rates decrease as tensile strain is increased; uniaxial tension relaxation rates approach the pure torsion rates at higher strains (about 2%). A phenomenological treatment is presented which shows that relaxation rates can be coupled to the strain fields in which they are observed and yet be consistent with the concepts of linear viscoelasticity and the Boltzmann superposition integral.
Sternstein, S. S.↗
Aerodynamic sound in a relaxing medium
A theory of aerodynamic sound propagation, when inhomogeneities characterized by a relaxation process are present in both the source and propagation region, is formulated. The details of the relaxation process need not be specified at the outset, although the relaxation process is characterized by a relaxation time and by an equilibrium and a frozen sound speed in a propagation region which is otherwise in equilibrium. Propagation is described in terms of a D'Alembertian characterized by the frozen sound speed relaxing toward one characterized by the equilibrium sound speed, while the source is interpreted in terms of a frozen Lighthill stress tensor relaxing toward the equilibrium stress tensor. An appropriate Green's function for the three-dimensional relaxing wave propagation operator is used to construct an exact integral for the aerodynamic sound. The sound generated far from the source is then estimated in terms of the aerodynamic sound source.
Liu, J. T. C.↗
Finite element models of non-Newtonian crater relaxation
The effects of a non-Newtonian rheology on the profiles of relaxing craters (such as those seen on the surfaces of the icy Galilean and Saturnian satellites) were studied. Two-dimensional finite element simulations of non-Newtonian viscous flow were performed, and the results were compared with those associated with Newtonian rheology. Viscous relaxation of craters in a non-Newtonian medium was significantly different from that in a Newtonian medium. Crater rims are observed to relax at a more rapid rate in a non-Newtonian region as a result of the movement of the low viscosity region to underneath the crater rim after the initial relaxation of the bowl. Significant differences are also found when central depth is plotted as a function of time. For a Newtonian medium, crater relaxation is exponential in form. In contrast, non-Newtonian crater relaxation is initially rapid, in response to the large initial stresses and small viscosities; however, as stresses decrease, this relaxation becomes extremely gradual.
Thomas, Paul J.↗
Relaxation of impact basins on icy satellites
The problem of relaxation of very large impact craters on icy satellites is addressed and the extent to which such studies can help place constraints on the nature of such satellite interiors is investigated. Very general calculations aimed at understanding the nature of relaxation of large impact structures, including the directions, relaxation velocities, and stress levels, are presented. The dependence of relaxation on such factors as silicate core size and viscosity gradients in the ice is examined. The general results are used to address whether comparing the current morphology of impact basins to estimates of their original shape will yield an understanding of the thermal and mechanical structure of the interiors of the icy satellites. It is found that the relaxation rates derived from models of satellite interiors can provide constraints on viscous layer thicknesses. High thermal gradients can permit substantial relaxation even in thin viscous layers. Finally, the constraints on the internal structure of Tethys arising from the extremely relaxed state of the Odysseus basin and the existence of Ithaca Chasma are discussed.
Thomas, Paul J.↗
Crater relaxation on Ganymede - Implications for ice rheology
Controversy has existed over whether or not viscous relaxation is an important process on the icy satellites. Previous models involved large extrapolations of Newtonian flow laws for ice, whereas ice is known to exhibit non-Newtonian behavior. Recently, the flow law parameters for ice at the appropriate temperatures and stresses have been measured. Numerical modeling of the viscous relaxation of basins on Ganymede using these parameters has given implausibly short relaxation times. However, this model treated ice as a purely viscous substance, so that no elastic lithosphere could develop near the surface. Here, ice is treated as a Maxwell visco-elastic material and numerically model the relaxation of basins on Ganymede. It is found that realistic Young's moduli lead to little relaxation occurring in basins even 4.0 Ga after their formation. Further, it is shown that within braod limits the near surface temperature gradient has little effect on this result. Finally, examination of the distribution of Maxwell times in the vicinity of the crater shows that most viscous relaxation occurs early in the basin's history when stresses are high, and thus Maxwell time is short. As stresses are relieved, the Maxwell time becomes long, and relaxation essentially ceases.
Hillgren, Valerie J.↗
Estimates of thermochemical relaxation lengths behind normal shock waves relevant to manned lunar and Mars return missions, the aeroassist flight experiment, and Mars entry
Thermochemical relaxation distances behind the strong normal shock waves associated with vehicles that enter the Earth atmosphere upon returning from a manned lunar or Mars mission are estimated. The relaxation distances for a Mars entry are estimated as well, in order to highlight the extent of the relaxation phenomena early in currently envisioned space exploration studies. The thermochemical relaxation length for the Aeroassist Flight Experiment is also considered. These estimates provide an indication as to whether finite relaxation needs to be considered in subsequent detailed analyses. For the Mars entry, relaxation phenomena that are fully coupled to the flow field equations are used. The relaxation-distance estimates can be scaled to flight conditions other than those discussed.
Howe, John T.↗