[ { "id": "authors:yr7rv-r7167", "collection": "authors", "collection_id": "yr7rv-r7167", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170104-174132362", "type": "book_section", "title": "Dynamical simulations of granular materials using the Caltech hypercube", "book_title": "C3P Proceedings of the third conference on Hypercube concurrent computers and applications", "author": [ { "family_name": "Werner", "given_name": "B. T.", "clpid": "Werner-B-T" }, { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" } ], "contributor": [ { "family_name": "Fox", "given_name": "Geoffrey", "clpid": "Fox-Geoffrey" } ], "abstract": "A technique for simulating the motion of granular materials using the Caltech Hypercube is described. We demonstrate that grain dynamics simulations run efficiently on the Hypercube and therefore that they offer an opportunity for greatly expanding the use of parallel simulations in studying granular materials. Several examples, which illustrate how the simulations can be used to extract information concerning the behavior of granular materials, are discussed.", "doi": "10.1145/63047.63085", "isbn": "0-89791-278-0", "publisher": "ACM", "place_of_publication": "New York, NY", "publication_date": "1988-12", "pages": "1313-1318" }, { "id": "authors:j9f9c-7a514", "collection": "authors", "collection_id": "j9f9c-7a514", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150127-083806802", "type": "article", "title": "Simulation of Eolian Saltation", "author": [ { "family_name": "Anderson", "given_name": "Robert S.", "clpid": "Anderson-R-S" }, { "family_name": "Haff", "given_name": "Peter K.", "clpid": "Haff-P-K" } ], "abstract": "Saltation is important in the transport of sand-sized granular material by wind and in the ejection of dust from the bed both on Earth and on Mars. The evolution of the saltating population and all its characteristic profiles is calculated from inception by pure aerodynamic entrainment through to steady state. Results of numerical simulations of single-grain impacts into granular beds are condensed into analytic expressions for the number and speeds of grains rebounding or rejected (splashed) from the bed. A model is combined with (i) this numerical representation, (ii) an expression for the aerodynamic entrainment rate, and (iii) the modification of the wind velocity profile by saltating grains. Calculated steady state mass fluxes are within the range of mass fluxes measured in wind tunnel experiments; mass flux is nonlinearly dependent on the shear velocity. Aerodynamically entrained grains in the system are primarily seeding agents; at steady state, aerodynamic entrainment is rare. The time for the entire system to reach steady state is roughly 1 second, or several long-trajectory hop times.", "doi": "10.1126/science.241.4867.820", "issn": "0036-8075", "publisher": "American Association for the Advancement of Science", "publication": "Science", "publication_date": "1988-08-12", "series_number": "4867", "volume": "241", "issue": "4867", "pages": "820-823" }, { "id": "authors:3sqs3-w4z28", "collection": "authors", "collection_id": "3sqs3-w4z28", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190214-144322722", "type": "article", "title": "Steady state saltation in air", "author": [ { "family_name": "Ungar", "given_name": "J. E.", "clpid": "Ungar-J-E" }, { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" } ], "abstract": "Coupled equations of motion for steady state saltation over an infinite plane are derived and solved for a simplified model of the grain\u2010surface impact process. Experimentally observed features of the wind velocity profile in saltation are qualitatively reproduced, including a diminution of the sub\u2010saltation layer mean wind speed, as the friction speed increases. In this model the surface impact velocity of the saltating grains remains relatively constant over a wide range of free\u2010stream shear stresses, and the grain mass flux increases with friction speed u_f* less rapidly than u_f^3.", "doi": "10.1111/j.1365-3091.1987.tb00778.x", "issn": "0037-0746", "publisher": "Wiley", "publication": "Sedimentology", "publication_date": "1987-04", "series_number": "2", "volume": "34", "issue": "2", "pages": "289-299" }, { "id": "authors:vhvx5-cgv20", "collection": "authors", "collection_id": "vhvx5-cgv20", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141029-132436484", "type": "article", "title": "Simulation of sputtering from liquid Cu targets", "author": [ { "family_name": "Shapiro", "given_name": "M. H.", "clpid": "Shapiro-M-H" }, { "family_name": "Lo", "given_name": "D. Y.", "clpid": "Lo-D-Y" }, { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Tombrello", "given_name": "T. A.", "clpid": "Tombrello-T-A" } ], "abstract": "The sputtering of Cu atoms from liquid targets by normally incident 5 keV Ar^+ ions was simulated using the multiple interaction molecular dynamics technique. Yields, energy distributions, and angular distributions of sputtered atoms were obtained at several temperatures slightly above and below the experimental melting point of copper. In all cases the resulting angular distributions of ejected atoms peaked more sharply than the cos \u03b8 behavior predicted by linear cascade theory. The ratio of yields from individual layers of the liquid targets, and the energy and angular distributions of ejected atoms generally were found to be similar to those obtained in previous simulations with solid Cu targets. Our results also are in qualitative agreement with Dumke's measurements of angular distributions and layer yield ratios of sputtered atoms from liquid Ga-In eutectic alloy targets. In particular, no marked changes in yields or energy distributions were observed when the temperature of the target was lowered below the nominal melting point of copper. The angular distributions were found to broaden with increasing temperature.", "doi": "10.1016/0168-583X(86)90525-2", "issn": "0168-583X", "publisher": "Elsevier", "publication": "Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms", "publication_date": "1986-03-01", "series_number": "1-3", "volume": "13", "issue": "1-3", "pages": "348-352" }, { "id": "authors:2m9w8-6fc83", "collection": "authors", "collection_id": "2m9w8-6fc83", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141104-145427348", "type": "article", "title": "Simulation of isotopic mass effects in sputtering", "author": [ { "family_name": "Shapiro", "given_name": "M. H.", "clpid": "Shapiro-M-H" }, { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Tombrello", "given_name": "T. A.", "clpid": "Tombrello-T-A" }, { "family_name": "Harrison", "given_name": "Don E., Jr.", "clpid": "Harrison-D-E-Jr" } ], "abstract": "The multiple interaction, molecular dynamics code SPUT1 has been used to simulate the effects of isotopic mass differences on atoms sputtered from single crystal Cu targets by normally incident Ar ions. Calculations were carried out for 1 keV and 5 keV ions incident on natural Cu targets (69.1% ^(63)Cu, 30.9% ^(65)Cu). and for 5 keV ions incident on pseudo-Cu targets composed of mixtures of natural Cu (63.546 amu) and \"very light\" Cu (50.837 amu) in the abundance ratios 1:3, 1:1, and 3:1. In all cases the sputtered ejecta showed an overall enrichment in the light isotope relative to the isotopic composition of the target. Preferential enrichment of the light isotope in the normal direction was pronounced. Material ejected at oblique angles was either depleted in the light isotope or had a much lower enrichment of the light isotope compared to material ejected normal to the target. Studies with the pseudo-Cu targets showed that smaller enrichments were obtained when the incident ion recoiled immediately back through the first layer of the target, while larger enrichments were associated with deeper penetration of the incident ion into the target crystallite. In both cases, the average energy of the light atoms in the collision cascade was found to be higher than that of the heavy atoms. However, this effect was enhanced with deeper penetration of the incident ion into the target. The preferential enrichment of the light ejected atoms normal to the target is largely the result of a strong momentum asymmetry in the collision cascades. Light atoms in the cascades, on average, carry far greater momentum towards the surface of the target than do the heavy atoms. A limited number of simulation runs also were carried out with heavy ions (74 amu) incident on pseudo-Cu targets. Overall enrichment of the light atoms in the sputtered material was reduced, but the angular variation of the isotopic yields persisted.", "doi": "10.1016/0168-583X(85)90709-8", "issn": "0168-583X", "publisher": "Elsevier", "publication": "Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms", "publication_date": "1985-08", "series_number": "1", "volume": "12", "issue": "1", "pages": "137-146" }, { "id": "authors:k3k37-kp041", "collection": "authors", "collection_id": "k3k37-kp041", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120702-103050439", "type": "article", "title": "Boundary conditions for high-shear grain flows", "author": [ { "family_name": "Hui", "given_name": "K.", "clpid": "Hiu-K" }, { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Ungar", "given_name": "J. E.", "clpid": "Ungar-J-E" }, { "family_name": "Jackson", "given_name": "R.", "clpid": "Jackson-R" } ], "abstract": "Boundary conditions are developed for rapid granular flows in which the rheology is dominated by grain\u2013grain collisions. These conditions are v_0=constdv_0/dy and u_0 = constdu_0/dy, where v and u are the thermal (fluctuation) and flow velocities respectively, and the subscript indicates that these quantities and their derivatives are to be evaluated at the wall These boundary conditions are derived from the nature of individual grain\u2013wall collisions, so that the proportionality constants involve the appropriate coefficient of restitution ew for the thermal velocity equation, and the fraction of diffuse (i.e. non-specular) collisions in the case of the flow-velocity equation. Direct application of these boundary conditions to the problem of Couette-flow shows that as long as the channel width h is very large compared with a grain diameter d it is permissible to set v=0 at the wall and to adopt the no-slip condition. Exceptions occur where d/h is not very small, when the wall is not rough, and when the grain\u2013wall collisions are very elastic. Similar insight into other flows can be obtained qualitatively by a dimensional analysis treatment of the boundary conditions. Finally, the more difficult problem of self-bounding fluids is discussed qualitatively.", "doi": "10.1017/S0022112084002883", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "1984-08", "volume": "145", "pages": "223-233" }, { "id": "authors:642jg-96e25", "collection": "authors", "collection_id": "642jg-96e25", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120712-123405855", "type": "article", "title": "Grain flow as a fluid-mechanical phenomenon", "author": [ { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" } ], "abstract": "The behaviour of granular material in motion is studied from a continuum point of view. Insofar as possible, individual grains are treated as the 'molecules' of a granular 'fluid'. Besides the obvious contrast in shape, size and mass, a key difference between true molecules and grains is that collisions of the latter are inevitably inelastic. This, together with the fact that the fluctuation velocity may be comparable to the flow velocity, necessitates explicit incorporation of the energy equation, in addition to the continuity and momentum equations, into the theoretical description. Simple 'microscopic' kinetic models are invoked for deriving expressions for the 'coefficients' of viscosity, thermal diffusivity and energy absorption due to collisions. The 'coefficients' are not constants, but are functions of the local state of the medium, and therefore depend on the local 'temperature' and density. In general the resulting equations are nonlinear and coupled. However, in the limit s \u00ab d, where s is the mean separation between neighbouring grain surfaces and d is a grain diameter, the above equations become linear and can be solved analytically. An important dependent variable, in this formulation, in addition to the flow velocity u, is the mean random fluctuation ('thermal') velocity v of an individual grain. With a sufficient flux of energy supplied to the system through the boundaries of the container, v can remain non-zero even in the absence of flow. The existence of a non-uniform v is the means by which energy can be 'conducted' from one part of the system to another. Because grain collisions are inelastic, there is a natural (damping) lengthscale, governed by the value of d, which strongly influences the functional dependence of v on position. Several illustrative examples of static (u = 0) systems are solved. As an example of grain flow, various Couette-type problems are solved analytically. The pressure, shear stress, and 'thermal' velocity function v are all determined by the relative plate velocity U (and the boundary conditions). If v is set equal to zero at both plates, the pressure and stress are both proportional to U^2, i.e. the fluid is non-Newtonian. However, if sufficient energy is supplied externally through the walls (v \u2260 0 there), then the forces become proportional to the first power of U. Some examples of Couette flow are given which emphasize the large effect on the grain system properties of even a tiny amount of inelasticity in grain\u2013grain collisions. From these calculations it is suggested that, for the case of Couette flow, the flow of sand is supersonic over most of the region between the confining plates.", "doi": "10.1017/S0022112083003419", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "1983-09", "volume": "134", "pages": "401-430" }, { "id": "authors:3jcr9-jzg70", "collection": "authors", "collection_id": "3jcr9-jzg70", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140908-143019888", "type": "article", "title": "A two-stage mechanism for escape of Na and K from Io", "author": [ { "family_name": "Summers", "given_name": "Michael E.", "clpid": "Summers-M-E" }, { "family_name": "Yung", "given_name": "Yuk L.", "orcid": "0000-0002-4263-2562", "clpid": "Yung-Y-L" }, { "family_name": "Haff", "given_name": "Peter K.", "clpid": "Haff-P-K" } ], "abstract": "It is generally accepted that Io is the source of S, O, Na and K which, after ionization, form the constituents of the Io plasma torus. The escape of S and O from Io can be understood in terms of the photochemistry of a predominantly SO_2 atmosphere created by the high vapour pressure of SO_2 (refs 1, 15). However, the vapour pressures of Na_2S, K_2S and other common compounds containing Na and K are negligible at the surface temperatures of Io. This has given rise to the suggestion that over part of Io's surface (the nightside) the atmosphere is thin enough so that surface sputtering by co-rotating ions can eject Na and K directly into the Io torus. The main objection to this idea is that it implies a 'Sun-locked' source for Na and K, while observations of the Na and K clouds around Io indicate a 'Jupiter-locked' ejection mechanism. We propose here that Na and K escape from Io in two stages. Atoms of Na and K are first sputtered into the atmosphere from the surface by high-energy magnetospheric ions. Atmospheric sputtering by low-energy co-rotating ions then removes these constituents (along with others present) out of Io's gravitational field. We suggest that the observed Na and K ejection asymmetry is due to preferential sputtering of atmospheric particles on the hemisphere of Io facing Jupiter. The estimated injection rates are sufficiently large to maintain the observed K, Na, and O clouds observed around Io.", "doi": "10.1038/304710a0", "issn": "0028-0836", "publisher": "Nature Publishing Group", "publication": "Nature", "publication_date": "1983-08-25", "series_number": "5928", "volume": "304", "issue": "5928", "pages": "710-712" }, { "id": "authors:090vg-mgd08", "collection": "authors", "collection_id": "090vg-mgd08", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141029-081234356", "type": "article", "title": "Possible isotopic fractionation effects in material sputtered from minerals", "author": [ { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Watson", "given_name": "C. C.", "clpid": "Watson-C-C" }, { "family_name": "Tombrello", "given_name": "T. A.", "clpid": "Tombrello-T-A" } ], "abstract": "We discuss in detail a model which makes definite predictions for the fractionation of isotopes in sputtered material. The fractionation patterns can be nonlinear, and the pattern for a particular set of isotopes depends on the chemical matrix within which those isotopes are contained. Calculations are presented for all nonmonoisotopic elements contained in the minerals perovskite, anorthite, ackermanite, enstatite, and troilite. All isotopes are fractionated at the level of approximately 4\u20136\u2030 per atomic mass unit. O is always positively fractionated (heavier isotopes sputtered preferentially), and heavier elements are generally negatively fractionated (lighter isotopes sputtered preferentially). The value of \u03b4(^(18)O:^(16)O) is always less by about 1.8\u2030 than a linear extrapolation based upon the calculated \u03b4(^(17)O:^(16)O) value would suggest. The phenomenon of both negative and positive fractionation patterns from a single target mineral can be used to make an experimental test of the proposed model.", "doi": "10.1029/JB086iB10p09553", "issn": "0148-0227", "publisher": "American Geophysical Union", "publication": "Journal of Geophysical Research B", "publication_date": "1981-10-10", "series_number": "B10", "volume": "86", "issue": "B10", "pages": "9553-9561" }, { "id": "authors:2yacj-eyw53", "collection": "authors", "collection_id": "2yacj-eyw53", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140923-134523450", "type": "article", "title": "Sputter ejection of matter from Io", "author": [ { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Watson", "given_name": "C. C.", "clpid": "Watson-C-C" }, { "family_name": "Yung", "given_name": "Yuk L.", "orcid": "0000-0002-4263-2562", "clpid": "Yung-Y-L" } ], "abstract": "The direct collisional interaction of magnetospheric particles with Io will lead to sputtering of atoms and molecules from the satellite into circum-Jovian space. The \u223c520-eV S (and \u223c260-eV O) ions composing the Io torus are the most effective agents for net sputter removal of matter from the satellite. An incident flux of \u223c10^(10) cm^(\u22122) s^(\u22121) is estimated to provide \u223c5 \u00d7 10^(10) S atoms cm^(\u22122) s^(\u22121) from sputtering of a (dayside) atmosphere with an exobase at a few hundred kilometers and up to \u223c10^(12) S atoms cm^(\u22122) s^(\u22121) from an atmosphere at 1500\u00b0K with an exobase at \u223c2.2 R_(Io). The supply of S (and O) required to stabilize the torus has been estimated by others to be from 10^(10) to 10^(12) cm^(\u22122) s^(\u22121). If Na and K are present in the atmosphere at a concentration level of 1%, the corresponding sputtering rates are calculated to be a few times 10^8 cm^(\u22122) s^(\u22121) for an exobase at several hundred kilometers. These numbers are large enough to supply the 10^7 cm^(\u22122) s^(\u22121) fluxes required to maintain the Na and K clouds. Sputtering can also remove heavy molecules, like Sn, from the atmosphere. At night, direct S sputtering of the unprotected surface is calculated to eject S and Na (1% concentration) at rates given approximately by \u223c10^(10) and \u223c10^8 cm^(\u22122) s^(\u22121), respectively. All atomic species residing on the surface must be ejected into circum-Jovian space at a rate approximately proportional to their (surface) abundances, if direct surface sputtering occurs, so that the particle content of the inner Jovian magnetosphere should map rather faithfully all species present on Io's surface. The processes of plume sputtering, avalanche cascading, and ionic saltation may lead to spatial and temporal variations in the number of ejected particles.", "doi": "10.1029/JA086iA08p06933", "issn": "0148-0227", "publisher": "American Geophysical Union", "publication": "Journal of Geophysical Research A", "publication_date": "1981-08-01", "series_number": "A8", "volume": "86", "issue": "A8", "pages": "6933-6938" }, { "id": "authors:9f01z-ppc92", "collection": "authors", "collection_id": "9f01z-ppc92", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:Haffpk79", "type": "monograph", "title": "Booming sands of the Mojave Desert and the Basin and Range Province, California", "author": [ { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" } ], "abstract": "The phenomenon of acoustically active desert sand dunes has been recorded since ancient times (1). These dunes are usually known in the present day as booming, barking, roaring, or singing sands. The most striking example of the phenomenon is associated with the displacement, on steep slopes exceeding the angle of shear of a large area of unstable sand. As the sand moves downhill a strong and persistent vibration is set up generating a readily noticeable shaking of the surrounding (undisplaced) sand, as well as a loud and pure audible tone similar to that made by a low-flying propellor aircraft. The sand displacement may occur naturally, or be induced by the observer. A list of references to old observations together with a recent study of the phenomenon at Sand Mountain, Nevada, may be found in ref. (2, 3). \n\nThe present paper deals with the acoustic properties of sand from several sites in the Mojave Desert of California and from the Basin and Range Province of California and (in one case) western Nevada, See Fig. 1.", "publisher": "California Institute of Technology", "publication_date": "1979-06" }, { "id": "authors:xmkbx-hht70", "collection": "authors", "collection_id": "xmkbx-hht70", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150903-112542633", "type": "article", "title": "Solar-wind sputtering of the martian atmosphere", "author": [ { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Switkowski", "given_name": "Z. E.", "clpid": "Switkowski-Z-E" }, { "family_name": "Tombrello", "given_name": "T. A.", "clpid": "Tombrello-T-A" } ], "abstract": "In the sputtering process an incident particle beam loses part of its energy to recoil motion of target atoms, some of which may escape through a nearby surface. The sputtering yield, S, is defined as the number of atoms ejected per incident particle. In the Solar System, sputtering will occur whenever the solar wind, consisting mainly of 1 keV AMU hydrogen and helium ions, strikes a material body.\nMany years ago, Wehner et al. suggested that solar wind-induced sputtering of the lunar surface should be an important cause of erosion; recently, analyses of returned lunar material have been interpreted quantitatively in\nterms of such solar-wind sputtering. Mars provides another\nexample of the interaction of the solar wind with a planetary body. However, in contrast to the lunar surface, the martian surface is largely protected from direct solar wind bombardment by its atmosphere. The primarily CO_2 atmosphere is thin by terrestrial standards but still opaque to the solar wind. We discuss here whether solar-wind sputtering of the martian atmosphere is a mechanism leading to significant mass loss.", "doi": "10.1038/272803a0", "issn": "0028-0836", "publisher": "Nature Publishing Group", "publication": "Nature", "publication_date": "1978-04-27", "series_number": "5656", "volume": "272", "issue": "5656", "pages": "803-804" }, { "id": "authors:nggmm-12m94", "collection": "authors", "collection_id": "nggmm-12m94", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150728-104609411", "type": "article", "title": "Sputtering by fast electrons", "author": [ { "family_name": "Scalo", "given_name": "J. M.", "clpid": "Scalo-J-M" }, { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Switkowski", "given_name": "Z. E.", "clpid": "Switkowski-Z-E" }, { "family_name": "Tombrello", "given_name": "T. A.", "clpid": "Tombrello-T-A" } ], "abstract": "Calculations are presented of collision cascade and knockon contributions to sputtering induced by fast electrons. The sputtering yield for MeV electrons bombarding carbon and iron is found to be ~10^(\u22127) to 10^(\u22126). Important erosion effects on astrophysical grains are possible.", "doi": "10.1016/0370-2693(77)90362-8", "issn": "0370-2693", "publisher": "Physics Letters B", "publication": "Physics Letters B", "publication_date": "1977-09-12", "series_number": "1", "volume": "70", "issue": "1", "pages": "137-140" }, { "id": "authors:0wmmf-epr40", "collection": "authors", "collection_id": "0wmmf-epr40", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141105-155414599", "type": "article", "title": "Mass fractionation of the lunar surface by solar wind sputtering", "author": [ { "family_name": "Switkowski", "given_name": "Z. E.", "clpid": "Switkowski-Z-E" }, { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Tombrello", "given_name": "T. A.", "clpid": "Tombrello-T-A" }, { "family_name": "Burnett", "given_name": "D. S.", "orcid": "0000-0001-9521-8675", "clpid": "Burnett-D-S" } ], "abstract": "The sputtering of the lunar surface by the solar wind is examined as a possible mechanism of mass fractionation. Simple arguments based on current theories of sputtering and the ballistics of the sputtered atoms suggest that most ejected atoms will have sufficiently high energy to escape lunar gravity. However, the fraction of atoms which falls back to the surface is enriched in the heavier atomic components in relation to the lighter ones. This material is incorporated into the heavily radiation-damaged outer surfaces of grains, where it is subject to resputtering. Calculations predict that an equilibrium surface layer, enriched in heavier atoms, will form with \u03b4(^(18)O) \u2248 +20\u2030 \u2248 \u03b4(^(30)Si) and that oxygen will be depleted on the surface layers of grains relative to the bulk composition by about 12.5%. These results are in fair agreement with experiment. The dependence of the calculated results upon the energy spectrum of sputtered particles is investigated. We conclude that mass fractionation by solar wind sputtering is likely to be an important phenomenon on the lunar surface but that the complex isotopic variations observed in lunar soils cannot be completely explained by this mechanism.", "doi": "10.1029/JB082i026p03797", "issn": "0148-0227", "publisher": "American Geophysical Union", "publication": "Journal of Geophysical Research", "publication_date": "1977-09-10", "series_number": "26", "volume": "82", "issue": "26", "pages": "3797-3804" }, { "id": "authors:gawea-ham04", "collection": "authors", "collection_id": "gawea-ham04", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150211-133842987", "type": "article", "title": "Muon Transfer in Gas Targets", "author": [ { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Rodrigo", "given_name": "E.", "clpid": "Rodrigo-E" }, { "family_name": "Tombrello", "given_name": "T. A.", "clpid": "Tombrello-T-A" } ], "abstract": "The transfer of a negative muon from a proton to a heavy atom Q, \u03bc,^-p + Q \u2192 p + \u03bc^-, Q, is treated in terms of a classical description of the \u03bcp trajectory. We discuss the muon transfer rate itself, the subsequent population of states in the atom Q, and the effects of electron screening. The polarizability of the \u03bcp atom emerges as a crucial factor in the transfer process.", "doi": "10.1016/0003-4916(77)90336-0", "issn": "0003-4916", "publisher": "Elsevier", "publication": "Annals of Physics", "publication_date": "1977-04", "series_number": "2", "volume": "104", "issue": "2", "pages": "363-379" }, { "id": "authors:xpvbk-d5870", "collection": "authors", "collection_id": "xpvbk-d5870", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:HAFpra77", "type": "article", "title": "Transport properties of negative muons in matter", "author": [ { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Vogel", "given_name": "P.", "orcid": "0000-0003-0587-5466", "clpid": "Vogel-P" } ], "abstract": "In deriving a formula for atomic capture ratios involving negative muons, Daniel postulates a model leading to a muon energy spectrum of a different character from that indicated by a more complete analysis. In this Comment we emphasize the dependence of the energy spectrum on both inelastic and capture processes, and suggest several experiments which may distinguish between different theoretical models.", "doi": "10.1103/PhysRevA.15.1336", "issn": "0556-2791", "publisher": "Physical Review A", "publication": "Physical Review A", "publication_date": "1977-03-01", "series_number": "3", "volume": "15", "issue": "3", "pages": "1336-1337" }, { "id": "authors:17679-jwg02", "collection": "authors", "collection_id": "17679-jwg02", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:HAFpra74", "type": "article", "title": "Capture of negative muons in atoms", "author": [ { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Vogel", "given_name": "P.", "orcid": "0000-0003-0587-5466", "clpid": "Vogel-P" }, { "family_name": "Winther", "given_name": "A.", "clpid": "Winther-A" } ], "abstract": "The frictional force derived from the stopping power of an electron gas is used in the classical equation of motion for the negative muons. We calculate the energy spectrum of the captured muons and the angular momentum distribution of muons at the energy of the electronic K orbit. The resulting P(l) distribution closely resembles the statistical 2l+1 distribution.", "doi": "10.1103/PhysRevA.10.1430", "issn": "0556-2791", "publisher": "Physical Review A", "publication": "Physical Review A", "publication_date": "1974-10-01", "series_number": "4", "volume": "10", "issue": "4", "pages": "1430-1432" }, { "id": "authors:4amf4-cf578", "collection": "authors", "collection_id": "4amf4-cf578", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150211-135306296", "type": "article", "title": "Energy Levels of Highly Excited Muonic Atoms", "author": [ { "family_name": "Griffith", "given_name": "J. E.", "clpid": "Griffith-J-E" }, { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Tombrello", "given_name": "T. A.", "clpid": "Tombrello-T-A" } ], "abstract": "Energy levels of muonic atom states with high principal quantum number are examined. A Thomas-Fermi type treatment is used in all but the lightest atoms to take account of the effects of electron shielding. Transition energies of the muon are compared to electron binding energies, and implications for muon lifetimes are discussed. The splitting of angular momentum substates is explicitly studied; transitions with no change in principal quantum number are unlikely to be important. Effective charges for the muon are computed. The possibility of an absorptive component of the muon potential is raised.", "doi": "10.1016/0003-4916(74)90444-8", "issn": "0003-4916", "publisher": "Elsevier", "publication": "Annals of Physics", "publication_date": "1974-09", "series_number": "1", "volume": "87", "issue": "1", "pages": "1-16" }, { "id": "authors:ee1rm-9xq76", "collection": "authors", "collection_id": "ee1rm-9xq76", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141103-090546031", "type": "article", "title": "Negative muon capture in very light atoms", "author": [ { "family_name": "Haff", "given_name": "P. K.", "clpid": "Haff-P-K" }, { "family_name": "Tombrello", "given_name": "T. A.", "clpid": "Tombrello-T-A" } ], "abstract": "The transition rates for unbound muons to be captured into atomic bound states are calculated as functions of (1) incident muon center-of-mass energy, (2) muon principal quantum number n, and (3) muon (final) angular momentum l, for the hydrogen, helium, and lithium atoms. These rates reflect differences in electron binding energies. At muon energies of several hundred electron volts, lithium K-shell electrons are more likely to be ejected than the L-shell electron, while this behavior is reversed for energies \u2272 10 eV. However, in each case when the capture rate is folded with a muon stopping power function, the result is that more than half of the unbound muons are absorbed above 75 eV. Implications for experiments which look at muon transfer processes are noted.", "doi": "10.1016/0003-4916(74)90435-7", "issn": "0003-4916", "publisher": "Elsevier", "publication": "Annals of Physics", "publication_date": "1974-07", "series_number": "1", "volume": "86", "issue": "1", "pages": "178-192" } ]