Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Smooth approximation”

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

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Potential Mars Surveyor 2001 Landing Sites: Low-Elevation Cratered "Highlands" in Central and Eastern Sinus Meridiani and Near Amenthes Fossae

The main scientific goal for the Mars Surveyor Program 2001 (MSP 01) landed mission is to collect and characterize 91 rock and 13 soil core samples using an integrated instrument suite onboard the Athena Rover. If possible, these samples will be retrieved and returned to Earth via a MSP 05 or MSP 07 mission. Preliminary engineering constraints for the MSP 01 landing site call for a location that lies between 15 S and 30 N, and below about 2 km elevation (based on Viking-era topography). Desirable landing sites for MSP 01 are to be located "in the ancient highlands where the environmental conditions may have been favorable to the preservation of evidence of possible prebiotic or biotic processes including the emergence (and, potentially, the persistence) of life". We interpret this to mean that the desirable sites include those that have evidence of aqueous sediments that might have been deposited during the Noachian and/or Hesperian Epochs of Mars' history. In addition to the search for subaqueous sedimentary deposits, we took into consideration the fact that the rover, Athena, will need to be able to access these materials. Thus, a site where aeolian deflation has occurred might be desirable because it might expose, in situ, layered sedimentary deposits. Deflated areas, of course, might include potential landing hazards in the form of meterscale buttes and mesas (e.g., Christmas Lake Valley, OR), thus careful study of such sites with high resolution images will be required before a decision is made to land. We have been examining three regions that have potential to be considered for MSP 01 landing sites. This work is based on Viking (VIS, IRTM) and Phobos 2 (Termoskan) observations and should be regarded as preliminary because we believe that the final site selection should also be based upon analysis of Mars Global Surveyor observations that help constrain mineralogy (TES) and local geomorphology (MOC, MOLA). (1) Eastern Sinus Meridiani Region (proposed by K. S. Edgett) Sinus Meridiani is a persistent low-albedo (< 0. 16) region on the martian equator that has been recognized for about 400 years. All of Sinus Meridiani is below the 2 km elevation constraint for MSP 01. The region includes cratered highlands, valley networks, aeolian dunes, and possible aqueous sedimentary deposits. The landing site study region is located in the eastern portion of Sinus Meridiani. It is bounded by latitudes 10 S to 2 N, longitudes 355 W to 345 W, and the elevations are mostly 1-2 km. The center of this area contains a medium-albedo (0.19-0.21), relatively smooth-surfaced deposit that was suggested by Rice to be a lacustrine deposit. Several potential landing areas can be suggested within this region. Based on Viking and Phobos 2 data, the favored sites so far are centered at 7.6 S, 346.9 W and 0.8 S, 349 W. Thermal inertias are 3.2-7.0 x 10(exp -3) cal /sq cm s(exp -0.5)/K; and rock abundances are around 2-6%. The site at 7.6 S, 346.9 W is at the southern end of the smooth, medium-albedo unit that might have a lacustrine origin. At this location, numerous channels appear to have drained toward the smooth unit. Viking images from orbit 747A show this area at about 15 m/pixel ground resolution. The images reveal that aeolian deflation has occurred along the deposit's margins. Bright (i.e., albedo >= 0.21) aeolian dunes are present on the channel floors and in some of the depressions on the smooth unit. The bright, apparently active dunes might consist of material (perhaps lakedeposited sands) that has been eroded from the smooth unit. The site at approximately 0.8 S, 349 W is selected because it offers an opportunity to solve a long-standing puzzle about Mars remote sensing. There are three main "color" units on Mars: "dark red, dark gray, and bright red". This landing site would allow the Athena rover an opportunity to investigate all three materials within close proximity (the best place on Mars to do so). There are no high resolution (better than 100 m/pixel) Viking or Mariner images of this site. (2) Central Sinus Meridiani Region (proposed by K. S. Edgett and T. J. Parker) Central Sinus Meridiani is characterized by two types of surfaces [4]. One is like typical martian cratered highlands elsewhere- there are old valley networks and old impact craters. The other is relatively smooth and flat. These two units are in contact around 3.1 S between 5 W and 4 E longitudes. Valley networks- including one at 6'S, 358 W that rivals the Grand Canyon of Arizona- once drained toward the smooth unit. Edgett and Parker [4] proposed that the smooth unit might consist of sediments laid down in a large Noachian-aged sea/ocean that would have covered much of the northern hemisphere. Schultz and Lutz [I I I suggested that it is a paleopolar layered deposit. Regardless, the smooth unit where it contacts the cratered terrain would make an excellent site for Athena rover to investigate. The site is best seen in Viking high resolution images from orbits 408B (about 30 m/pixel) and 746A (about 12 m/pixel). These images suggest that aeolian deflation has occurred along the margin of the smooth unit, and this deflation has exposed horizontal larrs of material. The elevation is about 0.5 km; thermal inertias are 6.5-8.0 x 10(exp -3) cal /sq cm s(exp -0.5) / K; rock abundances are 2-4%; and the surface is probably sandy with dark drifts and ripples but almost no actual dunes. We suggest a landing around 3.2 S, 3.0 W would test the aqueous sediment hypothesis and provide a potentially smooth surface on which to land. (3) Amenthes Fossae Region (proposed by S. N. Huntwork and K. S. Edgett) The Amenthes Fossae are a series of graben/fissures that are circumferential to the southeast side of Isidis Planitia. These fissures cross a variety of ancient, heavily cratered Noachian terrain and younger, Hesperian and Amazonian terrain. We focused our search on a region 0-15 N, 250 - 270 W. Elevations are -0.5 to 2 km. Depending upon whether Isidis Planitia was ever a water-rich environment, this region might have been influenced by aqueous sedimentation. Valley networks are common, and they drained toward the north and northwest. We focused our work on a set of Viking orbiter high-resolution images, 719A 1-48. These have resolutions 16-24 rri/pixel. We examined images 20-23, centered at 2 N, 258 W. This site, on the plains just southwest of a 42 km-diameter crater, includes a valley network channel, a relatively young crater ejecta deposit, a few buttes composed of presumably ancient, Noachian bedrock, and a "plains" unit. The plains might make an ideal landing surface, except for the presence of some fine-scale ridges (oriented approximately N-S). The ridges are probably yardangs, thus this site offers a place where aeolian deflation has probably exposed some of the layered rock units that comprise the "plains". Thermal inertias are 7.9-8.3 x 10(exp -3) cal/sq cm s(exp -0.5) /K and rock abundances are 10-15%. A rover traverse might include the opportunity to go down to the floor (and sample along the walls) of the valley network channel at 2 N 258.1 W.

Edgett, K. S.↗
NASA NTRS1994

UIT: Ultraviolet surface photometry of the spiral galaxy M74 (NGC 628)

Ultraviolet photometry, obtained from Ultraviolet Imaging Telescope (UIT) images at 1520 A (far-UV; magnitudes m(152)) and 2490 A (near-UV; magnitudes m(249)), of the spiral galaxy M74 (NGC 628) is compared with H-alpha, R, V, and B surface photometry and with models. M74's surface brightness profiles have a central peak with an exponential falloff; the exponential scale lengths of the profiles increase with decreasing wavelength for the broad-band images. The slope of the continuum-subtracted H-alpha profile is intermediate between those of far-UV and near-UV profiles, consistent with the related origins of H-alpha and UV emission in extreme Population I material. M74's color profiles all become bluer with increasing radius. The (m(152) - m(249)) color as measured by UIT averages near 0.0 (the color of an A0 star) over the central 20 sec radius and decreases from approximately -0.2 to approximately -0.4 from 20 sec to 200 sec. The spiral arms are the dominant component of the surface photometry colors; interarm regions are slightly redder. In the UV, M74's nuclear region resembles its disk/spiral arm material in colors and morphology, unlike galaxies such as M81. No UV 'bulge' is apparent. The m(152) - m(249) colors and models of M74's central region clearly demonstrate that there is no significant population of O or B stars present in the central 10 sec. M74's UV morphology and (m(152) - m(249)) color profiles are similar to those of M33, although M74 is approximately 0.5 mag redder. M81 has a smooth UV bulge which is much redder than the nuclear regions of M74 and M33. M74 is approximately 0.4 mag bluer than M81 in its outer disk, although M81 has bright UV sources only in spiral arms more than 5 kpc from its center. We investigate possible explanations for the color profiles of the galaxies and the differences among the galaxies: abundances; reddening due to internal dust; interplanetary magnetic field (IMF) variations, and the history of formation of the dominant generations of stars. Abundance and IMF variations do not produce large enough m(152) - m(249) or UV - V color differences. Comparing model UV/optical colors with those of M74 shows that M74's disk has undergone significant star formation over the past 500 Myr, and that either the star-formation history or the extinction varies systematically across M74's disk. Comparison of M74, M33, and M81 (UV - V) colors shows that M74 colors range from the bluest of M33's colors to the bluest of M81's. The failure of reddening models to cover the range of colors, and the known abundance range in such material, leads to the conclusion that star-formation history varies significantly as a function of radius in these galaxies, and that such variation is required to explain the range of colors observed in M74, M33, and M81.

Cornett, Robert H.↗
DOE OSTI2025

A Bayesian Framework for Spectral Reprojection

Abstract Fourier partial sum approximations yield exponential accuracy for smooth and periodic functions, but produce the infamous Gibbs phenomenon for non-periodic ones. Spectral reprojection resolves the Gibbs phenomenon by projecting the Fourier partial sum onto a Gibbs complementary basis, often prescribed as the Gegenbauer polynomials. Noise in the Fourier data and the Runge phenomenon both degrade the quality of the Gegenbauer reconstruction solution, however. Motivated by its theoretical convergence properties, this paper proposes a new Bayesian framework for spectral reprojection, which allows a greater understanding of the impact of noise on the reprojection method from a statistical point of view. We are also able to improve the robustness with respect to the Gegenbauer polynomials parameters. Finally, the framework provides a mechanism to quantify the uncertainty of the solution estimate.

Li, Tongtong (ORCID:0000000276644764)↗
NASA NTRS1974

Approximations to and local properties of diffusions with discontinuous controls

The paper discusses several properties of control systems defined by stochastic differential equations, which are defined by the method of Girsanov, using a transformation of measures, and where the controls are discontinuous. Uniqueness of the multivariate distributions of the process is proved, and it is shown that the process is a limit, in a natural sense, of a certain discrete time approximation. Other questions, concerning the effects on the distributions of the paths, and of the cost of approximating the control by a smooth control and concerning local properties of the solution, are discussed.

Kushner, H. J.↗
NASA NTRS1975

Multifrequency techniques for studying interplanetary scintillations

Rytov's approximation, or the method of smooth perturbations, is utilized to derive the temporal frequency spectra of the amplitude and phase fluctuations of multifrequency plane and spherical waves propagating in the interplanetary medium and solar corona. It is shown that multifrequency observations of interplanetary scintillations using either compact radio stars of spacecraft radio signals are desirable because the correlation of the multifrequency waves yields additional independent measurements of the solar wind and turbulence. Measurements of phase fluctuations are also desirable because, unlike amplitude fluctuations, they provide information on the full range of scale sizes for the electron-density fluctuations. It is also shown that a coherent dual-frequency radio system is particularly useful in making such measurements. In addition to providing a means for interpreting observations of multifrequency interplanetary scintillations, the present analysis is essential for estimating the effects of solar corona turbulence on the communications and navigation of a spacecraft whose line-of-sight path passes close to the sun.

Woo, R.↗
NASA NTRS1984

On gravity from SST, geoid from Seasat, and plate age and fracture zones in the Pacific

A composite map produced by combining 90 passes of SST data show good agreement with conventional GEM models. The SEASAT altimeter data were deduced and found to agree with both the SST and GEM fields. The maps are dominated (especially in the east) by a pattern of roughly east-west anomalies with a transverse wavelength of about 2000 km. Comparison with regional bathymetric data shows a remarkedly close correlation with plate age. Most anomalies in the east half of the Pacific could be partly caused by regional differences in plate age. The amplitude of these geoid or gravity anomalies caused by age differences should decrease with absolute plate age, and large anomalies (approximately 3 m) over old, smooth sea floor may indicate a further deeper source within or perhaps below the lithosphere. The possible plume size and ascent velocity necessary to supply deep mantle material to the upper mantle without complete thermal equilibration was considered. A plume emanating from a buoyant layer 100 km thick and 10,000 times less viscous than the surrounding mantle should have a diameter of about 400 km and must ascend at about 10 cm/yr to arrive still anomalously hot in the uppermost mantle.

Marsh, B. D.↗
NASA NTRS1989

LIMEX '87 ice surface characteristics - Implications for C-band SAR backscatter signatures

Ice surface characterization data collected in 1987, during the Labrador Sea Ice Margin Experiment, are analyzed to estimate the changes in snow and ice properties at the onset of melt. Surface measurements were made from an ice research vessel on several days (some of which had coincident remote-sensing flights) at a number of locations in the marginal ice zone. These data are used as input parameters in a simple scattering model to simulate the effects of variations in material properties upon C-band scattering signatures. Snow moisture and large-scale surface roughness are demonstrated to have the largest effect upon HH polarization scattering cross-section sigma(HH)(O) and large differences are predicted between undeformed floe surfaces and deformed or undulating rough ice surfaces. Using a parametric approach, an approximate picture of rough and smooth ice signatures and their relative contrast are provided. The models reproduce a trend observed in synthetic aperture radar (SAR) images of increasing backscatter contrast between deformed and underformed ice over an early period of warning: such observations are consistent with the results of analysis of SAR images to date. The model also reproduces a calibrated SAR-derived signature with a reasonable degree of accuracy.

Drinkwater, Mark R.↗
NASA NTRS1991

Uniform high order spectral methods for one and two dimensional Euler equations

Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. The authors present numerical results for the inviscid Burgers' equation, and for the one dimensional Euler equations including the interactions between a shock wave and density disturbance, Sod's and Lax's shock tube problems, and the blast wave problem. The interaction between a Mach 3 two dimensional shock wave and a rotating vortex is simulated.

Cai, Wei↗
NASA NTRS1993

Uniform high-order spectral methods for one- and two-dimensional Euler equations

Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. The authors present numerical results for the inviscid Burgers' equation, and for the one-dimensional Euler equations including the interactions between a shock wave and density disturbance, Sod's and Lax's shock tube problems, and the blast wave problem. The interaction between a Mach 3 two-dimensional shock wave and a rotating vortex is simulated.

Cai, Wei↗
DOE OSTI2020

HYDRODYNAMIC ANALYSIS OF MACROALGAE LOCAL MODEL USING COMPUTATIONAL FLUID DYNAMICS

In this article, a local scale, fully nonlinear coupled fluid-structural interaction (FSI) sugar kelp model has been developed using a computational fluid dynamics (CFD) method. In this model, to be consistent with available experimental data, the sugar kelp is approximated as elongated rectangles with smoothed isosceles triangles at the ends and a single kelp model with one end fixed in a channel with constant current model is developed. Several different current speeds are simulated, and the resulting drag forces and calculated drag coefficients are validated by comparison with experimental data from the literature. In a previous study, a global scale model was developed using a computational structural dynamics (CSD) method to simulate macroalgae farming system and guide the system configuration design. In the global scale model, the hydrodynamic forces are calculated using Morison’s equation and the kinematics and dynamics of the sugar kelp are simplified and the group of kelps attached to the long line is modeled as a slender structure with the same length and an effective diameter such that the volumes are consistent with the real physical system. This simplified model matches the weight and buoyancy but adjusting the hydrodynamic properties when the general hydrodynamic coefficients are employed. Therefore, optimal hydrodynamic coefficients used in global scale model were determined to obtain the hydrodynamic force more accurately. The validated local scale model is then be applied to determine the hydrodynamic coefficients of the simplified sugar kelp model for global dynamic analysis.

hydrodynamic modeling, macroalgae, CFD model↗
DOE OSTI2021

A Scalable Gradient Free Method for Bayesian Experimental Design with Implicit Models

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods have difficulties in efficiently estimating the posterior distribution and maximizing the mutual information (MI) between data and parameters. Recent work proposed the use of gradient ascent to maximize a lower bound on MI to deal with these issues. However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit models. In this paper, we propose a novel approach that leverages recent advances in stochastic approximate gradient ascent incorporated with a smoothed variational MI estimator for efficient and robust BED. Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. Several experiments show that our approach outperforms baseline methods, and significantly improves the scalability of BED in high-dimensional problems.

Zhang, Jiaxin↗
NASA NTRS1979

Fluctuations in microwave background radiation due to secondary ionization of the intergalactic gas in the universe

Secondary heating and ionization of the intergalactic gas at redshifts z approximately 10-30 could lead to the large optical depth of the Universe for Thomson scattering and could smooth the primordial fluctuations formed at z approximately 1500. It is shown that the gas motions connected with the large scale density perturbations at z approximately 10-15 must lead to the generation of secondary fluctuations of microwave background. The contribution of the rich clusters of galaxies and young galaxies to the fluctuations of microwave background is also estimated.

Sunyayev, R. A.↗
DOE OSTI2022

Diffuse X-ray scattering from polished silicon: application of the distorted wave Born approximation

Measured diffuse X-ray scattering data for a `smooth' as well as for a `rough' silicon sample were fit to theoretical expressions within the distorted wave Born approximation (DWBA). Data for the power spectral density (PSD) for both samples were also obtained by means of atomic force microscopy and optical interferometry. The Fourier transforms of trial correlation functions were fit to the PSD data and then applied to the DWBA formalism. The net correlation functions needed to fit the PSD data for each sample comprised the sum of two terms with different cutoff lengths and different self-affine fractal exponents. At zero distance these correlation functions added up to yield net values of σ 2 = (2) 2 and (71) 2 Å 2 for the smooth and rough samples, respectively. X-ray scattering data were obtained at beamline 1-BM of the Advanced Photon Source. Data and fits at values of q z = 0.05 and 0.10 Å −1 for the smooth sample are reported. Good fits for the smooth sample were obtained at both q z values simultaneously, that is, identical fitting parameters were applied at both values of q z . The smooth sample also exhibited weak Yoneda wings and a clear distinction between the strong specular scattering and the weak diffuse scattering. Data for the rough sample were qualitatively different and exhibited very weak scattering at the specular condition in contrast to extremely large Yoneda wings. Fits for the rough sample are reported for q z = 0.04, 0.05, and 0.06 Å −1 . Although the large Yoneda wings could be fit quite well in both position and amplitude, scattering near the specular condition could not be equally well fit by applying the same fitting parameters at all values of q z . Albeit imperfect, best-fitting results at the specular condition were obtained by invoking only diffuse scattering, that is, without including a separate theoretical expression for specular scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1988

A solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method.

Rosenfeld, Moshe↗
NASA NTRS1999

Improving Pixel Level Cloud Optical Property Retrieval using Monte Carlo Simulations

The accurate pixel-by-pixel retrieval of cloud optical properties from space is influenced by radiative smoothing due to high order photon scattering and radiative roughening due to low order scattering events. Both are caused by cloud heterogeneity and the three-dimensional nature of radiative transfer and can be studied with the aid of computer simulations. We use Monte Carlo simulations on variable 1-D and 2-D model cloud fields to seek for dependencies of smoothing and roughening phenomena on single scattering albedo, solar zenith angle, and cloud characteristics. The results are discussed in the context of high resolution satellite (such as Landsat) retrieval applications. The current work extends the investigation on the inverse NIPA (Non-local Independent Pixel Approximation) as a tool for removing smoothing and improving retrievals of cloud optical depth. This is accomplished by: (1) Delineating the limits of NIPA applicability; (2) Exploring NIPA parameter dependences on cloud macrostructural features, such as mean cloud optical depth and geometrical thickness, degree of extinction and cloud top height variability. We also compare parameter values from empirical and theoretical considerations; (3) Examining the differences between applying NIPA on radiation quantities vs direct application on optical properties; (4) Studying the radiation budget importance of the NIPA corrections as a function of scale. Finally, we discuss fundamental adjustments that need to be considered for successful radiance inversion at non-conservative wavelengths and oblique Sun angles. These adjustments are necessary to remove roughening signatures which become more prominent with increasing absorption and solar zenith angle.

Oreopoulos, Lazaros↗
NASA NTRS1989

Evaluation of the ride quality of a light twin engine airplane using a ride quality meter

A ride quality meter was used to establish the baseline ride quality of a light twin-engine airplane planned for use as a test bed for an experimental gust alleviation system. The ride quality meter provides estimates of passenger ride discomfort as a function of cabin noise and vibration (acceleration) in five axes (yaw axis omitted). According to the ride quality meter, in smooth air the cabin noise was the dominant source of passenger discomfort, but the total discomfort was approximately the same as that for the smooth-air condition. The researcher's subjective opinion, however, is that the total ride discomfort was much worse in the moderate turbulence than it was in the smooth air. The discrepancy is explained by the lack of measurement of the low-frequency accelerations by the ride quality meter.

Stewart, Eric C.↗
NASA NTRS1995

Chromospheric variations in main-sequence stars

The fluxes in passbands 0.1 nm wide and centered on the Ca II H and K emission cores have been monitored in 111 stars of spectral type F2-M2 on or near the main sequence in a continuation of an observing program started by O. C. Wilson. Most of the measurements began in 1966, with observations scheduled monthly until 1980, when observations were schedueld sevral times per week. The records, with a long-term precision of about 1.5%, display fluctuations that can be idntified with variations on timescales similar to the 11 yr cycle of solar activity as well as axial rotation, and the growth and decay of emitting regions. We present the records of chromospheric emission and general conclusions about variations in surface magnetic activity on timescales greater than 1 yr but less than a few decades. The results for stars of spectral type G0-K5 V indicate a pattern of change in rotation and chromospheric activity on an evolutionary timescale, in which (1) young stars exhibit high average levels of activity, rapid rotation rates, no Maunder minimum phase and rarely display a smooth, cyclic variation; (2) stars of intermediate age (approximately 1-2 Gyr for 1 solar mass) have moderate levels of activity and rotation rates, and occasional smooth cycles; and (3) stars as old as the Sun and older have slower rotation rates, lower activity levels and smooth cycles with occasional Maunder minimum-phases.

Baliunas, S. L.↗
NASA NTRS1993

Gas distribution and starbursts in shell galaxies

Detailed maps of most elliptical galaxies reveal that, whereas the greatest part of their luminous mass originates from a smooth distribution with a surface brightness approximated by a de Vaucouleurs law, a small percentage of their light is contributed by low surface brightness distortions termed 'fine structures'. The sharp-edged features called 'shells' are successfully reproduced by merger and infall models involving accretion from less massive companions. In this context, dwarf spheroidal and compact disk galaxies are likely progenitors of these stellar phenomena. However, it is probable that the sources of shell-forming material also contain significant amounts of gas. This component may play an important role in constraining the formation and evolution of shell galaxies. To investigate the effects of the gaseous component, numerical simulations were performed to study the tidal disruption of dwarf galaxies containing both gas and stars by more massive primaries, and the evolution of the ensuing debris. The calculations were performed with a hybrid N-body/hydrodynamics code. Collisionless matter is evolved using a conventional N-body technique and gas is treated using smoothed particle hydrodynamics in which self-gravitating fluid elements are represented as particles evolving according to Lagrangian hydrodynamic equations. An isothermal equation of state is employed so the gas remains at a temperature 104 K. Owing to the large mass ratio between the primary and companion, the primary is modeled as a rigid potential and the self-gravity of both galaxies is neglected.

Weil, Melinda L.↗