Assumption Of Uniform Density Research Articles

Lie group of invariance technique for analyzing propagation of strong shock wave in a rotating non‐ideal gas with azimuthal magnetic field

In this manuscript, the propagation of strong shock wave in a non‐ideal gas in the presence of azimuthal magnetic field with rotational effect is examined by using the Lie group of invariance technique with an assumption of uniform density in the undisturbed medium, whereas the azimuthal component of the fluid velocity and magnetic field are supposed to vary. The main advantage of this method is to reduce the number of independent variables by one. We obtained a special class of self‐similar solutions to the problem, and the flow profiles are depicted graphically behind the shock followed by a brief discussion on the behavior of solutions through graphs. The effects of variation in non‐ideal parameter, adiabatic index of the gas, Alfven–Mach number and ambient azimuthal velocity exponent on the flow variables are presented. All numerical calculations have been done using the “Mathematica”software.

Shock wave propagation in a non-ideal rotating medium with azimuthal magnetic field effect using Lie group technique

The present article demonstrates the propagation of a strong cylindrical shock wave in a rotating adiabatic flow of a van der Waals gas in the presence of an azimuthal magnetic field. Using the Lie group technique, self-similar solutions are obtained with an assumption of uniform density in the undisturbed medium. In contrast, the azimuthal component of the fluid velocity and the magnetic field are supposed to vary. The profiles of the flow variables are depicted graphically, followed by a brief discussion on the behavior of the solutions obtained through the graph. The effects of variation in the values of the adiabatic index, Alfvén Mach Number, non-idealness parameter, and the ambient azimuthal velocity exponent on the flow variables are discussed in detail. The computational work is performed by using Mathematica (a software package).

Spatially resolved electron density in the narrow line region of z < 0.02 radio AGNs

Context. Although studying outflows in the host galaxies of active galactic nuclei (AGNs) have moved to the forefront of extragalactic astronomy in recent years, estimating the energy associated with these outflows has been a major challenge. Determining the energy associated with an outflow often involves an assumption of uniform density in the narrow line region (NLR), which spans a wide range in the literature, leading to large systematic uncertainties in energy estimation. Aims. In this paper we present electron density maps for a sample of outflowing and non-outflowing Seyfert galaxies at z < 0.02 drawn from the Siding Spring Southern Seyfert Spectroscopic Snapshot Survey (S7) and try to understand the origin and values of the observed density structures to reduce the systematic uncertainties in outflow energy estimation. Methods. We use the ratio of the [S II]λ6716,6731 emission lines to derive spatially resolved electron densities (≲50–2000 cm−3). Using optical Integral Field Unit observations from the Wide Field Spectrograph (WiFeS), we are able to measure densities across the central 2–5 kpc of the selected AGN host galaxies. We compare the density maps with the positions of the H II regions derived from the narrow Hα component, ionization maps from [O III] and spatially resolved BPT diagrams to infer the origin of the observed density structures. We also use the electron density maps to construct density profiles as a function of distance from the central AGN. Results. We find a spatial correlation between the sites of high star formation and high electron density for targets without an active ionized outflow. The non-outflowing targets also show an exponential drop in the electron density as a function of distance from the centre, with a mean exponential index of ∼0.15. The correlation between the star forming sites and electron density ceases for targets with an outflow. The density within the outflowing medium is not uniform and shows both low- and high-density sites, most likely due to the presence of shocks and highly turbulent medium. We compare these results in the context of previous results obtained from fibre and slit spectra.

Star formation triggered by non-head-on cloud–cloud collisions, and clouds with pre-collision sub-structure

In an earlier paper, we used smoothed particle hydrodynamics (SPH) simulations to explore star formation triggered by head-on collisions between uniform-density 500M(circle dot) clouds, and showed that there is a critical collision velocity, v(CRIT). At collision velocities below vCRIT, a hub-and-spoke mode operates and delivers a monolithic cluster with a broad mass function, including massive stars (M-star greater than or similar to 10M(circle dot)) formed by competitive accretion. At collision velocities above vCRIT, a spider's-web mode operates and delivers a loose distribution of small sub-clusters with a relatively narrow mass function and no massive stars. Here we show that, if the head-on assumption is relaxed, vCRIT is reduced. However, if the uniform-density assumption is also relaxed, the collision velocity becomes somewhat less critical: a low collision velocity is still needed to produce a global hub-and-spoke system and a monolithic cluster, but, even at high velocities, large cores -capable of supporting competitive accretion and thereby producing massive stars - can be produced. We conclude that cloud-cloud collisions may be a viable mechanism for forming massive stars - and we show that this might even be the major channel for forming massive stars in the Galaxy.

Gravity field and solar component of the precession rate and nutation coefficients of Comet 67P/Churyumov–Gerasimenko

The aim of this study is first to determine the gravity field of the comet 67P Churyumov-Gerasimenko and second to derive the solar component of the precession rate and nutation coefficients of the spin axis of the comet nucleus, i.e. without the direct, usually larger, effect of outgassing. The gravity field, and related moments of inertia, are obtained from two polyhedra, that are provided by the OSIRIS and NAV-CAM experiments on Rosetta, and are based on the assumption of uniform density for the comet nucleus. We also calculate the forced precession rate as well as the nutation coefficients on the basis of Kinoshita's theory of rotation of the rigid Earth and adapted it to be able to indirectly include the effect of outgassing on the rotational parameters. The 2nd degree denormalized Stokes coefficients of comet 67P C-G turn out to be (bracketed numbers refer to second shape model) C20 = -6.74 [-7.93] * 10^-2, C22 = 2.60 [2.71] * 10^-2 consistent with normalized principal moments of inertia A/MR^2 = 0.13 [0.11], B/MR^2 = 0.23 [0.22], with polar moment c = C/MR^2 = 0.25, depending on the choice of the polyhedron model. The obliquity between the rotation axis and the mean orbit normal is 52 degree, and the precession rate only due to solar torques becomes 20-30 "/y. Oscillations in longitude caused by the gravitational pull of the Sun turn out to be of the order of 1', oscillations in obliquity can be estimated to be of the order of 0.5'.

The gravity tunnel in a non-uniform Earth

This paper examines the gravity tunnel using the internal structure of Earth as ascertained from seismic data. Numerically, it is found that the time taken to fall along the diameter is 38 min, compared to 42 min for a planet with uniform density. The time taken to fall along a straight line between any two points is no longer independent of distance but interpolates between 42 min for short trips and 38 min for long trips. The brachistochrone path (minimizing the time between any two points) is similar in shape to the uniform-density solution but tends to reach a greater maximum depth and takes less time to traverse. Although the assumption of uniform density works well in many cases, the simpler assumption of a constant gravitational field serves as a better approximation to the true results.

UV-driven chemistry in simulations of the interstellar medium

Our main purpose is to estimate the effect of assuming uniform density on the line-of-sight in PDR chemistry models, compared to a more realistic distribution for which total gas densities may well vary by several orders of magnitude. A secondary goal of this paper is to estimate the amount of molecular hydrogen which is not properly traced by the CO (J = 1 -> 0) line, the so-called "dark molecular gas". We use results from a magnetohydrodynamical (MHD) simulation as a model for the density structures found in a turbulent diffuse ISM with no star-formation activity. The Meudon PDR code is then applied to a number of lines of sight through this model, to derive their chemical structures. It is found that, compared to the uniform density assumption, maximal chemical abundances for H2, CO, CH and CN are increased by a factor 2 to 4 when taking into account density fluctuations on the line of sight. The correlations between column densities of CO, CH and CN with respect to those of H2 are also found to be in better overall agreement with observations. For instance, at N(H2) > 2.10^{20} cm-2, while observations suggest that d[log N(CO)]=d[log N(H2)] = 3.07 +/- 0.73, we find d[log N(CO)]=d[log N(H2)] =14 when assuming uniform density, and d[log N(CO)]=d[log N(H2)] = 5.2 when including density fluctuations.

Trunk density profile estimates from dual X-ray absorptiometry

Accurate body segment parameters are necessary to estimate joint loads when using biomechanical models. Geometric methods can provide individualized data for these models but the accuracy of the geometric methods depends on accurate segment density estimates. The trunk, which is important in many biomechanical models, has the largest variability in density along its length. Therefore, the objectives of this study were to: (1) develop a new method for modeling trunk density profiles based on dual X-ray absorptiometry (DXA) and (2) develop a trunk density function for college-aged females and males that can be used in geometric methods. To this end, the density profiles of 25 females and 24 males were determined by combining the measurements from a photogrammetric method and DXA readings. A discrete Fourier transformation was then used to develop the density functions for each sex. The individual density and average density profiles compare well with the literature. There were distinct differences between the profiles of two of participants (one female and one male), and the average for their sex. It is believed that the variations in these two participants’ density profiles were a result of the amount and distribution of fat they possessed. Further studies are needed to support this possibility. The new density functions eliminate the uniform density assumption associated with some geometric models thus providing more accurate trunk segment parameter estimates. In turn, more accurate moments and forces can be estimated for the kinetic analyses of certain human movements.

Nanodroplets on a Planar Solid Surface: Temperature, Pressure, and Size Dependence of Their Density and Contact Angles

The shape and the density of a liquid drop on a planar solid surface, embedded in an inert gas at constant temperature and pressure, were examined on the basis of a microscopic density functional approach that accounts for the entropic (temperature-dependent) and energetic contributions to the free energy of the system. Integro-differential equations describing the profile and the density of a cylindrical (2D) drop were derived by the variational minimization of the Gibbs free energy with respect to both the drop profile and density under the assumption of uniform density. The equations were solved numerically using the constraint of a constant number of molecules N(l) per unit length of the drop. It was shown that for temperatures lower than a certain temperature Tw the free energy against density has generally two minima, representing a stable equilibrium state and a metastable one. One of those minima is located at a density corresponding to the density of a normal liquid, whereas the other one is located at a density comparable to the density of the surrounding inert gas. For this reason, the latter state of the drop cannot be stable. For T > Tw, the minimum corresponding to the liquid state disappears, and no drop can be formed on the surface. The temperature Tw depends on N(l) and the external pressure p and increases when N(l) and p increase. The true wetting angle theta0 that the drop profile makes with the solid surface depends on the parameters characterizing the microscopic interactions, the density, and the surface densities. If in the thermodynamically stable state absolute value(cos theta0) > 1, then no drop is formed on the surface. If in that state absolute value(cos theta0) < 1, then at any pressure the true contact angle decreases when the temperature increases and approaches Tw. However, theta0 does not reach a zero value for T < or = Tw but has for T = Tw a discontinuity from a finite to a zero value. The true contact angle also depends on the number of molecules in the drop and on the external pressure. For all considered values of N(l), p, and microscopic parameters of the intermolecular interactions, the density of the drop decreases with increasing temperature. The rate of decrease is constant for temperatures sufficiently far from Tw and increases when T approaches Tw. At a given temperature and pressure, the density of the drop decreases with decreasing N(l). For relatively large drops (N(l) approximately = 10(14)-10(20)), the rate of decrease is very small, whereas for small droplets (N(l) approximately = 10(12)) it becomes much larger.

Experimental Validation of an Improved Squish Velocity Model for Bowl-in-Piston Combustion Chambers

A simple two-zone mass transfer model was used to predict the mean squish velocity history at the rim of a conventional bowl-in-piston combustion chamber. The chamber’s geometry produces gas flow that converges radially inwards (“squish”) as TDC (top dead center) is approached. The squish flow generates turbulence, which can be used to enhance the combustion rate. When compared with PIV (particle image velocimetry) measurements, the peak squish velocity at the bowl rim was 12% less than the value predicted by the simple mass transfer model. After a thorough examination, the assumption of uniform density in the simple model was strongly suspected to be the cause of this discrepancy. Improvements were made to the simple model to account for density variations that are caused by nonuniform heat transfer in the combustion chamber. The revised model yielded velocities that were in close agreement with PIV measurements.

Street-Weighted Interpolation Techniques for Demographic Count Estimation in Incompatible Zone Systems

Data processing for the spatial analysis of small-area social, demographic, and economic data often requires the combination of data spatially aggregated to two or more incompatible zone systems in a region, such as a set of enumeration districts that changes over time. Such situations can be addressed by areal interpolation—the transfer of data between zonal systems according to spatial algorithms. The authors test a technique of areal interpolation using geographic information systems (GIS) that employs a digital map layer representing streets and roads to derive varying density weights for small areas within aggregation zones. The technique reduces errors in estimation compared with estimates derived using the commonly applied area-weighting technique, with its assumption of uniform density. The street-weighting technique is much easier to use than other interpolation techniques that have also been shown to reduce error compared with area-based weighting.

Static effects of intermediate-range forces on polytropic stars of index N = 1

Recent investigations suggest the existence of fundamental intermediate-range forces. Most calculations of their effects have been carried out under the simplifying assumption of uniform density. In this paper the question of how nonuniformity in the density can alter these effects is discussed. It is shown that the effects of intermediate-range forces on the stellar mass and radius are insensitive to the shape of the matter density.

Viscous fluid spheres in general relativity

The spherically symmetric distribution of a dissipative fluid with nonvanishing bulk as well as shear viscosity is discussed. The cosmological constant is included in the field equations for more generality. The junction conditions are applied at the boundary of the sphere to match with the exterior Schwarzschild metric to yield the condition T11=0. In the presence of the bulk viscosity alone spatial homogeneity demands the vanishing of shear as well as the conformal flatness of the space-time. On the other hand, nonzero shear viscosity along with the uniform density assumption result in a unique temporal behavior of the matter density increasing always in the course of time.

The Uniform Density Assumption: Its Effect upon the Estimation of Body Segment Inertial Parameters

The effect of the uniform density assumption upon estimation of body segment inertial parameters was examined by employing directly measured, CT-derived, and cadaver-derived density values. Sectional and average density values for the right leg segments of a patient 29 years of age and a cadaver (65 years) were obtained with a GE 9800 computed tomography scanner using dual energy radiographic factors of 80 kV, 200 mAs, and 140 kV, 200 mAs. Careful sectioning of the cadaver leg following these scans permitted mass and density measurements to be directly performed. The results for both legs showed marked variation in cross-section density values throughout their lengths, which highlighted the limitations of the assumption of uniform segment density. The effect of employing this assumption was tested using a series of inertial parameter estimation strategies by means of mathematical modeling. Adoption of the uniform density assumption when estimating inertial parameters of the human leg segment was shown to produce only minor errors. However, greater errors were shown to be caused by inaccurate estimates of segment volume.

Shape from texture.

A central goal for visual perception is the recovery of the three-dimensional structure of the surfaces depicted in an image. Crucial information about three-dimensional structure is provided by the spatial distribution of surface markings, particularly for static monocular views: projection distorts texture geometry in a manner tha depends systematically on surface shape and orientation. To isolate and measure this projective distortion in an image is to recover the three dimensional structure of the textured surface. For natural textures, we show that the uniform density assumption (texels are uniformly distributed) is enough to recover the orientation of a single textured plane in view, under perspective projection. Furthermore, when the texels cannot be found, the edges of the image are enough to determine shape, under a more general assumption, that the sum of the lengths of the contours on the world plane is about the same everywhere. Finally, several experimental results for synthetic and natural images are presented.

Vapor condensation and the liquid state. An extension of Mayer’s theory

An extension of Mayer’s cluster theory beyond the gas spinodal density is discussed. Volume dependence of Mayer’s reducible cluster integrals bj(T,V) is examined and included in the discussion. It is concluded that Mayer’s first equation for the canonical partition function has a built in uniform density assumption and will give a van der Waals loop if correct bj(T,V) are used. The virial expansion is then meaningful in the liquid state as can be shown by the cumulant expansion method. An approximate but complete set of virial coefficients βk for simple fluid is constructed by supplementation of the known β1, β2, β3, β4, for the Lennard-Jones 12-6 potential with the β5, β6, ..., βN−1 given by Carnahan and Starling for the hard sphere potential. The virial series based on this set of βk gives remarkable agreement with the pressure isotherms obtained from Monte Carlo simulation of the Lennard-Jones fluid. To obtain the correct isotherms for a Lennard-Jones fluid not constrained to density homogeneity the uniform density canonical ensemble partition functions Q(T,V,N) obtained by integration of this virial series are used to construct a grand canonical ensemble partition function ∑N≥0λNQ(T,V,N). The isotherms obtained from these agree with the Monte Carlo results at densities corresponding to the homogeneous single phases of gas and of liquid, but display the proper constant pressure at the intermediate overall-average system densities appropriate to gas–liquid coexistence.

Dynamic structure of dark molecular clouds

view Abstract Citations (13) References (24) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Dynamic structure of dark molecular clouds. Kwok, S. Abstract Theoretical CO line profiles are calculated for dark molecular clouds in the case where the cloud is resolved. Assuming that the density and velocity structure of the cloud can be approximated by power laws, both crude analytical and detailed numerical calculations indicate that realistic profiles can be produced only under certain restricted combinations of density and velocity laws. The probable presence of density gradients implies that interpretation of CO profiles on the basis of the assumption of uniform density can lead to serious errors in the estimate of cloud masses. It is suggested that dark clouds and molecular clouds associated with H II regions may represent two consecutive evolutionary stages of stellar formation and that L134 is in the process of evolving from the former to the latter. Publication: The Astrophysical Journal Pub Date: October 1978 DOI: 10.1086/156472 Bibcode: 1978ApJ...225..107K Keywords: Abundance; Carbon Monoxide; Interstellar Gas; Molecular Spectra; Nebulae; Stellar Evolution; Doppler Effect; Emission Spectra; Gas Density; H Ii Regions; Radiative Transfer; Stellar Motions; Astrophysics; Carbon Monoxide:Molecular Clouds; Line Profiles:Molecular Clouds; Molecular Clouds: Structure full text sources ADS |

Uniform Placement of Sand

The Waterways Experiment Station employed the raining technique, involving free fall of sand to the specimen surface. Fot the gradation of sands used in this experiment, the circular rainer with a perforated plate was found to be the most satisfactory rainer and was adopted for the remainder of the study. Additional study study is required to develop a placement technique that will be satisfactory for placing gap graded and well-graded cohesionless soils homogeneously. As a result of this work it has become apparent that particular attention must be paid to uniformity of density within a lift for large size, laboratory constructed specimens of cohesionless material. In particular, the assumption of uniform density and the determination of a single density value in each lift could lead to misinterpretation of results in model tests in large specimens, where results may be influenced by local areas of varying density. /ASCE/

Parallel-Plate Plasma Problem

The parallel-plate plasma problem is considered under the assumption of uniform density and a specular reflection boundary condition at the plates. The impedance of the device is derived for several different models of the plasma medium. The impedance of a hydromagnetic medium exhibits resonances whenever the plate separation is an odd multiple of a half-wave-length, as defined by the dispersion relation, while the Boltzmann equation yields similar results which include, however, the presence of losses in a collisionless plasma. The predicted resonances in the impedance can most likely be observed at high frequencies where only electron motion is important. The low-frequency resonances would be difficult to observe in gas-discharge plasmas because of the high collision frequencies and because the resonances occur at small wavelengths.

ORBITAL CONSTRUCTIONS AND ELECTRON POPULATIONS IN THE TRANSITION ELEMENTS

Orbital constructions and electron populations for the bands in the transition elements have been worked out. With the assumption of uniform density of states in delocalized bands among nearest neighbors, it is possible to predict correctly the lattice elected by the elements. Manganese and iron are exceptions. Numerical values for electron populations in the several s, p, d, and hybrid bands, including their bonding, antibonding, and non-bonding levels, are obtained.