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Weakly nonlinear surface waves are examined in the context of the beam model for jetlike radio sources. By introducing a finite scale length, viz. the beam radius, geometrical dispersion can act to balance nonlinear wave growth and thereby produce solitons, localized wave packets of stable waveform. A method for obtaining a soliton equation from the MHD equations is presented and then applied to radio knots in jets.
A sequential modular computational scheme has been proposed for the calculation of temperature profiles in the melt and crystal including the melt-crystal interface shape and the crystal pulling rate for a fixed crystal radius. The heat transfer in the melt is assumed to occur by conduction only. The shape of melt-gas meniscus, described by Laplace-Young equation, is incorporated in the model and its effects on interface shape and pulling rate are examined. Further, the model incorporates the detailed radiation interaction among the various surfaces in the puller using the Gebhart enclosure theory which accounts for both direct and reflected radiation. The effects of various process parameters on the interface shape and the pulling rate have been investigated. The results of this study indicate that the shape of the melt-gas meniscus has a significant effect on the pulling rate and the interface shape in conformity with earlier studies. Further, it is shown that a simple radiation model (Stefan's model) is inadequate to model the radiation heat exchange in the Czochralski puller apparatus and the detailed Gebhart analysis is necessary for accurate calculation of both the temperature profile in the crystal as well as the interface shape.
Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased. The technique was used to predict the flow through a typical arcjet thruster geometry. Results indicate swirl and viscosity play an important role in the complex geometry of an arcjet.
Six numerical examples are presented for steady, two-dimensional, compressible, nonviscous flow in centrifugal compressors with thin straight blades, the center lines of which generate the surface of a right circular cone when rotated about the axis of the compressor. A seventh example is presented for incompressible flow. The solutions were obtained in a region of the compressors, including the impeller tip, that was considered to be unaffected by the diffuser vanes or by the impeller-inlet configuration. Each solution applies to radial and mixed flow compressors with various cone angles but with the same angle between blades on the conic flow surface. The solution also apply to radial and mixed flow turbines with the rotation and the flow direction reversed. The effects of variations in the following parameters were investigated: (1) flow rate, (2) impeller-tip speed, (3) variation of passage height with radius, and (4) angle between blades on conic flow surface. The numerical results are presented in plots of the streamlines and constant Mach number lines. Correlation equations are developed whereby the flow conditions in any impeller with straight blades can be determined (in the region investigated by this analysis) for all operating conditions.
In order to facilitate bounce-averaged guiding center simulations of geomagnetically trapped particles, we express the kinetic energy of a particle with magnetic coordinates (L,phi) as an analytic function of the first two adiabatic invariants (M, J) and the L value of the field line. The magnetic field model is axisymmetric, consisting of a dipolar B field plus a uniform southward magnetic field parallel to the dipole moment mu(sub E). This model magnetosphere is surrounded by a circular equatorial neutral line whose radius b is an adjustable parameter. The L value of a field line is (by definition) inversely proportional to the flux enclosed by the corresponding magnetic shell of equatorial radius r(sub 0), and the L value at the neutral line (r(sub 0) = b) is denoted L*. The azimuthal coordinate phi measures magnetic local time. The best functional representation found for the normalized difference (L(exp 3)a(exp 3)/mu(sub E))(B(sub m) - B(sub 0)) between mirror-point field B(sub m) and equatorial field B(sub 0) along any field line is a 5-term expansion in powers (2/3 through 6/3) of the quantity X equivalent to (La/mu(sub E))(exp 1/2)K, where K equivalent to (J(exp 2)/8m(sub 0)M)(exp 1/2) is an adiabatically conserved quantity independent of particle energy, m(sub 0) is the rest mass of the particle, and a is the radius of the Earth. This functional form is motivated by results for limiting cases in which particles mirror very near and very far from the magnetic equator. Expansion coefficients corresponding to various powers of X are obtained from least squares fits to numerically computed results for X as a function of L and B(sub m). These are accurately expressible as fourth-order polynomials in (r(sub 0)/b)(exp 3), hence indirectly as functions of L/L* = 3La/2b. This representation, which leads (except for a manageably small region of parameter space) to better than 1% accuracy in the specification of B(sub m) as a function of K and L, allows bounce-averaged guiding center simulations to be performed without actually tracing the bounce motions of individual particles. Bounce-averaged drifts L' (meridional) and phi' (azimuthal) are proportional to derivatives of the Hamiltonian H (sum of kinetic and potential energies) with respect to phi and L, respectively. Our formulation thus provides a computationally efficient method for tracing the bounce-averaged adiabatic motion (conserving all three invariants) and nonadiabatic transport (violating the third invariant while conserving the first two invariants) of geomagnetically trapped particles in the model magnetosphere.
A loosely coupled two-phase vacuum water plume model has been developed. This model consists of a source flow model to describe the expansion of water vapor, and the Lagrangian equations of motion for particle trajectories. Gas/Particle interaction is modeled through the drag force induced by the relative velocities. Particles are assumed traveling along streamlines. The equations of motion are integrated to obtain particle velocity along the streamline. This model has been used to predict the mass flux in a 5 meter radius hemispherical domain resulting from the burst of a water jet of 1.5 mm in diameter, mass flow rate of 24.2 g/s, and stagnation pressure of 21.0 psia, which is the nominal Orbiter water dump condition. The result is compared with an empirical water plume model deduced from a video image of the STS-29 water dump. To further improve the model, work has begun to numerically simulate the bubble formation and bursting present in a liquid stream injected into a vacuum. The technique of smoothed particle hydrodynamics was used to formulate this simulation. A status and results of the on-going effort are presented and compared to results from the literature.
On 18 March 2011, the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft was inserted into a 12-hour, near-polar orbit around Mercury, with an initial periapsis altitude of 200 km, initial periapse latitude of 60 deg N, and apoapsis at approximately 15,200 km altitude in the southern hemisphere. This orbit has permitted the mapping of regional gravitational structure in the northern hemisphere, and laser altimetry from the MESSENGER spacecraft has yielded a geodetically controlled elevation model for the same hemisphere. The shape of a planet combined with gravity provides fundamental information regarding its internal structure and geologic and thermal evolution. Elevations in the northern hemisphere exhibit a unimodal distribution with a dynamic range of 9.63 km, less than that of the Moon (19.9 km), but consistent with Mercury's higher surface gravitational acceleration. After one Earth-year in orbit, refined models of gravity and topography have revealed several large positive gravity anomalies that coincide with major impact basins. These candidate mascons have anomalies that exceed 100 mGal and indicate substantial crustal thinning and superisostatic uplift of underlying mantle. An additional uncompensated 1000-km-diameter gravity and topographic high at 68 deg N, 33 deg E lies within Mercury's northern volcanic plains. Mercury's northern hemisphere crust is generally thicker at low latitudes than in the polar region. The low-degree gravity field, combined with planetary spin parameters, yields the moment of inertia C/MR2 = 0.353 +/- 0.017, where M=3.30 x 10(exp 23) kg and R=2440 km are Mercury's mass and radius, and a ratio of the moment of inertia of Mercury's solid outer shell to that of the planet of Cm/C = 0.452 +/- 0.035. One proposed model for Mercury's radial density distribution consistent with these results includes silicate crust and mantle layers overlying a dense solid (possibly Fe-S) layer, a liquid Fe-rich outer core of radius 2030 +/- 37 km, and an assumed solid inner core. Magnetic field measurements indicate a northward offset of Mercury's axial magnetic dipole from the geographic equator by 479 +/-3 km and provide evidence for a regional-scale magnetic field approximately collocated with the northern volcanic plains of possible crustal origin. These results from MESSENGER indicate a complex and asymmetric evolution of internal structure and dynamics in this end-member inner planet.
The poorly known crustal equation of state plays a critical role in many observational phenomena associated with a neutron star. Here using semiclassical Monte Carlo simulations, we explore the possible configurations of the inner edge of the neutron star crust for a variety of baryon densities and proton fractions. Applying the Kirkwood-Buff theory to these two-component systems, we observe how the isothermal compressibility reaches a maximum when isolated nonsymmetric (or quasispherical) clusters are formed in an extremely dilute neutron gas. To determine the neutron fraction, we suggest a geometrical model based on the behavior of the proton-neutron pair correlation function. Accordingly, the equation of state of the inner crust is calculated, illustrating that the nuclear energy in β equilibrium follows a power-law behavior with baryon density. As a possible astrophysical outcome of this study, our results could help refine the mass-radius relation. Finally, our results pave the way towards further investigations of the impact of the proton-neutron pair correlation function on transport properties within the neutron star crust.
A mathematical model taking into account small (and constant) gravitational levels is developed for vaporization of an isolated liquid droplet suspended in a stagnant atmosphere. A goal of the present analysis is to see how small gravitational levels affect droplet gasification characteristics. Attention is focused upon determining the effects on gas-phase phenomena. The conservation equations arc normalized and nondimensionalized, and a small parameter that accounts for the effects of gravity is identified. This parameter is the square of the inverse of a Froude number based on the gravitational acceleration, the droplet radius, and a characteristic gas-phase velocity at the droplet surface. Asymptotic analyses are developed in terms of this parameter. In the analyses, different spatial regions are identified. Near a droplet, gravitational effects are negligible in the first approximation, and the flowfield is spherically symmetric to the leading order. Analysis shows, however, that outer zones exist where gravitational effects cannot be neglected; it is expected that a stagnation point will be present in an outer zone that is not present when gravity is totally absent. The leading order and higher-order differential equations for each zone are derived and solved. The solutions allow the effects of gravity on vaporization rates and temperature, velocity and species fields to be determined.
A frequency-domain thermoreflectance (FDTR) system with a frequency range of 1 Hz to 75 MHz is presented. The wide bandwidth of pump modulation frequency enables enhanced simultaneous thermophysical property characterization of bulk and thin-film materials. The wide bandwidth FDTR system is demonstrated with simultaneous measurements of in-plane and cross-plane thermal conductivities of sapphire and muscovite mica, thickness and thermal conductivity of gold/titanium thin films, and isotropic thermal conductivity and volumetric heat capacity of lithium niobate and silicon. Thermophysical properties measured with FDTR are compared to literature values or independent measurements for verification. Finally, at low frequencies, a negligible error was achieved in the numerical integration of the heat diffusion equation with a Gauss–Legendre quadrature method solved with 400 integration points and an upper integration limit of 16weff, where weff is the effective pump–probe 1/e2 radius.
We demonstrate that astrophysical constraints on the dense-matter equation of state place an upper bound on the color-superconducting gap in dense matter above the transition from nuclear matter to quark matter. Pairing effects in the color-flavor locked quark matter phase increase the pressure at high density, and if this effect is sufficiently large then the requirements of causality and mechanical stability make it impossible to reach such a pressure in a way that is consistent with what is known at lower densities. The intermediate-density equation of state is inferred by considering extensions of chiral effective field theory to neutron star densities, and conditioning these using current astrophysical observations of neutron star radius, maximum mass, and tidal deformability (PSR J0348+0432, PSR J1624-2230, PSR J0740+6620, GW170817). At baryon number chemical potential μ = 2.6 GeV we find a 95% upper limit on the color-flavor locked pairing gap Δ of 457 MeV using overly conservative assumptions and 216 MeV with more reasonable assumptions. Furthermore, this constraint may be strengthened by future astrophysical measurements as well as by future advances in high-density QCD calculations.
Application of statistical methods to the problem of identifying those material properties of artificial graphite having the strongest effect on ablation performance. Ablation performance, as determined by total length change during test, recession rate, surface temperature, surface texture, and degree of gouging, was measured on 40 different, commercially available, artificial graphites in a Mach 2 airstream having a nominal enthalpy of 2.2 MJ/kg and a stagnation pressure of 5.6 atm. Eighteen material properties were measured on these same graphites, and correlations between pairs of these material properties were developed where possible, reducing the original 18 properties to ten mutually independent properties. Multiple regression equations were formulated relating ablation performance to the reduced set of ten independent material properties, thereby identifying those material properties having the most pronounced effect on ablation performance. These regression equations reveal that for optimum ablation performance in the present environment, grain size should be small, ash content low, density and thermal conductivity high, and mean pore radius large.
An approximate numerical method for calculating flow profiles in arteries is developed. The theory takes into account the nonlinear terms of the Navier-Stokes equations as well as the nonlinear behaviour and large deformations of the arterial wall. Through the locally measured values of the pressure, pressure gradient, and pressure-radius function, the velocity distribution and wall shear at a given location along the artery can be determined. The computed results agree well with the corresponding experimental data.
The motion of a satellite with a magnetic damper in the plane of a circular polar orbit is studied. The asymptotics of periodic solutions are constructed for a satellite close to axisymmetric and the radius of convergence is evaluated for the power series obtained. In a broad range of values of parameters, a periodic solution is obtained by numerical integration of equations of motion of the satellite. The asymptotics of a bifurcated curve obtained (the curve on which origin of a pair of periodic solutions occurs) in the space of the parameters agrees well with the results of numerical computation with all physical values of these parameters. A breakdown is made of the space of the initial data of phase variables in the field of effect of different types of periodic motion.
The elasticity problem for a thick plate with a circular hole is formulated in a systematic fashion by using the z-component of the Galerkin vector and that of Muki's harmonic vector function. The problem was originally solved by Alblas. The reasons for reconsidering it are to develop a technique which may be used in solving the elasticity problem for a multilayered plate and to verify and extend the results given by Alblas. The problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Various stress components are tabulated as functions of a/h, z/h, r/a, and nu, a and 2h being the radius of the hole and the plate thickness and nu, the Poisson's ratio. The significant effect of the Poisson's ratio on the behavior and the magnitude of the stresses is discussed.
The computational dispersion properties of horizontally and time-horizontally staggered grids utilizing corresponding centered-difference techniques for approximation of the adjustment, or gravity wave equations, are examined in terms of their group velocity characteristics. Results are acquired for oceanic and atmospheric models, the former being characterized by a much smaller Rossby radius of deformation. For all grids considered additional filtering is required to control and even eliminate waves with poor computational dispersion characteristics. Computational dispersion properties along with other computational characteristics and requirements give some guidance for an optimal selection of an appropriate grid for an ocean or atmospheric model.
Closed-form linear response solutions are presented for the bending response of thin-walled laminated composite cylinders. Displacements and intralaminar stresses are computed using the Donnell theory, and interlaminar stresses are computed using 3D equilibrium equations of elasticity. Laminates with stacking sequencies and an aluminum cylinder are used to illustrate the displacement response, intralaminar, and interlaminar stresses for two length-to-radius ratios of 1 and 5. Data obtained indicate that if only fiber breakage causes ultimate failure, material failure will occur on the compression side of the cylinders, at the ends, due to fiber compression. The interlaminar normal stress is an order of magnitude smaller than the interlaminar shear stresses and it is not likely to initiate failure.
A simple method is developed for solving plane-plastic-stress problems with axial symmetry in the strain-hardening range which is based on the deformation theory of plasticity employing the finite-strain concept. The equations defining the problems are first reduced to two simultaneous nonlinear differential equations involving two dependent variables: (a) the octahedral shear strain, and (b) a parameter indicating the ratio of principal stresses. By multiplying the load and dividing the radius by an arbitrary constant, it is possible to solve these problems without iteration for any value of the modified load. The constant is determined by the boundary condition. This method is applied to a circular membrane under pressure, a rotating disk without and with a central hole, and an infinite plate with a circular hole. Two materials, inconel x and 16-25-6, the octahedral shear stress-strain relations of which do not follow the power law, are used. Distributions of octahedral shear strain, as well as of principal stresses and strains, are obtained. These results are compared with the results of the same problems in the elastic range.