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At least 397 records · Page 22

An experimental study of the effects of rapid rotation on turbulence

Experiments, large eddy simulations and direct numerical simulations all show that rapid rotation has a striking effect on homogeneous nearly isotropic turbulence. The cascade process is effectively inhibited by rotation, and thus dissipation is greatly reduced. Some attempts have been made to incorporate this effect in turbulence models. Numerical simulation further showed the somewhat surprising result that anisotropic homogeneous turbulence subjected to rotation tended towards an isotropic state; however, the residual anisotropy was not zero. Reynolds (1989) performed a detailed analysis using Rapid Distortion Theory (RDT) and showed that a reduction in the anisotropy is indeed expected and if the anisotropy is produced by irrotational strain then the anisotropy tensor b(sub ij) is asymptotically driven to half its initial value. Our objective is to extend the work of the experiments mentioned above to lower turbulent Rossby numbers and to confirm some of the results obtained by Reynolds (1989) for anisotropic turbulence.

Veeravalli, S. V.↗

Static assignment of complex stochastic tasks using stochastic majorization

We consider the problem of statically assigning many tasks to a (smaller) system of homogeneous processors, where a task's structure is modeled as a branching process, and all tasks are assumed to have identical behavior. We show how the theory of majorization can be used to obtain a partial order among possible task assignments. Our results show that if the vector of numbers of tasks assigned to each processor under one mapping is majorized by that of another mapping, then the former mapping is better than the latter with respect to a large number of objective functions. In particular, we show how measurements of finishing time, resource utilization, and reliability are all captured by the theory. We also show how the theory may be applied to the problem of partitioning a pool of processors for distribution among parallelizable tasks.

Nicol, David↗

Effect of Heterogeneities on the Reaction-zone of a Propagating Detonation Wave

Reactive burn models for propagating detonation waves in an explosive are based on the ZND (Zel'dovich-Von Neumann-Doring) theory. A key property of the ZND theory, which leads to self-sustaining detonation waves, is a sonic point relative to the front in the reaction zone. Moreover, burn models assume the explosive is a homogeneous material. This assumption is used for plastic-bonded explosives, even though they are heterogeneous materials. The heterogeneities are accounted for only with an empirical burn rate. Furthermore, the reaction-zone width can be less than the length scale of heterogeneities. This raises the question of the effect of heterogeneities on the reaction zone. In particular, whether the reaction zone can be steady and have a well defined sonic point. To examine this question we focus on PBX 9501 since there is data on the grain-binder heterogeneities and on the reaction-zone velocity time history of a steady planar detonation wave. Using pseudo-mesoscale 1-D simulations, we examine the effect of a detonation wave transversing explosive and binder segments of random length. The simulations show that the reaction zone is quasi-steady with only short wavelength small amplitude variations in the detonation wave pressure and speed. The main effect of the heterogeneities is to introduce noise in the pressure and velocity fields that propagates into the Taylor wave behind the detonation. This is consistent with the scatter in the reaction-zone measurements for PBX 9501.

42 ENGINEERING↗

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

Abstract A novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics (GH) is developed for predicting the response of complex physical phenomena. The method utilizes GDMaps to obtain a low‐dimensional representation of the underlying behavior of physical/mathematical systems with respect to uncertain input parameters. Using this representation, GH, an out‐of‐sample extension technique, is employed to create a global map from the input parameter space to a Grassmannian diffusion manifold. GH is further employed to locally map points on the diffusion manifold onto the tangent space of a Grassmann manifold. The exponential map is then used to project the points in the tangent space onto the Grassmann manifold, where reconstruction of the full solution is performed. The performance of the proposed surrogate model is verified with three examples. The first problem is a toy example used to illustrate the technique. In the second example, errors associated with the various mappings are assessed by studying response predictions of the electric potential of a dielectric cylinder in a homogeneous electric field. The last example applies the method for uncertainty prediction in the strain field evolution in a model amorphous material using the shear transformation zone theory of plasticity.

42 ENGINEERING↗

Homogeneous Lichnerowicz universes.

Homogeneous solutions of Einstein-Lichnerowicz equations for electrically charged fluid with infinite conductivity universes

RELATIVITY THEORY↗

Homogeneous nucleation and droplet growth in nitrogen

A one dimensional computer model of the homogeneous nucleation process and growth of condensate for nitrogen flows over airfoils is developed to predict the onset of condensation and thus to be able to take advantage of as much of Reynolds capability of cryogenic tunnels as possible. Homogeneous nucleation data were taken using a DFVLR CAST-10 airfoil in the 0.3-Meter Transonic Cryogenic Tunnel and are used to evaluate the classical liquid droplet theory and several proposed corrections to it. For predicting liquid nitrogen condensation effects, use of the arbitrary Tolman constant of 0.25 x 250 billionth m or the Reiss or Kikuchi correction agrees with the CAST-10 data. Because no solid nitrogen condensation were found experimentally during the CAST-10 experiments, earlier nozzle data are used to evaluate corrections to the classical liquid droplet theory in the lower temperature regime. A theoretical expression for the surface tension of solid nitrogen is developed.

Dotson, E. H.↗

Homogeneous turbulence subjected to mean flow with elliptic streamlines

Direct numerical simulations are performed for homogeneous turbulence with a mean flow having elliptic streamlines. This flow combines the effects of rotation and strain on the turbulence. Qualitative comparisons are made with linear theory for cases with high Rossby number. The nonlinear transfer process is monitored using a generalized skewness. In general, rotation turns off the nonlinear cascade; however, for moderate ellipticities and rotation rates the nonlinear cascade is turned off and then reestablished. Turbulence statistics of interest in turbulence modeling are calculated, including full Reynolds stress budgets.

Blaisdell, G. A.↗

LES on unstructured deforming meshes: Towards reciprocating IC engines

A variable explicit/implicit characteristics-based advection scheme that is second-order accurate in space and time has been developed recently for unstructured deforming meshes (O'Rourke & Sahota 1996a). To explore the suitability of this methodology for Large-Eddy Simulation (LES), three subgrid-scale turbulence models have been implemented in the CHAD CFD code (O'Rourke & Sahota 1996b): a constant-coefficient Smagorinsky model, a dynamic Smagorinsky model for flows having one or more directions of statistical homogeneity, and a Lagrangian dynamic Smagorinsky model for flows having no spatial or temporal homogeneity (Meneveau et al. 1996). Computations have been made for three canonical flows, progressing towards the intended application of in-cylinder flow in a reciprocating engine. Grid sizes were selected to be comparable to the coarsest meshes used in earlier spectral LES studies. Quantitative results are reported for decaying homogeneous isotropic turbulence, and for a planar channel flow. Computations are compared to experimental measurements, to Direct-Numerical Simulation (DNS) data, and to Rapid-Distortion Theory (RDT) where appropriate. Generally satisfactory evolution of first and second moments is found on these coarse meshes; deviations are attributed to insufficient mesh resolution. Issues include mesh resolution and computational requirements for a specified level of accuracy, analytic characterization of the filtering implied by the numerical method, wall treatment, and inflow boundary conditions. To resolve these issues, finer-mesh simulations and computations of a simplified axisymmetric reciprocating piston-cylinder assembly are in progress.

Haworth, D. C.↗

Shape of Strained Solid He-4 at Low Temperatures

(1) Interferometer apparatus for measuring surface profile (2) For small strains, the expected linear decrease in height is not seen. (3) For large strains, undulation and irreversible deformations begin to set in, but we cannot yet make clear connection with stress-driven instability theory. Torii and Balibar have observed appearances of deformations beyond threshold stress on He-4 solid surface. The difference of our results from theory real? We are not ready to claim in affirmative. To be able to answer: 1) improve crystal growth techniques; (orientation, annealing, better pressure control) 2) improve homogeneity of stress; (better alignment with vertical, better understanding of interaction between solid He-4 and walls) 4) improve optics.

Kojima, Harry↗

Theory of strong turbulence by renormalization

The hydrodynamical equations of turbulent motions are inhomogeneous and nonlinear in their inertia and force terms and will generate a hierarchy. A kinetic method was developed to transform the hydrodynamic equations into a master equation governing the velocity distribution, as a function of the time, the position and the velocity as an independent variable. The master equation presents the advantage of being homogeneous and having fewer nonlinear terms and is therefore simpler for the investigation of closure. After the closure by means of a cascade scaling procedure, the kinetic equation is derived and possesses a memory which represents the nonMarkovian character of turbulence. The kinetic equation is transformed back to the hydrodynamical form to yield an energy balance in the cascade form. Normal and anomalous transports are analyzed. The theory is described for incompressible, compressible and plasma turbulence. Applications of the method to problems relating to sound generation and the propagation of light in a nonfrozen turbulence are considered.

Tchen, C. M.↗

Discrete stochastic model of point defect-dislocation interaction for simulating dislocation climb

Dislocation climb is an important high temperature process in metals plasticity, responsible for the phenomena such as creep, swelling, or hardening. Climb is defined by the ability of dislocations to leave their original glide plane by interacting with point defects. As such, dislocation climb is controlled by point defect diffusion/absorption/emission, all of which involve thermal activation. The existing thermodynamically consistent models for climb are generally formulated in a continuum framework, through the definition of effective defect fluxes and climb propensities in response to thermodynamic driving forces. However, the point-wise discrete nature of vacancies (and/or self-interstitials) confers a highly discrete nature to the climb dynamics, which is also strongly affected by elastic forces. The combination of discreteness, thermal activation, and elasticity makes this process too challenging for direct atomistic methods such as molecular dynamics. Here we develop a kinetic Monte Carlo model that captures vacancy generation and transport kinetics acting in conjuction with the evolving elastic fields provided by discrete dislocation dynamics simulations. The two models are coupled via the applied stresses and stress gradients generated by dislocation structures at vacancy locations. Our simulations reveal two surprising results. First that climb is dominated by vacancy emission even when the background vacancy concentration is much higher than the equilibrium one. And, second, that climb velocities might be much faster than otherwise believed when one uses the classical theories of climb. These effects are due to the locality of vacancy-dislocation processes, which are not captured in classical treatments that assume smooth vacancy fluxes and homogeneous concentrations. We apply the method to study elementary climb processes in body-centered cubic iron and furnish climb mobility functions to be used in parametric dislocation dynamics and/or crystal plasticity simulations. Here, we apply the technique to study non-conservative plastic bypass of spherical precipitates by edge dislocations and point out the differences between our discrete approach and existing continuum formulations.

36 MATERIALS SCIENCE↗

Literary review and modeling outlook for radiation damage in fused-silica optical fibers

The purpose of this document is to distill, from literature, the effects of radiation damage in fused-silica optical fibers. This information will be used to design a theoretical framework capable of predictive modeling that will be published elsewhere. By inspection of the relevant literature, the devised method is calculation of defect amorphous structures by molecular dynamic techniques, and computation of the macroscopic dielectric function using density functional theory. The dielectric function is then used to directly compute the transmittance of the core material before and after irradiation via solution of Maxwell’s equations in a homogeneous medium.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Hamiltonian cosmology.

The study of cosmological models by means of equations of motion in Hamiltonian form is considered. Hamiltonian methods applied to gravity seem to go back to Rosenfeld (1930), who constructed a quantum-mechanical Hamiltonian for linearized general relativity theory. The first to notice that cosmologies provided a simple model in which to demonstrate features of Hamiltonian formulation was DeWitt (1967). Applications of the ADM formalism to homogeneous cosmologies are discussed together with applications of the Hamiltonian formulation, giving attention also to Bianchi-type universes. Problems involving the concept of superspace and techniques of quantization are investigated.

Ryan, M.↗

Electromagnetic diffraction efficiencies for plane reflection diffraction gratings

The theory and computer programs, based on electromagnetic theory, for the analysis and design of echelle gratings were developed. The gratings are designed for instruments that operate in the ultraviolet portion of the spectrum. The theory was developed so that the resulting computer programs will be able to analyze deep (up to 30 wavelengths) gratings by including as many as 100 real or homogeneous diffraction orders. The program calculates the complex amplitude coefficient for each of the diffracted orders. A check on the numerical method used to solve the integral equations is provided by a conservation of energy calculation.

Marathay, A. S.↗

The ratio of carbon monoxide to molecular hydrogen in interstellar dark clouds

LTE (C-13)O column densities are compared with the corresponding values of beam-convolved visual extinction at more than 100 locations within 38 different interstellar dark clouds. A roughly linear correlation is found to exist between these two quantities for visual extinctions in the range from about 1.5 to 5 mag. It is argued that this correlation can be extended up to about 10 mag and that the standard gas-to-extinction ratio can be expected to remain valid in the sources studied. The correlation of LTE (C-13)O column density with visual extinction is used to obtain an equation for the H2 column density associated with a given (C-13)O column density. It is shown that if the clouds studied are assumed to be chemically homogeneous, the equation obtained implies that at least 12% of all gas-phase carbon is in the form of CO. Comparison of the observational data with various theories proposed for molecule formation in dark clouds indicates that Langer's (1977) ion-molecule scheme accounts well for the observations when the fractionation channel of Watson et al. (1976) is included.

Dickman, R. L.↗

A continuum deformation theory for metal-matrix composites at high temperature

A continuum theory is presented for representing the high temperature, time dependent, hereditary deformation behavior of metallic composites that can be idealized as pseudohomogeneous continua with locally definable directional characteristics. Homogenization of textured materials (molecular, granular, fibrous) and applicability of continuum mechanics in structural applications depends on characteristic body dimensions, the severity of gradients (stress, temperature, etc.) in the structure and the relative size of the internal structure (cell size) of the material. The point of view taken here is that the composite is a material in its own right, with its own properties that can be measured and specified for the composite as a whole.

Robinson, D. N.↗

Overview of Methods for Deriving the Radiative Transfer Theory from the Maxwell Equations. I: Approach Based on the Far-Field Foldy Equations

In this paper, we revisit, with further enhancements and clarifications, the self-consistent first-principles approach developed previously for deriving the vector radiative transfer theory for a discrete random medium with a sparse concentration of particles. We specifically consider the case of a plane-parallel particulate layer embedded in an otherwise homogeneous unbounded medium. The solution method is based on the far-field Foldy equations, an order-of-scattering expansion for the total field derived under the Twersky approximation, the computation of the coherent field by assuming that the positions of the particles are uncorrelated, and the ladder approximation for the coherency dyadic. The latter yields an integral equation for the diffuse specific coherency dyadic, defined through an angular spectrum repre- sentation for the coherency dyadic, which in turn, gives the vector radiative transfer equation for the diffuse specific intensity column vector. We analyze specifically the computation of the coherent field for inhomogeneous particulate media and multiple species of particles, the continuous extension of the far-field representation to the near field, the Foldy approximation, and the Foldy integral equation for the coherent field. Finally, we discuss the transition from the vector to the scalar radiative transfer equation.

Doicu, Adrian↗