A solution of a time-dependent equation of radiative transfer
Time dependent radiative transfer equation for plane-parallel isotropic scattering medium in first Gaussian approximation
Code, A. D.↗
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The Eddington limit and supercritical accretion. II - Time-dependent calculations
Spherically symmetric, time-dependent accretion of an ionized hydrogen plasma onto a neutron star is calculated for accretion rates in excess of the Eddington limit. The coupled hydrodynamic and frequency integrated radiative transfer equations are solved on an Eulerian grid for these supercritical accretion flows. Our results indicate that steady state flows are limited to rates at or below the critical rate, with emergent luminosities equal to or less than the Eddington luminosity. Initially supercritical accretion rates generate a large pulse of radiation which reduces the accretion rate to the critical value and produces an extended quasi-static envelope.
Burger, H. L.↗
High spatial resolution models of time-dependent, layered mantle convection
Time-dependent models of Boussinesq convection are analyzed in order to determine the potential existence of the transient phase of multiple layered convection initially described by Ross and Sacks (1982, 1984). The initial thermal profile for subsolidus mantle convection is examined in terms of an adiabatic or a conductive profile. The effects of varied spatial resolution, aspect ratio, Rayleigh number, initial buoyancy, and supersolidus temperature cutoffs on mantle convection are investigated. It is observed that the data supports the existence of the transient phase of multiple layered convection.
Boss, A. P.↗
Time dependent heat transfer rates in high Reynolds number hypersonic flowfields
Time dependent heat transfer rates have been calculated from time dependent temperature measurements in the vicinity of shock-wave boundary-layer interactions due to conical compression ramps on an axisymmetric body. The basic model is a cylindrical body with a 10 degree conical nose. Four conical ramps, 20, 25, 30, and 35 degrees serve as shock wave generators. Flowfield surveys have been made in the vicinity of the conical ramp vertex, the separation point, and the reattachment point. A significant effort was made to characterize the natural frequencies and relative powers of the resulting fluctuations in heat transfer rates. This research effort, sponsored jointly by NASA and the Air Force, was conducted in the Air Force Flight Dynamics Directorate High Reynolds Facility. The nominal freestream Mach number was 6, and the freestream Reynolds numbers ranged from 2.2 million/ft to 30.0 million/ft. Experimental results quantify temperature response and the resulting heat transfer rates as a function of ramp angle and Reynolds number. The temperature response within the flowfield appears to be steady-state for all compression ramp angles and all Reynolds numbers, and hence, the heat transfer rates appear to be steady-state.
Flanagan, Michael J.↗
The simulated features of heliospheric cosmic-ray modulation with a time-dependent drift model. IV - The role of heliospheric neutral sheet deformation
Previous calculations with a time-dependent drift model revealed the model to be less successful in describing time-dependent modulation during periods of moderate to large solar activity. In this paper, it is argued that a major reason for this is that the previously used wavy heliospheric neutral sheet (HNS) description was based on an idealized HNS not subject to any spatial evolution while propagating radially outward. It is suggested that the deformation and compression of HNS wave peaks will lead to significant increases in the crossfield diffusion across these peaks (short-circuiting). The cosmic rays will effectively experience reduced tilt angles and therefore a reduction in the integrated HNS modulation effect between an observer and the heliospheric boundary. During periods of moderate to large solar activity these HNS deformation processes are progressively more frequent and should lead to a significant reduction in time-dependent modulation as predicted by drift models. Calculations done with radially propagating tilt angles that effectively decrease with radial distance give the expected reduction which improves the general description of modulation from 1987-1988.
Le Roux, J. A.↗
Theory of time-dependent intense-field collisional resonance fluorescence
The time-dependent theory of Courtens and Szoke (1977) is generalized using the approach of Burnett et al. (1982) to derive time-dependent spectral intensities of resonance fluorescence from atoms driven by a pulsed laser in the presence of collisions. These results are valid both for laser detunings inside and outside the usual impact region of the spectrum, including Zeeman degeneracy effects. This theory is applied to a simple but important example (J = 0 to J = 1) to obtain quantitative predictions for the observable scattered-light spectrum which can be directly compared with recent experiments.
Kleiber, P. D.↗
A time-dependent diffusion-convection model for the long-term modulation of cosmic rays
The model considered incorporates, to first order, the direct effects of the time-dependent diffusive propagation of interstellar cosmic rays in a slowly changing interplanetary medium. A one-dimensional model is discussed along with a three-dimensional radial wind. An evaluation is conducted of average diffusive propagation times. It is found that the effects of time-dependent diffusive propagation can be quite significant. A rigidity-dependent time delay or 'lag' in the modulated spectra is predicted.
Ogallagher, J. J.↗
Time-dependent mapping of the magnetic field at the core-mantle boundary
We consider the problem of constructing a time-dependent map of the magnetic field at the core-mantle boundary. We use almost all the available data from the last 300 years to produce two maps, one for the period 1690-1840 and the other for 1840-1990. We represent the spatial dependency of the field using spherical harmonics, the time dependency using a cubic B-spline basis, and seek the smoothest solutions compatible with the observations. We argue that, for observations from permanent magnetic observatories, the most efficient strategy is to use the first differences of annual means; for satellite data, the most efficient strategy is simply to limit the number of data used so as to minimize any tendency to map the crustal field into the core field. The resulting model fits the observatory data better than any previous model. The resulting time-dependent field map exhibits much of the same structure in the field and its secular variation identified in earlier studies.
Bloxham, Jeremy↗
Pulsed-field-gradient measurements of time-dependent gas diffusion
Pulsed-field-gradient NMR techniques are demonstrated for measurements of time-dependent gas diffusion. The standard PGSE technique and variants, applied to a free gas mixture of thermally polarized xenon and O2, are found to provide a reproducible measure of the xenon diffusion coefficient (5.71 x 10(-6) m2 s-1 for 1 atm of pure xenon), in excellent agreement with previous, non-NMR measurements. The utility of pulsed-field-gradient NMR techniques is demonstrated by the first measurement of time-dependent (i.e., restricted) gas diffusion inside a porous medium (a random pack of glass beads), with results that agree well with theory. Two modified NMR pulse sequences derived from the PGSE technique (named the Pulsed Gradient Echo, or PGE, and the Pulsed Gradient Multiple Spin Echo, or PGMSE) are also applied to measurements of time dependent diffusion of laser polarized xenon gas, with results in good agreement with previous measurements on thermally polarized gas. The PGMSE technique is found to be superior to the PGE method, and to standard PGSE techniques and variants, for efficiently measuring laser polarized noble gas diffusion over a wide range of diffusion times. Copyright 1998 Academic Press.
NASA Discipline Environmental Health↗
Relationship of mechanical characteristics and microstructural features to the time-dependent edge notch sensitivity of inconel 718 sheet
Time-dependent notch sensitivity of Inconel 718 sheet was observed at 900 F to 1200 F (482 - 649 C). It occurred when edge-notched specimens were loaded below the yield strength and smooth specimen tests showed that small amounts of creep consumed large rupture life fractions. The severity of the notch sensitivity was reduced by decreasing the solution temperature, increasing the time and/or temperature of aging and increasing the test temperature to 1400 F (760 C). Elimination of time-dependent notch sensitivity correlated with a change in dislocation motion mechanism from shearing to by-passing precipitate particles.
Wilson, D. J.↗
Time-dependent nonlinear cosmic ray shocks confirming abstract
Numerical studies of time dependent cosmic ray shock structures in planar geometry are interesting because analytical time-independent solutions are available which include the non-linear reactions on the plasma flow. A feature of these time asymptotic solutions is that for higher Mach numbers (M approximately 5) and for a low cosmic ray upstream pressure the solution is not uniquely determined by the usual conservation laws of mass, momentum and energy. These numerical solutions clearly indicate that much work needs to be done before we understand shock acceleration as a time dependent process. The slowness of the process is possibly due to the fact that there is a diffusive flux into the downstream region in addition to the usual advective losses. Analytic investigations of thie phenomenon are required.
Dorfi, E. A.↗
Choice of Variables and Preconditioning for Time Dependent Problems
We consider the use of low speed preconditioning for time dependent problems. These are solved using a dual time step approach. We consider the effect of this dual time step on the parameter of the low speed preconditioning. In addition, we compare the use of two sets of variables, conservation and primitive variables, to solve the system. We show the effect of these choices on both the convergence to a steady state and the accuracy of the numerical solutions for low Mach number steady state and time dependent flows.
Turkel, Eli↗
Exact solution of a quantum forced time-dependent harmonic oscillator
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
Yeon, Kyu Hwang↗
Applications of time-dependent perturbation theory.
Atomic and molecular time-dependent quantum- mechanical perturbation theory with differential equation formulation within Hartree-Fock approximation
TIME DEPENDENCY↗
A study of the kinematic dynamo equation with time-dependent coefficients
During an active star formation epoch the interstellar medium of a galaxy is in a hyperactive state, and the average turbulent velocity is higher than in the long periods between star formation epochs. The galactic magnetic field generated by dynamo action depends strongly on the turbulent velocity, so that generation of magnetic field should vary with star formation activity. This paper is a preliminary study of the kinematic dynamo equation with time-dependent coefficients simulating the time dependence of the star formation activities. Ko and Parker argued in a simple model that the thickness of the dynamo region is the most sensitive dynamo parameter. The present work shows that the effect of inflating the galactic disk suddenly is to transform a stationary magnetic field into a growing field while keeping the profile more or less intact. Plane wave solutions for a dynamo with power-law time-dependent parameters show that the field may decay first and then grow, and vice versa, which is quite different from a constant parameter dynamo.
Ko, Chung-Ming↗
A Unified Constitutive Relationship for the Time-dependent Behavior of Fast Breeder Alloys
Constitutive equations based on classical concepts of creep and plasticity generally rest on the assumption that the inelastic strain can be decomposed into two distinct and additive contributions, one time dependent (creep) and the other time dependent (plastic). It is suggested that an approach is to adopt a unified representation in which creep and plasticity are characterized as occurring simultaneously and interactively and time is an essential ingredient throughout. Examples of the inherent time dependency exhibited by some fast breeder alloys at elevated temperature are rate dependency under monotonic and cyclic straining, thermal recovery and strong creep-elasticity interaction. The stron influence of the recent history of plastic straining on stress relaxation is shown.
Robinson, D. N.↗
Supercritical time-dependent accretion onto compact objects. I - Neutron stars
The time-dependent flow resulting from spherically symmetric, supercritical accretion onto a nonmagnetic neutron star is computed for accretion rates between 3 and 30. In addition, the fully time-dependent self-consistent set of coupled radiation-hydrodynamic equations governing such flow has been solved. Effects that have not previously been treated are taken into account, including separate energy equations for ions and electrons allowing for nonequilibrium, variable Eddington factors in the radiation transfer to account for anisotropy of the radiation field due to highly spherically extended envelopes, and convection of ions, electrons and photons in the accretion envelope. It is found that supercritical flow, for material falling from a radius of less than 10 to the 10th cm, is characterized by stable accretion with no evidence of stellar wind outflow at any phase of the evolution.
Klein, R. I.↗
Time dependent turbulence modeling and analytical theories of turbulence
By simplifying the direct interaction approximation (DIA) for turbulent shear flow, time dependent formulas are derived for the Reynolds stresses which can be included in two equation models. The Green's function is treated phenomenologically, however, following Smith and Yakhot, we insist on the short and long time limits required by DIA. For small strain rates, perturbative evaluation of the correlation function yields a time dependent theory which includes normal stress effects in simple shear flows. From this standpoint, the phenomenological Launder-Reece-Rodi model is obtained by replacing the Green's function by its long time limit. Eddy damping corrections to short time behavior initiate too quickly in this model; in contrast, the present theory exhibits strong suppression of eddy damping at short times. A time dependent theory for large strain rates is proposed in which large scales are governed by rapid distortion theory while small scales are governed by Kolmogorov inertial range dynamics. At short times and large strain rates, the theory closely matches rapid distortion theory, but at long times it relaxes to an eddy damping model.
Rubinstein, R.↗