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Results for “nonlocal diffusion equations”

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.

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9 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

A rigorous cosmic-ray transport equation with no restrictions on particle energy.

A new transport equation for the cosmic-ray omnidirectional intensity is obtained. This equation follows exactly from the coupled pair of differential moment equations we presented earlier. It can be characterized as a nonlocal convection-diffusion equation in which the usual transport coefficients are replaced by time integral operators. The nonlocal equation is shown to reduce to the standard convection-diffusion form if the adiabatic approximation can be applied. In general, the adiabatic approximation does not apply; however, by going to the limits of infinite and zero gyroradius and, in addition, applying the adiabatic approximation, the large- and small-gyroradius transport theories due originally to Jokipii are regained. The validity of these theories as asymptotic limits and as approximate theories in the interplanetary magnetic field is discussed.

Klimas, A. J.↗
NASA NTRS1992

Effective diffusion equation in a random velocity field

The effects are studied of assumed random velocity fields on diffusion in a binary fluid. Random velocity fields can result, for example, from the high-frequency components of residual accelerations onboard spacecraft (often called g-jitter). An effective diffusion equation is derived for an average concentration which includes spatial and temporal correlations induced by the fluctuating velocity fields assumed to be Gaussianly distributed. The resulting equation becomes nonlocal, and if correlations between different components of the velocity field exist, it is also anisotropic. The simple limiting case of short correlation times is discussed and an effective diffusivity is obtained which reflects the enhanced mixing caused by the velocity fields. The results obtained in the limit of short correlation times are valid even if the probability distribution of the velocity field is not Gaussian.

Vinals, Jorge↗
NASA NTRS2003

Transient Interfacial Phenomena in Miscible Polymer Systems (TIPMPS)

Almost one hundred years ago Korteweg published a theory of how stresses could be induced in miscible fluids by concentration gradients, causing phenomena that would appear to be the same as with immiscible fluids. Miscible fluids could manifest a transient or effective interfacial tension (EIT). To this day, there has been no definitive experiment to confirm Korteweg's model but numerous fascinating and suggestive experiments have been reported. The goal of TIPMPS is to answer the question: Can concentration and temperature gradients in miscible materials induce stresses that cause convection? Many polymer processes involving miscible monomer and polymer systems could be affected by fluid flow and so this work could help understand miscible polymer processing, not only in microgravity, but also on earth. Demonstrating the existence of this phenomenon in miscible fluids will open up a new area of study for materials science. The science objectives of TIPMPS are: (1) Determine if convection can be induced by variation of the width of a miscible interface; (2) Determine if convection can be induced by variation of temperature along a miscible interface; (3) Determine if convection can be induced by variation of conversion along a miscible interface An interface between two miscible fluids can best be created via a spatially-selective photopolymerization of dodecyl acrylate with a photoinitiator, which allows the creation of precise and accurate concentration gradients between polymer and monomer. Optical techniques will be used to measure the refractive index variation caused by the resultant temperature and concentration fields. The viscosity of the polymer will be measured from the increase in the fluorescence of pyrene. Because the large concentration and temperature gradients cause buoyancy-driven convection that prevents the observation of the predicted flows, the experiment must be done in microgravity. In this report, we will consider our efforts to estimate the square gradient parameter, k, and our use of the estimates in modeling of the planned TIPMPS experiments. We developed a model consisting of the heat and diffusion equations with convective terms and of the Navier-Stokes equations with an additional volume force written in the form of the Korteweg stresses arising from nonlocal interaction in the fluid. The fluid's viscosity dependence on polymer conversion and temperature was taken from measurements of poly(dodecyl acrylate). Numerical modeling demonstrated that significant flows would arise for conditions corresponding to the planned experiments.

Pojman, John A.↗
NASA NTRS1989

An evaluation of the role of eddy diffusion in stratospheric interactive two-dimensional models

An interactive two-dimensional model of the stratosphere, consisting of a primitive equation dynamics module, a simplified HO(x) ozone model, and a full radiative transfer scheme, is used to study the effect of eddy diffusion in the model. Consideration is given to the effects of nonlocal forcing from dissipation in the model troposphere and frictional drag at mesospheric levels, mechanical damping in the stratosphere itself, and potential vorticity flux due to large scale waves. It is found that the ozone distributions generated with the model are very sensitive to the choice of values for the friction and the eddy diffusion coefficients. It is shown that reasonable latitudinal gradients of ozone may be obtained by using small values for the mechanical damping for the mid- and high-latitude stratopsphere.

Schneider, Hans R.↗
NASA NTRS1986

Solvability condition for needle crystals at large undercooling in a nonlocal model of solidification

It is explicitly shown that, in a realistic model of diffusion-controlled dendritic solidification, Ivantsov's continuous family of steady-state needle crystals is destroyed by the addition of surface tension. The starting point is in the exact integro-differential equation for the one-sided model, in two dimensions, in a moving frame of reference. In the limit of large undercooling, where the range of the diffusion field is much smaller than the radius of curvature of the tip of the needle, this problem is reduced to a linear, inhomogeneous differential equation of infinite order. A solvability condition for this equation is derived and it is shown that solutions cease to exist for arbitrarily small but finite isotropic surface tension.

Caroli, B.↗
NASA NTRS1983

The nonlocal theory of periodic density drift instabilities

The nonlocal theory of electrostatic density drift instabilities is developed for an arbitrary, periodic variation in plasma density. Linear Vlasov theory is applied to Fourier series representations of the plasma density, and the resulting equations are solved numerically. The growth rates of the universal drift instability are compared by using local and nonlocal theories. It is demonstrated that the local theory is inadequate if the nonlocal eigenfunctions of the electrostatic modes have significant amplitude over spatial regions wider than the regions of large plasma density gradients. Nonlocal effects can enhance wave-particle diffusion of a triangular-shaped variation and reduce wave-particle dissipation of a square-shaped irregularity.

Bernhardt, P. A.↗
NASA NTRS1992

Shadowing and the role of small diffusivity in the chaotic advection of scalars

Using techniques from shadowing theory, the solution of the scalar advection-diffusion equation is studied. It is shown that, under certain circumstances, the effect of small scalar diffusivity is to smooth the zero-diffusivity solution by averaging local fine-scaled structure against a Gaussian. The method of study depends on shadowing and thus fails for nonuniformly stretching systems, its failure suggesting the ways in which the effects of asymptotically small molecular diffusion can become nonlocal in chaotic fluid flows.

Klapper, I.↗
NASA NTRS1986

Magnetized thermal conduction fronts

The evolution of planar thermal conduction fronts in the presence of a dynamically weak, but otherwise self-consistent, magnetic field is considered. The field is assumed to be connected and untangled. In the diffusion limit for the thermal conductivity, these fronts exhibit self-similar behavior, even in the presence of a field. The role of the field is restricted to channeling the heat flux along its lines of force, and it enters into the problem as a dimensionless angle variable. 'Combing' (or opening) of insulating field lines by the evaporative flow is explicitly demonstrated. Unless the field is nearly perpendicular to the front normal in the hot gas, insulating effects are not profound. Self-similarity breaks down if the front becomes saturated, and under certain conditions magnetized saturated conduction fronts cannot propagate: the solution characteristics of the wave equation form caustics. The physical resolution is the advent of two-fluid (nonlocal) heating. Such Coulomb-heated fronts are expected to be relatively rare in typical astrophysical systems. The large-scale effects of a magnetic field on cloud evaporation in the interstellar medium are briefly discussed, and it is suggested that these fields preclude the presence of time-independent evaporative solutions. Thermal interfaces may then continue to evolve until radiative cooling halts their development; large tracts of warm 10,000 K gas may result.

Balbus, S. A.↗
NASA NTRS1981

Magnetic field diffusion and dissipation in reversed-field plasmas

A diffusion equation is derived which describes the evolution of a magnetic field in a plasma of arbitrary beta and resistivity. The equation is valid for a one-dimensional slab geometry, assumes the plasma remains in quasi-equilibrium throughout its evolution and does not include thermal transport. Scaling laws governing the rate of change of the magnetic energy, particle drift energy, and magnetic flux are calculated. It is found that the magnetic free energy can be substantially larger than the particle drift energy and can be an important energy reservoir in driving plasma instabilities (e.g., the lower-hybrid-drift instability). In addition, the effect of a spatially varying resistivity on the evolution of a reversed-field plasma is studied. The resistivity model used is based upon the anomalous transport properties associated with the nonlocal mode structure of the lower-hybrid-drift instability. The relevance of this research to laboratory plasmas (e.g., theta pinches, reversed-field theta pinches) and space plasmas (e.g., the earth's magnetotail) is discussed.

Drake, J. F.↗