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Results for “dispersive 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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Linear density drift instabilities in very low beta plasmas A different approach

This paper reports a study of the linear Vlasov electromagnetic dispersion equation for density drift instabilities in very low beta plasmas. A uniform magnetic field and a weak uniform density gradient are assumed. This paper differs from most other studies of this topic in three important ways: (1) no low frequency or long wavelength approximations are made, (2) no gauge condition is imposed and (3) a modification of the local approximation is used which is argued to be less arbitrary than the usual local approximation. Numerical solution of the resulting dispersion equation yields stabilization of the universal density drift instability at values of beta somewhat higher than those obtained from the local approximation, and near maximum growth shows no evidence of coupling between the universal and Alfven modes.

Gary, S. P.↗
NASA NTRS1993

On the stability of nongyrotropic ion populations - A first (analytic and simulation) assessment

The wave and dispersion equations for perturbations propagating parallel to an ambient magnetic field in magnetoplasmas with nongyrotropic ion populations show, in general, the occurrence of coupling between the parallel (left- and right-hand circularly polarized electromagnetic and longitudinal electrostatic) eigenmodes of the associated gyrotropic medium. These interactions provide a means to driving linearly one mode with free-energy sources of other modes in homogeneous media. Different types of nongyrotropy bring about distinct classes of coupling. The stability of a hydrogen magnetoplasma with anisotropic, nongyrotropic protons that only couple the electromagnetic modes to each other is investigated analytically (via solution of the derived dispersion equation) and numerically (via simulation with a hybrid code). Nongyrotropy enhances growth and enlarges the unstable spectral range relative to the corresponding gyrotropic situation. The relevance of the properties of nongyrotropic populations to space plasma environments is also discussed.

Brinca, A. L.↗
NASA NTRS1983

Pedersen density drift instabilities

This paper describes the linear kinetic theory of electrostatic-drift instabilities driven by Pedersen and density-drift velocities. The model uses a uniform magnetic field B; a weak, uniform density gradient in the x direction; and a weak, uniform electric field in the y direction. Weak charged-neutral collisions are represented by the addition of BGK model terms to the Vlasov equation. The resulting local dispersion equation is used to study the properties of the associated instabilities at ka(i) greater than about 1 (where k is the wave number and a(i) is the ion gyroradius). Results show that the E x B gradient drift instability at ka(i) = about 1 may grow in the auroral ionosphere primarily in the vicinity of 200 km and only if the electron density is sufficiently small.

Gary, S. P.↗
DOE OSTI2021

Toward more mechanistic representations of biogeochemical processes in stream and river networks: Implementation and demonstration of a multiscale model : Modeling Archive

This Modeling Archive supports the ORNL-SFA and IDEAS-Waterhsed publication submitted to Environmental Modeling and Software. A recently introduced multiscale model for representing the combined effect of hyporheic exchange flows and small-scale hyporheic-zone biogeochemical processes is extended from the reach scale to river network scales. The ADELS (Advection Dispersion Equation with Lagrangian Subgrid) model uses a one-dimensional advection-dispersion-reaction equation for the channel network and couples that equation at each channel location to a one-dimensional advection-reaction subgrid model representing an ensemble of streamlines that are diverted into the hyporheic zone before returning to the channel. The subgrid model is written in a computationally advantageous Lagrangian form with hyporheic age replacing the hyporheic travel distance. In the paper, we summarized implementation in the integrated surface/subsurface hydrology modeling system Advanced Terrestrial Simulator (ATS).

East Fork Poplar Creek↗
DOE OSTI2020

Vertical Transport of Water/Contaminant Due to Intermittent Water Influx on the Ground Surface of Vadose Zone - 20088

For movement of moisture and transport of contaminants in the vertical direction, two equations, the Richards equation and the advection-dispersion equation, are solved in a vadose zone for prescribed water and contaminant influx conditions at the ground surface. Two different boundary conditions are considered, one with a single peak of sinusoidal variation and four peaks of finite duration, each of which is sinusoidal in shape. The moisture migration is solved and then the contaminant transport, which is coupled to moisture movement, is solved. In the case of a single influx on the ground surface, at first the hydraulic head and moisture content show a peak. Then above the peak and below the ground surface, the peaks tend to die out, showing a tendency to return to the initial state. The vertical profile of concentration also shows a single peak, which soon becomes stagnant because downward water migration is faster than concentration profile movement. In the case of four intermittent array of peaks, the hydraulic head and moisture content profiles tend to merge and combine together. The concentration profiles show appearance of four peaks clearly. However, although the peak value of concentration remains quite constant, the values may vary with the sorption coefficient because of repeated influx of water and contaminant through the top boundary, the ground surface. The penetration depth decreases with an increasing sorption coefficient. (authors)

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

DPFEHM: a differentiable subsurface physics simulator

The Earth’s subsurface is a key resource that provides energy via fossil fuels and geothermal sources, stores drinking water, and is used in the fight against climate change via carbon sequestration. Simulating the physical processes that occur in the Earth’s subsurface with computers enables better use of this resource. DPFEHM is a Julia package that includes computer models with a focus on the Earth’s subsurface, especially fluid flow, which is critical for the aforementioned applications. DPFEHM is able to solve the groundwater flow equations (single phase flow), Richards equation (air/water), the advection-dispersion equation, and the 2d wave equation. One of the key features of DPFEHM is that it supports automatic differentiation, so it can be integrated into machine learning workflows using frameworks such as Flux or PyTorch. The automatic differentiation capabilities give it the same performance as adjoint methods.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1985

Linear analysis of an axially grooved rectangular gyrotron for harmonic operation

In an axially grooved rectangular waveguide the linearized Vlasov equation is solved to find the perturbed distribution function resulting from the electromagnetic forces on the electrons. The resulting beam current and the propagating electromagnetic waves of the cold tube are used in the inhomogeneous Maxwell's equation to derive the general dispersion equation. This equation is then transformed into the electron beam frame and the resulting linear growth rate of amplification is calculated. By maximizing the linear growth rate, the operational parameters of the gyrotron are then optimized.

Ferendeci, A. M.↗
NASA NTRS1988

A numerical model for gravity wave dissipation in the thermosphere

Two simplified models have been developed for the internal gravity wave dissipation due to viscosity, thermal conduction, and ion-drag in a multilayered, isothermal thermosphere. Both models use the WKB approximation, ray theory, and the time-averaged equations of gravity wave energy conservation. One model uses all the equations appropriate to a dissipative atmosphere, while the other uses the dispersion equation and polarization relations applicable to a nondissipative atmosphere, neglecting the viscous and thermal conduction contributions to the energy flux. Results from these models are compared to each other and to the results obtained by Klostermeyer (1973), using a full-wave model.

Hickey, M. P.↗
NASA NTRS1987

Effective propagation constants in dense random media under effective medium approximation

The effective medium approximation is applied to study the effective propagation constants in a dense random medium. The dyadic Green's function is introduced to establish the effective medium approximation formalism for electromagnetic waves. The multiple scattering equations and the Lippmann-Schwinger equations for the transition operator are obtained in the configuration average form. The dispersion equations of multiple scattering is derived by using a standard method in quantum mechanics. To obtain an expression for the effective propagation constants the matrix elements of the configuration average dyadic transiton operator are calculated in momentum representation. Numerical illustations are carried out to demonstrate the difference in the effective propagation constants between the use of this approximation and the well-known quasi-crystalline approximation. A comparison is made with measured loss tangent in dry snow.

Zhu, P. Y.↗
NASA NTRS1971

Waves along a cylindrical 'grid-like' antenna in an anisotropic compressible plasma.

The dispersion equation is obtained analytically of waves along an infinitely long cylindrical ?grid-like' antenna in an anisotropic compressible homogeneous plasma. Numerical solutions of this equation show that an external static magnetic field has great influence upon the anomalously dispersive region of the dispersion relation around the plasma frequency.

Yu, W.↗
DOE OSTI2021

Stability of expanding accretion shocks for an arbitrary equation of state

We present a theoretical stability analysis for an expanding accretion shock that does not involve a rarefaction wave behind it. The dispersion equation that determines the eigenvalues of the problem and the explicit formulae for the corresponding eigenfunction profiles are presented for an arbitrary equation of state and finite-strength shocks. For spherically and cylindrically expanding steady shock waves, we demonstrate the possibility of instability in a literal sense, a power-law growth of shock-front perturbations with time, in the range of $h_c< h<1+2 {\mathcal {M}}_2$ , where $h$ is the D'yakov-Kontorovich parameter, $h_c$ is its critical value corresponding to the onset of the instability and ${\mathcal {M}}_2$ is the downstream Mach number. Shock divergence is a stabilizing factor and, therefore, instability is found for high angular mode numbers. As the parameter $h$ increases from $h_c$ to $1+2 {\mathcal {M}}_2$ , the instability power index grows from zero to infinity. This result contrasts with the classic theory applicable to planar isolated shocks, which predicts spontaneous acoustic emission associated with constant-amplitude oscillations of the perturbed shock in the range $h_c< h<1+2 {\mathcal {M}}_2$ . Examples are given for three different equations of state: ideal gas, van der Waals gas and three-terms constitutive equation for simple metals.

Huete, César (ORCID:0000000232278520)↗
NASA NTRS1991

Dispersion relation for bianisotropic materials and its symmetry properties

The dispersion relation for an arbitrary general bianisotropic medium is derived in Cartesian coordinates, in a form well suited to imposing the boundary conditions when dealing with layered media with planar and parallel interfaces. Special cases of practical interest are also considered. Eleven fundamental coefficient families are identified by considering in detail all the symmetries present in the dispersion relation. An ad hoc expression of the determinant of the sum of two 3 x 3 matrices permits the use of a simple procedure to obtain the coefficients of the dispersion equation. The discussed symmetry properties have general validity, and this technique to evaluate the coefficients may be useful in other fields of application where dispersion relations are of importance.

Graglia, Roberto D.↗
NASA NTRS1989

Electrostatic wave generation above and below the plasma frequency by electron beams

The unmagnetized electrostatic dispersion equation is solved numerically to study the growth of electrostatic waves near the plasma frequency resulting from a unstable electron beam. An attempt is made to find the dispersion relations, frequencies of maximum growth, and the resonant or nonresonant character of the waves for particular beam parameters. It is found that the unstable waves do not have the Langmuir dispersion relation except in the limit of a very dilute beam with growth on the connected mode of O'Neil and Malmberg. The properties of the unstable mode depend strongly on beam parameters such as beam density, speed, and temperature.

Cairns, Iver H.↗
NASA NTRS1984

Correlation of auroral hiss and upward electron beams near the polar cusp

Data were obtained from the DE-1 high-altitude plasma instrument (HAPI) and plasma wave instrument (PWI) during outbound passes through the polar cusp near local noon. The observed distribution functions of electron beams are fitted by drifting Maxwellian functions and the observed distribution functions of hot background electrons by isotropic Maxwellian functions. In addition, the cold plasma density is inferred from knowledge of the electron plasma frequency and the measured density of the warm plasma, including the electron beam distribution. The empirically fitted plasma parameters, including density, temperature and drifting energy, are used to solve the linear dispersion equation for the resulting whistler mode emissions. Because the whistler mode becomes quasi-electrostatic for wave-normal angles near the resonance cone, the electrostatic approximation is used for the whistler mode dispersion relation. The results of wave instability analyses are then compared with the wave observations. A ray tracing of cusp hiss emission is conducted to locate the wave source region (at about one earth-radius).

Lin, C. S.↗
NASA NTRS2002

Lattice Boltzmann Equation On a 2D Rectangular Grid

We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean invariance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions; (b) Poiseuille flow with an arbitras~y inclined angle with respect to the lattice orientation: and (c) a cylinder &symmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations.

Bouzidi, MHamed↗
DOE OSTI2025

Generalized fractional approach to solving partial differential equations with arbitrary dispersion relations

The dynamics of physical systems are typically modeled by partial differential equations (PDEs). Because of the complexity in physical systems, PDE models rely on approximations or limiting cases. To model the full complexity of physical systems, it is necessary to use multiscale approaches where appropriate models are used at each level. Alternatively, complexity can be directly tackled by fractional integrodifferential equations that must be derived for each system. Here, we argue that complexity can be restored in PDEs by describing them from a fractional calculus perspective. Rather than deriving a fractional integrodifferential equation, we reinterpret the dispersion relation of the system by use of the Riesz definition, which contains the required information relating the energy and momentum space of the system and thus fully describes their dynamics. The approach is demonstrated by two examples: the Landau–Lifshitz equation in a 1D ferromagnetic chain and a modified KdV equation supporting surface gravity waves or Euler dispersion. The presented approach is applicable to fluids, soft matter, and solid-state matter and can be readily generalized to higher dimensions and more complex systems. While numerical calculations are needed to determine the fractional operator, the approach is analytical and can be utilized to determine analytical solutions and investigate nonlinear problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

The mirror and ion cyclotron anisotropy instabilities

The linear dispersion equation for fully electromagnetic waves and instabilities at arbitrary directions of propagation relative to a background magnetic field B(0) in a homogeneous Vlasov plasma is solved numerically for bi-Maxwellian particle distributions. For isotropic plasmas the dispersion and damping of the three modes below the proton cyclotron frequency are studied as functions of Beta(i) and T(e)/T(i). The transport ratios of helicity, cross-helicity, Alfven ratio, compressibility, and parallel compressibility are defined. Under the condition that the proton temperature perpendicular to B(0) is greater than the parallel temperature, the growth rates and transport ratios of the mirror instability and the ion cyclotron anisotropy instability are examined and compared. Both the proton parallel compressibility and the proton Alfven ratio are significantly different for the two growing modes.

Gary, S. P.↗