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Results for “Dispersion relations”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Comprehensive Analysis of the Relative Dispersion of Droplet-Size Distributions and Their Relationships to Key Physical Fog Processes Under Different Aerosol Conditions and Evolutionary Stages

The relative dispersion of cloud and fog droplets has significant impacts on aerosol indirect effects, radiative transfer, and microphysical processes. However, previous studies have been mostly concerned with clouds, with limited studies on fog, particularly those that examine the combined influences of all key physical processes and their roles during fog evolution. As such, this study aims to conduct a comprehensive investigation by examining the relationships between relative dispersion and other microphysical variables, as well as the underlying microphysical and dynamic processes, based on field fog campaigns in polluted and clean conditions. In polluted fog, droplet concentrations are higher, leading to smaller droplets and increased dispersion. The correlation between dispersion and droplet volume-mean radius is positive in the polluted fog, but shifts to negative in clean fog. Here, we attribute the difference to various microphysical processes like aerosol activation, condensation, collision-coalescence, and entrainment-mixing. In polluted fog, high aerosol concentrations, low supersaturations, and strong turbulence (entrainment-mixing) provide suitable conditions for the simultaneous occurrence of droplet condensation and aerosol activation, resulting in a positive correlation between dispersion and volume-mean radius, especially during the fog formation stage. In contrast, during the mature stage in clean fog, condensation is dominant with weak aerosol activation leading to a negative correlation between relative dispersion and volume-mean radius. The collision-coalescence process is more active in the mature stage, increasing radii and leading to the negative correlation between dispersion and volume-mean radius. This result sheds new light on understanding the relative dispersion and mechanisms in fog under different aerosol backgrounds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Convergence of Cloud Droplet Spectral Relative Dispersion During Entrainment‐Mixing Based on Particle‐Resolved Direct Numerical Simulations

Entrainment-mixing processes critically impact cloud microphysical properties, but their effects on the relative dispersion (d) of cloud droplet size distributions (CDSDs) remain elusive. A direct numerical simulation model is initialized with different CDSDs to fill the gap. These results show that d decreases for broad CDSDs and increases for narrow ones, ultimately converging to approximately 0.5 regardless of initial CDSDs during the evaporation-dominated mixing stage. The supersaturation fluctuation and the shape of CDSDs jointly influence the convergence behavior of d. Further sensitivity tests show that the initial microphysical/dynamical/thermodynamical conditions exert negligible effects on the final converged value of d but affect the convergence rate (k). The k generally increases with increasing droplet number concentration and dissipation rate, and increases with decreasing liquid water content, relative humidity of entrained air, and mixing fraction of cloudy air. A conceptual model with two timescales is proposed; k and the timescales are negatively correlated, meaning that slow mixing and/or evaporation process results in slow convergence of d. In conclusion, this finding provides an important reference for improving understanding and parameterization of d during the entrainment-mixing processes.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1974

Predictions of three-body-decays of mesons from pole-dominated dispersion relations

The investigation shows that the method of finite dispersion relations (FDR) as developed by Aviv and Nussinov (1970) is consistent with a wide range of three-body meson decays. The specific results vary with each reaction. For each possibility a definite form for the t-channel Regge-pole terms is selected. The results of the investigation indicate the basic reliability of an approach based on the FDR method and the finite-energy sum rules.

Thews, R. L.↗
NASA NTRS1972

Interpretation of dispersion relations for bounded systems.

Treatment of the problem of constructing normal modes for an arbitrarily bounded system from roots of the linear dispersion relation D(omega, k) = 0 for the corresponding infinite or periodically bounded system. For a system described by continuous macroscopic variables, and of general cylindrical form, each transverse eigenmode gives rise to a set of axial normal modes constructed from a pair of dominant roots of D = 0 satisfying the boundary conditions which are characterized by complex reflection coefficients for the dominant waves. The implications of the results for the interpretation of experiments on plasma waves and instabilities on finite cylinders are discussed, with particular reference to the effects of end-plate damping and axial current on Q-machines.

Rognlien, T. D.↗
DOE OSTI2026

Higher-order space-charge stability in anisotropic beams: Vlasov-Poisson derivation, refined dispersion relations, and stability charts

The Hofmann stability chart is used to screen working points in space-charge-dominated linacs. We identify two errors in its published higher-order dispersion relations: missing $(1\mp2\hatη^2/α)$ factors in the third-order $S^4$ coupling residues, and a sign error in the stated isotropic reduction of the fourth-order relation. Both corrections follow from Hofmann's Vlasov-Poisson equations without fitted parameters. They reproduce coherent tune-shift coefficients in the author's later monograph that the printed forms miss by 24% and 127%. Mode-resolved figures from a published application agree with the corrected relations and reject the printed forms, indicating an inconsistency between the 1998 equations and the calculations underlying those tested figures. We quantify the effect on the non-oscillatory stability chart. Inside the adopted $S^2\le10$ comparison domain, printed and corrected forms disagree on 0.73-2.11% of cells, with no preferred direction. Among excluded cells, disagreement reaches 22%, and the printed relation over-predicts instability at every sampled anisotropy. This concentration may help explain why the errors persisted, although it does not establish their historical cause. For PIP-II, the corrected chart flags four of thirty-two evaluable periods, including one on a third-order odd branch missed by a second-order screen. This count covers non-oscillatory modes only and remains conditional on an unresolved factor-five disagreement between two codes on transverse emittance growth.

Pathak, Abhishek [Fermilab] (ORCID:000000021704208↗
NASA NTRS1971

Conversion of electrostatic plasma waves into electromagnetic waves - Numerical calculation of the dispersion relation for all wavelengths.

The dispersion curves have been computed for a wide range of wavelengths from electromagnetic waves to electrostatic waves in a magnetoactive warm plasma with a Maxwellian velocity distribution function. The computation was carried out mainly for the perpendicular propagation mode. The upper hybrid resonance is the connection point of the electrostatic waves and the electromagnetic waves. The electrostatic waves not associated with the upper hybrid resonance are subjected to electron cyclotron damping when the wavelength becomes long. Oblique propagation is allowed for the electrostatic waves in a frequency range from the plasma frequency to the upper hybrid resonance frequency in the long-wavelength region where Landau damping can be neglected and where the electrostatic mode smoothly connects to the electromagnetic X-mode. In a slightly inhomogeneous plasma, the Bernstein-mode electrostatic wave can escape by being converted into the O-mode electromagnetic wave; two reflections take place during this escape process.

Oya, H.↗
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↗
DOE OSTI2025

Phonon Dispersion Relations and Electron-Phonon Coupling in Iridium

This dataset comprises inelastic neutron scattering measurements of iridium conducted at SNS (ARCS, ITPS-30061) and HFIR (HB-3, TAX, IPTS-25194). ARCS data collected using 50 meV incident energy and include both signal and background files at various temperatures (100 K to 700 K). HB-3 (TAX) measurements span a temperature range from 100 K to 700 K and are organized by run numbers. Background contributions from the sample environment, such as shiver-induced noise, are included for completeness. The details of data description can be found in description.txt.

iridium, phonon, electron-phonon coupling↗