scholarly journals Non-hydrodynamic Contributions to the End Effects in Time of Flight Swarm Experiments

1987 ◽  
Vol 40 (4) ◽  
pp. 519 ◽  
Author(s):  
Russell K Standish
Keyword(s):  
Distribution Function ◽  
Power Series ◽  
Transport Coefficients ◽  
Time Of Flight ◽  
Lithium Ions ◽  
End Effects ◽  
Flight Experiment ◽  
Drift Length ◽  
Order Of Magnitude ◽  
Hydrodynamic Effects

The hydrodynamic part of the distribution function of a swarm is separated from its nonhydrodynamic part using a projection operator, leading to an explicit expression for the timedependent transport coefficients. These are then related to a time of flight experiment. The contribution from non-hydrodynamic effects to the measured drift velocity is shown to be a power series in 11 d, where d is the drift length. A calculation based on an exactly soluble Fokker-Planck model shows that the correction to mobility measurements of lithium ions in helium due to non-hydrodynamic effects is of the same order of magnitude as those observed experimentally.

scholarly journals Electron Transport in Argon - Hydrogen Mixtures

1980 ◽  
Vol 33 (6) ◽  
pp. 975 ◽  
Author(s):  
GN Haddad ◽  
RW Crompton
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Cross Section ◽  
Transport Coefficients ◽  
Velocity Distribution Function ◽  
Significant Error ◽  
Cross Section Data ◽  
Section Data ◽  
Hydrogen Mixtures ◽  
Legendre Expansion

The transport coefficients υdr and D⊥/μ have been measured in mixtures of 0.5 % and 4 % hydrogen in argon. All measurements were made at 293 K. It is shown that for these mixtures the use of the solution of the Boltzmann equation based on the two-term Legendre expansion of the velocity distribution function introduces no significant error in the analysis of the transport data. All the experimental data have been predicted to within � 3.5 % using previously published cross section data.

scholarly journals Precise implications for real-space pair distribution function modeling of effects intrinsic to modern time-of-flight neutron diffractometers

2018 ◽  
Vol 74 (4) ◽  
pp. 293-307 ◽  
Author(s):  
Daniel Olds ◽  
Claire N. Saunders ◽  
Megan Peters ◽  
Thomas Proffen ◽  
Joerg Neuefeind ◽  
...  
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Amorphous Materials ◽  
Best Practice ◽  
Time Of Flight ◽  
Real Space ◽  
Mitigation Strategies ◽  
Total Scattering ◽  
Conventional Analysis ◽  
Pdf Analysis

Total scattering and pair distribution function (PDF) methods allow for detailed study of local atomic order and disorder, including materials for which Rietveld refinements are not traditionally possible (amorphous materials, liquids, glasses and nanoparticles). With the advent of modern neutron time-of-flight (TOF) instrumentation, total scattering studies are capable of producing PDFs with ranges upwards of 100–200 Å, covering the correlation length scales of interest for many materials under study. Despite this, the refinement and subsequent analysis of data are often limited by confounding factors that are not rigorously accounted for in conventional analysis programs. While many of these artifacts are known and recognized by experts in the field, their effects and any associated mitigation strategies largely exist as passed-down `tribal' knowledge in the community, and have not been concisely demonstrated and compared in a unified presentation. This article aims to explicitly demonstrate, through reviews of previous literature, simulated analysis and real-world case studies, the effects of resolution, binning, bounds, peak shape, peak asymmetry, inconsistent conversion of TOF to d spacing and merging of multiple banks in neutron TOF data as they directly relate to real-space PDF analysis. Suggestions for best practice in analysis of data from modern neutron TOF total scattering instruments when using conventional analysis programs are made, as well as recommendations for improved analysis methods and future instrument design.

scholarly journals Projection-operator methods for classical transport in magnetized plasmas. Part 1. Linear response, the Braginskii equations and fluctuating hydrodynamics

2018 ◽  
Vol 84 (4) ◽  
Author(s):  
John A. Krommes
Keyword(s):  
Distribution Function ◽  
Projection Operator ◽  
Linear Response ◽  
Transport Coefficients ◽  
Collision Operator ◽  
Transport Equations ◽  
Transport Processes ◽  
Projection Operators ◽  
Covariant Representation ◽  
Classical Transport

An introduction to the use of projection-operator methods for the derivation of classical fluid transport equations for weakly coupled, magnetised, multispecies plasmas is given. In the present work, linear response (small perturbations from an absolute Maxwellian) is addressed. In the Schrödinger representation, projection onto the hydrodynamic subspace leads to the conventional linearized Braginskii fluid equations when one restricts attention to fluxes of first order in the gradients, while the orthogonal projection leads to an alternative derivation of the Braginskii correction equations for the non-hydrodynamic part of the one-particle distribution function. The projection-operator approach provides an appealingly intuitive way of discussing the derivation of transport equations and interpreting the significance of the various parts of the perturbed distribution function; it is also technically more concise. A special case of the Weinhold metric is used to provide a covariant representation of the formalism; this allows a succinct demonstration of the Onsager symmetries for classical transport. The Heisenberg representation is used to derive a generalized Langevin system whose mean recovers the linearized Braginskii equations but that also includes fluctuating forces. Transport coefficients are simply related to the two-time correlation functions of those forces, and physical pictures of the various transport processes are naturally couched in terms of them. A number of appendices review the traditional Chapman–Enskog procedure; record some properties of the linearized Landau collision operator; discuss the covariant representation of the hydrodynamic projection; provide an example of the calculation of some transport effects; describe the decomposition of the stress tensor for magnetised plasma; introduce the linear eigenmodes of the Braginskii equations; and, with the aid of several examples, mention some caveats for the use of projection operators.

scholarly journals Cosmic ray feedback in the FIRE simulations: constraining cosmic ray propagation with GeV γ-ray emission

2019 ◽  
Vol 488 (3) ◽  
pp. 3716-3744 ◽  
Author(s):  
T K Chan ◽  
D Kereš ◽  
P F Hopkins ◽  
E Quataert ◽  
K-Y Su ◽  
...  
Keyword(s):  
Transport Coefficients ◽  
Cosmic Ray ◽  
Starburst Galaxies ◽  
Secondary Importance ◽  
Star Forming ◽  
First Results ◽  
Order Of Magnitude ◽  
Γ Ray ◽  
Field Lines ◽  
Formation Efficiency

ABSTRACT We present the implementation and the first results of cosmic ray (CR) feedback in the Feedback In Realistic Environments (FIRE) simulations. We investigate CR feedback in non-cosmological simulations of dwarf, sub-L⋆ starburst, and L⋆ galaxies with different propagation models, including advection, isotropic, and anisotropic diffusion, and streaming along field lines with different transport coefficients. We simulate CR diffusion and streaming simultaneously in galaxies with high resolution, using a two-moment method. We forward-model and compare to observations of γ-ray emission from nearby and starburst galaxies. We reproduce the γ-ray observations of dwarf and L⋆ galaxies with constant isotropic diffusion coefficient $\kappa \sim 3\times 10^{29}\, {\rm cm^{2}\, s^{-1}}$. Advection-only and streaming-only models produce order of magnitude too large γ-ray luminosities in dwarf and L⋆ galaxies. We show that in models that match the γ-ray observations, most CRs escape low-gas-density galaxies (e.g. dwarfs) before significant collisional losses, while starburst galaxies are CR proton calorimeters. While adiabatic losses can be significant, they occur only after CRs escape galaxies, so they are only of secondary importance for γ-ray emissivities. Models where CRs are ‘trapped’ in the star-forming disc have lower star formation efficiency, but these models are ruled out by γ-ray observations. For models with constant κ that match the γ-ray observations, CRs form extended haloes with scale heights of several kpc to several tens of kpc.

scholarly journals Inverse Chapman–Enskog Derivation of the Thermohydrodynamic Lattice-BGK Model for the Ideal Gas

1998 ◽  
Vol 09 (08) ◽  
pp. 1231-1245 ◽  
Author(s):  
B. M. Boghosian ◽  
P. V. Coveney
Keyword(s):  
Thermal Conductivity ◽  
Distribution Function ◽  
Relaxation Time ◽  
Equilibrium Distribution ◽  
Transport Coefficients ◽  
Ideal Gas ◽  
Equilibrium Distribution Function ◽  
Bgk Model ◽  
Constant Relaxation Time ◽  
The Ideal

A thermohydrodynamic lattice-BGK model for the ideal gas was derived by Alexander et al. in 1993, and generalized by McNamara et al. in the same year. In these works, particular forms for the equilibrium distribution function and the transport coefficients were posited and shown to work, thereby establishing the sufficiency of the model. In this paper, we rederive the model from a minimal set of assumptions, and thereby show that the forms assumed for the shear and bulk viscosities are also necessary, but that the form assumed for the thermal conductivity is not. We derive the most general form allowable for the thermal conductivity, and the concomitant generalization of the equilibrium distribution. In this way, we show that it is possible to achieve variable (albeit density-dependent) Prandtl number even within a single-relaxation-time lattice-BGK model. We accomplish this by demanding analyticity of the third moments and traces of the fourth moments of the equilibrium distribution function. The method of derivation demonstrates that certain undesirable features of the model — such as the unphysical dependence of the viscosity coefficients on temperature — cannot be corrected within the scope of lattice-BGK models with constant relaxation time.

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