Third-order transport coefficients of ions in electrostatic fields

1999 ◽  
Vol 110 (6) ◽  
pp. 3256-3257 ◽  
Author(s):  
Andreas D. Koutselos
Keyword(s):  
Transport Coefficients ◽  
Third Order ◽  
Electrostatic Fields

scholarly journals Critical behaviour of hydrodynamic series

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
M. Asadi ◽  
H. Soltanpanahi ◽  
F. Taghinavaz
Keyword(s):  
Chemical Potential ◽  
Transport Coefficients ◽  
Hydrodynamic Modes ◽  
Third Order ◽  
Hydrodynamic Mode ◽  
Strongly Coupled ◽  
Conformal Theory ◽  
Shear Dispersion ◽  
Type Iib String Theory ◽  
Hydrodynamic Transport

Abstract We investigate the time-dependent perturbations of strongly coupled $$ \mathcal{N} $$ N = 4 SYM theory at finite temperature and finite chemical potential with a second order phase transition. This theory is modelled by a top-down Einstein-Maxwell-dilaton description which is a consistent truncation of the dimensional reduction of type IIB string theory on AdS5×S5. We focus on spin-1 and spin-2 sectors of perturbations and compute the linearized hydrodynamic transport coefficients up to the third order in gradient expansion. We also determine the radius of convergence of the hydrodynamic mode in spin-1 sector and the lowest non-hydrodynamic modes in spin-2 sector. Analytically, we find that all the hydrodynamic quantities have the same critical exponent near the critical point θ = $$ \frac{1}{2} $$ 1 2 . Moreover, we propose a relation between symmetry enhancement of the underlying theory and vanishing of the only third order hydrodynamic transport coefficient θ1, which appears in the shear dispersion relation of a conformal theory on a flat background.

Third-order transport coefficients for charged particle swarms

1999 ◽  
Vol 110 (5) ◽  
pp. 2423-2430 ◽  
Author(s):  
Slobodan B. Vrhovac ◽  
Zoran Lj. Petrović ◽  
Larry A. Viehland ◽  
Thalanayar S. Santhanam
Keyword(s):  
Charged Particle ◽  
Transport Coefficients ◽  
Third Order ◽  
Particle Swarms

Third-order transport coefficients of ion swarms

2021 ◽  
Vol 155 (20) ◽  
pp. 204301
Author(s):  
Larry A. Viehland ◽  
Emerson Ducasse ◽  
Michelle Cordier ◽  
Aaron Trout ◽  
Jamiyanaa Dashdorj
Keyword(s):  
Transport Coefficients ◽  
Third Order

scholarly journals Third-order transport coefficients for localised and delocalised charged-particle transport

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Peter W. Stokes ◽  
Ilija Simonović ◽  
Bronson Philippa ◽  
Daniel Cocks ◽  
Saša Dujko ◽  
...  
Keyword(s):  
Charged Particle ◽  
Particle Transport ◽  
Transport Coefficients ◽  
Third Order ◽  
Charged Particle Transport

Third-order transport coefficients for electrons in N2 and CF4: effects of non-conservative collisions, concurrence with diffusion coefficients and contribution to the spatial profile of the swarm

2021 ◽  
Author(s):  
Ilija Simonovic ◽  
Danko Bošnjaković ◽  
Zoran Lj Petrovic ◽  
Ron D White ◽  
Sasa Dujko
Keyword(s):  
Boltzmann Equation ◽  
Cross Sections ◽  
Diffusion Tensor ◽  
Transport Coefficients ◽  
Electron Attachment ◽  
Third Order ◽  
Spatial Profile ◽  
Monte Carlo Simulation Technique ◽  
The Third ◽  
The Boltzmann Equation

Abstract Using a multi-term solution of the Boltzmann equation and Monte Carlo simulation technique we study behaviour of the third-order transport coefficients for electrons in model gases, including the ionisation model of Lucas and Saelee and modified Ness-Robson model of electron attachment, and in real gases, including N2 and CF4. We observe negative values in the E/n 0-profiles of the longitudinal and transverse third-order transport coefficients for electrons in CF4 (where E is the electric field and n 0 is the gas number density). While negative values of the longitudinal third-order transport coefficients are caused by the presence of rapidly increasing cross sections for vibrational excitations of CF4, the transverse third-order transport coefficient becomes negative over the E/n 0-values after the occurrence of negative differential conductivity. It is found that the accuracy of the two-term approximation for solving the Boltzmann equation is sufficient to investigate the behaviour of the third-order transport coefficients in N2, while for electrons in CF4 it produces large errors and is not even qualitatively correct . The influence of implicit and explicit effects of electron attachment and ionisation on the third-order transport tensor is investigated. In particular, we discuss the effects of attachment heating and attachment cooling on the third-order transport coefficients for electrons in the modified Ness-Robson model, while the effects of ionisation are studied for electrons in the ionisation model of Lucas and Saelee, N2 and CF4. The concurrence between the third-order transport coefficients and the components of the diffusion tensor, and the contribution of the longitudinal component of the third-order transport tensor to the spatial profile of the swarm are also investigated. For electrons in CF4 and CH4, we found that the contribution of the component of the third-order transport tensor to the spatial profile of the swarm between approximately 50 Td and 700 Td, is almost identical to the corresponding contribution for electrons in N2. This suggests that the recent measurements of third-order transport coefficients for electrons in N2 may be extended and generalized to other gases, such as CF4 and CH4.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

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