Estimation Of Transport Coefficients Research Articles

Estimating sediment transport diffusion coefficients from reconstructed rifted margin architecture: measurements in the Ogooué and Zambezi deltas

AbstractDiffusion‐based stratigraphic models are widely used to simulate sedimentary systems and margin deltas. Diffusion‐based models assume that the topographic evolution primarily depends from its slope. Limited attention has however been given to the calibration of the transport coefficients. Here, we evaluate transport coefficient values from natural examples, the Ogooué and Zambezi rifted margin deltas over the last 5 to 12 Ma respectively. We developed a method to estimate transport coefficients based on high resolution seismic stratigraphy analysis of the stratigraphic architecture of these deltas. For each stratigraphic sequence, we calibrated the sand/shale ratios of the deposits, we restored their depositional slopes, we estimated their uncompacted accumulated volumes and we calculated the transport coefficient (Kd) from the sediment flux/slope ratio. Estimated values of Kd fall within one order of magnitude (×0.1 km2/ka), a much narrower range than previously published values (×0.0001 to ×100 km2/ka). We show that the diffusion approximation is optimal at 10–100 km scale and 0.5–1 Ma time resolution, independently of the stratigraphic context. We show that the diffusion assumption is appropriate for the formation of the clinoforms (mainly gravity driven). It is however not optimal for the shelf and distal domains where additional processes (e.g., wave, flood, hemipelagic, turbidites, oceanic current), not accounted for it the diffusion assumption, significantly impact sediment transport. We documented a significant increase of Kd values after 0.9 Ma, coeval of an increase in the amplitude of eustatic variations at this time indicating that the calibration of Kd from present day sedimentary systems might not be optimal for simulations of sedimentary systems before the last million years.

SporTran: A code to estimate transport coefficients from the cepstral analysis of (multivariate) current time series

SporTran is a Python utility designed to estimate generic transport coefficients in extended systems, based on the Green-Kubo theory of linear response and the recently introduced cepstral analysis of the current time series generated by molecular dynamics simulations. SporTran can be applied to univariate as well as multivariate time series. Cepstral analysis requires minimum discretion from the user, in that it weakly depends on two parameters, one of which is automatically estimated by a statistical model-selection criterion that univocally determines the resulting accuracy. In order to facilitate the optimal refinement of these parameters, SporTran features an easy-to-use graphical user interface. A command-line interface and a Python API, easy to embed in complex data-analysis workflows, are also provided. Program summaryProgram Title:SporTranCPC Library link to program files:https://doi.org/10.17632/hm48f8kgj9.1Licensing provisions: GPLv3Programming language: PythonNature of problem: Given an M-variate time series, Jj(t), j=0,…M−1, typically describing a number of currents resulting from a molecular-dynamics simulation, SporTran estimates the transport coefficient κ=1/(Λ−1)00, where Λij=∫0∞〈Jj(t)Jk(0)〉dt is the matrix of the Onsager linear-response coefficients, and 〈⋅〉 indicates an equilibrium average over initial conditions.Solution method:i)It is first observed that the Onsager transport coefficients are the zero-frequency values of the cross power spectra of the currents under scrutiny: Λij=12Sij(ω=0), where Sij(ω)=∫−∞∞〈Ji(t)Jj(0)〉eiωtdt.ii)We next define the (cross) periodogram as the product of pairs of Fourier transforms of the current time series: Skij=ϵNJ˜kiJ˜kj⁎, where ϵ is the time step of the time series, N the number of their terms, and J˜kj=∑n=0N−1Jnje2πiknN their discrete Fourier transforms, and Jnj=Jj(ϵn).iii)As the current time series are realisations of a Gaussian process, in the long-time limit and for k≠k′ the Skij are uncorrelated complex Wishart random matrices (a matrix generalisation of the χ2 distribution) whose expectation, according to the Wiener-Khintchine theorem, is the cross power spectrum we are after. It follows that (Sk−1)00 is proportional to a set of uncorrelated χ2 deviates;iv)A consistent estimator for log⁡(κ)=−log⁡((Λ−1)00) is finally obtained by applying a low-pass filter to the process log⁡((Sk−1)00). The theoretical background of the methodology implemented in SporTran is thoroughly presented in Refs. [1-3].

Estimating transport coefficients of interacting pion gas with K-matrix cross sections

We estimate the transport coefficients, viz., shear and bulk viscosities as well as thermal and electrical conductivities, of hot pionic matter using a relativistic Boltzmann equation in a relaxation time approximation. We use K-matrix parametrization of pion–pion cross sections to estimate the transport coefficients which incorporate multiple heavy resonances while simultaneously preserving the unitarity of the S-matrix. We compare transport coefficients estimated using K-matrix parametrization with the existing literature on pionic transport coefficients. We find that the K-matrix scheme estimations are in reasonable agreement with previous results.

On the characterization of pore size distribution of building materials

Moisture affects significantly the energy performance of air conditioning systems, the durability of materials, and the health of occupants. One way of reducing those effects, without increasing the energy costs, is by means of using porous material ability of absorbing and releasing moisture from/to the adjacent environment, which attenuates the indoor relative humidity variation. This natural ability is intrinsically related to the porous microstructure. Therefore, the characterization of the pore space is an important research theme in the building physics area. This article aims to present a method for obtaining the pore size distribution based on adsorption isotherms and mercury porosimetry data. First, the theoretical formulation based on the Gibbs free energy for a two-phase (liquid–vapor) system, using the De Boer and Zwikker model, is presented, allowing the calculation of the critical adsorbed thickness for pore filling, critical radius, adsorbed moisture content, capillary condensation content, available surface for adsorption, and the distribution of micropores for a wide range of radius. The adsorption isotherm curve is estimated for high relative humidity values through mercury porosimetry, along with the adsorption curve obtained from the experiment. The pore volume distribution calculated by this method can be used to estimate transport coefficients for liquid and vapor phases.

Stochastic Fermi Energization of Coronal Plasma during Explosive Magnetic Energy Release

Abstract The aim of this study is to analyze the interaction of charged particles (ions and electrons) with randomly formed particle scatterers (e.g., large-scale local “magnetic fluctuations” or “coherent magnetic irregularities”) using the setup proposed initially by Fermi. These scatterers are formed by the explosive magnetic energy release and propagate with the Alfvén speed along the irregular magnetic fields. They are large-scale local fluctuations (δB/B ≈ 1) randomly distributed inside the unstable magnetic topology and will here be called Alfvénic Scatterers (AS). We constructed a 3D grid on which a small fraction of randomly chosen grid points are acting as AS. In particular, we study how a large number of test particles evolves inside a collection of AS, analyzing the evolution of their energy distribution and their escape-time distribution. We use a well-established method to estimate the transport coefficients directly from the trajectories of the particles. Using the estimated transport coefficients and solving the Fokker–Planck equation numerically, we can recover the energy distribution of the particles. We have shown that the stochastic Fermi energization of mildly relativistic and relativistic plasma can heat and accelerate the tail of the ambient particle distribution as predicted by Parker & Tidman and Ramaty. The temperature of the hot plasma and the tail of the energetic particles depend on the mean free path (λ sc) of the particles between the scatterers inside the energization volume.

Estimating transport coefficients in hot and dense quark matter

We compute the transport coefficients, namely, the coefficients of shear and bulk viscosity, as well as thermal conductivity, for hot and dense quark matter. The calculations are performed within the Nambu--Jona-Lasinio (NJL) model. The estimation of the transport coefficients is made using a quasiparticle approach of solving the Boltzmann kinetic equation within the relaxation time approximation. The transition rates are calculated in a manifestly covariant manner to estimate the thermal-averaged cross sections for quark-quark and quark-antiquark scattering. The calculations are performed for finite chemical potential also. Within the parameters of the model, the ratio of shear viscosity to entropy density has a minimum at the Mott transition temperature. At vanishing chemical potential, the ratio of bulk viscosity to entropy density, on the other hand, decreases with temperature, with a sharp decrease near the critical temperature, and vanishes beyond it. At finite chemical potential, however, it increases slowly with temperature beyond the Mott temperature. The coefficient of thermal conductivity also shows a minimum at the critical temperature.

Thermoelectric coefficients ofn-doped silicon from first principles via the solution of the Boltzmann transport equation

We present a first-principles computational approach to calculate thermoelectric transport coefficients via the exact solution of the linearized Boltzmann transport equation, also including the effect of nonequilibrium phonon populations induced by a temperature gradient. We use density functional theory and density functional perturbation theory for an accurate description of the electronic and vibrational properties of a system, including electron-phonon interactions; carriers' scattering rates are computed using standard perturbation theory. We exploit Wannier interpolation (both for electronic bands and electron-phonon matrix elements) for an efficient sampling of the Brillouin zone, and the solution of the Boltzmann equation is achieved via a fast and stable conjugate gradient scheme. We discuss the application of this approach to $n$-doped silicon. In particular, we discuss a number of thermoelectric properties such as the thermal and electrical conductivities of electrons, the Lorenz number and the Seebeck coefficient, including the phonon drag effect, in a range of temperatures and carrier concentrations. This approach gives results in good agreement with experimental data and provides a detailed characterization of the nature and the relative importance of the individual scattering mechanisms. Moreover, the access to the exact solution of the Boltzmann equation for a realistic system provides a direct way to assess the accuracy of different flavors of relaxation time approximation, as well as of models that are popular in the thermoelectric community to estimate transport coefficients.

PARTICLE ACCELERATION AND HEATING BY TURBULENT RECONNECTION

ABSTRACT Turbulent flows in the solar wind, large-scale current sheets, multiple current sheets, and shock waves lead to the formation of environments in which a dense network of current sheets is established and sustains “turbulent reconnection.” We constructed a 2D grid on which a number of randomly chosen grid points are acting as scatterers (i.e., magnetic clouds or current sheets). Our goal is to examine how test particles respond inside this large-scale collection of scatterers. We study the energy gain of individual particles, the evolution of their energy distribution, and their escape time distribution. We have developed a new method to estimate the transport coefficients from the dynamics of the interaction of the particles with the scatterers. Replacing the “magnetic clouds” with current sheets, we have proven that the energization processes can be more efficient depending on the strength of the effective electric fields inside the current sheets and their statistical properties. Using the estimated transport coefficients and solving the Fokker–Planck (FP) equation, we can recover the energy distribution of the particles only for the stochastic Fermi process. We have shown that the evolution of the particles inside a turbulent reconnecting volume is not a solution of the FP equation, since the interaction of the particles with the current sheets is “anomalous,” in contrast to the case of the second-order Fermi process.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. III. Cylindrical approximations for heat waves traveling inwards

In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on the heat equation in cylindrical geometry using the symmetry (Neumann) boundary condition at the plasma center. This means that the approximations derived here should be used only to estimate transport coefficients between the plasma center and the off-axis perturbative source. If the effect of cylindrical geometry is small, it is also possible to use semi-infinite domain approximations presented in Part I and Part II of this series. A number of new approximations are derived in this part, Part III, based upon continued fractions of the modified Bessel function of the first kind and the confluent hypergeometric function of the first kind. These approximations together with the approximations based on semi-infinite domains are compared for heat waves traveling towards the center. The relative error for the different derived approximations is presented for different values of the frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can be used to estimate the transport coefficients over a large parameter range for cases without convection and damping, cases with damping only, and cases with convection and damping. The relative error between the approximation and its underlying model is below 2% for the case, where only diffusivity and damping are considered. If also convectivity is considered, the diffusivity can be estimated well in a large region, but there is also a large region in which no suitable approximation is found. This paper is the third part (Part III) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part II, cylindrical approximations are treated for heat waves traveling towards the plasma edge assuming a semi-infinite domain.

Efficient parameter estimation in 2D transport models based on an adjoint formalism

An adjoint based optimization procedure is elaborated to estimate transport coefficients for plasma edge models based on a limited set of known profiles at different locations. It is shown that a set of adjoint equations can accurately determine all sensitivities towards transport coefficients at once. A proof of principle is provided on a simple geometry. The methodology is subsequently applied to assess whether a simple edge model can be tuned toward full B2-EIRENE profiles for a JET-configuration.

Infra-red thermography of laminar heat transfer during early thermal development inside a square mini-channel

Infra-red thermography (IRT) has been employed to experimentally scrutinize the thermo-hydrodynamics of very early part of hydrodynamically fully developed, but thermally developing, internal laminar flow of water (850⩾Re⩾100) in a mini-channel of square cross-section (5mm×5mm; aspect ratio=1.0; Dhyd 5mm). The channel is machined on that face of an aluminum substrate whose dimensions are 11mm×140mm; the total width of the substrate being 45mm. A constant heat flux boundary condition is provided on the substrate face which is opposite to that on which the mini-channel is machined. Thus, the mini-channel receives heat from three sides; the fourth side being covered by an insulating poly-carbonate material. IRT provides non-intrusive and high-resolution spatial measurement of local wall temperature in the streamwise direction. By assuming a one-dimensional heat transfer model in the transverse direction, the local value of heat flux and therefore the Nusselt number, in the thermally developing region, can be estimated. Moreover, a 3D conjugate heat transfer numerical model, exactly corresponding to the real experimental conditions, has also been developed. The conjugate effects in the experiment arising due to the substrate, as well as the high heat transfer coefficient in the early thermal development zone, are analyzed. The errors and discrepancy in the in situ boundary conditions which may creep in due to such effects, especially in the estimation of transport coefficients in the developing flow region, are scrutinized and delineated. It is concluded that experimental estimation of local heat flux is a primary requirement for minimizing the errors in estimating local Nusselt number in developing flows. This in turn, necessitates the use of non-intrusive field measurement techniques, such as IRT.

Cut-off radius effect of the isotropic periodic sum method for polar molecules in a bulk water system

Molecular dynamics simulation has been applied for water to compare the isotropic periodic sum (IPS) method for polar molecules (IPSp) to the normal IPS (IPSn) method and the Ewald sum by evaluating the diffusion coefficient and liquid structure. In our previous study, we have applied the IPSn method for bulk water and found notable deviation of the radial distribution function g(r). In this work, the IPSp gives a good estimation for the potential energy and the self-diffusion coefficient at a cut-off radius, r c, greater than 2.2 nm while avoiding the notable deviation of g(r) which appeared in the case of IPSn. The distance-dependent Kirkwood factor G k (r) was also calculated, and the truncation of a long-range interaction of the cut-off-like method (such as cut-off with or without the switch function and the reaction field) shows serious shortcomings for dipole–dipole correlations in bulk water systems. This was observed by comparing the shape to that of the Ewald sum. G k (r) of the cut-off-like method greatly deviates from that of the Ewald sum. However, the discrepancy of G k (r) for IPSp method was found to be much less than that of other typical cut-off-like methods. We conclude that the IPSp method is an adequately accurate technique for estimating transport coefficients and the liquid structure of water in a homogeneous system at long cut-off distances.

Self-Diffusion Coefficient and Viscosity in Fluids

Rate-based models suitable for equipment or transport-reaction modeling require a capability for predicting transport coefficients over a sufficient range of temperature and pressure. This paper demonstrates a relatively simple novel approach to correlate and estimate transport coefficients for pure components over the entire fluid region.The use of Chapman-Enskog transport coefficients for reducing self-diffusion coefficient and viscosity to dimensionless form results in relatively simple mathematical relationships between component dimensionless transport coefficients and residual entropy over the entire fluid region. Dimensionless self-diffusion coefficients and viscosities were calculated from extensive molecular dynamics simulation data and experimental data on argon, methane, ethylene, ethane, propane, and n-decane. These dimensionless transport coefficients were plotted against dimensionless residual entropy calculated from highly accurate reference equations of state.Based on experimental data, the new scaling model introduced here shows promise as: (1) an equation of state-based transport coefficient correlation over the entire fluid region (liquid, gas, and critical fluid), (2) a component transport coefficient correlation for testing transport data consistency, and (3) a component transport coefficient correlation for interpolation and extrapolation of self-diffusion coefficient and viscosity.

Self-Diffusion Coefficient and Viscosity in Fluids

Rate-based models suitable for equipment or transport-reaction modeling require a capability for predicting transport coefficients over a sufficient range of temperature and pressure. This paper demonstrates a relatively simple novel approach to correlate and estimate transport coefficients for pure components over the entire fluid region.The use of Chapman-Enskog transport coefficients for reducing self-diffusion coefficient and viscosity to dimensionless form results in relatively simple mathematical relationships between component dimensionless transport coefficients and residual entropy over the entire fluid region. Dimensionless self-diffusion coefficients and viscosities were calculated from extensive molecular dynamics simulation data and experimental data on argon, methane, ethylene, ethane, propane, and n-decane. These dimensionless transport coefficients were plotted against dimensionless residual entropy calculated from highly accurate reference equations of state.Based on experimental data, the new scaling model introduced here shows promise as: (1) an equation of state-based transport coefficient correlation over the entire fluid region (liquid, gas, and critical fluid), (2) a component transport coefficient correlation for testing transport data consistency, and (3) a component transport coefficient correlation for interpolation and extrapolation of self-diffusion coefficient and viscosity.

Communication: Generalizing Rosenfeld's excess-entropy scaling to predict long-time diffusivity in dense fluids of Brownian particles: From hard to ultrasoft interactions

Computer simulations are used to test whether a recently introduced generalization of Rosenfeld's excess-entropy scaling method for estimating transport coefficients in systems obeying molecular dynamics can be extended to predict long-time diffusivities in fluids of particles undergoing Brownian dynamics in the absence of interparticle hydrodynamic forces. Model fluids with inverse-power-law, Gaussian-core, and Hertzian pair interactions are considered. Within the generalized Rosenfeld scaling method, long-time diffusivities of ultrasoft Gaussian-core and Hertzian particle fluids, which display anomalous trends with increasing density, are predicted (to within 20%) based on knowledge of interparticle interactions, excess entropy, and scaling behavior of simpler inverse-power-law fluids.

Cutoff radius effect of the isotropic periodic sum method in homogeneous system. II. Water

Molecular dynamics simulation has been applied for water to compare the isotropic periodic sum (IPS) method [X. Wu and B. R. Brooks, J. Chem. Phys. 122, 044107 (2005)] with the Ewald sum based on the diffusion coefficient and liquid structure. The IPS method gives a good estimation for the self-diffusion coefficient at a cutoff radius, r(c), greater than 2.2 nm; however, the radial distribution function g(r) has a notable deviation. The peak of this deviation appears at specific intermolecular distances which are near each cutoff radius and decrease in proportion to the inverse of the cube of r(c). Thus the deviation becomes insignificant (less than 1%) at r(c) greater than 2.2 nm. The distance dependent Kirkwood factor G(k)(r) was also calculated, and since the truncation of a long-range interaction of the cutofflike method (such as cutoff with or without the switch function and the reaction field) shows serious shortcomings for dipole-dipole correlations in bulk water systems, this was observed by comparing the shape to that of the Ewald sum [Y. Yonetani, J. Chem. Phys. 124, 204501 (2006); D. van der Spoel and P. J. van Maaren, J. Chem. Theory Comput. 2, 1 (2006)]. The G(k)(r) of cutofflike method greatly deviate from that of the Ewald sum. However, the discrepancy of G(k)(r) for the IPS method was found to be much less than that of other typical cutofflike methods. In conclusion, the IPS method is an adequately accurate technique for estimating transport coefficients and the liquid structure of water in a homogeneous system at long cutoff distances.

Galactic Cosmic Ray modulation based on transport parameters obtained via test particle simulations

Our understanding of Galactic Cosmic Ray (GCR) modulation has advanced greatly in the last years. However, an appropriate knowledge of the components of the diffusion tensor is still lacking. Numerical simulations of test particle trajectories in the layer model of the Heliospheric Magnetic Field allow calculations of local transport coefficients. The layer model makes use of spacecraft data at different heliospheric locations to reproduce transport conditions; there are no special assumptions as to the form of the turbulence. We use these test particle estimated transport coefficients here as parameters for a numerical solution of the GCR transport equation in the case qA > 0. The solutions obtained with this set of parameters reproduce the observed cosmic ray proton spectrum at 1 AU and the radial profiles up to at least 20 AU in the ecliptic plane well.

System size and control parameter effects in reverse perturbation nonequilibrium molecular dynamics

The issue of system size effects in the reverse perturbation nonequilibrium molecular dynamics method for determining transport coefficients of fluids is examined for the case of the Lennard-Jones model. It is found that when adequate precautions are observed in obtaining linear temperature or momentum profiles, a 250 atom system is adequate for determining the thermal conductivity and the shear viscosity. Also, a means of determining the uncertainties in the transport coefficients is described. The conclusion is that this method is computationally competitive with other simulation methods for estimating transport coefficients.

A full radius gyrokinetic stability analysis for large aspect ratio finite-β tokamaks

Linear, fully gyrokinetic, full radius (global), large aspect ratio studies of Alfvén-ion temperature gradient mode (AITG) or kinetic ballooning modes or beta-induced Alfvén eigenmodes considering only “passing” species is presented. Effects hitherto completely neglected in a full radius approach such as B∥-fluctuations and the ones which have been treated partly [Phys. Plasmas 10, 1424 (2003)] such as Shafranov shifts are included. To this end, an existing code EM-GLOGYSTO has been upgraded to incorporate these effects. Among others, the most interesting results include: (i) For relatively large positive magnetic shear ŝ [1.25<ŝ<4.25, ŝ=d ln qs/d ln ρ, where qs(ρ) is safety factor and ρ minor radius], B∥ fluctuations have a benign effect on AITG growth rates and for positive but small shear (0.0<ŝ<2.7), B∥ fluctuations are too weak to play any crucial role. (ii) In the later case, inclusion of Shafranov shift leads to the following: (a) Growth rates without Shafranov shift effects are in general larger than those including Shafranov shift; (b) nonmonotonous dependence of growth rates and frequencies on β=2μ0NTi/B02; (c) the presence of multiple eigenmodes with competing growth rates for same values of β; (d) no sign of complete stabilization with increasing β. Finally eigenmode structures [φ,A∥,Aθ] with and without Shafranov shift are reported. The growth rates and frequencies thus obtained may serve as estimates of transport coefficients and for future bench marking of the (then) global electromagnetic, gyrokinetic, time evolution codes (particle-in-cell or otherwise).

Transport model of boundary plasma and estimation of transport coefficients

Equations to estimate transport coefficients of JFT-2M scrape-off layer plasma are derived. These equations use a plasma density, an ion temperature, an electron temperature and their decay lengths obtained from measurements. On the basis of these equations with measured values, transport coefficients for discharges with and without neutral beam heating of JFT-2M are evaluated.