Identification of Hydrodynamic Dispersion Tensor by Optimization Algorithm Based LBM/CMA-ES Combination

The hydrodynamic dispersion tensor (HDT) of a porous medium is a key parameter in engineering and environmental sciences. Its knowledge allows for example, to accurately predict the propagation of a pollution front induced by a surface (or subsurface) flow. This paper proposes a new mathematical model based on inverse problem-solving techniques to identify the HDT (noted D=) of the studied porous medium. We then showed that in practice, this new model can be written in the form of an integrated optimization algorithm (IOA). The IOA is based on the numerical solution of the direct problem (which solves the convection–diffusion type transport equation) and the optimization of the error function between the simulated concentration field and that observed at the application site. The partial differential equations of the direct model were solved by high resolution of (Δx=Δy=1 m) Lattice Boltzmann Method (LBM) whose computational code is named HYDRODISP-LBM (HYDRO-DISpersion by LBM). As for the optimization step, we opted for the CMA-ES (Covariance Matrix Adaptation-Evolution Strategy) algorithm. Our choice for these two methods was motivated by their excellent performance proven in the abundant literature. The paper describes in detail the operation of the coupling of the two computer codes forming the IOA that we have named HYDRODISP-LBM/CMA-ES. Finally, the IOA was applied at the Beauvais experimental site to identify the HDT D=. The geological analyzes of this site showed that the tensor identified by the IOA is in perfect agreement with the characteristics of the geological formation of the site which are connected with the mixing processes of the latter.

Measurement and Simulation of the Nonlocal Dispersion Tensor in Porous Media

<p>Nuclear Magnetic Resonance (NMR) techniques have been used extensively to characterise dispersion and diffusion in porous media. The completely non-invasive nature of the measurements and the ability to measure opaque samples provide the makings for an excellent tool. Detailed understanding of the microstructure of porous media leads to the ability to model and predict macroscopic effects such as ground water flow, oil extraction, blood perfusion and enable understanding of industrial catalytic reactors. The range of properties that NMR is capable of measuring is extensive but one particular quantity, the nonlocal dispersion tensor has long been identified as an ideal way to characterise dispersive effects at short time and length scales. The nonlocal dispersion tensor is a quantity that is included in theory proposed by Koch and Brady (1987) to explain non-Fickian dispersive behaviour. Demonstrated here is, for the first time, a method to measure the tensor. Details of the newly developed NMR pulse sequence and the post processing technique required to extract the nonlocal dispersion tensor are given. Successful measurements have been undertaken on model systems such as capillary flow and Couette flow. This enabled direct comparison with analytically calculated quantities and excellent agreement is found, thus verifying the methodology. A complete set of nonlocal dispersion components has been identified and measured in a model porous medium, in this case a random beadpack of monosized spheres. The new measurements provide the ability to infer and characterise the nature of fluid correlations, particularly at short length scales. In parallel, a simulation suite based on a lattice Boltzmann calculation (implemented by a co-worker Dr Andrew Jackson), has been used to independently generate the same nonlocal components as measured. The simulations have also been used to guide the design of further NMR experiments, to further investigate aspects of the new parameter space that the nonlocal dispersion tensor provides and to explore parts of the parameter space that are inaccessible by NMR. Finally, the methodology was adapted to enable nonlocal dispersion measurements on a 'real' porous medium, a Bentheimer sandstone.</p>

Measurement and Simulation of the Nonlocal Dispersion Tensor in Porous Media

<p>Nuclear Magnetic Resonance (NMR) techniques have been used extensively to characterise dispersion and diffusion in porous media. The completely non-invasive nature of the measurements and the ability to measure opaque samples provide the makings for an excellent tool. Detailed understanding of the microstructure of porous media leads to the ability to model and predict macroscopic effects such as ground water flow, oil extraction, blood perfusion and enable understanding of industrial catalytic reactors. The range of properties that NMR is capable of measuring is extensive but one particular quantity, the nonlocal dispersion tensor has long been identified as an ideal way to characterise dispersive effects at short time and length scales. The nonlocal dispersion tensor is a quantity that is included in theory proposed by Koch and Brady (1987) to explain non-Fickian dispersive behaviour. Demonstrated here is, for the first time, a method to measure the tensor. Details of the newly developed NMR pulse sequence and the post processing technique required to extract the nonlocal dispersion tensor are given. Successful measurements have been undertaken on model systems such as capillary flow and Couette flow. This enabled direct comparison with analytically calculated quantities and excellent agreement is found, thus verifying the methodology. A complete set of nonlocal dispersion components has been identified and measured in a model porous medium, in this case a random beadpack of monosized spheres. The new measurements provide the ability to infer and characterise the nature of fluid correlations, particularly at short length scales. In parallel, a simulation suite based on a lattice Boltzmann calculation (implemented by a co-worker Dr Andrew Jackson), has been used to independently generate the same nonlocal components as measured. The simulations have also been used to guide the design of further NMR experiments, to further investigate aspects of the new parameter space that the nonlocal dispersion tensor provides and to explore parts of the parameter space that are inaccessible by NMR. Finally, the methodology was adapted to enable nonlocal dispersion measurements on a 'real' porous medium, a Bentheimer sandstone.</p>

General dispersion properties of magnetized plasmas with drifting bi-Kappa distributions. DIS-K: Dispersion Solver for Kappa Plasmas

Space plasmas are known to be out of (local) thermodynamic equilibrium, as observations show direct or indirect evidences of non-thermal velocity distributions of plasma particles. Prominent are the anisotropies relative to the magnetic field, anisotropic temperatures, field-aligned beams or drifting populations, but also, the suprathermal populations enhancing the high-energy tails of the observed distributions. Drifting bi-Kappa distribution functions can provide a good representation of these features and enable for a kinetic fundamental description of the dispersion and stability of these collision-poor plasmas, where particle–particle collisions are rare but wave–particle interactions appear to play a dominant role in the dynamics. In the present paper we derive the full set of components of the dispersion tensor for magnetized plasma populations modelled by drifting bi-Kappa distributions. A new solver called DIS-K (DIspersion Solver for Kappa plasmas) is proposed to solve numerically the dispersion relations of high complexity. The solver is validated by comparing with the damped and unstable wave solutions obtained with other codes, operating in the limits of drifting Maxwellian and non-drifting Kappa models. These new theoretical tools enable more realistic characterizations, both analytical and numerical, of wave fluctuations and instabilities in complex kinetic configurations measured in-situ in space plasmas.

Modeling Transport and Adsorption of Arsenic Ions in Iron-Oxide Laden Porous Media. Part I: Theoretical Developments

The process of transport and trapping of arsenic ions in porous water filters is treated as a classic mass transport problem which, at the pore scale, is modeled using the traditional convection-diffusion equation, representing the migration of species present in very small (tracer) amounts in water. The upscaling, conducted using the volume averaging method, reveals the presence of two possible forms of the macroscopic equations for predicting arsenic concentrations in the filters. One is the classic convection-dispersion equation with the total dispersion tensor as its main transport coefficient, and which is obtained from a closure formulation similar to that of the passive diffusion problem. The other equation form includes an additional transport coefficient, hitherto ignored in the literature and identified here as the adsorption-induced vector. These two coefficients in the latter form are determined from a system of two closure problems that include the effects of both the passive diffusion as well as the adsorption of arsenic by the solid phase of the filter. This theoretical effort represents the first serious effort to introduce a detailed micro–macro coupling while modeling the transport of arsenic species in water filters representing homogeneous porous media.

Calibrating the BHB star distance scale and the halo kinematic distance to the Galactic Centre

ABSTRACT We report the first determination of the distance to the Galactic Centre based on the kinematics of halo objects. We apply the statistical-parallax technique to the sample of ∼2500 blue horizontal branch (BHB) stars compiled by Xue et al. to simultaneously constrain the correction factor to the photometric distances of BHB stars as reported by those authors and the distance to the Galactic Centre to find R = 8.2 ± 0.6 kpc. We also find that the average velocity of our BHB star sample in the direction of Galactic rotation, V0 = −240 ± 4 km s−1, is greater by about 20 km s−1 in absolute value than the corresponding velocity for halo RR Lyrae type stars (V0 = −222 ± 4 km s−1) in the Galactocentric distance interval from 6 to 18 kpc, whereas the total (σV) and radial (σr) velocity dispersion of the BHB sample are smaller by about 40–45 km s−1 than the corresponding parameters of the velocity dispersion ellipsoid of halo RR Lyrae type variables. The velocity dispersion tensor of halo BHB stars proved to be markedly less anisotropic than the corresponding tensor for RR Lyrae type variables: the corresponding anisotropy parameter values are equal to βBHB = 0.51 ± 0.02 and βRR = 0.71 ± 0.03, respectively.

Visualization of the Anisotropy of the Velocity Dispersion and Characteristics of the Multi-Velocity Continuum in the Regions of Multi-Stream Flows of Gas-Dust Media with Polydisperse Dust

Collisionless media devoid of intrinsic stresses, for example, a dispersed phase in a multiphase medium, have a much wider variety of space-time structures and features formed in them than collisional media, for example, a carrier, gas, or liquid phase. This is a consequence of the fact that evolution in such media occurs in phase space, i.e., in a space of greater dimensions than the usual coordinate space. As a consequence, the process of the formation of features in collisionless media (clustering or vice versa, a loss of continuity) can occur primarily in the velocity space, which, in contrast to the features in the coordinate space (folds, caustics, or voids), is poorly observed directly. To identify such features, it is necessary to use visualization methods that allow us to consider, in detail, the evolution of the medium in the velocity space. This article is devoted to the development of techniques that allow visualizing the degree of anisotropy of the velocity fields of collisionless interpenetrating media. Simultaneously tracking the behavior of different fractions in such media is important, as their behavior can be significantly different. We propose three different techniques for visualizing the anisotropy of velocity fields using the example of two- and three-continuum dispersed media models. We proposed the construction of spatial distributions of eccentricity fields (scalar fields), or fields of principal directions of the velocity dispersion tensor (tensor fields). In the first case, we used some simple eccentricity functions for dispersion tensors for two fractions simultaneously, which we call surrogate entropy. In the second case, to visualize the anisotropy of the velocity fields of three fractions simultaneously, we used an ordered array (3-vector) of eccentricities for the color representation through decomposition in three basic colors. In the case of a multi-stream flow, we used cluster analysis methods to identify sections of a multi-stream flow (beams) and used glyphs to visualize the entire set of beams (vector-tensor fields).

First Gaia dynamical model of the Milky Way disc with six phase space coordinates: a test for galaxy dynamics

ABSTRACT We construct the first comprehensive dynamical model for the high-quality subset of stellar kinematics of the Milky Way disc, with full 6D phase-space coordinates, provided by the Gaia Data Release 2. We adopt an axisymmetric approximation and use an updated Jeans Anisotropic Modelling (JAM) method, which allows for a generic shape and radial orientation of the velocity ellipsoid, as indicated by the Gaia data, to fit the mean velocities and all three components of the intrinsic velocity dispersion tensor. The Milky Way is the first galaxy for which all intrinsic phase space coordinates are available, and the kinematics are superior to the best integral-field kinematics of external galaxies. This situation removes the long-standing dynamical degeneracies and makes this the first dynamical model highly overconstrained by the kinematics. For these reasons, our ability to fit the data provides a fundamental test for both galaxy dynamics and the mass distribution in the Milky Way disc. We tightly constrain the volume average total density logarithmic slope, in the radial range 3.6–12 kpc, to be αtot = −2.149 ± 0.055 and find that the dark halo slope must be significantly steeper than αDM = −1 (NFW). The dark halo shape is close to spherical and its density is ρDM(R⊙) = 0.0115 ± 0.0020 M⊙ pc−3 (0.437 ± 0.076 GeV cm−3), in agreement with previous estimates. The circular velocity at the solar position vcirc(R⊙) = 236.5 ± 3.1 km s−1 (including systematics) and its gently declining radial trends are also consistent with recent determinations.

A Vectorized Regularization Method for Multivalued Parameters Identification

The identification of multivalued parameters is formulated as a constraint minimization problem called primal problem. We embed it in a family of perturbed problems and we associate a dual problem with it using the conjugate functions. Basing on the primal-dual relationship, under some qualification conditions on the parameters to be identified we elaborate the well posedeness, convergence and stability of the solution assuming. Numerical simulations are described in the end for the identification of discontinuous dispersion tensor in transport equations.

Stellar systems following the R1/m luminosity law

The Sérsic or R1/m model has become the de facto standard model to describe the surface brightness profiles of early-type galaxies and the bulges of spiral galaxies. The photometric, intrinsic, and dynamical properties of this model have been investigated, but mainly for fairly large Sérsic indices m. For small values of m, appropriate for low-mass and dwarf ellipticals, a detailed investigation of these properties is still lacking. In this study, we used a combination of numerical and analytical techniques to investigate the Sérsic model over the entire range of Sérsic parameters, focussing on the small m regime, where a number of interesting and surprising properties are found. For all values m < 1, the model is characterised by a finite central luminosity density, and for m < 1/2, even a central depression in the luminosity density profile. This behaviour translates to the dynamical properties: we show that all Sérsic models with m ⩾ 1/2 can be supported by an isotropic velocity dispersion tensor, and that these isotropic models are stable to both radial and non-radial perturbations. The models with m < 1/2, on the other hand, cannot be supported by an isotropic velocity dispersion tensor.