Modeling Approaches of Competitive Sorption and Transport of Trace Metals and Metalloids in Soils: A Review

Competition among various heavy metal species for available adsorption sites on soil matrix surfaces can enhance the mobility of contaminants in the soil environment. Accurate predictions of the fate and behavior of heavy metals in soils and geologic media requires the understanding of the underlying competitive-sorption and transport processes. In this review, we present equilibrium and kinetic models for competitive heavy metal sorption and transport in soils. Several examples are summarized to illustrate the impact of competing ions on the reactivities and mobility of heavy metals in the soil-water environment. We demonstrate that equilibrium Freundlich approaches can be extended to account for competitive sorption of cations and anions with the incorporation of competition coefficients associated with each reaction. Furthermore, retention models of the multiple-reaction type including the two-site nonlinear equilibrium-kinetic models and the concurrent-and consecutive-multireaction models were modified to describe commonly observed time-dependent behaviors of heavy metals in soils. We also show that equilibrium Langmuir and kinetic second-order models can be extended to simulate the competitive sorption and transport in soils, although the use of such models is limited due to their simplifying assumptions. A major drawback of the empirically based Freundlich and Langmuir approaches is that their associated parameters are specific for each soil. Alternatively, geochemical models that are based on ion-exchange and surface-complexation concepts are capable of quantifying the competitive behavior of several chemical species under a wide range of environmental conditions. Such geochemical models, however, are incapable of describing the time-dependent sorption behavior of heavy metal ions in competitive systems. Further research is needed to develop a general-purpose model based on physical and chemical mechanisms governing competitive sorption in soils.Competition among various heavy metal species for available adsorption sites on soil matrix surfaces can enhance the mobility of contaminants in the soil environment. Accurate predictions of the fate and behavior of heavy metals in soils and geologic media requires the understanding of the underlying competitive-sorption and transport processes. In this review, we present equilibrium and kinetic models for competitive heavy metal sorption and transport in soils. Several examples are summarized to illustrate the impact of competing ions on the reactivities and mobility of heavy metals in the soil-water environment. We demonstrate that equilibrium Freundlich approaches can be extended to account for competitive sorption of cations and anions with the incorporation of competition coefficients associated with each reaction. Furthermore, retention models of the multiple-reaction type including the two-site nonlinear equilibrium-kinetic models and the concurrent-and consecutive-multireaction models were modified to describe commonly observed time-dependent behaviors of heavy metals in soils. We also show that equilibrium Langmuir and kinetic second-order models can be extended to simulate the competitive sorption and transport in soils, although the use of such models is limited due to their simplifying assumptions. A major drawback of the empirically based Freundlich and Langmuir approaches is that their associated parameters are specific for each soil. Alternatively, geochemical models that are based on ion-exchange and surface-complexation concepts are capable of quantifying the competitive behavior of several chemical species under a wide range of environmental conditions. Such geochemical models, however, are incapable of describing the time-dependent sorption behavior of heavy metal ions in competitive systems. Further research is needed to develop a general-purpose model based on physical and chemical mechanisms governing competitive sorption in soils

Nature of magnetism in Ca3_3Co2_2O6_6

We find using LSDA+U band structure calculations that the novel one-dimensional cobaltate Ca$_3$Co$_2$O$_6$ is not a ferromagnetic half-metal but a Mott insulator. Both the octahedral and the trigonal Co ions are formally trivalent, with the octahedral being in the low-spin and the trigonal in the high-spin state. The inclusion of the spin-orbit coupling leads to the occupation of the minority-spin $d_{2}$ orbital for the unusually coordinated trigonal Co, producing a giant orbital moment (1.57 $\mu_{B}$). It also results in an anomalously large magnetocrystalline anisotropy (of order 70 meV), elucidating why the magnetism is highly Ising-like. The role of the oxygen holes, carrying an induced magnetic moment of 0.13 $\mu_{B}$ per oxygen, for the exchange interactions is discussed.Comment: 5 pages, 4 figures, and 1 tabl

Majorana Spin Liquids on a two-leg ladder

We realize a gapless Majorana Orbital Liquid (MOL) using orbital degrees of freedom and also an SU(2)-invariant Majorana Spin Liquid (MSL) using both spin and orbital degrees of freedom in Kitaev-type models on a 2-leg ladder. The models are exactly solvable by Kitaev's parton approach, and we obtain long-wavelength descriptions for both Majorana liquids. The MOL has one gapless mode and power law correlations in energy at incommensuare wavevectors, while the SU(2) MSL has three gapless modes and power law correlations in spin, spin-nematic, and local energy observables. We study the stability of such states to perturbations away from the exactly solvable points. We find that both MOL and MSL can be stable against allowed short-range parton interactions. We also argue that both states persist upon allowing $Z_2$ gauge field fluctuations, in that the number of gapless modes is retained, although with an expanded set of contributions to observables compared to the free parton mean field.Comment: 15 pages, 6 figures. Revised versio

Regression Depth and Center Points

We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least ceiling(n/(d+1)). as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions there exists a point that cannot escape to infinity without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our approach to related questions on the existence of partitions of the data into subsets such that a common plane has nonzero regression depth in each subset, and to the computational complexity of regression depth problems.Comment: 14 pages, 3 figure

Thermoelectric three-terminal hopping transport through one-dimensional nanosystems

A two-site nanostructure (e.g, a "molecule") bridging two conducting leads and connected to a phonon bath is considered. The two relevant levels closest to the Fermi energy are connected each to its lead. The leads have slightly different temperatures and chemical potentials and the nanos- tructure is also coupled to a thermal (third) phonon bath. The 3 x 3 linear transport ("Onsager") matrix is evaluated, along with the ensuing new figure of merit, and found to be very favorable for thermoelectric energy conversion.Comment: Accepted by Phys. Rev.

Mechanism of pseudogap probed by a local impurity

The response to a local strong non-magnetic impurity in the pseudogap phase is examined in two distinctly different scenarios: phase-fluctuation (PF) of pairing field and d-density-wave (DDW) order. In the PF scenario, the resonance state is generally double-peaked near the Fermi level, and is abruptly broadened by vortex fluctuations slightly above the transition temperature. In the DDW scenario, the resonance is single-peaked and remains sharp up to gradual intrinsic thermal broadening, and the resonance energy is analytically determined to be at minus of the chemical potential.Comment: 4 pages, 2 figure

Nucleon axial form factors from two-flavour Lattice QCD

We present preliminary results on the axial form factor $G_A(Q^2)$ and the induced pseudoscalar form factor $G_P(Q^2)$ of the nucleon. A systematic analysis of the excited-state contributions to form factors is performed on the CLS ensemble `N6' with $m_\pi = 340 \ \text{MeV}$ and lattice spacing $a \sim 0.05 \ \text{fm}$. The relevant three-point functions were computed with source-sink separations ranging from $t_s \sim 0.6 \ \text{fm}$ to $t_s \sim \ 1.4 \ \text{fm}$. We observe that the form factors suffer from non-trivial excited-state contributions at the source-sink separations available to us. It is noted that naive plateau fits underestimate the excited-state contributions and that the method of summed operator insertions correctly accounts for these effects.Comment: 7 pages, 12 figures; talk presented at Lattice 2014 -- 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014, Columbia University New York, N

Nucleon electromagnetic form factors in two-flavour QCD

We present results for the nucleon electromagnetic form factors, including the momentum transfer dependence and derived quantities (charge radii and magnetic moment). The analysis is performed using O(a) improved Wilson fermions in Nf=2 QCD measured on the CLS ensembles. Particular focus is placed on a systematic evaluation of the influence of excited states in three-point correlation functions, which lead to a biased evaluation, if not accounted for correctly. We argue that the use of summed operator insertions and fit ans\"atze including excited states allow us to suppress and control this effect. We employ a novel method to perform joint chiral and continuum extrapolations, by fitting the form factors directly to the expressions of covariant baryonic chiral effective field theory. The final results for the charge radii and magnetic moment from our lattice calculations include, for the first time, a full error budget. We find that our estimates are compatible with experimental results within their overall uncertainties.Comment: 22 pages, 10 figures, citations modifie