All soils harbor microaggregates, i.e., compound soil structures smaller than 250 μm. These microaggregates are composed of diverse mineral, organic and biotic materials that are bound together during pedogenesis by various physical, chemical and biological processes. Consequently, microaggregates can withstand strong mechanical and physicochemical stresses and survive slaking in water, allowing them to persist in soils for several decades. Together with the physiochemical heterogeneity of their surfaces, the three-dimensional structure of microaggregates provides a large variety of ecological niches that contribute to the vast biological diversity found in soils. As reported for larger aggregate units, microaggregates are composed of smaller building units that become more complex with increasing size. In this context, organo-mineral associations can be considered structural units of soil aggregates and as nanoparticulate fractions of the microaggregates themselves. The mineral phases considered to be the most important as microaggregate forming materials are the clay minerals and Fe-and Al-(hydr)oxides. Within microaggregates, minerals are bound together primarily by physicochemical and chemical interactions involving cementing and gluing agents. The former comprise, among others, carbonates and the short-range ordered phases of Fe, Mn, and Al. The latter comprise organic materials of diverse origin and probably involve macromolecules and macromolecular mixtures. Work on microaggregate structure and development has largely focused on organic matter stability and turnover. However, little is known concerning the role microaggregates play in the fate of elements like Si, Fe, Al, P, and S. More recently, the role of microaggregates in the formation of microhabitats and the biogeography and diversity of microbial communities has been investigated. Little is known regarding how microaggregates and their properties change in time, which strongly limits our understanding of micro-scale soil structure dynamics. Similarly, only limited information is available on the mechanical stability of microaggregates, while essentially nothing is known about the flow and transport of fluids and solutes within the micro-and nanoporous microaggregate systems. Any quantitative approaches being developed for the modeling of formation, structure and properties of microaggregates are, therefore, in their infancy. We respond to the growing awareness of the importance of microaggregates for the structure, properties and functions of soils by reviewing what is currently known about the formation, composition and turnover of microaggregates. We aim to provide a better understanding of their role in soil function, and to present the major unknowns in current microaggregate research. We propose a harmonized concept for aggregates in soils that explicitly considers the structure and build-up of microaggregates and the role of organo-mineral associations. We call for experiments, studies and modeling endeavors that will link informatio...

The graphene twist bilayer represents the prototypical system for investigating the stacking degree of freedom in few-layer graphenes. The electronic structure of this system changes qualitatively as a function of angle, from a large-angle limit in which the two layers are essentially decoupled-with the exception of a 28-atom commensuration unit cell for which the layers are coupled on an energy scale of ≈8 meV-to a small-angle strong-coupling limit. Despite sustained investigation, a fully satisfactory theory of the twist bilayer remains elusive. The outstanding problems are (i) to find a theoretically unified description of the large-and small-angle limits, and (ii) to demonstrate agreement between the low-energy effective Hamiltonian and, for instance, ab initio or tight-binding calculations. In this article, we develop a low-energy theory that in the large-angle limit reproduces the symmetry-derived Hamiltonians of Mele [Phys. Rev. B 81, 161405 (2010)], and in the small-angle limit shows almost perfect agreement with tight-binding calculations. The small-angle effective Hamiltonian is that of Bistritzer and MacDonald [Proc. Natl. Acad. Sci. (U.S.A.) 108, 12233 (2011)], but with the momentum scale K, the difference of the momenta of the unrotated and rotated special points, replaced by a coupling momentum scale g (c) = 8π √ 3a sin θ 2. Using this small-angle Hamiltonian, we are able to determine the complete behavior as a function of angle, finding a complex small-angle clustering of van Hove singularities in the density of states (DOS) that after a "zero-mode" peak regime between 0.90 • < θ < 0.15 • limits θ < 0.05 • to a DOS that is essentially that of a superposition DOS of all bilayer stacking possibilities. In this regime, the Dirac spectrum is entirely destroyed by hybridization for −0.25 < E < 0.25 eV with an average band velocity ≈0.3v (SLG) F (where SLG denotes single-layer graphene). We study the fermiology of the twist bilayer in this limit, finding remarkably structured constant energy surfaces with multiple Lifshitz transitions between Kand-centered Fermi sheets and a rich pseudospin texture.

In the first part of this article, we extend the formal upscaling of a diffusion–precipitation model through a two-scale asymptotic expansion in a level set framework to three dimensions. We obtain upscaled partial differential equations, more precisely, a non-linear diffusion equation with effective coefficients coupled to a level set equation. As a first step, we consider a parametrization of the underlying pore geometry by a single parameter, e.g. by a generalized “radius” or the porosity. Then, the level set equation transforms to an ordinary differential equation for the parameter. For such an idealized setting, the degeneration of the diffusion tensor with respect to porosity is illustrated with numerical simulations. The second part and main objective of this article is the analytical investigation of the resulting coupled partial differential equation–ordinary differential equation model. In the case of non-degenerating coefficients, local-in-time existence of at least one strong solution is shown by applying Schauder's fixed point theorem. Additionally, non-negativity, uniqueness, and global existence or existence up to possible closure of some pores, i.e. up to the limit of degenerating coefficients, is guaranteed.

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We perform the periodic homogenization (i. e. ε → 0) of the non-stationary Stokes-Nernst-Planck-Poisson system using two-scale convergence, where ε is a suitable scale parameter. The objective is to investigate the influence of different boundary conditions and variable choices of scalings in ε of the microscopic system of partial differential equations on the structure of the (upscaled) limit model equations. Due to the specific nonlinear coupling of the underlying equations, special attention has to be paid when passing to the limit in the electrostatic drift term. As a direct result of the homogenization procedure, various classes of upscaled model equations are obtained.