Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media

In this article, we present new random walk methods to solve flow and transport problems in saturated/unsaturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic conductivity and recharge fields, processes at the field and regional scales. The numerical schemes are based on global random walk algorithms (GRW) which approximate the solution by moving large numbers of computational particles on regular lattices according to specific random walk rules. To cope with the nonlinearity and the degeneracy of the Richards equation and of the coupled system, we implemented the GRW algorithms by employing linearization techniques similar to the -scheme developed in finite element/volume approaches. The resulting GRW -schemes converge with the number of iterations and provide numerical solutions that are first-order accurate in time and second-order in space. A remarkable property of the flow and transport GRW solutions is that they are practically free of numerical diffusion. The GRW solvers are validated by comparisons with mixed finite element and finite volume solvers in one- and two-dimensional benchmark problems. They include Richards’ equation fully coupled with the advection-diffusion-reaction equation and capture the transition from unsaturated to saturated flow regimes.publishedVersio

Fracture load of 3D printed PEEK inlays compared with milled ones, direct resin composite fillings, and sound teeth

Objective!#!The objective of this in vitro study was to investigate fracture load, fracture types, and impact of chewing simulation of human molars restored with 3D printed indirect polyetheretherketone (PEEK) inlays and compare these with milled indirect PEEK inlays, direct resin composite fillings, and sound teeth.!##!Materials and methods!#!A total of 112 molars with form congruent class I cavities were restored with (n = 16/group) 3D printed indirect PEEK inlays via fused layer manufacturing (FLM): (1) Essentium PEEK (ESS), (2) KetaSpire PEEK MS-NT1 (KET), (3) VESTAKEEP i4 G (VES), (4) VICTREX PEEK 450G (VIC), (5) milled indirect PEEK inlays JUVORA Dental Disc 2 (JUV), and (6) direct resin composite fillings out of Tetric EvoCeram (TET). Sound teeth (7) acted as positive control group. Half of the specimens of each group (n = 8) were treated in a chewing simulator combined with thermal cycling (1.2 million × 50 N; 12,000 × 5 °C/55 °C). Fracture load and fracture types of all molars were determined. Statistical analyses using Kolmogorov-Smirnov test and two-way ANOVA with partial eta squared (η!##!Results!#!ESS and TET demonstrated the lowest fracture load with a minimum of 956 N, whereas sound molars showed the highest values of up to 2981 N. Chewing simulation indicated no impact (p = 0.132). With regard to Weibull modulus, KET presented a lower value after chewing simulation than JUV, whereas TET had the highest value without chewing simulation. All indirect restorations revealed a tooth fracture (75-100%), direct resin composite fillings showed a restoration fracture (87.5%), and 50% of the sound teeth fractured completely or had cusp fractures.!##!Conclusions!#!All 3D printed and milled indirect PEEK inlays as well as the direct resin composite fillings presented a higher fracture load than the expected physiological and maximum chewing forces.!##!Clinical relevance!#!3D printing of inlays out of PEEK via FLM provided promising results in mechanics, but improvements in terms of precision and esthetics will be required to be practicable in vivo to represent an alternative dental material

Pore scale modeling of the mutual influence of roots and soil aggregation in the rhizosphere

Investigating plant/root-soil interactions at different scales is crucial to advance the understanding of soil structure formation in the rhizosphere. To better comprehend the underlying interwoven processes an explicit, fully dynamic spatial and image-based modeling at the pore scale is a promising tool especially taking into account experimental limitations. We develop a modeling tool to investigate how soil aggregation, root growth and root exudates mutually interact with each other at the micro-scale. This allows the simultaneous simulation of the dynamic rearrangement of soil particles, the input and turnover of particulate organic matter, root growth and decay as well as the deposition, redistribution and decomposition of mucilage in the rhizosphere. The interactions are realized within a cellular automaton framework. The most stable configuration is determined by the amount and attractiveness of surface contacts between the particles, where organo-mineral associations preferably lead to the formation of soil aggregates. Their break-up can be induced by root growth or the degradation of gluing agents previously created after the decomposition of particulate organic matter and mucilage. We illustrate the capability of our model by simulating a full life cycle of a fine root in a two-dimensional, horizontal cross section through the soil. We evaluate various scenarios to identify the role of different drivers such as soil texture and mucilage. We quantify the displacement intensity of individual particles and the variations in local porosity due to the change in available pore space as influenced by the root growth and observe compaction, gap formation and a biopore evolution. The simulation results support that the deposition of mucilage is an important driver for structure formation in the rhizosphere. Although mucilage is degraded within a few days after exudation, it leads to a persistent stabilization of the aggregated structures for both textures in the vicinity of the root within a time frame of 1000 days. Local porosity changes are quantified for exudation periods of 1, 10 and 100 days and are already pronounced for short-term exudation of mucilage. This stabilization is significantly different from the structures encountered when only POM could trigger the evolution of gluing spots, and is still present after complete degradation of the root

Application of a Cellular Automaton Method to Model the Structure Formation in Soils Under Saturated Conditions: A Mechanistic Approach

Soil functions are closely related to the structure of soil microaggregates. Yet, the mechanisms controlling the establishment of soil structure are diverse and partly unknown. Hence, the understanding of soil processes and functions requires the connection of the concepts on the formation and consolidation of soil structural elements across scales that are hard to observe experimentally. At the bottom level, the dynamics of microaggregate development and restructuring build the basis for transport phenomena at the continuum scale. By modeling the interactions of specific minerals and/or organic matter, we aim to identify the mechanisms that control the evolution of structure and establishment of stationary aggregate properties. We present a mechanistic framework based on a cellular automaton model to simulate the interplay between the prototypic building units of soil microaggregates quartz, goethite, and illite subject to attractive and repulsive electrostatic interaction forces. The resulting structures are quantified by morphological measures. We investigated shielding effects due to charge neutralization and the aggregate growth rate in response to the net system charge. We found that the fraction as well as the size of the interacting oppositely charged constituents control the size, shape, and amount of occurring aggregates. Furthermore, the concentration in terms of the liquid solid ratio has been shown to increase the aggregation rate. We further adopt the model for an assessment of the temporal evolution of aggregate formation due to successive formation of particle dimers at early stages in comparison to higher order aggregates at later stages. With that we show the effect of composition, charge, size ratio, time, and concentration on microaggregate formation by the application of a mechanistic model which also provides predictions for soil aggregation behavior in case an observation is inhibited by experimental limitations

Discrete-Continuum Multiphase Model for Structure Formation in Soils Including Electrostatic Effects

Structure formation and self organization in soils determine soil functions and regulate soil processes. Mathematically based modeling can facilitate the understanding of organizing mechanisms at different scales, provided that the major driving forces are taken into account. In this research we present an extension of the mechanistic model for transport, biomass development and solid restructuring that was proposed in a former publication of the authors. Three main extensions are implemented. First, arbitrary shapes for the building units (e.g., spherical, needle-like, or platy particles), and also their compositions are incorporated into the model. Second, a gas phase is included in addition to solid, biofilm, and fluid phases. Interaction rules within and between the phases are prescribed using a cellular automaton method (CAM) and a system of partial differential equations (PDEs). These result in a structural self organization of the respective phases which define the time-dependent composition of the computational domain. Within the non-solid phases, chemical species may diffuse and react. In particular a kinetic Langmuir isotherm for heterogeneous surface reactions and a Henry condition for the transfer from/into the gas phase are applied. As third important model extension charges and charge conservation laws are included into the model for both the solid phase and ions in solution, as electrostatic attraction is a major driving force for aggregation. The ions move obeying the Nernst-Planck equations. A fully implicit local discontinuous Galerkin (LDG) method is applied to solve the resulting equation systems. The operational, comprehensive model allows to study structure formation as a function of the size and shape of the solid particles. Moreover, the effect of attraction and repulsion by charges is thoroughly discussed. The presented model is a first step to capture various aspects of structure formation and self organization in soils, it is a process-based tool to study the interplay of relevant mechanisms in silico

Multifunctional and compact 3D FMCW MIMO radar system with rectangular array for medium-range applications

Miralles-Navarro, E.; Multerer, T.; Ganis, A.; Schoenlinner, B.; Prechtel, U.; Meusling, A.; Mietzner, J.... (2018). Multifunctional and compact 3D FMCW MIMO radar system with rectangular array for medium-range applications. IEEE Aerospace and Electronic Systems Magazine. 33(4):46-54. https://doi.org/10.1109/MAES.2018.160277S465433