Uncertainty quantification in a chemical system using error estimate-based mesh adaption

This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows.     

Minimal loading conditions for higher-order numerical homogenisation schemes

The present study deals with the formulation of minimal loading conditions for microscale applications in numerical two-scale modelling (FE²) approaches. From the homogenisation concept, a set of volume average rules constrains the microscale PDE to be solved. They are considered to be the minimal set of loading conditions and can be specified by additional polynomial or periodic assumptions, for example, on the microscale displacement field. Whereas the resulting volume integrals can be transformed into surface integrals for so-called first-order homogenisation schemes, this is not possible for a second-order homogenisation of second gradient or micromorphic effective media substituting a heterogeneous microcontinuum represented by a volume element on the microscale. Several numerical examples compare the minimal loading condition concept with standard techniques discussed in literature.     

Diffusion of biostimulators into plant tissues

Biostimulators are substances able to enhance the immune system of cultivated crops and support plant metabolism. Their utilization helps to reduce the amount of chemicals used in agriculture. To perform the desired effect, a biostimulator must be able to penetrate into the plant tissue. The time of penetration however, is limited, since the biostimulator must remain in a liquid state. This is of great importance—especially in field conditions, where the treated plants are exposed to different weather condition and other extrinsic factors. A mathematical model based on diffusion mechanisms has been elaborated to describe the biostimulator transport process from penetration of the leaves into the plant’s inner tissues. By means of the effective diffusion coefficient of the prepared specific protein hydrolyzate, this model can be used to estimate the time necessary for the uptake of the minimal active amount of the biostimulator.     

Lanthanide Identity Governs Guest-Induced Dimerization in LnIII[15-MC N(L-pheHA)-5])3+ Metallacrowns

Series of lanthanide-containing metallic coordination complexes are frequently presented as structurally analogous, due to the similar chemical and coordinative properties of the lanthanides. In the case of chiral (Ln^III[15-MC _N(L-pheHA)-5])³⁺ metallacrowns (MCs), which are well established supramolecular hosts, the formation of dimers templated by a dicarboxylate guest (muconate) in solution of neutral pH is herein shown to have a unique dependence on the identity of the MC's central lanthanide. Calorimetric data and nuclear magnetic resonance diffusion studies demonstrate that MCs containing larger or smaller lanthanides as the central metal only form monomeric host-guest complexes whereas analogues with intermediate lanthanides (for example, Eu, Gd, Dy) participate in formation of dimeric host-guest-host compartments. The driving force for the dimerization event across the series is thought to be a competition between formation of highly stable MCs (larger lanthanides) and optimally linked bridging guests (smaller lanthanides).     

Colourings of cubic graphs inducing isomorphic monochromatic subgraphs

A -bisection of a bridgeless cubic graph is a -colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes ( monochromatic components in what follows) have order at most . Ban and Linial Conjectured that every bridgeless cubic graph admits a -bisection except for the Petersen graph. A similar problem for the edge set of cubic graphs has been studied: Wormald conjectured that every cubic graph with has a -edge colouring such that the two monochromatic subgraphs are isomorphic linear forests (ie, a forest whose components are paths). Finally, Ando conjectured that every cubic graph admits a bisection such that the two induced monochromatic subgraphs are isomorphic. In this paper, we provide evidence of a strong relation of the conjectures of Ban-Linial and Wormald with Ando's Conjecture. Furthermore, we also give computational and theoretical evidence in their support. As a result, we pose some open problems stronger than the above-mentioned conjectures. Moreover, we prove Ban-Linial's Conjecture for cubic-cycle permutation graphs. As a by-product of studying -edge colourings of cubic graphs having linear forests as monochromatic components, we also give a negative answer to a problem posed by Jackson and Wormald about certain decompositions of cubic graphs into linear forests.     

Fractional electrical model for modified bismuth oxide

Modified bismuth oxide (Bi₂O₃) is of great importance to fuel cells and oxide varistors. The electrical parameters of Bi₂O₃ vary with its modifying components as well as with its aging temperature. This paper presents an analysis of impedance test results carried out to find an equivalent electric model and the relationship between the model's elements to various additives used to modify Bi₂O₃ and to changes in aging temperature. The proposed model was tested via computer simulation and the model parameters correlated to individual modifiers.     

Growth, thermal stability and structure of ultrathin Zn-layers on Pd(1 1 1)

Low-energy ion scattering with monolayer sensitivity was applied to investigate ultrathin films of zinc on Pd(1?1?1). Uptake curves taken at 150?K indicate the simultaneous growth of multilayers with negligible interlayer transport. Annealing experiments for two-monolayer films reveal a rapid decrease in the zinc content on the surface layer at temperatures above 300?K, forming a metastable state with a Pd:Zn surface ratio of approx. 1:1 in the temperature region between 400 and 550?K. This state is most easily explained as a slightly buckled p(2?×?1)-PdZn surface alloy, with Zn atoms located approx. 0.25?? above their Pd counterparts.     

An $$H^1$$-Galerkin mixed finite element method for time fractional reaction–diffusion equation

In this article, an \(H^1\)-Galerkin mixed finite element (MFE) method for solving time fractional reaction–diffusion equation is presented. The optimal time convergence order \(O(\varDelta t^{2-\alpha })\) and the optimal spatial rate of convergence in \(H^1\) and \(L^2\)-norms for variable \(u\) and its gradient \(\sigma \) are derived. Moreover, some numerical results are shown to support our theoretical analysis.     

Ockham’s Calculus of Strict Implication

In his main work Summa Logicae written around 1323, William of Ockham developed a system of propositional modal logic which contains almost all theorems of a modern calculus of strict implication. This calculus is formally reconstructed here with the help of modern symbols for the operators of conjunction, disjunction, implication, negation, possibility, and necessity.