Paradigms and Paradoxes: Fractional and Other Non-integer Charges in Chemistry—an Understanding of Aromaticity

Structural Chemistry - In the current study, the energetics of fractionally (and indeed arbitrary non-integer) charged species is explicitly discussed for the enhanced understanding of aromaticity...     

Imprisoned lightning: charge transport in trehalose-derived sugar glasses

Trehalose is a naturally occurring disaccharide noted for its ability to preserve the biological function of proteins and cell membranes during periods of stress—such as water deprivation or extreme temperature—by stabilizing the conformations of the macromolecules within a glassy matrix. This phenomenon makes use of the propensity for trehalose to interact strongly with protein functional groups and solvent water molecules via hydrogen bonding. Previously, it has been shown that trehalose sugar glasses also support long-range charge transport in oxidation-reduction reactions occurring between spatially separated donors and acceptors. Here, through the use of bulk Arrhenius DC-conductivity measurements, we infer that this anomalously high carrier mobility is due to proton hopping along a hydrogen bonding network formed by sorbed “water wires,” a process known as the Grotthuss mechanism. Additionally, we find that the apparent activation energy of the conductivity depends non-monotonically on the bias voltage. The possibility is raised for novel photovoltaic devices based on the entrapment of photosynthetic proteins within these glasses.     

Design and experimental validation of a nonlinear controller for underactuated surface vessels

Nonlinear Dynamics - This paper addresses the problem of trajectory tracking control of an underactuated surface vessel moving in a two-dimensional space in the presence of unknown disturbances. In...     

When does every definable nonempty set have a definable element?

The assertion that every definable set has a definable element is equivalent over $\mathsf{ZF}$ to the principle $\mathbf{V}=\mathbf{HOD}$, and indeed, we prove, so is the assertion merely that every Π₂‐definable set has an ordinal‐definable element. Meanwhile, every model of $\mathsf{ZFC}$ has a forcing extension satisfying $\mathbf{V}\ne \mathbf{HOD}$ in which every Σ₂‐definable set has an ordinal‐definable element. Similar results hold for $\mathbf{HOD}(\mathbb{R})$ and $\mathbf{HOD}({\mathrm{Ord}}^{\omega })$ and other natural instances of $\mathbf{HOD}(X)$.     

Interplay of thermochemistry and Structural Chemistry,the journal (volume 29, 2018, issues 3–4) and the discipline

The contents of issues 3 and 4 of Structural Chemistry from the calendar year 2018 are summarized in the present review. A brief thermochemical commentary and recommendations for future research have been added to the summary of each paper.

     

Development and analysis of a malaria transmission mathematical model with seasonal mosquito life-history traits

In this paper, we develop and analyze a malaria model with seasonality of mosquito life-history traits: periodic-mosquitoes per capita birth rate, -mosquitoes death rate, -probability of mosquito to human disease transmission, -probability of human to mosquito disease transmission, and -mosquitoes biting rate. All these parameters are assumed to be time dependent leading to a nonautonomous differential equation system. We provide a global analysis of the model depending on two threshold parameters and (with ). When , then the disease-free stationary state is locally asymptotically stable. In the presence of the human disease-induced mortality, the global stability of the disease-free stationary state is guarantied when . On the contrary, if , the disease persists in the host population in the long term and the model admits at least one positive periodic solution. Moreover, by a numerical simulation, we show that a sub-critical (backward) bifurcation is possible at . Finally, the simulation results are in accordance with the seasonal variation of the reported cases of a malaria-epidemic region in Mpumalanga province in South Africa.     

Cover Picture: Turning Spiroketals Inside Out: A Rearrangement Triggered by an Enol Ether Epoxidation (ChemistryOpen 5/2015)

Invited for this month''s cover picture is the group of Professor Mark Peczuh at the University of Connecticut. The cover picture compares the rearrangement of a small molecule to the process of turning a stuffed animal inside out. The recycled, inside-out stuffed animals are both artistic and philosophically provocative. They capture the essence of the rearrangement reaction because the compounds themselves turn inside out over the course of the reaction, extending the diversity of products that can arise from simple starting materials. Small molecules often have functional groups with latent reactivity; under the appropriate conditions, those groups can react with other compounds (e.g., reagents) and also with other groups in the same molecule in an intramolecular reaction. The research team found that the epoxidation of some highly functionalized spiroketal compounds promoted rearrangements of their structures that turned them inside out. Some of the features of the products led them to use X-ray crystallography or a combination of computer-assisted structure elucidation, computation, and a new version of the 1,1-ADEQUATE NMR experiment to determine their structures. For more details, see the Communication on p. 577 ff.     

A multigrid perspective on the parallel full approximation scheme in space and time

For the numerical solution of time‐dependent partial differential equations, time‐parallel methods have recently been shown to provide a promising way to extend prevailing strong‐scaling limits of numerical codes. One of the most complex methods in this field is the “Parallel Full Approximation Scheme in Space and Time” (PFASST). PFASST already shows promising results for many use cases and benchmarks. However, a solid and reliable mathematical foundation is still missing. We show that, under certain assumptions, the PFASST algorithm can be conveniently and rigorously described as a multigrid‐in‐time method. Following this equivalence, first steps towards a comprehensive analysis of PFASST using blockwise local Fourier analysis are taken. The theoretical results are applied to examples of diffusive and advective type.