Exchange Transformation Research Articles

Anomalous dynamics in symmetric triangular irrational billiards

We identify a symmetry induced mechanism which dominates the long time behaviour in symmetric triangular billiards. We rigorously prove the existence of invariant sets in symmetric irrational billiards on which the dynamics is governed by an interval exchange transformation. Counterintuitively, this property of symmetric irrational billiards is analogous to the case of general rational billiards, and it highlights the non-trivial impact of symmetries in non-hyperbolic dynamical systems. Our findings provide an explanation for the logarithmic subdiffusive relaxation processes observed in certain triangular billiards. In addition we are able to settle a long standing conjecture about the existence of non-periodic and not everywhere dense trajectories in triangular billiards.

Molecular guest exchange and subsequent structural transformation in CH4 – CO2 replacement occurring in sH hydrates as revealed by 13C NMR spectroscopy and molecular dynamic simulations

This study adopted experimental and computational approaches to investigate CH4 – CO2 replacement in the structure H (sH) CH4 + methylcyclopentane (MCP) hydrate for its dual functions of CH4 recovery and CO2 sequestration. Hydrate phase equilibria, 13C NMR spectra, and molecular dynamics (MD) simulations of CH4 + MCP – CO2 replacement were examined and compared with those of CH4 + neohexane (NH) – CO2 replacement to elucidate the molecular guest exchange behaviors in both systems. The structure I (sI) hydrates were thermodynamically favored in CO2-rich gas mixtures (CH4 + CO2 + MCP systems), and a structural transformation from sH to sI occurred when CO2 composition in the feed gas was higher than 20 %. The 13C NMR spectra indicated that the CO2 molecules preferred to occupy the large (51262) cages of sI and the medium (435663) cages of sH compared to the small (512) cages of both sI and sH during replacement. Following CO2 injection into the sH CH4 + MCP hydrate, the initial sH hydrate transformed to the sI hydrate with CH4 recovery of approximately 78 %. The MD simulations also demonstrated that structural transformation in the CH4 + MCP – CO2 replacement would occur at the lower CO2 enclathration ratio compared to the CH4 + NH – CO2 replacement, thereby leading to a lower CO2 concentration in the newly formed sI hydrate. This is the first study to provide both experimental and computational evidence of guest-dependent structural transformation in sH CH4 + liquid hydrocarbons – CO2 replacement.

Smooth generalized interval exchange transformations with wandering intervals, from explicit derived from pseudo-Anosov maps

Starting from any pseudo-Anosov map ϕ on a surface of genus , we construct explicitly a family of Derived from pseudo-Anosov maps f by adapting the construction of Smale’s derived from Anosov maps on the two-torus. This is done by perturbing ϕ at some fixed points. We first consider perturbations at every conical fixed point and then at regular fixed points. We establish the existence of a measure µ, supported by the non-trivial unique minimal component of the stable foliation of f, with respect to which f is mixing. In the process, we construct a uniquely ergodic generalized interval exchange transformation (GIET) with a wandering interval that is semi-conjugated to a self-similar interval exchange transformation. This GIET is obtained as the Poincaré map of a flow renormalized by f which parametrizes stable foliation. When f is , the flow and the GIET are .

Versatile Layered Hydroxide Precursors for Generic Synthesis of Cu‐Based Materials

The ability to mix multiple elements in a structure is crucial for obtaining Cu‐based nanostructures and microstructures with desirable physicochemical properties. Precursors containing multiple metal cations, such as layered double hydroxides, have been used for the synthesis of multielement materials. However, these precursors experience difficulty containing large cations, which limits the functionalities of the derived materials. Herein, the development of Cu‐based hydroxy double salts (HDSs), versatile precursors that accommodate a broad range of metal cations with homogeneous distributions, is reported. Up to 25 different metal cations are mixed with Cu in an HDS single phase, individually and simultaneously. The HDSs further exhibit useful properties with respect to anion exchange, exfoliation, and phase transformation to metal oxides. During the metal oxide transformation process, the formed crystal structures are mainly dependent on the ionic radius of the secondary metal cations. To prove their utility as precursors, the metal oxides derived from the HDSs are tested and found that they exhibited high catalytic activities for CO oxidation. This study significantly expands the compositional and structural freedom of Cu‐based multi‐elemental materials.

Molecular Guest Exchange and Subsequent Structural Transformation in Ch4 – Co2 Replacement Occurring in Sh Hydrates as Revealed by 13c Nmr Spectroscopy and Molecular Dynamic Simulations

Molecular Guest Exchange and Subsequent Structural Transformation in Ch4 – Co2 Replacement Occurring in Sh Hydrates as Revealed by 13c Nmr Spectroscopy and Molecular Dynamic Simulations

Combined NMR and Isothermal Titration Calorimetry Investigation Resolves Conditions for Ligand Exchange and Phase Transformation in CsPbBr3 Nanocrystals

Combined NMR and Isothermal Titration Calorimetry Investigation Resolves Conditions for Ligand Exchange and Phase Transformation in CsPbBr₃ Nanocrystals

Local rigidity for periodic generalised interval exchange transformations

In this article we study local rigidity properties of generalised interval exchange maps using renormalisation methods. We study the dynamics of the renormalisation operator $$\mathcal {R}$$ acting on the space of $$\mathcal {C}^{3}$$ -generalised interval exchange transformations at fixed points (which are standard periodic type IETs). We show that $$\mathcal {R}$$ is hyperbolic and that the number of unstable direction is exactly that predicted by the ergodic theory of IETs and the work of Forni and Marmi–Moussa–Yoccoz. As a consequence we prove that the local $$\mathcal {C}^1$$ -conjugacy class of a periodic interval exchange transformation, with d intervals, whose associated surface has genus g and whose Lyapounoff exponents are all non zero is a codimension $$g-1 +d-1$$ $$\mathcal {C}^1$$ -submanifold of the space of $$\mathcal {C}^{3}$$ -generalised interval exchange transformations. This solves a conjecture analogous to that of Marmi–Moussa–Yoccoz, stated for almost all IETs, in the special case of self-similar IETs.

Restoration of heavy metal-contaminated soil and water through biosorbents: A review of current understanding and future challenges.

Heavy metal pollution in soil and water is a potential threat to human health as it renders food quality substandard. Different biosorbents such as microbial and agricultural biomass have been exploited for heavy metal immobilization in soil and sorptive removal in waters. Biosorption is an effective and sustainable method for heavy metal removal in soil and water, but the inherent challenges are to find cheap, selective, robust, and cost-effective bioadsorbents. Microbial and agricultural biomass and their modified forms such as nanocomposites and carbonaceous materials (viz., biochar, nanobiochar, biocarbon), might be useful for sequestration of heavy metals in soil via adsorption, ion exchange, complexation, precipitation, and enzymatic transformation mechanisms. In this review, potential biosorbents and their metal removal capacity in soil and water are discussed. The microbial adsorbents and modified composites of agricultural biomasses show improved performance, stability, reusability, and effectively immobilize heavy metals from soil and water. In the future, researchers may consider the modified composites, encapsulated biosorbents for soil and water remediation.

Unconventional Approaches in Coordination Chemistry and Organometallic Reactivity.

This contribution highlights a number of approaches developed by coordination and organometallic chemists that go beyond mainstream inorganic reactivity. A few of these strategies have been known for decades and are fundamental tools in synthesis and catalysis, while others are more recent and still belong to a niche. Through selected examples, we show herein how transmetalation, metal exchange, metal cooperativity, and catalytic transformation of metal complexes provide unique new opportunities to expand the reactivity arsenal of inorganic systems for synthetic and technological applications.

Porous granules formation from oil crops by extrusion process: a theoretical perspective

The introduction of extruders, in particular how it works and its principles, must be started from the definition of the extrusion process, the description of its development and types, as well as its functions and advantages. In order to understand the process of extrusion technology, it is necessary to go into detailed descriptions and discussions together with theoretical insights of the subject. In the present article, we discuss a theoretical perspective of production of porous granules from oil crops by extrusion technology. Let’s divide this theoretical perspective into three steps. At first, we study the modeling of statics of oil crop mix compressibility together with carbon dioxide. At second, we study the heat exchange and phase transformation during the stroke of oil crop extruder filled with CO2. At third, we observe the deformation of the oil crops during the extrusion process. There is a probability that extrusion process of oil crop mix with the hard phase of carbon dioxide provides technological way that does not overheat the cellular structure. Potentially, the equation of Van der Waals is able to describe the change in volume of oil crops, which may be related with range of factors associated with volume expansion, calculated by equations as the expansion of granule material takes place at the outlet of extruder matrix. The extrusion processing of a mix of oil crops and carbon dioxide in hard phase at initial stage may likely occur as temperature declines. The resulting values show good compliance of theoretical results to experimental data on the example of coriander seeds.

Synergistic Effect of Bridging Thiolate and Hub Atoms for the Aromaticity Driven Symmetry Breaking in Atomically Precise Gold Nanocluster.

The symmetry of atomically precise nanoclusters is influenced by the specific geometry of the kernel and the arrangement of staple motifs. To understanding the role of ligand and its effect on the breaking of symmetry during ligand exchange transformation, it is necessary to have a mechanism of transformation in an atomically precise manner. Herein, we report the structural transformation from bipyramidal kernel to icosahedral kernel via ligand exchange. The transformation of [Au23(CHT)16]- to [Au25(2-NPT)18]- through ligand (aromatic) exchange revealed two important principles. First, the combined effort of experimental and theoretical study on structural analysis elucidated the mechanism of this structural transformation where "bridging thiolate" and "hub" gold atoms play a crucial role. Second, we have found that the higher crystal symmetry of the Au23 cluster is broken to lower crystal symmetry during the ligand exchange process. This showed that during ligand exchange, the hub atoms and μ3-S atoms get distorted and contributed to the ligand-staple motif formation. These phenomena specified that the ligand effects might be the pivotal factor to impose lower symmetry of the crystal system in the product clusters.

Metal Nanoparticles Confronted with Foreign Ligands: Mere Ligand Exchange or Further Structural Transformation?

Ligand exchange reactions have attracted extensive interest due to their utility in tailoring the properties and applications of metal nanoparticles, but these techniques are not well understood due to the unclearness of metal nanoparticles at an atomic level. The emerging ultrasmall metal nanoparticles (metal nanoclusters) provide excellent opportunities for investigating this challenging issue. Herein, it is revealed that structurally similar Au25 (SC2 H4 Ph)18 , Au24 Cd(SC2 H4 Ph)18, and Au24 Hg(SC2 H4 Ph)18 transform to Au24 (SCH2 Ph-t Bu)20 , Au24 Cd(SCH2 Ph-t Bu)18 and ≈5nm gold nanoparticles after reacting with HSCH2 Ph-t Bu, respectively. Based on this and some other facts, it is suggested that the intrinsic stability is one key factor that determines the ligand exchange direction, whether by mere ligand exchange or further structure transformation (including aggregation). Single crystal X-ray crystallography further reveals that the partial surface ligand configuration reverses after ligand exchange, providing structure evidence for the unimolecular nucleophilic substitution (SN 1)-like mechanism.

Diversity and potential function of bacterial communities in different upwelling systems

Upwelling is one of the most important processes in the marine ecosystem and plays an important role in nutrient transport. However, the bacterial community structure and function of upwelling areas in the South China Sea (SCS) have received little attention. This study provides a systematic insight into bacterial diversity and predicted metabolic functions related to upwelling areas using Illumina Miseq sequencing. The results suggest that bacterial communities exhibit different patterns of spatial distribution in different upwelling systems, and provides evidence for phylogenetic taxonomy shaped by ecological preferences. The bacterial community displayed a significant vertical gradient in upwelling systems. Oceanospirillales, Alteromonadales, Sphingomonadales, Flavobacteriales, Rhodobacterales, and Bacillales were dominant in areas of coastal upwelling, while Oceanospirillales, Alteromonadales, Rhodobacterales, and Lactobacillales were also abundant in areas of oceanic upwelling. Whereas, Lactobacillales, Pseudomonadales, and Alteromonadales were dominant in non-upwelling regions and displayed a uniform distribution among different depths. The predicted metagenome showed that functional metabolism shifts were consistent with taxon responses. Most of the gene families were significantly enriched and were more abundant in upwelling than non-upwelling regions, indicating that bacteria could increase their ability for metabolic exchange and nutrient transformation due to the upwelling effect. This study emphasized that upwelling induces a shift in the upwelling-driven microbe and metabolic functions, resulting in obvious impacts on material transformation.

A convexity criterion for unique ergodicity of interval exchange transformations

A criterion for unique ergodicity for points of a curve in the space of interval exchange transformation is given.

Effects of speciation on uranium removal efficiencies with polyamine-functionalized silica composite adsorbent in groundwater

Uranium (Ⅵ) exists as many species in natural water systems. In the recent years, its contamination to groundwater has been reported more frequently. To investigate the effects of speciation on the removal of uranium, this work investigated the uranium adsorption behaviors of a polyamine-grafted silica composite named SAER at the concentration level of μg/L in the alkaline carbonate solutions with other four resins. Results suggested that the change of uranium speciation had minor effect on the adsorption efficiencies of SAER, except the addition of calcium. This was resulted from that the protonated tetraethylenepentamine had a much higher affinity to the electronegative uranyl-carbonate species, leading to the complete removal of uranium through the simultaneous anion exchange and chemical transformation mechanisms; Column experiments confirmed that merely a small portion of calcium while no magnesium cations were involved in the uranium adsorption in the simulated groundwater. Finally, the integrated removal mechanisms were proposed. Overall, this work demonstrated the feasibility of a novel adsorbent for the effective removal of uranium from different water matrices as well as the mechanisms underlying the interaction of uranium and the functional groups on the adsorbents. Furthermore, it enhanced the understanding of uranium removal under environmentally relevant conditions.

A setup for study of co-deposited films

A setup for investigation of thermal desorption spectra of gases accumulated in thin films deposited by plasma sputtering of solid targets is described. Deposition and thermal desorption spectroscopy (TDS) are performed in two different vacuum chambers separated by a gate valve with the sample transferred between the chambers in-vacuo. The temperature of the substrate for deposited films can be varied in the range of 300–800 K; and the deposition rate is controlled by a quartz microbalance. Thermal desorption of co-deposited gases is analyzed by a quadrupole mass spectrometer. Sputtering rate and evaporation of the film during TDS are measured by quartz microbalances. Three experiments are described 1) trapping of deuterium by the growing chemically active Li film with subsequent decomposition and evaporation of the film, 2) temperature dependent deuterium trapping in the growing W film resulting in trapping with several binding energies, and 3) chemical interaction of D-Li layer with water vapor leading to isotopic H-D exchange and chemical transformation of the deposited film.

Renormalizing an infinite rational IET

We study an interval exchange transformation of \begin{document}$ [0, 1] $\end{document} formed by cutting the interval at the points \begin{document}$ \frac{1}{n} $\end{document} and reversing the order of the intervals. We find that the transformation is periodic away from a Cantor set of Hausdorff dimension zero. On the Cantor set, the dynamics are nearly conjugate to the \begin{document}$ 2 $\end{document} –adic odometer.

Interaction of Phosphate with Lithium Cobalt Oxide Nanoparticles: A Combined Spectroscopic and Calorimetric Study.

Adsorption of small ions such as phosphates to the surfaces of metal oxides can significantly alter the behavior of these materials, especially when present in the nanoscale form. Lithium cobalt oxide is a good model system for understanding small-molecule interactions with emerging nanomaterials because of its widespread use in lithium ion batteries and its known activity as a water oxidation catalyst. Here, we present a thermodynamic analysis of phosphate adsorption to LiCoO2 and corroborate the results with additional in situ techniques, including zeta potential measurements and attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectroscopy, at pH values relevant to potential environmental release scenarios. Flow microcalorimetry measurements of phosphate interaction with LiCoO2 at pH 7.4 show that there are two distinct exothermic processes taking place. Time-sequence in situ ATR-FTIR with two-dimensional correlation analysis reveals the spectroscopic signatures of these processes. We interpret the data as an interaction of phosphate with LiCoO2 that occurs through the release of two water molecules and is therefore, best described as a condensation process rather than a simple adsorption, consistent with prior studies, demonstrating that phosphate interaction with LiCoO2 is highly irreversible. Additional measurements for over longer times of 5 months show that phosphate adsorption terminates with one surface layer and that continued transformation over longer periods of time arises from H+/Li+ exchange and slow transformation to a cobalt hydroxide, with phosphate adsorbed to the surface only. To the best of our knowledge, this is the first time that flow microcalorimetry and two-dimensional correlation spectroscopy have been applied in tandem to clarify the specific chemical reactions that occur at the interface of solids and adsorbates.

Symbolic dynamics of piecewise contractions

A map is a piecewise contraction of n intervals (n-PC) if there exist and a partition of into intervals such that for every (). An infinite word over the alphabet is a natural coding of f if there exists such that whenever . We prove that if is a natural coding of an injective n-PC, then some infinite subword of is either periodic or isomorphic to a natural coding of a topologically transitive m-interval exchange transformation (m-IET), where . Conversely, every natural coding of a topologically transitive n-IET is also a natural coding of some injective n-PC.

Coordination of a Single Calcium Ion in the EF-hand Maintains the Off State of the Stromal Interaction Molecule Luminal Domain

Store operated calcium (Ca2+) entry (SOCE) is the process whereby endoplasmic reticulum (ER) Ca2+ store depletion causes Orai1-composed Ca2+ channels on the plasma membrane (PM) to open, mediating a rise in cytosolic Ca2+ levels. Stromal interaction molecules (STIMs) are the proteins that directly sense ER Ca2+ content and gate Orai1 channels due to store depletion. The trigger for STIM activation is Ca2+ unbinding from the ER lumen-oriented domains, which consist of a nonconserved amino (N) terminal region and EF-hand and sterile α motif (SAM) domains (EF–SAM), highly conserved from humans to Caenorhabditis elegans. Solution NMR structures of the human EF–SAM domains have been determined at high Ca2+ concentrations; however, no direct structural view of the Ca2+ binding mode has been elucidated. Further, no atomic resolution data currently exists on EF–SAM at low Ca2+ levels. Here, we determined the X-ray crystal structure of the C. elegans STIM luminal domain, revealing that EF–SAM binds a single Ca2+ ion with pentagonal bipyramidal geometry and an ancillary α-helix formed by the N-terminal region acts as a brace to stabilize EF–SAM. Using solution NMR, we observed EF-hand domain unfolding and a conformational exchange between folded and unfolded states involving the ancillary α-helix and the canonical EF-hand in low Ca2+. Remarkably, we also detected an α-helix (+Ca2+) to β-strand (−Ca2+) transition at the terminal SAM domain α-helix. Collectively, our analyses indicate that one canonically bound Ca2+ ion is sufficient to stabilize the quiescent luminal domain structure, precluding unfolding, conformational exchange, and secondary structure transformation.