Algorithmic randomness of continuous functions

We investigate notions of randomness in the space ${{\mathcal C}(2^{\mathbb N})}We investigate notions of randomness in the space of continuous functions on . A probability measure is given and a version of the Martin-L?f test for randomness is defined. Random continuous functions exist, but no computable function can be random and no random function can map a computable real to a computable real. The image of a random continuous function is always a perfect set and hence uncountable. For any , there exists a random continuous function F with y in the image of F. Thus the image of a random continuous function need not be a random closed set. The set of zeroes of a random continuous function is always a random closed set. Research partially supported by the National Science Foundation grants DMS 0532644 and 0554841 and 00652732. Thanks also to the American Institute of Mathematics for support during 2006 Effective Randomness Workshop; Remmel partially supported by NSF grant 0400307; Weber partially supported by NSF grant 0652326. Preliminary version published in the Third International Conference on Computability and Complexity in Analysis, Springer Electronic Notes in Computer Science, 2006.     

Room Temperature Incorporation of Arsenic Atoms into the Germanium (001) Surface**

Germanium has emerged as an exceptionally promising material for spintronics and quantum information applications, with significant fundamental advantages over silicon. However, efforts to create atomic-scale devices using donor atoms as qubits have largely focused on phosphorus in silicon. Positioning phosphorus in silicon with atomic-scale precision requires a thermal incorporation anneal, but the low success rate for this step has been shown to be a fundamental limitation prohibiting the scale-up to large-scale devices. Here, we present a comprehensive study of arsine (AsH₃) on the germanium (001) surface. We show that, unlike any previously studied dopant precursor on silicon or germanium, arsenic atoms fully incorporate into substitutional surface lattice sites at room temperature. Our results pave the way for the next generation of atomic-scale donor devices combining the superior electronic properties of germanium with the enhanced properties of arsine/germanium chemistry that promises scale-up to large numbers of deterministically placed qubits.     

Scalable Synthesis and Electrocatalytic Performance of Highly Fluorinated Covalent Organic Frameworks for Oxygen Reduction

In this study, we present a novel approach for the synthesis of covalent organic frameworks (COFs) that overcomes the common limitations of non-scalable solvothermal procedures. Our method allows for the room-temperature and scalable synthesis of a highly fluorinated DFTAPB-TFTA-COF, which exhibits intrinsic hydrophobicity. We used DFT-based calculations to elucidate the role of the fluorine atoms in enhancing the crystallinity of the material through corrugation effects, resulting in maximized interlayer interactions, as disclosed both from PXRD structural resolution and theoretical simulations. We further investigated the electrocatalytic properties of this material towards the oxygen reduction reaction (ORR). Our results show that the fluorinated COF produces hydrogen peroxide selectively with low overpotential (0.062 V) and high turnover frequency (0.0757 s⁻¹) without the addition of any conductive additives. These values are among the best reported for non-pyrolyzed and metal-free electrocatalysts. Finally, we employed DFT-based calculations to analyse the reaction mechanism, highlighting the crucial role of the fluorine atom in the active site assembly. Our findings shed light on the potential of fluorinated COFs as promising electrocatalysts for the ORR, as well as their potential applications in other fields.     

A Mechanistic Perspective on the Mechanochemical Method To Reduce Carbonyl Groups with Stainless Steel and Water

Mechanochemistry through high-speed ball milling has become an increasingly popular method for performing organic transformations. This newfound interest in high-speed ball milling is in part driven by the benefit of performing reactions in the absence of solvent. Mechanochemical reactions are often conducted in stainless-steel vials with stainless-steel balls. Since stainless steel is made of several readily oxidizable metals (Fe, Cr, and Ni), reduction reactions using water as a hydrogen source were explored using a temperature-controlled mixer mill. Mechanistic studies suggest that the reduction proceeds via a single electron transfer (SET) pathway, with iron and nickel being essential components for the reaction.     

Intrinsically Chiral Twist-Bend Nematogens: Interplay of Molecular and Structural Chirality in the NTB Phase

The front cover artwork is provided by Dr Rebecca Walker of the Liquid Crystals Group at the University of Aberdeen. The image is a cartoon depiction of the formation of the heliconical chiral twist-bend nematic phase (N*_TB) from its constituent bent molecules. The presence of a single enantiomer of the chiral, lactate-based liquid crystal dimers biases the formation of helices with only one handedness, unlike in the conventional N_TB phase, observed for achiral molecules, for which the left- and right-handed helices are doubly degenerate. Read the full text of the Research Article at 10.1002/cphc.202200807 .     

Detection of targets colocalized in clutter by big brown bats (Eptesicus fuscus)

Echolocating big brown bats (Eptesicus fuscus) frequently catch insects during aerial pursuits in open spaces, but they also capture prey swarming on vegetation, and from substrates. To evaluate perception of targets on cluttered surfaces, big brown bats were trained in a two-alternative forced-choice task to locate a target, varying in height, that was embedded partway in holes (clutter) cut in a foam surface. The holes were colocalized with the possible positions of the target at distances ranging from 25 to 35 cm. For successful perception of the target, the bat had to detect the echoes contributed by the target in the same time window that contained echoes from the clutter. Performance was assessed in terms of target reflective strength relative to clutter strength in the same time window. The bats detected the target whenever the target strength was greater than 1-2 dB above the clutter.     

Nonlinear piezoelectricity in epitaxial ferroelectrics at high electric fields

Nonlinear effects in the coupling of polarization with elastic strain have been predicted to occur in ferroelectric materials subjected to high electric fields. Such predictions are tested here for a PbZr0.2Ti0.8O3 ferroelectric thin film at electric fields in the range of several hundred MV/m and strains reaching up to 2.7%. The piezoelectric strain exceeds predictions based on constant piezoelectric coefficients at electric fields from approximately 200 to 400 MV/m, which is consistent with a nonlinear effect predicted to occur at corresponding piezoelectric distortions.     

Theoretical study of Si+(2PJ)–RG complexes and transport of Si+(2PJ) in RG (RG = He–Ar)

We calculate accurate interatomic potentials for the interaction of a singly charged silicon cation with a rare gas atom of helium, neon or argon. We employ the RCCSD(T) method, and basis sets of quadruple-ζ and quintuple-ζ quality; each point is counterpoise-corrected and extrapolated to the basis set limit. We consider the lowest electronic state of the silicon atomic cation, Si⁺(²P), and calculate the interatomic potentials for the terms that arise from this: ²Π and ²Σ⁺. We additionally calculate the interatomic potentials for the respective spin-orbit levels, and examine the effect on the spectroscopic parameters; we also derive effective ionic radii for C⁺ and Si⁺. Finally, we employ each set of potentials to calculate transport coefficients, and compare these to available data for Si⁺ in He.