The optimal shape of a pipe

In shape optimization, recently the question arose, whether or not the cylindrical pipe has the optimal shape for the transport of an incompressible fluid. In this short note, a proof will be presented that a cylindrical pipe with Poiseuille’s flow inside indeed is optimal for the transportation of an incompressible fluid under the criterion “energy dissipated by the fluid.” The proof reduces the problem to the minimization of a two-dimensional Dirichlet’s integral. This simpler problem can be solved with a symmetrization argument.     

On the Coriolis effect in acoustic waveguides

Rotation of an elastic medium gives rise to a shift of frequency of its acoustic modes, i.e., the time-period vibrations that exist in it. This frequency shift is investigated by applying perturbation theory in the regime of small ratios of the rotation velocity and the frequency of the acoustic mode. In an expansion of the relative frequency shift in powers of this ratio, upper bounds are derived for the first-order and the second-order terms. The derivation of the theoretical upper bounds of the first-order term is presented for linear vibration modes as well as for stable nonlinear vibrations with periodic time dependence that can be represented by a Fourier series.     

o-minimal analytic separation of sets in dimension 2

We study the Hardy field associated with an o-minimal expansion of the real numbers. If the set of analytic germs is dense in the Hardy field, then we can definably analytically separate sets in ${\mathbb{R}}^2$, and we can definably analytically approximate definable continuous unary functions. A similar statement holds for definable smooth functions.     

Cooperative Effect of Noncovalent Interactions on Tetrel Bonding in Halogenated Silanes

Tetrel bond, a weak noncovalent interaction between the σ-hole of a Group IV element (silicon in our case) and the cloud of an electronegative element (oxygen in our case) is the focus of this work. The percentage strengthening of tetrel bond has been investigated by optimizing 16 binary complexes of halogenated silane and water of general formula SiX_nH_4−n−H₂O and 16 ternary complexes, of general formula NaX−SiX_nH_4−n−H₂O, where X=F, Cl, Br and I and n=1, 2, 3 and 4 at various levels of theory defined within the formalism of density functional theory (DFT). With the addition of NaX, tetrel bond between Si and O in SiX_nH_4−n−H₂O gets strengthened up to 49 %, owing to cooperativity effect exerted by hydrogen bonding between X and H in the ternary complex NaX−SiX_nH_4−n−H₂O. In the series of complexes studied here, overall stabilization due to cooperativity lies between 10 kJ/mol to 170 kJ/mol. This large extent of reinforcement due to cooperativity has never been showcased before. The exceptional stabilization and reinforcement owe its genesis to the transformation of the ternary complex into a cluster orchestrated by the H-bonding in most of the cases and covalent bonding in few of the cases.     

A Chimeric DNA/RNA Antiparallel Quadruplex with Improved Stability

Nucleic acid quadruplexes are proposed to play a role in the regulation of gene expression, are often present in aptamers selected for specific binding functions and have potential applications in medicine and biotechnology. Therefore, understanding their structure and thermodynamic properties and designing highly stable quadruplexes is desirable for a variety of applications. Here, we evaluate DNA→RNA substitutions in the context of a monomolecular, antiparallel quadruplex, the thrombin-binding aptamer (TBA, GGTTGGTGTGGTTGG) in the presence of either K⁺ or Sr²⁺. TBA predominantly folds into a chair-type configuration containing two G-tetrads, with G residues in both syn and anti conformation. All chimeras with DNA→RNA substitutions (G→g) at G residues requiring the syn conformation demonstrated strong destabilization. In contrast, G→g substitutions at Gs with anti conformation increased stability without affecting the monomolecular chair-type topology. None of the DNA→RNA substitutions in loop positions affected the quadruplex topology; however, these substitutions varied widely in their stabilizing or destabilizing effects in an unpredictable manner. This analysis allowed us to design a chimeric DNA/RNA TBA construct that demonstrated substantially improved stability relative to the all-DNA construct. These results have implications for a variety of quadruplex-based applications including for the design of dynamic nanomachines.     

Mechanistic Insights into the Interface‐Directed Transformation of Thiols into Disulfides and Molecular Hydrogen by Visible‐Light Irradiation of Quantum Dots

Quantum dots (QDs) offer new and versatile ways to harvest light energy. However, there are few examples involving the utilization of QDs in organic synthesis. Visible‐light irradiation of CdSe QDs was found to result in virtually quantitative coupling of a variety of thiols to give disulfides and H₂ without the need for sacrificial reagents or external oxidants. The addition of small amounts of nickel(II) salts dramatically improved the efficiency and conversion through facilitating the formation of hydrogen atoms, thereby leading to faster regeneration of the ground‐state QDs. Mechanistic studies reveal that the coupling reaction occurs on the QD surfaces rather than in solution and offer a blueprint for how these QDs may be used in other photocatalytic applications. Because no sacrificial agent or oxidant is necessary and the catalyst is reusable, this method may be useful for the formation of disulfide bonds in proteins as well as in other systems sensitive to the presence of oxidants.     

Constraining Cyclic Peptides To Mimic Protein Structure Motifs

Many proteins exert their biological activities through small exposed surface regions called epitopes that are folded peptides of well‐defined three‐dimensional structures. Short synthetic peptide sequences corresponding to these bioactive protein surfaces do not form thermodynamically stable protein‐like structures in water. However, short peptides can be induced to fold into protein‐like bioactive conformations (strands, helices, turns) by cyclization, in conjunction with the use of other molecular constraints, that helps to fine‐tune three‐dimensional structure. Such constrained cyclic peptides can have protein‐like biological activities and potencies, enabling their uses as biological probes and leads to therapeutics, diagnostics and vaccines. This Review highlights examples of cyclic peptides that mimic three‐dimensional structures of strand, turn or helical segments of peptides and proteins, and identifies some additional restraints incorporated into natural product cyclic peptides and synthetic macrocyclic peptidomimetics that refine peptide structure and confer biological properties.     

Mechanically Interlocked Single‐Wall Carbon Nanotubes

Extensive research has been devoted to the chemical manipulation of carbon nanotubes. The attachment of molecular fragments through covalent‐bond formation produces kinetically stable products, but implies the saturation of some of the C? C double bonds of the nanotubes. Supramolecular modification maintains the structure of the SWNTs but yields labile species. Herein, we present a strategy for the synthesis of mechanically interlocked derivatives of SWNTs (MINTs). In the key rotaxane‐forming step, we employed macrocycle precursors equipped with two π‐extended tetrathiafulvalene SWNT recognition units and terminated with bisalkenes that were closed around the nanotubes through ring‐closing metathesis (RCM). The mechanically interlocked nature of the derivatives was probed by analytical, spectroscopic, and microscopic techniques, as well as by appropriate control experiments. Individual macrocycles were observed by HR STEM to circumscribe the nanotubes.     

An Aluminophosphate Molecular Sieve with 36 Crystallographically Distinct Tetrahedral Sites

The structure of the new medium‐pore aluminophosphate molecular sieve PST‐6 is determined by the combined use of rotation electron diffraction tomography, synchrotron X‐ray powder diffraction, and computer modeling. PST‐6 was prepared by calcination of another new aluminophosphate material with an unknown structure synthesized using diethylamine as a structure‐directing agent, which is thought to contain bridging hydroxy groups. PST‐6 has 36 crystallographically distinct tetrahedral sites in the asymmetric unit and is thus crystallographically the most complex zeolitic structure ever solved.