Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

[Nb@Ge13/14]3−: New Family Members of Ge-Based Intermetalloid Clusters

During the past two decades, single-atom-centered medium-sized germanium clusters [M@Ge_n] (M=transition metals, n>12) have been extensively explored, both from theoretical perspectives and experimental gas-phase syntheses. However, the actual structural arrangements of the Ge₁₃ and Ge₁₄ endohedral cages are still ambiguous and have long remained an unresolved problem for experimental implementation. In this work, we successfully synthesize 13-/14-vertex Ge clusters [Nb@Ge₁₃]³⁻ ( 1 ) and [Nb@Ge₁₄]³⁻ ( 2 ), which are structurally characterized and exhibit unprecedented topologies, neither classical deltahedra nor 3-connected polyhedral structures. Theoretical analysis indicates that the major stabilization of the Ge backbones arises due to the substantial interaction of Ge 4p-AOs with the endohedral Nb 4d-AOs through three/four-center two-electron bonds with an enhanced electron density accumulated over the shortest Nb−Ge13 contact in 1 . Low occupancies of the direct two-center two-electron (2c–2e) Nb−Ge and Ge−Ge σ bonds point to a considerable degree of electron delocalization over the Ge cages revealing their electron deficiency.     

Strong Pancake 2e/12c Bond in π-Stacking Phenalenyl Derivatives Avoiding Bond Conversion

The nature of the 2e/12c bond and its conversion to a carbon-carbon single bond in phenalenyl dimers have prompted a great deal of interests recently. In this work, we theoretically investigated a series of π-stacking phenalenyl derivatives with 2e/12c bonding character by density functional theory (DFT) calculations to elucidate origin of this unusual bond conversion. Results show that bond-conversion of the phenalenyl dimer easily occurs at room-temperature both dynamically and thermodynamically. However, bond-conversion of hetero π-stacking adducts, in which the two center carbon atoms were substituted by boron and nitrogen atoms, respectively, is much more difficult, because the 2e/12c bond is stabilized by its charge transfer character. Consequently, the bond-conversion is an endothermic process, albeit with a low conversion barrier. Interestingly, Lewis acid-base interactions would be induced by substitution of the center nitrogen atom to phosphorus atom. The 2e/12c bond is further stabilized by 5.9 kcal mol⁻¹ and its conversion is also thermodynamically unfavorable.     

Uncertainty quantification for dynamics of geometrically nonlinear structures coupled with internal acoustic fluids in presence of sloshing and capillarity

In this paper, we propose an uncertainty quantification analysis, which is the continuation of a recent work performed in a deterministic framework. The fluid–structure system under consideration is the one experimentally studied in the sixties by Abramson, Kana, and Lindholm from the Southwest Research Institute under NASA contract. This coupled system is constituted of a linear acoustic liquid contained in an elastic tank that undergoes finite dynamical displacements, inducing geometrical nonlinear effects in the structure. The liquid has a free surface on which sloshing and capillarity effects are taken into account. The problem is expressed in terms of the acoustic pressure field in the fluid, of the displacement field of the elastic structure, and of the normal elevation field of the free surface. The nonlinear reduced-order model constructed in the recent work evoked above is reused for implementing the nonparametric probabilistic approach of uncertainties. The objective of this paper is to present a sensitivity analysis of this coupled fluid–structure system with respect to uncertainties and to use a classical statistical inverse problem for carrying out the experimental identification of the hyperparameter of the stochastic model. The analysis show a significant sensitivity of the displacement of the structure, of the acoustic pressure in the liquid, and of the free-surface elevation to uncertainties in both linear and geometrically nonlinear simulations.     

Unconventional Secondary Structure Mimics: Ladder-Rungs

Secondary structures tend to be recognizable because they have repeating structural motifs, but mimicry of these does not have to follow such well-defined patterns. Bioinformatics studies to match side-chain orientations of a novel hydantoin triazole chemotype ( 1 ) to protein-protein interfaces revealed it tends to align well across parallel and antiparallel sheets, like rungs on a ladder. One set of these overlays was observed for the protein-protein interaction uPA⋅uPAR. Consequently, chemotype 1 was made with appropriate side-chains to mimic uPA at this interface. Biophysical assays indicate these compounds did in fact bind uPAR, and elicit cellular responses that affected invasion, migration, and wound healing.     

Reconciling Electrostatic and n→π* Orbital Contributions in Carbonyl Interactions

Interactions between carbonyl groups are prevalent in protein structures. Earlier investigations identified dominant electrostatic dipolar interactions, while others implicated lone pair n→π* orbital delocalisation. Here these observations are reconciled. A combined experimental and computational approach confirmed the dominance of electrostatic interactions in a new series of synthetic molecular balances, while also highlighting the distance-dependent observation of inductive polarisation manifested by n→π* orbital delocalisation. Computational fiSAPT energy decomposition and natural bonding orbital analyses correlated with experimental data to reveal the contexts in which short-range inductive polarisation augment electrostatic dipolar interactions. Thus, we provide a framework for reconciling the context dependency of the dominance of electrostatic interactions and the occurrence of n→π* orbital delocalisation in C=O⋅⋅⋅C=O interactions.     

Hydrodynamic instability of premixed flame propagating in narrow planar channel in the presence of gas flow

The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.     

Measurement of the hydrodynamic radii of PEE-G dendrons by diffusion spectroscopy on a benchtop NMR spectrometer

Benchtop nuclear magnetic resonance (NMR) spectroscopy is a useful tool for the rapid determination of the self-diffusion coefficient and the hydrodynamic radius of dendrons. The self-diffusion coefficients of the first four generations of poly ethoxy ethyl glycinamide (PEE-G) dendrons are measured by diffusion-ordered spectroscopy (DOSY) on a benchtop NMR equipped with diffusion gradient coils. The hydrodynamic radii of the dendrons are calculated via the Stokes–Einstein equation. The effects of solvent and pH are determined with the hydrodynamic radius increasing with generation and decreasing upon neutralization of an acidic solution. These measurements provide valuable information for biological and pharmaceutical applications of dendrons.     

Optimization of anionic conductivity through the coexistence of ionomer cluster and backbone-backbone morphologies in anion exchange membranes

Random copolymers of poly(4-vinylpyridine) and polyisoprene were synthesized, and subsequently quaternized with 1-alkylbromides. The number of carbons on the pendant side-chain of the resultant comb-shaped polymer, n, ranged from 2–8. The comb-shaped polymers were crosslinked employing thiol-ene chemistry to give mechanically robust ion conducting membranes. Analysis by wide and medium-angle X-ray scattering show three morphology regimes that are dependent on the number of carbons on the pendant side-chains. When n = 2, ionomer cluster morphology was dominant, when n = 8 backbone-backbone morphology was dominant, and when n = 3–6, the membrane showed a coexistence of both ionomer cluster and backbone-backbone morphologies. Evaluation of the water uptake of the membranes showed a maximum water uptake per cation of 9.5 when n = 5 at 95% relative humidity (RH) and 60°C. Conductivity of the samples characterized by electrochemical impedance spectroscopy showed bromide conductivity as high as 110 mS/cm when n = 3 at 95% RH and 90°C.