Quasi-steady deformation of a two-dimensional bubble placed within a potential viscous flow

The shape evolution of a two-dimensional bubble, bounded by a simple closed curve, which is initially placed within a potential viscous flow, is analysed. It is assumed that the influence of gravity and inertia forces is negligible, so the quasi-steady approximation can be applied. Reformulating the problem for Stokes equations with relevant boundary conditions at the free surface in terms of the bianalytic stress-stream function, and using the time-dependent conformal mappingz(,t) of a unit disk onto an unbounded flow domain sought, an infinite system of ordinary differential equations for the Laurent coefficients ofz(,t) is derived. A class of exact solutions is found for the case when the principal part of the complex velocity of the dominant flow at infinity is a polynomial, and the problem of formation of a pointed bubble is discussed.

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Sommario E analizzata l'evoluzione di una bolla bi-dimensionale, limitata da una curva chiusa semplice, inizialmente posta in un flusso potenziale viscoso. Si assume che l'influenza della gravità e delle forze inerziali sia trascurabile, cosicchè si può applicare l'approssimazione quasi-stazionaria. Riformulando il problema per le equazioni di Stokes con le opportune condizionial contorno sulla superficie libera in termini della funzione stress-stream bianalitica, e usando la tecnica delle trasformazioni conformi dipendenti dal tempoz(,t) di un disco unitario su un dominio di flusso non limitato incognito, viene derivato un sistema infinito di equazioni differenziali ordinarie per i coefficienti di Laurent diz(,t). Viene trovata una classe di soluzioni esatte per il caso in cui la parte principale della velocità complessa del flusso dominante all'infinito è una polinomiale, ed è discusso il problema della formazione di una bolla lenticolare.

     

Formic and acetic acids in a nitrogen matrix: Enhanced stability of the higher-energy conformer

Formic acid (HCOOH, FA) and acetic acid (CH(3)COOH, AA) are studied in a nitrogen matrix. The infrared (IR) spectra of cis and trans conformers of these carboxylic acids (and also of the HCOOD isotopologue of FA) are reported and analyzed. The higher-energy cis conformer of these molecules is produced by narrowband near-IR excitation of the more stable trans conformer, and the cis-to-trans tunneling decay is evaluated spectroscopically. The tunneling process in both molecules is found to be substantially slower in a nitrogen matrix than in rare-gas matrices, the cis-form decay constants being approximately 55 and 600 times smaller in a nitrogen matrix than in an argon matrix, for FA and AA respectively. The stabilization of the higher-energy cis conformer is discussed in terms of specific interactions with nitrogen molecule binding with the OH group of the carboxylic acid. This model is in agreement with the observed differences in the IR spectra in nitrogen and argon matrices, in particular, the relative frequencies of the νOH and τCOH modes and the relative intensities of the νOH and νC=O bands.     

Site-directed mutagenesis combined with oxidative methionine labeling for probing structural transitions of a membrane protein by mass spectrometry

Exposure of the membrane protein bacteriorhodopsin (BR) to SDS induces partial breakdown of the native conformation. The exact structural properties of this SDS state remain a matter of debate, despite its widespread use in BR folding experiments. The current work employs hydroxyl radical (·OH) labeling in conjunction with mass spectrometry (MS)-based peptide mapping for probing the solvent accessibility of individual BR segments in the presence of SDS. Previous work revealed methionine sulfoxide formation to be the dominant oxidative pathway. Those data suggested extensive unfolding of helices A and D in SDS. Unfortunately, the lack of Met residues in helices C and F implies that no direct information on the behavior of the latter two elements could be obtained. Here, we address this problem by employing two variants with additional Met residues, L93M (helix C) and V179M (helix F). The oxidation behavior of the resulting 11 methionines can be grouped into three categories: (1) extensively labeled both in native BR and in SDS (loop residues M32, M68, and M163); (2) protected in the native state but not in SDS (M20, M118); (3) always protected (M56, M60, M93, M145, M179, M209). These data show that a solvent-inaccessible core is retained in SDS. This core consists of partially intact helices B, C, E, F, and G. The termini of these helices are highly dynamic and/or unraveled, particularly on the cytoplasmic side. Overall, this work demonstrates how the use of engineered ·OH labeling sites can provide insights into structural properties of membrane proteins.     

Towards the Accurate Calculation of 183W NMR Chemical Shifts in Polyoxometalates: The Relevance of the Structure

DFT calculations were carried out to study ¹⁸³W NMR chemical shifts in the family of the Keggin anions with formula α‐[XW₁₂O₄₀]^q? (X=B, Al, Si, P, Ga, Ge, As, Zn), in the β‐ and γ‐[SiW₁₂O₄₀]^4? geometric isomers, in the derivative Dawson anion [P₂W₁₈O₆₂]^6?, and in the most symmetrical Lindqvist [W₆O₁₉]^2? anion and its derivative [W₁₀O₃₂]^4?. In this article, we show that the geometry employed in the calculation of NMR chemical shifts in polyoxotungstates is extremely important if we want to be quantitative. Using very large basis sets of QZ4P quality and taking into account the conductor‐like screening model (COSMO) to account for solvent effects (aqueous and organic solutions), good geometries were found for the polyoxoanions. From these optimal geometries the ¹⁸³W NMR chemical shifts were computed with the more standard basis sets of TZP quality and including spin–orbit corrections inside the zero‐order regular approximation (ZORA) to describe the relativistic effects of the internal electrons. With this strategy the mean absolute error between experimental and theoretical values was found to be less than 10 ppm, which is similar to the experimental error. We also discuss how the geometry of the polyoxoanion influences on the shielding.     

A critical look at the definition of multidimensional separations

Multidimensional (MD) separations, especially comprehensive two-dimensional (2D) separations such as comprehensive 2D LC (LC × LC), and comprehensive 2D GC (GC × GC), are potentially powerful separation techniques. It is important to have a clear definition of MD techniques to better understand the scope and boundaries of the subject. Widely accepted definitions of MD Separations have their roots in the definition proposed by Giddings. Giddings also added several comments that clarified the scope of his definition. However, some researchers extend Giddings’ definitions beyond their intended scope. Doing so disqualifies such comprehensive 2D techniques as LC × LC, GC × GC and 2D TLC from being considered as 2D techniques. In other instances, extended treatment of Giddings’ definition is used as a basis to justify design-parameters of comprehensive 2D separations despite the fact that these parameters lead to sub-optimal implementations. We believe that the shortcomings in the definition and its popular interpretations are serious enough to warrant attention, especially by those interested in designing optimal instrumentation for MD separations like comprehensive 2D GC. After discussion of the weaknesses in the currently used definitions, we propose to define n-dimensional analysis as one that generates n-dimensional displacement information. We believe that this definition captures the spirit of Giddings’ definition while avoiding the problems associated with its popular interpretations.     

Intermittent synchronization in a network of bursting neurons

Synchronized oscillations in networks of inhibitory and excitatory coupled bursting neurons are common in a variety of neural systems from central pattern generators to human brain circuits. One example of the latter is the subcortical network of the basal ganglia, formed by excitatory and inhibitory bursters of the subthalamic nucleus and globus pallidus, involved in motor control and affected in Parkinson's disease. Recent experiments have demonstrated the intermittent nature of the phase-locking of neural activity in this network. Here, we explore one potential mechanism to explain the intermittent phase-locking in a network. We simplify the network to obtain a model of two inhibitory coupled elements and explore its dynamics. We used geometric analysis and singular perturbation methods for dynamical systems to reduce the full model to a simpler set of equations. Mathematical analysis was completed using three slow variables with two different time scales. Intermittently, synchronous oscillations are generated by overlapped spiking which crucially depends on the geometry of the slow phase plane and the interplay between slow variables as well as the strength of synapses. Two slow variables are responsible for the generation of activity patterns with overlapped spiking, and the other slower variable enhances the robustness of an irregular and intermittent activity pattern. While the analyzed network and the explored mechanism of intermittent synchrony appear to be quite generic, the results of this analysis can be used to trace particular values of biophysical parameters (synaptic strength and parameters of calcium dynamics), which are known to be impacted in Parkinson's disease.     

Approximate analytical solution to normal emittance of semi-transparent layer of an absorbing, scattering, and refracting medium

A two-step approximate analytical solution for the normal emittance of a plane layer of an absorbing, scattering and refracting medium is derived analytically. The analysis is based on the transport approximation and the two-step solution method for radiative transfer. The high accuracy of the approximate solution, examined by comparing its results to those obtained independently by the discrete ordinates and Monte Carlo methods, makes it suitable for application in combined experimental-analytical studies to identify selected spectral radiative properties of dispersed media in the range of semi-transparency.     

Nonequilibrium evolution thermodynamics of vacancies

An alternative approach, nonequilibrium evolution thermodynamics, is compared with the classical Landau approach. A statistical justification of the approach is done with the help of a probability distribution function on an example of a solid with vacancies. Two kinds of kinetic equations are derived in terms of the internal energy and the modified free energy.     

Chirality-assisted electronic cloaking of confined States in bilayer graphene

We show that the strong coupling of pseudospin orientation and charge carrier motion in bilayer graphene has a drastic effect on transport properties of ballistic p-n-p junctions. Electronic states with zero momentum parallel to the barrier are confined under it for one pseudospin orientation, whereas states with the opposite pseudospin tunnel through the junction totally uninfluenced by the presence of confined states. We demonstrate that the junction acts as a cloak for confined states, making them nearly invisible to electrons in the outer regions over a range of incidence angles. This behavior is manifested in the two-terminal conductance as transmission resonances with non-Lorentzian, singular peak shapes. The response of these phenomena to a weak magnetic field or electric-field-induced interlayer gap can serve as an experimental fingerprint of electronic cloaking.     

Sensitizing of Sm<Superscript>3+</Superscript> fluorescence by silver dopant in the TiO<Subscript>2</Subscript> films

Composite material based on a TiO₂ matrix doped with Sm³⁺ ions and co-doped with silver was investigated. Samarium ions together with nano- and micro-aggregates of silver were incorporated into the titanium alkoxide during the sol-gel process. Samarium ions were excited either directly (λ _exc = 488 nm) or through the TiO₂ host (λ _exc = 355 nm). It was revealed that samarium fluorescence (λ _exc = 488 nm) in gelled TiO₂ films is enhanced by up to 20 times in the vicinity of silver inclusions. Sensitizing and plasmonic mechanisms of enhancement in Sm³⁺ fluorescence are discussed.