An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.     

Emergent biaxiality in nematic microflows illuminated by a laser beam

Anisotropic fluids (e.g. liquid crystals) offer a remarkable promise as optofluidic materials owing to the directional, tunable, and coupled interactions between the material, flow, and the optical fields. Here we present a comprehensive in silico treatment of this anisotropic interaction by performing nonequilibrium molecular dynamics simulations. We quantify the response of a nematic liquid crystal (NLC) undergoing a Poiseuille flow in the Stokes regime, while being illuminated by a laser beam incident perpendicular to the flow direction. We adopt a minimalistic model to capture the interactions, accounting for two features: first, the laser heats up the NLC locally; and second, the laser polarises the NLC and exerts an optical torque that tends to reorient molecules of the nematic phase. Because of this reorientation the liquid crystal exhibits small regions of biaxiality, where the nematic director is one symmetry axis and the axis of rotation for the reorientation of the molecules is the other one. We find that the relative strength of the viscous and the optical torques mediates the flow-induced response of the biaxial regions, thereby tuning the emergence, shape and location of the regions of enhanced biaxiality. The mechanistic framework presented here promises experimentally tractable routes toward novel optofluidic applications based on material-flow-light interactions.     

On <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">r</Emphasis></Superscript>-closing for flows on orientable and non-orientable 2-manifolds

We provide an affirmative answer to the C ^r -Closing Lemma, r ≥ 2, for a large class of flows defined on every closed surface.     

Spherical T-Duality

We introduce spherical T-duality, which relates pairs of the form (P, H) consisting of a principal SU(2)-bundle \({P \rightarrow M}\) and a 7-cocycle H on P. Intuitively spherical T-duality exchanges H with the second Chern class c ₂(P). Unless \({dim(M) \leq 4}\), not all pairs admit spherical T-duals and the spherical T-duals are not always unique. Nonetheless, we prove that all spherical T-dualities induce a degree-shifting isomorphism on the 7-twisted cohomologies of the bundles and, when \({dim(M) \leq 7}\), also their integral twisted cohomologies and, when \({dim(M) \leq 4}\), even their 7-twisted K-theories. While spherical T-duality does not appear to relate equivalent string theories, it does provide an identification between conserved charges in certain distinct IIB supergravity and string compactifications.     

Synthesis of nanoplate bismuth oxychloride—a visible light active material

We have synthesized bismuth oxychloride (BiOCl) by wet chemical route. Characterization of the synthesized samples has been carried out using XRD, SEM with EDAX, HRTEM, FT-IR, Raman Spectroscopy, PL and UV. XRD and SEM analysis confirms crystallite size varying from 20–40 nm. FTIR spectrum indicates that the prepared material is highly pure and there is no water molecule present. Raman and photoluminescence spectrum of the bismuth oxychloridenanoplate demonstrated strong blue light emission which brings them in a special class of materials which work under visible light exposure. UV-Vis spectroscopy shows very less charge carriers transit time under visible light thus confirming excellent photocatalytic properties of material.     

On cutting sequences of the <Emphasis Type="Italic">L</Emphasis>-shaped translation surface tiled by three squares

We consider a symbolic coding of bi-infinite non periodic geodesics on the L-shaped translation surface tiled by three squares. Each bi-infinite non periodic geodesic is associated with a cutting sequence corresponding to the sequence of labeled saddle connections hit. We prove that there is a relationship between the cutting sequences and the actions of some affine automorphisms of the translation surface. We also get an explicit formula to determine the direction of a bi-infinite non periodic geodesic by using the corresponding cutting sequence.     

A comparative study of the complexation of Am(III) and Eu(III) with TODGA in room temperature ionic liquid

On the growing awareness of the environmental impact associated with the use of volatile organic diluents, room temperature ionic liquid gained world-wild acceptance as environmentally benign diluents for actinide partitioning. The observed unusual behavior of less extraction efficiency of Eu with TODGA in RTIL in comparison with that of Am-TODGA was addressed in this paper. The stoichiometry of Am-TODGA complex was found to be 1:2 while that of Eu-TODGA was 1:1. More the ligand molecules associated in the metal ligand complex, the organophilicity of the complex will be more and the solubility of the metal–ligand complex in RTIL will be more which reflects in the higher distribution ratio for Am. In RTIL both Am and Eu showed slower kinetics of extraction with TODGA which can be attributed to the high viscosity coefficient of RTIL compared to the molecular diluents. The observed slower kinetics of extraction was quantified and found to follow first order kinetics with the rate constant of 5.5 × 10^?4 s^?1. The formation constant of Am-TODGA complex was found to be more (4.18 × 10⁸ M^?1) than Eu-TODGA complex (3.31 × 10⁸ M^?1) in RTIL. The parameters viz. diffusion coefficient, activation energy for Eu(III)/Eu(II) were determined and found to be 3.08 × 10^?8/cm² s^?1 (at 303 K) and 39.34 kJ mol^?1 respectively. The thermodynamic parameters ΔG, ΔH and ΔS for the reaction were evaluated using the linear regression of the plot of E ^0* versus T. The redox reaction was found to be exothermic with decrease in entropy value.     

Exploring the Structural Insights on Human Laforin Mutation K87A in Lafora Disease—A Molecular Dynamics Study

Lafora disease (LD) is an autosomal recessive, progressive form of myoclonus epilepsy which affects worldwide. LD occurs mainly in countries like southern Europe, northern Africa, South India, and in the Middle East. LD occurs with its onset mainly in teenagers and leads to decline and death within 2 to 10 years. The genes EPM2A and EPM2B are commonly involved in 90 % of LD cases. EPM2A codes for protein laforin which contains an amino terminal carbohydrate binding module (CBM) belonging to the CBM20 family and a carboxy terminal dual specificity phosphatase domain. Mutations in laforin are found to abolish glycogen binding and have been reported in wet lab methods. In order to investigate on structural insights on laforin mutation K81A, we performed molecular dynamics (MD) simulation studies for native and mutant protein. MD simulation results showed loss of stability due to mutation K87A which confirmed the structural reason for conformational changes observed in laforin. The conformational change of mutant laforin was confirmed by analysis using root mean square deviation, root mean square fluctuation, solvent accessibility surface area, radius of gyration, hydrogen bond, and principle component analysis. Our results identified that the flexibility of K87A mutated laforin structure, with replacement of acidic amino acid to aliphatic amino acid in functional CBM domain, have more impact in abolishing glycogen binding that favors LD.     

Padé approximants for functions with branch points — strong asymptotics of Nuttall–Stahl polynomials

Let f be a germ of an analytic function at infinity that can be analytically continued along any path in the complex plane deprived of a finite set of points, \({f \in \mathcal{A}(\bar{\mathbb{C}} \setminus A)}\), \({\# A< \infty}\). J. Nuttall has put forward the important relation between the maximal domain of f where the function has a single-valued branch and the domain of convergence of the diagonal Padé approximants for f. The Padé approximants, which are rational functions and thus single-valued, approximate a holomorphic branch of f in the domain of their convergence. At the same time most of their poles tend to the boundary of the domain of convergence and the support of their limiting distribution models the system of cuts that makes the function f single-valued. Nuttall has conjectured (and proved for many important special cases) that this system of cuts has minimal logarithmic capacity among all other systems converting the function f to a single-valued branch. Thus the domain of convergence corresponds to the maximal (in the sense of minimal boundary) domain of single-valued holomorphy for the analytic function \({f\in\mathcal{A}(\bar{\mathbb{C}} \setminus A)}\). The complete proof of Nuttall’s conjecture (even in a more general setting where the set A has logarithmic capacity 0) was obtained by H. Stahl. In this work, we derive strong asymptotics for the denominators of the diagonal Padé approximants for this problem in a rather general setting. We assume that A is a finite set of branch points of f which have the algebro-logarithmic character and which are placed in a generic position. The last restriction means that we exclude from our consideration some degenerated “constellations” of the branch points.