Role of dimensionality and axisymmetry in fluid pinch-off and coalescence

We present data on the pinch-off and coalescence of thin liquid alkane lenses floating on water. Pinch-off in quasi-2D lenses is distinctly different from pinch-off in axisymmetric 3D drops and involves a cascade of satellite droplets which extends to micron length scales. In contrast, coalescence of lenses is qualitatively similar to coalescence of 3D drops. Coalescence is predicted to involve entrainment of the exterior fluid as the droplets merge. This reentrant folding is obscured in 3D droplets but is clearly visible in coalescence of thin lenses.     

Actinobacterial Peroxidases: an Unexplored Resource for Biocatalysis

Peroxidases are redox enzymes that can be found in all forms of life where they play diverse roles. It is therefore not surprising that they can also be applied in a wide range of industrial applications. Peroxidases have been extensively studied with particular emphasis on those isolated from fungi and plants. In general, peroxidases can be grouped into haem-containing and non-haem-containing peroxidases, each containing protein families that share sequence similarity. The order Actinomycetales comprises a large group of bacteria that are often exploited for their diverse metabolic capabilities, and with recent increases in the number of sequenced genomes, it has become clear that this metabolically diverse group of organisms also represents a large resource for redox enzymes. It is therefore surprising that, to date, no review article has been written on the wide range of peroxidases found within the actinobacteria. In this review article, we focus on the different types of peroxidases found in actinobacteria, their natural role in these organisms and how they compare with the more well-described peroxidases. Finally, we also focus on work remaining to be done in this research field in order for peroxidases from actinobacteria to be applied in industrial processes.     

Smoothed integral equations

For a linear integral equation there is a resolvent equation and a variation of parameters formula . It is assumed that B is a perturbed convex function and that a(t) may be badly behaved in several ways. When the first two equations are treated separately by means of a Liapunov functional, restrictive conditions are required separately on a(t) and B(t,s). Here, we treat them as a single equation where S is an integral combination of a(t) and B(t,s). There are two distinct advantages. First, possibly bad behavior of a(t) is smoothed. Next, properties of S needed in the Liapunov functional can be obtained from an array of properties of a(t) and B(t,s) yielding considerable flexibility not seen in standard treatment. The results are used to treat nonlinear perturbation problems. Moreover, the function is shown to converge pointwise and in L²[0,∞) to x(t).     

Maximal admissible faces and asymptotic bounds for the normal surface solution space

The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significant improvements upon the best known asymptotic bounds on the number of admissible vertices, using polytopes in both the standard normal surface coordinate system and the streamlined quadrilateral coordinate system.To achieve these results we examine the layout of admissible points within these polytopes. We show that these points correspond to well-behaved substructures of the face lattice, and we study properties of the corresponding “admissible faces”. Key lemmata include upper bounds on the number of maximal admissible faces of each dimension, and a bijection between the maximal admissible faces in the two coordinate systems mentioned above.     

Relaxation and Recovery in Hydrogel Friction on Smooth Surfaces

Background

Hydrogels are crosslinked polymer networks that can absorb and retain a large fraction of liquid. Near a critical sliding velocity, hydrogels pressed against smooth surfaces exhibit time-dependent frictional behavior occurring over multiple timescales. The origin of these dynamics is unresolved

Objective

Here, we characterize this time-dependent regime and show that it is consistent with two distinct molecular processes: sliding-induced relaxation and quiescent recovery.

Methods

Our experiments use a custom pin-on-disk tribometer to examine poly(acrylic acid) hydrogels on smooth poly(methyl methacrylate) surfaces over a variety of sliding conditions, from minutes to hours.

Results

We show that at a fixed sliding velocity, the friction coefficient decays exponentially and reaches a steady-state value. The time constant associated with this decay varies exponentially with the sliding velocity, and is sensitive to any precedent frictional shearing of the interface. This process is reversible; upon cessation of sliding, the friction coefficient recovers to its original state. We also show that the initial direction of shear can be imprinted as an observable “memory”, and is visible after 24 hrs of repeated frictional shearing.

Conclusions

We attribute this behavior to nanoscale extension and relaxation dynamics of the near-surface polymer network, leading to a model of frictional relaxation and recovery with two parallel timescales.

     

The chemistry of phase selectivity in the synthesis of high-silica zeolites

In this review we discuss the roles that inorganic and organic components play in the synthesis of high-silica zeolites. We discuss the effects that heteroatom identity, heteroatom substitution, and SDA shape have on synthesis products. Then we summarize recent developments in zeolite synthesis that have been made by performing syntheses in concentrated fluoride media and by using germanium as a tetravalent heteroatom. Finally, we examine the combined roles that framework stability, framework/SDA interactions, and silanol defects may have in determining phase selectivity.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

Coupling routes to hexafluoro-1,3-butadiene, substituted-1,3-fluorine-containing butadienes and fluorinated polyenes

Hexafluoro-1,3-butadiene was readily prepared via a variety of self-coupling processes, such as Cu(0) mediated self-coupling of iodotrifluoroethene, Pd(0) catalyzed coupling of iodotrifluoroethene with the trifluorovinylzinc reagent, and CuBr₂ mediated coupling of the trifluorovinylzinc reagent. Perfluoro-2,3-dimethyl-1,3-butadiene was readily synthesized by the reaction of pentafluoropropenyl-2-zinc reagent with either CuBr₂ or FeCl₃. Alternatively, perfluoro-2,3-dimethyl-1,3-butadiene was prepared by oxidation of the pentafluoropropenyl-2-copper reagent with dioxygen. Cu(0) mediated coupling of an (E)-substituted ,β-difluoro-β-iodostyrene provided the first useful route to a (Z)(Z)-1,4-diaryl-1,3-tetrafluorobutadiene. Extension of the Cu(0) mediated coupling methodology to a perfluorodienyl iodide demonstrated a useful stereospecific route to perfluoropolyenes.