A RANS 3D model with unbounded eddy viscosities

We consider the Reynolds Averaged Navier–Stokes (RANS) model of order one (u,p,k)$(\mathbf{u},p,k)$ set in R³${\mathbb{R}}^3$ which couples the Stokes Problem to the equation for the turbulent kinetic energy by k-dependent eddy viscosities in both equations and a quadratic term in the k  -equation. We study the case where the velocity and the pressure satisfy periodic boundary conditions while the turbulent kinetic energy is defined on a cell with Dirichlet boundary conditions. The corresponding eddy viscosity in the fluid equation is extended to R³${\mathbb{R}}^3$ by periodicity. Our contribution is to prove that this system has a solution when the eddy viscosities are nondecreasing, smooth, unbounded functions of k, and the eddy viscosity in the fluid equation is a concave function.     

A comprehensive analysis in one run – in-depth conformation studies of protein–polymer chimeras by asymmetrical flow field-flow fractionation

Polymer-based protein engineering has enabled the synthesis of a variety of protein–polymer conjugates that are widely applicable in therapeutic, diagnostic and biotechnological industries. Accurate characterizations of physical–chemical properties, in particular, molar masses, sizes, composition and their dispersities are critical parameters that determine the functionality and conformation of protein–polymer conjugates and are important for creating reproducible manufacturing processes. Most of the current characterization techniques suffer from fundamental limitations and do not provide an accurate understanding of a sample''s true nature. In this paper, we demonstrate the advantage of asymmetrical flow field-flow fractionation (AF4) coupled with multiple detectors for the characterization of a library of complex, zwitterionic and neutral protein–polymer conjugates. This method allows for determination of intrinsic physical properties of protein–polymer chimeras from a single, rapid measurement.

Precise characterization of structural parameters and their polydispersities of protein–polymer conjugates is performed with rapid analysis using asymmetrical flow field-flow fractionation coupled with multiple detectors.     

Ultrafast X-ray experiments on structural changes in single crystals of polar molecules

Intramolecular charge transfer in aminobenzonitrile (DIABN) single crystals is studied by a combination of ultrafast techniques. The intramolecular dynamics is probed by time-resolved spectroscopy in the UV/Vis and mid-IR. The intermolecular structural response is investigated by transient X-ray scattering and transmission experiments. A theoretical analysis shows that diffuse scattering and dipole solvation determine the X-ray data. The observed dynamics results from charge transfer reaction leading to strong local changes of molecular dipole moments and related structural rearrangements in the crystal.     

Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons

We report results of the first analysis of collisions between stable fundamental (alias spinless) and vortical (spinning) three-dimensional dissipative solitons in a model of a laser cavity. The systematic analysis is carried out for values S=1 and S=2 of the vorticity of the latter soliton. With the increase of the collision momentum, Χ, the same generic scenarios are observed in either case: merger into a single fundamental soliton at both small and relatively large values of Χ, and the formation of two fundamental solitons in an intermediate interval of variation of the collision momentum Χ. At very large values of Χ, the collision seems quasi-elastic, but the vortex soliton eventually splits into two nonspinning fragments.     

On-line preferential solvation studies of polymers by coupled chromatographic-Fourier transform infrared spectroscopic flow-cell technique

Qualitative and quantitative comparison between liquid chromatography (LC) and LC coupled with Fourier transform infrared spectroscopy (LC-FTIR) to evaluate preferential solvation phenomenon of polymers in a mixed solvent has been performed. These studies show that LC-FTIR technique leads to detailed structural information without the requirement for determination of additional parameters for quantitative analysis except calibration. Appropriate experimental conditions for preferential solvation study have been established by variation of polymer concentration, molar mass and eluent content.     

Impact of slow gain dynamics on soliton molecules in mode-locked fiber lasers

We theoretically demonstrate and experimentally confirm the major influence of gain dynamics on soliton molecules that self-assemble in mode-locked lasers. Both slow gain recovery and depletion play a pivotal role in the formation of chirped soliton molecules characterized by an increasing separation from leading to trailing pulses. These chirped molecules actually consist of many pulses and may be termed macromolecules. They are experimentally observed in a fiber laser and numerically modeled by an approach that properly includes the slow gain dynamics. Furthermore, it is shown that these processes stabilize soliton trains in fiber lasers by inhibiting internal oscillations.     

Aggregating Knockoffs for False Discovery Rate Control with an Application to Gut Microbiome Data

Recent discoveries suggest that our gut microbiome plays an important role in our health and wellbeing. However, the gut microbiome data are intricate; for example, the microbial diversity in the gut makes the data high-dimensional. While there are dedicated high-dimensional methods, such as the lasso estimator, they always come with the risk of false discoveries. Knockoffs are a recent approach to control the number of false discoveries. In this paper, we show that knockoffs can be aggregated to increase power while retaining sharp control over the false discoveries. We support our method both in theory and simulations, and we show that it can lead to new discoveries on microbiome data from the American Gut Project. In particular, our results indicate that several phyla that have been overlooked so far are associated with obesity.     

Holon kinetic energy in the RVB state

We have used a low energy variational RVB wave function to evaluate the kinetic energy of holons in the dilute limit. We report results on a 5×5 cluster; from the first 8 moments of the density of states, we estimate a lower band edge for the holon, which is fairly insensitive to details of the RVB wave function. This band edge is higher than the corresponding one for a hole in the Néel state, by about 0.08t, in the limitU/t.