On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior

In the light of the visual angle model (VAM), an improved car-following model considering driver's visual angle, anticipated time and stabilizing driving behavior is proposed so as to investigate how the driver's behavior factors affect the stability of the traffic flow. Based on the model, linear stability analysis is performed together with bifurcation analysis, whose corresponding stability condition is highly fit to the results of the linear analysis. Furthermore, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived by nonlinear analysis, and we obtain the relationship of the two equations through the comparison. Finally, parameter calibration and numerical simulation are conducted to verify the validity of the theoretical analysis, whose results are highly consistent with the theoretical analysis.     

Hitherto-Unexplored Photodynamic Therapy of Ag2S and Enhanced Regulation Based on Polydopamine In Vitro and Vivo

Given their superior penetration depths, photosensitizers with longer absorption wavelengths present broader application prospects in photodynamic therapy (PDT). Herein, Ag₂S quantum dots were discovered, for the first time, to be capable of killing tumor cells through the photodynamic route by near-infrared light irradiation, which means relatively less excitation of the probe compared with traditional photosensitizers absorbing short wavelengths. On modification with polydopamine (PDA), PDA-Ag₂S was obtained, which showed outstanding capacity for inducing reactive oxygen species (increased by 1.69 times). With the addition of PDA, Ag₂S had more opportunities to react with surrounding O₂, which was demonstrated by typical triplet electron spin resonance (ESR) analysis. Furthermore, the PDT effects of Ag₂S and PDA-Ag₂S achieved at longer wavelengths were almost identical to the effects produced at 660 nm, which was proved by studies in vitro. PDA-Ag₂S showed distinctly better therapeutic effects than Ag₂S in experiments in vivo, which further validated the enhanced regulatory effect of PDA. Altogether, a new photosensitizer with longer absorption wavelength was developed by using the hitherto-unexplored photodynamic function of Ag₂S quantum dots, which extended and enhanced the regulatory effect originating from PDA.     

Mass distribution and skewness for passive scalar transport in pipes with polygonal and smooth cross sections

We extend our previous results characterizing the loading properties of a diffusing passive scalar advected by a laminar shear flow in ducts and channels to more general cross‐sectional shapes, including regular polygons and smoothed corner ducts originating from deformations of ellipses. For the case of the triangle and localized, cross‐wise uniform initial distributions, short‐time skewness is calculated exactly to be positive, while long‐time asymptotics shows it to be negative. Monte Carlo simulations confirm these predictions, and document the timescale for sign change. The equilateral triangle appears to be the only regular polygon with this property—all others possess positive skewness at all times. Alternatively, closed‐form flow solutions can be constructed for smooth deformations of ellipses, and illustrate how both nonzero short‐time skewness and the possibility of multiple sign switching in time is unrelated to domain corners. Exact conditions relating the median and the skewness to the mean are developed which guarantee when the sign for the skewness implies front (more mass to the right of the mean) or back (more mass to the left of the mean) “loading” properties of the evolving tracer distribution along the pipe. Short‐ and long‐time asymptotics confirm this condition, and Monte Carlo simulations verify this at all times. The simulations are also used to examine the role of corners and boundaries on the distribution for short‐time evolution of point source , as opposed to cross‐wise uniform, initial data.     

Strain induced strengthening of soft thermoplastic polyurethanes under cyclic deformation

We investigate the cyclic mechanical behavior in uniaxial tension of three different commercial thermoplastic polyurethane elastomers (TPU) often considered as a sustainable replacement for common filled elastomers. All TPU have similar hard segment contents and linear moduli but sensibly different large strain properties as shown by X-ray analysis. Despite these differences, we found a stiffening effect after conditioning in step cyclic loading which greatly differs from the common softening (also referred as Mullins effect) observed in chemically crosslinked filled rubbers. We propose that this self-reinforcement is related to the fragmentation of hard domains, naturally present in TPU, in smaller but more numerous sub-units that may act as new physical crosslinking points. The proposed stiffening mechanism is not dissimilar to the strain-induced crystallization observed in stretched natural rubber, but it presents a persistent nature. In particular, it may cause a local reinforcement where an inhomogeneous strain field is present, as is the case of a crack propagating in cyclic fatigue, providing a potential explanation for the well-known toughness and wear resistance of TPU.     

Morphology and microphase separation of star copolymers

Star copolymers have attracted significant interest due to their different characteristics compared with diblock copolymers, including higher critical micelle concentration, lower viscosity, unique spatial shape, or morphologies. Development of synthetic skills such as anionic polymerization and controlled radical polymerization have made it possible to make diverse architectures of polymers. Depending on the molecular architecture of the copolymer, numerous morphologies are possible, for instance, Archimedean tiling patterns and cylindrical microdomains at symmetric volume fraction for miktoarm star copolymers as well as asymmetric lamellar microdomains for star‐shaped copolymers, which have not been reported for linear block copolymers. In this review, we focus on morphologies and microphase separations of miktoarm (A_mB_n and ABC miktoarm) star copolymers and star‐shaped [(A‐b‐B)_n] copolymers with nonlinear architecture. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1–21     

Finite‐size corrections at the hard edge for the Laguerre β ensemble

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general .