Interactions of the vector breathers for the coupled Hirota system with $$4\times 4$$ 4 × 4 Lax pair

Nonlinear Dynamics - In this paper, we investigate the interactions of the vector breathers for the coupled Hirota system with $$4\times 4$$ Lax pair. Firstly, we give the first-order breather...     

Study on the Relationship between Emulsion Properties and Interfacial Rheology of Sugar Beet Pectin Modified by Different Enzymes

The contribution of rheological properties and viscoelasticity of the interfacial adsorbed layer to the emulsification mechanism of enzymatic modified sugar beet pectin (SBP) was studied. The component content of each enzymatic modified pectin was lower than that of untreated SBP. Protein and ferulic acid decreased from 5.52% and 1.08% to 0.54% and 0.13%, respectively, resulting in a decrease in thermal stability, apparent viscosity, and molecular weight (Mw). The dynamic interfacial rheological properties showed that the interfacial pressure and modulus (E) decreased significantly with the decrease of functional groups (especially proteins), which also led to the bimodal distribution of particle size. These results indicated that the superior emulsification property of SBP is mainly determined by proteins, followed by ferulic acid, and the existence of other functional groups also promotes the emulsification property of SBP.     

Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.     

Random copolymerization of macromonomers as a versatile strategy to synthesize mixed-graft block copolymers

The random copolymerization of norbornene-functionalized macromonomers was explored as a method of synthesizing mixed-graft block copolymers (mGBCPs). The copolymerization kinetics of a model system of polystyrene (PS) and poly(lactic acid) (PLA) macromonomers was first analyzed, revealing a gradient composition of side chains along the mGBCP backbone. The phase separation behavior of mGBCPs with PS and PLA side chains of various backbone lengths and side chain molar ratios was investigated, and increasing the backbone length was found to stabilize the phase-separated nanostructures. The graft architecture was also demonstrated to improve the processability of the mGBCP, compared to a linear counterpart. Investigations of mGBCPs comprised of polydimethylsiloxane and poly(ethylene oxide) side chains exemplified the diverse self-assembled morphologies, including a Frank-Kasper A15 phase, that can be obtained with mGBCPs synthesized by random copolymerization of macromonomers. Lastly, a ternary mGBCP was synthesized by the copolymerization of three macromonomers.     

Time-dependent Ginzburg–Landau equations for multi-gap superconductors

We numerically solve the time-dependent Ginzburg–Landau equations for two-gap superconductors using the finite-element technique. The real-time simulation shows that at low magnetic field, the vortices in small-size samples tend to form clusters or other disorder structures. When the sample size is large, stripes appear in the pattern. These results are in good agreement with the previous experimental observations of the intriguing anomalous vortex pattern, providing a reliable theoretical basis for the future applications of multi-gap superconductors.     

Synthesis and Self-Assembly of Mixed-Graft Block Copolymers

Mixed-graft block copolymers (mGBCPs) consist of two or more types of polymeric side chains grafted on a linear backbone in a random, alternating, or pseudo-alternating sequence. They can phase-separate with the backbone serving as the interface of the blocks, and the side chains dominate their self-assembly behavior. mGBCPs are an accessible polymer architecture for exploring the idea of encoding polymer properties through the macromolecular architecture, as there are two distinct structural components that can be tuned: the backbone and the side chains. In this Concept article, the current literature on the synthesis of mGBCPs is reviewed, and the advantages and disadvantages of each synthetic method are noted. The self-assembly of mGBCPs is also discussed where possible. Finally, directions for future research on mGBCP synthesis and self-assembly are suggested.