Existence and uniqueness of positive periodic solutions for a neutral Logarithmic population model

In this paper, by using an abstract continuous theorem of k-set contractive operator, the criteria is established for the existence, global attractivity of positive periodic solution of a neutral delay Logarithmic population model with multiple delays. The result improve the known ones in [S.P. Lu, W.G. Ge, Existence of positive periodic solutions for neutral Logarithmic population model with multiple delays, J. Comput. Appl. Math. 166 (2) (2004) 371-383].     

Well-posedness of the spatially homogeneous Landau equation for soft potentials

We consider the spatially homogeneous Landau equation of kinetic theory, and provide a differential inequality for the Wasserstein distance with quadratic cost between two solutions. We deduce some well-posedness results. The main difficulty is that this equation presents a singularity for small relative velocities. Our uniqueness result is the first one in the important case of soft potentials. Furthermore, it is almost optimal for a class of moderately soft potentials, that is for a moderate singularity. Indeed, in such a case, our result applies for initial conditions with finite mass, energy, and entropy. For the other moderately soft potentials, we assume additionally some moment conditions on the initial data. For very soft potentials, we obtain only a local (in time) well-posedness result, under some integrability conditions. Our proof is probabilistic, and uses a stochastic version of the Landau equation, in the spirit of Tanaka [H. Tanaka, Probabilistic treatment of the Boltzmann equation of Maxwellian molecules, Z. Wahrsch. Verw. Geb. 46 (1) (1978-1979) 67-105].     

矩阵方程X+A^{*}X^{-q}A=Q(q\geq 1)的Hermitian正定解

本文研究矩阵方程X A~*X~(-q)A=Q(q≥1)的Hermitian正定解,给出了存在正定解的充分条件和必要条件,构造了求解的迭代方法.最后还用数值例子验证了迭代方法的可行性和有效性.     

Global stability and asymptotics of some classes of rational difference equations

In this note we prove that the positive solutions of some classes of rational difference equations are globally asymptotically stable. Using a Berg's result, we also find asymptotics of some solutions of these equations.     

Experimental characterization of dynamic behaviour of gelatin-based material using DIC

In this paper, the dynamic response of gelatin-based soft material under impact loading is investigated. The dynamic tests are principally performed by the classical SHPB (Split Hopkinson Pressure Bars) technique. However, due to the very low mechanical impedance of the specimen compared with the Hopkinson bars, the feeble impact forces are measured by highly sensitive piezoelectric polyvinylidene fluoride (PVDF) pressure sensors instead of SHPB measurement system. The PVDF pressure sensors are placed on the interfaces between the specimen and the bars. During the impact test, the non-equilibrium stress state and inhomogeneous strain fields are developed in the specimen; a digital image correlation (DIC) technique is proposed to identify the inhomogeneous displacement fields using high speed photography. A non-parametric approach based on the DIC technique is developed to deduce the transient stress fields in the longitudinal and transverse directions from the displacement fields measured by DIC. The validation of the calculated stress fields is performed by comparing them with the stress measurements from the PVDF pressure sensor at the bottom end of the specimen. Furthermore, stress-strain response is carried out using this approach throughout the specimen. It is clearly shown that the average highest strain rate varies with position in the specimen. This lead to multiple stress-strain relations determined at different strain rates by only one impact test. The significant strain rate sensitivity is observed at the tested rate range from 81/s to 269/s. Under compression loading, the axial stress state is developed as a simple compression only in the central part of the specimen due to the friction at the interfaces between the specimen and the bars. According to the calculated results based on movement of “long waves”, the region of the simple compression stress state in the central part of the specimen is localized. It is observed that the axial stress is much more important than the transverse stress in the central part and this confirms the assumption of uni-axial compression stress state in the specimen.     

Mechanically Strong Janus Poly(N-isopropylacrylamide)/Graphene Oxide Hydrogels as Thermo-responsive Soft Robots

Simple preparation of stimuli-responsive hydrogels with good mechanical properties and mild stimuliresponsiveness is essential for their applications as smart soft robots.Mechanically strong Janus poly(Nisopropylacrylamide)/graphene oxide (PNIPAM/GO) nanocomposite hydrogels with stimuli-responsive bending behaviors are prepared through a simple one-step method by using molds made of a Teflon plate and a glass plate.Residual oxygen in the air bubbles on the Teflon plate surface affects the polymerization and hence the cross-linking density,leading to the different swelling/deswelling rates of the two sides of the gels.Therefore,the hydrogels exhibit bending/unbending behaviors upon heating/cooling in water.The incorporation of GO nanosheets dramatically enhances the mechanical properties of Janus hydrogels.Meanwhile,the photo-responsive property of the GO nanosheets also imparts the hydrogels with remotecontrollable deformation under IR irradiation.The application of the Janus PNIPAM/GO hydrogels as thermo-responsive grippers is demonstrated.     

Micro-patterning of vapor-phase polymerized poly(3,4-ethylenedioxythiophene) (PEDOT) using ink-jet printing/soft lithography

Highly conductive and transparent poly(3,4-ethylenedioxythiophene) (PEDOT) thin films can be prepared effectively via vapor-phase polymerization (VPP) with the addition of imidazole (Im) based derivatives. The addition of Im that has one and/or two alkyl substituents significantly improved the electrical conductivity of PEDOT thin films. In an effort to develop a facile PEDOT micro-patterning method, we investigated ink-jet printing and soft lithography. The procedure of oxidant patterning with a weak base followed by VPP of a 3,4-ethylenedioxythiophene (EDOT) monomer provides an effective and simple method for micro-patterning of an intrinsic conductive polymer (ICP).     

Peptide-induced patterning of gold nanoparticle thin films

In this work, the use of patterned proteins and peptides for the deposition of gold nanoparticles on several substrates with different surface chemistries is presented. The patterned biomolecule on the surface acts as a catalyst to precipitate gold nanoparticles from a precursor solution of HAuCl₄ onto the substrate. The peptide patterning on the surfaces was accomplished by physical adsorption or covalent attachment. It was shown that by using covalent attachment with a linker molecule, the influence of the surface properties from the different substrates on the biomolecule adsorption and subsequent nanoparticle deposition could be avoided. By adjusting the reaction conditions such as pH or HAuCl₄ concentration, the sizes and morphologies of deposited gold nanoparticle agglomerates could be controlled. Two biomolecules were used for this experiment, 3XFLAG peptide and bovine serum albumin (BSA). A micro-transfer molding technique was used to pattern the peptides on the substrates, in which a pre-patterned poly(dimethylsiloxane) (PDMS) mold was used to deposit a lift-off pattern of polypropylmethacrylate (PPMA) on the various substrates. The proteins were either physically adsorbed or covalently attached to the substrates, and an aqueous HAuCl₄ solution was applied on the substrates with the protein micropatterns, causing the precipitation of gold nanoparticles onto the patterns. SEM, AFM, and Electron Beam Induced Current (EBIC) were used for characterization.