Standard Systems of Discrete Differentiable Dynamical Systems

The theory of Liao standard systems of difference equations for discrete differentiable dynamical systems over compact manifolds has been developed. Some relations between the topological structures of their phase portraits and that of their corresponding linear systems have been presented as well.     

A Nonstandard Finite Difference Scheme for Solving One Dimensional Nonlinear Heat Transfer

A nonstandard finite difference scheme is developed to solve an initial-boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. Not only does the scheme satisfy the positivity condition, but it is also stable for large values of the equation parameters.     

Convergence in Law to Operator Fractional Brownian Motions

In this paper, we provide two approximations in law of operator fractional Brownian motions. One is constructed by Poisson processes, and the other generalizes a result of Taqqu (Z. Wahrscheinlichkeitstheor. Verw. Geb. 31:287–302, 1975).     

Size effects on tensile and fatigue behaviour of polycrystalline metal foils at the micrometer scale

Tensile and fatigue properties of as-rolled and annealed polycrystalline Cu foils with different thicknesses at the micrometer scale were investigated. Uniaxial tensile testing results showed that with decreasing foil thickness the uniform elongation decreases for both as-rolled and annealed foils, whereas the yield strength and ultimate tensile strength increase for as-rolled foils, but decrease for the annealed foils. For both the as-rolled or annealed foils, bending fatigue resistance decreases with decreasing the foil thickness. Deformation and fatigue damage behaviour of the free-standing foils were characterised as a function of foil thickness. In addition, the fatigue strength of various small-scale Cu foils was compared to understand the physical mechanisms of size effects on mechanical properties of the metallic material at micrometer scales.     

Addition of multiwalled carbon nanotube and graphene nanosheet in cobalt oxide film for enhancement of capacitance in electrochemical capacitors

In order to enhance the capacitance of electrochemical capacitors, multiwalled carbon nanotubes (MWCNTs) and graphene nanosheets (GNS) were added to cobalt oxide (Co₃O₄) paste. The composite film based on Co₃O₄/MWCNT/GNS (95:4:1 wt%) exhibited a capacitance of 294 F/g while the capacitance of Co₃O₄/MWCNT (95:5 wt%) and pure Co₃O₄ film is 205 and 163 F/g, respectively. The enhanced capacitance of Co₃O₄/MWCNT/GNS composite film was attributed to the electrochemical contributions of the Co₃O₄ nanoparticle attached to the GNS as well as their significantly increased specific surface areas by MWCNTs. Furthermore, the composite films showed faradaic redox capacitive behavior to double-layer capacitive behavior due to the different nanostructures of the composites.     

Coupling effects of depletion interactions in a three-sphere colloidal system

In a three-sphere system, the middle sphere is acted upon by two opposite depletion forces from the other two spheres. It is found that, in this system, the two depletion forces are coupled with each other and result in a strengthened depletion force. So the difference of the depletion forces of the three-sphere system and its corresponding two two-sphere systems is introduced to describe the coupling effect of the depletion interactions. The numerical results obtained by Monte-Carlo simulations show that this coupling effect is affected by both the concentration of small spheres and the geometrical confinement. Meanwhile, it is also found that the mechanisms of the coupling effect and the effect on the depletion force from the geometry factor are the same.     

Oscillation of coercivity between positive and negative in MnxGe1-x：H ferromagnetic semiconductor films

Amorphous MnxGe1-x :H ferromagnetic semiconductor films prepared in mixed Ar with 20% H2 by magnetron cosputtering show global ferromagnetism with positive coercivity at low temperatures. With increasing temperature, the coercivity of MnxGe1-x :H films first changes from positive to negative, and then back to positive again, which was not found in the corresponding MnxGe1-x and other ferromagnetic semiconductors before. For Mn0.4Ge0.6 :H film, the inverted Hall loop is also observed at 30 K, which is consistent with the negative coercivity. The negative coercivity is explained by the antiferromagnetic exchange coupling between the H-rich ferromagnetic regions separated by the H-poor non-ferromagnetic spacers. Hydrogenation is a useful method to tune the magnetic properties of MnxGe1-x films for the application in spintronics.     

First-principle study on optical properties of N-La-codoped anatase TiO

The electronic structures, deformation charge density, dipole moment, and optical properties of N-La-codoped anatase titanium dioxide (TiO2) are studied using the plane-wave ultrasoft pseudopotential method based on the density functional theory (DFT). The optical properties of two-ion-doped TiO2 are analyzed via electronic structures, deformation charge density, and dipole moment. For the model of N-La-doped TiO2 , a smaller atom fraction of N and La atoms induces better optical properties. The absorption edges of two doped TiO2 models redshift to the visible-light region.