A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.

     

对一个力学碰撞问题的讨论

对普通物理力学中有关碰撞的一个问题,从恢复系数e的取值角度出发,进行了详细求解和讨论,得到了更完整的结果.     

Electronic transport properties of bismuth nanobridges through silicon-nitride membranes

The electronic transport through nanostructured bismuth nanobridges has been investigated at low temperatures (T<2 K) and in magnetic fields B up to 8.5 T. The samples show reproducible resistance fluctuations as a function of B, superimposed on a large magnetoresistance of up to 50%. In addition, time-dependent resistance fluctuations in zero magnetic field demonstrate the presence of bistable scatterers in the constriction region of our samples, which are described by two-level systems. Their dynamics are shown to be sensitive to subtle modifications of the static scatterer configuration in their vicinity, which cannot be detected in the sample magnetofingerprint.     

用毛细管测量纯水表面张力系数的误差讨论

通过用毛细管测量纯水表面张力系数实验，得到管内径d与接触角θ的相对误差之间的关系曲线，由此说明实验测得的表面张力系数α和理论公式相比呈现一定的偏差，并简单地讨论了实验的理想状态与实际情况的差别．     

Adhesive bonding of glassy polymer surfaces by an ultrathin layer of a semicrystalline polymer

To develop a greater understanding of interfacial interactions between a semicrystalline polymer and a glassy polymer, adhesion tests were performed on very thin layers of poly(ethylene oxide) (PEO) sandwiched between two layers of poly(tetramethyl bisphenol A polycarbonate) (TMPC). The tests were designed to provide intimate contact between the surfaces while they were heated above the melting point of the PEO and cooled back to room temperature. A contact mechanics approach, based on the Johnson, Kendall, and Roberts theory, was used to determine values of the energy release rate describing the energetic driving force for crack propagation within the interfacial region. The ability to measure crack propagation at large values of the energy release rate was limited by rupture of the silicone elastomer that was used to provide a sufficiently compliant matrix for the adhesion experiment. By cycling the tensile stress at relatively low loading levels, we were able to measure fatigue crack propagation at values of the energy release rate that did not result in failure of the elastomer. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3809–3821, 2004     

The exponential power law: partial wetting kinetics and dynamic contact angles

An equation for the kinetics of partial drop spreading is proposed. This equation was empirically derived from experimental data for the spreading kinetics of partially wetting liquids in terms of the wet area versus time. The equation has the form of an exponential power law (EPL), and transforms into the well-known power law for complete wetting, when the equilibrium contact angle approaches zero. The EPL fits very well available experimental data. To lend additional support to the validity of this generalized equation, it will be demonstrated that when it is transformed to present the dynamic contact angle (DCA), it fits very well DCA experimental data for other wetting processes, such as capillary flow and tape coating.     

Critical Behavior of Two Interacting Linear Polymer Chains in a Good Solvent

A model of two interacting (chemically different) linear polymer chains is solved exactly using the real-space renormalization group transformation on a family of Sierpinski gasket type fractals and on a truncated 4-simplex lattice. The members of the family of the Sierpinski gasket-type fractals are characterized by an integer scale factorb which runs from 2 to ∞. The Hausdorff dimensiond _F of these fractals tends to 2 from below asb → ∞. We calculate the contact exponenty for the transition from the State of segregation to a State in which the two chains are entangled forb = 2-5. Using arguments based on the finite-size scaling theory, we show that forb→∞, y = 2 - v(b) d _F, wherev is the end-toend distance exponent of a chain. For a truncated 4-simplex lattice it is shown that the system of two chains either remains in a State in which these chains are intermingled in such a way that they cannot be told apart, in the sense that the chemical difference between the polymer chains completely drop out of the thermodynamics of the system, or in a State in which they are either zipped or entangled. We show the region of existence of these different phases separated by tricritical lines. The value of the contact exponenty is calculated at the tricritical points.     

Contact angle hysteresis of liquid drops as means to measure adhesive energy of zein on solid substrates

Adhesion of zein to solid substrates has been studied using surface energy profiles as indices and by adhesion mapping using atomic force microscopy (AFM). Different plasticizers like glycerol and sorbitol have been used to form mixed films with zein and properties of these films are studied using surface energy profiles. Comparison of the results from the different mixed samples with those from the pure zein films showed that force mapping could identify areas rich in protein. The adhesion maps produced were deconvoluted from sample topography and contrasted with the data obtained from contact angle measurements. A comparison of the two methods shows that the extent of contact angle hysteresis is indicative of both hydrophobicity of the surface as well as the force of adhesion. Mechanical properties and microstructure of zein films prepared by casting from solutions and using Langmuir-Blodgett film technique have been investigated. Pure zein seemed brittle and exhibited an essentially linear relationship between stress and strain. Films with plasticizer were tougher than these films. In general, mixed films showed better mechanical properties than pure films and had higher ultimate tensile strength and increased per cent elongation. Further, the mixed films of zein showed a higher force of adhesion compared to the pure films.     

Comparison of the boundary theory with the contact rule of phase regions and Gupta’s method

The phase boundary theory and the contact rule of phase regions are compared, and some weaknesses of the latter are manifested. The comparison between the Gupta’s method and the boundary theory method for constructing multicomponent isobaric sections is also presented.