Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow

A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded. Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function theorem. Supported by the Swiss National Science Foundation. Fellowship PBEL2–114311.     

πNN过程对Gottfried求和规则破坏的贡献

指出在计算πNN过程对核子结构函数的贡献时,将反冲核子视为物理核子更为合理.对Gottfried求和规则破坏、对质子中海夸克分布u和d不对称u(x)–d(x)等方面的贡献给出了详细的计算,与已有实验进行比较.结果表明π介子交换不是导致这一破坏以及影响核子结构函数的效应的惟一来源.     

Recoil spectrometry: Ion accelerator based elemental characterisation of surface layers

Recoil Spectrometry covers a group of techniques that are very similar to the well known Rutherford backscattering Spectrometry technique, but with the important difference that one measures the recoiling target atom rather than the projectile ion. This makes it possible to determine both the identity of the recoil and its depth of origin from its energy and velocity, using a suitable detector system. The incident ion is typically high-energy (30–100MeV)³⁵C1,⁸¹Br or¹²⁷I. Low concentrations of light elements such as C, O and N can be profiled in a heavy matrix such as Fe or GaAs. Here we present an overview of mass and energy dispersive recoil Spectrometry and illustrate its successful use in some typical applications.     

一类具有粘性项的拟线性抛物型方程组*

研究了一类具有非线性源项和粘性项的拟线性抛物型方程组的初边值问题．通过构造稳定集, 证明了此问题整体解的存在性, 并建立了解的长时间行为．同时在放松函数的适当假设条件下, 得到了初始能量非负时解的爆破性质及解的生命区间估计．     

Leray–Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress–strain relation

We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba–Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. We prove the existence of global-in-time weak solutions satisfying an energy inequality under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.     

Influence of isotacticity and molecular weight on the properties of metallocenic isotactic polypropylene

The relationships between structure and properties have been established for isotactic polypropylene, iPP, homopolymers synthesized by metallocene catalyst systems. These iPPs exhibit different isotacticity degrees and molecular weights, and several thermal treatments during their processing have been applied. The most important factor affecting the structure and properties of these polymers is the isotacticity content. The thermal treatment, i.e., the rate of cooling from the melt, is also important and a clear molecular weight effect has been also found for the sample with lowest M_w. These factors affect the thermal properties, the degree of crystallinity and, therefore, the structural parameters and the viscoelastic behavior. A slow cooling from melt favors the formation of the γ phase instead of the α modification. The storage modulus, Young modulus and microhardness values increase as crystallinity does, independently of the origin of this increase: higher isotacticity or application of a slow crystallization from the melt.     

Molecular mechanism of physical gelation of hydrocarbons by fatty acid amides of natural amino acids

A variety of fatty acid amides of different naturally occurring l-amino acids have been synthesized and they are found to form gels with various hydrocarbons. The gelation properties of these compounds were studied by a number of physical methods including FTIR spectroscopy, X-ray diffraction, scanning electron microscopy, differential scanning calorimetry, rheology, and it was found that gelation depended critically on the fatty acid chain length and the nature of the amino acid. Among them l-alanine based gelators were found to be the most efficient and versatile gelators as they self-assemble into a layered structure to form the gel network. Mechanisms for the assembly and formation of gels from these molecules are discussed.     

Viscoelastic and thermal characterization of crosslinked PVC

Soft PVC is employed for the manufacturing of a wide range of products with different properties and a relatively low cost. The utilization of soft PVC is restricted by the poor thermal, chemical and mechanical resistance properties. Also, plasticizer migration can modify the properties or can make useless the materials for some applications because of toxicity or a general loss of properties. PVC crosslinking is the most effective way to improve mechanical and transport properties of rigid or flexible PVC at high temperatures, but at the same time the thermal stability of PVC may be significantly reduced. In this work, the crosslinking reaction of plasticized poly(vinyl chloride) (PVC) through difunctional amines was studied. The mechanisms involved in the crosslinking reaction were explained by Fourier transform infrared (FTIR) analysis. The thermal activated crosslinking reaction was studied by cone and plate rheometry, analyzing the evolution of viscoelastic properties of the suspension as a function of time and temperature. The effect of the addition of crosslinking agents on the thermal stability of the polymer was studied by thermogravimetric analysis (TGA), which revealed that crosslinking reactions promote thermal degradation phenomena in the polymer matrix. This is attributed to the formation of HCl and other species promoting polymer degradation during crosslinking, thus leading to higher weight loss during thermal treatment with respect to unmodified PVC plastisols. This was also confirmed by an evident yellowing after crosslinking, especially at higher temperatures.     

The recoil of rigid PVC

Polyvinyl chloride (PVC) is widely used in industry, but it is difficult to find any extensive discussion of theological relations that describe it. The present paper discusses the behaviour of rigid PVC in extensional deformations at various temperatures. In the tests, a step elongation was applied at an initial time, then after a delay the specimen was cut, permitting recoil. Both linear and nonlinear strain regimes were studied; the linear relaxation properties (relaxation function, storage modulus) were cross-checked with eccentric-disk measurements. In the non-linear strain regime a single-integral constitutive equation of the KBKZ Wagner type was used. Separability of time and strain effects was demonstrated in our tests and so a damping function could be found which was only a function of strain. Video recordings of recoil were made, and detailed predictions of the strain-time behaviour were checked against experiments.Various constitutive equation proposals were used in the comparison, and the separated kernel integral irreversible model performed reasonably well; some other models of a differential type, and a Doi-Edwards model were not as accurate.Dedicated to Professor Arthur S. Lodge on the occasion of his 70th birthday and his retirement from the University of Wisconsin.     

Sloshing waves in a heated viscoelastic fluid layer in an excited rectangular tank

In this paper, we have investigated the motion of a heated viscoelastic fluid layer in a rectangular tank that is subjected to a horizontal periodic oscillation. The mathematical model of the current problem is communicated with the linearized Navier–Stokes equation of the viscoelastic fluid and heat equation together with the boundary conditions that are solved by means of Laplace transform. Time domain solutions are consequently computed by using Durbin's numerical inverse Laplace transform scheme. Various numerical results are provided and thereby illustrated graphically to show the effects of the physical parameters on the free-surface elevation time histories and heat distribution. The numerical applications revealed that increasing the Reynolds number as well as the relaxation time parameter leads to a wider range of variation of the free-surface elevation, especially for the short time history.