Regularity of the solutions for micro-macro models near equilibrium

In this paper, we study the regularity of solutions to two microscopic-macroscopic models: Hookean spring model and FENE dumbbell model. By making use of the structure of Fokker-Planck operator and establishing the general Hardy-Littlewood's inequality, we show that the classical solutions near the equilibrium obtained in [F. Lin, C. Liu, Ping Zhang, On a micro-macro model for polymeric fluids near equilibrium, Comm. Pure Appl. Math. 60 (6) (2007) 838-866] and [F. Lin, Ping Zhang, The FENE dumbbell model near equilibrium, Acta Math. Sinica (Chin. Ser.) 24 (2008) 529-538] become smooth with respect to the end-to-end vector variable q for any positive time.     

Spectral Properties of Schrödinger Operators on Domains with Varying Orders of Thinness

We consider the Schrödinger operator on two types of domains depending on a small parameter : dumbbell domains and thin domains with varying orders of thinness. In both situations we compare the eigenvalues and eigenvectors of the Schrödinger operator with the corresponding eigenvalues and eigenvectors of a limit operator defined on the limit domain.     

Investigation of radiation-induced mixed interstitial configurations in a dilute nickel 1 at.% silicon alloy

Abstract

X-ray energy spectra induced by 1 MeV protons and the energy spectra of the backscattered protons have been examined in the <100> and <110> directions of Ni crystals containing 1 at.% Si. The channeling method was used to investigate interactions between the radiation-induced defects and the silicon atoms. From the measured minimum yields and from the shape of the angular scans the fraction of silicon atoms is determined, which are displaced into the <100> and <110> channels due to proton or helium irradiations and subsequent annealing treatments. In undamaged crystals about 98 % of the silicon atoms are on normal lattice sites. After irradiation a dose dependent fraction of the silicon atoms is displaced 0.05 nm away from the substitutional position indicating the formation of a mixed dumbbell consisting of one selfinterstitial atom and one silicon atom. However, the experimental data can also be interpreted by the assumption of a NiSi₂ complex, in which the silicon atoms are displaced 0.08 nm from the lattice site. Subsequent annealing from 50 K to 160 K does not change the configuration and the concentration of the silicon complexes. At room temperature the silicon atoms in the complex are positioned 0.04 nm from the lattice position. The silicon complexes were totally am ihilated at 400 K.     

Lattice Boltzmann Simulation of Sedimentation of a Single Elastic Dumbbell in a Newtonian Fluid

Based on the lattice Boltzmann method (LBM), the sedimentations of a single elastic dumbbell in a Newtonian fluid under different initial positions and orientations, and also that of the elastic dumbbells with different free lengths of the spring under the same initial conditions have been simulated. All of the numerical results show that the final orientations of the elastic dumbbells are in the same horizontal direction, and the final positions of their centroids are all on the centerline of the tube no matter what the initial positions and orientations of the elastic dumbbell or the free lengths of the spring are. When the elastic dumbbell finally falls down vertically, the two circular cylinders of the elastic dumbbell rotate around their own symmetry-axis respectively, and their angular velocities are equal but opposite to each other. For the sedimentations of the elastic dumbbells with different free lengths of the spring, the shorter of the free length is, the faster the final angular velocity and vertical velocity of the circular cylinder will be.     

磁动式测氧仪中铂丝哑铃球系统的研究

磁动式测氧仪是一种良好的测量气体含氧量的设备。从氧气是顺磁性、氮气为抗磁性物质,且氧气的磁化率显著高于其它气体的特点出发,分析了磁动式测氧仪测量混合气体中氧气含量的原理,分析了充氮玻璃哑铃球系统在非均匀梯度磁场中的受力情况,报道了磁动式测氧仪的核心部件——铂丝哑铃球反射镜系统的设计方案,并介绍了其技术性能和实现方案。设计一个光学装置,有效地调节了铂丝哑铃球反射镜系统的质心平衡问题。实验结果表明,该系统的稳定性、灵敏度和转动阻尼等性能良好。     

The non-isothermal elastic dumbbell: A model for the thermal conductivity of a polymer solution

In a flowing polymeric liquid, molecular orientation will give rise to anisotropic conduction of heat. In this paper, a theory is presented relating the thermal conductivity tensor to the deformation history of the fluid. The basis of this theory is formed by the Hookean dumbbell. It is shown that the anisotropy of the thermal conductivity is proportional to the polymer contribution to the extra-stress tensor. This stress-thermal law makes it relatively simple to incorporate anisotropic heat conduction into the numerical simulation of a flowing polymeric liquid.     

Sticky dumbbells: from Hookean dumbbells to transient network

The Green-Tobolsky theory of transient networks is merged to the Hookean dumbbell model by considering Hookean sticky dumbbells, whose beads can randomly be stuck to a network submitted to affine deformation, or be set free from the network and undergo a free diffusive Brownian motion in the solvent. Sticking to and releasing from the network is treated as an instantaneous chemical reaction. This model has a closed-form solution, in which the stress is the sum of two (resp. three) Maxwellian codeformational relaxations for dumbbells with one (resp. two) sticking beads. When Brownian diffusion is faster than the chemical kinetics, one of the modes of two-sticking beads dumbbells is the Green-Tobolsky network relaxation, whereas the other modes correspond to fast configurational relaxations. In the opposite limit of fast chemical kinetics compared to Brownian relaxation, the effect of the network is to slow down the configurational response of Hookean dumbbells. Sticky dumbbells thus realise a continuous transition from Hookean dumbbells to transient networks.     

Extensional flow —a mathematical perspective

Extensional flow has been studied extensively for less than half the lifetime of the word rheology, although measurement of viscosity from extensional flow experiments can be traced back to the beginning of this century. In recent years extensional flow has, however, attracted a great deal of attention in conferences, workshops and special issues of journals. This has coincided with interest, both scientific and industrial, in elasticoviscous fluids, notably polymer solutions and molten polymers. The particular success of specialized, carefully targetted or focussed, workshops is highlighted.A personal reflection is offered here on some of the issues in extensional flow from the point of view of an applied mathematician. The state of the art, as far as extensional viscosity is concerned, is briefly surveyed. Both theoretical and practical aspects of the task of obtaining useful extensional flow properties are outlined, drawing heavily on a recent review by James and Walters. Particular attention is paid to spinning experiments, drawing heavily on recent theoretical investigations by the author. The merits of defining a spinning viscosity, in addition to the formally defined tensile viscosity, are advanced. The idea of general approximations for extensional flows is reviewed and some aspects of this are highlighted, particularly in connection with Metzner's idea of extensional primary field (EPF) approximations. Finally qualitative investigations of the behaviour of model fluids (in model flows) are illustrated and a new result on the boundedness of solutions for unsteady uniaxial extension of a FENS-P dumbbell model is presented.Presented as a keynote lecture at the 4the European Rheology Conference, September 4–9, 1994, Seville, Spain     

Gas‐phase synthesis of Fe‐Bi metastable and dumbbell particles

Fe‐Bi nanoparticles were prepared in the gas‐phase by DC magnetron sputtering and in‐fight annealing. The morphological, structural and compositional properties were investigated by High‐resolution transmission electron microscopy, energy dispersive X‐ray spectroscopy and scanning transmission electron microscopy. High‐resolution microscopy studies show that primary particles produced without in‐flight annealing are spherical with a diameter of about 50 nm. Particles sintered at 773 K acquire a dumbbell structure with Fe‐FeO and Bi sections.     

Synthesis and Characterization of Monodisperse Thermosensitive Dumbbell‐Shaped Microgels

Monodisperse thermosensitive dumbbell‐shaped core‐shell microgels are fabricated, which consist of a polystyrene core with a cross‐linked poly (N‐isopropylacrylamide) shell. The morphology of the microgels was investigated through cryogenic transmission electron microscopy and depolarized dynamic light scattering. The effective volume fraction and aspect ratio of the system could be adjusted through the swelling of the thermosensitive shell. We observe a phase transition of the microgels to an ordered, crystal‐like state, which is apparent through Bragg‐reflections in the visible range. These observations are further supported by rheological measurements where the shear‐melting of the crystal phase is clearly detected.