Thermodynamics of polycrystalline materials treated by the theory of mixtures with continuous diversity

The physics of polycrystalline materials is described via microscopic processes such as grain boundary migration, grain growth, grain rotation, polygonization (the bending and breaking of crystallites) and evolution of dislocation density. The importance of taking these processes into account lies in their influence on the macroscopic mechanical behaviour of the material. Constitutive equations to describe such phenomena have been proposed in the literature. The main result of this paper is to give a general and thermodynamically consistent approach for such constitutive equations. The framework of the Theory of Mixtures with Continuous Diversity (TMCD) is used. The inclusion of both orientation and grain-size distributions is presented in this paper for the first time. Their introduction requires the formulation of a new and general constitutive theory that is, therefore, given. The method of Lagrange multipliers used in the context of the entropy principle (Liu, Arch. Rat. Mech. Anal. 46, 131–148 (1972)) provides the restrictions of the second law of thermodynamics on the constitutive equations. The success of this work is that all the main results present in the literature can be incorporated in this framework.     

Effect of induced magnetic field on natural convection in vertical concentric annuli

In the present paper,we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a radial magnetic field.The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account.The transport equations concerned with the considered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity,induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylinder of concentric annuli.The effects of the various physical parameters appearing into the model are demonstrated through graphs and tables.It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap between the cylinders is less or equal to 1.70 times the radius of inner cylinder,while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder.These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases.It is also found that as the Hartmann number increases,there is a flattening tendency for both the velocity and the induced magnetic field.The influence of the induced magnetic field is to increase the velocity profiles.     

Polymerization Induced Microphase Separation for the Fabrication of Nanostructured Materials

Polymerization induced microphase separation (PIMS) is a strategy used to develop unique nanostructures with highly useful morphologies through the microphase separation of emergent block copolymers during polymerization. In this process, nanostructures are formed with at least two chemically independent domains, where at least one domain is composed of a robust crosslinked polymer. Crucially, this synthetically simple method is readily used to develop nanostructured materials with the highly coveted co-continuous morphology, which can also be converted into mesoporous materials by selective etching of one domain. As PIMS exploits a block copolymer microphase separation mechanism, the size of each domain can be tightly controlled by modifying the size of block copolymer precursors, thus providing unparalleled control over nanostructure and resultant mesopore sizes. Since its inception 11 years ago, PIMS has been used to develop a vast inventory of advanced materials for an extensive range of applications including biomedical devices, ion exchange membranes, lithium-ion batteries, catalysis, 3D printing, and fluorescence-based sensors, among many others. In this review, we provide a comprehensive overview of the PIMS process, summarize latest developments in PIMS chemistry, and discuss its utility in a wide variety of relevant applications.     

Laser-induced thermal effects in hexagonal MoO3 nanorods

Laser-induced thermal effects on the hexagonal MoO₃ nanorods at different power density levels were studied using Raman spectroscopy and scanning electron microscopy techniques. The structural features of the nanorods were accompanied by varying the incident laser power from 8.0 to 600 mW by using a gradual increasing rate and a sudden increasing incident laser power. It was shown that the photoeffects observed on the MoO₃ nanorods critically depends on the exposure rate. By gradually increasing the incident laser power up to 600 mW, morphology of the nanorods were completely preserved, and the observed thermal behavior was discussed on the basis of thermal contact at nanoscale. However, when the irradiation intensity was suddenly increased, it was observed that overheating of h-MoO₃ nanorods at relatively lower laser powers (80 mW) sublimate the nanorods around the laser spot region. The MoO₃ molecules on vapor-phase at high temperatures condense and crystallize next to the laser spot on the orthorhombic (α-MoO₃) and monoclinic (β-MoO₃) phases. Furthermore, the nanorods closest to the laser spot region undergo a structural phase (and morphological) transition from h-MoO₃ phase to α-MoO₃ phase.     

Non-Conventional Behaviour of Castor Oil Under High Pressure

Castor oil shows non-conventional physical and chemical behaviour when submitted to pressure. This paper gives a brief presentation of the specific physical properties of castor oil under pressure up to 1.0 GPa. The changes of permittivity, dielectric loss and the structure of the high-pressure induced phases of castor oil are also described.     

闭模糊拟阵的特征

给出Goetchel和Voxman定义的模糊拟阵成为闭模糊拟阵的三个充分必要条件。     

Induced norms, states, and numerical ranges

It is shown that two induced norms are the same if and only if the corresponding norm numerical ranges or radii are the same, which in turn is equivalent to the vector states and mixed states arising from the norms being the same. The proofs depend on an auxiliary result of independent interest which concerns when two closed convex sets in a topological vector space are multiples of each other.

     

Induced path transit function, monotone and Peano axioms

The induced path transit function J(u,v) in a graph consists of the set of all vertices lying on any induced path between the vertices u and v. A transit function J satisfies monotone axiom if x,y∈J(u,v) implies J(x,y)⊆J(u,v). A transit function J is said to satisfy the Peano axiom if, for any u,v,w∈V,x∈J(v,w), y∈J(u,x), there is a z∈J(u,v) such that y∈J(w,z). These two axioms are equivalent for the induced path transit function of a graph. Planar graphs for which the induced path transit function satisfies the monotone axiom are characterized by forbidden induced subgraphs.     

Focusing particles by induced charge electrokinetic flow in a microchannel

A novel method of sheathless particle focusing by induced charge electrokinetic flow in a microchannel is presented in this paper. By placing a pair of metal plates on the opposite walls of the channel and applying an electrical field, particle focusing is achieved due to the two pairs of vortex that constrain the flow of the particle solution. As an example, the trajectories of particles under different electrical fields with only one metal plate on one side channel wall were numerically simulated and experimentally validated. Other flow focusing effects, such as the focused width ratio (focused width/channel width) and length ratio (focused length/half‐length of metal plate) of the sample solution, were also numerically studied. The results show that the particle firstly passes through the gaps between the upstream vortices and the channel walls. Afterwards, the particle is focused to pass through the gap between the two downstream vortices that determine the focused particle position. Numerical simulations show that the focused particle stream becomes thin with the increases in the applied electrical field and the length of the metal plates. As regards to the focused length ratio of the focused stream, however, it slightly increases with the increase in the applied electrical field and almost keeps constant with the increase in the length of the metal plate. The size of the focused sample solution, therefore, can be easily adjusted by controlling the applied electrical field and the sizes of the metal plates.