The Armstrong–Frederick cyclic hardening plasticity model with Cosserat effects

We propose an extension of the cyclic hardening plasticity model formulated by Armstrong and Frederick which includes micropolar effects. Our micropolar extension establishes coercivity of the model which is otherwise not present. We study then existence of solutions to the quasistatic, rate-independent Armstrong–Frederick model with Cosserat effects which is, however, still of non-monotone, non-associated type. In order to do this, we need to relax the pointwise definition of the flow rule into a suitable weak energy-type inequality. It is shown that the limit in the Yosida approximation process satisfies this new solution concept. The limit functions have a better regularity than previously known in the literature, where the original Armstrong–Frederick model has been studied.     

Observation and analysis of near-surface atmospheric aerosol optical properties in urban Beijing

Year-round measurements of the mass concentration and optical properties of fine aerosols(PM_2.5) from June 2009 to May 2010 at an urban site in Beijing were analyzed.The annual mean values of the PM_2.5 mass concentration,absorption coefficient（Ab）,scattering coefficient（Sc） and single scattering albedo（SSA）at 525 nm were 67±66μg/m³,64 ±62 Mm^-1,360 ±405 Mm^-1 and 0.82 ±0.09,respectively.The bulk mass absorption efficiency and scattering efficiency of the PM_2.5 at 525 nm were 0.78 m²/g and 5.55 m²/g,respectively.The Ab and Sc showed a similar diurnal variation with a maximum at night and a minimum in the afternoon,whereas SSA displayed an opposite diurnal pattern.Significant increases in the Ab and Sc were observed in pollution episodes caused by the accumulation of pollutants from both local and regional sources under unfavorable weather conditions.Aerosol loadings in dust events increased by several times in the spring,which had limited effects on the Ab and Sc due to the low absorption and scattering efficiency of dust particles.The frequency of haze days was the highest in autumn because of the high aerosol absorption and scattering under unfavorable weather conditions.The daily PM_2.5concentration should be controlled to a level lower than 64 μg/m³ to prevent the occurrence of haze days according to its exponentially decreased relationship with visibility.     

Levi-Civita functional equations and the status of spectral synthesis on semigroups

We show, contrary to some published statements, that spectral synthesis does not generally hold for commutative semigroups that are not groups. On the positive side we prove that it holds if the semigroup is a monoid with no prime ideal. For semigroups with a prime ideal, the picture is not so clear. On the negative side we provide a variety of examples illustrating the failure of spectral synthesis for many semigroups with prime ideals, but we also give examples of semigroups with prime ideals on which spectral synthesis holds.

     

Majorana stellar representation for mixed-spin (s, 1/2) systems

By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere,Majorana’s stellar representation provides an intuitive geometric perspective to comprehend the quantum system with highdimensional Hilbert space.However,the representation of a two-spin coupling system on a Bloch sphere has not been solved satisfactorily yet.Here,a practical method is presented to resolve the problem for the mixed-spin(s,1/2)system and describe the entanglement of the system.The system can be decomposed into two spins:spin-(s+1/2)and spin-(s?1/2)at the coupling bases,which can be regarded as independent spins.Besides,any pure state may be written as a superposition of two orthonormal states with one spin-(s+1/2)state and the other spin-(s?1/2)state.Thus,the whole initial state can be regarded as a state of a pseudo spin-1/2.In this way,the mixed spin decomposes into three spins.Therefore,the state can be represented by(2s+1)+(2s?1)+1=4s+1 sets of stars on a Bloch sphere.Finally,some examples are given to show symmetric patterns on the Bloch sphere and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on the Bloch sphere.     

π–π Interactions Between Aromatic Groups in Amphiphilic Molecules: Directing Hierarchical Growth of Porous Zeolites

The development of hierarchical macro- or mesoporous zeolites is essential in zeolite synthesis because the size of the micropores limits mass transport and their use as industrial catalysts for bulky molecules. Although major breakthroughs have been achieved, fabricating crystallographically ordered mesoporous zeolites using a templating strategy is still an unsolved challenge. This minireview highlights our recent efforts on the self-assembly of amphiphilic molecules to obtain ordered hierarchical MFI zeolites by introducing aromatic groups into the hydrophobic tail of the amphiphilic molecules. Owing to the geometric matching between the self-assembled aromatic tails and the MFI framework, a) single-crystalline mesostructured zeolite nanosheets (SCZNs), b) SCZNs with a 90° rotational intergrowth structure, c) a hierarchical MFI zeolite with a two-dimensional square P4mm mesostructure, and d) a single-crystalline mesoporous ZSM-5 with three-dimensional pores and sheetlike mesopores layered along the a-axis were successfully synthesized.