Existence of strong minimizers for the Griffith static fracture model in dimension two

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate $SB{D}^p$ functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy $GSB{D}^p$ functions by $SB{V}^p$ ones.     

Polymeric Electron Carriers

Polymers containing 1,4-dihydronicotinamide (P-NAH) alloxan (P-A), and viologen (P-V²⁺) moieties were synthesized and characterized. P-NAH reduced various organic substances such as lipoic acid, alloxan, and viologens and also immobilized quinone mediated by alloxan. P-A was reduced to the polymer-bearing alloxan radical and the dialuric acid structure without crosslinks by one- and two-electron reduction, respectively, and P-A also mediated the redox reaction occurring between aqueous and organic (water-immiscible) layers. P-V²⁺ was converted to the stable viologen radical reversibly by one-electron reduction. Electric potentials and currents on photo-reduction of P-V²⁺ and catalytic behavior of P-V²⁺ in the reduction of carbonyl compounds were examined.     

New symmetric azomethinic dimer: the influence of structural heterogeneity on the liquid crystalline behaviour

The paper deals with the study of the thermotropic liquid crystalline properties of a new azomethinic symmetric dimer and some of its structural heterogeneous mixtures with one of its reagents. Their thermotropic behaviour was monitored by polarised light microscopy, differential scanning microscopy and variable temperature X-ray diffraction measurements. The influence of the structural heterogeneity on the mesomorphic behaviour was established and some similarities with the mesomorphic behaviour of the polydisperse polymers were underlined.     

From Dislocation Motion to an Additive Velocity Gradient Decomposition, and Some Simple Models of Dislocation Dynamics

A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a ``small deformation" setting, a suite of simplified and interesting models consisting of a nonlocal Ginzburg Landau equation, a nonlocal level set equation, and a nonlocal generalized Burgers equation is derived. In the finite deformation setting, it is shown that an additive decomposition of the total velocity gradient into elastic and plastic parts emerges naturally from a micromechanical starting point that involves no notion of plastic deformation but only the elastic distortion, material velocity, dislocation density and the dislocation velocity. Moreover, a plastic spin tensor emerges naturally as well.     

Three trithiadiazepines and a trithiatriazepine

The structures of 6‐nitro‐1,3λ⁴δ²,5,2,4‐trithiadiazepine [C₂HN₃O₂S₃, ( 1 )], 6,7‐dinitro‐1,3λ⁴δ²,5,2,4‐trithiadiazepine [C₂N₄O₄S₃, ( 2 )], 1,3λ⁴δ²,5,2,4‐trithiadiazepine‐6,7‐dicarbonitrile [C₄N₄S₃, ( 3 )] and 7‐acetyl‐1,3λ⁴δ²,5,2,4,6‐trithiatriazepine [C₃H₃N₃OS₃, ( 4 )] presented here include the most precise determinations of these seven‐membered 10 π‐electron aromatic ring systems published to date. Both ( 2 ) and ( 3 ) are sited around crystallographic twofold axes with half a molecule per asymmetric unit. Comparison with other published derivatives of these rings reveals the effect of substituents on bonding, conformations and intermolecular interactions, including π‐stacking. The deformation density analysis of ( 2 ) is consistent with the expected bonding electron density from other theoretical and experimental studies.     

Design rule of indium bump in infrared focal plane array for longer cycling life

In light of the proposed equivalent method, a three-dimensional structural modeling of InSb infrared focal plane arrays (IRFPAs) is created, and the simulated strain distribution is identical to the deformation distribution on the top surface of InSb IRFPAs. After comparing the deformation features at different regions with the structural characteristics of IRFPAs, we infer that the flatness of InSb IRFPAs will be improved with a thinner indium bump array, and this inference is verified by subsequent simulation results. That is, when the diameter of indium bump is smaller than 20 μm, the simulated Z-components of strain on the whole top surface of InSb IRFPAs is uniform, and the deformation amplitude is small. When the diameter of indium bump is larger than 28 μm, the simulated Z-components of strain increases rapidly with the thicker indium bump, and the flatness of InSb IRFPAs is worsened rapidly. According to the changing trend of deformation amplitude with diameters of indium bump, and employing element pitches normalization method, a design rule of indium bump is proposed. That is, when the diameter of indium bump is shorter than 0.4 times the element pitch, the flatness of InSb IRFPAs is in an acceptable range. This design rule was supported by different IRFPAs with different formats delivered by several main research groups for achieving a longer cycling life.     

Three dimensional accurate morphology measurements of polystyrene standard particles on silicon substrate by electron tomography

Polystyrene latex (PSL) nanoparticle (NP) sample is one of the most widely used standard materials. It is used for calibration of particle counters and particle size measurement tools. It has been reported that the measured NP sizes by various methods, such as Differential Mobility Analysis, dynamic light scattering (DLS), optical microscopy (OM), scanning electron microscopy (SEM) and atomic force microscopy (AFM), differ from each other. Deformation of PSL NPs on mica substrate has been reported in AFM measurements: the lateral width of PSL NPs is smaller than their vertical height. To provide a reliable calibration standard, the deformation must be measured by a method that can reliably visualize the entire three dimensional (3D) shape of the PSL NPs. Here we present a method for detailed measurement of PSL NP 3D shape by means of electron tomography in a transmission electron microscope. The observed shape of the PSL NPs with 100 nm and 50 nm diameter were not spherical, but squished in direction perpendicular to the support substrate by about 7.4% and 12.1%, respectively. The high difference in surface energy of the PSL NPs and that of substrate together with their low Young modulus appear to explain the squishing of the NPs without presence of water film.     

On the Nano/Micro-Mechanics of Metallic Glass

Metallic glass (MG) is amorphous and has some outstanding properties such as ultrahigh strength, superior elasticity, and excellent thermo-plasticity. However, as MG is relatively new to the metal family, the relationship between its physical properties and amorphous structure is still unclear. This article aims to provide an insightful discussion through a comprehensive review about the investigations in the past few decades on the scientific mechanisms of this class of material. The discussion of the paper will include the following key aspects: (1) the formation mechanism of an amorphous structure through glass transition, (2) the structural characterization and models, (3) the micromechanics of plastic event and shear band, and (4) the correlation between the amorphous structure and its mechanical properties.