Remarks on the breakdown of smooth solutions for the 3-D Euler equations

The authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3-D Euler equations. In other words, if a solution of the Euler equations is initially smooth and loses its regularity at some later time, then the maximum vorticity necessarily grows without bound as the critical time approaches; equivalently, if the vorticity remains bounded, a smooth solution persists.Partially supported by O.N.R. Contract No. N00014-76-C-0316 and N.S.F. Grant No. MCS-81-01639Partially supported by N.S.F. Grant No. MCS-82-00171Partially supported by N.S.F. Grant No. MCS-81-02360     

Fatigue Crack Nucleation at Σ3(1 1 2) Boundary in a Ferritic Stainless Steel

The effect of a geometrical relationship between a grain boundary (GB) plane and a tensile axis on intergranular fatigue cracking along 3(1 1 2) twin boundaries has been investigated in Fe-30%Cr alloy crystals. Fatigue experiments were carried out on the three kinds of the specimens containing the 3(1 1 2) twin boundary. It was found that the fatigue cracking behavior was sensitive to the geometry of the GB plane. In a specimen where both the GB plane and a slip vector lying in the GB plane in adjacent grains are inclined to the tensile axis at 45°, the fatigue cracks were nucleated preferentially along the twin boundary at a stress amplitude of 170 MPa. The specimen with the GB plane normal to the tensile axis showed that the fatigue crack was initiated from a slip band formed within a constituent grain at a stress amplitude of 300 MPa. When the GB plane was inclined to the tensile axis but the slip vector lying in the GB plane was normal to the tensile axis, development of additional slips formed perpendicular to the GB plane were observed at a specific site of the GB. Initiation of intergranular fatigue cracks at the site was recognized at a stress amplitude of 250 MPa. It can be suggested that the GB plane normal to the tensile axis provides the highest fatigue performance among them. The difference in the cracking property among these specimens could be understood in terms of the effective Schmid factor derived from elastically incompatible stress.     

Biow-up of solutions of some nonlinear hyperbolic equations

We prove that any nontrivial solution of certain nonlinear hyperbolic partial differential equations of second order blows up in a finite time if the initial data are localized, the initial velocity being on the average non-negative.     

Excitation and decay dynamics of 1s2s inner-shell double-vacancy states of neon atoms

The photo-excitation and Auger decay processes of inner-shell double vacancy states 1s2s2p^6（1,3^S）3s3p of neutral neon atoms have been studied theoretically. Multi-configuration Dirac-Fock （MCDF） calculations have been carried out, with electron correlation effects taken into consideration. The relaxation of core and excited orbitals and configuration interaction are found to be crucial to creating the double vacancy states by single photo-absorption. The predominant decay paths for the double vacancy states turn out to be of the LLM Auger decay to 1s 2s^22p^53s（3p）, KLL Auger decay to 1s^22s2p^43s3p, and KLM Auger decay to 1s^22p^63s（3p）. They lead to further Auger decay, creating the neon ions of multiple charge states. For both double and single vacancy states the spectator type of Auger process is dominated in all the Auger decay processes. Theoretical Anger electron spectra are presented for further investigations, experimental and theoretical.     

Measurement of the vector A y and tensor A yy , A xx , A xz analyzing powers for the dd → 3H p reaction at 200 MeV

The data on the vector A _y and tensor A _yy , A _xx , A _xz analyzing powers for the d → ³H p reaction have been obtained at the energy of the initial deuteron of 200MeV in the angular range of 0–95 degrees in the c.m.s. The calculations performed within one-nucleon exchange model with the use of the standard three-nucleon bound state wave functions fail to reproduce the data on the tensor analyzing powers.     

Room-Temperature Phosphorescence from a Series of 3-Pyridylcarbazole Derivatives

Exploration of pure metal-free organic molecules that exhibit strong room-temperature phosphorescence (RTP) is an emerging research topic. In this regard, unveiling the design principles for an efficient RTP molecule is an essential, but challenging, task. A small molecule is an ideal platform to precisely understand the fundamental role of each functional component because the parent molecule can be easily derivatized. Here, the RTP behaviors of a series of 3-pyridylcarbazole derivatives are presented. Experimental studies in combination with theoretical calculations reveal the crucial role of the n orbital on the central pyridine ring in the dramatic enhancement of the intersystem crossing between the charge-transfer-excited singlet state and the locally excited triplet states. Single-crystal X-ray crystallographic studies apparently indicate that both the pyridine ring and fluorine atom contribute to the enhancement of the RTP because of the restricted motion owing to weak C−H⋅⋅⋅N and H⋅⋅⋅F hydrogen-bonding interactions. The single crystal of the fluorine-substituted derivative shows an ultra-long phosphorescent lifetime (τ_P) of 1.1 s and a phosphorescence quantum yield (Φ_P) of 1.2 %, whereas the bromine-substituted derivative exhibits τ_P of 0.15 s with a Φ_P of 7.9 %. We believe that this work provides a fundamental and universal guideline for the generation of pure organic molecules exhibiting strong RTP.     

Synthesis of Anthracene Derivatives with Azaacene-Containing Iptycene Wings and the Utilization as a Dopant for Solution-Processed Organic Light-Emitting Diodes

Substituted acene derivatives are regarded as promising materials for organic electronic devices such as organic light-emitting diodes (OLEDs). In particular, anthracene derivatives are known to exhibit good fluorescence property, with the air stability and solubility in common organic solvents expected to give advantages for solution-processed device fabrication. In this study, a series of bistriisopropylsilyl(TIPS)ethynyl anthracene derivatives with azaacene-containing iptycene wings have been synthesized by using condensation reactions. Effects of size of azaacenes on optical properties and packing structures were investigated. UV/Vis absorption and fluorescence spectra indicate that the π-elongation of iptycene units has small effects on the overall π-system, which is also supported by electrochemical measurements. Secondly, single-crystal X-ray analysis implies that the molecules likely have interactions with the iptycene units of adjacent molecules, while the iptycene wings and TIPSethynyl groups can prevent the central anthracene unit from undesirable non-radiative energy loss. Finally, the most emissive derivative was used as a dopant for solution-processed OLEDs, showing obvious electroluminescence with a luminance of over 920 cd m⁻².     

A Hydroperoxide-Mediated Decarboxylation of α-Ketoacids Enables the Chemoselective Acylation of Amines

Strategies for the formation of amide bonds, that is, one of the most basic and important transformations in organic synthesis, have so far focused predominantly on dehydration reactions. Herein, we report and demonstrate the practical utility of a novel decarboxylative amidation of α-ketoacids by using inexpensive tert-butyl hydroperoxide (TBHP), which is characterized by high yields, a broad substrate scope, mild reaction conditions, and a unique chemoselectivity. These features enable the synthesis of peptides from amino acid derived α-ketoacids under preservation of the stereochemical information.