Note on loss of regularity for solutions of the 3—D incompressible euler and related equations

One of the central problems in the mathematical theory of turbulence is that of breakdown of smooth (indefinitely differentiable) solutions to the equations of motion. In 1934 J. Leray advanced the idea that turbulence may be related to the spontaneous appearance of singularities in solutions of the 3—D incompressible Navier-Stokes equations. The problem is still open. We show in this report that breakdown of smooth solutions to the 3—D incompressible slightly viscous (i.e. corresponding to high Reynolds numbers, or highly turbulent) Navier-Stokes equations cannot occur without breakdown in the corresponding solution of the incompressible Euler (ideal fluid) equation. We prove then that solutions of distorted Euler equations, which are equations closely related to the Euler equations for short term intervals, do breakdown.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041, and partially supported by the National Science Foundation under Grant No. MCS-82-01599     

Source breakup dynamics in Au + Au collisions at sqrt[s(NN)]=200 GeV via three-dimensional two-pion source imaging

A three-dimensional correlation function obtained from midrapidity, low p(T), pion pairs in central Au+Au collisions at sqrt[s(NN)]=200 GeV is studied. The extracted model-independent source function indicates a long range tail in the directions of the pion pair transverse momentum (out) and the beam (long). A proper breakup time tau(0) ~ 9 fm/c and a mean proper emission duration Delta tau ~ 2 fm/c, leading to sizable emission time differences ({|Delta t(LCM)|} approximately 12 fm/c), are required to allow models to be successfully matched to these tails. The model comparisons also suggest an outside-in "burning" of the emission source reminiscent of many hydrodynamical models.     

铝电解中SnO2+Sb2O3+CuO惰性阳极的电流效率、腐蚀性及结构变化

系统研究了霍尔赫鲁特铝电解池中SnO₂基惰性阳极 (96%SnO₂+2%Sb₂O₃+2%CuO)的电流效率,腐蚀性以及结构变化. 评价了各种操作参数(温度、电流密度、阴阳两级的距离、冰晶石量比、Al₂O₃ 浓度和电解质组成)对电流效率和腐蚀性的影响.     

Comparative Hydrodynamic Study on Non-Aqueous Soluble Archaeological Wood Consolidants: Butvar B-98 and PDMS-OH Siloxanes

Butvar B-98 and PDMS-OH both have a demonstrable ability as consolidants for archaeological wood. This makes them both potential treatment options for the Oseberg collection, which is one of the most important archaeological finds from the Viking era. Both Butvar B-98 and PDMS-OH are soluble in organic solvents, offering a useful alternative to aqueous-based consolidants. Extensive characterisation studies were carried out on both of these polymers, with the use of analytical ultracentrifugation and viscometry, for the benefit of conservators wanting to know more about the physical properties of these materials. Short column sedimentation equilibrium analysis using SEDFIT-MSTAR revealed a weight-average molar mass (weight-average molecular weight) M_w of (54.0 ± 1.5) kDa (kg · mol⁻¹) for Butvar B-98, while four samples of PDMS-OH siloxanes (each with a different molar mass) had an M_w of (52.5 ± 3.0) kDa, (38.8 ± 1.5) kDa, (6.2 ± 0.7) kDa and (1.6 ± 0.1) kDa. Sedimentation velocity confirmed that all polymers were heterogeneous, with a wide range of molar masses. All molecular species showed considerable conformational asymmetry from measurements of intrinsic viscosity, which would facilitate networking interactions as consolidants. It is anticipated that the accumulated data on these two consolidants will enable conservators to make a more informed decision when it comes to choosing which treatment to administer to archaeological artefacts.     

Metabolic compartmentalization in the human cortex and hippocampus: evidence for a cell- and region-specific localization of lactate dehydrogenase 5 and pyruvate dehydrogenase

Background  

For a long time now, glucose has been thought to be the main, if not the sole substrate for brain energy metabolism. Recent data nevertheless suggest that other molecules, such as monocarboxylates (lactate and pyruvate mainly) could be suitable substrates. Although monocarboxylates poorly cross the blood brain barrier (BBB), such substrates could replace glucose if produced locally.     

High-level correlated approach to the jellium surface energy, without uniform-gas input

We resolve the long-standing controversy over the metal surface energy: Density-functional methods that require uniform-electron-gas input agree with each other, but not with high-level correlated calculations such as Fermi hypernetted chain and diffusion Monte Carlo calculations that predict the uniform-gas correlation energy. Here we apply the inhomogeneous Singwi-Tosi-Land-Sj?lander method, and find that the density functionals are indeed reliable (because the surface energy is bulklike). Our work also vindicates the use of uniform-gas-based nonlocal kernels in time-dependent density-functional theory.     

Cycloaddition Reactions of an Active Cyclic Phosphane/Borane Pair with Alkenes,Alkynes, and Carbon Dioxide

The active six-membered cyclo-FLP 6 undergoes a rapid P/B addition reaction to carbon dioxide. At elevated temperature, the resulting heterobicyclo[2.2.2]octane derived product 7 undergoes ring opening and equilibrates with the cyclotetramer (7)₄ . In the large macrocyclic structure, four monomeric six-membered cyclo-FLP units are connected by four CO₂ molecules to form the supramolecular ring system. The P/B cyclo-FLP 6 undergoes a variety of additional cycloaddition reactions.     

A generalization of the Mitchell Lemma: The Ulmer Theorem and the Gabriel–Popescu Theorem revisited

We prove a generalization of the Mitchell Lemma, and we show that it is a key lemma that can be used in order to deduce in a unified easier way several important results. Thus, the Ulmer Theorem, the generalized Gabriel–Popescu Theorem and the generalized Takeuchi Lemma are all consequences of the generalized Mitchell Lemma.