Transition to turbulence, small disturbances, and sensitivity analysis I: A motivating problem

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new “mostly linear” theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence. In this part, we study a highly sensitive one-dimensional Burgers' equation as a motivating problem. Sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance. Also, sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem. In the second part of this work, this analysis will be extended to the three-dimensional Navier-Stokes equations to show that small disturbances have great potential to trigger transition to turbulence.     

Monte Carlo study of electron correlation functions for small molecules

A study is made of electron-electron correlation functions for use in trial wave functions for small molecules. New forms are proposed that have only a few variational parameters, and these parameters have physical meanings that are easily discerned. Total energies for H₂, LiH and Li₂ computed using these correlation functions are presented, and comparison is made with previous forms, including the Jastrow-Pade form often used in Monte Carlo studies. We further treat the possibility that correlation depends not only on the separation of a pair of electrons but also on the location of the electron pair relative to the nuclei — indicative of a density-dependent or many body correlation effect. Our results indicate that such a many-body correlation effect is weakly present.This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098     

Additivity of tunnel number for small knots

We show that for small knots , and that for small knots . Received: March 10, 1997.     

Flow dimension and capacity for structuring urban street networks

This paper aims to measure the efficiency of urban street networks (a kind of complex networks) from the perspective of the multidimensional chain of connectivity (or flow). More specifically, we define two quantities: flow dimension and flow capacity, to characterize structures of urban street networks. To our surprise, for the topologies of urban street networks, previously confirmed as a form of small world and scale-free networks, we find that (1) the range of their flow dimensions is rather wider than their random and regular counterparts, (2) their flow dimension shows a power-law distribution, and (3) they have a higher flow capacity than their random and regular counterparts. The findings confirm that (1) both the wider range of flow dimensions and the higher flow capacity can be a signature of small world networks, and (2) the flow capacity can be an alternative quantity for measuring the efficiency of networks or that of the individual nodes. The findings are illustrated using three urban street networks (two in Europe and one in the USA).     

Small deviation probability via chaining

We obtain several extensions of Talagrand’s lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential behaviour of covering numbers. The corresponding results are also proved for non-Gaussian symmetric stable processes, both for the cases of critically small and critically large entropy. The results extensively use the classical chaining technique; at the same time they are meant to explore the limits of this method.     

亚纯函数涉及小函数的奇异方向

本文研究了平面上亚纯函数的奇异方向.利用角域内Ahlfors-Shimize特征函数和几个已有的关于函数增长性估计的引理,证明了复平面上的零级超越亚纯函数存在一条涉及小函数的T方向.推广了吴昭君和孙道椿给出的结果.     

Timelessness Strictly inside the Quantum Realm

Time is one of the undisputed foundations of our life in the real world. Here it is argued that inside small isolated quantum systems, time does not pass as we are used to, and it is primarily in this sense that quantum objects enjoy only limited reality. Quantum systems, which we know, are embedded in the everyday classical world. Their preparation as well as their measurement-phases leave durable records and traces in the entropy of the environment. The Landauer Principle then gives a quantitative threshold for irreversibility. With double slit experiments and tunneling as paradigmatic examples, it is proposed that a label of timelessness offers clues for rendering a Copenhagen-type interpretation of quantum physics more “realistic” and acceptable by providing a coarse but viable link from the fundamental quantum realm to the classical world which humans directly experience.     

Study on the emulsification and oxidative stability of ovalbumin-pectin-pumpkin seed oil emulsions using ovalbumin solution prepared by ultrasound

Pumpkin seed oil (PSO), which is a valuable compound with high nutritional value used for the prevention of various chronic diseases, is prone to oxidation. In this work, small and uniform (su) ovalbumin (OVA) and pectin (PEC) were used to stabilize PSO in the form of an emulsion. The results showed that suOVA-PEC-PSO emulsion with a droplet size of 9.82 ± 0.05 μm was successfully self-assembled from PSO, PEC, and suOVA solution (with a droplet size of 230.13 ± 14.10 nm) treated with 300 W ultrasound, owing to the formation of a more stable interfacial film on the surface of droplets. The interfacial, rheological, emulsifying, and antioxidant properties of the suOVA-PES-PSO emulsions were excellent, owing to the synergistic effects between PEC and suOVA solution. Moreover, the physical stability of the suOVA-PEC-PSO emulsions to salt stress, a freeze-thaw cycle, and heat treatment was also increased and the oxidation of linolenic acid was notably delayed. These results have extended the food-related applications of OVA and PSO, and provide a promising foundation for further exploration of the self-assembly of composite emulsions by small and uniform proteins.     

The S.M.A.R.T. (small mass,affordable, rapid,transfer-less) digestion method for heavy metal determinations

The S.M.A.R.T. (small mass, affordable, rapid, transfer-less) digestion method was developed to determine heavy metal concentrations in small sample masses. The S.M.A.R.T. digestion method is a hot water bath digestion where sample digestion and dilution are performed in the original sample tube. This method is faster than the typical methods used and reduces potential sources of error. Masses as small as 0.01 g have been digested and analysed using this method. The preparation and digestion time is reduced from 10 h to less than 4 h. Acid volumes are reduced from millilitres to microlitres and the only disposable supplies needed are sample tubes and pipette tips. Method accuracy was determined by digesting seven replicates of two standard reference materials using the S.M.A.R.T. method and analysing samples by inductively coupled plasma mass spectrometry. The S.M.A.R.T. digestion method was found to provide excellent recoveries for Al (76 ± 2.7%), Mn (99 ± 11%), Co (92 ± 17%), Ni (93 ± 28%), Cu (109 ± 33%), Zn (97 ± 7.1%), As (108 ± 20%), Sr (90 ± 12%), Mo (84 ± 23%), Ag (91 ± 1.8%), Cd (95 ± 6.2%), Sn (139 ± 52%) and Pb (95 ± 22%). This study has successfully developed an efficient and reproducible digestion method for heavy metal determination in limited biomass samples.     

Laser induced electronic acceleration process in nano dot

A physical model of the laser induced electron transport in dielectric with small size is discussed. The model assumes that free electrons are originally existent or produced by impact detrapping. The free electrons transporting in low dimensional dielectrics interact with phonons and surface. When the laser electric field strength is high enough, the inelastic electron scattering such as impact ionization and cascade processes will play important roles. A small size effect has been found in electron absorbing laser energy under the conditions that the laser wavelength is in near infrared zone and the material has size in nanometer level. This is a very significative effect to enlighten us on preparing ultrahigh threshold laser films with new nano-structure.