Anomalous scaling of passive scalar in turbulence and in equilibrium

We analyze multi-point correlation functions of a tracer in an incompressible flow at scales far exceeding the scale $L$ at which fluctuations are generated (quasi-equilibrium domain) and compare them with the correlation functions at scales smaller than $L$ (turbulence domain). We demonstrate that the scale invariance can be broken in the equilibrium domain and trace this breakdown to the statistical integrals of motion (zero modes) as has been done before for turbulence. Employing Kraichnan model of short-correlated velocity we identify the new type of zero modes, which break scale invariance and determine an anomalously slow decay of correlations at large scales

A Two-Coordinate Nickel Imido Complex That Effects C−H Amination

An exceptionally low coordinate nickel imido complex, (IPr*)Ni═N(dmp) (2) (dmp = 2,6-dimesitylphenyl), has been prepared by the elimination of N_2 from a bulky aryl azide in its reaction with (IPr*)Ni(η^6-C_7H_8) (1). The solid-state structure of 2 features two-coordinate nickel with a linear C−Ni−N core and a short Ni−N distance, both indicative of multiple-bond character. Computational studies using density functional theory showed a Ni═N bond dominated by Ni(dπ)−N(pπ) interactions, resulting in two nearly degenerate singly occupied molecular orbitals (SOMOs) that are Ni−N π* in character. Reaction of 2 with CO resulted in nitrene-group transfer to form (dmp)NCO and (IPr*)Ni(CO)_3 (3). Net C−H insertion was observed in the reaction of 2 with ethene, forming the vinylamine (dmp)NH(CH═CH_2) (5) via an azanickelacyclobutane intermediate, (IPr*)Ni{N,C:κ^2-N(dmp)CH_2CH_2} (4)

Forty Years of Codification of Estates and Trusts Law: Lessons for the Next Generation

In this paper we develop two theses. First, we argue that uniform law proposals that ask courts and practitioners to abandon revered legal traditions and ways of thinking about estates and trusts, even when they are intent-furthering proposals, face resistance until in time the glories of the past and the risks of a new legal regime fade in importance in legal thought. Second, we argue that, especially within an environment in which states seek to gain competitive advantage over their counterparts in other states, the glories of the past and the risks of a new legal regime fade fastest when a uniform law proposal limits the effect of intent-defeating rules. Uniform laws tend to fall into three categories: (1) statutes that usurp older statutory-based laws; (2) statutes, typically remedial in nature, that reverse the common law; and (3) statutes that predominantly codify the common law. We look at examples of each to show how the interplay between revered legal traditions and donative freedom affects the reception of uniform law proposals. We also pay particular attention to intent-defeating common law doctrines and the risks that uniform law drafters face when they attempt to codify them in an environment where there is stiff jurisdictional competition for estate planning business

Quantitative Assessment of the Anatomical Footprint of the C1 Pedicle Relative to the Lateral Mass: A Guide for C1 Lateral Mass Fixation

Study Design: Anatomic study. Objectives: To determine the relationship of the anatomical footprint of the C1 pedicle relative to the lateral mass (LM). Methods: Anatomic measurements were made on fresh frozen human cadaveric C1 specimens: pedicle width/height, LM width/height (minimum/maximum), LM depth, distance between LM’s medial aspect and pedicle’s medial border, distance between LM’s lateral aspect to pedicle’s lateral border, distance between pedicle’s inferior aspect and LM’s inferior border, distance between arch’s midline and pedicle’s medial border. The percentage of LM medial to the pedicle and the distance from the center of the LM to the pedicle’s medial wall were calculated. Results: A total of 42 LM were analyzed. The C1 pedicle’s lateral aspect was nearly confluent with the LM’s lateral border. Average pedicle width was 9.0 ± 1.1 mm, and average pedicle height was 5.0 ± 1.1 mm. Average LM width and depth were 17.0 ± 1.6 and 17.2 ± 1.6 mm, respectively. There was 6.9 ± 1.5 mm of bone medial to the medial C1 pedicle, which constituted 41% ± 9% of the LM’s width. The distance from C1 arch’s midline to the medial pedicle was 13.5 ± 2.0 mm. The LM’s center was 1.6 ± 1 mm lateral to the medial pedicle wall. There was on average 3.5 ± 0.6 mm of the LM inferior to the pedicle inferior border. Conclusions: The center of the lateral mass is 1.6 ± 1 mm lateral to the medial wall of the C1 pedicle and approximately 15 mm from the midline. There is 6.9 ± 1.5 mm of bone medial to the medial C1 pedicle. Thus, the medial aspect of C1 pedicle may be used as an anatomic reference for locating the center of the C1 LM for screw fixation

Equation-free implementation of statistical moment closures

We present a general numerical scheme for the practical implementation of statistical moment closures suitable for modeling complex, large-scale, nonlinear systems. Building on recently developed equation-free methods, this approach numerically integrates the closure dynamics, the equations of which may not even be available in closed form. Although closure dynamics introduce statistical assumptions of unknown validity, they can have significant computational advantages as they typically have fewer degrees of freedom and may be much less stiff than the original detailed model. The closure method can in principle be applied to a wide class of nonlinear problems, including strongly-coupled systems (either deterministic or stochastic) for which there may be no scale separation. We demonstrate the equation-free approach for implementing entropy-based Eyink-Levermore closures on a nonlinear stochastic partial differential equation.Comment: 7 pages, 2 figure

Vortices within vortices: hierarchical nature of vortex tubes in turbulence

The JHU turbulence database [1] can be used with a state of the art visualisation tool [2] to generate high quality fluid dynamics videos. In this work we investigate the classical idea that smaller structures in turbulent flows, while engaged in their own internal dynamics, are advected by the larger structures. They are not advected undistorted, however. We see instead that the small scale structures are sheared and twisted by the larger scales. This illuminates the basic mechanisms of the turbulent cascade.Comment: 2 pages, 1 low quality video, 1 high quality vide

Synthesis and Characterization of Three-Coordinate Ni(III)-Imide Complexes

A new family of low-coordinate nickel imides supported by 1,2-bis(di-tert-butylphosphino)ethane was synthesized. Oxidation of nickel(II) complexes led to the formation of both aryl- and alkyl-substituted nickel(III)-imides, and examples of both types have been isolated and fully characterized. The aryl substituent that proved most useful in stabilizing the Ni(III)-imide moiety was the bulky 2,6-dimesitylphenyl. The two Ni(III)-imide compounds showed different variable-temperature magnetic properties but analogous EPR spectra at low temperatures. To account for this discrepancy, a low-spin/high-spin equilibrium was proposed to take place for the alkyl-substituted Ni(III)-imide complex. This proposal was supported by DFT calculations. DFT calculations also indicated that the unpaired electron is mostly localized on the imide nitrogen for the Ni(III) complexes. The results of reactions carried out in the presence of hydrogen donors supported the findings from DFT calculations that the adamantyl substituent was a significantly more reactive hydrogen-atom abstractor. Interestingly, the steric properties of the 2,6-dimesitylphenyl substituent are important not only in protecting the Ni═N core but also in favoring one rotamer of the resulting Ni(III)-imide, by locking the phenyl ring in a perpendicular orientation with respect to the NiPP plane