On a criterion for vortex breakdown

A criterion for the onset of vortex breakdown is proposed. Based upon previous experimental, computational, and theoretical studies, an appropriately defined local Rossby number is used to delineate the region where breakdown occurs. In addition, new numerical results are presented which further validate this criterion. A number of previous theoretical studies concentrating on inviscid standing-wave analyses for trailing wing-tip vortices are reviewed and reinterpreted in terms of the Rossby number criterion. Consistent with previous studies, the physical basis for the onset of breakdown is identified as the ability of the flow to sustain such waves. Previous computational results are reviewed and re-evaluated in terms of the proposed breakdown criterion. As a result, the cause of breakdown occurring near the inflow computational boundary, common to several numerical studies, is identified. Finally, previous experimental studies of vortex breakdown for both leading edge and trailing wing-tip vortices are reviewed and quantified in terms of the Rossby number criterion

Variational quantum Monte Carlo simulations with tensor-network states

We show that the formalism of tensor-network states, such as the matrix product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of this approach by explicit MPS calculations for the transverse Ising chain with up to N=256 spins at criticality, using periodic boundary conditions and D*D matrices with D up to 48. The computational cost of our scheme formally scales as ND^3, whereas standard MPS approaches and the related density matrix renromalization group method scale as ND^5 and ND^6, respectively, for periodic systems.Comment: 4+ pages, 2 figures. v2: improved data, comparisons with exact results, to appear in Phys Rev Let

Katabatic wind-driven exchange in fjords

Author Posting. © American Geophysical Union, 2017. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 122 (2017): 8246–8262, doi:10.1002/2017JC013026.The general issue of katabatic wind-driven exchange in fjords is considered using an idealized numerical model, theory, and observations. Two regimes are identified. For fjords narrower than a viscous boundary layer width, the exchange is limited by a balance between wind and friction in lateral boundary layers. For the nonlinear viscous parameterization used here, this boundary layer thickness depends on the properties of the fjord, such as stratification and length, as well as on the wind stress and numerical parameters such as grid spacing and an empirical constant. For wider fjords typical of east Greenland, the balance is primarily between wind, the along-fjord pressure gradient, and acceleration, in general agreement with previous two-layer nonrotating theories. It is expected that O(10%) of the surface layer will be flushed out of the fjord by a single wind event. Application of the idealized model to a typical katabatic wind event produces outflowing velocities that are in general agreement with observations in Sermilik Fjord, a large glacial fjord in southeast Greenland. The presence of a sill has only a minor influence on the exchange until the sill penetrates over most of the lower layer thickness, in which cases the exchange is reduced. It is concluded that the multiple katabatic wind events per winter that are experienced by the fjords along east Greenland represent an important mechanism of exchange between the fjord and shelf, with implications for the renewal of warm, salty waters at depth and for the export of glacial freshwater in the upper layer.National Science Foundation Grant Numbers: OCE-1533170, OCE-1434041, PLR-1418256; NOAA Climate and Global Change Postdoctoral Fellowship2018-04-2

A simple interpretation of quantum mirages

In an interesting new experiment the electronic structure of a magnetic atom adsorbed on the surface of Cu(111), observed by STM, was projected into a remote location on the same surface. The purpose of the present paper is to interpret this experiment with a model Hamiltonian, using ellipses of the size of the experimental ones, containing about 2300 atoms. The charge distribution for the different wavefunctions is analyzed, in particular, for those with energy close to the Fermi energy of copper Ef. Some of them show two symmetric maxima located on the principal axis of the ellipse but not necessarily at the foci. If a Co atom is adsorbed at the site where the wavefunction with energy $E_F$ has a maximum and the interaction is small, the main effect of the adsorbed atom will be to split this particular wavefunction in two. The total charge density will remain the same but the local density of states will present a dip at Ef at any site where the charge density is large enough. We relate the presence of this dip to the observation of quantum mirages. Our interpretation suggests that other sites, apart from the foci of the ellipses, can be used for projecting atomic images and also indicates the conditions for other non magnetic adsorbates to produce mirages.Comment: 3 pages, 3 Fig

Analysis of Different Types of Regret in Continuous Noisy Optimization

The performance measure of an algorithm is a crucial part of its analysis. The performance can be determined by the study on the convergence rate of the algorithm in question. It is necessary to study some (hopefully convergent) sequence that will measure how "good" is the approximated optimum compared to the real optimum. The concept of Regret is widely used in the bandit literature for assessing the performance of an algorithm. The same concept is also used in the framework of optimization algorithms, sometimes under other names or without a specific name. And the numerical evaluation of convergence rate of noisy algorithms often involves approximations of regrets. We discuss here two types of approximations of Simple Regret used in practice for the evaluation of algorithms for noisy optimization. We use specific algorithms of different nature and the noisy sphere function to show the following results. The approximation of Simple Regret, termed here Approximate Simple Regret, used in some optimization testbeds, fails to estimate the Simple Regret convergence rate. We also discuss a recent new approximation of Simple Regret, that we term Robust Simple Regret, and show its advantages and disadvantages.Comment: Genetic and Evolutionary Computation Conference 2016, Jul 2016, Denver, United States. 201

Manganese tricarbonyl complexes with asymmetric 2 2‑iminopyridine ligands: toward decoupling steric and electronic 3 factors in electrocatalytic CO2 reduction

Manganese tricarbonyl bromide complexes incorporating IP (2-(phenylimino)pyridine) derivatives, [MnBr(CO)3(IP)], are demonstrated as a new group of catalysts for CO2 reduction, which represent the first example of utilization of (phenylimino)pyridine ligands on manganese centers for this purpose. The key feature is the asymmetric structure of the redox-noninnocent ligand that permits independent tuning of its steric and electronic properties. The α-diimine ligands and five new Mn(I) compounds have been synthesized, isolated in high yields, and fully characterized, including X-ray crystallography. Their electrochemical and electrocatalytic behavior was investigated using cyclic voltammetry and UV−vis−IR spectroelectrochemistry within an OTTLE cell. Mechanistic investigations under an inert atmosphere have revealed differences in the nature of the reduction products as a function of steric bulk of the ligand. The direct ECE (electrochemical−chemical−electrochemical) formation of a five-coordinate anion [Mn(CO)3(IP)]−, a product of two-electron reduction of the parent complex, is observed in the case of the bulky DIPIMP (2-[((2,6-diisopropylphenyl)imino)methyl]pyridine), TBIMP (2-[((2-tert-butylphenyl)imino)methyl]-pyridine), and TBIEP (2-[((2-tert-butylphenyl)imino)ethyl]pyridine) derivatives. This process is replaced for the least sterically demanding IP ligand in [MnBr(CO)3(IMP)] (2-[(phenylimino)methyl]pyridine) by the stepwise formation of such a monoanion via an ECEC(E) mechanism involving also the intermediate Mn−Mn dimer [Mn(CO)3(IMP)]2. The complex [MnBr(CO)3(IPIMP)] (2-[((2-diisopropylphenyl)imino)methyl]pyridine), which carries a moderately electron donating, moderately bulky IP ligand, shows an intermediate behavior where both the five-coordinate anion and its dimeric precursor are jointly detected on the time scale of the spectroelectrochemical experiments. Under an atmosphere of CO2 the studied complexes, except for the DIPIMP derivative, rapidly coordinate CO2, forming stable bicarbonate intermediates, with no dimer being observed. Such behavior indicates that the CO2 binding is outcompeting another pathway: viz., the dimerization reaction between the five-coordinate anion and the neutral parent complex. The bicarbonate intermediate species undergo reduction at more negative potentials (ca. −2.2 V vs Fc/Fc+ ), recovering [Mn(CO)3(IP)]− and triggering the catalytic production of CO

Structure and variability of the Denmark Strait Overflow: Model and observations

We report on a combined modeling and observational effort to understand the Denmark Strait Overflow (DSO). Four cruises over the course of 3 years mapped hydrographic properties and velocity fields with high spatial resolution. The observations reveal the mean path of the dense water, as well as the presence of strong barotropic flows, energetic variability, and strong bottom friction and entrainment. A regional sigma coordinate numerical model of interbasin exchange using realistic bottom topography and an overflow forced only by an upstream reservoir of dense fluid is compared with the observations and used to further investigate these processes. The model successfully reproduces the volume transport of dense water at the sill, as well as the 1000-m descent of the dense water in the first 200 km from the sill and the intense eddies generated at 1–3 day intervals. Hydraulic control of the mean flow is indicated by a region supercritical to long gravity waves in the dense layer located approximately 100 km downstream of the sill in both model and observations. In addition, despite the differences in surface forcing, both model and observations exhibit similar transitions from mostly barotropic flow at the sill to a bottom-trapped baroclinic flow downstream, indicating the dominant role of the overflow in determining the full water column dynamics

Mediation in the Law Curriculum

Cited by Lord Neuberger in ‘Educating Future Mediators’ at the 4th Civil Mediation Council National Conference, May 201