A note on leapfrogging vortex rings

In this paper we provide examples, by numerical simulation using the Navier-Stokes equations for axisymmetric laminar flow, of the 'leapfrogging' motion of two, initially identical, vortex rings which share a common axis of symmetry. We show that the number of clear passes that each ring makes through the other increases with Reynolds number, and that as long as the configuration remains stable the two rings ultimately merge to form a single vortex ring

The relationship between the optical Halpha filaments and the X-ray emission in the core of the Perseus cluster

NGC 1275 in the centre of the Perseus cluster of galaxies, Abell 426, is surrounded by a spectacular filamentary Halpha nebula. Deep Chandra X-ray imaging has revealed that the brighter outer filaments are also detected in soft X-rays. This can be due to conduction and mixing of the cold gas in the filaments with the hot, dense intracluster medium. We show the correspondence of the filaments in both wavebands and draw attention to the relationship of two prominent curved NW filaments to an outer, buoyant radio bubble seen as a hole in the X-ray image. There is a strong resemblance in the shape of the hole and the disposition of the filaments to the behaviour of a large air bubble rising in water. If this is a correct analogy, then the flow is laminar and the intracluster gas around this radio source is not turbulent. We obtain a limit on the viscosity of this gas.Comment: Accepted for publication in MNRA

Superheating fields of superconductors: Asymptotic analysis and numerical results

The superheated Meissner state in type-I superconductors is studied both analytically and numerically within the framework of Ginzburg-Landau theory. Using the method of matched asymptotic expansions we have developed a systematic expansion for the solutions of the Ginzburg-Landau equations in the limit of small $\kappa$, and have determined the maximum superheating field $H_{\rm sh}$ for the existence of the metastable, superheated Meissner state as an expansion in powers of $\kappa^{1/2}$. Our numerical solutions of these equations agree quite well with the asymptotic solutions for $\kappa<0.5$. The same asymptotic methods are also used to study the stability of the solutions, as well as a modified version of the Ginzburg-Landau equations which incorporates nonlocal electrodynamics. Finally, we compare our numerical results for the superheating field for large-$\kappa$ against recent asymptotic results for large-$\kappa$, and again find a close agreement. Our results demonstrate the efficacy of the method of matched asymptotic expansions for dealing with problems in inhomogeneous superconductivity involving boundary layers.Comment: 14 pages, 8 uuencoded figures, Revtex 3.

Simple Viscous Flows: from Boundary Layers to the Renormalization Group

The seemingly simple problem of determining the drag on a body moving through a very viscous fluid has, for over 150 years, been a source of theoretical confusion, mathematical paradoxes, and experimental artifacts, primarily arising from the complex boundary layer structure of the flow near the body and at infinity. We review the extensive experimental and theoretical literature on this problem, with special emphasis on the logical relationship between different approaches. The survey begins with the developments of matched asymptotic expansions, and concludes with a discussion of perturbative renormalization group techniques, adapted from quantum field theory to differential equations. The renormalization group calculations lead to a new prediction for the drag coefficient, one which can both reproduce and surpass the results of matched asymptotics

A new method for the solution of the Schrodinger equation

We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wave function and, finally, a short distance scale, in which the wave function is sizable. The key feature of our method is the introduction of an arbitrary parameter in the last two scales, which is then used to optimize a perturbative expansion in a suitable parameter. We apply the method to the quantum anharmonic oscillator and find excellent results.Comment: 4 pages, 4 figures, RevTex

Private trade and monopoly structures : the East India Companies and the commodity trade to Europe in the eighteenth century

Our research is about the trade in material goods from Asia to Europe over this period, and its impact on Europe’s consumer and industrial cultures. It entails a comparative study of Europe’s East India Companies and the private trade from Asia over the period. The commodities trade was heavily dependent on private trade. The historiography to date has left a blind spot in this area, concentrating instead on corruption and malfeasance. Taking a global history approach we investigate the trade in specific consumer goods in many qualities and varieties that linked merchant communities and stimulated information flows. We set out how private trade functioned alongside and in connection with the various European East India companies; we investigate how this changed over time, how it drew on the Company infrastructure, and how it took the risks and developed new and niche markets for specific Asian commodities that the Companies could not sustain

A complex ray-tracing tool for high-frequency mean-field flow interaction effects in jets

This paper presents a complex ray-tracing tool for the calculation of high-frequency Green’s functions in 3D mean field jet flows. For a generic problem, the ray solution suffers from three main deficiencies: multiplicity of solutions, singularities at caustics, and the determining of complex solutions. The purpose of this paper is to generalize, combine and apply existing stationary media methods to moving media scenarios. Multiplicities are dealt with using an equivalent two-point boundary-value problem, whilst non-uniformities at caustics are corrected using diffraction catastrophes. Complex rays are found using a combination of imaginary perturbations, an assumption of caustic stability, and analytic continuation of the receiver curve. To demonstrate this method, the ray tool is compared against a high-frequency modal solution of Lilley’s equation for an off-axis point source. This solution is representative of high-frequency source positions in real jets and is rich in caustic structures. A full utilization of the ray tool is shown to provide excellent results<br/

Local Causal States and Discrete Coherent Structures

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the \localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht

Organometallic iridium(III) anticancer complexes with new mechanisms of action: NCI-60 screening, mitochondrial targeting, and apoptosis

Platinum complexes related to cisplatin, cis-[PtCl2(NH3)2], are successful anticancer drugs; however, other transition metal complexes offer potential for combating cisplatin resistance, decreasing side effects, and widening the spectrum of activity. Organometallic half-sandwich iridium (IrIII) complexes [Ir(Cpx)(XY)Cl]+/0 (Cpx = biphenyltetramethylcyclopentadienyl and XY = phenanthroline (1), bipyridine (2), or phenylpyridine (3)) all hydrolyze rapidly, forming monofunctional G adducts on DNA with additional intercalation of the phenyl substituents on the Cpx ring. In comparison, highly potent complex 4 (Cpx = phenyltetramethylcyclopentadienyl and XY = N,N-dimethylphenylazopyridine) does not hydrolyze. All show higher potency toward A2780 human ovarian cancer cells compared to cisplatin, with 1, 3, and 4 also demonstrating higher potency in the National Cancer Institute (NCI) NCI-60 cell-line screen. Use of the NCI COMPARE algorithm (which predicts mechanisms of action (MoAs) for emerging anticancer compounds by correlating NCI-60 patterns of sensitivity) shows that the MoA of these IrIII complexes has no correlation to cisplatin (or oxaliplatin), with 3 and 4 emerging as particularly novel compounds. Those findings by COMPARE were experimentally probed by transmission electron microscopy (TEM) of A2780 cells exposed to 1, showing mitochondrial swelling and activation of apoptosis after 24 h. Significant changes in mitochondrial membrane polarization were detected by flow cytometry, and the potency of the complexes was enhanced ca. 5× by co-administration with a low concentration (5 μM) of the γ-glutamyl cysteine synthetase inhibitor L-buthionine sulfoximine (L-BSO). These studies reveal potential polypharmacology of organometallic IrIII complexes, with MoA and cell selectivity governed by structural changes in the chelating ligands

Updated tests of scaling and universality for the spin-spin correlations in the 2D and 3D spin-S Ising models using high-temperature expansions

We have extended, from order 12 through order 25, the high-temperature series expansions (in zero magnetic field) for the spin-spin correlations of the spin-S Ising models on the square, simple-cubic and body-centered-cubic lattices. On the basis of this large set of data, we confirm accurately the validity of the scaling and universality hypotheses by resuming several tests which involve the correlation function, its moments and the exponential or the second-moment correlation-lengths.Comment: 21 pages, 8 figure