A buoyant flow structure in a magnetic field: Quasi-steady states and linear-nonlinear transitions

The confined evolution of a buoyant blob of fluid subject to a vertical magnetic field is investigated in the limit of low magnetic Reynolds number. When the applied magnetic field is strong, the rise velocity of the blob is small. As the vorticity diffuses along the magnetic field lines, a quasi-steady state characterised by a balance between the work done by buoyancy and Ohmic dissipation is eventually reached at time tqs(L2/δ2)τ, where L is the axial dimension of the fluid domain, δ is the radius of the buoyant blob and τ is the magnetic damping time. However, when the applied magnetic field is weak or the axial length is sufficiently large compared to the blob size, the growth of axial velocity eventually makes the advection of vorticity significant. The typical time for the attainment of this nonlinear phase is , where N0 is the magnetic interaction parameter at time t=τ. The order-of-magnitude estimates for the timescales tqs and tnl are verified by computational experiments that capture both the linear and nonlinear phases

Tricks with the lorenz curve

This note develops, for the Gini coefficient of inequality, a very simple generalization that directly incorporates judgments on ‘relative inter-group inequality aversion' by making the inequality measure sensitive to the skewness of the Lorenz curve. The resulting family of inequality indices can be seen as complements to the Gini coefficient: some members of the family reflect ‘left-leaning', and others ‘right-leaning', distributional values relative to the ‘centrist' position assumed by Gini.Lorenz Curve, Gini coefficient, skewness

Confinement of rotating convection by a laterally varying magnetic field

Spherical shell dynamo models based on rotating convection show that the flow within the tangent cylinder is dominated by an off-axis plume that extends from the inner core boundary to high latitudes and drifts westward. Earlier studies explained the formation of such a plume in terms of the effect of a uniform axial magnetic field that significantly increases the lengthscale of convection in a rotating plane layer. However, rapidly rotating dynamo simulations show that the magnetic field within the tangent cylinder has severe lateral inhomogeneities that may influence the onset of an isolated plume. Increasing the rotation rate in our dynamo simulations (by decreasing the Ekman number $E$) produces progressively thinner plumes that appear to seek out the location where the field is strongest. Motivated by this result, we examine the linear onset of convection in a rapidly rotating fluid layer subject to a laterally varying axial magnetic field. A cartesian geometry is chosen where the finite dimensions $(x,z)$ mimic $(\phi,z)$ in cylindrical coordinates. The lateral inhomogeneity of the field gives rise to a unique mode of instability where convection is entirely confined to the peak-field region. The localization of the flow by the magnetic field occurs even when the field strength (measured by the Elsasser number $\varLambda$) is small and viscosity controls the smallest lengthscale of convection. The lowest Rayleigh number at which an isolated plume appears within the tangent cylinder in spherical shell dynamo simulations agrees closely with the viscous-mode Rayleigh number in the plane layer linear magnetoconvection model. The localized excitation of viscous-mode convection by a laterally varying magnetic field provides a mechanism for the formation of isolated plumes within Earth's tangent cylinder.Comment: 12 figures, 3 table

The Nature of Rights

The twentieth century saw a vigorous debate over the nature of rights. Will theorists argued that the function of rights is to allocate domains of freedom. Interest theorists portrayed rights as defenders of well-being. Each side declared its conceptual analysis to be closer to an ordinary understanding of what rights there are, and to an ordinary understanding of what rights do for rightholders. Neither side could win a decisive victory, and the debate ended in a standoff. This article offers a new analysis of rights. The first half of the article sets out an analytical framework adequate for explicating all assertions of rights. This framework is an elaboration of Hohfeld’s, designed around a template for displaying the often complex internal structures of rights. Those unfamiliar with Hohfeld’s work should find that the exposition here presumes no prior knowledge of it. Those who know Hohfeld will find innovations in how the system is defined and presented. Any theorist wishing to specify precisely what is at stake within a controversy over some particular right may find this framework useful. The analytical framework is then deployed in the second half of the article to resolve the dispute between the will and interest theories. Despite the appeal of freedom and well-being as organizing ideas, each of these theories is clearly too narrow. We accept rights, which do not (as the will theory holds) define domains of freedom; and we affirm rights whose aim is not (as the interest theory claims) to further the interests of the rightholder. A third theory, introduced here, is superior in describing the functions of rights as they are commonly understood

Online detection of temporal communities in evolving networks by estrangement confinement

Temporal communities result from a consistent partitioning of nodes across multiple snapshots of an evolving complex network that can help uncover how dense clusters in a network emerge, combine, split and decay with time. Current methods for finding communities in a single snapshot are not straightforwardly generalizable to finding temporal communities since the quality functions used for finding static communities have highly degenerate landscapes, and the eventual partition chosen among the many partitions of similar quality is highly sensitive to small changes in the network. To reliably detect temporal communities we need not only to find a good community partition in a given snapshot but also ensure that it bears some similarity to the partition(s) found in immediately preceding snapshots. We present a new measure of partition distance called "estrangement" motivated by the inertia of inter-node relationships which, when incorporated into the measurement of partition quality, facilitates the detection of meaningful temporal communities. Specifically, we propose the estrangement confinement method, which postulates that neighboring nodes in a community prefer to continue to share community affiliation as the network evolves. Constraining estrangement enables us to find meaningful temporal communities at various degrees of temporal smoothness in diverse real-world datasets. Specifically, we study the evolution of voting behavior of senators in the United States Congress, the evolution of proximity in human mobility datasets, and the detection of evolving communities in synthetic networks that are otherwise hard to find. Estrangement confinement thus provides a principled approach to uncovering temporal communities in evolving networks

Statistics and geometry of passive scalars in turbulence

We present direct numerical simulations (DNS) of the mixing of the passive scalar at modest Reynolds numbers (10 =< R_\lambda =< 42) and Schmidt numbers larger than unity (2 =< Sc =< 32). The simulations resolve below the Batchelor scale up to a factor of four. The advecting turbulence is homogeneous and isotropic, and maintained stationary by stochastic forcing at low wavenumbers. The passive scalar is rendered stationary by a mean scalar gradient in one direction. The relation between geometrical and statistical properties of scalar field and its gradients is examined. The Reynolds numbers and Schmidt numbers are not large enough for either the Kolmogorov scaling or the Batchelor scaling to develop and, not surprisingly, we find no fractal scaling of scalar level sets, or isosurfaces, in the intermediate viscous range. The area-to-volume ratio of isosurfaces reflects the nearly Gaussian statistics of the scalar fluctuations. The scalar flux across the isosurfaces, which is determined by the conditional probability density function (PDF) of the scalar gradient magnitude, has a stretched exponential distribution towards the tails. The PDF of the scalar dissipation departs distinctly, for both small and large amplitudes, from the lognormal distribution for all cases considered. The joint statistics of the scalar and its dissipation rate, and the mean conditional moment of the scalar dissipation, are studied as well. We examine the effects of coarse-graining on the probability density to simulate the effects of poor probe-resolution in measurements.Comment: 13 pages, 10 Postscript figures (2 with reduced quality