arXiv subjects

David W. Hughes

Publications and source records attributed to David W. Hughes.

15 recordsLinked to original sources

arXiv2025

A jackknife bias correction for nonlinear network data models with fixed effects

I introduce a new method for bias correction of dyadic models with agent-specific fixed effects, including the dyadic link formation model with homophily and degree heterogeneity. The proposed approach uses a jackknife procedure to deal with the incidental parameters problem. The method can be applied to both directed and undirected networks, allows for non-binary outcome variables, and can be used to bias correct estimates of average effects and counterfactual outcomes. I also show how the jackknife can be used to bias correct fixed-effect averages over functions that depend on multiple nodes, e.g. triads or tetrads in the network. As an example, I implement specifica- tion tests for dependence across dyads, such as reciprocity or transitivity. Finally, I demonstrate the usefulness of the estimator in an application to a gravity model for import/export relationships across countries.

econ.EM↗

arXiv2024

Efficient Bias Correction for Cross-section and Panel Data

Bias correction can often improve the finite sample performance of estimators. We show that the choice of bias correction method has no effect on the higher-order variance of semiparametrically efficient parametric estimators, so long as the estimate of the bias is asymptotically linear. It is also shown that bootstrap, jackknife, and analytical bias estimates are asymptotically linear for estimators with higher-order expansions of a standard form. In particular, we find that for a variety of estimators the straightforward bootstrap bias correction gives the same higher-order variance as more complicated analytical or jackknife bias corrections. In contrast, bias corrections that do not estimate the bias at the parametric rate, such as the split-sample jackknife, result in larger higher-order variances in the i.i.d. setting we focus on. For both a cross-sectional MLE and a panel model with individual fixed effects, we show that the split-sample jackknife has a higher-order variance term that is twice as large as that of the `leave-one-out' jackknife.

econ.EM↗

arXiv2023

Salt fingering staircases and the three-component Phillips effect

Understanding the dynamics of staircases in salt fingering convection presents a long-standing theoretical challenge to fluid dynamicists. Although there has been significant progress, particularly through numerical simulations, there are a number of conflicting theoretical explanations as to the driving mechanism underlying staircase formation. The Phillips effect proposes that layering in stirred stratified flow is due to an antidiffusive process, and it has been suggested that this mechanism may also be responsible for salt fingering staircases. However, the details of this process, as well as mathematical models to predict the evolution and merger dynamics of staircases, have yet to be developed. We generalise the theory of the Phillips effect to a three-component system (e.g. temperature, salinity, energy) and demonstrate the first regularised nonlinear model of layering based on mixing-length parameterisations. The model predicts both the inception of layering and its long-term evolution through mergers , whilst generalising, and remaining consistent with, previous results for double-diffusive layering based on flux ratios. Our model of salt fingering is formulated using spatial averaging processes and closed by a mixing length parameterised in terms of the kinetic energy and the salt and temperature gradients. The model predicts a layering instability for a bounded range of parameter values in the salt fingering regime. Nonlinear solutions show that an initially unstable linear buoyancy gradient develops into layers, which merge through a process of stronger interfaces growing at the expense of weaker interfaces. Mergers increase the buoyancy gradient across interfaces, and increase the buoyancy flux through the staircase.

physics.flu-dyn↗

arXiv2018

Stability of scrape-off layer plasma: a modified Rayleigh-Benard problem

We present a linear stability analysis of a two-dimensional fluid model used to study the plasma dynamics in the scrape-off layer of tokamaks. The model equations are based on the Braginskii fluid equations under the assumptions of drift ordering and an electrostatic plasma. The model also employs the common slab geometry approximation, whereby the magnetic field is assumed constant and straight, with the effects of curvature reintroduced as effective gravitational terms. We demonstrate that the governing plasma equations for the scrape-off layer can be viewed as describing a thermal convection problem with additional effects. The new features include a non-uniform basic state gradient, linear damping terms, and additional advective terms. We characterise the conditions at the onset of instability, and perform an extensive parameter scan to describe how the stability threshold varies as a function of plasma parameters.

physics.plasm-ph↗

arXiv2018

Mean Field Electrodynamics: Triumphs and Tribulations

The theory of mean field electrodynamics, now celebrating its fiftieth birthday, has had a profound influence on our modelling of cosmical dynamos, greatly enhancing our understanding of how such dynamos may operate. Here I discuss some of its undoubted triumphs, but also some of the problems that can arise in a mean field approach to dynamos in fluids (or plasmas) that are both highly turbulent and also extremely good electrical conductors, as found in all astrophysical settings.

astro-ph.SR↗

arXiv2017

Jets and large-scale vortices in rotating Rayleigh-Bénard convection

One of the most prominent dynamical features of turbulent, rapidly-rotating convection is the formation of large-scale coherent structures, driven by Reynolds stresses resulting from the small-scale convective flows. In spherical geometry, such structures consist of intense zonal flows that are invariant along the rotation axis. In planar geometry, long-lived, depth-invariant structures also form at large scales, but, in the absence of horizontal anisotropy, they consist of vortices that grow to the domain size. In this work, through the introduction of horizontal anisotropy into a numerical model of planar rotating convection by the adoption of unequal horizontal box sizes (i.e. $L_x \le L_y$, where the $xy$-plane is horizontal), we investigate whether unidirectional flows and large-scale vortices can coexist. We find that only a small degree of anisotropy is required to bring about a transition from dynamics dominated by persistent large-scale vortices to dynamics dominated by persistent unidirectional flows parallel to the shortest horizontal direction. When the anisotropy is sufficiently large, the unidirectional flow consists of multiple jets, generated on a timescale smaller than a global viscous timescale, thus signifying that the upscale energy transfer does not spontaneously feed the largest available mode in the system. That said, the multiple jets merge on much longer timescales. Large-scale vortices of size comparable with $L_x$ systematically form in the flanks of the jets and can be persistent or intermittent. This indicates that large-scale vortices, either coexisting with jets or not, are a robust dynamical feature of planar rotating convection.

physics.flu-dyn↗

arXiv2017

Large-scale-vortex dynamos in planar rotating convection

Several recent studies have demonstrated how large-scale vortices may arise spontaneously in rotating planar convection. Here we examine the dynamo properties of such flows in rotating Boussinesq convection. For moderate values of the magnetic Reynolds number ($100 \lesssim Rm \lesssim 550$, with $Rm$ based on the box depth and the convective velocity), a large-scale (i.e. system-size) magnetic field is generated. The amplitude of the magnetic energy oscillates in time, nearly out of phase with the oscillating amplitude of the large-scale vortex. The large-scale vortex is disrupted once the magnetic field reaches a critical strength, showing that these oscillations are of magnetic origin. The dynamo mechanism relies on those components of the flow that have length scales lying between that of the large-scale vortex and the typical convective cell size; smaller-scale flows are not required. The large-scale vortex plays a crucial role in the magnetic induction despite being essentially two-dimensional; we thus refer to this dynamo as a large-scale-vortex dynamo. For larger magnetic Reynolds numbers, the dynamo is small scale, with a magnetic energy spectrum that peaks at the scale of the convective cells. In this case, the small-scale magnetic field continuously suppresses the large-scale vortex by disrupting the correlations between the convective velocities that allow it to form. The suppression of the large-scale vortex at high $Rm$ therefore probably limits the relevance of the large-scale-vortex dynamo to astrophysical objects with moderate values of $Rm$, such as planets. In this context, the ability of the large-scale-vortex dynamo to operate at low magnetic Prandtl numbers is of great interest.

physics.flu-dyn↗

arXiv2016

Strong field dynamo action in rapidly rotating convection with no inertia

The Earth's magnetic field is generated by dynamo action driven by convection in the outer core. For numerical reasons, inertial and viscous forces play an important role in geodynamo models; however, the primary dynamical balance in the Earth's core is believed to be between buoyancy, Coriolis and magnetic forces. The hope has been that by setting the Ekman number to be as small as computationally feasible, an asymptotic regime would be reached in which the correct force balance is achieved. However, recent analyses of geodynamo models suggest that the desired balance has still not yet been attained. Here we adopt a complementary approach consisting of a model of rapidly rotating convection in which inertial forces are neglected from the outset. Within this framework we are able to construct a new branch of solutions in which the dynamo generates a strong magnetic field that satisfies the expected force balance. The resulting strongly magnetized convection is dramatically different to the corresponding solutions in which the field is weak.

astro-ph.EP↗

arXiv2015

Generation of magnetic fields by large-scale vortices in rotating convection

We propose a new self-consistent dynamo mechanism for the generation of large-scale magnetic fields in natural objects. Recent computational studies have described the formation of large-scale vortices (LSVs) in rotating turbulent convection. Here we demonstrate that for magnetic Reynolds numbers below the threshold for small-scale dynamo action, such turbulent flows can sustain large-scale magnetic fields --- i.e. fields with a significant component on the scale of the system.

physics.flu-dyn↗

arXiv2014

Large-scale vortices in rapidly rotating Rayleigh-Bénard convection

Using numerical simulations of rapidly rotating Boussinesq convection in a Cartesian box, we study the formation of long-lived, large-scale, depth-invariant coherent structures. These structures, which consist of concentrated cyclones, grow to the horizontal size of the box, with velocities significantly larger than the convective motions. We vary the rotation rate, the thermal driving and the aspect ratio in order to determine the domain of existence of these large-scale vortices (LSV). We find that two conditions are required for their formation. First, the Rayleigh number, a meaure of the thermal driving, must be several times its value at the linear onset of convection; this corresponds to Reynolds numbers, based on the convective velocity and the box depth, $\gtrsim 100$. Second, the rotational constraint on the convective structures must be strong. This requires that the local Rossby number, based on the convective velocity and the horizontal convective scale, $\lesssim 0.15$. Simulations in which certain wavenumbers are artificially suppressed in spectral space suggest that the LSV are produced by the interactions of small-scale, depth-dependent convective motions. The presence of LSV significantly reduces the efficiency of the convective heat transport.

physics.flu-dyn↗

arXiv2014

Incorporating Velocity Shear into the Magneto-Boussinesq Approximation

Motivated by consideration of the solar tachocline, we derive, via an asymptotic procedure, a new set of equations incorporating velocity shear and magnetic buoyancy into the Boussinesq approximation. We demonstrate, by increasing the magnetic field scale height, how these equations are linked to the magneto-Boussinesq equations of Spiegel and Weiss (1982).

astro-ph.SR↗

arXiv2011

Solar Magnetic Fields

This review provides an introduction to the generation and evolution of the Sun's magnetic field, summarising both observational evidence and theoretical models. The eleven year solar cycle, which is well known from a variety of observed quantities, strongly supports the idea of a large-scale solar dynamo. Current theoretical ideas on the location and mechanism of this dynamo are presented. The solar cycle influences the behaviour of the global coronal magnetic field and it is the eruptions of this field that can impact on the Earth's environment. These global coronal variations can be modelled to a surprising degree of accuracy. Recent high resolution observations of the Sun's magnetic field in quiet regions, away from sunspots, show that there is a continual evolution of a small-scale magnetic field, presumably produced by small-scale dynamo action in the solar interior. Sunspots, a natural consequence of the large-scale dynamo, emerge, evolve and disperse over a period of several days. Numerical simulations can help to determine the physical processes governing the emergence of sunspots. We discuss the interaction of these emerging fields with the pre-existing coronal field, resulting in a variety of dynamic phenomena.

astro-ph.SR↗

arXiv2009

The Turbulent Magnetic Diffusivity Tensor for Time-Dependent Mean Fields

We re-examine the nature of the turbulent magnetic diffusivity tensor of mean field electrodynamics and show that an inconsistency arises if it is calculated via consideration of time-independent magnetic fields. Specifically, the predicted growth rate of the mean magnetic field is, in general, incorrect. We describe how the traditional expansion procedure for the mean electromotive force should be extended, and illustrate the consistency of this approach by means of a perturbation analysis for a mean magnetic field varying on long spatial scales. Finally we examine the magnitude of this new contribution to the magnetic diffusion for a particular flow.

astro-ph.SR↗

arXiv2008

Large-scale Dynamo Action Driven by Velocity Shear and Rotating Convection

By incorporating a large-scale shear flow into turbulent rotating convection, we show that a sufficiently strong shear can promote dynamo action in flows that in the absence of shear do not act as dynamos. Our results are consistent with a dynamo driven by either the shear-current effect or by the interaction between a fluctuating $α$-effect and the velocity shear; they are though inconsistent with either a classical $α^2$ or $αω$ mean field dynamo.

astro-ph↗

arXiv2007

The Nonlinear Evolution of Instabilities Driven by Magnetic Buoyancy: A New Mechanism for the Formation of Coherent Magnetic Structures

Motivated by the problem of the formation of active regions from a deep-seated solar magnetic field, we consider the nonlinear three-dimensional evolution of magnetic buoyancy instabilities resulting from a smoothly stratified horizontal magnetic field. By exploring the case for which the instability is continuously driven we have identified a new mechanism for the formation of concentrations of magnetic flux.

astro-ph↗