Linear and nonlinear contributions to the localization and dynamics of internal gravity waves in a stably stratified turbulent channel flow are investigated using data from direct numerical simulations (DNS). The classification into linear and nonlinear mechanisms is based on the resolvent formulation of the Navier–Stokes equations, which interprets velocity and temperature fluctuations (flow response) as the result of a linear operator (resolvent) acting on the nonlinear advection terms (forcing). Spatial and spatio-temporal power spectral densities computed from DNS data demonstrate that the stratified flow response is localized in spectral space and in the channel core, while the nonlinear forcing is broadband and spans up to the entire channel height. The localization of the velocity and temperature fluctuations in wavenumber and frequency is captured by the leading singular value of the resolvent operator. The wall-normal localization on the other hand results from a combination of linear dynamics and nonlinear forcing, and the latter is further examined using the cross-spectral density (CSD) tensor. Wall-normal subsets of the forcing CSD lead to flow responses that reveal a three-layer structure. The middle one hosts the critical layer of the gravity wave, and is termed the outer layer since it is flanked by an inner layer at the wall and the core region at the channel centre. Forcing within this outer layer generates the majority of the flow response in the channel core. Furthermore, a decomposition of the forcing CSD into velocity and temperature demonstrates that each imprints distinct phase relations on their associated responses, which lead to destructive interference and localization of the gravity waves in the channel core.

Sweeping changes in abortion politics are underway in the Americas. Argentina, Mexico, Colombia, and Uruguay have legalized abortion in recent years, marking a sea change in the most Catholic region of the world. At the same time, several states in the United States have restricted abortion access following the US Supreme Court’s decision to overturn Roe vs. Wade, and numerous Central American countries have moved to fully criminalize the practice. Abortion is now legal in countries where it was long taboo, whereas the United States is characterized by a patchwork of laws that spans from some of the most progressive in the world to near-total bans. What explains this changing panorama in terms of reproductive rights in the Americas?

In a vertical channel driven by an imposed horizontal temperature gradient, numerical simulations (Gao et al., Phys. Rev. E, vol. 88, 2013, 023010; Phys. Rev. E, vol. 91, 2015, 013006; Phys. Rev. E, vol. 97, 2018, 053107) have previously shown steady, time-periodic and chaotic dynamics. We explore the observed dynamics by constructing invariant solutions of the three-dimensional Oberbeck–Boussinesq equations, characterizing the stability of these equilibria and periodic orbits, and following the bifurcation structure of the solution branches under parametric continuation in Rayleigh number. We find that in a narrow vertically periodic domain of aspect ratio 10, the flow is dominated by the competition between three and four co-rotating rolls. We demonstrate that branches of three- and four-roll equilibria are connected and can be understood in terms of their discrete symmetries. Specifically, the $D_4$ symmetry of the four-roll branch dictates the existence of qualitatively different intermediate branches that themselves connect to the three-roll branch in a transcritical bifurcation due to $D_3$ symmetry. The physical appearance, disappearance, merging and splitting of rolls along the connecting branch provide a physical and phenomenological illustration of the equivariant theory of $D_3$–$D_4$ mode interaction. We observe other manifestations of the competition between three and four rolls, in which the symmetry in time or in the transverse direction is broken, leading to limit cycles or wavy rolls, respectively. Our work highlights the interest of combining numerical simulations, bifurcation theory and group theory, in order to understand the transitions between and origin of flow patterns.

The future of public humanities will be determined by the infrastructural investments that support its continued development. These include, in the context of the United States, increased federal funding for the National Endowment for the Humanities; a serious re-engagement in the material support of new humanities scholarly production by private foundations; and a focused effort by humanities organizations to cultivate philanthropic donors. This manifesto argues that the humanities are the rightful inheritance of every person, regardless of background or position. If we are to take seriously both the resource needs of humanities research—which demand that funds be allocated for highly trained scholars to read, interpret, authenticate, preserve, and circulate primary source material—and the idea that no one has a higher claim than anyone else to these sources and processes and the insights they yield—which demands that individuals outside of the academy explicitly experience them selves as equal participants in the humanities—then our approach to both research infrastructure and public engagement must radically shift to emphasize repair. Repair, here, is the interpersonal, intellectual, strategic, repetitious, time-intensive work of ensuring that every individual can claim this rightful cultural inheritance. It is the work of creating the conditions for encounters between individuals and the vastness of history, culture, and difference. The future of public humanities must be in the creation of replicable models for these encounters, in the knowledge that in every instance, the work of the humanities is and must be unreproducible.

This investigation sheds light on the social history of pathogenic dirt and its significance for shaping medical practices during the nineteenth century. It consists of an analysis focusing on Swedish medicine, using 8800 yearly reports written 1820–1900 by Swedish provincial doctors for the National Board of Health in Stockholm. The main argument is that the provincial doctors’ perceptions of the relationship between dirt and health during this century can be better understood by focusing on similarities in the handling of different kinds of pathological dirt over the course of many decades, rather than seeing interest in cleanliness as something mostly unprecedented. A novel cleanliness regime became dominant during the latter third of the century, meant to counter a new hybrid between everyday dirt – bodily emanations from healthy bodies – and matter believed to have caused miasmatic and contagionistic disease. New ideas about filth and its impact on health played a crucial role in the development of public health and sanitation movements, and were a precondition for everyday dirt becoming a central medical problem around the turn of the twentieth century, but as is shown, they built on old precedents. Thus, the miasmatic and contagionistic approach to disease shaped conceptions of hygiene and cleanliness.

First predicted by Richtmyer in 1960 and experimentally confirmed by Meshkov in 1969, the Richtmyer–Meshkov instability (RMI) is crucial in fields such as physics, astrophysics, inertial confinement fusion and high-energy-density physics. These disciplines often deal with strong shocks moving through condensed materials or high-pressure plasmas that exhibit non-ideal equations of state (EoS), thus requiring theoretical models with realistic fluid EoS for accurate RMI simulations. Approximate formulae for asymptotic growth rates, like those proposed by Richtmyer, are helpful but rely on heuristic prescriptions for compressible materials. These prescriptions can sometimes approximate the RMI growth rate well, but their accuracy remains uncertain without exact solutions, as the fully compressible RMI growth rate is influenced by both vorticity deposited during shock refraction and multiple sonic wave refractions. This study advances previous work by presenting an analytic, fully compressible theory of RMI for reflected shocks with arbitrary EoS. It compares theoretical predictions with heuristic prescriptions using ideal gas, van der Waals gas and three-term constitutive equations for simple metals, the latter being analysed with detailed and simplified ideal-gas-like EoS. We additionally offer an alternative explicit approximate formula for the asymptotic growth rate. The comprehensive model also incorporates the effects of constant-amplitude acoustic waves at the interface, associated with the D'yakov–Kontorovich instability in shocks.

In network science, one of the significant and challenging subjects is the detection of communities. Modularity [1] is a measure of community structure that compares connectivity in the network with the expected connectivity in a graph sampled from a random null model. Its optimisation is a common approach to tackle the community detection problem. We present a new method for modularity maximisation, which is based on the observation that modularity can be expressed in terms of total variation on the graph and signless total variation on the null model. The resulting algorithm is of Merriman–Bence–Osher (MBO) type. Different from earlier methods of this type, the new method can easily accommodate different choices of the null model. Besides theoretical investigations of the method, we include in this paper numerical comparisons with other community detection methods, among which the MBO-type methods of Hu et al. [2] and Boyd et al. [3], and the Leiden algorithm [4].

Turbulent circular pipe flows subjected to axial system rotation are studied using direct numerical simulations (DNS) for a wide range of rotation numbers of $Ro_b = 0\unicode{x2013}20$ at a fixed Reynolds number. To ensure that energetic turbulent eddy motions are captured at high rotation numbers, long pipes up to $L_z = 180{\rm \pi} R$ are used in DNS. Two types of energy-containing flow structures have been observed. The first type is hairpin structures that are characteristic of the turbulent boundary layer developing over the pipe wall for both non-rotating and axially rotating flows. The second type is Taylor columns forming at moderate and high rotation numbers. Based on the study of two-point autocorrelation coefficients, it is observed that Taylor columns exhibit quasi-periods in both axial and azimuthal directions. According to the premultiplied spectra, Taylor columns feature one single characteristic axial length scale at the moderate rotation numbers but two at high rotation numbers. It is discovered that the axial system rotation suppresses the sweep events systematically and impedes the formation of hairpin structures. As the rotation number is increased, the turbulence kinetic energy held by Taylor columns enhances rapidly associated with significant increases in their axial length scales.

Many physical systems exhibit limit-cycle oscillations that can typically be modeled as stochastically driven self-oscillators. In this work, we focus on a self-oscillator model where the nonlinearity is on the damping term. In various applications, it is crucial to determine the nonlinear damping term and the noise intensity of the driving force. This article presents a novel approach that employs a deep operator network (DeepONet) for parameter identification of self-oscillators. We build our work upon a system identification methodology based on the adjoint Fokker–Planck formulation, which is robust to the finite sampling interval effects. We employ DeepONet as a surrogate model for the operator that maps the first Kramers–Moyal (KM) coefficient to the first and second finite-time KM coefficients. The proposed approach can directly predict the finite-time KM coefficients, eliminating the intermediate computation of the solution field of the adjoint Fokker–Planck equation. Additionally, the differentiability of the neural network readily facilitates the use of gradient-based optimizers, further accelerating the identification process. The numerical experiments demonstrate that the proposed methodology can recover desired parameters with a significant reduction in time while maintaining an accuracy comparable to that of the classical finite-difference approach. The low computational time of the forward path enables Bayesian inference of the parameters. Metropolis-adjusted Langevin algorithm is employed to obtain the posterior distribution of the parameters. The proposed method is validated against numerical simulations and experimental data obtained from a linearly unstable turbulent combustor.

We study Morita equivalence for idempotent rings with involution. Following the ideas of Rieffel, we define Rieffel contexts, and we also introduce Morita $*$-contexts and enlargements for rings with involution. We prove that two idempotent rings with involution have a joint enlargement if and only if they are connected by a unitary and full Rieffel context. These conditions are also equivalent to having a unitary and surjective Morita $*$-context between those rings. We also examine how the mentioned conditions are connected to the existence of certain equivalence functors between the categories of firm modules over the given rings with involution.

Aerodynamic breakup of vaporizing drops is commonly seen in many spray applications. While it is well known that vaporization can modulate interfacial instabilities, the impact of vaporization on drop aerobreakup is poorly understood. Detailed interface-resolved simulations were performed to systematically study the effect of vaporization, characterized by the Stefan number, on the drop breakup and acceleration for different Weber numbers and density ratios. It is observed that the resulting asymmetric vaporization rates and strengths of Stefan flow on the windward and leeward sides of the drop hinder bag development and prevent drop breakup. The critical Weber number thus generally increases with the Stefan number. The modulation of the boundary layer also contributes to a significant increase of drag coefficient. Numerical experiments were performed to affirm that the drop volume reduction plays a negligible role and the Stefan flow is the dominant reason for the breakup suppression and drag enhancement observed.

In this work, the Riemann–Hilbert (RH) problem is employed to study the multiple high-order pole solutions of the cubic Camassa–Holm (cCH) equation with the term characterizing the effect of linear dispersion under zero boundary conditions and nonzero boundary conditions. Under the reflectionless situation, we generalize the residue theorem and obtain the multiple high-order pole solutions of cCH equation by solving an algebraic system. During the process of establishing the solution of RH problem, to simplify the calculations involving the implicitly expressed of variables (x, t) in the solution, we introduce a new scale (y, t) to ensure the solution of RH problem is explicitly expressed with respect to it. Finally, the exact solutions are obtained for cases involving one high-order pole and N high-order poles.

A novel fast-running model is developed to predict the three-dimensional (3-D) distribution of turbulent kinetic energy (TKE) in axisymmetric wake flows. This is achieved by mathematically solving the partial differential equation of the TKE transport using the Green's function method. The developed solution reduces to a double integral that can be computed numerically for a wake prescribed by any arbitrary velocity profile. It is shown that the solution can be further simplified to a single integral for wakes with Gaussian-like velocity-deficit profiles. Wind tunnel experiments were performed to compare model results against detailed 3-D laser Doppler anemometry data measured within the wake flow of a porous disk subject to a uniform free-stream flow. Furthermore, the new model is used to estimate the TKE distribution at the hub-height level of the rotating non-axisymmetric wake of a model wind turbine immersed in a rough-wall boundary layer. Our results show the important impact of operating conditions on TKE generation in wake flows, an effect not fully captured by existing empirical models. The wind-tunnel data also provide insights into the evolution of important turbulent flow quantities such as turbulent viscosity, mixing length and the TKE dissipation rate in wake flows. Both mixing length and turbulent viscosity are found to increase with the streamwise distance. The turbulent viscosity, however, reaches a plateau in the far-wake region. Consistent with the non-equilibrium theory, it is also observed that the normalised energy dissipation rate is not constant, and it increases with the streamwise distance.

We present a one-parameter family Fλ of transcendental entire functions with zeros, whose Newton’s method yields wandering domains, coexisting with the basins of the roots of Fλ. Wandering domains for Newton maps of zero-free functions have been built before by, e.g. Buff and Rückert [23] based on the lifting method. This procedure is suited to our Newton maps as members of the class of projectable functions (or maps of the cylinder), i.e. transcendental meromorphic functions f(z) in the complex plane that are semiconjugate, via the exponential, to some map g(w), which may have at most a countable number of essential singularities. In this paper, we make a systematic study of the general relation (dynamical and otherwise) between f and g, and inspect the extension of the logarithmic lifting method of periodic Fatou components to our context, especially for those g of finite-type. We apply these results to characterize the entire functions with zeros whose Newton’s method projects to some map g which is defined at both 0 and $\infty$. The family Fλ is the simplest in this class, and its parameter space shows open sets of λ-values in which the Newton map exhibits wandering or Baker domains, in both cases regions of initial conditions where Newton’s root-findingmethod fails.

Because nuclear power development entails massive initial investments in power plants, along with institutional innovations in regulation, law, and basic physical infrastructure, there are strong grounds to support the pervasiveness of the central state in the industry. Furthermore, considering the scale economies in reactor installation, standardization in design, and enhanced learning by doing, little scope remains for the consideration of decentralized business interests. This article argues that competition, in the sense of rivalry between firms, can nonetheless be a driving force behind the nuclear industry. To illustrate the point, we draw a comparative, eventful history of two Iberian nations, Portugal and Spain: Portugal has failed several attempts to introduce nuclear power, while Spain has become one of the largest nuclear power nations in Europe. A fine-grained analysis of the circumstances surrounding the nuclear history of both countries is presented, highlighting the key variables of business history and the role of the central state and political actors in economic policy.

Let $f:X\to Y$ be a surjective projective map, and let L be a holomorphic line bundle on X equipped with a (singular) semi-positive Hermitian metric h. In this article, by studying the canonical metric on the direct image sheaf of the twisted relative canonical bundles $K_{X/Y}\otimes L\otimes \mathscr {I}(h)$, we obtain that this metric has dual Nakano semi-positivity when h is smooth and there is no deformation by f and that this metric has locally Nakano semi-positivity in the singular sense when h is singular.

Vertical thermal convection is a non-equilibrium system in which both buoyancy and shear forces play a role in driving the convective flow. Beyond the onset of convection, the driven dissipative system exhibits chaotic dynamics and turbulence. In a three-dimensional domain extended in both the vertical and the transverse dimensions, Gao et al. (Phys. Rev. E, vol. 97, 2018, 053107) have observed a variety of convection patterns which are not described by linear stability analysis. We investigate the fully nonlinear dynamics of vertical convection using a dynamical-systems approach based on the Oberbeck–Boussinesq equations. We compute the invariant solutions of these equations and the bifurcations that are responsible for the creation and termination of various branches. We map out a sequence of local bifurcations from the laminar base state, including simultaneous bifurcations involving patterned steady states with different symmetries. This atypical phenomenon of multiple branches simultaneously bifurcating from a single parent branch is explained by the role of $D_4$ symmetry. In addition, two global bifurcations are identified: first, a homoclinic cycle from modulated transverse rolls and second, a heteroclinic cycle linking two symmetry-related diamond-roll patterns. These are confirmed by phase space projections as well as the functional form of the divergence of the period close to the bifurcation points. The heteroclinic orbit is shown to be robust and to result from a 1:2 mode interaction. The intricacy of this bifurcation diagram highlights the essential role played by dynamical systems theory and computation in hydrodynamic configurations.

This article contributes to historiographical examinations of gender and capitalism in eighteenth-century India. Focusing on the fragile nature of revenue farming ventures in this period, the article illustrates how propertied women in the Eastern Gangetic plains used matriarchal authority and affect to lead their agrarian and mercantile family firms into commercial transactions. The article shows that the household was the locus of these commercial relationships and that of the competing and layered sovereignties of distinct state and non-state actors. At the same time, matriarchs exercised their authority beyond it. Travelling in palanquins, or having their kin conduct transactions on their behalf, they asserted their maternal authority and social status in different publics to protect their firms’ interests. In a second key argument, the article suggests that Mughal law, fostered by native officials in the early colonial courts in Banaras, facilitated propertied women’s participation in this economy. Matriarchs demonstrated a keen understanding of this fractured jurisdictional landscape and used it to their advantage as they manoeuvred from one legal forum to another. The third argument of this article illustrates that colonial regulations redefined, and could even compromise, propertied women’s engagements in land revenue transactions. These shifts were made possible through the mobilization of gender and specific understandings of womanhood and the household. In this article, I show that these attempts to disenfranchise propertied women in Banaras were intimately connected to the Company’s vision of a colonial public in which it could monopolize sovereignty.