The featured article ‘Break-up of a falling drop containing dispersed particles’ (Nitsche and Batchelor, J. Fluid Mech., 1997, vol. 340, pp. 161–175) is G. K. Batchelor's last published paper with his former postdoctoral associate J. M. Nitsche. The objective of the study was to investigate the randomness of the velocities of interacting rigid particles falling under gravity through a viscous fluid at a small Reynolds number and its consequence for the breakup of a falling cloud of particles. The study focused on a quintessential problem of the collective dynamics of interacting particles and has been an inspiration for subsequent work.

Given a connected reductive algebraic group G over an algebraically closed field, we investigate the Picard group of the moduli stack of principal G-bundles over an arbitrary family of smooth curves.

There is this view propounded by some theorists which claims that some conceptions of the nature of time are incompatible with the Christian position on the defeat of evil. The aim of this article is twofold. First, to clarify exactly which thesis about time’s nature is taken to be problematic for the defeat of evil. And second, to show that scriptural support for understanding the defeat of evil as requiring that evil not be in the range of the existential quantifier, something implicitly contended by those who put forward this problem, is weak and that these passages can be read in plausible ways which are affirmable by those who endorse the ‘problematic’ thesis.

Vaccination is the most important method to control the spread of SARS-CoV-2, the virus that causes COVID-19, and vaccination is key to this goal. This paper highlights considerations for policy development around vaccination attestation and proof requirements, specifically in rural Appalachia. Migrant and immigrant farmworkers are integral to the food and goods supply chain globally; they have been disproportionately impacted by COVID-19, therefore these policies need to take extensive precautions for farmworkers to systematically and easily comply with vaccination status submission procedures. In this paper, we present steps to equitably manage and implement vaccine mandates: (1) Develop and establish policies to support safe workplace standards for everyone, including vaccination policies; (2) Utilize equitable methods to collect vaccine verification; (3) Use effective and inclusive methods to implement the policies by using these techniques; (4) Integrate key populations to develop and strengthen policies to improve health equity.

There is a growing awareness that diversity, health equity, and inclusion play a significant role in improving patient outcomes and advancing knowledge. The Pediatric Heart Network launched an initiative to incorporate diversity, health equity, and inclusion into its 2021 Scholar Award Funding Opportunity Announcement. This manuscript describes the process of incorporating diversity, health equity, and inclusion into the Pediatric Heart Network Scholar Award and the lessons learned. Recommendations for future Pediatric Heart Network grant application cycles are made which could be replicated by other funding agencies.

Research in Roman interior design and wall painting has undergone two major shifts in the past century. The first, in the 1980s, steered away from the tradition of purely art historical studies that had elucidated the basic principles of artistic developments, iconographies, and pictorial programs. Instead, researchers focused on the Roman house as a social space, with private and public zones inhabited by individuals of different social standing. The second shift, occurring in the new millennium, saw researchers returning to the decoration of the house; however, they were now more intrigued by the cognition and reception of the paintings and how they were conceived to create atmospheres, mnemonic paths, and impressions on their viewers. Simultaneously, important insights into the often-multifunctional use of space were provided by finds analysis.

The accepted approach of competition law to non-horizontal mergers, largely based on the Chicago School of Antitrust Law and Economics paradigms, is criticized on both sides of the Atlantic as too lenient, disregarding developments of economic theory, and no longer adequate in the reality of the digital economy. Current economic research confirms the legitimacy of fears about the effects of non-horizontal concentrations that were raised before the Chicago School put them into doubt. The disbelief in the accuracy of the former US non-horizontal mergers policy resulted in the Federal Trade Commission and the Antitrust Division of the Department of Justice adopting new Vertical Merger Guidelines. The changes introduced were considered insufficient, which led to the unilateral repeal of the guidelines by the FTC and the start of work on new guidelines introducing a stricter approach. The new U.S. 2023 Merger Guidelines introduced far-reaching changes taking into account the modern views of economists and empirical research on vertical mergers. Comparatively, the EU Commission’s Non–Horizontal Merger Guidelines still do not fully correspond to what empirical research and contemporary economic theories say about the possible effects of vertical mergers. Thus, the revision of the EU guidelines seems necessary.

Static analysis of logic programs by abstract interpretation requires designing abstract operators which mimic the concrete ones, such as unification, renaming, and projection. In the case of goal-driven analysis, where goal-dependent semantics are used, we also need a backward-unification operator, typically implemented through matching. In this paper, we study the problem of deriving optimal abstract matching operators for sharing and linearity properties. We provide an optimal operator for matching in the domain $\mathtt{ShLin}^{\omega }$, which can be easily instantiated to derive optimal operators for the domains $\mathtt{ShLin}^2$ by Andy King and the reduced product $\mathtt{Sharing} \times \mathtt{Lin}$.

The quest for corporate accountability remains unabated in the business and human rights (BHR) field. This paper examines the role of multinational corporations (MNCs) and Business Interest Associations (BIA) as entrepreneurs, antipreneurs and saboteurs in setting human rights standards. Through this conceptualization, this paper argues that corporate accountability remains elusive because of corporate actors’ normative power and influence in the BHR norm contestation. It attributes corporate actors’ influence in the norm contestation to the UN multistakeholder design that sees nonstate actors as partners and stakeholders in setting global human rights standards. This paper then argues that to force a norm change in the BHR field, there is a need to rethink the BHR governance model. Corporate actors must be reconceptualized as ‘regulated individuals’ during norm discussions and standard-setting processes.

In this essay, I use Martin Luther King Jr.'s “Letter from Birmingham Jail” to open questions about international order and disorder. The idea of order is central to modern discourse on international politics, but the concept is often ill defined and ambiguous. King's ideas clarify three issues: First, is order understood as an objective condition of a system or a political judgment about its suitability for social life? Second, does compliance with law lead naturally to order? And third, is order always preferable to disorder? The way King answers each question is somewhat different than the conventional wisdom in international relations. IR scholars typically assume that international order is a universal good and that compliance with law enhances it. King highlights the gap between order as defined by the authorities in Alabama and his own lived experience. I use the difference to map the terrain of scholarship on international order and disorder and to draw implications for concepts, research methods, and political judgment.

Scholarly and practitioner interest in authentic leadership has grown at an accelerating rate over the last decade, resulting in a proliferation of publications across diverse social science disciplines. Accompanying this interest has been criticism of authentic leadership theory and the methods used to explore it. We conducted a systematic review of 303 scholarly articles published from 2010 to 2023 to critically assess the conceptual and empirical strengths and limitations of this literature and map the nomological network of the authentic leadership construct. Results indicate that much of the extant research does not follow best practices in terms of research design and analysis. Based on the findings obtained, an agenda for advancing authentic leadership theory and research that embraces a signaling theory perspective is proposed.

One of the problems with the problem of world order is that what makes for order within societies is often precisely what makes for disorderly relations between them. I argue in this short essay that many of the problems with the problem of world order arise from assumptions that are widely shared within a discipline where the language of power and interest dominates and where a view of states as “like units” permeates. With more emphasis on values and visions of the good life, and acceptance that the ontological foundation of IR is difference rather than sameness, the debates about the problem of world order would take on a different form. The essay adapts the work of Hedley Bull and introduces the concept of “resilience-governance” to distinguish between resilience as a practice of self-governance taking place within ordering domains and resilience as a practice of “diversity-governance” taking place between ordering domains. The combination of the two allows for a bifocal view into how practices of resilience as self-governance may produce order within individual domains but will at the same time increase diversity and difference between the ordering domains, hence making the practices of resilience as diversity-governance much more challenging.

This study closely replicates Wong, Zhao, & MacWhinney (2018), who found that cognitive linguistics–inspired instruction (i.e., schematic diagram feedback) demonstrated a superiority effect over traditional instruction (i.e., rule and exemplar feedback or corrective feedback) on the translation test but not the cloze test. While the original study adopted the null hypothesis testing approach, the current study adopted Bayesian mixed effects logistic models to investigate how different variables might affect the learnability of prepositions among 81 Chinese-speaking learners of English. The research design, materials, and procedure are nearly identical to those of the original study except for an added delayed posttest. Our findings are generally consistent with the results reported in the original study, indicating that the cognitive linguistics–informed instruction demonstrates superiority effect. Furthermore, these positive learning outcomes persist over time, as evidenced by the results of the delayed posttest.

Losses due to wake interactions between wind turbines can significantly reduce the power output of wind farms. The possibility of active flow control by wake deflection downstream of yawed horizontal-axis wind turbines has motivated research on the fluid mechanics involved. We summarize the findings of a wind tunnel study (Bastankhah & Porté-Agel, J. Fluid Mech., vol. 806, 2016, pp. 506–541) of the flow associated with a yawed model wind turbine, and the insights and modelling developments that have followed this important study.

We study the Abel-Jacobi image of the Ceresa cycle $W_{k, e}-W_{k, e}^-$, where $W_{k, e}$ is the image of the k-th symmetric product of a curve X with a base point e on its Jacobian variety. For certain Fermat quotient curves of genus g, we prove that for any choice of the base point and $k \leq g-2$, the Abel-Jacobi image of the Ceresa cycle is non-torsion. In particular, these cycles are non-torsion modulo rational equivalence.

Discussions of the liberal international order, both inside and outside the academy, tend to take its necessity and desirability for granted. While its specific contours and content are left somewhat open in such debates, the idea that this international order is essential for global peace and stability is left largely unquestioned. What is more, the potential loss or end of this order is often taken to mean a return to anarchy, chaos, and disorder. In this essay, I question the presumed necessity and desirability of the liberal international order that most discussions of it seem to share. By rethinking the international order as processual, emergent, and grounded in the social and political contexts that shape its constitution and operation, I suggest that fears about the crisis of international order are less about international order itself and more about the loss of a specific order. This specific order, I argue, constituted in part through processes of racialization, is not so much a rules-based order of sovereign equality but rather an international order of White sovereignty that secures the domination and rule of some over others, of Whiteness over non-Whiteness. Recognizing the role of White sovereignty in the contemporary international order points toward a need to take seriously calls for abolition. Rather than signifying a return to chaos and disorder, the prospect and promise of abolition represents a call to break free from the constraints of the present order and reach into an as-yet-unimaginable future.