The article studies an initial boundary valueproblem (ibvp) for the radial solutions of the nonlinear Schrödinger (NLS) equation in a radially symmetric region $\Omega\in \mathbb R^n$ with boundaries. All such regions can be classified into three types: a ball Ω0 centred at origin, a region Ω1 outside a ball, and an n-dimensional annulus Ω2. To study the well-posedness of those ibvps, the function spaces for the boundary data must be specified in terms of the solutions in appropriate Sobolev spaces. It is shown that when $\Omega = \Omega_1$, the ibvp for the NLS equation is locally well-posed in $ C( [0, T^*]; H^s(\Omega_1))$ if the initial data is in $H^s(\Omega_1)$ and boundary data is in $ H^{\frac{2s+1}{4}}(0, T)$ with $s \geq 0$. This is the optimal regularity for the boundary data and cannot be improved. When $\Omega = \Omega_2$, the ibvp is locally well-posed in $ C( [0, T^*]; H^s(\Omega_2))$ if the initial data is in $ H^s(\Omega_2)$ and boundary data is in $ H^{\frac{s+1}{2}}(0, T)$ with $s \geq 0$. In this case, the boundary data requires $1/4$ more derivative compared to the case when $\Omega = \Omega_1$. When $\Omega = \Omega_0$ with n = 2 (the case with n > 2 can be discussed similarly), the ibvp is locally well-posed in $ C( [0, T^*]; H^s(\Omega_0))$ if the initial data is in $ H^s(\Omega_0)$ and boundary data is in $ H^{\frac{s+1}{2}}(0, T)$ with s > 1 (or $s \gt n/2$). Due to the lack of Strichartz estimates for the corresponding boundary integral operator with $ 0 \leq s \leq 1$, the local well-posedness can only be achieved for s > 1. It is noted that the well-posedness results on Ω0 and Ω2 are the first ones for the ibvp of NLS equations in bounded regions of higher dimension.

In a recent article Jack Mulder, Jr gives a Plantinga-style defence of the Virgin Mary’s free consent to bear Jesus at the Annunciation. Against Mulder, I argue that a theodicy (rather than a defence) is necessary to undermine my arguments, that Mulder’s Catholic appeal to Mary’s Immaculate Conception amounts to a kind of freedom-undermining metaphysical grooming, and therefore Marian consent remains invalid.

The friction drag of the axial flow along the outer surface of a cylinder varies with the cylinder radius and flow conditions. This study included direct numerical simulations of the axial turbulent flow along a circular cylinder under different conditions for obtaining the turbulence statistics and wall friction coefficient. Then the characteristics of velocity streaks were observed from a geometrical perspective of turbulence structures around the circular cylinder, and compared with the characteristics of the turbulence structures in a boundary layer on a flat plate. The results showed that the velocity streak spacing and the distance between the velocity streak and the cylinder surface in the viscous length scale do not vary substantively with the radius of the cylinder, and are the same as those of the turbulent flow along a flat plate. Therefore, they can be considered geometrical characteristics of the turbulence structure independent of the cylinder radius. Moreover, the friction coefficient per pair of high- and low-speed velocity streaks is the same as that of flat-plate turbulent flow, independent of the cylinder radius, and can be regarded as a dynamical characteristic for a pair of velocity streaks. Two equations were derived based on the characteristics of wall turbulence. The characteristics of the turbulence predicted by the two formulae were consistent with the simulation results. Consequently, we showed that the wall friction coefficient and number of the velocity streak pairs, which are statistical and structural characteristics of wall turbulence, can be predicted appropriately by specifying the radius Reynolds number.

This essay explores what can be learned from understanding EU law as a language in the literary sense of being a set of resources for manifold ethical and political expression and social action. As a contribution to new methodological approaches to studying EU law, it will propose a method highlighting how EU law can be studied in such a way by paying attention to the various linguistic and structural features of a legal text while, at the same time, diversifying the rationales through which we understand and make sense of such textual features. The Sayn–Wittgenstein decision will serve as point of reference in order to illustrate the value-added of this new theoretical and methodological insight to understanding EU law. This essay will conclude that it is not only worth taking the language of EU law seriously because it allows us to ’see’ more in the law, but also because it enables us to elevate the deeper ideas about Europe to the surface of the language we use when writing and speaking about EU law and to thereby contribute to a more productive dialogue about the foundations and future of the EU polity.

Spanwise vortex instability and the growth of secondary hairpin-like vortical structures in the wake of an oscillating foil are investigated numerically at Reynolds number 8000 in a range of chord-based Strouhal number ($0.32 \le St_c \le 0.56$). The phase-offset ($\phi$) between the heaving and pitching motion is $\phi = 90^\circ$. The wake at the lowest $St_c$ (0.32) is characterized by a single system of streamwise hairpin-like structures that evolve from the core vorticity outflux of the secondary leading edge vortex (LEV) over the foil boundary. The primary LEV features spanwise dislocations, but it does not reveal substantial changes advecting downstream. Increasing $St_c$ beyond 0.32 reveals that the transition in spanwise instability characterizes the deformation of primary LEV cores, which subsequently transforms to hairpin-like secondary structures. At higher $St_c$, stronger trailing edge vortices (TEVs) grow in close proximity to the primary LEVs, which contributes to an enhanced localized vortex compression and tilting near dislocations. This phenomenon amplifies the undulation amplitude of primary LEVs, eventually leading to vortex tearing. The larger circulation of TEVs with increasing $St_c$ provides an additional explanation for an accelerated vortex compression that coincides with a faster transition of spanwise LEV instability to secondary hairpin-like structures in the wake.

The most common method to characterize the electrical response of a nanofluidic system is through its steady-state current–voltage response. In Part 1, we demonstrated that this current–voltage response depends on the geometry, the layout of the surface charge and the effects of advection. We demonstrated that each configuration has a unique steady-state signature. Here, we will elucidate the behaviour of the time-transient response. Similar to the steady-state response, we will show that each configuration has its own unique time-transient signature when subjected to electroosmotic instability. We show that bipolar systems behave differently than unipolar systems. In unipolar systems, the instability appears only at one end of the system. In contrast, in bipolar systems the instability will either appear on both sides of the nanochannel or not at all. If it does appear on both sides, the instability will eventually vanish on one or both sides of the system. In Part 1, these phenomena were explained using steady-state considerations of the behaviour of the fluxes. Here, we will examine the time-transient behaviour to reveal the governing principles that are, on the one hand, not so different from unipolar systems and, on the other hand, remarkably different.

This review article explores the role of land-grant Extension amidst an escalating epistemic crisis, where misinformation and the contestation of knowledge severely impact public trust and policymaking. We delve into the historical mission of land-grant institutions to democratize education and extend knowledge through Cooperative Extension Services, highlighting their unique position to address contemporary challenges of information disorder and declining public confidence in higher education. Land-grant universities can reaffirm their relevance and leadership in disseminating reliable information by reasserting their foundational principles of unbiased, objective scholarship and deep engagement with diverse stakeholders. This reaffirmation comes at a critical time when societal trust in science and academia is waning, necessitating a recommitment to community engagement and producing knowledge for the public good. The article underscores the necessity for these institutions to adapt to the changing information landscape by fostering stakeholder-engaged scholarship and enhancing accessibility, thus reinforcing their vital role in upholding the integrity of public discourse and policy.

This study focuses on the practicalities of establishing and maintaining AI infrastructure, as well as the considerations for responsible governance by investigating the integration of a pre-trained large language model (LLM) with an organisation’s knowledge management system via a chat interface. The research adopts the concept of “AI as a constituted system” to emphasise the social, technical, and institutional factors that contribute to AI’s governance and accountability. Through an ethnographic approach, this article details the iterative processes of negotiation, decision-making, and reflection among organisational stakeholders as they develop, implement, and manage the AI system. The findings indicate that LLMs can be effectively governed and held accountable to stakeholder interests within specific contexts, specifically, when clear institutional boundaries facilitate innovation while navigating the risks related to data privacy and AI misbehaviour. Effective constitution and use can be attributed to distinct policy creation processes to guide AI’s operation, clear lines of responsibility, and localised feedback loops to ensure accountability for actions taken. This research provides a foundational perspective to better understand algorithmic accountability and governance within organisational contexts. It also envisions a future where AI is not universally scaled but consists of localised, customised LLMs tailored to stakeholder interests.

Microscopic irregularity (roughness) of bounding surfaces affects macroscopic dynamics of fluid flows. Its effect on bulk flow is usually quantified empirically by means of a roughness coefficient. A new approach, which treats rough surfaces (e.g. parallel plates) as random fields whose statistical properties can be inferred from measurements, is presented. The mapping of a random flow domain onto its deterministic counterpart, and the subsequent stochastic averaging of the transformed Stokes equations, yield expressions for the effective viscosity and roughness coefficient in terms of the statistical characteristics of the irregular geometry of the boundaries. The analytical nature of the solutions allows one to handle surface roughness characterized by short correlation lengths, a challenging feature for numerical stochastic simulations.

Open data promises various benefits, including stimulating innovation, improving transparency and public decision-making, and enhancing the reproducibility of scientific research. Nevertheless, numerous studies have highlighted myriad challenges related to preparing, disseminating, processing, and reusing open data, with newer studies revealing similar issues to those identified a decade prior. Several researchers have proposed the open data ecosystem (ODE) as a lens for studying and devising interventions to address these issues. Since actors in the ecosystem are individually and collectively impacted by the sustainability of the ecosystem, all have a role in tackling the challenges in the ODE. This paper asks what the contributions of open data intermediaries may be in addressing these challenges. Open data intermediaries are third-party actors providing specialized resources and capabilities to (i) enhance the supply, flow, and/or use of open data and/or (ii) strengthen the relationships among various open data stakeholders. They are critical in ensuring the flow of resources within the ODE. Through semi-structured interviews and a validation exercise in the European Union context, this study explores the potential contribution of open data intermediaries and the specific ODE challenges they may address. This study identified 20 potential contributions, addressing 27 challenges. The findings of this study pave the way for further inquiry into the internal incentives (viable business models) and external incentives (policies and regulations) to direct the contributions of open data intermediaries toward addressing challenges in the ODE.

In a questionnaire, participants judged the increase in SARS-CoV-2 virus exposure when moving closer to an infected person. Earlier studies have shown that the actual increase in virus exposure is underestimated and the present study replicated and extended these studies. The primary purpose was to investigate to what extent questionnaire judgments about hypothetical situations can predict judgments and actual behavior in real physical space. Participants responded to a questionnaire and the same participants also took part in a parallel study that was conducted in a room with a mannequin representing a virus infected person. The earlier reported bias in the perception of exposure as a function of distance to a virus source was replicated in the questionnaire and the physical laboratory study. A linear function connected median exposure judgments at the same distances from a virus source in the questionnaire and in the laboratory, R2 = 0.99. When asked to move to a distance that would give a prescribed exposure level, a linear function described the relationship between questionnaire distance judgments and moves to distances in the physical space, R2 = 0.95. We concluded that questionnaire data about perceived virus exposures are reliable indicators of real behavior. For health reasons, the significant underestimations of the steep increase of virus exposure during an approach to a virus source need to be stressed in communications to policy makers, the public, professionals working close to clients, nursing staff, and other care providers.

Among the factors identified to account for non-take-up of social benefits, there has been limited research on ‘process costs’, particularly regarding the impact of geographic access. Using Israeli data on field office openings from 1993 to 2021, this paper investigates the impact of geographic access on the take-up of the five largest social security programs in Israel. Based on staggered openings and closings of social security field offices, we find that geographic access has no significant impact on the take-up of either automatic enrollment programs, such as child allowances, or non-automatic programs, such as disability benefits. These findings suggest that the effect of geographic access on the take-up of social benefits may have been overstated in previous studies. We propose the following hypothesis to explain the surprising findings: If enhanced geographic access is driven by political favoritism, opening of new service points may lead to the misallocation of resources and, in effect, increase administrative burdens, thereby undermining rather than improving the take-up of social benefits.

In spray cleaning, a multitude of small drops, violently accelerated by a high-speed gas stream, strike a dirty surface. This process is extremely effective: very little dirt can resist it. This is true even for dirt particles whose characteristic size is less than 100 nm. Spray cleaning is classically modelled by balancing particle adhesion with either inertial stress or viscous shear near the surface, the latter being calculated using droplet size and velocity as the characteristic length and velocity. This results in dimensionless numbers that are often well below one, suggesting that the mechanical stress exerted on the surface by the drop impact that detaches the particle is not well captured. Using quantitative nanoscale measurements, we show that the remarkable efficiency of spray cleaning results from the forced spreading of each droplet on the surface, which generates an unsteady and inhomogeneous shear confined to a boundary layer entrained in the wake of the liquid–solid contact line. In the very first moments of impact, the boundary layer is extremely thin, yielding a gigantic stress: the contact line of the spreading droplets sweeps all the surface particles away. We propose a quantitative model of spray cleaning based on this unsteady surface stress, which agrees well with (i) experimental data obtained with spray droplets of $34\ \mathrm {\mu }$m mean radius impacting the surface to be cleaned at a mean velocity ranging between 30 and 70 m s$^{-1}$ and contamination by nanoparticles of varying nature and shape and (ii) data in the literature on spray cleaning.

The theme of the 2024 Business History Conference was “doing business in the public interest,” but what does it actually mean to “do business in the public interest?” This presidential address challenges the idea of shareholder primacy as the main purpose of business enterprises historically and examines various ways that business historians might approach the idea of businesses acting in a public interest. In particular, it analyzes instances in which corporations made a decision in the public interest without clear evidence that it would benefit their bottom line; cases where it would demonstrably hurt their bottom line to prioritize the public; corporations that made a decision allegedly in the public interest that actually turned out to be bad for the public interest; and corporations that made a decision that was bad for the public interest that also turned out to be bad for their own bottom line.

Ever since Alexander Thom visited Calanais in the Outer Hebrides, groups of Neolithic monuments in western Scotland have been studied in relation to the land and the sky. Less attention has been paid to their close relationship with the sea. These places were secluded and could be difficult or dangerous to reach, yet details of their architecture suggest that there were close links between them. How important were long distance connections between 3000 and 2000 bc? Were some ceremonial centres visited by boat? And was the journey itself treated as a rite of passage? The case extends to structures in Orkney and Ireland.

We study the planar 3-colorablesubgroup $\mathcal{E}$ of Thompson’s group F and its even part ${\mathcal{E}_{\rm EVEN}}$. The latter is obtained by cutting $\mathcal{E}$ with a finite index subgroup of F isomorphic to F, namely the rectangular subgroup $K_{(2,2)}$. We show that the even part ${\mathcal{E}_{\rm EVEN}}$ of the planar 3-colorable subgroup admits a description in terms of stabilisers of suitable subsets of dyadic rationals. As a consequence ${\mathcal{E}_{\rm EVEN}}$ is closed in the sense of Golan and Sapir. We then study three quasi-regular representations associated with ${\mathcal{E}_{\rm EVEN}}$: two are shown to be irreducible and one to be reducible.