To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure no-reply@cambridge.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Understanding the solutal convection is a crucial step towards accurate prediction of CO$_2$ sequestration in deep saline aquifers. In this study, pore-scale resolved direct numerical simulations (DNS) are performed to analyse the scaling laws of the solutal convection in porous media. The porous media studied are composed of uniformly distributed square or circular elements. The Rayleigh numbers in the range $426 \le Ra \le 80\,000$, the Darcy numbers in the range $1.7\times 10^{-8} \le Da \le 8.8\times 10^{-6}$ and the Schmidt numbers in the range $250 \le Sc \le 10^4$ are considered in the DNS. The main time, length and velocity scales affecting the solutal convection are classified as the diffusive scales ($t_I$, $l_I$ and $u_I$), the convective scales ($t_{II}$, $l_{II}$ and $u_{II}$) and the shut-down scales ($t_{III}$, $l_{III}$ and $u_{III}$). These scales determine the pore-scale Rayleigh number $Ra_K$ and the Rayleigh number $Ra$. Based on the DNS results, the scaling laws for the transient dissolution flux are proposed in the different regimes of convection. It is found that the onset time of convection ($t_{oc}$) and the period of the flux-growth regime ($\Delta t_{fg}$) vary linearly with the convective time scale $t_{II}$. The merging of the original plumes and the re-initiation of the new plumes start in the same period, resulting in the merging re-initiation regime. Horizontal dispersion plays an important role in plume merging. The dissolution flux $F$ and the time since the onset of convection $t^{\ast }$ have an $F / u_{II} \sim (t^{\ast }/ t_{II})^{-0.2}$ scaling in the later stage of the merging re-initiation regime. This scaling is caused by the merging of the low-wavenumber plumes. It becomes more pronounced with decreasing porosity and leads to the nonlinear relationship between the Sherwood number $Sh$ and $Ra$ when the domain is not high enough for the plumes to fully develop. According to the DNS results, a regime is expected that is independent of both $Ra$ and $Ra_K$, while the dimensionless constant flux $F_{cf}/u_{II}$ in this regime decreases with decreasing porosity. When the mean solute concentration reaches approximately 30 %, convection enters the shut-down regime. For large $Ra$, the dimensionless flux in the shut-down regime follows the scaling law $F/u_{III}\sim (t/t_{III})^{-1.2}$ at large porosity ($\phi =0.56$) and $F/u_{III}\sim (t/t_{III})^{-1.5}$ at small porosity ($\phi =0.36$ or $0.32$). The study shows the significant pore-scale effect on the convection. The DNS cases in this study are mainly for simplified geometries and large $Ra_K$. This can lead to uncertainties of the obtained scaling coefficients. It is important to determine the scaling coefficients for real geological formations to predict a real CO$_2$ sequestration process.
Let $L=-\Delta +V$ be a Schrödinger operator in ${\mathbb R}^n$ with $n\geq 3$, where $\Delta $ is the Laplace operator denoted by $\Delta =\sum ^{n}_{i=1}({\partial ^{2}}/{\partial x_{i}^{2}})$ and the nonnegative potential V belongs to the reverse Hölder class $(RH)_{q}$ with $q>n/2$. For $\alpha \in (0,1)$, we define the operator
where $\{e^{-tL^\alpha } \}_{t>0}$ is the fractional heat semigroup of the operator L, $\{v_j\}_{j\in \mathbb Z}$ is a bounded real sequence and $\{a_j\}_{j\in \mathbb Z}$ is an increasing real sequence.
We investigate the boundedness of the operator $T_N^{L^{\alpha }}$ and the related maximal operator $T^*_{L^{\alpha }}f(x):=\sup _N \vert T_N^{L^{\alpha }} f(x)\vert $ on the spaces $L^{p}(\mathbb {R}^{n})$ and $BMO_{L}(\mathbb {R}^{n})$, respectively. As extensions of $L^{p}(\mathbb {R}^{n})$, the boundedness of the operators $T_N^{L^{\alpha }}$ and $T^*_{L^{\alpha }}$ on the Morrey space $L^{\rho ,\theta }_{p,\kappa }(\mathbb {R}^{n})$ and the weak Morrey space $WL^{\rho ,\theta }_{1,\kappa }(\mathbb {R}^{n})$ has also been proved.
We introduce gradient flow aggregation, a random growth model. Given existing particles $\{x_1,\ldots,x_n\} \subset \mathbb{R}^2$, a new particle arrives from a random direction at $\infty$ and flows in direction of the vector field $\nabla E$ where $ E(x) = \sum_{i=1}^{n}{1}/{\|x-x_i\|^{\alpha}}$, $0 < \alpha < \infty$. The case $\alpha = 0$ refers to the logarithmic energy ${-}\sum\log\|x-x_i\|$. Particles stop once they are at distance 1 from one of the existing particles, at which point they are added to the set and remain fixed for all time. We prove, under a non-degeneracy assumption, a Beurling-type estimate which, via Kesten’s method, can be used to deduce sub-ballistic growth for $0 \leq \alpha < 1$, $\text{diam}(\{x_1,\ldots,x_n\}) \leq c_{\alpha} \cdot n^{({3 \alpha +1})/({2\alpha + 2})}$. This is optimal when $\alpha = 0$. The case $\alpha = 0$ leads to a ‘round’ full-dimensional tree. The larger the value of $\alpha$, the sparser the tree. Some instances of the higher-dimensional setting are also discussed.
Developing a model to describe the shock-accelerated cylindrical fluid layer with arbitrary Atwood numbers is essential for uncovering the effect of Atwood numbers on the perturbation growth. The recent model (J. Fluid Mech., vol. 969, 2023, p. A6) reveals several contributions to the instability evolution of a shock-accelerated cylindrical fluid layer but its applicability is limited to cases with an absolute value of Atwood numbers close to $1$, due to the employment of the thin-shell correction and interface coupling effect of the fluid layer in vacuum. By employing the linear stability analysis on a cylindrical fluid layer in which two interfaces separate three arbitrary-density fluids, the present work generalizes the thin-shell correction and interface coupling effect, and thus, extends the recent model to cases with arbitrary Atwood numbers. The accuracy of this extended model in describing the instability evolution of the shock-accelerated fluid layer before reshock is confirmed via direct numerical simulations. In the verification simulations, three fluid-layer configurations are considered, where the outer and intermediate fluids remain fixed and the density of the inner fluid is reduced. Moreover, the mechanisms underlying the effect of the Atwood number at the inner interface on the perturbation growth are mainly elucidated by employing the model to analyse each contribution. As the Atwood number decreases, the dominant contribution of the Richtmyer–Meshkov instability is enhanced due to the stronger waves reverberated inside the layer, leading to weakened perturbation growth at initial in-phase interfaces and enhanced perturbation growth at initial anti-phase interfaces.
We consider uniqueness problems for meromorphic inner functions on the upper half-plane. In these problems, we consider spectral data depending partially or fully on the spectrum, derivative values at the spectrum, Clark measure, or the spectrum of the negative of a meromorphic inner function. Moreover, we consider applications of these uniqueness results to inverse spectral theory of canonical Hamiltonian systems and obtain generalizations of the Borg-Levinson two-spectra theorem for canonical Hamiltonian systems and unique determination of a Hamiltonian from its spectral measure under some conditions.
The resolvent analysis reveals the worst-case disturbances and the most amplified response in a fluid flow that can develop around a stationary base state. The recent work by Padovan et al. (J. Fluid Mech., vol. 900, 2020, A14) extended the classical resolvent analysis to the harmonic resolvent analysis framework by incorporating the time-varying nature of the base flow. The harmonic resolvent analysis can capture the triadic interactions between perturbations at two different frequencies through a base flow at a particular frequency. The singular values of the harmonic resolvent operator act as a gain between the spatiotemporal forcing and the response provided by the singular vectors. In the current study, we formulate the harmonic resolvent analysis framework for compressible flows based on the linearized Navier–Stokes equation (i.e. operator-based formulation). We validate our approach by applying the technique to the low-Mach-number flow past an airfoil. We further illustrate the application of this method to compressible cavity flows at Mach numbers of 0.6 and 0.8 with a length-to-depth ratio of $2$. For the cavity flow at a Mach number of 0.6, the harmonic resolvent analysis reveals that the nonlinear cross-frequency interactions dominate the amplification of perturbations at frequencies that are harmonics of the leading Rossiter mode in the nonlinear flow. The findings demonstrate a physically consistent representation of an energy transfer from slow-evolving modes toward fast-evolving modes in the flow through cross-frequency interactions. For the cavity flow at a Mach number of 0.8, the analysis also sheds light on the nature of cross-frequency interaction in a cavity flow with two coexisting resonances.
Diphtheria, a highly contagious disease that can be prevented through vaccination, is emerging in Khyber-Pakhtunkhwa, Pakistan, an area known for its instability, which presents a severe risk of becoming an epidemic. This is particularly concerning, as the Government of Pakistan intends to send (push back, actually) Afghan refugees back to Afghanistan. This research aims to study the outbreak from an epidemiological perspective and suggest ways to manage it.
Methods
The study uses data from the Khyber Pakhtunkhwa Department of Health Information System, which systematically collects data throughout the province.
Results
Data from the provincial District Health Information System showed 291 confirmed cases of diphtheria across 28 districts, highlighting the considerable public health challenge posed by the disease’s capacity to spread widely. Among these, 16 cases were confirmed through laboratory tests, emphasizing the urgent need for better diagnostic services to identify diphtheria quickly and accurately. The research points out 4 specific outbreaks confirmed in laboratories in Batagram, Charsadda, Khyber, and Kohat, showcasing the broad geographic reach of the disease and the necessity for targeted public health initiatives in these areas.
Conclusions
By adopting a comprehensive and multi-faceted approach, there is a significant opportunity to reduce and ultimately eliminate the risk of diphtheria becoming an uncontrolled epidemic in the region.
The objective of this study was to explore the burden of disasters and adverse health outcomes during and following disasters in Bangladesh.
Methods
We analyzed 6 788 947 respondents’ data from a cross-sectional and nationally representative 2021 Bangladesh Disaster-related Statistics (BDRS). The key explanatory variables were the types of disasters respondents faced, while the outcome variables were the disease burden during and following disasters. Descriptive statistics were used to determine disease burden. A multilevel mixed-effects logistic regression model assessed the association between disease burden and disaster types, along with socio-demographic characteristics of respondents.
Results
Nearly 50% of respondents experienced diseases during disasters, rising to 53.4% afterward. Fever, cough and diarrhea were prevalent during and after disasters, with increases in skin diseases, malnutrition, and asthma post-disaster. Vulnerable groups, such as children aged 0–4, hijra individuals, those with lower education, people with disabilities, and rural residents, especially in Chattogram, Rangpur, and Sylhet divisions, were most affected. Floods, cyclones, thunderstorms, and hailstorms significantly increased disease likelihood during and after disasters.
Conclusions
The study underscores the complex relationship between disasters and health outcomes in Bangladesh, stressing the need for targeted public health interventions, improved health care infrastructure, and evidence-based policies to mitigate disaster-related health risks.
We use a novel experiment in China to examine the effects of having a quasi-official investor own a small number of shares on specific firm outcomes. We find that, relative to control firms, pilot firms experience an increase in dissenting votes from independent directors, a reduction in tunneling and earnings management activities, and an improvement in merger performance. Independent directors questioned by the quasi-official shareholder in activism events subsequently lose board seats in the director market. Overall, our results shed light on a new mechanism for enhancing the protection of minority shareholders.
In this article, I argue that iconographic pathography provides a transformational form of storytelling for ill persons and the communities around them. This work addresses the reduction of illness narration to clinical vocabularies. It targets often excluded communities—chronic and terminal narrators—as well as promotes ethical practices of creative and collaborative inclusion for ecclesial communities. I use Devan Stahl’s Imaging and Imagining Illness as an example of this distinctive form of pathography, first differentiating it from other narrative forms of the genre as well as contextualizing its decentralized narrational form with criteria drawn from icons’ emergence within early Christian art. I claim that such decentralized narration changes the trajectory of self-understanding for the ill person as well as the ethical response required for those who bear witness to such narratives.
Modular floating solar farms exhibit periodic open surface coverages due to the strip configuration of floating modules that support the photovoltaic (PV) panels on top. The associated modulations in the surface boundary layer and its turbulence characteristics are investigated in the present study under fully developed open channel flows. Different coverage percentages of 100 % (i.e. full cover), 60 %, 30 % and 0 % (i.e. open surface) were tested and measurements were obtained using particle image velocimetry. The results showed that the turbulence statistics are similar when the coverage decreases from 100 % to 60 %. However, with 30 %, both the turbulence intensities and Reynolds stresses increase substantially, reaching up to 50 % higher compared with the 100 % coverage, and the boundary layer thickness increases by more than 25 %. The local skin friction beneath the openings increases by 50 %. Analysis of spanwise vortices and premultiplied spectra indicates that the periodic coverage elongates the hairpin vortex packets and reduces their inclination angle, imposing limitations on sustainable coherent structures. At 30 %, flow detachment and smaller-scale vortices become dominant, reducing the mean velocities and increasing the turbulence intensities. Decreasing coverage percentage with flow detachment also shifts the energy transfer to higher wavenumbers, increasing energy dissipation and decreasing the bulk flow velocity. The kinetic energy and Reynolds stress carried by very large-scale motions decreases from 40 %–50 % with the 100 % and 60 % coverage to around 30 %–40 % with the 30 % coverage. Further research studies involving spanwise heterogeneity, higher Reynolds number and varying submergence of PV modules are needed for environmental considerations.
We propose a theoretical method to decompose the solution of a Stokes flow past a body immersed in a confined fluid into two simpler problems, related separately to the two geometrical elements of these systems: (i) the body immersed in the unbounded fluid (represented by its Faxén operators); and (ii) the domain of the confinement (represented by its Stokesian multipoles). Specifically, by using a reflection method, and assuming linear and reciprocal boundary conditions (Procopio & Giona, Phys. Fluids, vol. 36, issue 3, 2024, 032016), we provide the expression for the velocity field, the forces, torques and higher-order moments acting on the body in terms of: (i) the volume moments of the body in the unbounded ambient flow; (ii) the multipoles in the domain of the confinement; (iii) the collection of all the volumetric moments on the body immersed in all the regular parts of the multipoles considered as ambient flows. A detailed convergence analysis of the reflection method is developed. In light of the practical applications, we estimate the truncation error committed by considering only the lower-order moments (thus, truncating the matrices) and the errors associated with the approximated expressions available in the literature for force and torques. We apply the theoretical results to the archetypal hydrodynamic system of a sphere with Navier-slip boundary conditions near a plane wall with no-slip boundary conditions, to determine forces and torques on a translating and rotating sphere as a function of the slip length and of the distance of the sphere from the plane. The hydromechanics of a spheroid is also addressed.
We give a simple sufficient condition for Quinn’s ‘bordism-type’ spectra to be weakly equivalent to commutative symmetric ring spectra. We also show that the symmetric signature is (up to weak equivalence) a monoidal transformation between symmetric monoidal functors, which implies that the Sullivan–Ranicki orientation of topological bundles is represented by a ring map between commutative symmetric ring spectra. In the course of proving these statements, we give a new description of symmetric L theory which may be of independent interest.
This article presents a systematic review on the use of eye-tracking technology to assess the mental workload of unmanned aircraft system (UAS) operators. With the increasing use of unmanned aircraft in military and civilian operations, understanding the mental workload of these operators has become essential for ensuring mission effectiveness and safety. The review covered 26 studies that explored the application of eye-tracking to capture nuances of visual attention and assess cognitive load in real-time. Traditional methods such as self-assessment questionnaires, although useful, showed limitations in terms of accuracy and objectivity, highlighting the need for advanced approaches like eye-tracking. By analysing gaze patterns in simulated environments that reproduce real challenges, it was possible to identify moments of higher mental workload, areas of concentration and sources of distraction. The review also discussed strategies for managing mental workload, including adaptive design of human-machine interfaces. The analysis of the studies revealed a growing relevance and acceptance of eye-tracking as a diagnostic and analytical tool, offering guidelines for the development of interfaces and training that dynamically respond to the cognitive needs of operators. It was concluded that eye-tracking technology can significantly contribute to the optimisation of UAS operations, enhancing both the safety and efficiency of military and civilian missions.
African contemporary choreographers increasingly delink from Eurocentric performance conventions and work toward establishing local conditions of production and consumption by performing in public spaces. Although the labor undertaken to shift power asymmetries does not always result in structural changes, their art may be considered decolonial creative expression. Based on ethnographic research at the third and fourth editions (2022 and 2023) of Fatou Cissé’s street performance festival, La ville en mouv’ment (The City in Movement), in Dakar, Senegal, the author argues that decolonial potentiality extends beyond the precarious economic conditions to encapsulate the artists’ return to public space and futurist aesthetics.
Recently, Alanazi et al. [‘Refining overpartitions by properties of nonoverlined parts’, Contrib. Discrete Math.17(2) (2022), 96–111] considered overpartitions wherein the nonoverlined parts must be $\ell $-regular, that is, the nonoverlined parts cannot be divisible by the integer $\ell $. In the process, they proved a general parity result for the corresponding enumerating functions. They also proved some specific congruences for the case $\ell =3$. In this paper we use elementary generating function manipulations to significantly extend this set of known congruences for these functions.
In the study of plane curves, one of the problems is to classify the embedded topology of plane curves in the complex projective plane that have a given fixed combinatorial type, where the combinatorial type of a plane curve is data equivalent to the embedded topology in its tubular neighborhood. A pair of plane curves with the same combinatorial type but distinct embedded topology is called a Zariski pair. In this paper, we consider Zariski pairs consisting of conic-line arrangements that arise from Poncelet’s closure theorem. We study unramified double covers of the union of two conics that are induced by a $2m$-sided Poncelet transverse. As an application, we show the existence of families of Zariski pairs of degree $2m+6$ for $m\geq 2$ that consist of reducible curves having two conics and $2m+2$ lines as irreducible components.