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The main purpose of this paper is to establish the theory of the multi-parameter Hardy spaces More precisely, Street (2014) studied the

The synchronization of self-oscillating systems is vital to various biological functions, from the coordinated contraction of heart muscle to the self-organization of slime molds. Through modeling, we design bioinspired materials systems that spontaneously form shape-changing self-oscillators, which communicate to synchronize both their temporal and spatial behavior. Here, catalytic reactions at the bottom of a fluid-filled chamber and on mobile, flexible sheets generate the energy to “pump” the surrounding fluid, which also transports the immersed sheets. The sheets exert a force on the fluid that modifies the flow, which in turn affects the shape and movement of the flexible sheets. This feedback enables a single coated (active) and even an uncoated (passive) sheet to undergo self-oscillation, displaying different oscillatory modes with increases in the catalytic reaction rate. Two sheets (active or passive) introduce excluded volume, steric interactions. This distinctive combination of the hydrodynamic, fluid–structure, and steric interactions causes the sheets to form coupled oscillators, whose motion is synchronized in time and space. We develop a heuristic model that rationalizes this behavior. These coupled self-oscillators exhibit rich and tunable phase dynamics, which depends on the sheets’ initial placement, coverage by catalyst and relative size. Moreover, through variations in the reactant concentration, the system can switch between the different oscillatory modes. This breadth of dynamic behavior expands the functionality of the coupled oscillators, enabling soft robots to display a variety of self-sustained, self-regulating moves.

We demonstrate and develop dyadic–probabilistic methods in connection with non-homogeneous bilinear operators, namely singular integrals and square functions. We develop the full non-homogeneous theory of bilinear singular integrals using a modern point of view. The main result is a new global While proving our bilinear results we also advance and refine the linear theory of Calderón–Zygmund operators by improving techniques and results. For example, we simplify and make more efficient some non-homogeneous summing arguments appearing in

Many geometric and analytic properties of sets hinge on the properties of elliptic measure, notoriously missing for sets of higher co-dimension. The aim of this manuscript is to develop a version of elliptic theory, associated to a linear PDE, which ultimately yields a notion analogous to that of the harmonic measure, for sets of codimension higher than 1. To this end, we turn to degenerate elliptic equations. Let In another article to appear, we will prove that when

In this paper, we develop via real variable methods various characterisations of the Hardy spaces in the multi-parameter flag setting. These characterisations include those via, the non-tangential and radial maximal function, the Littlewood–Paley square function and area integral, Riesz transforms and the atomic decomposition in the multi-parameter flag setting. The novel ingredients in this paper include (1) establishing appropriate discrete Calderón reproducing formulae in the flag setting and a version of the Plancherel–Pólya inequalities for flag quadratic forms; (2) introducing the maximal function and area function via flag Poisson kernels and flag version of harmonic functions; (3) developing an atomic decomposition via the finite speed propagation and area function in terms of flag heat semigroups. As a consequence of these real variable methods, we obtain the full characterisations of the multi-parameter Hardy space with the flag structure.

Atomic clocks are vital in a wide array of technologies and experiments, including tests of fundamental physics 1 . Clocks operating at optical frequencies have now demonstrated fractional stability and reproducibility at the 10 −18 level, two orders of magnitude beyond their microwave predecessors 2 . Frequency ratio measurements between optical clocks are the basis for many of the applications that take advantage of this remarkable precision. However, the highest reported accuracy for frequency ratio measurements has remained largely unchanged for more than a decade 3 – 5 . Here we operate a network of optical clocks based on 27 Al +  (ref. 6 ), 87 Sr (ref. 7 ) and 171 Yb (ref. 8 ), and measure their frequency ratios with fractional uncertainties at or below 8 × 10 −18 . Exploiting this precision, we derive improved constraints on the potential coupling of ultralight bosonic dark matter to standard model fields 9 , 10 . Our optical clock network utilizes not just optical fibre 11 , but also a 1.5-kilometre free-space link 12 , 13 . This advance in frequency ratio measurements lays the groundwork for future networks of mobile, airborne and remote optical clocks that will be used to test physical laws 1 , perform relativistic geodesy 14 and substantially improve international timekeeping 15 . A network of optical atomic clocks based on three different atomic species is reported and their frequency ratios are measured with uncertainties at or below 8 × 10 −18 .

Direct numerical simulations (DNS) of oscillatory flow around a cylinder show that the Stokes–Wang (S–W) solution agrees exceptionally well with DNS results over a much larger parameter space than the constraints of $\\beta K^2\\ll 1$ and $\\beta \\gg 1$ specified by the S–W solution, where $K$ is the Keulegan–Carpenter number and $\\beta$ is the Stokes number. The ratio of drag coefficients predicted by DNS and the S–W solution, $\\varLambda _K$, mapped out in the $K\\text {--}\\beta$ space, shows that $\\varLambda _K < 1.05$ for $K\\leq {\\sim }0.8$ and $1 \\leq \\beta \\leq 10^6$, which contradicts its counterpart based on experimental results. The large $\\varLambda _K$ values are primarily induced by the flow separation on the cylinder surface, rather than the development of three-dimensional (Honji) instabilities. The difference between two-dimensional and three-dimensional DNS results is less than 2 % for $K$ smaller than the corresponding $K$ values on the iso-line of $\\varLambda _K = 1.1$ with $\\beta = 200\\text {--}20\\,950$. The flow separation actually occurs over the parameter space where $\\varLambda _K\\approx 1.0$. It is the spatio-temporal extent of flow separation rather than separation itself that causes large $\\varLambda _K$ values. The proposed measure for the spatio-temporal extent, which is more sensitive to $K$ than $\\beta$, correlates extremely well with $\\varLambda _K$. The conventional Morison equation with a quadratic drag component is fundamentally incorrect at small $K$ where the drag component is linearly proportional to the incoming velocity with a phase difference of ${\\rm \\pi} /4$. A general form of the Morison equation is proposed by considering both viscous and form drag components and demonstrated to be superior to the conventional equation for $K < {\\sim }2.0$.

Corals rely almost exclusively on the ambient flow of water to support their respiration, photosynthesis, prey capture, heat exchange and reproduction. Coral tentacles extend to the flow, interact with it and oscillate under the influence of waves. Such oscillating motions of flexible appendages are considered adaptive for reducing the drag force on flexible animals in wave-swept environments, but their significance under slower flows is unclear. Using in situ and laboratory measurements of the motion of coral tentacles under wave-induced flow, we investigated the dynamics of the tentacle motion and its impact on mass transfer. We found that tentacle velocity preceded the water velocity by approximately one-quarter of a period. This out-of-phase behaviour enhanced mass transfer at the tentacle tip by up to 25% as compared with an in-phase motion. The enhancement was most pronounced under flows slower than 3.2 cm s −1 , which are prevalent in many coral-reef environments. We found that the out-of-phase motion results from the tentacles' elasticity, which can presumably be modified by the animal. Our results suggest that the mechanical properties of coral tentacles may represent an adaptive advantage that improves mass transfer under the limiting conditions of slow ambient flows. Because the mechanism we describe operates by enhancing convective processes, it is expected to enhance other fitness-determining transport phenomena such as heat exchange and particle capture.

Precise timekeeping is critical to metrology, forming the basis by which standards of time, length, and fundamental constants are determined. Stable clocks are particularly valuable in spectroscopy because they define the ultimate frequency precision that can be reached. In quantum metrology, the qubit coherence time defines the clock stability, from which the spectral linewidth and frequency precision are determined. We demonstrate a quantum sensing protocol in which the spectral precision goes beyond the sensor coherence time and is limited by the stability of a classical clock. Using this technique, we observed a precision in frequency estimation scaling in time T as T −3/2 for classical oscillating fields. The narrow linewidth magnetometer based on single spins in diamond is used to sense nanoscale magnetic fields with an intrinsic frequency resolution of 607 microhertz, which is eight orders of magnitude narrower than the qubit coherence time.

Abdussamie, N., Subramaniam, T., Gannan, A., and Rohouma W., 2024. Hydrodynamic analysis of an oscillating water column wave energy converter. In: Phillips, M.R.; Al-Naemi, S., and Duarte, C.M. (eds.), Coastlines under Global Change: Proceedings from the International Coastal Symposium (ICS) 2024 (Doha, Qatar). Journal of Coastal Research, Special Issue No. 113, pp. 624-628. Charlotte (North Carolina), ISSN 0749-0208. Wave energy offers a promising renewable energy source with added benefits for coastal protection. This study investigates the hydrodynamic performance of a fixed Oscillating Water Column (OWC) Wave Energy Converter (WEC) under different wave conditions, focusing on wave period, wave height, and device draft. The obtained results show that peak hydrodynamic efficiency occurs at the natural frequency of the water column and decreases with increased draft due to reduced water mass in the OWC chamber. This highlights the need for thorough evaluation of site-specific wave conditions for optimal power extraction. These findings are crucial for the geometry optimization and site selection of fixed OWC devices, contributing to the advancement of wave energy conversion technology and sustainable energy solutions.