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Breaking wave impacts on rigid structures have been extensively studied, yet the role of structural elasticity in shaping the impact and response remains insufficiently understood. In this study, we experimentally investigate the hydroelastic behaviour of a vertical cantilever plate subjected to multimodal solitary breaking wave impacts. The plate is mounted near the still water level on a 1 : 10 sloping beach, and the wave height-to-depth ratio ($H/h$) is varied from 0.15 to 0.40 to systematically control the impact type from non-breaking to highly aerated wave impacts. We show that aeration significantly affects hydroelastic impacts. The spatio-temporal extent of the impact pressure on the elastic plate increases with air entrapment, while the peak pressure becomes highly sensitive as the wave approaches the flip-through regime. Pressure oscillations associated with bubble formation induce high-frequency structural vibrations, particularly under low-aeration conditions. Furthermore, we find that the elasticity has a limited effect on the peak pressure, impact duration and impulse, but increases the maximum quasi-hydrostatic force on the plate for the scenarios investigated. Following the impact, two distinct free-top deflections are identified, i.e. a deflection $\Delta x_{\textit{imp}}$ with high acceleration induced by the impact pressure and a deflection $\Delta x_{{hp}}$ with high magnitude caused by the maximum quasi-hydrostatic pressure. These deflections scale with the Cauchy number as $\Delta x_{\textit{imp}}/l \sim Ca_{\textit{imp}}/6$ and $\Delta x_{{hp}}/l \sim Ca_{{hp}}/12$ (where l is the plate length), exhibiting parabolic and linear trends with $H/h$, respectively. This work presents a benchmark dataset and introduces a predictive law for structural deflection, providing practical insights into hydroelastic effects across various impact regimes.
Astrobiology is a scientific field that is very interdisciplinary and developing very fast, with many new discoveries generating a high level of attention in both the scientific community and the public. A central goal of astrobiology is to discover life beyond Earth which is, with our current instrumentation and knowledge, arguably within our reach. However, knowledge exchange crossing disciplinary boundaries is becoming increasingly challenging due to different usage of nomenclature and scientific controversies often limited to subdisciplines. There have been some efforts to compile organized databases of terms, concepts and other relevant material within some of the subfields contributing to astrobiology, for example through manually curated online portals designed to benefit students, teachers and practitioners of astrobiology-related research. However, the developments within the subfields and the potentially premature communication of research findings are too fast for objective research portals to remain reliable and up-to-date enough to enable well-informed scientific discussions. We suggest here a novel strategy for developing an online tracers portal as a self-maintaining and self-updating information platform, that would allow not only for a relatively unbiased selection of research results, but also provide fast access to latest scientific discoveries together with potential controversies, such that users of the tracers portal can form their own opinion on all available data rather than obtaining an already filtered and potentially biased selection of information.
Hubble’s law gives us the simple and obvious interpretation that we currently live in an expanding universe. The inverse of Hubble’s constant defines the "Hubble time" which effectively marks the time in the past since the expansion began. more realistically, one would expect the universe expansion to be slowed by the persistent inward pull of gravity from its matter. We consider how various theoretical models for the universe connect with the observable redshift that indicates its expansion.
We have seen how a star’s color or peak wavelength indicates its characteristic temperature near the stellar surface. But what about the temperature in the star’s deep interior? Intuitively, we expect this to be much higher than at the surface, but under what conditions does it become hot enough to allow for nuclear fusion to power the star’s luminosity? And how does it scale quantitatively with the overall stellar properties, like mass, radius, and luminosity? To answer these questions, we identify two distinct considerations.
The post-main-sequence evolution of stars with higher initial mass (>8 solar masses) has some distinct differences from those of solar and intermediate-mass stars. We show how multiple-shell burning can lead to core-collapse supernovae, which are important in generating elements heavier than iron. Some supernovae can lead to the curious stellar end points of neutron stars and black holes.
Exoplanets are planets orbiting stars other than our sun. While some have now been detected (or confirmed) by direct imaging, most exoplanet detections have been made via two other more indirect techniques, known as the radial velocity and transit methods. These methods have analogs in the study of stellar binary systems, as outlined in Chapter 10. We explore the population of known exoplanets and how we must compensate for observational biases inherent in each of these techniques.
We start with some of the historical work on measuring distances to galaxies, leading to the Hubble (or Hubble-Lemaitre) law, a linear proportionality between recession velocity and and a galaxy’s distance, with a proportionality constant known as the Hubble constant. For more distant galaxies, it becomes increasingly difficult to detect and resolve even giant stars like Cepheid variables as individual objects, limiting their utility in testing the Hubble law to larger distances and redshifts. For much larger distances, an important alternative method is the Tully–Fisher relation.
To test which of these models applies to our universe, one needs to extend redshift measurements to large distances, out to several Giga-light years. The most successful approach has been to use white dwarf supernovae (SN type Ia) as very luminous standard candles. One of the greatest surprises of modern astronomy is that the expansion of the universe must be accelerating! This implies there must be a positive, repulsive force that pushes galaxies apart, in opposition to gravity. We dub this force "dark energy."
Earth’s moon is quite distinct from other moons in the solar system, in being a comparable size to Earth. We explore the theory that a giant impact in the chaotic early solar system led to the Moon’s formation, and bombardment by ice-laden asteroids provided the abundant water we find on our planet. Further we find that Earth’s magnetic field shields us from solar wind protons, that protect our atmosphere from being stripped away. The icy moons of Jupiter and Saturn are the best targets for exploring if life exists elsewhere in the solar system.
The close proximity of the Sun, and its extreme apparent brightness, makes it by far the most important star for lives here on Earth. In modern times we have access to powerful telescopes, both on the ground and in space, that observe and monitor the Sun over a wide range of wavelength bands. These vividly demonstrate that the Sun is in fact highly structured and variable over a wide range of spatial and temporal scales.
As a basis for interpreting observations of binary systems in terms of the orbital velocity of the component stars, we review the astrometric and spectrometric techniques used to measure the motion of stars through space. Nearby stars generally exhibit some systematic motion relative to the Sun, generally with components both transverse (i.e., perpendicular) to and along (parallel to) the observed line of sight.
Our initial introduction of surface brightness characterized it as a flux confined within an observed solid angle. But actually the surface brightness is directly related to a more general and fundamental quantity known as the "specific intensity." The light we see from a star is the result of competition between thermal emission and absorption by material within the star.
We now consider why stars shine with such extreme brightness. Over the long-term (i.e., millions of years), the enormous energy emitted comes from the energy generated (by nuclear fusion) in the stellar core, as discussed further in Chapter 18. But the more immediate reason stars shine is more direct, namely because their surfaces are so very hot. We explore the key physical laws governing such thermal radiation and how it depends on temperature.
The effect of Stokes number on turbulence modulation in particle-laden channel flow is investigated through four-way coupled point-particle direct numerical simulations, with the mass loading fixed at 0.6 and the friction Stokes number $St^+$ varying from 3 to 300. A full transition pathway is observed, from a drag-enhanced to a drag-reduced regime, eventually approaching the single-phase state as $St^+$ increases towards 300. A set of transport equations for the particle phase is derived analytically to characterise the interphase coupling, within the framework of the point-based statistical description of particle-laden turbulence. By virtue of this, two dominant mechanisms are identified and quantitatively characterised: a positive, particle-induced extra transport that decreases monotonically with increasing $St^+$, and a negative, particle-induced extra dissipation that varies non-monotonically with $St^+$. The coupling of these two mechanisms leads to a direct contribution of the particle phase to the shear stress balance, the turbulent kinetic energy budgets and the Reynolds stress budgets. Consequently, as $St^+$ increases, the self-sustaining cycle of near-wall turbulence transitions from being augmented to being suppressed and, eventually, returns to the single-phase state. This gives rise to an indirect effect, manifested as a non-monotonic modulation of Reynolds shear stress and turbulence production rate. Taken together, complex interplays between particle-modified turbulent transport, particle-induced extra transport and extra dissipation are analysed and summarised, providing a holistic physical picture composed of consistent interpretations of turbulence modulation induced by small heavy particles.