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In these notes we present the basics of the water wave theory. Specifically, after introducing briefly the basic concepts of continuum mechanics, we derive the physical laws describing the physics of an inviscid, incompressible fluid, namely the Euler equations. Euler equations are the governing equations of water waves, but because of the great difficulties in the theoretical and numerical studies of these equations, simple, approximate mathematical models have been derived instead.

The models are usually simplified so as to be valid for specific types of waves. Water waves are usually divided into categories depending on their amplitude and their wavelength compared to the water depth. Some waves such as the Tsunami waves are generated in the deep ocean as waves of small amplitude with large wavelength, but as they approach the shoreline they grow in amplitude while their wavelength is decreased.

Here, we will derive models for long waves with or without using the small amplitude assumption. Document type : Preprints, Working Papers, Identifiers HAL Id : hal, version 2. Mach disks are also seen in the exhaust trails of fighter jets. Credit: Roman Uchytel. A weird species of ancient Australian marsupial had enormous claws, and elbows that were almost completely rigid — a characteristic found in no other mammal, living or extinct.

Large marsupials called palorchestids thrived in Australia for some 25 million years, until as recently as 50, years ago. Scientists long mistook them for ancient kangaroos, but eventually realized that these animals were more similar to horse-sized versions of wombats. In an attempt to describe the appearance and movements of these little-known marsupials, Hazel Richards at Monash University in Clayton, Australia, and her colleagues examined the limbs of more than 60 fossil specimens from 3 species.

The authors hope to learn more about palorchestids as more fossils are unearthed or identified in museum collections. PLoS One The drizzle lasted for more than 7. The scientists used lasers and radar to probe Antarctic clouds. In very cold clouds, water usually freezes around dust particles to form ice.

The authors suggest that, in this case, there were probably too few dust particles in the air for ice to form. As a result, the water remained liquid as it fell through the sky. Supercooled drizzle has been spotted at a few other places on the planet. But it might be widespread over Antarctica and the Southern Ocean, because those regions have just the right combination of low dust levels and chilly temperatures.

A male honeybee mates with a queen in mid-air. The semen that a male transfers to a female degrades her vision — and with it her ability to mate with other males. Evolutionary theory predicts that a male should attempt to prevent queens from mating with other males. In keeping with that prediction, research has suggested that natural insemination alters the activity of vision-related genes in female bees. To determine the consequences of such changes, Joanito Liberti at the University of Copenhagen and his colleagues artificially inseminated queen bees and found that they became less responsive to light and were more likely to get lost on mating flights than were queens given saline.

Inseminated queens also tended to leave their hives on mating flights two days earlier than control queens. The researchers propose that this early departure was an attempt to compensate for their poor vision. Workers inspect drugs at a factory in Wuhan, China.

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A chemical reaction used in drug manufacturing around the world has had an eco-friendly makeover. A widely used industrial reaction that produces toxic waste could be replaced by one that yields only one by-product — water. Since , that activation has often been carried out by a process called the Mitsunobu reaction, which requires two activating chemicals — one explosive — and generates two by-products, one of which is toxic. Seeking a greener version of the Mitsunobu reaction, Ross Denton at the University of Nottingham, UK, and his colleagues used a compound called a phosphine oxide as a catalyst to jump-start the reaction.

Wave | water |

The researchers say that their catalyst provides a more environmentally friendly way of making both drugs and agrochemicals. Science Circular features on Titan resemble earthly lakes excavated by sub-surface explosions. Liquid methane and ethane collect in low-lying basins on Titan, creating lakes and seas — features that are rare in the Solar System.

A similar process causes sinkholes to appear in limestone on Earth. The scientists noticed that many of these lakes have tall rims that rise steeply from the surrounding terrain. On Earth, similar rims are seen on craters that form when water and magma interact underground and then explode through the surface. Nature Geosci. A skin-cancer cell. Cells might rely on cues from their internal skeletons to expand without becoming cancerous.

A cell must finely control its volume: it needs to grow to replicate, but if it swells too large, it teeters towards cancerous malignancy. Scientists have struggled to learn how individual cells achieve this balance, but one clue came from research that pointed to a pair of proteins called YAP and TAZ.

Cell Biol. Artist Tom Yendell, who was born without arms, wields a paintbrush between his toes.

Dispersion (water waves)

Two artists who paint by holding brushes between their toes have finely tuned brain regions that map onto individual toes — a feature not seen in most people. In humans and other primates, each individual finger is represented by its own sliver in a region of the brain called the somatosensory cortex. Some non-human primates also have maps of toes in their brains, but humans do not. To find out whether humans who rely on their toes to an extraordinary extent have toe maps, Daan Wesselink at University College London and his colleagues scanned the brains of two men who were born without arms and who use their toes to paint, write and manipulate objects for daily tasks.

The researchers did not see such organized activity in the brains of 11 people with hands. The authors suggest that toe maps are formed in the years before the age of During this crucial period, the brain is most malleable. Cell Rep. Observations by the Sloan Foundation 2. Instead, researchers typically infer this attribute by comparing observations of stars with the results of models that predict how these bodies evolve through their lifetimes.

Some stars, for instance, eventually bloat into giants. Giada Casali at the University of Florence in Italy and her colleagues have found an alternative method. Leaves marred by the bacterium Pseudomonas syringae , which deploys a protein that mimics those of the plants it infects.

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Bacteria rely on a previously unknown trick to disarm a protein that is crucial for defending plants and animals from disease. Found in a wide variety of living things, heat shock protein 90 HSP90 helps to fold and assemble molecules that detect pathogen invasion and fight off infection. But Vincent Tagliabracci, at the University of Texas Southwestern Medical Center in Dallas, and his colleagues have found that bacteria can undermine this defence.

Waves of seismic origin

The researchers infected plants with the bacterium Pseudomonas syringae , a major plant pathogen that secretes a virulence protein called HopBF1. The team found that this protein mimics plant molecules that bind to HSP Compounds that inhibit HopBF1 might help to control crop pathogens, the authors say. HSP90 also promotes the growth and survival of many cancer cells, raising the tantalizing prospect that a therapeutic form of HopBF1 might block a wide range of tumour types.

Correction: An earlier picture caption incorrectly said that the bacterium Pseudomonas syringae had damaged the pictured leaf. An insect had damaged the leaf. Cell Just-hatched sea turtles scurry towards the safety of the waves, leaving trails similar to those seen in newly described fossils.

People Slammed By Massive Waves

The first known record of baby sea turtles making their run for the ocean has been revealed by fossilized tracks dating back about , years. After emerging from eggs buried in sandy nests, sea-turtle hatchlings race towards the ocean, which offers refuge from land-based predators.

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Credit: Jan de Vynck. Some of the imprints resemble those made by modern loggerhead sea turtles Caretta caretta ; other traces look like those made by modern leatherback turtles Dermochelys coriacea. Today, both these species typically nest in warmer regions more than 1, kilometres to the northeast, and rarely appear along the Cape south coast, suggesting that climate and sand temperatures were higher there when the tracks were made.

The authors speculate that a layer of fine, dry sand blew across the prints when they were fresh, aiding their preservation. A newly reported isotope offers the hope of testing fundamental principles of nuclear structure. Physicists have found an exotic variant of potassium that is much longer-lived than predicted — hinting at the existence of other more-extreme atoms that stretch the known limits of nuclear structure. Isotopes are alternative forms of a single chemical element, each with the same number of protons but differing numbers of neutrons.

If an isotope has too few neutrons, the nucleus can no longer hold itself together.