Concepts inSolving general shallow wave equations on surfaces
Wave equation
The wave equation is an important second-order linear partial differential equation for the description of waves ¿ as they occur in physics ¿ such as sound waves, light waves and water waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics. Historically, the problem of a vibrating string such as that of a musical instrument was studied by Jean le Rond d'Alembert, Leonhard Euler, Daniel Bernoulli, and Joseph-Louis Lagrange.
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Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R ¿ for example, the surface of a ball. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.
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Surface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in the floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface. This property is caused by cohesion of similar molecules, and is responsible for many of the behaviors of liquids. Surface tension has the dimension of force per unit length, or of energy per unit area.
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In physics, a wave is a disturbance or oscillation that travels through spacetime, accompanied by a transfer of energy. Wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium¿that is, with little or no associated mass transport. They consist, instead, of oscillations or vibrations around almost fixed locations. Waves are described by a wave equation which sets out how the disturbance proceeds over time.
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Capillary
Capillaries are the smallest of a body's blood vessels and are parts of the microcirculation. Their endothelial linings are only one cell thick. These microvessels, measuring 5-10 ¿m in diameter, connect arterioles and venules, and enable the exchange of water, oxygen, carbon dioxide, and many other nutrients and waste chemical substances between blood and surrounding tissues.
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Rigid body
In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it. Even though such an object cannot physically exist due to relativity, objects can normally be assumed to be perfectly rigid if they are not moving near the speed of light.
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Solid
Solid is one of the three classical states of matter. It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to each other, either in a regular geometric lattice or irregularly.
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