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A two-dimensional gas is a collection of objects constrained to move in a planar or other two-dimensional space in a gaseous state. The objects can be: classical ideal gas elements such as rigid disks undergoing elastic collisions; elementary particles, or any ensemble of individual objects in physics which obeys laws of motion without binding interactions.
The mathematical similarities between the expressions for shear viscocity, thermal conductivity and diffusion coefficient of the ideal (dilute) gas is not a coincidence; It is a direct result of the Onsager reciprocal relations (i.e. the detailed balance of the reversible dynamics of the particles), when applied to the convection (matter flow ...
In 499 AD Aryabhata, a great mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, used this method in the Aryabhatiya (section 2.8). This yields as a special case the well-known formula for the area of a triangle , by considering a triangle as a degenerate trapezoid in which one of the parallel sides has ...
For very large dimension, the shows that Monte-Carlo integration is most likely a better choice, but for 2 and 3 dimensions, equispaced sampling is efficient. This is exploited in computational solid state physics where equispaced sampling over primitive cells in the reciprocal lattice is known as Monkhorst-Pack integration .
In January 2006, as a result of the Russia-Ukraine gas dispute, interest in the Trans-Caspian Gas Pipeline project was rekindled. [7] On 11 January 2006, Azerbaijan's prime-minister Artur Rasizade proposed to his Kazakhstan counterpart Daniyal Akhmetov that Kazakhstan gas be exported through the South Caucasus Pipeline to Turkey and from there to the European market. [8]
Suppose that we want to solve the differential equation ′ = (,). The trapezoidal rule is given by the formula + = + ((,) + (+, +)), where = + is the step size. [1]This is an implicit method: the value + appears on both sides of the equation, and to actually calculate it, we have to solve an equation which will usually be nonlinear.
where P is the pressure of the gas, V is the volume of the gas, and k is a constant for a particular temperature and amount of gas. Boyle's law states that when the temperature of a given mass of confined gas is constant, the product of its pressure and volume is also constant. When comparing the same substance under two different sets of ...
A gas meter is a specialized flow meter, used to measure the volume of fuel gases such as natural gas and liquefied petroleum gas. Gas meters are used at residential, commercial, and industrial buildings that consume fuel gas supplied by a gas utility. Gases are more difficult to measure than liquids, because measured volumes are highly ...