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[1]: 117 The formula above is known as the Langevin paramagnetic equation. Pierre Curie found an approximation to this law that applies to the relatively high temperatures and low magnetic fields used in his experiments. As temperature increases and magnetic field decreases, the argument of the hyperbolic tangent decreases.
The concepts of negative temperature state, [4] and of the convective cells [5] contributed much to the understanding of the diffusion. The underlying physics may be explained as follows. The process can be a transport driven by the thermal fluctuations, corresponding to the lowest possible random electric fields.
Artistic representation of Earth's magnetosphere. The plasma sheet is highlighted in yellow. In the magnetosphere, the plasma sheet is a sheet-like region of denser (0.3-0.5 ions/cm 3 versus 0.01-0.02 in the lobes) [citation needed] hot plasma and lower magnetic field located on the magnetotail and near the equatorial plane, between the magnetosphere's north and south lobes.
Schematic view of the different current systems which shape the Earth's magnetosphere. In many MHD systems most of the electric current is compressed into thin nearly-two-dimensional ribbons termed current sheets. [10] These can divide the fluid into magnetic domains, inside of which the currents are relatively weak.
For the limit , the magnetic diffusion equation = is just a vector-valued form of the heat equation. For a localized initial magnetic field (e.g. Gaussian distribution) within a conducting material, the maxima and minima will asymptotically decay to a value consistent with Laplace's equation for the given boundary conditions.
where is the Boltzmann constant, is the mass of the ion, is its charge, is the temperature of the electrons and is the temperature of the ions. Normally γ e is taken to be unity, on the grounds that the thermal conductivity of electrons is large enough to keep them isothermal on the time scale of ion acoustic waves, and γ i is taken to be 3 ...
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The thermodynamic limit is essentially a consequence of the central limit theorem of probability theory. The internal energy of a gas of N molecules is the sum of order N contributions, each of which is approximately independent, and so the central limit theorem predicts that the ratio of the size of the fluctuations to the mean is of order 1/N 1/2.