multipole expansion sentence in Hindi
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- The FMM has also been applied in accelerating the iterative solver in the Rokhlin and is based on the multipole expansion of the vector Helmholtz equation.
- A related approach is to divide the charges into those nearby the point of observation, and those far enough away to allow a multipole expansion.
- Formally, the field can be expressed as a multipole expansion : A dipole field, plus a quadrupole field, plus an octupole field, etc.
- While expansions of scalar functions are by far the most common application of multipole expansions, they may also be generalized to describe tensors of arbitrary rank.
- As in the multipole expansion, we can replicate the highly non-trivial high-energy by a generic set of effective point-like interactions.
- The field of a point dipole has a particularly simple form, and the order-1 term in the multipole expansion is precisely the point dipole field.
- The multipole expansion of the electromagnetic field finds application in a number of problems involving spherical symmetry, for example antennae radiation patterns, or nuclear gamma decay.
- However, in the multipole expansion of a " magnetic " field, the " monopole " term is always exactly zero ( for ordinary matter ).
- Theoretically, an electric dipole is defined by the first-order term of the multipole expansion, and consists of two equal and opposite charges infinitely close together.
- The interest of these new vector fields is to separate the radial dependence from the angular one when using spherical coordinates, so that a vector field admits a multipole expansion
- Taylor expansion in " d " / " R " ( see multipole expansion and quadrupole ) allows this potential to be expressed as a series.
- It is not possible to construct a field whose multipole expansion contains nonzero odd terms, and that is also consistent with the experimentally-observed behavior of magnetic fields.
- When dealing with subsets of the multipole expansion, the base ordering of the components ( according to whatever ordering scheme has been agreed on ) is usually not changed.
- This Taylor expansion is known as the multipole expansion of V because the terms in this series can be regarded as energies of two interacting multipoles, one on each monomer.
- Even more important : As foundation for the idea of orthonormal function system, which leads to Fourier transformation, multipole expansion, etc and has applications in virtually any kind of physics.
- Multipole expansions are also useful in numerical simulations, and form the basis of the Fast Multipole Method of Rokhlin, a general technique for efficient computation of energies and forces in systems of interacting particles.
- And in the source itself, or as soon as one enters a region of inhomogeneous materials, the multipole expansion is no longer valid and the full solution of Maxwell's equations is generally required.
- If the overlap center is not at an atom, one can move the origin of the multipole expansion to the nearest distributed multipole site, re-expressing the series to account for the change of origin.
- This medium can be seen as an idealization growing from the multipole expansion of the potential of an arbitrarily complex charge distribution, truncation of the expansion, and the forcing of the truncated form to apply everywhere.
- Formally, the field can be expressed as a multipole expansion : A dipole field, plus a quadrupole field, plus an octopole field, etc . in the Amp�re model, but this can be very cumbersome mathematically.
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