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Later, cable theory with its mathematical derivatives allowed ever more sophisticated neuron models to be explored by workers such as Jack, Rall, Redman, Rinzel, Idan Segev, Tuckwell, Bell, and Iannella. More recently, cable theory has been applied to model electrical activity in bundled neurons in the white matter of the brain. [1]
The magnetic field inside a coaxial cable can be divided into three regions, each of which will therefore contribute to the electrical inductance seen by a length of cable. [ 11 ] The inductance L cen {\displaystyle L_{\text{cen}}\,} is associated with the magnetic field in the region with radius r < a {\displaystyle r<a\,} , the region inside ...
The penetration depth for a good conductor can be calculated from the following equation: [5] =, where δ is the penetration depth (m), f is the frequency (Hz), μ is the magnetic permeability of the material (H/m), and σ is the electrical conductivity of the material (S/m).
They were developed by Oliver Heaviside who created the transmission line model, and are based on Maxwell's equations. Schematic representation of the elementary component of a transmission line. The transmission line model is an example of the distributed-element model. It represents the transmission line as an infinite series of two-port ...
In the Meissner phase, a screening current is within the London penetration depth. Exceeding H c1, vortices start to penetrate into the superconductor. These vortices are pinned on the surface (Bean–Livingston barrier). In the area below the surface, which is penetrated by the vortices, is a current with the density J c.
A time-domain reflectometer; an instrument used to locate the position of faults on lines from the time taken for a reflected wave to return from the discontinuity.. A signal travelling along an electrical transmission line will be partly, or wholly, reflected back in the opposite direction when the travelling signal encounters a discontinuity in the characteristic impedance of the line, or if ...
Ginzburg–Landau theory introduced the superconducting coherence length ξ in addition to London magnetic field penetration depth λ. According to Ginzburg–Landau theory, in a type-II superconductor / > /. Ginzburg and Landau showed that this leads to negative energy of the interface between superconducting and normal phases.
Applying the transmission line model based on the telegrapher's equations as derived below, [1] [2] the general expression for the characteristic impedance of a transmission line is: = + + where R {\displaystyle R} is the resistance per unit length, considering the two conductors to be in series ,