And it was this unification of the equations that Maxwell presented, that led the collective set to be known as Maxwell's Equations. So, if we add the displacement current to Ampere's Law as written in Equation [6], then we have the final form of Ampere's Law: ...
It is shown that, with the assistance of a bicomplex vector field, defined as a combination of the electric and the magnetic fields, the number of unknown quantities is practically reduced by half whereas the Helmholtz equation may no longer be necessary in the development of the final ...
Homework Statement I have to take the curved space - time homogenous and inhomogeneous maxwell equations, \triangledown ^{a}F_{ab} = -4\pi j_{b} and...
To include the dissipation terms in the evolution, we propose solving a differential equation for these terms using an implicit Nordsieck method in a predictor-corrector form as described by Byrne and Hindmarsh [6]; see also [8, Ch. III-6]. For example, consider corrections to (14). Define...
Therefore, we are forced to solve the Maxwell equation in conformal frames, transforming then the final results into the physical ones. This can be done by transform- ing the potential Ac derived in the conformal frame {tc, xc}O into the potential A of the physical frame {t, x}O , of...
After time t = 0, the plate begins to oscillate and slide with constant acceleration in the x-direction and induces the motion into the fluid. Owing to the shear the fluid is gradually moved, its velocity being of the form Eq. (7.6) and the governing equation is given by Eq. (7.8)....
Its properties can be better understood when one observes that it is also the unit source solution of the Green's function in an infinite medium for the diffusion equation (Carlslaw and Jaeger, 1959): (9.6)∂fN∂σ2=∂2fN∂x2, where σ2 plays the role of time in diffusion. Thu...
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Complex equations should be entered using Math-Type or an equation editor. Tables and figures should be placed in separate sections at the end of the manuscript (not placed in the text). Authors should prepare their manuscript in Microsoft Word and upload the manuscripts using the fewest file ...
Equation (3) reveals the intimate connection between ABC transporters and autonomous Maxwell Demons. In fact, it exhibits the structure of a logical “AND” function for the necessary requirements to let ABC transporters work (each one of them is highlighted by round brackets in the equation for...