Liénard’s generalisationIn this pedagogical article, we elucidate the direct derivation of total power emitted by an accelerating charged particle, known as Liénard's generalisation, using differentiation under integral sign technique.doi:10.1007/s12045-018-0662-7Biswas, Anindya Kumar...
The stochastic movement of the particle turns its classical action integral into a stochastic variable. 3. Nature tries to minimize the expected value for the action, in which the particle’s velocity is consider to be a control parameter of the optimization. The principles formulated above are...
An exception, note E geometrically derives the integral term in D'Alemberts formula which is used in the SI This derivation is originated here. With this I have shown the linkage between the analysis sections “Stationary planar source and elimination of the wake”, “Moving planar source and ...
the expression under the radical in the quadratic formula is called the discriminant, i.e., d = b 2 –4ac the nature of the roots of a quadratic equation can be determined based on the value of d. if d = 0, the two roots are real and equal if d > 0, the roots are real and...
arXiv:hep-th/0610245v123Oct2006OnthePath-IntegralDerivationoftheAnomalyfortheHermitianEquivalentoftheComplexPT-SymmetricQuarticHamiltonianH.F.Jones1,..
signal will achieve some steady-state value a prior to the arrival of the first reflections from the far end of the line. The ratio of a to v indicates the input impedance of the structure, which under the circumstances stated should equal the characteristic impedance of the transmission line...
The presence of exp(–2DλQ) under the integral of Eq. (18) significantly reduces the Bv contribution to the integral and thus to the permeability for the poor rock compared to good rock. Download: Download full-size image Fig. 4. The effect on the exponential of the Laplace ...
where the absolute value of the change in kinetic energy,EΔKis the energy difference between energy levelsmandnand\(\frac{1}{2}{k}_{f}\)is the harmonic force-constant. The Hamiltonian for the attenuation of a wave under a well potential in a box is therefore proposed to: ...
As a result, we obtain an exact relation between the holonomy along a loop with the integral of the curvature form over a surface that it encloses. The derivation of this result can be viewed as an alternative proof of the non-Abelian Stokes theorem in two dimensions with some ...
The presence of exp(–2DλQ) under the integral of Eq. (18) significantly reduces the Bv contribution to the integral and thus to the permeability for the poor rock compared to good rock. Download: Download full-size image Fig. 4. The effect on the exponential of the Laplace ...