Related papers: Deriving the method of images for conductors
Existence of the magnetic monopole is compatible with the fundamental laws of nature, however, this illusive particle has yet to be detected experimentally. In this work, we show that an electric charge near the topological surface state…
This paper deals with different image theorems, i.e., Love's equivalence principle, the induction equivalence principle and the physical optics equivalence principle, in the spherical geometry. The deviation of image theorem approximation…
The observed output of an interferometer is the result of interference among the parts of the input light beam traveling along each possible optical path. In complex systems, writing down all these possible optical paths and computing their…
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…
Is it possible to form an image using light produced by stimulated emission? Here we study light scatter off an assembly of excited chromophores. Due to the Optical Theorem, stimulated emission is necessarily accompanied by excited state…
Path homology plays a central role in digraph topology and GLMY theory more general. Unfortunately, the computation of the path homology of a digraph $G$ is a two-step process, and until now no complete description of even the underlying…
We consider the problem of recovering an isotropic conductivity outside some perfectly conducting or insulating inclusions from the interior measurement of the magnitude of one current density field $|J|$. We prove that the conductivity…
A model for the extraction of the charge density dependent mobility and variable contact resistance in thin film transistors is proposed by performing a full derivation of the current-voltage characteristics both in the linear and…
A new method ( PI-DFT ) which combines path integrals and density functional theory is proposed as a pathway to many fields of physics. Within path integral theory it is possible to construct particle densities without explicitly…
This paper describes the use of Feynman photon path integrals to compute the probability of detecting reflected, diffracted, and scattered photons at different points in space after interacting with conduction electrons. Five examples are…
We introduce {\em quadri-tilings} and show that they are in bijection with dimer models on a {\em family} of graphs $\{R^*\}$ arising from rhombus tilings. Using two height functions, we interpret a sub-family of all quadri-tilings, called…
We consider the propagation of charge carriers in planar graphene under the combined influence of a constant transversal magnetic field $B$ and an in-plane varying electric potential $\phi(x)$. By suitably designing the potential landscape…
For a three-dimensional theory with a coupling $\phi \epsilon ^{\mu \nu \lambda} v_\mu F_{\nu \lambda}$, where $v_\mu$ is an external constant background, we compute the interaction potential within the structure of the gauge-invariant but…
We prove that the notion of a derived voltage graph comes from an adjunction between the category of voltage graphs and a category of group labeled graphs.
We consider a charged conductor of arbitrary shape, in electrostatic equilibrium, with one or more cavities inside it, and with fixed charges placed outside the conductors and inside the cavities. The field inside a particular cavity is…
Richard Feynman's method of path integrals is based on the fundamental assumption that a system starting at a point A and arriving at a point B takes all possible paths from A to B, with each path contributing its own (complex) probability…
Let $X$ be a complex manifold, and let $Y$ and $D$ be two reduced simple-normal-crossing (snc) divisors on $X$ with no common irreducible components. Given a proper locally K\"ahler morphism $\pi \colon X \to \Delta$ from $X$ to a complex…
In this pedagogical work we point out a subtle mistake that can be done by undergraduate or graduate students in the computation of the electrostatic energy of a system containing charges and perfect conductors if they naively use the image…
This paper seeks to show that the beam screen of the LHC has an important effect on the electric field of the LHC beam, a few tens of sigmas away from its center. To do so, we develop two new methods for finding the effect of a complex…
The Riemann Theorem states, that for any nontrivial connected and simply connected domain on the Riemann sphere there exists some its conformal bijection to the exterior of the unit disk. In this paper we find an explicit form of this map…