Related papers: Deriving the method of images for conductors
Large-scale text-to-image generative models have been a revolutionary breakthrough in the evolution of generative AI, allowing us to synthesize diverse images that convey highly complex visual concepts. However, a pivotal challenge in…
The wave function $\psi$ is interpreted as charge density, or charge distribution, at each point in space. This is a physical interpretation of $\psi$. The notion of speed can be associated with $\psi$, which leads to the concept of…
The primary purpose of this paper is to present the concept of dichotomy in image illumination modeling based on the power function. In particular, we review several mathematical properties of the power function to identify the limitations…
An approximate equation for the effective conductivity sigma_eff of systems with a finite maximal scale of inhomogeneities is deduced. An exact solution of this equation is found and its physical meaning is discussed. A two-phase randomly…
We present an exact calculation of the effective geometry-induced quantum potential for a particle confined on a helicoidal ribbon. This potential leads to the appearance of localized states at the rim of the helicoid. In this geometry the…
The usual strategy for deducing the $\pi\mbox{--}\pi^\ast$ electronic energy (or optical bandgap) in a molecule with an "infinite" number of conjugated double bonds consists in fitting a function with some adjustable parameters to the…
A simple method is used to extrapolate the form factor for the process gamma* gamma *--->pi^0 when two virtual photons produce a pi ^0 from the region of large spacelike photon virtualities to the experimentally accessible case when one of…
We discuss the method of $\Phi$-derivable approximations in gauge theories. There, two complications arise, namely the violation of Bose symmetry in correlation functions and the gauge dependence. For the latter we argue that the error…
We describe a method for calculating the probability with which the wall of a plasma absorbs an electron at low energy. The method, based on an invariant embedding principle, expresses the electron absorption probability as the probability…
Using the linear fractional transformation, connecting effective conductivities sigma_{e} of isotropic two-phase systems with and without magnetic field, explicit approximate expressions for sigma_{e} in a magnetic field are obtained. They…
Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…
The free energy of a field theory can be considered as a functional of the free correlation function. As such it obeys a nonlinear functional differential equation which can be turned into a recursion relation. This is solved order by order…
The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed…
We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach…
We prove a descriptive theorem on the extrinsic geometry of an embedded minimal surface of injectivity radius zero in a homogeneously regular Riemannian three-manifold, in a certain small intrinsic neighborhood of a point of almost-minimal…
In a Scanning Tunneling Microscope (STM), when a tunneling electron treated as a point charge enters the barrier region between the tip and the sample, it induces image charges on the conducting surfaces, which modifies the shape of the…
Application of the generalized continuity equation reveals that the drift current in conductors is equivalent to a negative diffusion current. A phenomenological model of conductivity is developed using the generalized continuity equations.…
This work is devoted to the derivation and the matematical study of a new model for water-soluble polymers and metal ions interactions, which are used in chemistry for their wide range of applications. First, we motivate and derive a model…
We report an extension of the source imaging method for analyzing three-dimensional sources from three-dimensional correlations. Our technique consists of expanding the correlation data and the underlying source function in spherical…
The frequency-dependent longitudinal and Hall conductivities --- $\sigma_{xx}$ and $\sigma_{xy}$ --- are dimensionless functions of $\omega/T$ in 2+1 dimensional CFTs at nonzero temperature. These functions characterize the spectrum of…