Related papers: Conversion Matrix Method of Moments for Time-Varyi…
We present application examples of a graphical method for the efficient construction of potential matrix elements in quantum physics or quantum chemistry. The simplicity and power of this method are illustrated through several examples. In…
During the last decade, possibilities to realize new phenomena and create new applications by varying system properties in time have gained increasing attention in many research fields, spanning a wide range from acoustics to optics. While…
The features of the quasi-static analysis of multiconductor transmission lines by the method of moments are described. Comparison of their efficiency of methods for adaptive mesh refinement is carried out on the example of calculating…
While new light sources allow for unprecedented resolution in experiments with X-rays, a theoretical understanding of the scattering cross-section is lacking. In the particular case of strongly correlated electron systems, numerical…
We describe a method for obtaining the scattering matrix for nuclear or chemical reactions on a finite lattice. Aside from the preparation of the initial and final states as wave packets, the only other operation required is unitary time…
Causality creates an asymmetry between space and time, even though the wave equation treats them on equal footing. In this work, we leverage this asymmetry to construct a cross-mapping between space and time. This cross-mapping is applied…
The paper aims to emphasise how switched systems can be analysed with elementary techniques which require only undergraduate-level linear algebra and differential equations. It is also emphasised how math software can become useful for…
The transmission matrix (TM) is a representation to describe the light scattering process through a scattering medium. The degree of control elements in TM is correlated with the capacity of evaluating enormous equations with tremendous…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
We consider the scattering matrix approach to quantum electron transport in meso- and nano-conductors. This approach is an alternative to the more conventional kinetic equation and Green's function approaches, and often is more efficient…
Linear mixed models with large imbalanced crossed random effects structures pose severe computational problems for maximum likelihood estimation and for Bayesian analysis. The costs can grow as fast as $N^{3/2}$ when there are N…
The method of moments is widely used for the reduction of kinetic equations into fluid models. It consists in extracting the moments of the kinetic equation with respect to a velocity variable, but the resulting system is a priori…
This paper presents a new method, based on the well-known method of moments (MoM), for the numerical electromagnetic analysis of scattering and radiation from metallic or dielectric structures, or both structure types in the same…
A transfer matrix method is presented for solving the scattering problem for the quasi one-dimensional massless Dirac equation applied to graphene in the presence of an arbitrary inhomogeneous electric and perpendicular magnetic field. It…
Scattering wave systems that are periodically modulated in time offer many new degrees of freedom to control waves both in spatial and frequency domains. Such systems, albeit linear, do not conserve frequency and require the adaptation of…
Higher-order accurate solution to electromagnetic scattering problems are obtained at reduced computational cost in a {\it p}-variable finite volume time domain method. Spatial operators of lower, including first-order accuracy, are…
This paper proposes a semidefinite programming based method for estimating moments of a stochastic hybrid system (SHS). For polynomial SHSs -- which consist of polynomial continuous vector fields, reset maps, and transition intensities --…
Improvement of numerical methods for calculating charge transport quantities of materials from the Boltzmann transport equation (BTE) is important for prediction of material properties. In particular, techniques which allow for more…
This paper introduces a formal definition of the transfer ABCD parameters in time-varying electromagnetic systems. The formal definition comes after the rearrangement of the fields $D$ and $B$ at the inputs and outputs of the temporal…
Transparent boundary conditions for the time-dependent Schrodinger equation are implemented using the R-matrix method. The employed scattering formalism is suitable for describing open quantum systems and provides the framework for the…