Related papers: Markov Chains for Modeling Complex Luminescence, A…
The refraction of light by dispersion-free dielectric media can be modeled using well-localized macroscopic wave packets, enabling a description in terms of pseudo-particles. This approach is often used in thought experiments to illustrate…
We propose a technique of compensating the spurious reflections implied by the multiple-scattering (MS) method, commonly used for analyzing finite photonic crystal (PC) systems, to obtain exact values of characteristic parameters, such as…
Neutron and X-ray reflectometry are important methods for studying thin multilayer systems. The Parratt method and the method of characteristic matrices, also referred to as transfer matrices, are used for simulation, evaluation of…
The conductance of a normal-metal mesoscopic system in proximity to superconducting electrode(s) is calculated. The normal-metal part may have a general geometry, and is described as a ``circuit'' with ``leads'' and ``junctions''. The…
We present a solution method for the integrable system (derivative nonlinear Schr\"odinger II system) or the Chen--Lee--Liu system. This is done by presenting a solution technique for the inverse scattering problem for the corresponding…
The direct and inverse scattering problems are analyzed for a first-order discrete system associated with the semi-discrete version of the derivative NLS system. The Jost solutions, the scattering coefficients, the bound-state dependency…
Light is a union of electric and magnetic fields, and nowhere is their complex relationship more evident than in the near fields of nanophotonic structures. There, complicated electric and magnetic fields varying over subwavelength scales…
Discrete-time discrete-state finite Markov chains are versatile mathematical models for a wide range of real-life stochastic processes. One of most common tasks in studies of Markov chains is computation of the stationary distribution.…
This paper shows how one can use Sequential Monte Carlo methods to perform what is typically done using Markov chain Monte Carlo methods. This leads to a general class of principled integration and genetic type optimization methods based on…
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to…
The tail chain of a Markov chain can be used to model the dependence between extreme observations. For a positive recurrent Markov chain, the tail chain aids in describing the limit of a sequence of point processes $\{N_n,n\geq1\}$,…
By measuring the transmission of near-resonant light through an atomic vapor confined in a nano-cell we demonstrate a mesoscopic optical response arising from the non-locality induced by the motion of atoms with a phase coherence length…
This paper concerns the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models with normalized random measure priors. Making use of some recent posterior characterizations for the class of…
We introduce a theory to analyze the behavior of light emitters in nanostructured environments rigorously. Based on spectral theory, the approach opens the possibility to quantify precisely how an emitter decays to resonant states of the…
To maximize the accuracy of background simulation and event reconstruction, high-energy neutrino telescopes require detailed knowledge of light propagation over a large volume of detection medium. If light scattering and absorption leng ths…
We investigate the spectral distribution of large sample covariance matrices with independent columns and entries in the columns that stem from Markov chains. We characterize the limiting spectral densities by their moments.…
In this paper, it is presented a methodology for implementing arbitrarily constructed time-homogenous Markov chains with biochemical systems. Not only discrete but also continuous-time Markov chains are allowed to be computed. By employing…
Light transport in strongly scattering porous photocatalytic materials governs the spatial distribution of absorbed photons and therefore the generation of charge carriers driving photocatalytic reactions. Yet translating measured optical…
Luminescent coupling is a characteristic of multi-junction solar cells which has often been neglected in models of their performance. The effect describes the absorption of light emitted from a higher band gap semiconductor by a lower band…
Many systems are partially stochastic in nature. We have derived data driven approaches for extracting stochastic state machines (Markov models) directly from observed data. This chapter provides an overview of our approach with numerous…