Mesoscopic models in the reaction-diffusion framework have gained recognition as a viable approach to describing chemical processes in cell biology. The resulting computational problem is a continuous-time Markov chain on a discrete and typically very large state space. Due to the many temporal and spatial scales involved many different types of computationally more effective multiscale models ...

Using a modified version of the split-step Fourier method, we analyze the effect of noise on soliton propagation inside erbium-doped fiber amplifiers. In fact, noise from forward-propagating amplified spontaneous emission, associated with a Markov immigration process, is included in the analysis of soliton amplification. Moreover, this algorithm accounts for the real spectral gain profile of th...

The following text is a summary of the same-titled talk given within the frame of the seminar ’AKNUM: Seminar aus Numerik’ at the Vienna University of Technology. We address time splitting methods for the Schrödinger equation. In particular, we concentrate on the Strang splitting and prove second order convergence in the case of a bounded potential and given bounds on the (iterated) commutators...

Metrology, the science of measurement, involves the determination of physical quantities from experiment, along with estimates of their associated uncertainties. In this endeavour, a mathematical model of the measurement system is required in order to extract information from the experimental data. For the measurements to be reliable, these models must be validated (shown to be fit for purpose)...

We develop a method for non-paraxial beam propagation that obtains a speed improvement over the Finite-Difference Split-Step method (FDSSNP) recently reported by Sharma et al. The method works in the eigen-basis of the Laplace operator ∇2 T ) , and in general requires half as many operations to propagate one step forward so that a 2X speedup can be realized. However, the new formulation allows ...

We investigate the propagation characteristics of superGaussian beam in highly nonlocal nonlinear media. The optical beam propagation has been modeled by well known nonlocal nonlinear Schrödinger equation. The variational method is employed to find the initial beam propagation parameters and then split step Fourier method is used for numerical simulations. A generalized exact analytical solutio...

Pulse propagation in a birefringent medium carries due weightage and importance in passive modelocking of fiber lasers. We have carried out study of nonlinear effects in birefringent medium by simulating pulse propagation using adaptive step size method, which is globally an efficient algorithm for solving Schrodinger type equations using split step Fourier method. Nonlinear optical loop mirror...

We consider a nonlocal scalar conservation law proposed by Andrew C. Fowler to describe the dynamics of dunes, and we develop a numerical procedure based on splitting methods to approximate its solutions. We begin by proving the convergence of the well-known Lie formula, which is an approximation of the exact solution of order one in time. We next use the split-step Fourier method to approximat...

Fluorescence microscopy is an important and ubiquitous tool in biological imaging due to the high specificity with which fluorescent molecules can be attached to an organism and the subsequent nondestructive in-vivo imaging allowed. Focused-light microscopies allow three-dimensional fluorescence imaging but their resolution is restricted by diffraction. This effect is particularly limiting in t...