Related papers: Lambert function methods for laser dynamics with t…
A robust, fast and accurate method for solving the Colebrook-like equations is presented. The algorithm is efficient for the whole range of parameters involved in the Colebrook equation. The computations are not more demanding than…
Semiconductor lasers with time-delayed optical feedback display a wide range of dynamical regimes, which have found various practical applications. They also provide excellent testbeds for data analysis tools for characterizing complex…
A matrix-analytic method is proposed for solving a system of linear integral equations arises in three tandem servers. The approach is by modelling the cumulative distribution function (cdf) of the service time as a matrix exponential…
Time delay is ubiquitous in many experimental and real-world situations. It is often unclear whether time delay plays a significant role in observed phenomena, and if it does, how long the time lag really is. This would be invaluable…
Efficient time integration methods based on operator splitting are introduced for the Westervelt equation, a nonlinear damped wave equation that arises in nonlinear acoustics as mathematical model for the propagation of sound waves in high…
Evaluating the Wigner function of quantum states in the entangled state representation is introduced, based on which we present a new approach for deriving time evolution formula of Wigner function in laser process. Application of this…
In Density Functional Theory simulations based on the LAPW method, each self-consistent field cycle comprises dozens of large dense generalized eigenproblems. In contrast to real-space methods, eigenpairs solving for problems at distinct…
We propose a numerical method to solve the Wigner equation in quantum systems of spinless, non-relativistic particles. The method uses a spectral decomposition into $L^2(\mathbb{R}^d)$ basis functions in momentum-space to obtain a system of…
Let $\{b_{j}\}_{j=1}^{k}$ be meromorphic functions, and let $w$ be admissible meromorphic solutions of delay differential equation $$w'(z)=w(z)\left[\frac{P(z, w(z))}{Q(z,w(z))}+\sum_{j=1}^{k}b_{j}(z)w(z-c_{j})\right]$$ with distinct delays…
A numerical method is proposed for computing time-periodic and relative time-periodic solutions in dissipative wave systems. In such solutions, the temporal period, and possibly other additional internal parameters such as the propagation…
In reaction rate theory, in input-output type models and in reaction-diffusion problems when the total derivatives are replaced by fractional derivatives the solutions are obtained in terms of Mittag-Leffler functions and their…
In this work, a long-cavity semiconductor laser subject to optical feedback is exploited to generate repetitive temporal patterns with enhanced intra-pattern sample diversity. Stable limit cycle dynamics characterized by multiple frequency…
The function $y = g(x) = \mathrm{log}\big(W(e^x)\big)$, where $W()$ denotes the Lambert W function, is the solution to the equation $y + e^y = x$. It appears in various problem situations, for instance the calculation of current-voltage…
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
Time-Delay Interferometry (TDI) is the data processing technique that cancels the large laser phase fluctuations affecting the one-way Doppler measurements made by unequal-arm space-based gravitational wave interferometers. By taking finite…
In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for…
Lambert's problem is a classical boundary value problem in analytical mechanics. It arises when trying to determine the energy required to place a particle, subject to a central gravitational potential, in a "free fall" trajectory…
We report on a methodology for the evaluation of the DC characteristics, small-signal frequency response and large-signal dynamic response of carrier and photon density responses in semiconductor laser diodes. A single mode laser is…
We consider a wide-aperture surface-emitting laser with a saturable absorber section subjected to time-delayed feedback. We adopt the mean-field approach assuming a single longitudinal mode operation of the solitary VCSEL. We investigate…