Related papers: Lambert function methods for laser dynamics with t…
In this work, the time-dependent solution for the Lotka-Volterra Predator-Prey model is derived with the help of the Lambert W function. This allows an exact analytical expression for the period of the associated limit-cycle oscillations…
This brief note complements some results regarding a recently developed technique for the stability analysis of linear time-invariant, time delay systems using the matrix Lambert W function. By means of a numeric example, it is shown that…
Measuring attenuation coefficients is a fundamental problem that can be solved with diverse techniques such as X-ray or optical tomography and lidar. We propose a novel approach based on the observation of a sample from a few different…
We apply a recently proposed method for the analysis of time series from systems with delayed feedback to experimental data generated by a CO_2 laser. The method is able to estimate the delay time with an error of the order of the sampling…
Studying time-dependent behavior in lasers is analytically difficult due to the saturating non-linearity inherent in the Maxwell-Bloch equations and numerically demanding because of the computational resources needed to discretize both time…
We show that time-delayed feedback methods, which have successfully been used to control unstable periodic ortbits, provide a tool to stabilize unstable steady states. We present an analytical investigation of the feedback scheme using the…
In this paper, we propose a delayed perturbation of Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler type matrix function and delayed Mittag-Leffler type matrix function. With the help of the…
In this paper we study the identification of a time-varying linear system from its response to a known input signal. More specifically, we consider systems whose response to the input signal is given by a weighted superposition of delayed…
We study the dynamics of multipulse solutions in mode-locked lasers in presence of time-delayed feedback stemming, e.g., from reflections upon optical elements, and carrier dynamics. We demonstrate that the dynamics of such a high…
The applications of the recent results obtained in the theory of generalized Lambert functions, to the mean field theory of ferromagnetism are presented. As a consequence, all the predictions of the Weiss theory of ferromagnetism can be…
We describe an algorithm to evaluate all the complex branches of the Lambert W function with rigorous error bounds in interval arithmetic, which has been implemented in the Arb library. The classic 1996 paper on the Lambert W function by…
A numerical approach to solve the perturbed Lambert's problem is presented. The proposed technique uses the Theory of Functional Connections, which allows the derivation of a constrained functional that analytically satisfies the boundary…
This study presents an analytical method for tuning PI controllers in First-Order with Time Delay (FOTD) systems, leveraging the Lambert W function. The Lambert W function enables exact pole placement, yielding analytical expressions for PI…
A novel model of a semiconductor laser with optical feedback is presented, generalizing Lang-Kobayashi equations to the case of incoherent feedback. The equations are supplemented by a stochastic variable which models random phase…
Using a thermal gas, we model the signal of a trapped interferometer. This interferometer uses two short laser pulses, separated by time T, which act as a phase grating for the matter waves. Near time 2T, there is an echo in the cloud's…
We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by…
Time-delayed optical feedback is known to trigger a wide variety of complex dynamical behavior in semiconductor lasers. Adding a second optical feedback loop is naturally expected to further increase the complexity of the system and its…
The Lambert-W explicit solutions to the QCD renormalization group (RG) equation are considered up to fourth order in the ${\bar {MS}}$ scheme. We compare, systematically, these solutions with the conventional asymptotical (iterative)…
We start with the explicit solution, in terms of the Lambert W function, of the renormalization group equation (RGE) for the gauge coupling in the supersymmetric Yang-Mills theory described by the well-known beta function of Novikov et…
We formulate the problem of a two-level system in a linearly polarized laser field in terms of a nonlinear Riccati-type differential equation and solve the equation analytically in time intervals much shorter than half the optical period.…