相关论文: Lambert function methods for laser dynamics with t…
The Lambert $W$ function, giving the solutions of a simple transcendental equation, has become a famous function and arises in many applications in combinatorics, physics, or population dyamics just to mention a few. In the last decade it…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
Intracavity frequency-doubled solid-state lasers exhibit intensity fluctuations of their light output, which are cause by nonlinear dynamical processes. Up to now, there are different solutions to this problem, but they reduce the output…
Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six--dimensional phase space, making simulations of…
A previously published algorithm for trajectory tracking control of tethered wings, i.e. kites, is updated in light of recent experimental evidence. The algorithm is, furthermore, analyzed in the framework of delay differential equations.…
Lambert's problem has been long studied in the context of space operations; its solution enables accurate orbit determination and spacecraft guidance. This work offers an analytical solution to Lambert's problem using the Koopman Operator…
Numerical modelling of several coupled passive linear dynamical systems (LDS) is considered. Since such component systems may arise from partial differential equations, transfer function descriptions, lumped systems, measurement data, etc.,…
A method is presented for solving the discrete-time finite-horizon Linear Quadratic Regulator (LQR) problem subject to auxiliary linear equality constraints, such as fixed end-point constraints. The method explicitly determines an affine…
Experimental and theoretical studies of laser-induced breakdown in dielectrics provide conflicting conclusions about the possibility to trigger ionization avalanche on the sub-picosecond time scale and the relative importance of…
We propose a semi-analytical method of calculating the timing fluctuations in mode-locked semiconductor lasers and apply it to study the effect of delayed coherent optical feedback on pulse timing jitter in these lasers. The proposed method…
Being a powerful tool for linear time-invariant (LTI) systems, system response analysis can also be applied to the so-called linear space-invariant (LSI) but time-varying systems, which is a dual of the conventional LTI problems. In this…
The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q^2-plane is established. The corresponding analytic coupling is reconstructed via a…
Time-distributed optical feedback in semiconductor lasers has gained attention for its ability to produce high-quality chaos and effectively suppress the time-delay signature. However, the fundamental impact of the distribution of feedback…
In the continuous time random walk model, the time-fractional operator usually expresses an infinite waiting time probability density. Different from that usual setting, this work considers the tempered time-fractional operator, which…
Several distributions and families of distributions are proposed to model skewed data, think, e.g., of skew-normal and related distributions. Lambert W random variables offer an alternative approach where, instead of constructing a new…
The stabilization of steady states is studied in a modified Lang-Kobayashi model of a semiconductor laser. We show that multiple time-delayed feedback, realized by a Fabry-Perot resonator coupled to the laser, provides a valuable tool for…
This paper investigates the generalized convexity properties of the Lambert $W$ function, defined as the solution to $W(z)e^{W(z)}=z$. Focusing on $H_{p,q}$-convexity and concavity with respect to H\"older means, we derive necessary and…
We establish a rigorous mathematical framework connecting graphene nanoribbon quantum sensing to the Lambert W function through the finite square well (FSW) analogy. The Lambert W function, defined as the inverse of $f(W) = We^W$, provides…
An important challenge when coupling two different time dependent problems is to increase parallelization in time. We suggest a multirate Neumann-Neumann waveform relaxation algorithm to solve two heterogeneous coupled heat equations. In…
Originating from a system theory and an input/output point of view, I introduce a new class of generalized distributions. A parametric nonlinear transformation converts a random variable $X$ into a so-called Lambert $W$ random variable $Y$,…