Related papers: Delay Equations and Radiation Damping
The transition states and dividing surfaces used to find rate constants for bimolecular reactions are shown to undergo qualitative changes, known as Morse bifurcations, and to exist for a large range of energies, not just immediately above…
We study the effect of radiation damping on the classical scattering of charged particles. Using a perturbation method based on the Runge-Lenz vector, we calculate radiative corrections to the Rutherford cross section, and the corresponding…
We investigate a two-component reaction-diffusion system with a slow-fast structure and spatially varying coefficients $f_1$ and $f_2$ appearing in the slow equation. Under mild boundedness and regularity conditions on $f_1$ and $f_2$ the…
We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective…
These notes provide two derivations of the Lorentz-Dirac equation. The first is patterned after Landau and Lifshitz and is based on the observation that the half-retarded minus half-advanced potential is entirely responsible for the…
Radiation reaction, the force experienced by an accelerated charge due to radiation emission, has long been the subject of extensive theoretical and experimental research. Experimental verification of a quantum, strong-field description of…
The properties of a one space-dimension, one particle dynamical system under the influence of a purely dissipative force are investigated. Assuming this force depends only on the velocity, it is demonstrated, in contrast to the case of…
We explore theoretically the navigation of an active particle based on delayed feedback control. The delayed feedback enters in our expression for the particle orientation which, for an active particle, determines (up to noise) the…
We investigate the effect of time delay on the dynamical model of love. The local stability analysis proves that the time delay on the return function can cause a Hopf bifurcation and a cyclic love dynamics. The condition for the occurrence…
In classical electrodynamics for rotating with variable angular velocity charged rigid sphere are found: the exact values of electromagnetic fields, the flux of radiating energy and the exact integral equation of rotation including the…
We consider several models of State Dependent Delay Differential Equations (SDDEs), in which the delay is affected by a small parameter. This is a very singular perturbation since the nature of the equation changes. Under some conditions,…
The Brusselator reaction-diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the…
Expectation values of the electromagnetic field and the electric current are introduced at space-time resolution which belongs to the quantum domain. These allow us to approach some key features of classical electrodynamics from the…
Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the…
We analyze canard explosions in delayed differential equations with a one-dimensional slow manifold. This study is applied to explore the dynamics of the van der Pol slow-fast system with delayed self-coupling. In the absence of delays,…
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here we address a key question which arises in this context: Are…
We consider the effects of strong dissipation in quantum systems with a notion of locality, which induces a hierarchy of many-body relaxation timescales as shown in [Phys. Rev. Lett. 124, 100604 (2020)]. If the strength of the dissipation…
A detailed study of the slow manifold of a model exhibiting mixed-mode oscillations is presented. A scenario for the emergence of mixed-mode states which does not involve phase locking on a 2-torus is constructed. We show that mixed-modes…
In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a…
Let us give a two dimensional family of real vector fields. We suppose that there exists a stationary point where the linearized vector field has successively a stable focus, an unstable focus and an unstable node. When the parameter moves…