Related papers: Order reductions of Lorentz-Dirac-like equations
We discuss the unstable character of the solutions of the Lorentz-Dirac equation and stress the need of methods like order reduction to derive a physically acceptable equation of motion. The discussion is illustrated with the paradigmatic…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
The Landau-Lifshitz equation is the first in an infinite series of approximations to the Lorentz-Abraham-Dirac equation obtained from `reduction of order'. We show that this series is divergent, predicting wildly different dynamics at…
The instability of "physical" preaccelerative solution of the Lorentz-Dirac equation is explicitly shown
The Landau-Lifshitz equation is considered as an approximation of the Abraham-Lorentz-Dirac equation. It is derived from the Abraham-Lorentz-Dirac equation by treating radiation reaction terms as a perturbation. However, while the…
We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
The paper discusses the problem of the Lorentz contraction in accelerated systems, in the context of the special theory of relativity. Equal proper accelerations along different world lines are considered, showing the differences arising…
In this paper we discuss reduced order models for the approximation of parametric eigenvalue problems. In particular, we are interested in the presence of intersections or clusters of eigenvalues. The singularities originating by these…
The Landau-Lifshitz equation is obtained from the Lorentz-Abraham-Dirac equation through `reduction of order'. It is the first in a divergent series of approximations that, after resummation, eliminate runaway solutions. Using Borel plane…
One more paradox of classical Lorentz-Dirac preaccelerative solution is found: the formation of the event horizon.
The molecule solution of an equation related to the lattice Boussinesq equation is derived with the help of determinantal identities. It is shown that this equation can for certain sequences be used as a numerical convergence acceleration…
In this paper we consider a reduced order method for the approximation of the eigensolutions of the Laplace problem with Dirichlet boundary condition. We use a time continuation technique that consists in the introduction of a fictitious…
We take the viewpoint that the physically acceptable solutions of the Lorentz--Dirac equation for radiation back-reaction are actually determined by a second order equation of motion, the self-force being given as a function of spacetime…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…
We present a C program to compute by successive approximations the regular order reduction of a large class of ordinary differential equations, which includes evolution equations in electrodynamics and gravitation. The code may also find…
The scalar difference equation $x_{n+1}=f_{n}(x_{n},x_{n-1},...,x_{n-k})$ may exhibit symmetries in its form that allow for reduction of order through substitution or a change of variables. Such form symmetries can be defined generally…
We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
To improve the presentation we modified the title and used the framework of perturbation modeling of long-term dynamics so as to present the Lorentz-Abraham-Dirac equation as the lowest order, asymptotic differential relation for the…