Related papers: Extending near-axis equilibria in DESC
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
We consider nonlinear delay differential and renewal equations with infinite delay. We extend the work of Gyllenberg et al, Appl. Math. Comput. (2018) by introducing a unifying abstract framework, and derive a finite-dimensional…
Formation control deals with the design of decentralized control laws that stabilize mobile, autonomous agents at prescribed distances from each other. We call any configuration of the agents a target configuration if it satisfies the…
We develop an asymptotical control theory for one of the simplest distributed (infinite dimensional) oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of…
This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of…
We present a new method for constructing equilibrium phase models for stellar systems, which we call the iterative method. It relies on constrained, or guided evolution, so that the equilibrium solution has a number of desired parameters…
We present a survey of some aspects and new results on configurations, i.e. disjoint unions of constellations of infinitely near points, local and global theory, with some applications and results on generalized Enriques diagrams, singular…
Based on recent works on transverse exponential stability, we establish some necessary and sufficient conditions for the existence of a (locally) exponential synchronizing control law. We show that the existence of a structured synchronizer…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
We present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in the macroscopic continuum equation is…
The stability of a galaxy model is most easily assessed through N-body simulation. Particle-mesh codes have been widely used for this purpose, since they enable the largest numbers of particles to be employed. We show that the functional…
In this study, we explore the influence of the helicity of the magnetic axis-defined as the self-linking number of the curve-on the quality of quasi-isodynamic stellarator-symmetric configurations constructed using the near-axis expansion…
The aim of this paper is to construct six-dimensional symplectic thin-lens transport maps for the tracking program SIXTRACK, continuing an earlier report by using another method which consistes in applying Lie series and exponentiation as…
In this paper, we extend the definition of qx-asymptotic function, for extended real-valued function that define on an infinite dimensional topological normed space without lower semicontinuity or quasi-convexity condition. As the main…
We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
A deep equilibrium model (DEQ) is implicitly defined through an equilibrium point of an infinite-depth weight-tied model with an input-injection. Instead of infinite computations, it solves an equilibrium point directly with root-finding…
Decentralized optimization is a promising parallel computation paradigm for large-scale data analytics and machine learning problems defined over a network of nodes. This paper is concerned with decentralized non-convex composite problems…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
We present a technique for approximating generic normalization constants subject to constraints. The method is then applied to derive the exact asymptotics for the conditional normalization constant of constrained exponential random graphs.