Related papers: Microlocal Projector for Complete Flow
In this paper we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of L. Polterovich and M. Schwarz, we study the role of…
We extend to $\mathrm{C}\times \mathrm{W}^{1,2}$-local minimizers and nonautonomous perturbation function, the necessary optimality conditions derived in [1], via continuous-time approximations, for $\mathrm{W}^{1,2}\times…
We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…
We construct and analyze a projection-free linearly implicit method for the approximation of flows of harmonic maps into spheres. The proposed method is unconditionally energy stable and, under a sharp discrete regularity condition,…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
This paper is concerned with the characterizations of quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems. Some properties of the solutions and the characterization of the minimal linear…
Generalizing F-nilpotent completion for a ring spectrum F we first define the notion of completion with respect to a thick subcategory in a monogenic stable homotopy category. Specializing this to the thick subcategory generated by…
We provide an abstract framework for the study of certain spectral properties of parabolic systems; specifically, we determine under which general conditions to expect the presence of absolutely continuous spectral measures. We use these…
We show that an optimized projection functions method can automatically construct maximally localized Wannier functions even for bands with nontrivial topology. We demonstrate this method on a tight-binding model of a two-dimensional…
Optical metamaterials have the potential to control the flow of light at will which may lead to spectacular applications as the perfect lens or the cloaking device. Both of these optical elements require invariant effective material…
Assume that R is a local regular ring containing an infinite perfect field, or that R is the local ring of a point on a smooth scheme over an infinite field. Let K be the field of fractions of R and the characteristic of K is not 2. Let X…
We prove that for any open Riemann surface $M$ and any non constant harmonic function $h:M \to \mathbb{R},$ there exists a complete conformal minimal immersion $X:M \to \mathbb{R}^3$ whose third coordinate function coincides with $h.$ As a…
This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical…
This paper develops a new approach to small time local attainability of smooth manifolds of any dimension, possibly with boundary and to prove H\"older continuity of the minimum time function. We give explicit pointwise conditions of any…
Superfluidity, the ability of a liquid or gas to flow with zero viscosity, is one of the most remarkable implications of collective quantum coherence. In equilibrium systems like liquid 4He and ultracold atomic gases, superfluid behaviour…
Recently, the complexity behind manipulations of reflected fields by metasurfaces has been addressed showing that, even in the simplest scenarios, non-local response and excitation of auxiliary evanescent fields are required for perfect…
In this work we consider a flow network for which the goal is to solve a practical optimal regulation problem in the presence of input saturation. Based on Lyapunov arguments we propose distributed controllers which guarantee global…
We provide formulas for projectors onto a polyhedral set, i.e. the intersection of a finite number of halfspaces. To this aim we formulate the problem of finding the projection as a convex optimization problem and we solve explicitly…
An unconstrained optimal control policy is completely decentralized if computing actuation for each subsystem only requires information directly available to its own subcontroller. Parameters that admit a completely decentralized optimal…
We propose theoretically an optical diode based on exciton-polaritons in semiconductor microcavities. A flow of polaritons in the bistable regime is used to send signals through an asymmetric fixed potential that favours the tunneling of…