Related papers: Quantitative Geometric Control in Linear Kinetic T…
We show that for cubic scalar field theories in five and more spacetime dimensions, and for the $T = 0$ limit of the Caldeira-Leggett model, the quantum master equation for long-wavelength modes initially unentangled from short-distance…
In this work we provide a computationally tractable procedure for designing affine control policies, applied to constrained, discrete-time, partially observable, linear systems subject to set bounded disturbances, stochastic noise and…
We consider hypoelliptic equations of kinetic Fokker-Planck type, also known as Kolmogorov or ultraparabolic equations, with rough coefficients in the drift-diffusion operator. We give novel short quantitative proofs of the De Giorgi…
We get fractional symmetric Fokker - Planck and Einstein - Smoluchowski kinetic equations, which describe evolution of the systems influenced by stochastic forces distributed with stable probability laws. These equations generalize known…
We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and find…
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest…
We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Under appropriate conditions, there is a…
We study linear cosmological perturbations in the most general teleparallel gravity setting, where gravity is mediated by the torsion and nonmetricity of a flat connection alongside the metric. For a general linear perturbation of this…
We examine spectral operator-theoretic properties of linear and nonlinear dynamical systems with globally stable attractors. Using the Kato Decomposition we develop a spectral expansion for general linear autonomous dynamical systems with…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
The goal of the present article is to study controllability properties of mixed systems of linear parabolic-transport equations, with possibly non-diagonalizable diffusion matrix, on the one-dimensional torus. The equations are coupled by…
The generalization of the Koopman operator to systems with control input and the derivation of a nonlinear fundamental lemma are two open problems that play a key role in the development of data-driven control methods for nonlinear systems.…
Transport properties of asymmetric molecular structure are studied within the kinetic equation approach, taking into consideration the electron interaction in the self-consistent manner (SCF procedure). The device is made of a molecule…
In gauge theories, globally charged observables necessarily depend non-locally on the kinematical fields, with this dependence extending to the asymptotic boundary of spacetime. Despite this, we show that a subset of such observables can be…
We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a…
In this paper, we present a geometric approach for computing the controlled invariant set of a continuous-time control system. While the problem is well studied for in the ellipsoidal case, this family is quite conservative for constrained…
We study general semilinear scalar-field equations on the real line with variable coefficients in the linear terms. These coefficients are uniformly small, but slowly decaying, perturbations of a constant-coefficient operator. We are…
A key problem in the attempt to quantize the gravitational field is the choice of boundary conditions. These are mixed, in that spatial and normal components of metric perturbations obey different sets of boundary conditions. In the…
A class of boundary conditions for canonical general relativity are proposed and studied at the quasi-local level. It is shown that for untrapped or marginal surfaces, fixing the area element on the 2-surface (rather than the induced…
Lane-free vehicle movement has been recently proposed for connected automated vehicles (CAV) due to various potential advantages. One such advantage stems from the fact that incremental changes of the road width in lane-free traffic lead to…