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We extend the recently developed discrete geometric singular perturbation theory to the non-normally hyperbolic regime. Our primary tool is the Takens embedding theorem, which provides a means of approximating the dynamics of particular…
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…
In this paper we present a general framework in which one can rigorously study the effect of spatio-temporal noise on traveling waves, stationary patterns and oscillations that are invariant under the action of a finite-dimensional set of…
Stacked Intelligent Metasurfaces (SIM) have emerged as a revolutionary architecture for next-generation wireless communications, offering wave-domain signal processing capabilities with significantly reduced hardware complexity compared to…
The spectral theory for weakly stationary processes valued in a separable Hilbert space has known renewed interest in the past decade. Here we follow earlier approaches which fully exploit the normal Hilbert module property of the time…
An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the finite-scale Hamiltonian dynamics is governed by…
Stacked intelligent metasurfaces (SIMs) facilitate computation by cascaded programmable layers so that part of the signal processing can be performed in the wave domain during signal propagation, rather than solely after reception. This…
Extensive work has demonstrated that equivariant neural networks can significantly improve sample efficiency and generalization by enforcing an inductive bias in the network architecture. These applications typically assume that the domain…
New insights into transport properties of nanostructures with a linear dispersion along one direction and a quadratic dispersion along another are obtained by analysing their spectral stability properties under small perturbations.…
This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…
A group-theoretical approach for studying localized periodic and quasiperiodic vibrations in 2D and 3D lattice dynamical models is developed. This approach is demonstrated for the scalar models on the plane square lattice. The…
An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…
Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
When used with coherent light, optical imaging systems, even diffraction-limited, are inherently unable to reproduce both the amplitude and the phase of a two-dimensional field distribution because their impulse response function varies…
Stacked intelligent metasurfaces (SIMs), which integrate multiple programmable metasurface layers, have recently emerged as a promising technology for advanced wave-domain signal processing. SIMs benefit from flexible spatial…
We show how the recent extension of spectral submanifold (SSM) theory to delay differential equations (DDEs) enables data-driven model reduction of nonlinear delay systems. First, using a scalar DDE with a single discrete delay, we compare…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any…
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…