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We present a diagrammatic theory for coherent backscattering from disordered dilute media in the nonlinear regime. The approach is non-perturbative in the strength of the nonlinearity. We show that the coherent backscattering enhancement…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
An unprecedented comparison of closed-form incoherent GN (InGN) models is presented with heterogeneous spans and partially loaded links in elastic optical networks. Results reveal that with accumulated dispersion correction and modulation…
A non-perturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line…
The classical theory of modulation instability (MI) attributed to Bespalov-Talanov in optics and Benjamin-Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact…
The coordinate invariant theory of generalised functions of Colombeau and Meril is reviewed and extended to enable the construction of multi-index generalised tensor functions whose transformation laws coincide with their counterparts in…
We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function,…
We study an ensemble of random matrices (the Rosenzweig-Porter model) which, in contrast to the standard Gaussian ensemble, is not invariant under changes of basis. We show that a rather complete understanding of its level correlations can…
Dissipation is a ubiquitous phenomenon in dynamical systems encountered in nature because no finite system is fully isolated from its environment. In optical systems, a key challenge facing any technological application has traditionally…
This paper proposes a new extended-state observer-based framework for adaptive nonlinear regulator design of a class of nonlinear systems, in the general nonequilibrium theory. By augmenting an extended-state observer with an internal…
Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms…
We revisit the paradigm of unified dark energy discussing in detail the averaging problem in this type of scenarios, highlighting the need for a full non-linear treatment. We also address the question of if and how models with one or…
In this article we develop an effective theory of pulse propagation in a nonlinear and disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel…
We introduce general results on well-posedness and output regulation of regular linear systems with nonautonomous controllers. We present a generalization of the internal model principle for time-dependent controllers with asymptotically…
The non-perturbative renormalization-group approach is extended to lattice models, considering as an example a $\phi^4$ theory defined on a $d$-dimensional hypercubic lattice. Within a simple approximation for the effective action, we solve…
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media…
In this paper we show how nonlinear internal models can be effectively used in the design of output regulators for nonlinear systems. This result provides a significant enhancement of the non-equilibrium theory for output regulation, which…
We introduce diffusively coupled networks where the dynamical system at each vertex is planar Hamiltonian. The problems we address are synchronisation and an analogue of diffusion-driven Turing instability for time-dependent homogeneous…
The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We…
Density matrix perturbation theory [Phys. Rev. Lett. Vol. 92, 193001 (2004)] provides an efficient framework for the linear scaling computation of response properties [Phys. Rev. Lett. Vol. 92, 193002 (2004)]. In this article, we generalize…