Related papers: Universality in Three-Frequency Resonances
We proved two Three Circles Theorems for harmonic functions on manifolds in integral sense. As one application, on manifold with nonnegative Ricci curvature, whose tangent cone at infinity is the unique metric cone with unique conic…
Interpretation of dispersionless integrable hierarchies as equations of coisotropic deformations for certain algebras and other algebraic structures like Jordan triple systInterpretation of dispersionless integrable hierarchies as equations…
The transmission of electromagnetic wave through the planar chiral structure, loaded with the gyrotropic medium on the longitudinal magnetic field is studied. The frequency dependence of the metamaterial resonance and the angle of rotation…
We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.
The global behaviour of nonlinear systems is extremely important in control and systems theory since the usual local theories will only give information about a system in some neighbourhood of an operating point. Away from that point, the…
Improving the interpretability of deep neural networks has recently gained increased attention, especially when the power of deep learning is leveraged to solve problems in physics. Interpretability helps us understand a model's ability to…
Investigating dispersion surface morphology of sonic metamaterials is crucial in providing information on related phenomena as inertial coupling, acoustic transparency, polarisation, and absorption. In the present study, we look into…
Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by…
We analyse a new class of statistical systems, which simulate different systems of random surfaces on a lattice. Geometrical hierarchy of the energy functionals on which these theories are based produces corresponding hierarchy of the…
The possibility of production of pulses with scale-invariant properties at presence of fluctuations of parameters of self-oscillatory system with three-dimensional phase space is shown. The system of equations of inertial nonlinearity…
We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminium plate may have an…
The complex configurations of dynamic friction patterns-regarding real time contact areas- are transformed into appropriate networks. With this transformation of a system to network space, many properties can be inferred about the structure…
We show that resonance phenomena can be treated as nonequilibrium phase transitions. Resonance phenomena, similar to equilibrium phase transitions, are accompanied by some kind of symmetry breaking and can be characterized by order…
Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order…
We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations.…
Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…
When waves are propagated through a medium with scatters and these elements are positioned periodically, as in the crystal structures, multiple scattering leads to a phenomenon known as banded structures. This means that waves can propagate…
We address the problem of calculating momentum distributions of particles emerging from the three-body decay of a many-body resonance. We show that these distributions are determined by the asymptotics of the coordinate-space complex-energy…
We apply the linear response theory developed in \cite{Ruelle} to analyze how a periodic signal of weak amplitude, superimposed upon a chaotic background, is transmitted in a network of non linearly interacting units. We numerically compute…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…