Related papers: Universality in Three-Frequency Resonances
We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental…
The frequency dependence of the interlayer conductivity of a layered Fermi liquid in a magnetic field which is tilted away from the normal to the layers is considered. For both quasi-one- and quasi-two-dimensional systems resonances occur…
Self-organized network dynamics prevails for systems across physics, biology and engineering. How external signals generate distributed responses in networked systems fundamentally underlies their function, yet is far from fully understood.…
Three-wave interactions form the basis of our understanding of many pattern forming systems because they encapsulate the most basic nonlinear interactions. In problems with two comparable length scales, it is possible for two waves of the…
We consider {\it small solutions} of a vibrating mechanical system with smooth non-linearities for which we provide an approximate solution by using a triple scale analysis; a rigorous proof of convergence of the triple scale method is…
The unreduced, universally nonperturbative analysis of arbitrary many-body interaction process reveals the irreducible, purely dynamic source of randomness. It leads to the universal definition of real system complexity (physics/9806002),…
We determine exact exponential asymptotics of eigenfunctions and of corresponding transfer matrices of the almost Mathieu operators for all frequencies in the localization regime. This uncovers a universal structure in their behavior,…
We study scattering resonances of finite one-dimensional systems of high-contrast resonators beyond the subwavelength regime. Introducing a novel tridiagonal frequency-dependent capacitance matrix, we derive quantitative asymptotic…
We analytically determine the properties of three interacting fermions in a harmonic trap subject to an external rotation. Thermodynamic quantities such as the entropy and energy are calculated from the third order quantum virial expansion.…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
Self-organization through noisy interactions is ubiquitous across physics, mathematics, and machine learning, yet how long-range structure emerges from local noisy dynamics remains poorly understood. Here, we investigate three paradigmatic…
Finite-dimensional wave turbulence refers to the chaotic dynamics of interacting wave `clusters' consisting of finite number of connected wave triads with exact three-wave resonances. We examine this phenomenon using the example of…
We describe a new kind of resonance occuring in relativistic three-body hierarchical systems: the precession resonance, occuring when the relativistic precession timescale of a binary equals the period of a distant perturber. We find that,…
The dynamics of baryon string model Y (three-string) is considered with using the approach that implies defining a classical motion of the system on the base of given initial position and initial velocities of string points. The analysis…
The paper deals with the interaction between buckling and resonance instabilities of mechanical systems. Taking into account the effect of geometric nonlinearity in the equations of motion through the geometric stiffness matrix, the problem…
In this Letter we report new effects of resonance detuning on various dynamical parameters of a generic 3-wave system. Namely, for suitably chosen values of detuning the variation range of amplitudes can be significantly wider than for…
We define the Farey web --- a collection of loci in the parameter plane of families of simple non-invertible maps of the circle. We prove some results about the arrangement of these loci and their relationships with other dynamically…
Possibility to establish macroscopic phenomenological theory for biological systems, akin to the akin to the well-established framework of thermodynamics, is briefly reviewed. We introduce the concept of an evolutionary fluctuation-response…
Physical systems and signals are often characterized by complex functions of frequency in the harmonic-domain. The extension of such functions to the complex frequency plane has been a topic of growing interest as it was shown that specific…
Relativistic constituent quark models generally describe three-quark systems with particular interactions. The corresponding invariant mass eigenvalue spectra and pertinent eigenstates should exhibit the multiplet structure anticipated for…