Related papers: Frobenius-Perron Operator Approach to the Beam-Bea…
We present the applications of nonlinear local harmonic analysis methods to the modelling of beam-beam interaction. Our approach is based on methods provided the possibility to work with dynamical beam localization in phase space. The…
In this paper we propose a model of random compositions of cylinder maps, which in the simplified form is as follows: $(\theta,r)\in \mathbb T\times \mathbb R=\mathbb A$ and \begin{eqnarray} \nonumber f_{\pm 1}:…
The paper is devoted to the observability study of a dynamic system, which describes the vibrations of an elastic beam with an attached rigid body and distributed control actions. The mathematical model is derived using Hamilton's principle…
This paper studies the stability of discrete-time polynomial dynamical systems on hypergraphs by utilizing the Perron-Frobenius theorem for nonnegative tensors with respect to the tensors Z-eigenvalues and Z-eigenvectors. Firstly, for a…
Theory of the spectrum of localized two-level quasi-particle renormalized due to interaction with polarization phonons at cryogenic temperature is developed using the generalized method of Feynman-Pines diagram technique. Using the…
The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was…
We provide and study complete sets of one-loop renormalization group equations of several Finkel'stein non-linear $\sigma$-models, the effective field theories describing the diffusive quantum fluctuations in correlated disordered systems.…
We study the quantum coherent-tunneling between two Bose-Einstein condensates separated through an oscillating trap potential. The cases of slowly and rapidly varying in time trap potential are considered. In the case of a slowly varying…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
We demonstrate a new technique for the experimental measurement of the spectral coherence of microresonator optical frequency combs. Specifically, we use a spectral interference method, typically used in the context of supercontinuum…
Attractively interacting two-component mixtures of fermionic particles confined in a one-dimensional harmonic trap are investigated. Properties of balanced and imbalanced systems are systematically explored with the exact diagonalization…
The microscopic basis for the stability of itinerant ferromagnetism in correlated electron systems is examined. To this end several routes to ferromagnetism are explored, using both rigorous methods valid in arbitrary spatial dimensions, as…
We prove that twisting and filamentation occur near a family of stable steady states for one dimensional periodic Vlasov-Poisson system, describing the electron dynamics under a fixed ion background. More precisely, we establish the growth…
A mathematical model of a simply supported Euler-Bernoulli beam with attached spring-mass system is considered. The model is controlled by distributed piezo actuators and lumped force. We address the issue of asymptotic behavior of…
Nonlinear spin dynamics are essential in exploring nonequilibrium quantum phenomena and have broad applications in precision measurement. Among these systems, the combination of a bias magnetic field and feedback mechanisms can induce…
Optomechanical Brillouin nonlinearities -- arising from the coupling between traveling photons and phonons -- have become the basis for a range of powerful optical signal processing and sensing technologies. The dynamics of such…
A system of harmonic oscillators coupled via nonlinear interaction is a fundamental model in many branches of physics, from biophysics to electronics and condensed matter physics. In quantum optics, weak nonlinear interaction between light…
This article is dedicated to the investigation of the stabilization problem of a flexible beam attached to the center of a rotating disk. We assume that the feedback law contains a nonlinear torque control applied on the disk and nonlinear…
In polarized proton operation in the Relativistic Heavy Ion Collider (RHIC) coherent beam-beam modes are routinely observed with beam transfer function measurements. These modes can become unstable under external excitation or in the…
Boundary equilibria bifurcation (BEB) arises in piecewise-smooth systems when an equilibrium collides with a discontinuity set under parameter variation. Singularly perturbed BEB refers to a bifurcation arising in singular perturbation…