相关论文: Tube Rupture in Aperiodic Nonlinear Oscillators: T…

We study the nonlinear oscillator z'' + omega^2 z + g(t) z^2 = 0 with a time-dependent coefficient g(t). We show that this equation admits an exact quadratic invariant I(z,p,t) provided that g(t) = alpha2(t)^(-5/2) and that alpha2(t)…

We investigate the rupture of invariant tubes in a class of nonautonomous dynamical systems arising from time-dependent Ermakov-type equations. Starting from an exactly tube-integrable reference system, we analyze a time-dependent invariant…

This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion $\tau(t)$ of the state trajectory. For a system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there exists a…

In this Letter we investigate the rupture instability of thin liquid films by means of a bifurcation analysis in the vicinity of the short-scale instability threshold. The rupture time estimate obtained in closed form as a function of the…

We consider synchrony patterns in coupled phase oscillator networks that correspond to invariant tori. For specific nongeneric coupling, these tori are equilibria relative to a continuous symmetry action. We analyze how the invariant tori…

The interaction between deformable surfaces and oscillatory driving is known to yield complex secondary time-averaged flows due to inertial and elastic nonlinearities. Here, we revisit the problem of oscillatory flow in a cylindrical tube…

The decays tau -> 3 pi + nu(tau) are analyzed at one loop order in the framework of Generalized Chiral Perturbation Theory, in order to test the sensitivity to the size of spontaneous chiral symmetry breaking parameters, contained in the…

This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem…

Sufficiently inclusive observables in the decay of the tau lepton can be calculated using the methods of perturbative QCD. These include the asymmetry parameter $A_\tau$ that determines that angular distribution of the total hadron momentum…

We study the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy. We compute and analyze the fixed-dimension perturbative expansion of the renormalization-group functions to four loops. The relations of these…

We study the global boundedness of the solutions of a non-smooth forced oscillator with a periodic and real analytic forcing. We show that the impact map associated with this discontinuous equation becomes a real analytic and exact…

This paper focuses on using curvature and torsion to describe the stability of linear time-invariant system. We prove that for a two-dimensional system $\dot{r}(t)= Ar(t)$, (i) if there exists an initial value, such that zero is not the…

The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…

We present a rigorous analysis of the Landau-Zener linear-in-time term crossing problem for quadratic-nonlinear systems relevant to the coherent association of ultracold atoms in degenerate quantum gases. Our treatment is based on an exact…

In this paper we study long time stability of a class of nontrivial, quasi-periodic solutions depending on one spacial variable of the cubic defocusing non-linear Schr\"odinger equation on the two dimensional torus. We prove that these…

Considering a nonlinear system in Byrnes-Isidori form that is subject to unbounded perturbations, we apply Lyapunov redesign via feedback linearisation for trajectory tracking. Leveraging the ideas of tube-based geometric characterisation…

Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This…

In this paper we are interested in the mathematical and numerical analysis of the time-dependent Galbrun equa- tion in a rigid duct. This equation models the acoustic propagation in presence of flow [1]. We propose a regu- larized…

We study the excitation and damping of tides in close binary systems, accounting for the leading order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct effects: three-mode nonlinear interactions…

A tube conveying a large amount of fluid with a free outlet does not sit still. We construct and analyze a nonlinear evolution equation describing such phenomena. Two types of boundary conditions at the inlet are considered, one for which…