Related papers: The capture into parametric autoresonance
We study a Hamiltonian system of type describing a charged particle resonant interaction with an electromagnetic wave. We consider an ensemble of particles that repeatedly pass through the resonance with the wave, and study evolution of the…
We consider the convected Helmholtz equation with a generalized Myers boundary condition (a boundary condition of the second-order) and characterize the set of physical parameters for which the problem is weakly well-posed. The model comes…
The two layer model is a 2+1/2 degrees of freedom non autonomous dynamical system whose lower order expansion exhibits capture in resonance, numerically detected in a previous paper by the authors. In this paper, we reframe the model along…
The widespread availability of quantum entanglement with photons, in the guise of two-mode squeezed states, can be attributed to the phenomenon of parametric down-conversion. A reinterpretation of this effect with macroscopic mechanical…
We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity…
The generalized hyper-Ramsey resonance formula originally published in Phys. Rev. A vol 92, 023416 (2015) is derived using a Cayley-Klein spinor parametrization. The shape of the interferometric resonance and the associated composite…
The Rayleigh's criterion infamously imposes a minimum separation between two incoherent sources for them to be distinguishable via classical methods. In this work, we demonstrate the emergence of two-photon beats from the interference of a…
We study the asymptotic behavior of solutions to the second boundary value problem for a parabolic PDE of Monge-Amp\`ere type arising from optimal mass transport. Our main result is an exponential rate of convergence for solutions of this…
Pulsar dynamic spectra sometimes show organised interference patterns; these patterns have been shown to have power spectra which often take the form of parabolic arcs, or sequences of inverted parabolic arclets whose apexes themselves…
This paper studies the asymptotic stability of solution to an initial-boundary value problem for a hyperbolic-elliptic coupled system on two-dimensional half space, where the data on the boundary and at the far field are prescribed as $u_-$…
Leading terms of asymptotic expansions for the general complex solutions of the fifth Painlev\'e equation as $t\to\imath\infty$ are found. These asymptotics are parameterized by monodromy data of the associated linear ODE. $$…
We investigate the microwave absorption of a pinned, two-dimensional Wigner crystal in a strong magnetic field at finite temperatures. Using a model of a uniform commensurate pinning potential, we analyze thermal broadening of the…
An approach is proposed for recovering affine correspondences (ACs) from orientation- and scale-invariant, e.g. SIFT, features. The method calculates the affine parameters consistent with a pre-estimated epipolar geometry from the point…
Parametric excitation of rotons by oscillating electric field exhibits a narrow resonance at the roton minimum frequency. The resonance width is in good agreement with experimental results on the microwave absorption in superfluid helium.
We extend similarity reductions of the coupled (2+1)-dimensional three-wave resonant interaction system to its Lax pair. Thus we obtain new 3x3 matrix Fuchs--Garnier pairs for the third and fifth Painleve' equations, together with the…
We theoretically explore a variant of RABBITT spectroscopy in which the attosecond-pulse train comprises isolated pairs of consecutive harmonics of the fundamental infrared probe frequency. In this scheme, one-photon and two-photon…
This work studies front formation in the Allen-Cahn equation with a parameter heterogeneity which slowly varies in space. In particular, we consider a heterogeneity which mediates the local stability of the zero state and subsequent…
We present a parameter-decoupled superresolution framework for estimating sub-wavelength separations of passive two-point sources without requiring prior knowledge or control of the source. Our theoretical foundation circumvents the need to…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…
We study the one-dimensional Helmholtz equation with (possibly perturbed) quasiperiodic coefficients. Quasiperiodic functions are the restriction of higher dimensional periodic functions along a certain (irrational) direction. In classical…