Related papers: Monodromy in the resonant swing spring
Propellant sloshing is a well-known, but not completely mastered phenomenon in space vehicles. It is particularly critical in both microgravity environments - such as interplanetary spacecraft requiring high pointing stability - and high-g…
The spin magnetic moment of a single proton in a cryogenic Penning trap was coupled to the particle's axial motion with a superimposed magnetic bottle. Jumps in the oscillation frequency indicate spin-flips and were identified using a…
Nonlinear damping plays a significant role in several area of physics and it is becoming increasingly important to understand its underlying mechanism. However, microscopic origin of nonlinear damping is still a debatable topic. Here, we…
The monodromy conjecture is a mysterious open problem in singularity theory. Its original version relates arithmetic and topological/geometric properties of a multivariate polynomial $f$ over the integers, more precisely, poles of the…
We study dynamics of a nonlinear pendulum under a periodic force with small amplitude and slowly decreasing frequency. It is well known that when the frequency of the external force passes through the value of the frequency of the…
The problem of description of superintegrable systems (i.e., systems with closed trajectories in a certain domain) in the class of rotationally symmetric natural mechanical systems goes back to Bertrand and Darboux. We describe all…
We show that attractive, translation invariant, one-dimensional spin systems started from the unit step function possess the following basic property. At any time, the entire configuration from a point onward is stochastically decreasing…
We build a combinatorial invariant, called the spectral monodromy from the spectrum of a non-selfadjoint h -pseudodifferential operator with two degrees of freedom in the semi-classical limit. We treat small non-selfadjoint perturbation of…
A simple two charge system, one charge being suspended on a spring, exhibits complex behavior including bistability, hysteresis and catastrophic response to gradual variation of the external parameters. We discuss these complex features…
We algorithmically determine the monodromy of the local system on the smooth part of the Radon transformation of a generic simple perverse sheaf on the projective plane.
The many-body Green's function theory with the random-phase approximation is applied to the study of easy-plane spin-1/2 ferromagnets in an in-plane magnetic field. We demonstrate that the usual procedure, in which only the three Green's…
We develop here the method for obtaining approximate stability boundaries in the space of parameters for systems with parametric excitation. The monodromy (Floquet) matrix of linearized system is found by averaging method. For system with 2…
It is shown that in an anisotropic harmonic trap that rotates with the properly chosen rotation rate, the force of gravity leads to a resonant behavior. Full analysis of the dynamics in an anisotropic, rotating trap in 3D is presented and…
Computation of spin-resummed observables in post-Minkowskian dynamics typically involve evaluation of Feynman integrals deformed by an exponential factor, where the exponent is a linear sum of the momenta being integrated. Such integrals…
Ramsey spectroscopy has become a powerful technique for probing non-equilibrium dynamics of internal (pseudospin) degrees of freedom of interacting systems. In many theoretical treatments, the key to understanding the dynamics has been to…
We study dynamics of the inverted pendulum on the wheel on a soft surface and under a proportional-integral-derivative controller. The behaviour of such pendulum is modelled by a system with a differential inclusion. If the the system has a…
This paper reports numerical studies of a compressible version of the Ising spin glass in two dimensions. Compressibility is introduced by adding a term that couples the spin-spin interactions and local lattice deformations to the standard…
Inspired by the experimental results of Cuevas et al. (Physical Review Letters 102, 224101 (2009)), we consider theoretically the behavior of a chain of planar rigid pendulums suspended in a uniform gravitational field and subjected to a…
I consider the dynamics of mean motion resonances between pairs of co-planar planets and derive a new integrable Hamiltonian model for planets' resonant motion. The new model generalizes previously-derived integrable Hamiltonians for…
The dynamics of nonlinear oscillators are investigated. We study the formation of $1:2$ resonance in nonlinear periodically forced oscillators due to period doubling of the primary $1:1$ resonance, or born independently. We compute the…