We study two resonant Hamiltonian systems on the phase space L2(R → C): the quintic one-dimensional continuous resonant equation, and a cubic resonant system that appears as the modified scattering limit of a specific NLS equation. We prove that these systems approximate the dynamics of the quintic and cubic one-dimensional NLS with harmonic trapping in the small data regime on long times scale...

In present paper there is the consideration of mathematical model of food plant (resource) – consumer (insect population) – pathogen system dynamics which is constructed as a system of ordinary differential equations. The dynamic regimes of model are analyzed and, in particular, with the help of numerical methods it is shown that trigger regimes (regimes with two stable attractors) can be reali...

The transition between the transient and the stationary regimes of stimulated Raman scattering is examined computationally for pulses with a sharp initial rise. We find that the transient-regime predictions are useful for times less than T2 regardless of the pulse duration and that the stationary-regime predictions become useful only for times much greater than T2 . © 1996 Optical Society of Am...

Consider the mean field limit of a model for multiple HTTP sources multiplexed through a drop-tail router. The limit may exhibit two stationary regimes. In the fluid regime the flows are independent, there are no packet losses and the average throughput is high. In the turbulent regime the flows are synchronized, there are periodic congestion epochs with packet losses and the average throughput...

The distinction of enantiomers is a key aspect of chemical analysis. In mass spectrometry the distinction of enantiomers has been achieved by ionizing the sample with circularly polarized laser pulses and comparing the ion yields for light of opposite handedness. While resonant excitation conditions are expected to be most efficient, they are not required for the detection of a circular dichroi...

A new model for studying energy transfer is introduced. It consists of a ‘‘resonant duo’’—a resonant quartet where extra symmetries support a reduced subsystem with only two degrees of freedom—where one mode is forced by white noise and the other is damped. This system has a single free parameter: the quotient of the damping coefficient to the amplitude of the forcing times the square root of t...

Firstly, bilinear Fourier Restriction estimates –which are well-known for free waves– are extended to adapted spaces of functions of bounded quadratic variation, under quantitative assumptions on the phase functions. This has applications to nonlinear dispersive equations, in particular in the presence of resonances. Secondly, critical global well-posedness and scattering results for massive Di...

The bifurcated states of a rotating tokamak plasma in the presence of a static, resonant, erroreld are found to be strongly analogous to the bifurcated states of a conventional induction motor. The two plasma states are the \unreconnected" state, in which the plasma rotates and erroreld driven magnetic reconnection is suppressed, and the \fully reconnected" state, in which the plasma rotation a...

This Letter reports on how the interfaces in the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) class undergo, in the course of time, a transition from the flat, growing regime to the stationary one. Simulations of the polynuclear growth model and experiments on turbulent liquid crystal reveal universal functions of the KPZ class governing this transition, which connect the distribution and correl...