相关论文: Linear stability analysis of collective neutrino o…

The dense neutrino flux streaming from a core-collapse supernova can undergo self-induced flavor conversion caused by neutrino-neutrino refraction. Numerical studies of these nonlinear effects are challenging because representing the…

The Neumann problem of linear elasticity is singular with a kernel formed by the rigid motions of the body. There are several tricks that are commonly used to obtain a non-singular linear system. However, they often cause reduced accuracy…

Neutrino-neutrino interactions in dense neutrino streams, like those emitted by a core-collapse supernova, can lead to self-induced neutrino flavor conversions. While this is a nonlinear phenomenon, the onset of these conversions can be…

A dense neutrino medium can experience collective flavor oscillations through nonlinear neutrino-neutrino refraction. To make this multi-dimensional flavor transport problem more tractable, all existing studies have assumed certain…

We study neutrino oscillations in space within a realistic model in which both the source and the target are considered to be stationary having Gaussian-form localizations. The model admits an exact analytic solution in field theory which…

We theoretically propose and investigate an optical analogue of neutrino oscillations in a pair of vertically displaced binary waveguide arrays with longitudinally modulated effective refractive index. Optical propagation is modelled…

Neutrino oscillations in a hot and dense astrophysical environment such as a core-collapse supernova pose a challenging, seven-dimensional flavor transport problem. To make the problem even more difficult (and interesting), neutrinos can…

Neutrino flavor oscillations in the presence of ambient neutrinos is nonlinear in nature which leads to interesting phenomenology that has not been well understood. It was recently shown that, in the two-dimensional, two-beam neutrino Line…

We consider the implementation of the split-step method where the linear part of the nonlinear Schr\"odinger equation is solved using a finite-difference discretization of the spatial derivative. The von Neumann analysis predicts that this…

It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…

We study the oscillations of neutrinos in a model in which the neutrino is coupled to a localized, idealized source and detector. By varying the spatial and temporal resolution of the source and detector we are able to model the full range…

The rich phenomenology of collective neutrino oscillations has been studied only in one-dimensional or spherically symmetric systems. Motivated by the non-spherical example of coalescing neutron stars, presumably the central engines of…

We reveal that even weak inherent discreteness of a nonlinear model can lead to instabilities of the localized modes it supports. We present the first example of an oscillatory instability of dark solitons, and analyse how it may occur for…

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…

We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…

We investigate the causes of the curious property of neutrino oscillations of looking as an interference between fully distinguishable particles. The sources of this effect are identified as to be determined by the many particle nature of…

I utilize the Petrov-Galerkin formulation and develop a new method for solving the unsteady collisionless Boltzmann equation in both the linear and nonlinear regimes. In the first order approximation, the method reduces to a linear…

An earlier paper presented the potentially significant discovery that disturbances in simplified simulations of a stellar disc model that was predicted to be stable in linear theory grew to large amplitude over a long period of time. The…

This paper focuses on identifying the cause and proposing a remedy for the problem of spurious pressure oscillations in a sharp-interface immersed boundary finite element method for incompressible flow problems in moving domains. The…

We consider numerical instability that can be observed in simulations of localized solutions of the generalized nonlinear Schr\"odinger equation (NLS) by a split-step method where the linear part of the evolution is solved by a…