Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real ...

It is shown that dark solitons display an inherent instability for a strong saturation of the nonlinear refractive index provided that the background intensity exceeds a certain critical value. Such an instability manifests itself as a drift of a black soliton that transform into a gray soliton and radiation.

We study the control of modulational instability and pattern formation in a nonlinear dissipative feedback system with a periodic modulation of the material refractive index. We use a one-dimensional photonic lattice in a single-mirror feedback configuration and identify three mechanisms for pattern control: bandgap suppression of instability modes, periodicity induced pattern modes, and orient...

Recently, Kim and others (2009) proposed a stock market instability index ( SMII ) and a corresponding p-value using a nonparametric model fitted to a stable period. However, this SMII has failed to explain the 2008 global financial market crisis because its data-driven approach relies excessively on data from the stable period upon which it is based. To resolve this problem, this study conside...

Background and Aim: Degenerative lumbar spine disease can lead to lumbar spine instability. The patients can present with Low Back Pain (LBP), radicular pain, and motor and sensory dysfunction. Age >50, female sex and pregnancies are among prevalent risk factors. The degeneration process usually starts from the intervertebral discs progressing to involve facet joints, ligaments, and vertebral b...

We develop a general instability index theory for an eigenvalue problem of the type Lu = λu′, for a class of self-adjoint operators L on the line R. More precisely, we construct an Evans-like function to show (a real eigenvalue) instability in terms of a Vakhitov-Kolokolov type condition on the wave. If this condition fails, we show by means of Lyapunov-Schmidt reduction arguments and the Kapit...

this paper presents a model of a catchment area in northwest of iran. the researchers have studied ajichai basin which is located in the east part of orumiyeh lake, located at the longitude of 47 52’ e to 45 32’ e and the latitude of 37 26’ n to 38 30’ n. the researchers have chosen the data from tabriz upper air station which is the only one in the area. the research data are seven instability...

In this talk I review three fatal flaws of the DGP braneworld model, which has been put forward as a possible model for late time acceleration without a cosmological constant; Ghosts, Cosmological Crashes, and Instability of the 5D vacuum. The talk is based on work in collaboration with Charmousis, Kaloper, Myers and Padilla. 2) (The title refers to a film: The three burials of Melquiades Estra...

The emergence of second-harmonic generation (SHG) is a pivotal issue to the development of nano-optical devices and interfaces. Here, we perform a classical analysis of the SHG dynamics with the aim of determining critical values of the electric field. The signals of the SHG process are nonlinear, so it seems reasonable that chaos theory can be a suitable tool to analyze their dynamics. For thi...

The Prediction Accuracy Index (PAI) monitors stability, defined as whether the predictive power of a model has deteriorated due to change in distribution explanatory variables since its development. This paper shows how PAI is related Mahalanobis distance, an established statistic for examining high leverage observations data. relationship used explore properties PAI, including tools can be dec...