We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideas to those of other authors. We emphasize methods that (a) show promise as practical design tools, (b) are effective when the nonlinearity is large, and (c) have a strong theoretical basis. TABLE OF CONTENTS

Developing the idea of fast particle mixing due to a strong nonlinearity of the beam-beam interaction, the distribution function of the weak bunch in the ,_ phase space of vertical motion is found. The features of this distribution are discussed and compared to the Gaussian one.

The transient absorption bleaching and velocity overshoot of photoexcited carriers in GaAs and Si have been observed by the intense few-circle terahertz (THz) probe pulse in the optical pump-terahertz probe (OPTP) configuration. The free-carrier THz nonlinearity is attributed to the transient electron redistribution in conduction band induced by the strong THz electric field component.

In this paper, we study a class of nonlocal semilinear elliptic problems with inhomogeneous strong Allee effect. By means of variational approach, we prove that the problem has at least two positive solutions for large λ under suitable hypotheses about nonlinearity. We also prove some nonexistence results. In particular, we give a positive answer to the conjecture of Liu-Wang-Shi.

Three-dimensional dynamic scatterplots can reveal characteristics of data – such as certain kinds of clustering and nonlinearity – that are not apparent in marginal two-dimensional views of the data. The experiments reported in this paper address the detection of nonlinearity in 3D dynamic scatterplots. Employing graduate-student subjects, we designed datasets that incorporated varying degrees ...

We studied the relative accuracy of drifting gratings and noise stimuli for functionally characterizing neural populations using two-photon calcium imaging. Calcium imaging has the potential to distort measurements due to nonlinearity in the conversion from spikes to observed fluorescence. We demonstrate a dramatic impact of fluorescence saturation on functional measurements in ferret V1 by sho...

We study nonlinear systems of hyperbolic (in a wider sense) PDE's in R d describing wave propagation with the initial data in the form of a finite sum of wavepackets referred to as multi-wavepackets. The problem involves two small parameters β and ̺ where: (i) 1 β is a factor describing spatial extension of the wavepackets; (ii) 1 ̺ is a factor describing the relative magnitude of the linear part...

We study a modified version of the stochastic susceptible-infected-refractory-susceptible (SIRS) model by employing a nonlinear (exponential) reinforcement in the contagion rate and no diffusion. We run simulations for complete and random graphs as well as d-dimensional hypercubic lattices (for d=3,2,1). For weak nonlinearity, a continuous nonequilibrium phase transition between an absorbing an...

Introduction: In recent years, the use of magnetic resonance (MR) images in radiation treatment planning has drawn considerable attention. However, although the extent of a tumor can be determined in great detail on MR images, the geometric accuracy of these images is limited by distortions stemming from the inhomogeneity of the static background magnetic field, the nonlineari...

Heart rate variability analysis is fast gaining acceptance as a potential non-invasive means of autonomic nervous system assessment in research as well as clinical domains. In this study, a new nonlinear analysis method is used to detect age related changes in the degree of nonlinearity and stochastic nature of heart rate variability signals. The data obtained from an online and widely used pub...