The method of harmonic balance (HB) is a spectrally accurate used to obtain periodic steady state solutions dynamical systems subjected perturbations. We adapt HB solve for the stress response Giesekus model under large amplitude oscillatory shear (LAOS) deformation. transforms system differential equations set nonlinear algebraic in Fourier coefficients. Convergence studies find that differenc...

The time-strain separable Kaye–Bernstein–Kearsley–Zappas model (tssKBKZM) is a popular integral constitutive equation that used to the nonlinear response of materials using only their linear viscoelastic properties and damping function. In oscillatory shear, numerical evaluation tssKBKZM complicated by infinite domain integration, nature integrand. To avoid these problems, spectrally accurate m...

The characterization of functional network structures among multiple neurons is essential to understanding neural information processing. Information geometry (IG), a theory developed for investigating a space of probability distributions has recently been applied to spike-train analysis and has provided robust estimations of neural interactions. Although neural firing in the equilibrium state ...

The study of the symmetric properties differential equations is essential for identifying effective methods solving them. In this paper, we examine oscillatory behavior solutions Emden–Fowler-type mixed non-linear neutral with both canonical and non-canonical operators. By utilizing integral conditions averaging method, present new sufficient to ensure that all are oscillatory. Our results enha...

This paper is concerned with a 1D Schrödinger scattering problem involving both oscillatory and evanescent regimes, separated by jump discontinuities in the potential function, to avoid "turning points". We derive a non-overlapping domain decomposition method to split the original problem into sub-problems on these regions, both for the continuous and afterwards for the discrete problem. Furthe...

[1] A method for extracting time-varying oscillatory motions from time series records is applied to Lagrangian trajectories from a numerical model of eddies generated by an unstable equivalent barotropic jet on a beta plane. An oscillation in a Lagrangian trajectory is represented mathematically as the signal traced out as a particle orbits a time-varying ellipse, a model which captures wavelik...

Background: Quantifying the robustness of biochemical models is important both for determining the validity of a natural system model and for designing reliable and robust synthetic biochemical networks. Several tools have been proposed in the literature. Unfortunately, multiparameter robustness analysis suffers from computational limitations. Results: A novel method for quantifying the robustn...