Significance Of Nonlinearity Research Articles

Magnetic potential based formulation for linear and non-linear 3D RF sheath simulation

This paper reports a new numerical scheme to simulate the radio-frequency (RF) induced RF sheath, which is suitable for a large 3D simulation. In the RF sheath boundary model, the tangential component of the electric field () is given by the gradient of a scalar electric field potential. We introduce two additional scalar potentials for the tangential components of the magnetic field, which effectively impose the normal electric displacement (D n ) on the plasma sheath boundary condition via in-homogeneous Neumann boundary condition and constrain the tangential electric field on the surface as curl-free (). In our approach, the non-linear sheath impedance is formulated as a natural extension of the large thickness (or asymptotic) sheath limit (), allowing for handling both asymptotic and non-linear regimes seamlessly. The new scheme is implemented using the Petra-M finite element method analysis framework and is verified with simulations in the literature. The significance of non-linearity is discussed in various plasma conditions. An application of this scheme to asymptotic RF sheath simulation on the WEST ICRF antenna side limiters is also discussed.

Influence of experimental observations on n-propylbenzene kinetic parameter estimates

We calculate the derivatives of best estimates of kinetic parameters of an n-propylbenzene shock tube oxidation model, as determined by a weighted least-squares optimisation, with respect to experimental observations and compare these derivatives to some influence diagnostics based on omission of data points which are widely used in linear regression analysis. The considered data set comprises of 2378 measured concentrations of 37 stable species at various temperatures, pressures, and equivalence ratios. The methods studied are computationally affordable, as they require only a single optimisation and do not require the use of surrogate models. We find that the diagnostics offer many insights into how individual observations influence parameter estimates, such as which observations determine which parameters to what extent. Additionally, the significance of non-linearities in the model responses is investigated. While we observe that they can be of substantial importance to the derivatives of the best parameter estimates with respect to the experimental data, and improve the numerical conditioning of the involved matrix inversion, we find that results obtained from the linear omission-based diagnostics frequently agree, at least qualitatively, with those obtained from the derivatives.

Measurement of Hydrodynamic Coefficients on a Planing Hull Using Forced Roll Oscillations

For planing hulls, dynamic lift reduces the submergence of the hull, allowing small motions to result in large changes in hydrodynamic forces and moments. This article explores various modeling assumptions associated with transverse plane dynamics in roll and the hydrodynamic forces in the planing regime. The significance of nonlinearities in the roll hydrodynamic forces for planing hulls was investigated with regard to roll amplitude, model speed, model displacement, and roll oscillation frequency. A wooden 20° deadrise prismatic planing hull was tested at steady roll angles and in dynamic roll at various roll amplitudes and frequencies. Two displacements, three model speeds, three roll amplitudes, and four roll oscillation frequencies were tested. The measured wetted lengths, roll-restoring coefficient, roll-added inertia coefficient, and roll-damping coefficient are presented. The roll-restoring moment is found to be nonlinear with roll amplitude, the added inertia coefficient shows some dependence on model speed, and the roll-damping coefficient shows some amplitude dependence.

Modeling the dynamics of interest rate volatility with skewed fat-tailed distributions

This paper proposes generalized parametric models of the short-term interest rate that nest one-factor CEV and discrete time GARCH models. The paper estimates the generalized and nested models with skewed fat-tailed distributions to determine the correct specification of the conditional distribution of interest rates. The results indicate that the discrete time models that incorporate the level and GARCH effects into the diffusion function and that accommodate the tail-thickness of the interest rate distribution perform much better than the CEV model in forecasting the future volatility of interest rates. The results also show that the significance of nonlinearity in the drift function relies crucially on the specification of the volatility function.

A comprehensive analysis of the short-term interest-rate dynamics

This paper provides a comprehensive analysis of the short-term interest-rate dynamics based on three different data sets and two flexible parametric specifications. The significance of nonlinearity in the short-rate drift declines with increasing maturity for the interest-rate series used in the study. Using a flexible diffusion specification and incorporating GARCH volatility and non-normal innovation reduce the need for a nonlinear drift specification. Finally, the nonlinear drift specification performs better than the linear drift specification only when the short-term interest-rate levels reach historical highs.

A Comprehensive Analysis of the Short-Term Interest Rate Dynamics

This paper provides a comprehensive analysis of the short-term interest-rate dynamics based on three different data sets and two flexible parametric specifications. The significance of nonlinearity in the short-rate drift declines with increasing maturity for the interest-rate series used in the study. Using a flexible diffusion specification and incorporating GARCH volatility and non-normal innovation reduce the need for a nonlinear drift specification. Finally, the nonlinear drift specification performs better than the linear drift specification only when the short-term interest-rate levels reach historical highs.

Experimental Study of the Probability Distributions of Green Water on the Bow of Floating Production Platforms

Abstract Results of an experimental program with a model of a moored floating production storage and offloading vessel are used to study the probability distributions associated with various phenomena related with green water loading. Separate analysis of wave height and crests are performed in order to assess the presence and significance of nonlinearities. Time series of pitch motion and relative motion are analyzed to check for linearity of the response process. Probability distributions of the occurrence of water on deck and of the conditional distribution water height above deck are also studied.

Detection of nonlinearity in multivariate calibration

The present study categorises and compares several graphical and numerical methods to detect the presence of nonlinearity in multivariate calibration. The focus is on (quadratic) nonlinearity in the relationship between the property of interest (e.g. concentration) and the set of instrumental (e.g. absorbance) measurements. The explored techniques are applied to three simulated data sets where (non)linearity of the relationship is known, and to four experimental near infrared (NIR) data sets. Mallows augmented partial residual plot is recommended as the most universal diagnostic plot to detect nonlinearity. The significance of nonlinearity is evaluated using the runs test.

AN ENCOMPASSING APPROACH TO MODELING FISHERY DYNAMICS: MODELING DYNAMIC NONLINEAR SYSTEMS

Uncertainty about the nature and significance of nonlinearities and the manner in which dynamics affect future realizations makes model specification the most difficult aspect of modeling dynamic systems. By interpreting several popular fishery models as subcases of a nesting dynamic Taylor series approximation, we isolate the specification differences between these models in a way that accounts for commonalities. On the argument that the differences due to alternative nonlinear forms are likely to be small compared to more mundane considerations such as delay difference and general dynamic lag specification, we propose an alternative model that uses the terms from the first order approximation common to all models combined with a data‐based determination of the appropriate lags using the methods of state space time series analysis. Finally, the success of the alternative models is judged in an application to Pacific halibut data.

The Significance of Nonlinearity in the Natural Sciences

Despite its somewhat pretentious title, this is a useful book. It is the second of two volumes covering the proceedings of the fourteenth in the series of winter meetings in Miami, Orbis Scientiae 1977.