An adaptive Newton-method based on a dynamical systems approach

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.

The impacts of volcanic aerosol on stratospheric ozone and the Northern Hemisphere polar vortex: separating radiative-dynamical changes from direct effects due to enhanced aerosol heterogeneous chemistry

After major volcanic eruptions the enhanced aerosol causes ozone changes due to greater heterogeneous chemistry on the particle surfaces (HET-AER) and from dynamical effects related to the radiative heating of the lower stratosphere (RAD-DYN). We carry out a series of experiments with an atmosphere–ocean–chemistry–climate model to assess how these two processes change stratospheric ozone and Northern Hemispheric (NH) polar vortex dynamics. Ensemble simulations are performed under present day and preindustrial conditions, and with aerosol forcings representative of different eruption strength, to investigate changes in the response behaviour. We show that the halogen component of the HET-AER effect dominates under present-day conditions with a global reduction of ozone (−21 DU for the strongest eruption) particularly at high latitudes, whereas the HET-AER effect increases stratospheric ozone due to N2O5 hydrolysis in a preindustrial atmosphere (maximum anomalies +4 DU). The halogen-induced ozone changes in the present-day atmosphere offset part of the strengthening of the NH polar vortex during mid-winter (reduction of up to −16 m s-1 in January) and slightly amplify the dynamical changes in the polar stratosphere in late winter (+11 m s-1 in March). The RAD-DYN mechanism leads to positive column ozone anomalies which are reduced in a present-day atmosphere by amplified polar ozone depletion (maximum anomalies +12 and +18 DU for present day and preindustrial, respectively). For preindustrial conditions, the ozone response is consequently dominated by RAD-DYN processes, while under present-day conditions, HET-AER effects dominate. The dynamical response of the stratosphere is dominated by the RAD-DYN mechanism showing an intensification of the NH polar vortex in winter (up to +10 m s-1 in January). Ozone changes due to the RAD-DYN mechanism slightly reduce the response of the polar vortex after the eruption under present-day conditions.

A Dynamical Tool to Study the Cultural Context of Conflict Escalation

The present article describes research in progress which is developing a simple, replicable methodology aimed at identifying the regularities and specificity of human behavior in conflict escalation and de-escalation prooesses. These research efforts will ultimately be used to study conflict dynamics across cultures. The experimental data collected through this methodology, together with case studies and aggregated, time-series macro data are key for identifying relevant parameters, systems' properties, and micromechanisms defining the behavior of naturally occurring conflict escalation and de-escalation dynamics. This, in turn, is critical for the development of realistic, empirically supported computational models. The article outlines the theoretical assumptions of Dynamical Systems Theory with regard to conflict dynamics, with an emphasis on the process of conflict escalation and de-escalation. Next, work on a methodology for empirical study of escalation processes from a DST perspective is outlined. Specifically, the development of a progressive scenario methodology designed to map escalation sequences, together with anexample of a preliminary study based on the proposed researcb paradigm, is presented. Implications of the approach for the study of culture are discussed.