Non-linear Brane Dynamics in 6 Dimensions

We consider a dynamical brane world in a six dimensional spacetime containing a singularity. Using the Israel conditions we study the motion of a 4-brane embedded in this setup. We analize the brane behavior when its position is perturbed about a fixed point and solve the full non-linear dynamics in the several possible scenarios. We also investigate the possible gravitational shortcuts and calculate the delay between graviton and photon signals and the ratio of the corresponding subtended horizons.Comment: 5 pages, 2 figures. Contribution to the Proceedings of "Renormalization Group and Anomalies in Gravitation and Cosmology", Ouro Preto, Brazil, March 200

Modelling and simulation of advanced non-linear autopilot designs

This paper presents the simulation in ESL of a non-linear 6 degree-of-freedom missile model with an advanced, non-linear, multivariable autopilot designed using Rate Actuated Inverse Dynamics (RAID) methods. High performance control of non-linear systems requires the design of advanced, non-linear control systems, such as those used in autopilot design. Traditional linear control system design and analysis techniques are not sufficient for non-linear systems and current non-linear analysis methods are extremely limited. Therefore, the only method available to fully assess the performance of non-linear controller designs is simulation of the non-linear system. For this reason it is an essential part of the analysis and design process of these types of controllers. Non-linear dynamics can be continuous or discontinuous, the aerodynamics of a missile are non-linear but since they are continuous they do not represent a simulation challenge. However, there are multiple sets of discontinuous dynamics present in both the missile control surface model and the autopilot which can lead to multiple discontinuities being reached simultaneously, providing a challenging modeling exercise. The paper demonstrates how this kind of behavior can be successfully modeled and simulated within ESL using a simple switching logic

Non-linear dynamics of cosmic strings with non-scaling loops

At early stages the dynamics of cosmic string networks is expected to be influenced by an excessive production of small loops at the scales of initial conditions l_{min}. To understand the late time behavior we propose a very simple analytical model of strings with a non-scaling population of loops. The complicated non-linear dynamics is described by only a single parameter N ~ 2/(1-C(l_{min})) where C(l) is a correlation function of the string tangent vectors. The model predicts an appearance of two new length scales: the coherence length \xi ~ t/N^2 and the cross-correlation length \chi ~ t/N. At the onset of evolution N ~ 10 and at late times N is expected to grow logarithmically due to cosmological stretching and emission of small loops. The very late time evolution might be modified further when the gravitational back-reaction scale grows larger than l_{min}.Comment: 5 pages, minor corrections, accepted for publication in Physical Review

Entanglement, Non-linear Dynamics, and the Heisenberg Limit

We show that the quantum Fisher information provides a sufficient condition to recognize multi-particle entanglement in a $N$ qubit state. The same criterion gives a necessary and sufficient condition for sub shot-noise phase sensitivity in the estimation of a collective rotation angle $\theta$. The analysis therefore singles out the class of entangled states which are {\it useful} to overcome classical phase sensitivity in metrology and sensors. We finally study the creation of useful entangled states by the non-linear dynamical evolution of two decoupled Bose-Einstein condensates or trapped ions.Comment: Phys. Rev. Lett. 102, 100401 (2009

Non linear inflationary dynamics: evidence from the UK

This paper estimates a variety of models of inflation using quarterly data for the UK between 1965 and 2001. We find strong evidence that the persistence of inflation is nonlinear and that inflation adjusted more rapidly in periods of macroeconomic stress such as the mid-1970s, the early 1980s and the late 1980s-early 1990s. Our results imply that inflation will respond more strongly and more rapidly to changes in interest rates when the price level is further away from the steady state level. This has implications for optimal monetary policy

A Linear Evolution for Non-Linear Dynamics and Correlations in Realistic Nuclei

A new approach to high energy evolution based on a linear equation for QCD generating functional is developed. This approach opens a possibility for systematic study of correlations inside targets, and, in particular, inside realistic nuclei. Our results are presented as three new equations. The first one is a linear equation for QCD generating functional (and for scattering amplitude) that sums the 'fan' diagrams. For the amplitude this equation is equivalent to the non-linear Balitsky-Kovchegov equation. The second equation is a generalization of the Balitsky-Kovchegov non-linear equation to interactions with realistic nuclei. It includes a new correlation parameter which incorporates, in a model dependent way, correlations inside the nuclei. The third equation is a non - linear equation for QCD generating functional (and for scattering amplitude) that in addition to the 'fan' diagrams sums the Glauber-Mueller multiple rescatterings.Comment: 22 pages, 6 figure

Non-linear Dynamics and Primordial Curvature Perturbations from Preheating

In this paper I review the theory and numerical simulations of non-linear dynamics of preheating, a stage of dynamical instability at the end of inflation during which homogeneous inflaton explosively decays and deposits its energy into excitation of other matter fields. I focus on preheating in chaotic inflation models, which proceeds via broad parametric resonance. I describe a simple method to evaluate Floquet exponents, calculating stability diagrams of Mathieu and Lame equations describing development of instability in $m^2\phi^2$ and $\lambda\phi^4$ preheating models. I discuss basic numerical methods and issues, and present simulation results highlighting non-equilibrium transitions, topological defect formation, late-time universality, turbulent scaling and approach to thermalization. I explain how preheating can generate large-scale primordial (non-Gaussian) curvature fluctuations manifest in cosmic microwave background anisotropy and large scale structure, and discuss potentially observable signatures of preheating.Comment: 15 pages, 10 figures; review for CQG special issu