Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure

In-plane magnetic reorientation in coupled ferro- and antiferromagnetic thin films

By studying coupled ferro- (FM) and antiferromagnetic (AFM) thin film systems, we obtain an in-plane magnetic reorientation as a function of temperature and FM film thickness. The interlayer exchange coupling causes a uniaxial anisotropy, which may compete with the intrinsic anisotropy of the FM film. Depending on the latter the total in-plane anisotropy of the FM film is either enhanced or reduced. Eventually a change of sign occurs, resulting in an in-plane magnetic reorientation between a collinear and an orthogonal magnetic arrangement of the two subsystems. A canted magnetic arrangement may occur, mediating between these two extremes. By measuring the anisotropy below and above the N\'eel temperature the interlayer exchange coupling can be determined. The calculations have been performed with a Heisenberg-like Hamiltonian by application of a two-spin mean-field theory.Comment: 4 pages, 4 figure

A study of low-energy transfer orbits to the Moon: towards an operational optimization technique

In the Earth-Moon system, low-energy orbits are transfer trajectories from the earth to a circumlunar orbit that require less propellant consumption when compared to the traditional methods. In this work we use a Monte Carlo approach to study a great number of such transfer orbits over a wide range of initial conditions. We make statistical and operational considerations on the resulting data, leading to the description of a reliable way of finding "optimal" mission orbits with the tools of multi-objective optimization

Spin Reorientations Induced by Morphology Changes in Fe/Ag(001)

By means of magneto-optical Kerr effect we observe spin reorientations from in-plane to out-of-plane and vice versa upon annealing thin Fe films on Ag(001) at increasing temperatures. Scanning tunneling microscopy images of the different Fe films are used to quantify the surface roughness. The observed spin reorientations can be explained with the experimentally acquired roughness parameters by taking into account the effect of roughness on both the magnetic dipolar and the magnetocrystalline anisotropy.Comment: 4 pages with 3 EPS figure

Metastable Random Field Ising model with exchange enhancement: a simple model for Exchange Bias

We present a simple model that allows hysteresis loops with exchange bias to be reproduced. The model is a modification of the T=0 random field Ising model driven by an external field and with synchronous local relaxation dynamics. The main novelty of the model is that a certain fraction f of the exchange constants between neighbouring spins is enhanced to a very large value J_E. The model allows the dependence of the exchange bias and other properties of the hysteresis loops to be analyzed as a function of the parameters of the model: the fraction f of enhanced bonds, the amount of the enhancement J_E and the amount of disorder which is controlled by the width sigma of the Gaussian distribution of the random fields.Comment: 8 pages, 11 figure

A biophysical model of cell adhesion mediated by immunoadhesin drugs and antibodies

A promising direction in drug development is to exploit the ability of natural killer cells to kill antibody-labeled target cells. Monoclonal antibodies and drugs designed to elicit this effect typically bind cell-surface epitopes that are overexpressed on target cells but also present on other cells. Thus it is important to understand adhesion of cells by antibodies and similar molecules. We present an equilibrium model of such adhesion, incorporating heterogeneity in target cell epitope density and epitope immobility. We compare with experiments on the adhesion of Jurkat T cells to bilayers containing the relevant natural killer cell receptor, with adhesion mediated by the drug alefacept. We show that a model in which all target cell epitopes are mobile and available is inconsistent with the data, suggesting that more complex mechanisms are at work. We hypothesize that the immobile epitope fraction may change with cell adhesion, and we find that such a model is more consistent with the data. We also quantitatively describe the parameter space in which binding occurs. Our results point toward mechanisms relating epitope immobility to cell adhesion and offer insight into the activity of an important class of drugs.Comment: 13 pages, 5 figure

Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms

This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators

Analysis of Capture Trajectories into Periodic Orbits About Libration Points

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77033/1/AIAA-33796-456.pd

Spacecraft Formation Dynamics and Design

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76961/1/AIAA-13002-440.pd