Dynamics of Perturbed Relative Equilibria of Point Vortices on the Sphere or Plane

Stable assemblages of localized vortices exist which have particle-like properties, such as mass, and which can interact with one another when they closely approach. In this article I calculate the mass of these localized states and numerically investigate some aspects of their interactions.Comment: 14 pages, 3 figure

Reduction of the planar 4-vortex system at zero momentum

The system of four point vortices in the plane has relative equilibria that behave as composite particles, in the case where three of the vortices have strength $-\Gamma/3$ and one of the vortices has strength $\Gamma$. These relative equilibria occur at nongeneric momenta. The reduction of this system, at those momenta, by continuous and then discrete symmetries, classifies the 4-vortex states which have been observed as products of collisions of two such composite particles. In this article I explicitly calculate these reductions, and show they are qualitatively identical one degree of freedom systems on a cylinder. The flows on these reduced systems all have one stable equilibrium and one unstable equilibrium, and all the orbits are periodic except for two homoclinic connections to the unstable equilibrium.Comment: Minor typographical corrections and slightly revised introduction. 9 pages, 5 figures. To appear EQUIDIFF/99 proceeding

Skew critical problems

Skew critical problems occur in continuous and discrete nonholonomic Lagrangian systems. They are analogues of constrained optimization problems, where the objective is differentiated in directions given by an apriori distribution, instead of tangent directions to the constraint. We show semiglobal existence and uniqueness for nondegenerate skew critical problems, and show that the solutions of two skew critical problems have the same contact as the problems themselves. Also, we develop some infrastructure that is necessary to compute with contact order geometrically, directly on manifolds

The Transversal Relative Equilibria of a Hamiltonian System with Symmetry

We show that, given a certain transversality condition, the set of relative equilibria \mcl E near p_e\in\mcl E of a Hamiltonian system with symmetry is locally Whitney-stratified by the conjugacy classes of the isotropy subgroups (under the product of the coadjoint and adjoint actions) of the momentum-generator pairs $(\mu,\xi)$ of the relative equilibria. The dimension of the stratum of the conjugacy class (K) is $\dim G+2\dim Z(K)-\dim K$, where Z(K) is the center of K, and transverse to this stratum \mcl E is locally diffeomorphic to the commuting pairs of the Lie algebra of $K/Z(K)$. The stratum \mcl E_{(K)} is a symplectic submanifold of P near p_e\in\mcl E if and only if $p_e$ is nondegenerate and K is a maximal torus of G. We also show that there is a dense subset of G-invariant Hamiltonians on P for which all the relative equilibria are transversal. Thus, generically, the types of singularities that can be found in the set of relative equilibria of a Hamiltonian system with symmetry are those types found amongst the singularities at zero of the sets of commuting pairs of certain Lie subalgebras of the symmetry group.Comment: 18 page

Satellite-derived cloud fields during the FIRE cirrus IFO case study

The First ISCCP Regional Experiment (FIRE) Cirrus Intensive Field Observation (IFO) program measured cirrus cloud properties with a variety of instruments from the surface, aircraft, and satellites. Surface and aircraft observations provide a small scale point and line measurements of different micro- and macro-physical properties of advecting and evolving cloud systems. Satellite radiance data may be used to measure the areal variations of the bulk cloud characteristics over meso- and large scales. Ideally, the detailed cloud properties derived from the small scale measurements should be tied to the bulk cloud properties typically derived from the satellite data. Full linkage of these data sets for a comprehensive description of a given cloud field, one of the goals of FIRE, should lead to significant progress in understanding, measuring, and modeling cirrus cloud systems. The relationships derived from intercomparisons of lidar and satellite data by Minnis et al. are exploited in a mesoscale analysis of the satellite data taken over Wisconsin during the Cirrus IFO case study

Monte Carlo Simulation of Deffuant opinion dynamics with quality differences

In this work the consequences of different opinion qualities in the Deffuant model were examined. If these qualities are randomly distributed, no different behavior was observed. In contrast to that, systematically assigned qualities had strong effects to the final opinion distribution. There was a high probability that the strongest opinion was one with a high quality. Furthermore, under the same conditions, this major opinion was much stronger than in the models without systematic differences. Finally, a society with systematic quality differences needed more tolerance to form a complete consensus than one without or with unsystematic ones.Comment: 8 pages including 5 space-consuming figures, fir Int. J. Mod. Phys. C 15/1

A comparison of ISCCP and FIRE satellite cloud parameters

One of the goals of the First ISCCP Regional Experiment (FIRE) is the quantification of the uncertainties in the cloud parameter products derived by the International Satellite Cloud Climatology Project (ISCCP). This validation effort has many facets including sensitivity analyses and comparisons to similar data or theoretical results with known accuracies. The FIRE provides cloud-truth data at particular points or along particular lines from surface and aircraft measurement systems. Relating these data to the larger, area-averaged ISCCP results requires intermediate steps using higher resolution satellite data analyses. Errors in the cloud products derived with a particular method can be determined by performing analyses of high resolution satellite data over the area surrounding the point or line measurement. This same analysis technique may then be used to derive cloud parameters over a larger area containing similar cloud fields. It is assumed that the uncertainties found for the small scale analyses are the same for the large scale so that the method has been calibrated for the particular cloud type; i.e., its accuracy is known. Differences between the large scale results using the ISCCP technique and the calibrated method can be computed and used to determine if any significant biases or rms errors occur in the ISCCP results. Selected ISCCP results are compared to cloud parameters derived using the hybrid bispectral threshold method over the FIRE IFO and extended observation areas

Ultrathin oxides: bulk-oxide-like model surfaces or unique films?

To better understand the electronic and chemical properties of wide-gap oxide surfaces at the atomic scale, experimental work has focused on epitaxial films on metal substrates. Recent findings show that these films are considerably thinner than previously thought. This raises doubts about the transferability of the results to surface properties of thicker films and bulk crystals. By means of density-functional theory and approximate GW corrections for the electronic spectra we demonstrate for three characteristic wide-gap oxides (silica, alumina, and hafnia) the influence of the substrate and highlight critical differences between the ultrathin films and surfaces of bulk materials. Our results imply that monolayer-thin oxide films have rather unique properties.Comment: 5 pages, 3 figures, accepted by PR