Stabilizing periodic orbits above the elliptic plane in the solar sail 3-body problem

We consider periodic orbits high above the ecliptic plane in the Elliptic Restricted Three-Body Problem where the third massless body is a solar sail. Periodic orbits above the ecliptic are of practical interest as they are ideally positioned for the year-round constant imaging of, and communication with, the poles. Initially we identify an unstable periodic orbit by using a numerical continuation from a known periodic orbit above the ecliptic in the circular case with the eccentricity as the varying parameter. This orbit is then used to construct a reference trajectory for the sail to track. In addition we illustrate an alternative method for constructing a periodic reference trajectory based on a time-delayed feedback mechanism. The reference trajectories are then tracked using a linear feedback regulator (LQR) where the control actuation is delivered by varying the solar sails orientation. Using this method it is shown that a 'near term' solar sail is capable of performing stable periodic motions high above the ecliptic

Embedding formulae for scattering in a waveguide containing polygonal obstacles

For certain wave scattering problems embedding formulae can be derived, which express the solution, or far-field behaviour of the solution, for arbitrary plane wave incident angle in terms of the corresponding quantities for a finite number of other related problems. Their scope has so far been limited to scattering in R^2, and to a lesser extent R^3; in this paper we derive embedding formulae for wave scattering in a class of two-dimensional waveguide. The waveguide is straight and of uniform width outside a finite length region within which the boundaries are piecewise-linear and the waveguide can contain polygonal obstacles, a restriction being that all boundaries of the waveguide and obstacles must be inclined at a rational angle to the axis of the waveguide. Once solutions are determined for a finite set of incident propagating modes, the embedding formulae provide expressions for reflection and transmission coefficients for all remaining incident propagating modes. The precise number of solutions required is a function of the number and nature of the corners of the boundaries and obstacles. The formulae are illustrated for a particular waveguide geometry for which the problem can be formulated as an integral equation and approximate numerical solutions determined using the Galerkin method

Some Exact Results on the Potts Model Partition Function in a Magnetic Field

We consider the Potts model in a magnetic field on an arbitrary graph $G$. Using a formula of F. Y. Wu for the partition function $Z$ of this model as a sum over spanning subgraphs of $G$, we prove some properties of $Z$ concerning factorization, monotonicity, and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for $Z$ for cyclic strip graphs.Comment: 5 pages, late

Characterization of rapidly solidified commercial grey cast iron in drop-tube

This study presents containerless solidification of BS 1452 grade 250 commercial grey cast iron using 6.5m drop-tube apparatus. It gives a comparative summary of microstructural changes that occur between the rapidly cooled droplet particles as against its conventional slowly cooled control as-cast sample. The bulk as-received sample was melted and rapidly cooled during free fall in high vacuum containerless equipment. These rapidly solidified samples were collected and sieved into size ranges from >850 μm to <53 μm diameter, corresponding to estimated cooling rate of 500 K s-1 to 75,000 K s-1 with each sieve fraction being prepared for metallographic characterization. The analytical methods used include; light optical microscope and scanning electron microscopy, x-ray diffraction and differential thermal analyses. The result of this investigation reveals that the microstructure of the as-cast sample shows flake graphite randomly dispersed in ferrite matrix which is typical of slowly cooled grey cast iron. In contrast, flake graphite was absent in virtually all drop-tube samples even those with modest cooling rate. The evolved microstructure clearly shows the effect of cooling rate on the transformation from the conventional to rapidly solidified droplet particles in terms of microsegregation

Partition Function Zeros of a Restricted Potts Model on Lattice Strips and Effects of Boundary Conditions

We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for strips of the square and triangular lattices of various widths $L_y$ and arbitrarily great lengths $L_x$, with a variety of boundary conditions, and with $Q$ and $v$ restricted to satisfy conditions corresponding to the ferromagnetic phase transition on the associated two-dimensional lattices. From these calculations, in the limit $L_x \to \infty$, we determine the continuous accumulation loci ${\cal B}$ of the partition function zeros in the $v$ and $Q$ planes. Strips of the honeycomb lattice are also considered. We discuss some general features of these loci.Comment: 12 pages, 12 figure

Distribution of the molecular absorption in front of the quasar B0218+357

The line of sight to the quasar B0218+357, one of the most studied lensed systems, intercepts a z=0.68 spiral galaxy, which splits its image into two main components A and B, separated by ca. 0.3'', and gives rise to molecular absorption. Although the main absorption component has been shown to arise in front of image A, it is not established whether some absorption from other velocity components is also occuring in front of image B. To tackle this question, we have observed the HCO+(2-1) absorption line during the commissioning phase of the new very extended configuration of the Plateau de Bure Interferometer, in order to trace the position of the absorption as a function of frequency. Visibility fitting of the self-calibrated data allowed us to achieve position accuracy between ~12 and 80 mas per velocity component. Our results clearly demonstrate that all the different velocity components of the HCO+(2-1) absorption arise in front of the south-west image A of the quasar. We estimate a flux ratio fA/fB = 4.2 (-1.0;+1.8 at 106 GHz.Comment: accepted for publication in A&A Letter special issue for the new extended configuration of the Plateau de Bure Interferomete

MERLIN/VLA imaging of the gravitational lens system B0218+357

Gravitational lenses offer the possibility of accurately determining the Hubble parameter (H_0) over cosmological distances, and B0218+357 is one of the most promising systems for an application of this technique. In particular this system has an accurately measured time delay (10.5+/-0.4 d; Biggs et al. 1999) and preliminary mass modelling has given a value for H_0 of 69 +13/-19 km/s/Mpc. The error on this estimate is now dominated by the uncertainty in the mass modelling. As this system contains an Einstein ring it should be possible to constrain the model better by imaging the ring at high resolution. To achieve this we have combined data from MERLIN and the VLA at a frequency of 5 GHz. In particular MERLIN has been used in multi-frequency mode in order to improve substantially the aperture coverage of the combined data set. The resulting map is the best that has been made of the ring and contains many new and interesting features. Efforts are currently underway to exploit the new data for lensing constraints using the LensClean algorithm (Kochanek & Narayan 1992).Comment: Accepted for publication in MNRAS. 6 pages, 4 included PostScript figure

Did local civil rights protest liberalize whites’ racial attitudes?

Mazumder investigates the long-term effect of protest on political attitudes. He finds that whites have more liberal views on race and are more likely to be Democrats in counties where Civil Rights protest was reported in the early 1960s. The analysis omits a crucial predictor of protest and of racial attitudes: college education. We include the proportion of adults with a college degree and the number of college students at the county level. The inclusion of these variables, along with some other contextual variables from the original dataset, cuts the effect of protest by about half. Protest is no longer statistically significant in eight out of nine combinations of outcome variables and protest measures. The size of the effect remains trivial when we shift analysis from the county to the individual level. Even accounting for the individual’s own education, the county’s proportion of college graduates is strongly associated with racial liberalism. This finding emphasizes the importance of education as a contextual variable. Our conclusion highlights two methodological lessons. First, causal inference should be paired with sustained historical inquiry that specifies plausible mechanisms. Second, statistical tests for sensitivity can induce complacency about the risk of confounding

Revised phase diagram for the Pt-Ti system from 30 to 60 at.% platinum

Alloys of the Ti-Pt system between 30 and 61 at.% Pt were studied using metallography with optical and scanning electron microscopy (SEM), X-ray diffraction (XRD), and differential thermal analysis (DTA). A phase of nominal composition Ti4Pt3, in the range 41.7-43.4 at.% Pt was found in samples containing between 30 and 47 at.% Pt, and was apparently formed by a peritectoid reaction between β-TiPt and Ti3Pt at 1205±10°C. The eutectic reaction between Ti3Pt and β-TiPt was found to be at ∼35 at.% Pt and 1424±10°C, and the Ti3Pt phase melted at circa 1500°C. The other phase boundaries agreed with the published literature, except that a slightly wider range was found at 1200°C for β-TiPt. © 2004 Elsevier B.V. All rights reserved