Combinatorial identities for binary necklaces from exact ray-splitting trace formulae

Based on an exact trace formula for a one-dimensional ray-splitting system, we derive novel combinatorial identities for cyclic binary sequences (P\'olya necklaces).Comment: 15 page

Mississippi State University Research / Demonstration Module

A final report on the Mississippi State Module Planning Grant prepared by E. T. Kohler and R. C. Maxson in September of 1968

Star formation environments and the distribution of binary separations

We have carried out K-band speckle observations of a sample of 114 X-ray selected weak-line T Tauri stars in the nearby Scorpius-Centaurus OB association. We find that for binary T Tauri stars closely associated to the early type stars in Upper Scorpius, the youngest subgroup of the OB association, the peak in the distribution of binary separations is at 90 A.U. For binary T Tauri stars located in the direction of an older subgroup, but not closely associated to early type stars, the peak in the distribution is at 215 A.U. A Kolmogorov-Smirnov test indicates that the two binary populations do not result from the same distibution at a significance level of 98%. Apparently, the same physical conditions which facilitate the formation of massive stars also facilitate the formation of closer binaries among low-mass stars, whereas physical conditions unfavorable for the formation of massive stars lead to the formation of wider binaries among low-mass stars. The outcome of the binary formation process might be related to the internal turbulence and the angular momentum of molecular cloud cores, magnetic field, the initial temperature within a cloud, or - most likely - a combination of all of these. We conclude that the distribution of binary separations is not a universal quantity, and that the broad distribution of binary separations observed among main-sequence stars can be explained by a superposition of more peaked binary distributions resulting from various star forming environments. The overall binary frequency among pre-main-sequence stars in individual star forming regions is not necessarily higher than among main-sequence stars.Comment: 7 pages, Latex, 4 Postscript figures; also available at http://spider.ipac.caltech.edu/staff/brandner/pubs/pubs.html ; accepted for publication in ApJ Letter

Sorption, Desorption and Exchange of Cesium on Glaciofluvial Deposits

Distribution ratios and isotherms for Sorption, desorption and isotope-exchange of cesium (labelled with Cs-137) were measured on grain size fractions (<2mm) of quatemary glaciofluvial deposits. Sediment materials from two locations within Switzerland and synthetic groundwaters of different compositions were used. The investigated concentration range for cesium was 10"" — 10"' M. Cesium introduced into the system with the solid phase may influence the measurements at the lowest concentrations. Depending on the experimental conditions, the distribution ratios vary between 3 and 30'000 ml/g. The isotherms are non-linear. Normalization of the cesium concentration in the solid with the cation-exchange capacity leads to nearly identical isotherms for all size fractions of the two geographic locations. Desorption and exchange are retarded at the higher cesium concentrations. This can be explained by structural changes in clay minerals which dominate the Sorption of cesium on this material. Variations in the composition of the groundwater influence the Sorption of cesium only sHghtly; potassium and hydrogen ions are the main competitors

Torsion Degrees of Freedom in the Regge Calculus as Dislocations on the Simplicial Lattice

Using the notion of a general conical defect, the Regge Calculus is generalized by allowing for dislocations on the simplicial lattice in addition to the usual disclinations. Since disclinations and dislocations correspond to curvature and torsion singularities, respectively, the method we propose provides a natural way of discretizing gravitational theories with torsion degrees of freedom like the Einstein-Cartan theory. A discrete version of the Einstein-Cartan action is given and field equations are derived, demanding stationarity of the action with respect to the discrete variables of the theory

A Multiplicity Census of Young Stars in Chamaeleon I

We present the results of a multiplicity survey of 126 stars spanning ~0.1-3 solar masses in the ~2-Myr-old Chamaeleon I star-forming region, based on adaptive optics imaging with the ESO Very Large Telescope. Our observations have revealed 30 binaries and 6 triples, of which 19 and 4, respectively, are new discoveries. The overall multiplicity fraction we find for Cha I (~30%) is similar to those reported for other dispersed young associations, but significantly higher than seen in denser clusters and the field, for comparable samples. Both the frequency and the maximum separation of Cha I binaries decline with decreasing mass, while the mass ratios approach unity; conversely, tighter pairs are more likely to be equal mass. We confirm that brown dwarf companions to stars are rare, even at young ages at wide separations. Based on follow-up spectroscopy of two low-mass substellar companion candidates, we conclude that both are likely background stars. The overall multiplicity fraction in Cha I is in rough agreement with numerical simulations of cloud collapse and fragmentation, but its observed mass dependence is less steep than predicted. The paucity of higher-order multiples, in particular, provides a stringent constraint on the simulations, and seems to indicate a low level of turbulence in the prestellar cores in Cha I.Comment: Accepted for publication in Ap

A double-lined spectroscopic orbit for the young star HD 34700

We report high-resolution spectroscopic observations of the young star HD 34700, which confirm it to be a double-lined spectroscopic binary. We derive an accurate orbital solution with a period of 23.4877 +/- 0.0013 days and an eccentricity of e = 0.2501 +/- 0.0068. The stars are found to be of similar mass (M2/M1 = 0.987 +/- 0.014) and luminosity. We derive also the effective temperatures (5900 K and 5800 K) and projected rotational velocities (28 km/s and 22 km/s) of the components. These values of v sin i are much higher than expected for main-sequence stars of similar spectral type (G0), and are not due to tidal synchronization. We discuss also the indicators of youth available for the object. Although there is considerable evidence that the system is young --strong infrared excess, X-ray emission, Li I 6708 absorption (0.17 Angstroms equivalent width), H alpha emission (0.6 Angstroms), rapid rotation-- the precise age cannot yet be established because the distance is unknown.Comment: 17 pages, including 2 figures and 2 tables. Accepted for publication in AJ, to appear in February 200

Forces Induced by Non-Equilibrium Fluctuations: The Soret-Casimir Effect

The notion of fluctuation-induced forces is generalized to the cases where the fluctuations have nonequilibrium origin. It is shown that a net force is exerted on a single flat plate that restricts scale-free fluctuations of a scalar field in a temperature gradient. This force tends to push the object to the colder regions, which is a manifestation of thermophoresis or the Soret effect. In the classic two-plate geometry, it is shown that the Casimir forces exerted on the two plates differ from each other, and thus the Newton's third law is violated.Comment: 8 pages, 5 postscript figures, uses (old) RevTe