Affine actions on non-archimedean trees

We initiate the study of affine actions of groups on $\Lambda$-trees for a general ordered abelian group $\Lambda$; these are actions by dilations rather than isometries. This gives a common generalisation of isometric action on a $\Lambda$-tree, and affine action on an $\R$-tree as studied by I. Liousse. The duality between based length functions and actions on $\Lambda$-trees is generalised to this setting. We are led to consider a new class of groups: those that admit a free affine action on a $\Lambda$-tree for some $\Lambda$. Examples of such groups are presented, including soluble Baumslag-Solitar groups and the discrete Heisenberg group.Comment: 27 pages. Section 1.4 expanded, typos corrected from previous versio

Electronic Structure of LuRh2Si2: "Small" Fermi Surface Reference to YbRh2Si2

We present band structure calculations and quantum oscillation measurements on LuRh2Si2, which is an ideal reference to the intensively studied quantum critical heavy-fermion system YbRh2Si2. Our band structure calculations show a strong sensitivity of the Fermi surface on the position of the silicon atoms zSi within the unit cell. Single crystal structure refinement and comparison of predicted and observed quantum oscillation frequencies and masses yield zSi = 0.379c in good agreement with numerical lattice relaxation. This value of zSi is suggested for future band structure calculations on LuRh2Si2 and YbRh2Si2. LuRh2Si2 with a full f electron shell represents the "small" Fermi surface configuration of YbRh2Si2. Our experimentally and ab initio derived quantum oscillation frequencies of LuRh2Si2 show strong differences with earlier measurements on YbRh2Si2. Consequently, our results confirm the contribution of the f electrons to the Fermi surface of YbRh2Si2 at high magnetic fields. Yet the limited agreement with refined fully itinerant local density approximation calculations highlights the need for more elaborated models to describe the Fermi surface of YbRh2Si2.Comment: 12 pages 10 figure

Viking navigation

A comprehensive description of the navigation of the Viking spacecraft throughout their flight from Earth launch to Mars landing is given. The flight path design, actual inflight control, and postflight reconstruction are discussed in detail. The preflight analyses upon which the operational strategies and performance predictions were based are discussed. The inflight results are then discussed and compared with the preflight predictions and, finally, the results of any postflight analyses are presented

Andreev reflection spectroscopy of the heavy-fermion superconductor CeCoIn5_5 along three different crystallographic orientations

Andreev reflection spectroscopy has been performed on the heavy-fermion superconductor (HFS) CeCoIn$_5$ single crystals along three different crystallographic orientations, (001), (110), and (100), using Au tips as counter-electrodes. Dynamic conductance spectra are reproducible over wide temperature ranges and consistent with each other, ensuring the spectroscopic nature. Features common to all directions are: i) asymmetric behaviors of the background conductance, which we attribute to the emerging coherent heavy-fermion liquid; ii) energy scales (~1 meV) for conductance enhancement due to Andreev reflection; iii) magnitudes of enhanced zero-bias conductance (10 - 13 %). These values are an order of magnitude smaller than the predicted value by the Blonder-Tinkham-Klapwijk (BTK) theory, but comparable to those for other HFSs. Using the d-wave BTK model, we obtain an energy gap of ~ 460 ueV. However, it is found that extended BTK models considering the mismatch in Fermi surface parameters do not account for our data completely, which we attribute to the shift of spectral weight to low energy as well as to the suppressed Andreev reflection. A qualitative comparison of the conductance spectra with calculated curves shows a consistency with d$_{x^2-y^2}$-symmetry, providing the first spectroscopic evidence for the order parameter symmetry and resolving the controversy over the location of the line nodes.Comment: invited talk submitted to the 8th M2S conference to be held in Dresden Germany, July 9-14, 2006, 4 pages, 3 figure

Fermi-surface reconstruction and two-carrier model for the Hall effect in YBa2Cu4O8

Pulsed field measurements of the Hall resistivity and magnetoresistance of underdoped YBa2Cu4O8 are analyzed self-consistently using a simple model based on coexisting electron and hole carriers. The resultant mobilities and Hall numbers are found to vary markedly with temperature. The conductivity of the hole carriers drops by one order of magnitude below 30 K, explaining the absence of quantum oscillations from these particular pockets. Meanwhile the Hall coefficient of the electron carriers becomes strongly negative below 50 K. The overall quality of the fits not only provides strong evidence for Fermi-surface reconstruction in Y-based cuprates, it also strongly constrains the type of reconstruction that might be occurring.Comment: 5 pages, 4 figures, updated after publication in Physical Review B (Rapid Communication

Positivity of Spin Foam Amplitudes

The amplitude for a spin foam in the Barrett-Crane model of Riemannian quantum gravity is given as a product over its vertices, edges and faces, with one factor of the Riemannian 10j symbols appearing for each vertex, and simpler factors for the edges and faces. We prove that these amplitudes are always nonnegative for closed spin foams. As a corollary, all open spin foams going between a fixed pair of spin networks have real amplitudes of the same sign. This means one can use the Metropolis algorithm to compute expectation values of observables in the Riemannian Barrett-Crane model, as in statistical mechanics, even though this theory is based on a real-time (e^{iS}) rather than imaginary-time (e^{-S}) path integral. Our proof uses the fact that when the Riemannian 10j symbols are nonzero, their sign is positive or negative depending on whether the sum of the ten spins is an integer or half-integer. For the product of 10j symbols appearing in the amplitude for a closed spin foam, these signs cancel. We conclude with some numerical evidence suggesting that the Lorentzian 10j symbols are always nonnegative, which would imply similar results for the Lorentzian Barrett-Crane model.Comment: 15 pages LaTeX. v3: Final version, with updated conclusions and other minor changes. To appear in Classical and Quantum Gravity. v4: corrects # of samples in Lorentzian tabl

The Fermi surface and f-valence electron count of UPt3

Combining old and new de Haas-van Alphen (dHvA) and magnetoresistance data, we arrive at a detailed picture of the Fermi surface of the heavy fermion superconductor UPt3. Our work was partially motivated by a new proposal that two 5f valence electrons per formula unit in UPt3 are localized by correlation effects -- agreement with previous dHvA measurements of the Fermi surface was invoked in its support. Comprehensive comparison with our new observations shows that this 'partially localized' model fails to predict the existence of a major sheet of the Fermi surface, and is therefore less compatible with experiment than the originally proposed 'fully itinerant' model of the electronic structure of UPt3. In support of this conclusion, we offer a more complete analysis of the fully itinerant band structure calculation, where we find a number of previously unrecognized extremal orbits on the Fermi surface.Comment: 23 pages, 12 figures, latex, iopart clas

Imaginative Representations of Two- and Three-Dimensional Matrices in Children with Nonverbal Learning Disabilities

Children with non-verbal learning disabilities (NLD) are characterized by high verbal and poor non-verbal intelligence, poor cognitive abilities, school difficulties, and—sometimes—depressive symptoms. NLD children lack visuospatial working memory, but it is not clear whether they encounter difficulties in mental imagery tasks. In the present study, NLD adolescents without depressive symptoms, depressed adolescents without NLD symptoms, and a control group were administered a mental imagery task requiring them to imagine to move along the cells of a 2-D (5 × 5) or 3-D (3 × 3 × 3) matrix. Results showed that NLD adolescents had difficulty at performing the imagery task when a 3-D pattern was involved. It is suggested that 3-D mental imagery tasks tap visuospatial processes which are weak in NLD individuals. In addition, their poor cognitive performance cannot be attributed to a depressive state, as the depressed group had a performance similar to that of controls

Content analysis: What are they talking about?

Quantitative content analysis is increasingly used to surpass surface level analyses in Computer-Supported Collaborative Learning (e.g., counting messages), but critical reflection on accepted practice has generally not been reported. A review of CSCL conference proceedings revealed a general vagueness in definitions of units of analysis. In general, arguments for choosing a unit were lacking and decisions made while developing the content analysis procedures were not made explicit. In this article, it will be illustrated that the currently accepted practices concerning the ‘unit of meaning’ are not generally applicable to quantitative content analysis of electronic communication. Such analysis is affected by ‘unit boundary overlap’ and contextual constraints having to do with the technology used. The analysis of e-mail communication required a different unit of analysis and segmentation procedure. This procedure proved to be reliable, and the subsequent coding of these units for quantitative analysis yielded satisfactory reliabilities. These findings have implications and recommendations for current content analysis practice in CSCL research