Spin gap in the Quasi-One-Dimensional S=1/2 Antiferromagnet: Cu2(1,4-diazacycloheptane)2Cl4

Cu_{2}(1,4-diazacycloheptane)_{2}Cl_{4} contains double chains of spin 1/2 Cu^{2+} ions. We report ac susceptibility, specific heat, and inelastic neutron scattering measurements on this material. The magnetic susceptibility, $\chi(T)$, shows a rounded maximum at T = 8 K indicative of a low dimensional antiferromagnet with no zero field magnetic phase transition. We compare the $\chi(T)$ data to exact diagonalization results for various one dimensional spin Hamiltonians and find excellent agreement for a spin ladder with intra-rung coupling $J_1 = 1.143(3)$ meV and two mutually frustrating inter-rung interactions: $J_2 = 0.21(3)$ meV and $J_3 = 0.09(5)$ meV. The specific heat in zero field is exponentially activated with an activation energy $\Delta = 0.89(1)$ meV. A spin gap is also found through inelastic neutron scattering on powder samples which identify a band of magnetic excitations for $0.8 < \hbar\omega < 1.5$ meV. Using sum-rules we derive an expression for the dynamic spin correlation function associated with non-interacting propagating triplets in a spin ladder. The van-Hove singularities of such a model are not observed in our scattering data indicating that magnetic excitations in Cu_{2}(1,4-diazacycloheptane)_{2}Cl_{4} are more complicated. For magnetic fields above $H_{c1} \simeq 7.2$ T specific heat data versus temperature show anomalies indicating a phase transition to an ordered state below T = 1 K.Comment: 9 pages, 8 postscript figures, LaTeX, Submitted to PRB 8/4/97, e-mail Comments to [email protected]

Crystal Structure and Magnetism of the Linear-Chain Copper Oxides Sr5Pb3-xBixCuO12

The title quasi-1D copper oxides (0=< x =<0.4) were investigated by neutron diffraction and magnetic susceptibility studies. Polyhedral CuO4 units in the compounds were found to comprise linear-chains at inter-chain distance of approximately 10 A. The parent chain compound (x = 0), however, shows less anisotropic magnetic behavior above 2 K, although it is of substantially antiferromagnetic (mu_{eff}= 1.85 mu_{B} and Theta_{W} = -46.4 K) spin-chain system. A magnetic cusp gradually appears at about 100 K in T vs chi with the Bi substitution. The cusp (x = 0.4) is fairly characterized by and therefore suggests the spin gap nature at Delta/k_{B} ~ 80 K. The chain compounds hold electrically insulating in the composition range.Comment: To be published in PR

The Origin of Primordial Dwarf Stars and Baryonic Dark Matter

I present a scenario for the production of low mass, degenerate dwarfs of mass $>0.1 M_{\odot}$ via the mechanism of Lenzuni, Chernoff & Salpeter (1992). Such objects meet the mass limit requirements for halo dark matter from microlensing surveys while circumventing the chemical evolution constraints on normal white dwarf stars. I describe methods to observationally constrain this scenario and suggest that such objects may originate in small clusters formed from the thermal instability of shocked, heated gas in dark matter haloes, such as suggested by Fall & Rees (1985) for globular clusters.Comment: TeX, 4 pages plus 2 postscript figures. To appear in Astrophysical Journal Letter

The Nature of the Dense Core Population in the Pipe Nebula: Thermal Cores Under Pressure

In this paper we present the results of a systematic investigation of an entire population of starless dust cores within a single molecular cloud. Analysis of extinction data shows the cores to be dense objects characterized by a narrow range of density. Analysis of C18O and NH3 molecular-line observations reveals very narrow lines. The non-thermal velocity dispersions measured in both these tracers are found to be subsonic for the large majority of the cores and show no correlation with core mass (or size). Thermal pressure is thus the dominate source of internal gas pressure and support for most of the core population. The total internal gas pressures of the cores are found to be roughly independent of core mass over the entire range of the core mass function (CMF) indicating that the cores are in pressure equilibrium with an external source of pressure. This external pressure is most likely provided by the weight of the surrounding Pipe cloud within which the cores are embedded. Most of the cores appear to be pressure confined, gravitationally unbound entities whose nature, structure and future evolution are determined by only a few physical factors which include self-gravity, the fundamental processes of thermal physics and the simple requirement of pressure equilibrium with the surrounding environment. The observed core properties likely constitute the initial conditions for star formation in dense gas. The entire core population is found to be characterized by a single critical Bonnor-Ebert mass. This mass coincides with the characteristic mass of the Pipe CMF indicating that most cores formed in the cloud are near critical stability. This suggests that the mass function of cores (and the IMF) has its origin in the physical process of thermal fragmentation in a pressurized medium.Comment: To appear in the Astrophysical Journa

Structured evaluation of virtual environments for special-needs education

This paper describes the development of a structured approach to evaluate experiential and communication virtual learning environments (VLEs) designed specifically for use in the education of children with severe learning difficulties at the Shepherd special needs school in Nottingham, UK. Constructivist learning theory was used as a basis for the production of an evaluation framework, used to evaluate the design of three VLEs and how they were used by students with respect to this learning theory. From an observational field study of student-teacher pairs using the VLEs, 18 behaviour categories were identified as relevant to five of the seven constructivist principles defined by Jonassen (1994). Analysis of student-teacher behaviour was used to provide support for, or against, the constructivist principles. The results show that the three VLEs meet the constructivist principles in very different ways and recommendations for design modifications are put forward

Microscopic Electron Models with Exact SO(5) Symmetry

We construct a class of microscopic electron models with exact SO(5) symmetry between antiferromagnetic and d-wave superconducting ground states. There is an exact one-to-one correspondence between both single-particle and collective excitations in both phases. SO(5) symmetry breaking terms can be introduced and classified according to irreducible representations of the exact SO(5) algebra. The resulting phase diagram and collective modes are identical to that of the SO(5) nonlinear sigma model.Comment: 5 pages, LATEX, 4 eps fig

Replica theory for learning curves for Gaussian processes on random graphs

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of training examples. We analyse a challenging problem in the area of non-parametric inference where an effectively infinite number of parameters has to be learned, specifically Gaussian process regression. When the inputs are vertices on a random graph and the outputs noisy function values, we show that replica techniques can be used to obtain exact performance predictions in the limit of large graphs. The covariance of the Gaussian process prior is defined by a random walk kernel, the discrete analogue of squared exponential kernels on continuous spaces. Conventionally this kernel is normalised only globally, so that the prior variance can differ between vertices; as a more principled alternative we consider local normalisation, where the prior variance is uniform

Acceptability, Precision and Accuracy of 3D Photonic Scanning for Measurement of Body Shape in a Multi-Ethnic Sample of Children Aged 5-11 Years: The SLIC Study.

Information on body size and shape is used to interpret many aspects of physiology, including nutritional status, cardio-metabolic risk and lung function. Such data have traditionally been obtained through manual anthropometry, which becomes time-consuming when many measurements are required. 3D photonic scanning (3D-PS) of body surface topography represents an alternative digital technique, previously applied successfully in large studies of adults. The acceptability, precision and accuracy of 3D-PS in young children have not been assessed