Total Chiral Symmetry Breaking during Crystallization: Who needs a "Mother Crystal"?

Processes that can produce states of broken chiral symmetry are of particular interest to physics, chemistry and biology. Chiral symmetry breaking during crystallization of sodium chlorate occurs via the production of secondary crystals of the same handedness from a single "mother crystal" that seeds the solution. Here we report that a large and "symmetric" population of D- and L-crystals moves into complete chiral purity disappearing one of the enantiomers. This result shows: (i) a new symmetry breaking process incompatible with the hypothesis of a single "mother crystal"; (ii) that complete symmetry breaking and chiral purity can be achieved from an initial system with both enantiomers. These findings demand a new explanation to the process of total symmetry breaking in crystallization without the intervention of a "mother crystal" and open the debate on this fascinating phenomenon. We present arguments to show that our experimental data can been explained with a new model of "complete chiral purity induced by nonlinear autocatalysis and recycling".Comment: 5 pages, 4 figures, Added reference

Converging evidence for the neuroanatomic basis of combinatorial semantics in the angular gyrus

Human thought and language rely on the brain's ability to combine conceptual information. This fundamental process supports the construction of complex concepts from basic constituents. For example, both “jacket” and “plaid” can be represented as individual concepts, but they can also be integrated to form the more complex representation “plaid jacket.” Although this process is central to the expression and comprehension of language, little is known about its neural basis. Here we present evidence for a neuroanatomic model of conceptual combination from three experiments. We predicted that the highly integrative region of heteromodal association cortex in the angular gyrus would be critical for conceptual combination, given its anatomic connectivity and its strong association with semantic memory in functional neuroimaging studies. Consistent with this hypothesis, we found that the process of combining concepts to form meaningful representations specifically modulates neural activity in the angular gyrus of healthy adults, independent of the modality of the semantic content integrated. We also found that individual differences in the structure of the angular gyrus in healthy adults are related to variability in behavioral performance on the conceptual combination task. Finally, in a group of patients with neurodegenerative disease, we found that the degree of atrophy in the angular gyrus is specifically related to impaired performance on combinatorial processing. These converging anatomic findings are consistent with a critical role for the angular gyrus in conceptual combination

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

Complete homochirality induced by the nonlinear autocatalysis and recycling

A nonlinear autocatalysis of a chiral substance is shown to achieve homochirality in a closed system, if the back-reaction is included. Asymmetry in the concentration of two enantiomers or the enantiometric excess increases due to the nonlinear autocatalysis. Furthermore, when the back-reaction is taken into account, the reactant supplied by the decomposition of the enantiomers is recycled to produce more and more the dominant one, and eventually the homochirality is established.Comment: 4 pages, 2 figure

S=1/2 chains and spin-Peierls transition in TiOCl

We study TiOCl as an example of an S=1/2 layered Mott insulator. From our analysis of new susceptibility data, combined with LDA and LDA+U band structure calculations, we conclude that orbital ordering produces quasi-one-dimensional spin chains and that TiOCl is a new example of Heisenberg-chains which undergo a spin-Peierls transition. The energy scale is an order of magnitude larger than that of previously known examples. The effects of non-magnetic Sc impurities are explained using a model of broken finite chains.Comment: 5 pages, 5 figures (color); details on crystal growth added; to be published in Phys. Rev.

Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings

We suggest a general rule for the shift quantum numbers k of the relative ground states of antiferromagnetic Heisenberg spin rings. This rule generalizes well-known results of Marshall, Peierls, Lieb, Schultz, and Mattis for even rings. Our rule is confirmed by numerical investigations and rigorous proofs for special cases, including systems with a Haldane gap. Implications for the total spin quantum number S of relative ground states are discussed as well as generalizations to the XXZ model.Comment: 8 pages, 2 figures, submitted to Phys. Rev. B. More information at http://www.physik.uni-osnabrueck.de/makrosysteme

Thermodynamic Properties and Elementary Excitations in Quantum Sine-Gordon Spin System KCuGaF6

Thermodynamic properties and elementary excitations in $S=1/2$ one-dimensional Heisenberg antiferromagnet KCuGaF$_6$ were investigated by magnetic susceptibility, specific heat and ESR measurements. Due to the Dzyaloshinsky-Moriya interaction with alternating $D$-vectors and/or the staggered $g$-tensor, the staggered magnetic field is induced when subjected to external magnetic field. Specific heat in magnetic field clearly shows the formation of excitation gap, which is attributed to the staggered magnetic field. The specific heat data was analyzed on the basis of the quantum sine-Gordon (SG) model. We observed many ESR modes including one soliton and three breather excitations characteristic of the quantum SG model.Comment: 4 pages, 5 figures, to appear in J. Phys. Soc. Jpn., vol. 76, no.

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

Spin-Peierls Dimerization of a s=1/2 Heisenberg Antiferromagnet on a Square Lattice

Dimerization of a spin-half Heisenberg antiferromagnet on a square lattice is investigated for several possible dimerized configurations, some of which are shown to have lower ground state energies than the others. In particular, the lattice deformations resulting in alternate stronger and weaker couplings along both the principal axes of a square lattice are shown to result in a larger gain in magnetic energy. In addition, a `columnar' configuration is shown to have a lower ground state energy and a faster increase in the energy gap parameter than a `staggered' configuration. The inclusion of unexpanded exchange coupling leads to a power law behaviour for the magnetic energy gain and energy gap, which is qualitatively different from that reported earlier. Instead of increasing as $\delta ^{x}$, the two quantities depend on $\delta$ as $\delta ^{\nu}/| \ln \delta | .$ This is true both in the near critical regime $(0\leq \delta \leq 0.1)$ as well as in the far regime $(0\leq \delta <1)$. It is suggested that the unexpanded exchange coupling is as much a source of the logarithmic dependence as a correction due to the contribution of umklapp processes. Staggered magnetization is shown to follow the same $\delta$-dependence in all the configurations in the small $\delta$-regime, while for $0\leq \delta <1$, it follows the power law $\delta ^{x}$.Comment: 12 pages, 7 Postscript figures, RevTex forma