Rational quantum integrable systems of D_N type with polarized spin reversal operators

We study the spin Calogero model of D_N type with polarized spin reversal operators, as well as its associated spin chain of Haldane-Shastry type, both in the antiferromagnetic and ferromagnetic cases. We compute the spectrum and the partition function of the former model in closed form, from which we derive an exact formula for the chain's partition function in terms of products of partition functions of Polychronakos-Frahm spin chains of type A. Using a recursion relation for the latter partition functions that we derive in the paper, we are able to numerically evaluate the partition function, and thus the spectrum, of the D_N-type spin chain for relatively high values of the number of spins N. We analyze several global properties of the chain's spectrum, such as the asymptotic level density, the distribution of consecutive spacings of the unfolded spectrum, and the average degeneracy. In particular, our results suggest that this chain is invariant under a suitable Yangian group, and that its spectrum coincides with that of a Yangian-invariant vertex model with linear energy function and dispersion relation.Comment: 26 pages, 5 figures, typeset in LaTe

The Berry-Tabor conjecture for spin chains of Haldane-Shastry type

According to a long-standing conjecture of Berry and Tabor, the distribution of the spacings between consecutive levels of a "generic'' integrable model should follow Poisson's law. In contrast, the spacings distribution of chaotic systems typically follows Wigner's law. An important exception to the Berry-Tabor conjecture is the integrable spin chain with long-range interactions introduced by Haldane and Shastry in 1988, whose spacings distribution is neither Poissonian nor of Wigner's type. In this letter we argue that the cumulative spacings distribution of this chain should follow the "square root of a logarithm'' law recently proposed by us as a characteristic feature of all spin chains of Haldane-Shastry type. We also show in detail that the latter law is valid for the rational counterpart of the Haldane-Shastry chain introduced by Polychronakos.Comment: LaTeX with revtex4, 6 pages, 6 figure

Vasoreactivity in CADASIL: comparison to structural MRI and neuropsychology

Impaired cerebrovascular reactivity precedes histological and clinical evidence of CADASIL in animal models. We aimed to more fully characterise peripheral and cerebral vascular function and reactivity in a cohort of adult CADASIL patients, and explore the associations of these with conventional clinical, imaging and neuropsychological measures. 22 adults with CADASIL gave informed consent to participate in an exploratorystudy of vascular function in CADASIL. Clinical assessment, comprehensive vascular assessment, MRI and neuropsychological testing were conducted. Transcranial Doppler and arterial spin labelling MRI with hypercapnia challenge both measured cerebral vasoreactivity. Number and volume of lacunes, subcortical hyperintensity volume, microbleeds and normalised brain volume were assessed on MRI scans. Analysis was exploratory and examined associations between different markers. The results showed that cerebrovascular reactivity measured by ASL correlated with peripheral vasoreactivity measured by flow mediated dilatation. Subjects with >5 lacunes were older, with evidence of atherosclerosis and had impaired cerebral and peripheral vasoreactivity. Subjects with depressive symptoms, disability or delayed processing speed, also had impaired vasoreactivity, as well as more lacunes and brain atrophy. Impaired vasoreactivity and vascular dysfunction may play a significant role in the pathophysiology of CADASIL and vascular tests may be important to include in both longitudinal and clinical trials

Water vapor emission from IRC+10216 and other carbon-rich stars: model predictions and prospects for multitransition observations

We have modeled the emission of H2O rotational lines from the extreme C-rich star IRC+10216. Our treatment of the excitation of H2O emissions takes into account the excitation of H2O both through collisions, and through the pumping of the nu2 and nu3 vibrational states by dust emission and subsequent decay to the ground state. Regardless of the spatial distribution of the water molecules, the H2O 1_{10}-1_{01} line at 557 GHz observed by the Submillimeter Wave Astronomy Satellite (SWAS) is found to be pumped primarily through the absorption of dust-emitted photons at 6 $\mu$m in the nu2 band. As noted by previous authors, the inclusion of radiative pumping lowers the ortho-H2O abundance required to account for the 557 GHz emission, which is found to be (0.5-1)x10^{-7} if the presence of H2O is a consequence of vaporization of orbiting comets or Fischer-Tropsch catalysis. Predictions for other submillimeter H2O lines that can be observed by the Herschel Space Observatory (HSO) are reported. Multitransition HSO observations promise to reveal the spatial distribution of the circumstellar water vapor, discriminating among the several hypotheses that have been proposed for the origin of the H2O vapor in the envelope of IRC+10216. We also show that, for observations with HSO, the H2O 1_{10}-1_{01} 557 GHz line affords the greatest sensitivity in searching for H2O in other C-rich AGB stars.Comment: 35 pages, 12 figures, to be published in The Astrophysical Journa

Efficient Exploration of Quantified Uncertainty in Granular Crystals

Granular crystals present unique nonlinear properties that support standing waves. These depend on precompression and impurities. Thus, they can be used for different applications such as impact and shock dissipation. There are different models which rely on reasonable approximations and assumptions. While experimental results show good agreement with theory, there are experimental errors that are not easily explained and are usually attributed to the approximations made and phenomena that are not accounted for. This might be the result of not quantifying the uncertainty, since variables like the grain size, position, mass and Young modulus, of each particle, are uncertain. Building a response surface is computationally expensive, because the underlying mapping to be learned is a high dimensional problem. This work presents a way of quantifying uncertainty in granular crystals in a computationally efficient way. To accomplish this, a low dimensional response surface is approximated through the method of active subspaces. Within this framework, special structure within the inputs is exploited to project it onto a lower dimensional manifold. The problem of subspace approximation is then treated as an optimization problem, with the use of the Bayesian Information Criterion (BIC). We treat the underlying function to be learned as a Gaussian Process and use Gaussian process regression to generate predictive distributions for test inputs. Distributions obtained through these methods, present a model for uncertainty propagation and could potentially be used to better understand the experimental errors for different models