Quadratic invariants for discrete clusters of weakly interacting waves

We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix with entries 1, −1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N − M* ≥ N − M, where M* is the number of linearly independent rows in Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney–Hasegawa–Mima wave model, and by showing a classification of small (up to three-triad) clusters

Resonant X-ray diffraction studies on the charge ordering in magnetite

Here we show that the low temperature phase of magnetite is associated with an effective, although fractional, ordering of the charge. Evidence and a quantitative evaluation of the atomic charges are achieved by using resonant x-ray diffraction (RXD) experiments whose results are further analyzed with the help of ab initio calculations of the scattering factors involved. By confirming the results obtained from X-ray crystallography we have shown that RXD is able to probe quantitatively the electronic structure in very complex oxides, whose importance covers a wide domain of applications.Comment: 4 pages 4 figures, accepted for publication in PR

Superconductivity in the Cuprates as a Consequence of Antiferromagnetism and a Large Hole Density of States

We briefly review a theory for the cuprates that has been recently proposed based on the movement and interaction of holes in antiferromagnetic (AF) backgrounds. A robust peak in the hole density of states (DOS) is crucial to produce a large critical temperature once a source of hole attraction is identified. The predictions of this scenario are compared with experiments. The stability of the calculations after modifying some of the original assumptions is addressed. We find that if the dispersion is changed from an antiferromagnetic band at half-filling to a tight binding $cosk_x + cosk_y$ narrow band at $=0.87$, the main conclusions of the approach remain basically the same i.e. superconductivity appears in the $d_{x^2 - y^2}$-channel and $T_c$ is enhanced by a large DOS. The main features distinguishing these ideas from more standard theories based on antiferromagnetic correlations are here discussed.Comment: RevTex, 7 pages, 5 figures are available on reques

Qualitative understanding of the sign of t' asymmetry in the extended t-J Model and relevance for pairing properties

Numerical calculations illustrate the effect of the sign of the next nearest-neighbor hopping term t' on the 2-hole properties of the t-t'-J model. Working mainly on 2-leg ladders, in the -1.0 < t'/t < 1.0 regime, it is shown that introducing t' in the t-J model is equivalent to effectively renormalizing J, namely t' negative (positive) is equivalent to an effective t-J model with smaller (bigger) J. This effect is present even at the level of a 2x2 plaquette toy model, and was observed also in calculations on small square clusters. Analyzing the transition probabilities of a hole-pair in the plaquette toy model, it is argued that the coherent propagation of such hole-pair is enhanced by a constructive interference between both t and t' for t'>0. This interference is destructive for t'<0.Comment: 5 pages, 4 figures, to appear in PRB as a Rapid Communicatio

A Kolmogorov-Zakharov Spectrum in AdSAdS Gravitational Collapse

We study black hole formation during the gravitational collapse of a massless scalar field in asymptotically $AdS_D$ spacetimes for $D=4,5$. We conclude that spherically symmetric gravitational collapse in asymptotically $AdS$ spaces is turbulent and characterized by a Kolmogorov-Zakharov spectrum. Namely, we find that after an initial period of weakly nonlinear evolution, there is a regime where the power spectrum of the Ricci scalar evolves as $\omega^{-s}$ with the frequency, $\omega$, and $s\approx 1.7\pm 0.1$.Comment: 5 pages, 4 figures. v2: Typos, other initial profile considered for universality, error analysis, close to PRL versio

Experimental study of the inverse cascade in gravity wave turbulence

We perform experiments to study the inverse cascade regime of gravity wave turbulence on the surface of a fluid. Surface waves are forced at an intermediate scale corresponding to the gravity-capillary wavelength. In response to this forcing, waves at larger scales are observed. The spectrum of their amplitudes exhibits a frequency-power law at high enough forcing. Both observations are ascribed to the upscale wave action transfers of gravity wave turbulence. The spectrum exponent is close to the value predicted by the weak turbulence theory. The spectrum amplitude is found to scale linearly with the mean injected power. We measure also the distributions of the injected power fluctuations in the presence of upscale (inverse) transfers or in the presence of a downscale (direct) cascade in gravity wave turbulence.Comment: in press in EPL (2011

Modeling Kelvin wave cascades in superfluid helium

We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the later and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via using a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and closeness of numerics for the higher-order DAM to the analytical predictions for the lower-order DAM

Comparative performance of MRI-derived PRECISE scores and delta-radiomics models for the prediction of prostate cancer progression in patients on active surveillance

Objectives: To compare the performance of the PRECISE scoring system against several MRI-derived delta-radiomics models for predicting histopathological prostate cancer (PCa) progression in patients on active surveillance (AS). // Methods: The study included AS patients with biopsy-proven PCa with a minimum follow-up of 2 years and at least one repeat targeted biopsy. Histopathological progression was defined as grade group progression from diagnostic biopsy. The control group included patients with both radiologically and histopathologically stable disease. PRECISE scores were applied prospectively by four uro-radiologists with 5–16 years’ experience. T2WI- and ADC-derived delta-radiomics features were computed using baseline and latest available MRI scans, with the predictive modelling performed using the parenclitic networks (PN), least absolute shrinkage and selection operator (LASSO) logistic regression, and random forests (RF) algorithms. Standard measures of discrimination and areas under the ROC curve (AUCs) were calculated, with AUCs compared using DeLong’s test. // Results: The study included 64 patients (27 progressors and 37 non-progressors) with a median follow-up of 46 months. PRECISE scores had the highest specificity (94.7%) and positive predictive value (90.9%), whilst RF had the highest sensitivity (92.6%) and negative predictive value (92.6%) for predicting disease progression. The AUC for PRECISE (84.4%) was non-significantly higher than AUCs of 81.5%, 78.0%, and 80.9% for PN, LASSO regression, and RF, respectively (p = 0.64, 0.43, and 0.57, respectively). No significant differences were observed between AUCs of the three delta-radiomics models (p-value range 0.34–0.77). // Conclusions: PRECISE and delta-radiomics models achieved comparably good performance for predicting PCa progression in AS patients

Neutron Resonance Spectroscopy of 117Sn from1 eV to 1.5 keV

Parity violation has been studied recently for neutron resonances in 117Sn. The neutron resonance spectroscopy is essential for the analysis of the parity violation data. We have measured neutron resonances in 117Sn for neutron energies from 1 to 1500 eV using the time-of-flight method and the (n,γ) reaction. The sample was enriched to 87.6% 117Sn. Neutron scattering and radiative widths were determined, and orbital angular momentum assignments were made with a Bayesian analysis. The s-wave and p-wave strength functions and average level spacings were determined