trans-Cyclo­hex-2-ene-1,4-diyl bis­(4-nitro­phen­yl) dicarbonate

Although the title mol­ecule, C20H16N2O10, does not possess mol­ecular inversion symmetry, it lies on a crystallographic inversion centre which imposes disorder on the central cyclo­hexene ring. In addition, the cyclo­hexene ring has non-symmetry-related disorder over two sites, with the ratio of the major and minor components being 0.54:0.46. The overall effect is to produce four disorder components for the atoms of the cyclo­hexene ring. The side chain is perfectly ordered and the dihedral angle between the atoms of the carbonate group (O=CO2—) and the benzene ring is 72.99 (6)°

Ambient vibration recording for single-station, array and building studies made simple : CityShark II

This article describes an improved data acquisition system from a previous system dedicated to one-sensor site studies, aimed at recording ambient vibrations (microtremors). A multi-channel and/or remote triggering system is proposed. The system was conceived by IRD-Leas, France, and used at ISTerre, France, for research activities. The size, weight of this high quality system and its autonomy (no need to be connected to a laptop) make it a real portable device. The sys- tem acquires data with 24-bit delta-sigma ADCs in the 10 - 1000 sps range at 10 - 20 bit resolution on up to 18 channels in the multi-channel version. The input stage dynamics is available at ±2.5 V or ±5 V. The dynamic range varies, for example, from 108 dB at 100 sps to 90 dB at 250 sps. Gain is selectable from 1 (0 dB) to 8192 (78 dB) by powers of two (6 dB). Its very low level of internal noise allows recording of very low tension signals without missing code. Con- tinuous recording and GPS may also be implemented in the system. While primarily dedicated to ambient vibration recordings, this system can be connected to any type of device delivering an output tension in the ±5 V range

Polymeric Separation Media: Binding of a§ unsaturated Carbonyl Compounds to Insoluble Resins through Michael Additions or Chelation of Derivatives

This is the publisher's version, also available electronically from "http://www.degruyter.com"

A direct route to cyclic organic nanostructures via ring-expansion metathesis polymerization of a dendronized macromonomer

Cyclic organic nanostructures were prepared via ring-expansion metathesis polymerization of a dendronized norbornene macromonomer. The strategy provides a direct, efficient route to nanoscale rings in a single operation. AFM imaging confirmed toroidal features having diameters of ca. 35−40 nm

Extreme value distributions and Renormalization Group

In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. So far, only affine rescalings have been considered. We show, however, that more general rescalings are natural and lead to new limit distributions, apart from the Gumbel, Weibull, and Fr\'echet families. The problem is approached using the language of Renormalization Group transformations in the space of probability densities. The limit distributions are fixed points of the transformation and the study of the differential around them allows a local analysis of the domains of attraction and the computation of finite-size corrections.Comment: 16 pages, 5 figures. Final versio

Using Extreme Value Theory for Determining the Probability of Carrington-Like Solar Flares

Space weather events can negatively affect satellites, the electricity grid, satellite navigation systems and human health. As a consequence, extreme space weather has been added to the UK and other national risk registers. By their very nature, extreme space weather events occur rarely and, therefore, statistical methods are required to determine the probability of their occurrence. Space weather events can be characterised by a number of natural phenomena such as X-ray (solar) flares, solar energetic particle (SEP) fluxes, coronal mass ejections and various geophysical indices (Dst, Kp, F10.7). In this paper extreme value theory (EVT) is used to investigate the probability of extreme solar flares. Previous work has assumed that the distribution of solar flares follows a power law. However such an approach can lead to a poor estimation of the return times of such events due to uncertainties in the tails of the probability distribution function. Using EVT and GOES X-ray flux data it is shown that the expected 150-year return level is approximately an X60 flare whilst a Carrington-like flare is a one in a 100-year event. It is also shown that the EVT results are consistent with flare data from the Kepler space telescope mission.Comment: 13 pages, 4 figures; updated content following reviewer feedbac

Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers

Some results on the ordered statistics of eigenvalues for one-dimensional random Schr\"odinger Hamiltonians are reviewed. In the case of supersymmetric quantum mechanics with disorder, the existence of low energy delocalized states induces eigenvalue correlations and makes the ordered statistics problem nontrivial. The resulting distributions are used to analyze the problem of classical diffusion in a random force field (Sinai problem) in the presence of weakly concentrated absorbers. It is shown that the slowly decaying averaged return probability of the Sinai problem, \mean{P(x,t|x,0)}\sim \ln^{-2}t, is converted into a power law decay, \mean{P(x,t|x,0)}\sim t^{-\sqrt{2\rho/g}}, where $g$ is the strength of the random force field and $\rho$ the density of absorbers.Comment: 10 pages ; LaTeX ; 4 pdf figures ; Proceedings of the meeting "Fundations and Applications of non-equilibrium statistical mechanics", Nordita, Stockholm, october 2011 ; v2: appendix added ; v3: figure 2.left adde

Deformations of the Tracy-Widom distribution

In random matrix theory (RMT), the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists in removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristc of extreme values of an uncorrelated sequence, is obtained.Comment: 9 pages, 1 figur

The Largest Cluster in Subcritical Percolation

The statistical behavior of the size (or mass) of the largest cluster in subcritical percolation on a finite lattice of size $N$ is investigated (below the upper critical dimension, presumably $d_c=6$). It is argued that as $N \to \infty$ the cumulative distribution function converges to the Fisher-Tippett (or Gumbel) distribution $e^{-e^{-z}}$ in a certain weak sense (when suitably normalized). The mean grows like $s_\xi^* \log N$, where $s_\xi^*(p)$ is a ``crossover size''. The standard deviation is bounded near $s_\xi^* \pi/\sqrt{6}$ with persistent fluctuations due to discreteness. These predictions are verified by Monte Carlo simulations on $d=2$ square lattices of up to 30 million sites, which also reveal finite-size scaling. The results are explained in terms of a flow in the space of probability distributions as $N \to \infty$. The subcritical segment of the physical manifold ($0 < p < p_c$) approaches a line of limit cycles where the flow is approximately described by a ``renormalization group'' from the classical theory of extreme order statistics.Comment: 16 pages, 5 figs, expanded version to appear in Phys Rev

Assessment of multireference approaches to explicitly correlated full configuration interaction quantum Monte Carlo.

The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schrödinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansion of Slater determinants, the FCIQMC method suffers from a basis set incompleteness error that decays very slowly with the size of the employed single particle basis. The FCIQMC results obtained in a small basis set can be improved significantly with explicitly correlated techniques. Here, we present a study that assesses and compares two contrasting "universal" explicitly correlated approaches that fit into the FCIQMC framework: the [2]R12 method of Kong and Valeev [J. Chem. Phys. 135, 214105 (2011)] and the explicitly correlated canonical transcorrelation approach of Yanai and Shiozaki [J. Chem. Phys. 136, 084107 (2012)]. The former is an a posteriori internally contracted perturbative approach, while the latter transforms the Hamiltonian prior to the FCIQMC simulation. These comparisons are made across the 55 molecules of the G1 standard set. We found that both methods consistently reduce the basis set incompleteness, for accurate atomization energies in small basis sets, reducing the error from 28 mEh to 3-4 mEh. While many of the conclusions hold in general for any combination of multireference approaches with these methodologies, we also consider FCIQMC-specific advantages of each approach.Royal Societ