757 research outputs found
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
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
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 is the strength of the random force field and 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
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 is investigated (below
the upper critical dimension, presumably ). It is argued that as the cumulative distribution function converges to the Fisher-Tippett
(or Gumbel) distribution in a certain weak sense (when suitably
normalized). The mean grows like , where is a
``crossover size''. The standard deviation is bounded near with persistent fluctuations due to discreteness. These
predictions are verified by Monte Carlo simulations on 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 . The subcritical segment of the physical manifold ()
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
Reversible Photomechanical Switching of Individual Engineered Molecules at a Surface
We have observed reversible light-induced mechanical switching for a single
organic molecule bound to a metal surface. Scanning tunneling microscopy (STM)
was used to image the features of an individual azobenzene molecule on Au(111)
before and after reversibly cycling its mechanical structure between trans and
cis states using light. Azobenzene molecules were engineered to increase their
surface photomechanical activity by attaching varying numbers of tert-butyl
(TB) ligands ("legs") to the azobenzene phenyl rings. STM images show that
increasing the number of TB legs "lifts" the azobenzene molecules from the
substrate, thereby increasing molecular photomechanical activity by decreasing
molecule-surface coupling.Comment: related theoretical paper: cond-mat/061220
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