465 research outputs found
Calculation of the absorption spectrum of benzene in condensed phase. A study of the solvent effects
Lyapunov exponents of Green's functions for random potentials tending to zero
We consider quenched and annealed Lyapunov exponents for the Green's function
of , where the potentials , are i.i.d.
nonnegative random variables and is a scalar. We present a
probabilistic proof that both Lyapunov exponents scale like as
tends to 0. Here the constant is the same for the quenched as for
the annealed exponent and is computed explicitly. This improves results
obtained previously by Wei-Min Wang. We also consider other ways to send the
potential to zero than multiplying it by a small number.Comment: 16 pages, 3 figures. 1 figure added, very minor corrections. To
appear in Probability Theory and Related Fields. The final publication is
available at http://www.springerlink.com, see
http://www.springerlink.com/content/p0873kv68315847x/?p=4106c52fc57743eba322052bb931e8ac&pi=21
Quenched large deviations for multidimensional random walk in random environment with holding times
We consider a random walk in random environment with random holding times,
that is, the random walk jumping to one of its nearest neighbors with some
transition probability after a random holding time. Both the transition
probabilities and the laws of the holding times are randomly distributed over
the integer lattice. Our main result is a quenched large deviation principle
for the position of the random walk. The rate function is given by the Legendre
transform of the so-called Lyapunov exponents for the Laplace transform of the
first passage time. By using this representation, we derive some asymptotics of
the rate function in some special cases.Comment: This is the corrected version of the paper. 24 page
Molecular Spiders with Memory
Synthetic bio-molecular spiders with "legs" made of single-stranded segments
of DNA can move on a surface which is also covered by single-stranded segments
of DNA complementary to the leg DNA. In experimental realizations, when a leg
detaches from a segment of the surface for the first time it alters that
segment, and legs subsequently bound to these altered segments more weakly.
Inspired by these experiments we investigate spiders moving along a
one-dimensional substrate, whose legs leave newly visited sites at a slower
rate than revisited sites. For a random walk (one-leg spider) the slowdown does
not effect the long time behavior. For a bipedal spider, however, the slowdown
generates an effective bias towards unvisited sites, and the spider behaves
similarly to the excited walk. Surprisingly, the slowing down of the spider at
new sites increases the diffusion coefficient and accelerates the growth of the
number of visited sites.Comment: 10 pages, 3 figure
Positive temperature versions of two theorems on first-passage percolation
The estimates on the fluctuations of first-passsage percolation due to
Talagrand (a tail bound) and Benjamini--Kalai--Schramm (a sublinear variance
bound) are transcribed into the positive-temperature setting of random
Schroedinger operators.Comment: 15 pp; to appear in GAFA Seminar Note
Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz Potential
The Schwarz function has played an elegant role in understanding and in
generating new examples of exact solutions to the Laplacian growth (or "Hele-
Shaw") problem in the plane. The guiding principle in this connection is the
fact that "non-physical" singularities in the "oil domain" of the Schwarz
function are stationary, and the "physical" singularities obey simple dynamics.
We give an elementary proof that the same holds in any number of dimensions for
the Schwarz potential, introduced by D. Khavinson and H. S. Shapiro [17]
(1989). A generalization is also given for the so-called "elliptic growth"
problem by defining a generalized Schwarz potential. New exact solutions are
constructed, and we solve inverse problems of describing the driving
singularities of a given flow. We demonstrate, by example, how \mathbb{C}^n -
techniques can be used to locate the singularity set of the Schwarz potential.
One of our methods is to prolong available local extension theorems by
constructing "globalizing families". We make three conjectures in potential
theory relating to our investigation
Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher
We consider large deviations for nearest-neighbor random walk in a uniformly
elliptic i.i.d. environment. It is easy to see that the quenched and the
averaged rate functions are not identically equal. When the dimension is at
least four and Sznitman's transience condition (T) is satisfied, we prove that
these rate functions are finite and equal on a closed set whose interior
contains every nonzero velocity at which the rate functions vanish.Comment: 17 pages. Minor revision. In particular, note the change in the title
of the paper. To appear in Probability Theory and Related Fields
Insight into the mechanism of modulated syntheses: in situ synchrotron diffraction studies on the formation of Zr-fumarate MOF
In this work, the formation of a Zr-based metal-organic framework (MOF), Zr-fumarate MOF (Zr-fum MOF), is studied in situ by energy-dispersive diffraction. The Zr-fum MOF can be synthesised in DMF as well as in water-based synthesis systems. In both cases, its formation requires modulation, i.e. a monocarboxylic acid which is used as the modulator has to be added to the synthesis mixture. In general, different mechanisms of modulation are possible, for example, deprotonation of the linker molecule (deprotonation modulation) or coordination modulation (wherein the molecules of the modulator compete with the linker molecules for the coordination sites at the inorganic building units). Independently of the specific mechanism, modulation often improves the reproducibility of the MOF synthesis and the crystallinity of the product and may be used to control crystal size and morphology. This study is the first to investigate the kinetics of modulated MOF syntheses with regard to coordination modulation. According to this concept, the addition of a modulator usually decelerates the reaction. Our kinetic investigations show that this is the case for the formation of Zr-fum MOF in the water-based synthesis with formic acid used as a modulator. On the contrary, the addition of formic acid to the DMF-based synthesis results in an accelerating effect. This unexpected effect can be attributed to a small amount of water present in formic acid. Correspondingly, the addition of water to the synthesis mixture also showed an accelerating effect. These investigations emphasise the subtle interplay of the different ingredients in a MOF synthesis. In the case of the Zr-fum MOF, both the modulator formic acid and the water content strongly affect the kinetics of crystallisation. Quantitative evaluation of the kinetic data using the Gualtieri equation provides additional insight into the mechanisms of coordination-modulated MOF formation reactions and excludes the idea of deprotonation modulation.DFG/Porous Metal–Organic Frameworks/1362DESY/I-2011055
Starting the conversation: land issues and critical conservation studies in post-colonial Africa
This thematic issue brings together the scholarly fields of critical conservation studies and African land issues, a relationship largely unexplored to date. The alienation of land for conservation purposes, introduced to Africa under colonial rule and still taking place today, has fundamental impacts on the politics of land and land use, and is contested in contemporary nation-states - including those that are attempting to implement land restitution and reform. The contributors explore these issues in a range of African contexts. Three key themes are identified: the problematic constructions of ‘community’ by outside agencies; spatial exclusion and the silencing of local voices; and the neoliberalisation of conservation spaces. In contributing to new perspectives on these themes, this thematic issue shows how discourses and practices of conservation, increasingly shaped by neoliberalism, currently impact on land ownership, access and use. It further highlights some important historical continuities. These trends can be observed in transfrontier conservation areas, on state-owned land used for conservation and ‘green’ initiatives, but also on private land where conservation is increasingly turned to commercial purposes.International Bibliography of Social Science
Excited Random Walk in One Dimension
We study the excited random walk, in which a walk that is at a site that
contains cookies eats one cookie and then hops to the right with probability p
and to the left with probability q=1-p. If the walk hops onto an empty site,
there is no bias. For the 1-excited walk on the half-line (one cookie initially
at each site), the probability of first returning to the starting point at time
t scales as t^{-(2-p)}. Although the average return time to the origin is
infinite for all p, the walk eats, on average, only a finite number of cookies
until this first return when p<1/2. For the infinite line, the probability
distribution for the 1-excited walk has an unusual anomaly at the origin. The
positions of the leftmost and rightmost uneaten cookies can be accurately
estimated by probabilistic arguments and their corresponding distributions have
power-law singularities near the origin. The 2-excited walk on the infinite
line exhibits peculiar features in the regime p>3/4, where the walk is
transient, including a mean displacement that grows as t^{nu}, with nu>1/2
dependent on p, and a breakdown of scaling for the probability distribution of
the walk.Comment: 14 pages, 13 figures, 2-column revtex4 format, for submission to J.
Phys.
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