4,424 research outputs found
Complete Exact Solution of Diffusion-Limited Coalescence, A + A -> A
Some models of diffusion-limited reaction processes in one dimension lend
themselves to exact analysis. The known approaches yield exact expressions for
a limited number of quantities of interest, such as the particle concentration,
or the distribution of distances between nearest particles. However, a full
characterization of a particle system is only provided by the infinite
hierarchy of multiple-point density correlation functions. We derive an exact
description of the full hierarchy of correlation functions for the
diffusion-limited irreversible coalescence process A + A -> A.Comment: 4 pages, 2 figures (postscript). Typeset with Revte
Entanglement vs. gap for one-dimensional spin systems
We study the relationship between entanglement and spectral gap for local
Hamiltonians in one dimension. The area law for a one-dimensional system states
that for the ground state, the entanglement of any interval is upper-bounded by
a constant independent of the size of the interval. However, the possible
dependence of the upper bound on the spectral gap Delta is not known, as the
best known general upper bound is asymptotically much larger than the largest
possible entropy of any model system previously constructed for small Delta. To
help resolve this asymptotic behavior, we construct a family of one-dimensional
local systems for which some intervals have entanglement entropy which is
polynomial in 1/Delta, whereas previously studied systems, such as free fermion
systems or systems described by conformal field theory, had the entropy of all
intervals bounded by a constant times log(1/Delta).Comment: 16 pages. v2 is final published version with slight clarification
Priority diffusion model in lattices and complex networks
We introduce a model for diffusion of two classes of particles ( and )
with priority: where both species are present in the same site the motion of
's takes precedence over that of 's. This describes realistic situations
in wireless and communication networks. In regular lattices the diffusion of
the two species is normal but the particles are significantly slower, due
to the presence of the particles. From the fraction of sites where the
particles can move freely, which we compute analytically, we derive the
diffusion coefficients of the two species. In heterogeneous networks the
fraction of sites where is free decreases exponentially with the degree of
the sites. This, coupled with accumulation of particles in high-degree nodes
leads to trapping of the low priority particles in scale-free networks.Comment: 5 pages, 3 figure
Crystal constructions in Number Theory
Weyl group multiple Dirichlet series and metaplectic Whittaker functions can
be described in terms of crystal graphs. We present crystals as parameterized
by Littelmann patterns and we give a survey of purely combinatorial
constructions of prime power coefficients of Weyl group multiple Dirichlet
series and metaplectic Whittaker functions using the language of crystal
graphs. We explore how the branching structure of crystals manifests in these
constructions, and how it allows access to some intricate objects in number
theory and related open questions using tools of algebraic combinatorics
Volatile Decision Dynamics: Experiments, Stochastic Description, Intermittency Control, and Traffic Optimization
The coordinated and efficient distribution of limited resources by individual
decisions is a fundamental, unsolved problem. When individuals compete for road
capacities, time, space, money, goods, etc., they normally make decisions based
on aggregate rather than complete information, such as TV news or stock market
indices. In related experiments, we have observed a volatile decision dynamics
and far-from-optimal payoff distributions. We have also identified ways of
information presentation that can considerably improve the overall performance
of the system. In order to determine optimal strategies of decision guidance by
means of user-specific recommendations, a stochastic behavioural description is
developed. These strategies manage to increase the adaptibility to changing
conditions and to reduce the deviation from the time-dependent user
equilibrium, thereby enhancing the average and individual payoffs. Hence, our
guidance strategies can increase the performance of all users by reducing
overreaction and stabilizing the decision dynamics. These results are highly
significant for predicting decision behaviour, for reaching optimal behavioural
distributions by decision support systems, and for information service
providers. One of the promising fields of application is traffic optimization.Comment: For related work see http://www.helbing.or
Experimental demonstration of a squeezing enhanced power recycled Michelson interferometer for gravitational wave detection
Interferometric gravitational wave detectors are expected to be limited by
shot noise at some frequencies. We experimentally demonstrate that a power
recycled Michelson with squeezed light injected into the dark port can overcome
this limit. An improvement in the signal-to-noise ratio of 2.3dB is measured
and locked stably for long periods of time. The configuration, control and
signal readout of our experiment are compatible with current gravitational wave
detector designs. We consider the application of our system to long baseline
interferometer designs such as LIGO.Comment: 4 pages 4 figure
Bregman Voronoi Diagrams: Properties, Algorithms and Applications
The Voronoi diagram of a finite set of objects is a fundamental geometric
structure that subdivides the embedding space into regions, each region
consisting of the points that are closer to a given object than to the others.
We may define many variants of Voronoi diagrams depending on the class of
objects, the distance functions and the embedding space. In this paper, we
investigate a framework for defining and building Voronoi diagrams for a broad
class of distance functions called Bregman divergences. Bregman divergences
include not only the traditional (squared) Euclidean distance but also various
divergence measures based on entropic functions. Accordingly, Bregman Voronoi
diagrams allow to define information-theoretic Voronoi diagrams in statistical
parametric spaces based on the relative entropy of distributions. We define
several types of Bregman diagrams, establish correspondences between those
diagrams (using the Legendre transformation), and show how to compute them
efficiently. We also introduce extensions of these diagrams, e.g. k-order and
k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set
of points and their connexion with Bregman Voronoi diagrams. We show that these
triangulations capture many of the properties of the celebrated Delaunay
triangulation. Finally, we give some applications of Bregman Voronoi diagrams
which are of interest in the context of computational geometry and machine
learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures
Remote sensing for cost-effective blue carbon accounting
Blue carbon ecosystems (BCE) include mangrove forests, tidal marshes, and seagrass meadows, all of which are currently under threat, putting their contribution to mitigating climate change at risk. Although certain challenges and trade-offs exist, remote sensing offers a promising avenue for transparent, replicable, and cost-effective accounting of many BCE at unprecedented temporal and spatial scales. The United Nations Framework Convention on Climate Change (UNFCCC) has issued guidelines for developing blue carbon inventories to incorporate into Nationally Determined Contributions (NDCs). Yet, there is little guidance on remote sensing techniques for monitoring, reporting, and verifying blue carbon assets. This review constructs a unified roadmap for applying remote sensing technologies to develop cost-effective carbon inventories for BCE – from local to global scales. We summarise and discuss (1) current standard guidelines for blue carbon inventories; (2) traditional and cutting-edge remote sensing technologies for mapping blue carbon habitats; (3) methods for translating habitat maps into carbon estimates; and (4) a decision tree to assist users in determining the most suitable approach depending on their areas of interest, budget, and required accuracy of blue carbon assessment. We designed this work to support UNFCCC-approved IPCC guidelines with specific recommendations on remote sensing techniques for GHG inventories. Overall, remote sensing technologies are robust and cost-effective tools for monitoring, reporting, and verifying blue carbon assets and projects. Increased appreciation of these techniques can promote a technological shift towards greater policy and industry uptake, enhancing the scalability of blue carbon as a Natural Climate Solution worldwide
Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4
We study the symmetries of pure N=2 supergravity in D=4. As is known, this
theory reduced on one Killing vector is characterised by a non-linearly
realised symmetry SU(2,1) which is a non-split real form of SL(3,C). We
consider the BPS brane solutions of the theory preserving half of the
supersymmetry and the action of SU(2,1) on them. Furthermore we provide
evidence that the theory exhibits an underlying algebraic structure described
by the Lorentzian Kac-Moody group SU(2,1)^{+++}. This evidence arises both from
the correspondence between the bosonic space-time fields of N=2 supergravity in
D=4 and a one-parameter sigma-model based on the hyperbolic group SU(2,1)^{++},
as well as from the fact that the structure of BPS brane solutions is neatly
encoded in SU(2,1)^{+++}. As a nice by-product of our analysis, we obtain a
regular embedding of the Kac-Moody algebra su(2,1)^{+++} in e_{11} based on
brane physics.Comment: 70 pages, final version published in JHE
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