946 research outputs found
Three dimensional structure from intensity correlations
We develop the analysis of x-ray intensity correlations from dilute ensembles
of identical particles in a number of ways. First, we show that the 3D particle
structure can be determined if the particles can be aligned with respect to a
single axis having a known angle with respect to the incident beam. Second, we
clarify the phase problem in this setting and introduce a data reduction scheme
that assesses the integrity of the data even before the particle reconstruction
is attempted. Finally, we describe an algorithm that reconstructs intensity and
particle density simultaneously, thereby making maximal use of the available
constraints.Comment: 17 pages, 9 figure
Ordering monomial factors of polynomials in the product representation
The numerical construction of polynomials in the product representation (as
used for instance in variants of the multiboson technique) can become
problematic if rounding errors induce an imprecise or even unstable evaluation
of the polynomial. We give criteria to quantify the effects of these rounding
errors on the computation of polynomials approximating the function . We
consider polynomials both in a real variable and in a Hermitian matrix. By
investigating several ordering schemes for the monomials of these polynomials,
we finally demonstrate that there exist orderings of the monomials that keep
rounding errors at a tolerable level.Comment: Latex2e file, 7 figures, 32 page
Global convergence of a non-convex Douglas-Rachford iteration
We establish a region of convergence for the proto-typical non-convex
Douglas-Rachford iteration which finds a point on the intersection of a line
and a circle. Previous work on the non-convex iteration [2] was only able to
establish local convergence, and was ineffective in that no explicit region of
convergence could be given
Magnetic Properties of Undoped
The Heisenberg antiferromagnet, which arises from the large Hubbard
model, is investigated on the molecule and other fullerenes. The
connectivity of leads to an exotic classical ground state with
nontrivial topology. We argue that there is no phase transition in the Hubbard
model as a function of , and thus the large solution is relevant for
the physical case of intermediate coupling. The system undergoes a first order
metamagnetic phase transition. We also consider the S=1/2 case using
perturbation theory. Experimental tests are suggested.Comment: 12 pages, 3 figures (included
Quantum spin models with exact dimer ground states
Inspired by the exact solution of the Majumdar-Ghosh model, a family of
one-dimensional, translationally invariant spin hamiltonians is constructed.
The exchange coupling in these models is antiferromagnetic, and decreases
linearly with the separation between the spins. The coupling becomes
identically zero beyond a certain distance. It is rigorously proved that the
dimer configuration is an exact, superstable ground state configuration of all
the members of the family on a periodic chain. The ground state is two-fold
degenerate, and there exists an energy gap above the ground state. The
Majumdar-Ghosh hamiltonian with two-fold degenerate dimer ground state is just
the first member of the family.
The scheme of construction is generalized to two and three dimensions, and
illustrated with the help of some concrete examples. The first member in two
dimensions is the Shastry-Sutherland model. Many of these models have
exponentially degenerate, exact dimer ground states.Comment: 10 pages, 8 figures, revtex, to appear in Phys. Rev.
Cost–benefit analysis of controlling rabies: placing economics at the heart of rabies control to focus political will
Rabies is an economically important zoonosis. This paper describes the extent of the economic impacts of the disease and some of the types of economic analyses used to understand those impacts, as well as the trade-offs between efforts to manage rabies and efforts to eliminate it. In many cases, the elimination of rabies proves more cost-effective over time than the continual administration of postexposure prophylaxis, animal testing and animal vaccination. Economic analyses are used to inform and drive policy decisions and focus political will, placing economics at the heart of rabies control
The sloppy model universality class and the Vandermonde matrix
In a variety of contexts, physicists study complex, nonlinear models with
many unknown or tunable parameters to explain experimental data. We explain why
such systems so often are sloppy; the system behavior depends only on a few
`stiff' combinations of the parameters and is unchanged as other `sloppy'
parameter combinations vary by orders of magnitude. We contrast examples of
sloppy models (from systems biology, variational quantum Monte Carlo, and
common data fitting) with systems which are not sloppy (multidimensional linear
regression, random matrix ensembles). We observe that the eigenvalue spectra
for the sensitivity of sloppy models have a striking, characteristic form, with
a density of logarithms of eigenvalues which is roughly constant over a large
range. We suggest that the common features of sloppy models indicate that they
may belong to a common universality class. In particular, we motivate focusing
on a Vandermonde ensemble of multiparameter nonlinear models and show in one
limit that they exhibit the universal features of sloppy models.Comment: New content adde
Testing the Growth Rate Hypothesis in Vascular Plants with Above- and Below-Ground Biomass
The growth rate hypothesis (GRH) proposes that higher growth rate (the rate of change in biomass per unit biomass, μ) is associated with higher P concentration and lower C∶P and N∶P ratios. However, the applicability of the GRH to vascular plants is not well-studied and few studies have been done on belowground biomass. Here we showed that, for aboveground, belowground and total biomass of three study species, μ was positively correlated with N∶C under N limitation and positively correlated with P∶C under P limitation. However, the N∶P ratio was a unimodal function of μ, increasing for small values of μ, reaching a maximum, and then decreasing. The range of variations in μ was positively correlated with variation in C∶N∶P stoichiometry. Furthermore, μ and C∶N∶P ranges for aboveground biomass were negatively correlated with those for belowground. Our results confirm the well-known association of growth rate with tissue concentration of the limiting nutrient and provide empirical support for recent theoretical formulations
Low-energy sector of the S=1/2 Kagome antiferromagnet
Starting from a modified version of the the S=1/2 Kagome antiferromagnet to
emphasize the role of elementary triangles, an effective Hamiltonian involving
spin and chirality variables is derived. A mean-field decoupling that retains
the quantum nature of these variables is shown to yield a Hamiltonian that can
be solved exactly, leading to the following predictions: i) The number of low
lying singlet states increase with the number of sites N like 1.15 to the power
N; ii) A singlet-triplet gap remains in the thermodynamic limit; iii) Spinons
form boundstates with a small binding energy. By comparing these properties
with those of the regular Kagome lattice as revealed by numerical experiments,
we argue that this description captures the essential low energy physics of
that model.Comment: 4 pages including 3 figure
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