4,966 research outputs found
Random trees between two walls: Exact partition function
We derive the exact partition function for a discrete model of random trees
embedded in a one-dimensional space. These trees have vertices labeled by
integers representing their position in the target space, with the SOS
constraint that adjacent vertices have labels differing by +1 or -1. A
non-trivial partition function is obtained whenever the target space is bounded
by walls. We concentrate on the two cases where the target space is (i) the
half-line bounded by a wall at the origin or (ii) a segment bounded by two
walls at a finite distance. The general solution has a soliton-like structure
involving elliptic functions. We derive the corresponding continuum scaling
limit which takes the remarkable form of the Weierstrass p-function with
constrained periods. These results are used to analyze the probability for an
evolving population spreading in one dimension to attain the boundary of a
given domain with the geometry of the target (i) or (ii). They also translate,
via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main
modifications in Sect. 5-6 and conclusio
A low noise 410-495 heterodyne two tuner mixer, using submicron Nb/Al2O3/Nb tunneljunctions
A 410-495 GHz heterodyne receiver, with an array of two Nb/Al2O3/Nb tunneljunctions as mixing element is described. The noise temperature of this receiver is below 230 K (DSB) over the whole frequency range, and has lowest values of 160 K in the 435-460 GHz range. The calculated DSB mixergain over the whole frequency range varies from -11.9 plus or minus 0.6 dB to -12.6 plus or minus 0.6 dB and the mixer noise is 90 plus or minus 30 K
Comparison of measured and predicted performance of a SIS waveguide mixer at 345 GHz
The measured gain and noise of a SIS waveguide mixer at 345 GHz have been compared with theoretical values, calculated from the quantum mixer theory using a three port model. As a mixing element, we use a series array of two Nb-Al2O3-Nb SIS junctions. The area of each junction is 0.8 sq microns and the normal state resistance is 52 omega. The embedding impedance of the mixer has been determined from the pumped DC-IV curves of the junction and is compared to results from scale model measurements (105 x). Good agreement was obtained. The measured mixer gain, however, is a factor of 0.45 plus or minus 0.5 lower than the theoretical predicted gain. The measured mixer noise temperature is a factor of 4-5 higher than the calculated one. These discrepancies are independent on pump power and are valid for a broad range of tuning conditions
Multipole radiation in a collisonless gas coupled to electromagnetism or scalar gravitation
We consider the relativistic Vlasov-Maxwell and Vlasov-Nordstr\"om systems
which describe large particle ensembles interacting by either electromagnetic
fields or a relativistic scalar gravity model. For both systems we derive a
radiation formula analogous to the Einstein quadrupole formula in general
relativity.Comment: 21 page
The impact of climate change on incomes and convergence in Africa
© 2019 Elsevier Ltd Climate change is projected to detrimentally affect African countriesâ economic development, while income inequalities across economies is among the highest on the planet. However, it is projected that income levels would converge on the continent. Hitherto there is limited evidence on how climate change could affect projected income convergence, accelerating, slowing down, or even reversing this process. Here, we analyze convergence considering climate-change damages, by employing an economic model embedding the three dimensions of risks at the country-level: exposure, vulnerability and hazards. The results show (1) with historical mean climate-induced losses between 10 and 15 percent of GDP per capita growth, the majority of African economies are poorly adapted to their current climatic conditions, (2) Western and Eastern African countries are projected to be the most affected countries on the continent and (3) As a consequence of these heightened impacts on a number of countries, inequalities between countries are projected to widen in the high warming scenario compared to inequalities in the low and without warming scenarios. To mitigate the impacts of economic development and inequalities across countries, we stress (1) the importance of mitigation ambition and Africa's leadership in keeping global mean temperature increase below 1.5 °C, (2) the need to address the current adaptation deficit as soon as possible, (3) the necessity to integrate quantitatively climate risks in economic and development planning and finally (4) we advocate for the generalization of a special treatment for the most vulnerable countries to access climate-related finance. The analysis raises issues on the ability of African countries to reach their SDGs targets and the potential increasing risk of instability, migration across African countries, of decreased trade and economic cooperation opportunities as a consequence of climate change â exacerbating its negative consequences
Waves attractors in rotating fluids: a paradigm for ill-posed Cauchy problems
In the limit of low viscosity, we show that the amplitude of the modes of
oscillation of a rotating fluid, namely inertial modes, concentrate along an
attractor formed by a periodic orbit of characteristics of the underlying
hyperbolic Poincar\'e equation. The dynamics of characteristics is used to
elaborate a scenario for the asymptotic behaviour of the eigenmodes and
eigenspectrum in the physically relevant r\'egime of very low viscosities which
are out of reach numerically. This problem offers a canonical ill-posed Cauchy
problem which has applications in other fields.Comment: 4 pages, 5 fi
On static shells and the Buchdahl inequality for the spherically symmetric Einstein-Vlasov system
In a previous work \cite{An1} matter models such that the energy density
and the radial- and tangential pressures and
satisfy were considered in the context of
Buchdahl's inequality. It was proved that static shell solutions of the
spherically symmetric Einstein equations obey a Buchdahl type inequality
whenever the support of the shell, satisfies
Moreover, given a sequence of solutions such that then the
limit supremum of was shown to be bounded by
In this paper we show that the hypothesis
that can be realized for Vlasov matter, by constructing a
sequence of static shells of the spherically symmetric Einstein-Vlasov system
with this property. We also prove that for this sequence not only the limit
supremum of is bounded, but that the limit is
since for Vlasov matter.
Thus, static shells of Vlasov matter can have arbitrary close to
which is interesting in view of \cite{AR2}, where numerical evidence is
presented that 8/9 is an upper bound of of any static solution of the
spherically symmetric Einstein-Vlasov system.Comment: 20 pages, Late
Recommended from our members
The impact of climate change on incomes and convergence in Africa
© 2019 Elsevier Ltd Climate change is projected to detrimentally affect African countriesâ economic development, while income inequalities across economies is among the highest on the planet. However, it is projected that income levels would converge on the continent. Hitherto there is limited evidence on how climate change could affect projected income convergence, accelerating, slowing down, or even reversing this process. Here, we analyze convergence considering climate-change damages, by employing an economic model embedding the three dimensions of risks at the country-level: exposure, vulnerability and hazards. The results show (1) with historical mean climate-induced losses between 10 and 15 percent of GDP per capita growth, the majority of African economies are poorly adapted to their current climatic conditions, (2) Western and Eastern African countries are projected to be the most affected countries on the continent and (3) As a consequence of these heightened impacts on a number of countries, inequalities between countries are projected to widen in the high warming scenario compared to inequalities in the low and without warming scenarios. To mitigate the impacts of economic development and inequalities across countries, we stress (1) the importance of mitigation ambition and Africa's leadership in keeping global mean temperature increase below 1.5 °C, (2) the need to address the current adaptation deficit as soon as possible, (3) the necessity to integrate quantitatively climate risks in economic and development planning and finally (4) we advocate for the generalization of a special treatment for the most vulnerable countries to access climate-related finance. The analysis raises issues on the ability of African countries to reach their SDGs targets and the potential increasing risk of instability, migration across African countries, of decreased trade and economic cooperation opportunities as a consequence of climate change â exacerbating its negative consequences
Force distributions in a triangular lattice of rigid bars
We study the uniformly weighted ensemble of force balanced configurations on
a triangular network of nontensile contact forces. For periodic boundary
conditions corresponding to isotropic compressive stress, we find that the
probability distribution for single-contact forces decays faster than
exponentially. This super-exponential decay persists in lattices diluted to the
rigidity percolation threshold. On the other hand, for anisotropic imposed
stresses, a broader tail emerges in the force distribution, becoming a pure
exponential in the limit of infinite lattice size and infinitely strong
anisotropy.Comment: 11 pages, 17 figures Minor text revisions; added references and
acknowledgmen
Arc Statistics in Clusters: Galaxy Contribution
The frequency with which background galaxies appear as long arcs as a result
of gravitational lensing by foreground clusters of galaxies has recently been
found to be a very sensitive probe of cosmological models by Bartelmann et al.
(1998). They have found that such arcs would be expected far less frequently
than observed (by an order of magnitude) in the currently favored model for the
universe, with a large cosmological constant . Here we
analyze whether including the effect of cluster galaxies on the likelihood of
clusters to generate long-arc images of background galaxies can change the
statistics. Taking into account a variety of constraints on the properties of
cluster galaxies, we find that there are not enough sufficiently massive
galaxies in a cluster for them to significantly enhance the cross section of
clusters to generate long arcs. We find that cluster galaxies typically enhance
the cross section by only .Comment: 19 pages, 1 figure, uses aasms4.sty, submitted to Ap
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