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 countries’ 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 – 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 $\rho\geq 0,$ and the radial- and tangential pressures $p\geq 0$ and $q,$ satisfy $p+q\leq\Omega\rho, \Omega\geq 1,$ 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, $[R_0,R_1], R_0>0,$ satisfies $R_1/R_0<1/4.$ Moreover, given a sequence of solutions such that $R_1/R_0\to 1,$ then the limit supremum of $2M/R_1$ was shown to be bounded by $((2\Omega+1)^2-1)/(2\Omega+1)^2.$ In this paper we show that the hypothesis that $R_1/R_0\to 1,$ 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 $2M/R_1$ is bounded, but that the limit is $((2\Omega+1)^2-1)/(2\Omega+1)^2=8/9,$ since $\Omega=1$ for Vlasov matter. Thus, static shells of Vlasov matter can have $2M/R_1$ arbitrary close to $8/9,$ which is interesting in view of \cite{AR2}, where numerical evidence is presented that 8/9 is an upper bound of $2M/R_1$ of any static solution of the spherically symmetric Einstein-Vlasov system.Comment: 20 pages, Late

The impact of climate change on incomes and convergence in Africa

© 2019 Elsevier Ltd Climate change is projected to detrimentally affect African countries’ 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 – 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 $\Omega_\Lambda \sim 0.7$. 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 $\lesssim 15$.Comment: 19 pages, 1 figure, uses aasms4.sty, submitted to Ap