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

Data-driven PDE discovery with evolutionary approach

The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation discovery techniques. The existing methods of PDE (partial derivative equations) discovery are bound with the sparse regression. However, sparse regression is restricting the resulting model form, since the terms for PDE are defined before regression. The evolutionary approach described in the article has a symbolic regression as the background instead and thus has fewer restrictions on the PDE form. The evolutionary method of PDE discovery (EPDE) is described and tested on several canonical PDEs. The question of robustness is examined on a noised data example

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

Controls on the CO2 seasonal cycle

Surface pressure measurement performed by the Viking landers show substantial variations in pressure on seasonal timescales that are characterized by two local minima and two local maxima. These variations have widely been attributed to the seasonal condensation and sublimation of CO2 in the two polar regions. It has been somewhat of a surprise that the amplitude of the minimum and maximum that is dominated by the CO2 cycle in the north was much weaker than the corresponding amplitude of the south-dominated extrema. Another surprise was that the seasonal pressure cycle during years 2 and 3 of the Viking mission was so similar to that for year 1, despite the occurrence of two global dust storms during year 1 and none during years 2 and 3. An energy balance model that incorporates dynamical factors from general circulation model (GCM) runs in which the atmospheric dust opacity and seasonal date were systematically varied was used to model the observed seasonal pressure variations. The energy balance takes account of the following processes in determining the rates of CO2 condensation and sublimation at each longitudinal and latitudinal grid point: solar radiation, infrared radiation from the atmosphere and surface, subsurface heat conduction, and atmospheric heat advection. Condensation rates are calculated both at the surface and in the atmosphere. In addition, the energy balance model also incorporates information from the GCM runs on seasonal redistribution of surface pressure across the globe. Estimates of surface temperature of the seasonal CO2 caps were used to define the infrared radiative losses from the seasonal polar caps. The seasonal pressure variations measured at the Viking lander sites were closely reproduced

Effects of Hydrogen Annealing, Sulfur Segregation and Diffusion on the Cyclic Oxidation Resistance of Superalloys: a Review

This review is based on the phenomenon of improved oxide scale adhesion for desulfurized superalloys. The proposed adhesion mechanism involves sulfur interfacial segregation and scale-metal bond weakening. Sulfur surface segregation on superalloys is examined as a function of temperature and sulfur content and related to classical behavior predicted by the McLean isotherm. Effective desulfurization to less than 1 ppmw can be accomplished by hydrogen annealing and is governed by sulfur diffusion kinetics in nickel. Hydrogen annealing results in excellent cyclic oxidation resistance for a number of advanced superalloys. The concept of a critical sulfur content is discussed in terms of practical annealing conditions and section thicknesses

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 Einstein-Vlasov sytem/Kinetic theory

The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic- and special relativistic physics, e.g. to model the dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In 1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (e.g. fluid models). The first part of this paper gives an introduction to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental in order to get a good comprehension of kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity (http://www.livingreviews.org

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