The hunt for self-similar core collapse

Core collapse is a prominent evolutionary stage of self-gravitating systems. In an idealised collisionless approximation, the region around the cluster core evolves in a self-similar way prior to the core collapse. Thus, its radial density profile outside the core can be described by a power law, $\rho \propto r^{-\alpha}$. We aim to find the characteristics of core collapse in $N$-body models. In such systems, a complete collapse is prevented by transferring the binding energy of the cluster to binary stars. The contraction is, therefore, more difficult to identify. We developed a method that identifies the core collapse in $N$-body models of star clusters based on the assumption of their homologous evolution. We analysed different models (equal- and multi-mass), most of which exhibit patterns of homologous evolution, yet with significantly different values of $\alpha$: the equal-mass models have $\alpha \approx 2.3$, which agrees with theoretical expectations, the multi-mass models have $\alpha \approx 1.5$ (yet with larger uncertainty). Furthermore, most models usually show sequences of separated homologous collapses with similar properties. Finally, we investigated a correlation between the time of core collapse and the time of formation of the first hard binary star. The binding energy of such a binary usually depends on the depth of the collapse in which it forms, for example from $100\,kT$ to $10^4\,kT$ in the smallest equal-mass to the largest multi-mass model, respectively. However, not all major hardenings of binaries happened during the core collapse. In the multi-mass models, we see large transfers of binding energy of $\sim 10^4\,kT$ to binaries that occur on the crossing timescale and outside of the periods of the homologous collapses.Comment: 12 pages, 5 tables, 14 figures, Accepted for publication in A&

Experimental Observation of Localized Modes in a Dielectric Square Resonator

We investigated the frequency spectra and field distributions of a dielectric square resonator in a microwave experiment. Since such systems cannot be treated analytically, the experimental studies of their properties are indispensable. The momentum representation of the measured field distributions shows that all resonant modes are localized on specific classical tori of the square billiard. Based on these observations a semiclassical model was developed. It shows excellent agreement with all but a single class of measured field distributions that will be treated separately.Comment: 6 pages, 5 figures, 1 tabl

Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models

Boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices $K^{\pm}(\theta)$. For the six vertex model the general solution depending on four arbitrary parameters is found. For the $A_{n-1}$ models all diagonal solutions are found. The associated integrable magnetic Hamiltonians are explicitly derived.Comment: 9 pages,latex, LPTHE-PAR 92-4

Climatic potential and risks for apple growing by 2040

The impact of climatic change in 1971–2040 on the potential production areas and risks to nine apple cultivars (Malus domestica Borkh.) was studied over continental Finland using agro-climatic indices and gridded daily mean (Tm) and minimum temperatures from the Rossby Centre regional atmospheric climate model (RCA3) with SRES A2. Point data on daily minimum temperatures from 14 weather stations and low and high warming scenarios were also used. From the 1970’s to the present day, the areas of successful maturing of fruits have strongly expanded northwards. It is predicted that in 2011–2040, the warming of climate will allow expansion of commercial production in the south-eastern lake area, and a wider selection of cultivars for home gardens up to latitudes 65–66°N. Risk of extremely low temperatures (Tm< -26 °C) has reduced from 1980’s to the present but may not reduce much more in 2011–2040. Risk to shoots from fluctuating temperatures in winter and spring is likely to increase under the high warming scenario, more in the south-west than in the south-east. Risk to trees from cold days (Tm< -15 °C) with a concurrent thin snow cover is not predicted to increase. In the western inland of the country, below latitude 63°N, and in the south-western coast areas the frost risk during flowering may increase, especially in the early flowering cultivars. In order to adapt to and gain from the climatic change, breeding and testing targets should be modified within five years and they should include reduced sensitivity to temperature fluctuation in winter, late flowering, and frost tolerance of flowers

Efficient interface conditions for the finite difference beam propagation method

It is shown that by adapting the refractive indexes in the vicinity of interfaces, the 2-D beam propagation method based on the finite-difference (FDBPM) scheme can be made much more effective. This holds especially for TM modes propagating in structures with high-index contrasts, such as surface polaritons. A short discussion is given on the applicability of the FDBP

Exact signal correlators in continuous quantum measurements

This article provides an exact formula for the signal n-point correlation functions of detectors continuously measuring an arbitrary quantum system, in the presence of detection imperfections. The derivation uses only continuous stochastic calculus techniques, but the final result is easily understood from a discrete picture of repeated interactions with qubits or from a parallel with continuous matrix product states. This result provides a crude yet efficient a way to estimate system parameters directly from experimental data, without requiring non-linear state reconstruction