The scalability of the matrices in direct Trefftz method in 2D Laplace problem

This paper presents an interesting property of the matrices that may be obtained with the use of direct Trefftz method. It is proved analytically for 2D Laplace problem that values of the elements of matrices describing the capacitance of two scaled domains are inversely proportional to the scalability factor. As an example of the application the capacitance extraction problem is chosen. Concise description of the algorithm in which the scalability property can be utilized is given. Furthermore some numerical results of the algorithm are presented

Magnetic impurity transition in a 'd+s'-wave superconductor

We consider the superconducting state of $d+s$ symmetry with finite concentration of Anderson impurities in the limit $\Delta_s/\Delta_d \ll 1$. The model consists of a BCS-like term in the Hamiltonian and the Anderson impurity treated in the self-consistent large-$N$ mean field approximation. Increasing impurity concentration or lowering the ratio $\Delta_s/\Delta_d$ drives the system through a transition from a state with two sharp peaks at low energies and exponentially small density of states at the Fermi level to one with $N(0) \simeq (\Delta_s/\Delta_d)^2$. This transition is discontinuous if the energy of the impurity resonance is the smallest energy scale in the problem.Comment: 3 pages, 2 figures, presented at the International Conference on Quantum Criticality and Novel Phases (QCNP09, Dresden

Multimodal transition and stochastic antiresonance in squid giant axons

The experimental data of N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, and G. Matsumoto, Physica D \textbf{43}, 318 (1990), on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the Hodgkin-Huxley model. The minimum of the firing rate as a function of the stimulus amplitude $I_0$ in the high-frequency regime is due to the multimodal transition. Below this singular point only odd multiples of the driving period remain and the system is highly sensitive to noise. The coefficient of variation has a maximum and the firing rate has a minimum as a function of the noise intensity which is an indication of the stochastic coherence antiresonance. The model calculations reproduce the frequency of occurrence of the most common modes in the vicinity of the transition. A linear relation of output frequency vs. $I_0$ for above the transition is also confirmed.Comment: 5 pages, 9 figure

A Framework for Blockchain Interoperability and Runtime Selection

The suitability of a particular blockchain for a given use case depends mainly on the blockchain's functional and non-functional properties. Such properties may vary over time, and thus, a selected blockchain may become unsuitable for a given use case. This uncertainty may hinder the widespread adoption of blockchain technologies in general. To mitigate the impact of volatile blockchain properties, we propose a framework that monitors several blockchains, allows the user to define functional and non-functional requirements, determines the most appropriate blockchain, and enables the switchover to that chain at runtime. Our evaluation using a reference implementation shows that switching to another blockchain can save cost and enable users to benefit from better performance and a higher level of trust

Multichannel Kondo impurities in superconductors

We discuss the effect of multichannel Kondo impurities on superconductivity. In the strong coupling regime such impurities are pairbreakers, in contrast to the ordinary Kondo effect. Measurements of $T_c$-suppression may help in identifying impurities displaying this more exotic exchange coupling to the conduction band.Comment: 3 pages, 4 figures, uuencoded compressed postscript file, submitted to SCES'94 (Amsterdam

Cellular Automata Model of Macroevolution

In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting from one common ancestor they appear by "mutations" of existent species, and then survive or extinct depending on the balance of local ecological interactions. Monte-Carlo numerical simulations show that this model is able to qualitatively reproduce phenomena that have been observed in other models and in nature.Comment: 8 pages, 3 figures, Fourteenth National Conference on Application of Mathematics in Biology and Medicine, Leszno 2008 (POLAND

Expansion of Kes 73, a Shell Supernova Remnant Containing a Magnetar

Of the 30 or so Galactic magnetars, about 8 are in supernova remnants (SNRs). One of the most extreme magnetars, 1E 1841-045, is at the center of the SNR Kes 73 (G27.4+0.0), whose age is uncertain. We measure its expansion using three Chandra observations over 15 yr, obtaining a mean rate of 0.023% +/- 0.002% per yr. For a distance of 8.5 kpc, we obtain a shell velocity of 1100 km/s and infer a blast-wave speed of 1400 km/s. For Sedov expansion into a uniform medium, this gives an age of 1800 yr. Derived emission measures imply an ambient density of about 2 cm$^{-3}$ and an upper limit on the swept-up mass of about 70 solar masses, with lower limits of tens of solar masses, confirming that Kes 73 is in an advanced evolutionary stage. Our spectral analysis shows no evidence for enhanced abundances as would be expected from a massive progenitor. Our derived total energy is $1.9 \times 10^{51}$ erg, giving a very conservative lower limit to the magnetar's initial period of about 3 ms, unless its energy was lost by non-electromagnetic means. We see no evidence of a wind-blown bubble as would be produced by a massive progenitor, or any evidence that the progenitor of Kes 73/1E 1841-045 was anything but a normal red supergiant producing a Type IIP supernova, though a short-lived stripped-envelope progenitor cannot be absolutely excluded. Kes 73's magnetar thus joins SGR 1900+14 as magnetars resulting from relatively low-mass progenitors.Comment: 9 pages, 2 figures, 2 tables, accepted for publication in Ap