Numerical Calibration of Steiner trees

International audienceIn this paper we propose a variational approach to the Steiner tree problem, which is based on calibrations in a suitable algebraic environment for polyhedral chains which represent our candidates. This approach turns out to be very efficient from numerical point of view and allows to establish whether a given Steiner tree is optimal. Several examples are provided

Pion susceptibility of the QCD vacuum from an effective quark-quark interaction

A modified method for calculating the pion vacuum susceptibility from an effective quark-quark interaction model is derived. Within this approach it is shown that the pion vacuum susceptibility is free of ultraviolet divergence and is much smaller than the previous estimations.Comment: 13 pages, 2 figure

Measuring the Hidden Aspects of Solar Magnetism

2008 marks the 100th anniversary of the discovery of astrophysical magnetic fields, when George Ellery Hale recorded the Zeeman splitting of spectral lines in sunspots. With the introduction of Babcock's photoelectric magnetograph it soon became clear that the Sun's magnetic field outside sunspots is extremely structured. The field strengths that were measured were found to get larger when the spatial resolution was improved. It was therefore necessary to come up with methods to go beyond the spatial resolution limit and diagnose the intrinsic magnetic-field properties without dependence on the quality of the telescope used. The line-ratio technique that was developed in the early 1970s revealed a picture where most flux that we see in magnetograms originates in highly bundled, kG fields with a tiny volume filling factor. This led to interpretations in terms of discrete, strong-field magnetic flux tubes embedded in a rather field-free medium, and a whole industry of flux tube models at increasing levels of sophistication. This magnetic-field paradigm has now been shattered with the advent of high-precision imaging polarimeters that allow us to apply the so-called "Second Solar Spectrum" to diagnose aspects of solar magnetism that have been hidden to Zeeman diagnostics. It is found that the bulk of the photospheric volume is seething with intermediately strong, tangled fields. In the new paradigm the field behaves like a fractal with a high degree of self-similarity, spanning about 8 orders of magnitude in scale size, down to scales of order 10 m.Comment: To appear in "Magnetic Coupling between the Interior and the Atmosphere of the Sun", eds. S.S. Hasan and R.J. Rutten, Astrophysics and Space Science Proceedings, Springer-Verlag, Heidelberg, Berlin, 200

Малошумящий программируемый усилитель постоянного тока с дистанционным управлением

Introduction. The developmental direction of information-measuring systems used to record, pre-process and analyse excess low-frequency noise (flicker noise) in modern experimental technology is well known. Every measuring channel is presented in the form of a multistage circuit with specified parameters at each stage. This creates difficulties in adapting a measuring system to specific experimental conditions. While the solution may be to unify all the components of the channel, the problem lies in estimating the intrinsic noise of the electronic elements which provide a change in amplifier parameters. Objective. To analyse the intrinsic noise of electronic potentiometers. To develop a low-noise unified DC amplifier with the possibility of external digital control parameters. To study the characteristics of a DC amplifier thus developed. Materials and methods. The superposition method was used to perform theoretical calculation of noise gain for each component of a non-inverting amplifier. Experimental studies were based on a system consisting of a low-noise amplifying path and spectroanalyser using the data acquisition module E14-440. Software "Power-Graph" was used. Results. The results of the theoretical analysis of noise amplification for metal-film resistors and experimental studies of the characteristics of electronic potentiometers indicated that their noise voltages specific values are almost identical. The use of a digital potentiometer as a feedback element and a low-noise bipolar-powered bias source (AD8400) permitted the implementation of a unified module with cascading capability. External digital control was based on a single-chip microcontroller PIC18F2550, using the "Master-Slave" channel level protocol and ASCII-command-line interface based on RS-485 network. This control enabled adaptation for measuring electronic component noise, low currents and voltages, flicker noise and the construction of systems for information collecting and processing. Conclusion. The theoretical and practical results achieved herein enable the design of multichannel distributed DC measuring systems. The systems will offer adaptability for measuring channels to the tasks required, and the possibility of correction of real time characteristics.Введение. В современной технике эксперимента известно направление, связанное с разработкой информационно-измерительных систем регистрации и анализа избыточных низкочастотных шумов. Любой измерительный канал представлен в виде многокаскадной схемы с заданными параметрами каждого каскада, что затрудняет адаптацию измерительной системы к конкретным условиям эксперимента. Решением проблемы является унификация всех компонентов канала, однако при этом одной из основных проблем является оценка собственных шумов электронных элементов, обеспечивающих изменение параметров усилителя. Цель работы. Анализ собственных шумов электронных потенциометров, разработка малошумящего унифицированного усилителя постоянного тока с возможностью внешнего цифрового управления параметрами и исследование его характеристик. Материалы и методы. С помощью метода суперпозиции произведен теоретический расчет шумового усиления для каждого компонента неинвертирующего усилителя. Экспериментальные исследования проводились на базе установки, представляющей собой малошумящий усилительный тракт и спектроанализатор на основе модуля сбора данных E14-440 и программного обеспечения «PowerGraph». Результаты. По результатам теоретических расчетов шумового усиления для металлопленочных резисторов и экспериментальных исследований характеристик электронных потенциометров показано, что их удельные значения напряжений шумов практически идентичны. Использование цифрового потенциометра в качестве элемента обратной связи и малошумящего источника смещения с двухполярным питанием (AD8400), позволяют реализовать на их основе унифицированный модуль с возможностью каскадирования. Внешнее цифровое управление на основе однокристального микроконтроллера PIC18F2550, разработанного протокола канального уровня «Master-Slave» и ASCII-интерфейса командной строки на базе сети RS-485 позволяет адаптировать его к задачам измерения шумов электронных компонентов, малых токов и напряжений, фликкер-шумов, построения распределенных систем сбора и обработки информации. Заключение. Полученные теоретические и практические результаты делают возможным проектирование многоканальных распределенных измерительных систем постоянного тока с адаптацией измерительных каналов к поставленным задачам и возможностями программной коррекции характеристик в реальном времени

Radiating Shear-Free Gravitational Collapse with Charge

We present a new shear free model for the gravitational collapse of a spherically symmetric charged body. We propose a dissipative contraction with radiation emitted outwards. The Einstein field equations, using the junction conditions and an ansatz, are integrated numerically. A check of the energy conditions is also performed. We obtain that the charge delays the black hole formation and it can even halt the collapse.Comment: 22 pages, 9 figures. It has been corrected several typos and included several references. Accepted for publication in GR

Coulomb excitation of 68^{68}Ni at safe energies

The $B(E2;0^+\to2^+)$ value in $^{68}$Ni has been measured using Coulomb excitation at safe energies. The $^{68}$Ni radioactive beam was post-accelerated at the ISOLDE facility (CERN) to 2.9 MeV/u. The emitted $\gamma$ rays were detected by the MINIBALL detector array. A kinematic particle reconstruction was performed in order to increase the measured c.m. angular range of the excitation cross section. The obtained value of 2.8$^{+1.2}_{-1.0}$ 10$^2$ e$^2$fm$^4$ is in good agreement with the value measured at intermediate energy Coulomb excitation, confirming the low $0^+\to2^+$ transition probability.Comment: 4 pages, 5 figure

Generation of Ultrastable Microwaves via Optical Frequency Division

There has been increased interest in the use and manipulation of optical fields to address challenging problems that have traditionally been approached with microwave electronics. Some examples that benefit from the low transmission loss, agile modulation and large bandwidths accessible with coherent optical systems include signal distribution, arbitrary waveform generation, and novel imaging. We extend these advantages to demonstrate a microwave generator based on a high-Q optical resonator and a frequency comb functioning as an optical-to-microwave divider. This provides a 10 GHz electrical signal with fractional frequency instability <8e-16 at 1 s, a value comparable to that produced by the best microwave oscillators, but without the need for cryogenic temperatures. Such a low-noise source can benefit radar systems, improve the bandwidth and resolution of communications and digital sampling systems, and be valuable for large baseline interferometry, precision spectroscopy and the realization of atomic time

Dynamics of the Acetylcholinesterase Tetramer

Acetylcholinesterase rapidly hydrolyzes the neurotransmitter acetylcholine in cholinergic synapses, including the neuromuscular junction. The tetramer is the most important functional form of the enzyme. Two low-resolution crystal structures have been solved. One is compact with two of its four peripheral anionic sites (PAS) sterically blocked by complementary subunits. The other is a loose tetramer with all four subunits accessible to solvent. These structures lacked the C-terminal amphipathic t-peptide (WAT domain) that interacts with the proline-rich attachment domain (PRAD). A complete tetramer model (AChEt) was built based on the structure of the PRAD/WAT complex and the compact tetramer. Normal mode analysis suggested that AChEt could exist in several conformations with subunits fluctuating relative to one another. Here, a multiscale simulation involving all-atom molecular dynamics and Cα-based coarse-grained Brownian dynamics simulations was carried out to investigate the large-scale intersubunit dynamics in AChEt. We sampled the ns-μs timescale motions and found that the tetramer indeed constitutes a dynamic assembly of monomers. The intersubunit fluctuation is correlated with the occlusion of the PAS. Such motions of the subunits “gate” ligand-protein association. The gates are open more than 80% of the time on average, which suggests a small reduction in ligand-protein binding. Despite the limitations in the starting model and approximations inherent in coarse graining, these results are consistent with experiments which suggest that binding of a substrate to the PAS is only somewhat hindered by the association of the subunits

Theory of disk accretion onto supermassive black holes

Accretion onto supermassive black holes produces both the dramatic phenomena associated with active galactic nuclei and the underwhelming displays seen in the Galactic Center and most other nearby galaxies. I review selected aspects of the current theoretical understanding of black hole accretion, emphasizing the role of magnetohydrodynamic turbulence and gravitational instabilities in driving the actual accretion and the importance of the efficacy of cooling in determining the structure and observational appearance of the accretion flow. Ongoing investigations into the dynamics of the plunging region, the origin of variability in the accretion process, and the evolution of warped, twisted, or eccentric disks are summarized.Comment: Mostly introductory review, to appear in "Supermassive black holes in the distant Universe", ed. A.J. Barger, Kluwer Academic Publishers, in pres

Electrophysical properties of nanoporous cerium dioxide–water system

The impedance of nanoporous cerium dioxide with adsorbed water is investigated in the frequency range 103–104 Hz at temperatures near the water–ice phase transition. Here we show that the manifestation of impedance peculiarities at phase transition is caused by the dielectric constant of the matrix