Розрахунок кумулянтів і параметрів функції розподілу методом Монте-Карло та із рівняння для неї

Calculations results of the moments, central moments, cumulants and parameters of the distribution function of a beam of ions implanted in a solid body were analyzed. To analyze the differences between the results of modeling this process by the Monte Carlo method, which is widely used for practically important targets, and the results of the solution of the corresponding integrodifferential equations that describe ions distribution analytically, in the simple case of axial symmetry of the ion beam, when all moments of odd order along the transverse Cartesian coordinate is considered equal to zero due to the symmetry of the problem. It is shown that the same moments obtained by the Monte Carlo method is not exactly equal to zero, but slowly decrease with an increase in the number of ions, as predicted by statistics, and then remain approximately constant. Increasing the number of ions for Monte Carlo simulation reduces the statistical component of this error, but does not affect on the component arising from the application of a simplified model of ion-atom collisions. Pages of the article in the issue: 112 - 115 Language of the article: UkrainianПроаналізовано результати розрахунку моментів, центральних моментів, кумулянтів та параметрів функції розподілу пучка іонів імплантованих у тверде тіло. Для аналізу відмінностей між результатами моделювання цього процесу методом Монте-Карло, який широко використовується для практично важливих мішеней, та результатами розв’язку інтегродиференціальних рівнянь, які його описують аналітично, розглянуто випадок осьової симетрії пучка іонів, коли всі моменти непарного порядку по поперечній декартовій координаті рівні нулю в силу симетрії задачі. Показано, що ці ж самі моменти, отримані методом Монте-Карло повільно спадають до нуля із збільшенням кількості іонів, як і передбачається статистикою, і залишаються приблизно сталими

Trends of Macroeconomic Models

This article provides an overview and analysis of the ideas of the leading macroeconomists expressed in the issue “Rebuilding Macroeconomic Theory”, Oxford Review of Economic Policy journal. These ideas were expressed in connection with the discussion of the future of macroeconomic models. The motivation for the discussion lies in the poor performance of macroeconomic models before the global economic crisis of 2007–2008 and in the subsequent period of recovery. The main issue considered by economists is the possible changes in the basic neoKeynesian model and DSGE-models as a whole. It was found that there are three directions for the solution of the issue. First, the rejection of the primary role of DSGE-models in the analysis of modern macroeconomics and the use of other types of models. Secondly, the elimination of defciencies of existing models associated with poor justifcation at the micro level, as well as an unsatisfactory description of fnancial frictions. Thirdly, it is possible not to make any targeted efforts, since the class of DSGE-models is still the most efcient. The paper concludes that the second path of development is more preferable

Shape of primary proton spectrum in multi-TeV region from data on vertical muon flux

It is shown, that primary proton spectrum, reconstructed from sea-level and underground data on muon spectrum with the use of QGSJET 01, QGSJET II, NEXUS 3.97 and SIBYLL 2.1 interaction models, demonstrates not only model-dependent intensity, but also model-dependent form. For correct reproduction of muon spectrum shape primary proton flux should have non-constant power index for all considered models, except SIBYLL 2.1, with break at energies around 10-15 TeV and value of exponent before break close to that obtained in ATIC-2 experiment. To validate presence of this break understanding of inclusive spectra behavior in fragmentation region in p-air collisions should be improved, but we show, that it is impossible to do on the basis of the existing experimental data on primary nuclei, atmospheric muon and hadron fluxes.Comment: Submitted to Phys. Rev.

Beta-Delayed fission of 230Am

The exotic decay process of β-delayed fission (βDF) has been studied in the neutron-deficient isotope Am230. The Am230 nuclei were produced in the complete fusion reaction Pb207(Al27,4n)Am230 and separated by using the GARIS gas-filled recoil ion separator. A lower limit for the βDF probability PβDF(Am230)>0.30 was deduced, which so far is the highest value among all known βDF nuclei. The systematics of βDF in the region of Am230 will be discussed

Early onset of ground-state deformation in the neutron-deficient polonium isotopes

In-source resonant ionization laser spectroscopy of the even-$A$ polonium isotopes $^{192-210,216,218}$Po has been performed using the $6p^37s$ $^5S_2$ to $6p^37p$ $^5P_2$ ($\lambda=843.38$ nm) transition in the polonium atom (Po-I) at the CERN ISOLDE facility. The comparison of the measured isotope shifts in $^{200-210}$Po with a previous data set allows to test for the first time recent large-scale atomic calculations that are essential to extract the changes in the mean-square charge radius of the atomic nucleus. When going to lighter masses, a surprisingly large and early departure from sphericity is observed, which is only partly reproduced by Beyond Mean Field calculations.Comment: As submitted to PR

On inconsistency of experimental data on primary nuclei spectra with sea level muon intensity measurements

For the first time a complete set of the most recent direct data on primary cosmic ray spectra is used as input into calculations of muon flux at sea level in wide energy range $E_\mu=1-3\cdot10^5$ GeV. Computations have been performed with the CORSIKA/QGSJET and CORSIKA/VENUS codes. The comparison of the obtained muon intensity with the data of muon experiments shows, that measurements of primary nuclei spectra conform to sea level muon data only up to several tens of GeV and result in essential deficit of muons at higher energies. As it follows from our examination, uncertainties in muon flux measurements and in the description of nuclear cascades development are not suitable to explain this contradiction, and the only remaining factor, leading to this situation, is underestimation of primary light nuclei fluxes. We have considered systematic effects, that may distort the results of the primary cosmic ray measurements with the application of the emulsion chambers. We suggest, that re-examination of these measurements is required with the employment of different hadronic interaction models. Also, in our point of view, it is necessary to perform estimates of possible influence of the fact, that sizable fraction of events, identified as protons, actually are antiprotons. Study of these cosmic ray component begins to attract much attention, but today nothing definite is known for the energies $>40$ GeV. In any case, to realize whether the mentioned, or some other reasons are the sources of disagreement of the data on primaries with the data on muons, the indicated effects should be thoroughly analyzed

Dynamic Separation of Chaotic Signals in the Presence of Noise

The problem of separation of an observed sum of chaotic signals into the individual components in the presence of noise on the path to the observer is considered. A noise threshold is found above which high-quality separation is impossible. Below the threshold, each signal is recovered with any prescribed accuracy. This effect is shown to be associated with the information content of the chaotic signals and a theoretical estimate is given for the threshold.Comment: PDF, 12 pages, 6 figures, submitted to Phys. Rev.