Attractiveness of periodic orbits in parametrically forced systemswith time-increasing friction

We consider dissipative one-dimensional systems subject to a periodic force and study numerically how a time-varying friction affects the dynamics. As a model system, particularly suited for numerical analysis, we investigate the driven cubic oscillator in the presence of friction. We find that, if the damping coefficient increases in time up to a final constant value, then the basins of attraction of the leading resonances are larger than they would have been if the coefficient had been fixed at that value since the beginning. From a quantitative point of view, the scenario depends both on the final value and the growth rate of the damping coefficient. The relevance of the results for the spin-orbit model are discussed in some detail.Comment: 30 pages, 6 figure

Integral operators with the generalized sine-kernel on the real axis

The asymptotic properties of integral operators with the generalized sine kernel acting on the real axis are studied. The formulas for the resolvent and the Fredholm determinant are obtained in the large x limit. Some applications of the results obtained to the theory of integrable models are considered.Comment: 17 pages, 2 Postscript figures, submitted to Theor. Math. Phy

Глобальне опитування дорослих щодо вживання тютюну (GATS): звіт за результатами дослідження: Україна, 2010

Tobacco use is a major preventable cause of premature death and disease worldwide, presently causing over 5 million deaths each year and expected to cause over 8 million deaths yearly by 2030. Within the European Region, tobacco is responsible for approximately 1.6 million deaths a year. The World Health Organization (WHO) Tobacco Free Initiative (TFI) aims to reduce the global burden of disease and death caused by tobacco, thereby protecting present and future generations from the devastating health, social, environmental, and economic consequences of tobacco consumption and exposure to tobacco smoke. This will be accomplished by providing global policy leadership -- promoting the WHO Framework Convention on Tobacco Control (FCTC), as well as the MPOWER package of tobacco policies as a key entry point to the WHO FCTC. Within the European Region, 46 countries and the European Community have ratified the Treaty. Ukraine ratified the WHO FCTC in 2006. In August 2006, the WHO and the United States Centers for Disease Control and Prevention (CDC) convened an expert consultation to discuss adult tobacco surveillance and made recommendations for the development of a standard survey protocol. The Global Adult Tobacco Survey (GATS) enables countries to collect data on key tobacco control measures in the adult population. The aim of the GATS is to collect data on tobacco use and tobacco control measures using a standardized questionnaire, sample design, and data collection/management procedures among adults aged 15 years and older. Results from the GATS will assist countries in the formulation, tracking and implementation of effective tobacco control interventions, and countries will be able to compare results of their survey with results from other countries implementing the GATS.Вживання тютюну – основна причина передчасних смертей та хвороб в усьому світі, яким людство здатне запобігти. На сьогоднішній день від вживання тютюну щороку гине понад 5 мільйонів людей; очікується, що до 2030 року ця цифра зросте до 8 мільйонів смертей щорічно. У Європейському регіоні тютюн винен у смерті близько 1,6 мільйона людей на рік. Ініціатива "Звільнення від тютюну" (Tobacco Free Initiative (TFI)) Всесвітньої Організації Охорони Здоров’я (ВООЗ) покликана зменшити глобальний тягар хвороб і смертей, спричинених вживанням тютюну, таким чином захищаючи теперішні та майбутні покоління від шкідливих наслідків куріння для здоров’я, негативних соціальних, економічних та екологічних наслідків, пов’язаних із вживанням тютюну та впливом тютюнового диму. Цієї мети буде досягнуто через глобальне стратегічне лідерство – просування Рамкової конвенції ВООЗ із боротьби проти тютюну, так само як і через комплекс антитютюнових заходів MPOWER, що є ключовим інструментом реалізації Рамкової конвенції. У Європейському регіоні Конвенцію ратифікували 46 країн та Європейське співтовариство. Україна ратифікувала Рамкову конвенцію ВООЗ із боротьби проти тютюну 2006 року. У серпні 2006 року ВООЗ і Центри з контролю та профілактики захворювань США (ЦКПЗ) скликали експертну нараду, аби обговорити питання нагляду за вживанням тютюну серед дорослого населення й виробити рекомендації щодо розроблення стандартизованої програми опитування. "Глобальне опитування дорослого населення щодо вживання тютюну" (The Global Adult Tobacco Survey – GATS) дає країнам змогу зібрати дані щодо ключових антитютюнових заходів серед дорослого населення. Мета проекту GATS – збір даних щодо вживання тютюну і заходів контролю над тютюном із використанням стандартизованих анкети, дизайну вибірки й процедур збору та обробки даних серед населення віком 15 років і старші. Результати проекту GATS допоможуть країнам у розробленні, відстеженні і втіленні ефективних заходів контролю над тютюном, і країни матимуть змогу порівняти свої результати із результатами інших країн, які беруть участь у проекті.Bloomberg Global Initiative to reduce tobacco us

The effect of a warm electron beam on slow electron-acoustic solitons

The effects of the inclusion of finite drift speed of a warm electron component on the existence of arbitrary amplitude slow electron-acoustic solitons are investigated in a model with ions and cool, warm, and hot electrons. All plasma species are treated as adiabatic fluids. For fixed densities of the cool, warm, and hot electrons, the admissible Mach number ranges of the supported negative potential solitons are found to widen with increasing warm electron beam speed, up to a maximum value of vdbwo = 0.7. Beyond this maximum value, the soliton Mach number ranges become narrower and vanish completely at vdbwo = 1.084 where a switch to positive polarity solitons occurs. For a fixed value of the drift speed of the warm electrons, the cool electron density value at which the switch to positive polarity soliton occurs is the lowest when there is no streaming of the warm electrons but increases with increasing drift speed

Bloch electron in a magnetic field and the Ising model

The spectral determinant det(H-\epsilon I) of the Azbel-Hofstadter Hamiltonian H is related to Onsager's partition function of the 2D Ising model for any value of magnetic flux \Phi=2\pi P/Q through an elementary cell, where P and Q are coprime integers. The band edges of H correspond to the critical temperature of the Ising model; the spectral determinant at these (and other points defined in a certain similar way) is independent of P. A connection of the mean of Lyapunov exponents to the asymptotic (large Q) bandwidth is indicated.Comment: 4 pages, 1 figure, REVTE

Nonintersecting Brownian motions on the half-line and discrete Gaussian orthogonal polynomials

We study the distribution of the maximal height of the outermost path in the model of $N$ nonintersecting Brownian motions on the half-line as $N\to \infty$, showing that it converges in the proper scaling to the Tracy-Widom distribution for the largest eigenvalue of the Gaussian orthogonal ensemble. This is as expected from the viewpoint that the maximal height of the outermost path converges to the maximum of the $\textrm{Airy}_2$ process minus a parabola. Our proof is based on Riemann-Hilbert analysis of a system of discrete orthogonal polynomials with a Gaussian weight in the double scaling limit as this system approaches saturation. We consequently compute the asymptotics of the free energy and the reproducing kernel of the corresponding discrete orthogonal polynomial ensemble in the critical scaling in which the density of particles approaches saturation. Both of these results can be viewed as dual to the case in which the mean density of eigenvalues in a random matrix model is vanishing at one point.Comment: 39 pages, 4 figures; The title has been changed from "The limiting distribution of the maximal height of nonintersecting Brownian excursions and discrete Gaussian orthogonal polynomials." This is a reflection of the fact that the analysis has been adapted to include nonintersecting Brownian motions with either reflecting of absorbing boundaries at zero. To appear in J. Stat. Phy

Small BGK waves and nonlinear Landau damping

Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p)) of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria and any spatial period. Indeed, in W^{s,p} (s<1+(1/p)) neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose's linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some W^{s,p} (p>1,s>1+(1/p)) neighborhood. Furthermore, when p=2,we prove that there exist no nontrivial invariant structures in the H^{s} (s>(3/2)) neighborhood of stable homogeneous states. These results suggest the long time dynamics in the W^{s,p} (s>1+(1/p)) and particularly, in the H^{s} (s>(3/2)) neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for linearly stable homogeneous state. This suggests that the contrasting dynamics in W^{s,p} spaces with the critical power s=1+(1/p) is a trully nonlinear phenomena which can not be traced back to the linear level

Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices

We compute analytically the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W=X^T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value =N/c decreases for large N as $\sim \exp[-\frac{\beta}{2}N^2 \Phi_{-}(\frac{2}{\sqrt{c}}+1;c)]$, where \beta=1,2 correspond respectively to real and complex Wishart matrices, c=N/M < 1 and \Phi_{-}(x;c) is a large deviation function that we compute explicitly. The result for the Anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of constrained Wishart matrices whose eigenvalues are forced to be smaller than a fixed barrier. The numerical simulations are in excellent agreement with the analytical predictions.Comment: Published version. References and appendix adde