Chaos in the Outer Solar System

We study the effect of a perturber on the energy and angular momentum of a test particle on a highly eccentric orbit. We find that both the energy and angular momentum of the test particle are adiabatic invariants when the perturber is on a circular orbit with radius much smaller than the periaps of the test particle. We derive analytical expression for the energy change, or kick, of the test particle with every periaps passage. Using this kick function we formulate mapping for the highly eccentric test particle. We also analyze the stability of resonances and find conditions for asymmetric libration to occur. The resonance widths for highly eccentric orbits are calculated and the criterion for the onset of global chaos is determined

Self-dual SU(2) invariant Einstein metrics and modular dependence of theta-functions

We simplify Hitchin's description of SU(2)-invariant self-dual Einstein metrics, making use of the tau-function of related four-pole Schlesinger system.Comment: A wrong sign in the formula for W_1 is corrected; we thank Owen Dearricott who pointed out this mistake in the original version of the pape

Primordial Bispectrum Information from CMB Polarization

After the precise observations of the Cosmic Microwave Background (CMB) anisotropy power spectrum, attention is now being focused on the higher order statistics of the CMB anisotropies. Since linear evolution preserves the statistical properties of the initial conditions, observed non-Gaussianity of the CMB will mirror primordial non-Gaussianity. Single field slow-roll inflation robustly predicts negligible non-Gaussianity so an indication of non-Gaussianity will suggest alternative scenarios need to be considered. In this paper we calculate the information on primordial non-Gaussianity encoded in the polarization of the CMB. After deriving the optimal weights for a cubic estimator we evaluate the Signal-to-Noise ratio of the estimator for WMAP, Planck and an ideal cosmic variance limited experiment. We find that when the experiment can observe CMB polarization with good sensitivity, the sensitivity to primordial non-Gaussianity increases by roughly a factor of two. We also test the weakly non-Gaussian assumption used to derive the optimal weight factor by calculating the degradation factor produced by the gravitational lensing induced connected four-point function. The physical scales in the radiative transfer functions are largely irrelevant for the constraints on the primordial non-Gaussianity. We show that the total (S/N)^2 is simply proportional to the number of observed pixels on the sky.Comment: To be submitted to PRD, 25 pages, 6 figure

Consistency relation for single scalar inflation

Single scalar field inflation with a generic, non-quadratic in derivatives, field Lagrangian is considered. It is shown that non-Gaussianity of curvature perturbations is characterized by two dimensionless amplitudes. One of these amplitudes can be expressed in terms of the usual inflationary observables -- the scalar power, the tensor power, and the tensor index. This consistency relation provides an observational test for the single scalar inflation.Comment: 6 page

CMB Anisotropies from Outflows in Lyman Break Galaxies

Thomson scattering of the Cosmic Microwave Background (CMB) on moving electrons in the outflows of Lyman Break Galaxies (LBGs) at redshifts 2-8 contributes to the small-scale CMB anisotropies. The net effect produced by each outflow depends on its level of deviation from spherical symmetry, caused either by an anisotropic energy injection from the nuclear starburst or quasar activity, or by an inhomogeneous intergalactic environment. We find that for plausible outflow parameters consistent with spectroscopic observations of LBGs, the induced CMB anisotropies on arcminute scales reach up to $\sim 1 \mu$K, comparable to the level produced during the epoch of reionization.Comment: 5 pages, 2 figures; to be submitted to MNRA

Effect of cyclosporin and tacrolimus on kidney function in liver recipients

The objective of the study was to evaluate the dynamics of renal function, depending on the use of various calcineurin inhibitors in the long-term postoperative period in liver recipients in real clinical practic

Gender and age differences of compliance in liver transplant recipients

The aim of the paper was to evaluate the compliance in patients who have undergone orthotopic liver transplantation (OLT). A voluntary anonymous survey was conducted among liver transplant recipients. The control group included patients with chronic non-infectious diseases requiring persistent treatment. Liver transplant patients have higher levels of general, behavioral and emotional compliance compared to patients with chronic diseases. Neither gender nor age differences were identified in any types of complianc

Limits on non-Gaussianities from WMAP data

We develop a method to constrain the level of non-Gaussianity of density perturbations when the 3-point function is of the "equilateral" type. Departures from Gaussianity of this form are produced by single field models such as ghost or DBI inflation and in general by the presence of higher order derivative operators in the effective Lagrangian of the inflaton. We show that the induced shape of the 3-point function can be very well approximated by a factorizable form, making the analysis practical. We also show that, unless one has a full sky map with uniform noise, in order to saturate the Cramer-Rao bound for the error on the amplitude of the 3-point function, the estimator must contain a piece that is linear in the data. We apply our technique to the WMAP data obtaining a constraint on the amplitude f_NL^equil of "equilateral" non-Gaussianity: -366 < f_NL^equil < 238 at 95% C.L. We also apply our technique to constrain the so-called "local" shape, which is predicted for example by the curvaton and variable decay width models. We show that the inclusion of the linear piece in the estimator improves the constraint over those obtained by the WMAP team, to -27 < f_NL^local < 121 at 95% C.L.Comment: 20 pages, 12 eps figure

Bifurcation stability of spherical shells under dispersed cracking in shear materials

З використанням структурно-ймовірнісного підходу до моделювання сумісного процесу тріщиноутворення й деформування матеріалів розроблено методику розв'язання задач біфуркаційної стійкості тонкостінних елементів конструкцій із пошкоджуваних матеріалів при одноразовому та повторюваному (циклічному) навантаженні. На прикладі рівномірно обтисненої сферичної оболонки показано, що при повторюваному навантаженні тонкостінні елементи конструкцій із пошкоджуваних зсувом матеріалів можуть втрачати стійкість при навантаженнях, менших верхніх критичних. Неоднозначність критичних навантажень пов'язана із залежністю процесу накопичення пошкодженості в матеріалі тонкостінних конструкцій від рівня та характеру навантаження. Зазначене явище може бути однією з можливих причин розкиду експериментальних даних та розбіжності теоретичних і експериментальних результатів з визначення критичних навантажень для сферичних і циліндричних оболонок.The present paper deals with the method for solution of the bifurcation stability of thin-walled structural elements of damage materials under single and cyclic loading. This method is developed by using a structural-probabilistic approach to modeling joint processes of cracking and deformation of materials. The phenomenon of the bifurcation stability in elastic part of deformation of thin-walled structures of damaging materials under cyclic loading, the values of which are smaller than corresponding static critical efforts, are considered. The main purpose of solving such problems is to determine of the limiting number of a given load, at which the structure loses stability. It should be mentioned, that the possibility of loss stability of thin-walled structures at loads less than the upper critical is related to the type of failure of the material, such as destruction by rupture or destruction by shear. In the case of destruction by rupture, when microcracks are parallel to the direction of compressive stress, this phenomenon does not take place, because in this type of damage under repeated compression of the same load a material behaves as a continuous medium. The density of microcracks is not increased. This type of stability loss is possible for thin-walled structures made of materials which are damaged by shear, when microcracks are formed on the sloping planes to the direction of the load. Under such type of microfractures, the effective cross-sectional area decreases. It leads to increase of true tangential stresses in the material under constant conditional stresses of repetitive loading. The proposed method consists of the following: construction of the constitutive equations for the damaged material by using the Eshelbi method for determining the effective elastic properties of the damaged medium; the model of microdamages accumulation basing on the Treska Saint-Venant, fracture criterion which is formulated in full true tangential stresses in random sections of structural elements and two-parameter power law distribution of limit values of shear microstrength of structural elements and procedures for solving problems bifurcation stability of spherical shells. It should be noted, that the true stresses differ from the conditional in that the former refer to the areas of the damaged medium whereas the latter to the areas of the continuous medium. On an example of uniformly compressed spherical shell it is shown that the structire can lose stability under loads smaller than the upper critical. From the expression for the critical stress it follows that the ambiguity of critical loads depends on the density of the accumulated damages in material in thin-walled structures, which is associated with the nature of the load. This phenomenon could be one of the possible reason of dispersion in the experimental data and the discrepancy between theoretical and experimental results. For steel spherical shell 15X2MF numerical results are obtained