Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation

Einstein's relation E=Mc^2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems which do not accelerate. By contrast, Newtonian approach to the mass is based on an accelerated motion. We study here a particular neoclassical field model of a particle governed by a nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the nonlinear KG equation and its energy density concentrate at a trajectory, then this trajectory and the energy must satisfy the relativistic version of Newton's law with the mass satisfying Einstein's relation. Therefore the internal energy of a localized wave affects its acceleration in an external field as the inertial mass does in Newtonian mechanics. We demonstrate that the "concentration" assumptions hold for a wide class of rectilinear accelerating motions

Integrability and regularity of 3D Euler and equations for uniformly rotating fluids

AbstractWe consider 3D Euler and Navier-Stokes equations describing dynamics of uniformly rotating fluids. Periodic boundary conditions are imposed, and the ratio of domain periods is assumed to be generic (nonresonant). We show that solutions of 3D Euler/Navier-Stokes equations can be decomposed as U(t, x1, x2, x3) = Ũ(t, x1, x2) + V(t, x1, x2, x3) + r where Ũ is a solution of the 2D Euler/Navier-Stokes system with vertically averaged initial data (axis of rotation is taken along the vertical 3). Here r is a remainder of order Ro12a where Roa = (H0U0(Щ0L20) is the anisotropic Rossby number (H0—height, L0—horizontal length scale, Щ0—angular velocity of background rotation, U0—horizontal velocity scale); Roa = (H0L0)Ro where H0L0 is the aspect ratio and Ro = U0(Щ0L0) is a Rossby number based on the horizontal length scale L0. The vector field V(t, x1, x2, x3) which is exactly solved in terms of 2D dynamics of vertically averaged fields is phase-locked to the phases 2Щ0t, τ1(t), and τ2(t). The last two are defined in terms of passively advected scalars by 2D turbulence. The phases τ1(t) and τ2(t) are associated with vertically averaged vertical vorticity curl Ū(t) · e3 and velocity Ū3(t); the last is weighted (in Fourier space) by a classical nonlocal wave operator. We show that 3D rotating turbulence decouples into phase turbulence for V(t, x1, x2, x3) and 2D turbulence for vertically averaged fields Ū(t, x1, x2) if the anisotropic Rossby number Roa is small. The mathematically rigorous control of the error r is used to prove existence on a long time interval T∗ of regular solutions to 3D Euler equations (T∗ → +∞, as Roa → 0); and global existence of regular solutions for 3D Navier-Stokes equations in the small anisotropic Rossby number case

Collecting Samples From Online Services: How to Use Screeners to Improve Data Quality

Increasingly, marketing and consumer researchers rely on online data collection services. While actively-managed data collection services directly assist with the sampling process, minimally-managed data collection services, such as Amazon’s Mechanical Turk (MTurk), leave researchers solely responsible for recruiting, screening, cleaning, and evaluating responses. The research reported here proposes a 2 × 2 framework based on sampling goal and methodology for screening and evaluating the quality of online samples. By sampling goals, screeners can be categorized as selection, which involves matching the sample with the targeted population; or as accuracy, which involves ensuring that participants are appropriately attentive. By methodology, screeners can be categorized as direct, which screens individual responses; and as statistical, which provides quantitative signals of low quality. Multiple screeners for each of the four categories are compared across three MTurk samples, two actively-managed data collection samples (Qualtrics and Dynata), and a student sample. The results suggest the need for screening in every online sample, particularly for the MTurk samples, with the fewest supplier-provided filters. Recommendations are provided for researchers and journal reviewers that provide greater transparency with respect to sample practices

Brewster-angle measurements of sea-surface reflectance using a high resolution spectroradiometer

This paper describes the design, construction and testing of a ship-borne spectroradiometer based on an imaging spectrograph and cooled CCD array with a wavelength range of 350-800 nm and 4 nm spectral sampling. The instrument had a minimum spectral acquisition time of 0.1 s, but in practice data were collected over periods of 10 s to allow averaging of wave effects. It was mounted on a ship's superstructure so that it viewed the sea surface from a height of several metres at the Brewster angle (53 degrees) through a linear polarizing filter. Comparison of sea-leaving spectra acquired with the polarizer oriented horizontally and vertically enabled estimation of the spectral composition of sky light reflected directly from the sea surface. A semi-empirical correction procedure was devised for retrieving water-leaving radiance spectra from these measurements while minimizing the influence of reflected sky light. Sea trials indicated that reflectance spectra obtained by this method were consistent with the results of radiance transfer modelling of case 2 waters with similar concentrations of chlorophyll and coloured dissolved organic matter. Surface reflectance signatures measured at three locations containing blooms of different phytoplankton species were easily discriminated and the instrument was sufficiently sensitive to detect solar-stimulated fluorescence from surface chlorophyll concentrations down to 1 mg m−3

Gut physiology mediates a trade-off between adaptation to malnutrition and susceptibility to food-borne pathogens.

The animal gut plays a central role in tackling two common ecological challenges, nutrient shortage and food-borne parasites, the former by efficient digestion and nutrient absorption, the latter by acting as an immune organ and a barrier. It remains unknown whether these functions can be independently optimised by evolution, or whether they interfere with each other. We report that Drosophila melanogaster populations adapted during 160 generations of experimental evolution to chronic larval malnutrition became more susceptible to intestinal infection with the opportunistic bacterial pathogen Pseudomonas entomophila. However, they do not show suppressed immune response or higher bacterial loads. Rather, their increased susceptibility to P. entomophila is largely mediated by an elevated predisposition to loss of intestinal barrier integrity upon infection. These results may reflect a trade-off between the efficiency of nutrient extraction from poor food and the protective function of the gut, in particular its tolerance to pathogen-induced damage

Multi-scale analysis of compressible viscous and rotating fluids

We study a singular limit for the compressible Navier-Stokes system when the Mach and Rossby numbers are proportional to certain powers of a small parameter \ep. If the Rossby number dominates the Mach number, the limit problem is represented by the 2-D incompressible Navier-Stokes system describing the horizontal motion of vertical averages of the velocity field. If they are of the same order then the limit problem turns out to be a linear, 2-D equation with a unique radially symmetric solution. The effect of the centrifugal force is taken into account

Quantum theory of resonantly enhanced four-wave mixing: mean-field and exact numerical solutions

We present a full quantum analysis of resonant forward four-wave mixing based on electromagnetically induced transparency (EIT). In particular, we study the regime of efficient nonlinear conversion with low-intensity fields that has been predicted from a semiclassical analysis. We derive an effective nonlinear interaction Hamiltonian in the adiabatic limit. In contrast to conventional nonlinear optics this Hamiltonian does not have a power expansion in the fields and the conversion length increases with the input power. We analyze the stationary wave-mixing process in the forward scattering configuration using an exact numerical analysis for up to $10^3$ input photons and compare the results with a mean-field approach. Due to quantum effects, complete conversion from the two pump fields into the signal and idler modes is achieved only asymptotically for large coherent pump intensities or for pump fields in few-photon Fock states. The signal and idler fields are perfectly quantum correlated which has potential applications in quantum communication schemes. We also discuss the implementation of a single-photon phase gate for continuous quantum computation.Comment: 10 pages, 11 figure

Програмне правове забезпечення виконання рішень та застосування практики Європейського суду з прав людини в Україні

Бабін Б. В. Програмне правове забезпечення виконання рішень та застосування практики Європейського суду з прав людини в Україні / Б. В. Бабін // Правове забезпечення ефективного виконання рішень і застосування практики Європейського суду з прав людини : матер. 2-­ї Міжнар. наук.-­практ. конф. (Одеса, 20-­21 вересня 2013 р.) / за ред. С. В. Ківалова ; НУ «ОЮА». – Одеса : Фенікс, 2013. – С. 199-222.У статті визначено специфіку програмного правового забезпечення реалізації в Україні норм та практики ЄСПЛ, вироблено пропозиції з удосконалення такого забезпечення. автор визначився із роллю та перспективами застосування державних програм розвитку, цільових та інтеграційних програм у відповідних процесах, дослідив значен­ня нормотворчого та бюджетного програмування у цій сфері, вказав на наявні недоліки відповідних правових механізмів та ув’язаної з ними державної політики. запропоновано схвалення державної ці­льової програми із запровадження в Україні стандартів Європей­ської конвенції про права людини та відповідної практики ЄСПЛ на п’ятирічний період із визначенням міністерства юстиції України як її головного відповідального виконавця.В статье определена специфика программного правового обеспече­ния реализации в украине норм и практики еспч, разработаны пред­ложения по совершенствованию такого обеспечения. Автор определился с ролью и перспективами использования государственных программ развития, целевых и интеграционных программ в соответ­ствующих правовых процессах, исследовал значение нормотворчес­ кого и бюджетного программирования в данной сфере, указал на имеющиеся недостатки соответствующих правовых механизмов и увязанной с ними государственной политики. предложено приня­тие государственной целевой программы по внедрению в Украине стандартов Европейской конвенции о правах человека и соответ­ствующей практики еспч на пятилетний период с определением Министерства юстиции Украины как ее главного ответственного исполнителя.The article outlines the specifics of programming legal prohibition the re­alization ECtHR’s norms and practice in Ukraine, it produces the propos­als for improving such programmatic implementation. Author determined the role and prospects of using the state development programs, state targeted and integration programs in relevant legal processes, investigat­ed the value of the legislative and budgetary programming in this area, pointed out the disadvantages of specified legal mechanisms and of the state policy, tallied with them. There proposed approving the State target program for implementation in Ukraine of the standards of the ECHR and the relevant case law of the ECthR on five­year period with the definition of the Ministry of Justice of Ukraine as its main responsible body

Anisotropy and non-universality in scaling laws of the large scale energy spectrum in rotating turbulence

Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale $L_f$, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the \textit{inverse cascade} range at a small but fixed Rossby number, {$\mathcal{R}o_f \approx 0.05$}. Several {numerical simulations with} helical and non-helical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve the inverse cascade range with {reasonably} large Reynolds number, the analysis is based on large eddy simulations which include the effect of helicity on eddy viscosity and eddy noise. Thus, we model the small scales and resolve explicitly the large scales. We show that the large-scale energy spectrum has at least two solutions: one that is consistent with Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of energy in two-dimensional (2D) turbulence with a {$\sim k_{\perp}^{-5/3}$} scaling, and the other that corresponds to a steeper {$\sim k_{\perp}^{-3}$} spectrum in which the three-dimensional (3D) modes release a substantial fraction of their energy per unit time to 2D modes. {The spectrum that} emerges {depends on} the anisotropy of the forcing function{,} the former solution prevailing for forcings in which more energy is injected into 2D modes while the latter prevails for isotropic forcing. {In the case of anisotropic forcing, whence the energy} goes from the 2D to the 3D modes at low wavenumbers, large-scale shear is created resulting in another time scale $\tau_{sh}$, associated with shear, {thereby producing} a $\sim k^{-1}$ spectrum for the {total energy} with the 2D modes still following a {$\sim k_{\perp}^{-5/3}$} scaling