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

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

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

Thermodynamic Limit Of The Ginzburg-Landau Equations

We investigate the existence of a global semiflow for the complex Ginzburg-Landau equation on the space of bounded functions in unbounded domain. This semiflow is proven to exist in dimension 1 and 2 for any parameter values of the standard cubic Ginzburg-Landau equation. In dimension 3 we need some restrictions on the parameters but cover nevertheless some part of the Benjamin-Feijer unstable domain.Comment: uuencoded dvi file (email: [email protected]

Anomalous diffusion in polymers: long-time behaviour

We study the Dirichlet boundary value problem for viscoelastic diffusion in polymers. We show that its weak solutions generate a dissipative semiflow. We construct the minimal trajectory attractor and the global attractor for this problem.Comment: 13 page

Energy transfer in turbulence under rotation

It is known that rapidly rotating turbulent flows are characterized by the emergence of simultaneous upscale and downscale energy transfer. Indeed, both numerics and experiments show the formation of large-scale anisotropic vortices together with the development of small-scale dissipative structures. However the organization of interactions leading to this complex dynamics remains unclear. Two different mechanisms are known to be able to transfer energy upscale in a turbulent flow. The first is characterized by two-dimensional interactions among triads lying on the two-dimensional, three-component (2D3C) manifold, namely on the Fourier plane perpendicular to the rotation axis. The second mechanism is three-dimensional and consists of interactions between triads with the same sign of helicity (homochiral). Here, we present a detailed numerical study of rotating flows using a suite of high Reynolds number direct numerical simulations within different parameter regimes to analyze both upscale and downscale cascade ranges. We find that the upscale cascade at wave numbers close to the forcing scale is generated by increasingly dominant homochiral interactions which couple the three-dimensional bulk and the 2D3C plane. This coupling produces an accumulation of energy in the 2D3C plane, which then transfers energy to smaller wave numbers thanks to the two-dimensional mechanism. In the forward cascade range, we find that the energy transfer is dominated by heterochiral triads and is dominated primarily by interaction within the fast manifold where $k_z\ne0$. We further analyze the energy transfer in different regions in the real-space domain. In particular, we distinguish high-strain from high-vorticity regions and we uncover that while the mean transfer is produced inside regions of strain, the rare but extreme events of energy transfer occur primarily inside the large-scale column vortices

Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent

In this paper the long time behaviour of the solutions of 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H_{0}^{1}(\Omega)\times L_{2}(\Omega) and then it is proved that this global attractor is a bounded subset of H^{2}(\Omega)\times H^{2}(\Omega) and also a global attractor in H^{2}(\Omega)\cap H_{0}^{1}(\Omega)\times H_{0}^{1}(\Omega)

Some qualitative properties of the solutions of the Magnetohydrodynamic equations for nonlinear bipolar fluids

In this article we study the long-time behaviour of a system of nonlinear Partial Differential Equations (PDEs) modelling the motion of incompressible, isothermal and conducting modified bipolar fluids in presence of magnetic field. We mainly prove the existence of a global attractor denoted by \A for the nonlinear semigroup associated to the aforementioned systems of nonlinear PDEs. We also show that this nonlinear semigroup is uniformly differentiable on \A. This fact enables us to go further and prove that the attractor \A is of finite-dimensional and we give an explicit bounds for its Hausdorff and fractal dimensions.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s10440-014-9964-

Patterns of suspended particulate matter across the continental margin in the Canadian Beaufort Sea during summer

The particulate beam attenuation coefficient at 660&thinsp;nm, cp(660), was measured in conjunction with properties of suspended particle assemblages in August 2009 within the Canadian Beaufort Sea continental margin, a region heavily influenced by freshwater and sediment discharge from the Mackenzie River, but also by sea ice melt. The mass concentration of suspended particulate matter (SPM) ranged from 0.04 to 140&thinsp;g&thinsp;m−3, its composition varied from mineral to organic dominated, and the median particle diameter determined over the range 0.7–120&thinsp;µm varied from 0.78 to 9.45&thinsp;µm, with the fraction of particles &lt;1&thinsp;µm in surface waters reflecting the degree influenced by river water. Despite this range in particle characteristics, a strong relationship between SPM and cp(660) was found and used to determine SPM distributions across the shelf based on measurements of cp(660) taken during summer seasons of 2004, 2008, and 2009. SPM spatial patterns on the stratified shelf reflected the vertically sheared two-layer estuarine circulation and SPM sources (i.e., fluvial inputs, bottom resuspension, and biological productivity). Along-shelf winds generated lateral Ekman flows, isopycnal movements, and upwelling or downwelling at the shelf break. Cross-shelf transects measured during three summers illustrate how sea ice meltwater affects river plume extent, while the presence of meltwater on the shelf was associated with enhanced near-bottom SPM during return flow of upwelled Pacific-origin water. SPM decreased sharply past the shelf break with further transport of particulate matter occurring near the bottom and in interleaving nepheloid layers. These findings expand our knowledge of particle distributions in the Beaufort Sea controlled by river discharge, sea ice, and wind, each of which is sensitive to weather and climate variations.</p