Directional Soliton and Breather Beams

Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the uni-directional nonlinear Schr\"odinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field. As the coherence is diagonal, the scale in the crest direction becomes finite, consequently, a beam dynamics forms. Spatio-temporal measurements of the water surface elevation are obtained by stereo-reconstructing the positions of the floating markers placed on a regular lattice and recorded with two synchronized high-speed cameras. Experimental results, based on the predictions obtained from the (2D+1) hyperbolic NLSE equation, are in excellent agreement with the theory. Our study proves the existence of such unique and coherent wave packets and has serious implications for practical applications in optical sciences and physical oceanography. Moreover, unstable wave fields in this geometry may explain the formation of directional large amplitude rogue waves with a finite crest length within a wide range of nonlinear dispersive media, such as Bose-Einstein condensates, plasma, hydrodynamics and optics

Simulation as a method for asymptotic system behavior identification (e.g. water frog hemiclonal population systems)

Studying any system requires development of ways to describe the variety of its conditions. Such development includes three steps. The first one is to identify groups of similar systems (associative typology). The second one is to identify groups of objects which are similar in characteristics important for their description (analytic typology). The third one is to arrange systems into groups based on their predicted common future (dynamic typology). We propose a method to build such a dynamic topology for a system. The first step is to build a simulation model of studied systems. The model must be undetermined and simulate stochastic processes. The model generates distribution of the studied systems output parameters with the same initial parameters. We prove the correctness of the model by aligning the parameters sets generated by the model with the set of the original systems conditions evaluated empirically. In case of a close match between the two, we can presume that the model is adequately describing the dynamics of the studied systems. On the next stage, we should determine the probability distribution of the systems transformation outcome. Such outcomes should be defined based on the simulation of the transformation of the systems during the time sufficient to determine its fate. If the systems demonstrate asymptotic behavior, its phase space can be divided into pools corresponding to its different future state prediction. A dynamic typology is determined by which of these pools each system falls into. We implemented the pipeline described above to study water frog hemiclonal population systems. Water frogs (Pelophylax esculentus complex) is an animal group displaying interspecific hybridization and non-mendelian inheritance

Mean field approximation of two coupled populations of excitable units

The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the inter-ensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains where the stationary state is stable, the scenarios for the onset and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical inter-population couplings.Comment: 5 figure

Interaction of marine geodesy, satellite technology and ocean physics

The possible applications of satellite technology in marine geodesy and geodetic related ocean physics were investigated. Four major problems were identified in the areas of geodesy and ocean physics: (1) geodetic positioning and control establishment; (2) sea surface topography and geoid determination; (3) geodetic applications to ocean physics; and (4) ground truth establishment. It was found that satellite technology can play a major role in their solution. For solution of the first problem, the use of satellite geodetic techniques, such as Doppler and C-band radar ranging, is demonstrated to fix the three-dimensional coordinates of marine geodetic control if multi-satellite passes are used. The second problem is shown to require the use of satellite altimetry, along with accurate knowledge of ocean-dynamics parameters such as sea state, ocean tides, and mean sea level. The use of both conventional and advanced satellite techniques appeared to be necessary to solve the third and fourth problems

Measuring the spin of the primary black hole in OJ287

The compact binary system in OJ287 is modelled to contain a spinning primary black hole with an accretion disk and a non-spinning secondary black hole. Using Post Newtonian (PN) accurate equations that include 2.5PN accurate non-spinning contributions, the leading order general relativistic and classical spin-orbit terms, the orbit of the binary black hole in OJ287 is calculated and as expected it depends on the spin of the primary black hole. Using the orbital solution, the specific times when the orbit of the secondary crosses the accretion disk of the primary are evaluated such that the record of observed outbursts from 1913 up to 2007 is reproduced. The timings of the outbursts are quite sensitive to the spin value. In order to reproduce all the known outbursts, including a newly discovered one in 1957, the Kerr parameter of the primary has to be $0.28 \pm 0.08$. The quadrupole-moment contributions to the equations of motion allow us to constrain the `no-hair' parameter to be $1.0\:\pm\:0.3$ where 0.3 is the one sigma error. This supports the `black hole no-hair theorem' within the achievable precision. It should be possible to test the present estimate in 2015 when the next outburst is due. The timing of the 2015 outburst is a strong function of the spin: if the spin is 0.36 of the maximal value allowed in general relativity, the outburst begins in early November 2015, while the same event starts in the end of January 2016 if the spin is 0.2Comment: 12 pages, 6 figure

A note on Keen's model: The limits of Schumpeter's "Creative Destruction"

This paper presents a general solution for a recent model by Keen for endogenous money creation. The solution provides an analytic framework that explains all significant dynamical features of Keen's model and their parametric dependence, including an exact result for both the period and subsidence rate of the Great Moderation. It emerges that Keen's model has just two possible long term solutions: stable growth or terminal collapse. While collapse can come about immediately from economies that are nonviable by virtue of unsuitable parameters or initial conditions, in general the collapse is preceded by an interval of exponential growth. In first approximation, the duration of that exponential growth is half a period of a sinusoidal oscillation. The period is determined by reciprocal of the imaginary part of one root of a certain quintic polynomial. The real part of the same root determines the rate of growth of the economy. The coefficients of that polynomial depend in a complicated way upon the numerous parameters in the problem and so, therefore, the pattern of roots. For a favorable choice of parameters, the salient root is purely real. This is the circumstance that admits the second possible long term solution, that of indefinite stable growth, i.e. an infinite period.Comment: 25 pages, 12 figures, JEL classification: B50, C62, C63, E12, E4