Dynamics Of Rays Research Articles

Feeding ecology and trophic position of a Mediterranean endemic ray: consistency between sexes, maturity stages and seasons

The study of trophic ecology of marine predators is crucial to better understand the ecological factors that condition their role within marine ecosystems. Here we investigated the trophic habits and position of a Mediterranean endemic predator, the starry ray, Raja asterias. Specifically, we quantified the diet composition of this endemic ray in a highly exploited area of the NW Mediterranean, and we evaluated the effects of sex, maturity-stage and season on its feeding habits. Our results revealed that the starry ray is a predator of crustaceans (crabs and shrimps), and to a lower extent on teleosts, molluscs and polychaetes. This species has a high trophic position within its food web and feeds mainly on crabs (mainly Liocarcinus depurator and Goneplax rhomboides), independent of their sex, maturity-stage or season. The great importance of crabs in the diet of starry ray may be due to the fact that crabs are the dominant crustaceans in terms of biomass and abundance in the area where starry rays were collected, thus allowing them to exploit the most abundant food resource. Since the starry ray has shown a progressive decline on the catch, further research is needed to analyse the main drivers of starry ray dynamics in the Western Mediterranean Sea. Our results present important new data that will allow us to further explore the population dynamics of starry rays and the role of crustacean availability and fishing activity.

THE CHARACTERISTIC CAUCHY PROBLEM FOR DIRAC FIELDS ON CURVED BACKGROUNDS

On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighborhood of the vertex. This is done for data in L2 and we give an explicit definition of the space of data on the light-cone producing a solution in H1. The method is based on energy estimates following Hörmander [A remark on the characteristic Cauchy problem, J. Funct. Anal.93(2) (1990) 270–277]. The data for the characteristic Cauchy problem are only a half of the field, the other half is recovered from the characteristic data by integration of the constraints, consisting of the restriction of the Dirac equation to the cone. A precise analysis of the dynamics of light rays near the vertex of the cone is done in order to understand the integrability of the constraints; for this, the Geroch–Held–Penrose formalism is used.

Transient chaos in optical metamaterials

We investigate the dynamics of light rays in two classes of optical metamaterial systems: (1) time-dependent system with a volcano-shaped, inhomogeneous and isotropic refractive-index distribution, subject to external electromagnetic perturbations and (2) time-independent system consisting of three overlapping or non-overlapping refractive-index distributions. Utilizing a mechanical-optical analogy and coordinate transformation, the wave-propagation problem governed by the Maxwell's equations can be modeled by a set of ordinary differential equations for light rays. We find that transient chaotic dynamics, hyperbolic or nonhyperbolic, are common in optical metamaterial systems. Due to the analogy between light-ray dynamics in metamaterials and the motion of light in matter as described by general relativity, our results reinforce the recent idea that chaos in gravitational systems can be observed and studied in laboratory experiments.

Hydrodynamic view of electrodynamics: energy rays and electromagnetic effective stress

Energy rays (‘photon trajectories’) based upon the hydrodynamic formulation of electrodynamics are presented for time-dependent electromagnetic wave propagation. We derive Cauchy's equation of motion for the electromagnetic effective force governing the dynamics of energy rays. The effective force generated by the electromagnetic effective stress provides a surface force acting on the energy fluid element. For the head-on collision of two electromagnetic Gaussian pulses, the electromagnetic effective force, analogous to the role played by the quantum force in Bohmian mechanics, guides these non-crossing energy rays. For an electromagnetic pulse traveling from free space to a dielectric medium, the energy rays guided by the electromagnetic effective stress display reflection and refraction at the interface.

Rooms with a view: A novel approach to iterated multidimensional wave conversion

Ray tracing in the presence of linear mode conversion leads to a ‘splitting’ of an incoming ray into two outgoing rays. When the rays are confined to a cavity, the rays can re-enter the conversion region many times, leading to iterated conversion. In this paper, we present new methods for the analysis of this problem. These involve a shift from local to global methods of analysis, and a shift in emphasis from the study of ray evolution in the dispersion surface to the study of the iterated dynamics of rays crossing the conversion surface. The analytical methods are quite general and can be applied in phase spaces of arbitrary dimension. In two spatial dimensions, ( x, y), i.e. with a four-dimensional ray space, ( x, y, k x , k y ), rays are confined to three-dimensional regions called rooms, with one room for each wave type. In these rooms the rays do not cross, but when they intersect the conversion surface a family of converted rays is produced in the other room. The use of rooms allows a full view of the phase space dynamics of the iterated conversion of ray families. A simple two-dimensional model, inspired by the Budden resonance model, is presented as an example of these ideas.

Pump and amplification dynamics of gamma rays in a nuclear medium with the hidden population inversion

The features of the pump dynamics of isomeric nuclei excited by X-rays of a repetitively pulsed relativistic electron beam followed by the production of a medium with the negative absorption of gamma quanta are analysed. In the extended nuclear medium, the pump excites a travelling hidden-population-inversion wave with the anisotropic gamma amplification, which becomes positive in the case of the excess over the critical pump parameter equal to the product of the peak spectral power density of the X-ray source and the relative duration of an ultrashort relativistic electron bunch. In the alternative scheme with orthogonal directions of pumping X-rays and a flux of amplified gamma quanta, the absence of the amplification anisotropy opens up the possibility for constructing a standard two-mirror resonator with Bragg single-crystal reflectors. The critical peak value of the spectral pump power density is compared with the known characteristics of relativistic-electron X-ray sources by examples of some nuclides.

Asymptotic analysis of high-frequency acoustic modes in rapidly rotating stars

The asteroseismology of rapidly rotating pulsating stars is hindered by our poor knowledge of the effect of the rotation on the oscillation properties. Here we present an asymptotic analysis of high-frequency acoustic modes in rapidly rotating stars. We study the Hamiltonian dynamics of acoustic rays in uniformly rotating polytropic stars and show that the phase space structure has a mixed character, regions of chaotic trajectories coexisting with stable structures like island chains or invariant tori. In order to interpret the ray dynamics in terms of acoustic mode properties, we then use tools and concepts developed in the context of quantum physics. Accordingly, the high-frequency acoustic spectrum is a superposition of frequency subsets associated with dynamically independent phase space regions. The sub-spectra associated with stable structures are regular and can be modelled through EBK quantization methods while those associated with chaotic regions are irregular but with generic statistical properties. The results of this asymptotic analysis are successfully confronted with the properties of numerically computed high-frequency acoustic modes. The implications for the asteroseismology of rapidly rotating stars are discussed.

Dynamics of charged particle fluxes in Earth’s troposphere since 1990

Temporal variations of charged particle fluxes in the Earth’s atmosphere at altitudes below ∼16 km do not always correlate with variations above ∼16 km and the dynamics of primary cosmic rays. Variations of particle fluxes in the troposphere grew in the 1990s, rather synchronously in the Murmansk and Moscow regions but not in Antarctica. During the last decade, the annual wave in the opposite phase with temperature has often been observed in the northern hemisphere at all altitudes below ∼16 km. The phase of this variation coincides with the phase of the expected temperature effect of cosmic ray muons but its amplitude is several times larger than expected.

Wave chaos in rapidly rotating stars

The effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens fresh perspectives for rapidly rotating star seismology and also provides a potentially observable manifestation of wave chaos in a large-scale natural system.

The sea and ocean 3D acoustic waveguide: rays dynamics and chaos phenomena

It has been carried out modeling of the sea and ocean 3D acoustic waveguide. On the basis of Hamiltonian equations of rays it is studied a dynamics of rays. It has been shown that for acoustic waveguide in a shallow sea with non-level bottom under the rays propagation in a waveguide dependence of the of temporal frequency upon the output angle represents a fractal measure in accordance with Abdullaev-Zaslavsky result. For the ocean 3D acoustic waveguide on the basis of solving the eiconal equations in the Hamiltonian form it has been studied the fractal dynamics, including the chaotic one. There are presented the data of numerical solution of equations for the typical acoustic channel in the North-Atlantic region. The conditions for the Arnold diffusion effect realization are discussed.

Dynamics of cosmic rays in the atmospheric electrostatic field and production of particles by thunderclouds

Acceleration of particles in the atmospheric electrostatic field is considered taking into account multiple elastic scattering. The critical field strength necessary for implementing runaway effect of charged particles under different initial conditions is analytically obtained. The process of cyclic particle production in strong thunderstorm fields is considered. It is shown that this mechanism can be used to describe the strong increases (sometimes with exponential segments) observed during thunderstorms in the intensity of the soft component.

Simulating the effects of temperature on individual and population growth of Rhinoptera bonasus: a coupled bioenergetics and matrix modeling approach

Cownose rays Rhinoptera bonasus typify the K-selected life history strategy that makes their population dynamics susceptible to variation in natural and anthropogenic factors. We used an individual-based bioenergetics model, coupled to a matrix projection model, to predict how water temperatures warmer and cooler than current conditions would affect the individual growth and the population dynamics of cownose rays. The bioenergetics model simulated the daily growth, survival, and reproductive output of a cohort of female individuals from birth over their lifetime. Warmer and cooler temperature scenarios under alternative assumptions about ray movement were simulated. Under warmer conditions, daily consumption rate would have to increase by about 12% or weights- at-age would decrease by 10 to 17%, while under cooler conditions, daily consumption would have to decrease by about 14% or weights-at-age would increase by about 15%. Slowed individual growth under warmer water temperatures translated into slowed population growth rate, decreased net reproductive rate, longer generation time, and higher but delayed age-specific reproductive val- ues. For example, under the scenario that resulted in the slowest individual growth rates, the popu- lation growth rate would decrease from 0.027 to 0.005 yr -1 . Population growth rates were more sen- sitive to variation in survival rates, especially those of mature age-classes, than to fertility rates. Our coupling of an individual-based bioenergetics model with a matrix projection model offers a poten- tially powerful approach for relating how, with limited to moderate information, changes in environ- mental variables and habitat that affect individual growth can be expressed as population-level responses.

Chaos in composite billiards

The mechanisms and features of the chaotic behavior in billiards with ray splitting (refraction) are considered. In contrast to ordinary billiards, the law of motion in composite billiards that is coded with a sequence of ray visits to different media is shown to be deterministically chaotic. The analysis is performed in terms of a geometrical-dynamical approach in which a symmetric phase space is used instead of the ordinary Hamiltonian phase space. The chaotization elements in composite billiards of a general position are studied. The dynamics of rays in ring billiards consisting of two concentric media with different refractive indices is considered.

Quantum chaos in optical systems: the annular billiard.

We study the dielectric annular billiard as a quantum chaotic model of a micro-optical resonator. It differs from conventional billiards with hard-wall boundary conditions in that it is partially open and composed of two dielectric media with different refractive indices. The interplay of reflection and transmission at the different interfaces gives rise to rich dynamics of classical light rays and to a variety of wave phenomena. We study the ray propagation in terms of Poincaré surfaces of section and complement it with full numerical solutions of the corresponding wave equations. We introduce and develop an S-matrix approach to open optical cavities which proves very suitable for the identification of resonances of intermediate width that will be most important in future applications like optical communication devices. We show that the Husimi representation is a useful tool in characterizing resonances and establish the ray-wave correspondence in real and phase space. While the simple ray picture provides a good qualitative description of certain system classes, only the wave description reveals the quantitative details.

Optimized absorption in a chaotic double-clad fiber amplifier

Double-clad fibers with a doped single-mode core and a noncylindrical multimode chaotic cladding are shown to provide optimal pump-power absorption in power amplifiers. Based on the chaotic dynamics of rays in such fibers, we propose a quantitative theory for the pump-absorption ratio and favorably compare the predictions of the theory with numerical results obtained through an adapted beam-propagation scheme.

Three-dimensional classical dynamics of acoustic rays in a quasirealistic ocean

Simulations on multimegameter range scales are presented for the dynamics of classical acoustic rays in a three-dimensional ocean waveguide which contains sound-speed inhomogeneities derived from an ocean general circulation model. The inhomogeneities include scales equal to and larger than mesoscales (>20 km). Both horizontal and vertical two-dimensional deterministic ray propagation through mesoscale environments are known to exhibit chaotic behavior in the sense of exponential divergence of neighboring trajectories that are initially infinitesimally separated. The extra degree of freedom provided by an acoustic phase speed that is fully three dimensional allows a richer, more complex structure to be revealed. We use a Hamiltonian prescription for the ray dynamics to reveal this structure geometrically via the phase space evolution of the associated Lagrangian manifold. The linear transformation matrices for this system which describe how elements of phase space volume distort under the action of the dynamics are examined for a large subset of trajectories. It is shown that their associated exponential rates of divergence vary orders of magnitude. The relative importance of horizontal versus vertical folding in the trajectory manifolds is also discussed.

Peculiarities of the solar proton events of 19 October 1989 and 23 March 1991 according to the measurements onboard the Mir space station

Flux and dose rate dynamics of solar cosmic rays were measured by the Lyulin dosimeter during the events 19 October 1989 and 23 March 1991. The maximum dose rate registered was 0.4, 0.12 and 0.01 cGy/hour, respectively. Based on the latitude distribution of particle flux a power law form for the energy spectra of solar protons in the anisotropic phase of the events on 19 October 1989 and 23 March 1991 was determined. It was obtained that after the development of geomagnetic storm protons with energies more than 1 GeV were registered.

Classical chaotic dynamics of sound rays in 3-D inhomogeneous waveguide media

The chaotic dynamics of sound rays in a near-bottom waveguide channel is studied on the basis of the Hamiltonian dynamics of nonparaxial rays in inhomogeneous moving media. The bottom is assumed to have a two-dimensional roughness. The mapping of the coordinates of the rays upon reflection from the rough bottom is derived through a solution of the corresponding ray equations in an unperturbed waveguide with a horizontal bottom. A numerical analysis of the mapping reveals that a chaotic instability of rays which start out at small angles from the horizontal develops at short distances from the source. Because of this instability, the path segments of a ray along the horizontal coordinates and the signal passage time along a ray are random functions of the angle at which the ray emerges from the source. Upon a further reflection of rays from the rough bottom, there is a diffusion of rays in a stochastic ring which forms in the plane of horizontal ray directions as a result of the overlap and intersection of resonance curves. A qualitative analysis of this effect is carried out. This effect leads to a nearly isotropic distribution of ray directions.

Chaos and Dynamics of Rays in Waveguide Media

Chaos and Dynamics of Rays in Waveguide Media

Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media

We discuss the geometrical theory of wave propagation in regularly inhomogeneous waveguide media from the point of view of nonlinear Hamiltonian dynamics. We consider ray dynamics in waveguides with periodic longitudinal inhomogeneities, including the phenomenon of spatial nonlinear resonance of rays, which leads to the formation of an effective waveguide channel in the neighborhood of the ray in resonance with the periodic inhomogeneities. We consider different properties of spatially resonant rays: the optical path length and propagation velocity of a signal along rays trapped in a separate nonlinear resonance; the fractal properties of rays, such as the devil's staircase form of the dependence of the spatial oscillation frequency of the ray and the propagation time of a signal along the rays. The trajectory of sound rays in a model of the ocean with transverse flow is considered using the adiabatic invariant method and the transverse drift of a ray with respect to the main propagation direction of sound is described. We consider the conditions for dynamical chaos of rays in a waveguide with longitudinal periodic inhomogeneities. We examine the conditions for internal spatial nonlinear resonance and chaos of rays in waveguides with an irregular cross section and their effect on the propagation velocity of a signal. We study the connection between the structure of the wave front and the dynamics of rays in waveguide channels with regular inhomogeneities. Finally, we discuss the applicability of geometrical optics in waveguides under the conditions of nonlinear resonance and chaos of rays, and the relation between this problem and quantum chaos.