Modulation instability-induced fading in phase-sensitive optical time-domain reflectometry

Phase-sensitive optical time-domain reflectometry (?OTDR) is a simple and effective tool allowing the distributed monitoring of vibrations along single-mode fibers. We show in this Letter that modulation instability (MI) can induce a position-dependent signal fading in long-range ?OTDR over conventional optical fibers. This fading leads to a complete masking of the interference signal recorded at certain positions and therefore to a sensitivity loss at these positions. We illustrate this effect both theoretically and experimentally. While this effect is detrimental in the context of distributed vibration analysis using ?OTDR, we also believe that the technique provides a clear and insightful way to evidence the Fermi?Pasta?Ulam recurrence associated with the MI process.

Propagation of Cross-Section Uncertainties in Criticality Calculations in the Framework of UAM-Phase I Using MCNPX-2.7e and SCALE-6.1

In the framework of the OECD/NEA project on Benchmark for Uncertainty Analysis in Modeling (UAM) for Design, Operation, and Safety Analysis of LWRs, several approaches and codes are being used to deal with the exercises proposed in Phase I, “Specifications and Support Data for Neutronics Cases.” At UPM, our research group treats these exercises with sensitivity calculations and the “sandwich formula” to propagate cross-section uncertainties. Two different codes are employed to calculate the sensitivity coefficients of to cross sections in criticality calculations: MCNPX-2.7e and SCALE-6.1. The former uses the Differential Operator Technique and the latter uses the Adjoint-Weighted Technique. In this paper, the main results for exercise I-2 “Lattice Physics” are presented for the criticality calculations of PWR. These criticality calculations are done for a TMI fuel assembly at four different states: HZP-Unrodded, HZP-Rodded, HFP-Unrodded, and HFP-Rodded. The results of the two different codes above are presented and compared. The comparison proves a good agreement between SCALE-6.1 and MCNPX-2.7e in uncertainty that comes from the sensitivity coefficients calculated by both codes. Differences are found when the sensitivity profiles are analysed, but they do not lead to differences in the uncertainty.

Hard transition to chaotic dynamics in Alfven wave fronts

The derivative nonlinear Schrodinger DNLS equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model equal dampings of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase, no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic relaxation oscillations that are absent for zero growth rate. This hard transition in phase-space behavior occurs for left-hand LH polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable, with damping less than about unstable wave frequency 2/4 x ion cyclotron frequency. The structural stability of the transition was explored by going into a fully 3-wave model different dampings of daughter waves,four-dimensional flow; both models differ in significant phase-space features but keep common features essential for the transition.

Reduced three-wave model to study the hard transition to chaotic dynamics in Alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model (equal damping of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase), no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic dynamics that is absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralelling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable.

Fully 3-wave model to study the hard transition to chaotic dynamics in alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. No matter how small the growth rate of the unstable wave, the four-dimensional flow for the three wave amplitudes and a relative phase, with both resistive damping and linear Landau damping, exhibits chaotic relaxation oscillations that are absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable. The parameter domain developing chaos is much broader than the corresponding domain in a reduced 3-wave model that assumes equal dampings of the daughter waves

A method for revealing phase space structures of general time dependent dynamical systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a “heuristic argument” that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper “side-by-side” comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (“time averages”) are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.

PIC computation of electron current collection to a moving bare tether in the mesothermal condition

In tethered satellite technology, it is important to estimate how many electrons a spacecraft can collect from its ambient plasma by a bare electrodynamic tether. The analysis is however very difficult because of the small but significant Geo-magnetic field and the spacecraft’s relative motion to both ions and electrons. The object of our work is the development of a numerical method, for this purpose. Particle-In-Cell (PIC) method, for the calculation of electron current to a positive bare tether moving at orbital velocity in the ionosphere, i.e. in a flowing magnetized plasma under Maxwellian collisionless conditions. In a PIC code, a number of particles are distributed in phase space and the computational domain has a grid on which Poisson equation is solved for field quantities. The code uses the quasi-neutrality condition to solve for the local potential at points in the plasma which coincide with the computational outside boundary. The quasi-neutrality condition imposes ne - ni on the boundary. The Poisson equation is solved in such a way that the presheath region can be captured in the computation. Results show that the collected current is higher than the Orbital Motion Limit (OML) theory. The OML current is the upper limit of current collection under steady collisionless unmagnetized conditions. In this work, we focus on the flowing effects of plasma as a possible cause of the current enhancement. A deficit electron density due to the flowing effects has been worked and removed by introducing adiabatic electron trapping into our model.

Noise-induced attractor annihilation in the delayed feedback logistic map

We study dynamics of the bistable logistic map with delayed feedback, under the influence of white Gaussian noise and periodic modulation applied to the variable. This system may serve as a model to describe population dynamics under finite resources in noisy environment with seasonal fluctuations. While a very small amount of noise has no effect on the global structure of the coexisting attractors in phase space, an intermediate noise totally eliminates one of the attractors. Slow periodic modulation enhances the attractor annihilation.

Lagrangian descriptors: a method for revealing phase space structures of general time dependent dynamical systems

Lagrangian descriptors are a recent technique which reveals geometrical structures in phase space and which are valid for aperiodically time dependent dynamical systems. We discuss a general methodology for constructing them and we discuss a "heuristic argument" that explains why this method is successful. We support this argument by explicit calculations on a benchmark problem. Several other benchmark examples are considered that allow us to assess the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field ("time averages"). In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods.

Análisis de sistemas dinámicos y complejos en la Liga Profesional de Balonmano de España = Complex and dynamical systems analysis in Spanish Professional Handball League

El propósito de esta tesis fue estudiar el rendimiento ofensivo de los equipos de balonmano de élite cuando se considera el balonmano como un sistema dinámico complejo no lineal. La perspectiva de análisis dinámica dependiente del tiempo fue adoptada para evaluar el rendimiento de los equipos durante el partido. La muestra general comprendió los 240 partidos jugados en la temporada 2011-2012 de la liga profesional masculina de balonmano de España (Liga ASOBAL). En el análisis posterior solo se consideraron los partidos ajustados (diferencia final de goles ≤ 5; n = 142). El estado del marcador, la localización del partido, el nivel de los oponentes y el periodo de juego fueron incorporados al análisis como variables situacionales. Tres estudios compusieron el núcleo de la tesis. En el primer estudio, analizamos la coordinación entre las series temporales que representan el proceso goleador a lo largo del partido de cada uno de los dos equipos que se enfrentan. Autocorrelaciones, correlaciones cruzadas, doble media móvil y transformada de Hilbert fueron usadas para el análisis. El proceso goleador de los equipos presentó una alta consistencia a lo largo de todos los partidos, así como fuertes modos de coordinación en fase en todos los contextos de juego. Las únicas diferencias se encontraron en relación al periodo de juego. La coordinación en los procesos goleadores de los equipos fue significativamente menor en el 1er y 2º periodo (0–10 min y 10–20 min), mostrando una clara coordinación creciente a medida que el partido avanzaba. Esto sugiere que son los 20 primeros minutos aquellos que rompen los partidos. En el segundo estudio, analizamos los efectos temporales (efecto inmediato, a corto y a medio plazo) de los tiempos muertos en el rendimiento goleador de los equipos. Modelos de regresión lineal múltiple fueron empleados para el análisis. Los resultados mostraron incrementos de 0.59, 1.40 y 1.85 goles para los periodos que comprenden la primera, tercera y quinta posesión de los equipos que pidieron el tiempo muerto. Inversamente, se encontraron efectos significativamente negativos para los equipos rivales, con decrementos de 0.50, 1.43 y 2.05 goles en los mismos periodos respectivamente. La influencia de las variables situacionales solo se registró en ciertos periodos de juego. Finalmente, en el tercer estudio, analizamos los efectos temporales de las exclusiones de los jugadores sobre el rendimiento goleador de los equipos, tanto para los equipos que sufren la exclusión (inferioridad numérica) como para los rivales (superioridad numérica). Se emplearon modelos de regresión lineal múltiple para el análisis. Los resultados mostraron efectos negativos significativos en el número de goles marcados por los equipos con un jugador menos, con decrementos de 0.25, 0.40, 0.61, 0.62 y 0.57 goles para los periodos que comprenden el primer, segundo, tercer, cuarto y quinto minutos previos y posteriores a la exclusión. Para los rivales, los resultados mostraron efectos positivos significativos, con incrementos de la misma magnitud en los mismos periodos. Esta tendencia no se vio afectada por el estado del marcador, localización del partido, nivel de los oponentes o periodo de juego. Los incrementos goleadores fueron menores de lo que se podría esperar de una superioridad numérica de 2 minutos. Diferentes teorías psicológicas como la paralización ante situaciones de presión donde se espera un gran rendimiento pueden ayudar a explicar este hecho. Los últimos capítulos de la tesis enumeran las conclusiones principales y presentan diferentes aplicaciones prácticas que surgen de los tres estudios. Por último, se presentan las limitaciones y futuras líneas de investigación. ABSTRACT The purpose of this thesis was to investigate the offensive performance of elite handball teams when considering handball as a complex non-linear dynamical system. The time-dependent dynamic approach was adopted to assess teams’ performance during the game. The overall sample comprised the 240 games played in the season 2011-2012 of men’s Spanish Professional Handball League (ASOBAL League). In the subsequent analyses, only close games (final goal-difference ≤ 5; n = 142) were considered. Match status, game location, quality of opposition, and game period situational variables were incorporated into the analysis. Three studies composed the core of the thesis. In the first study, we analyzed the game-scoring coordination between the time series representing the scoring processes of the two opposing teams throughout the game. Autocorrelation, cross-correlation, double moving average, and Hilbert transform were used for analysis. The scoring processes of the teams presented a high consistency across all the games as well as strong in-phase modes of coordination in all the game contexts. The only differences were found when controlling for the game period. The coordination in the scoring processes of the teams was significantly lower for the 1st and 2nd period (0–10 min and 10–20 min), showing a clear increasing coordination behavior as the game progressed. This suggests that the first 20 minutes are those that break the game-scoring. In the second study, we analyzed the temporal effects (immediate effect, short-term effect, and medium-term effect) of team timeouts on teams’ scoring performance. Multiple linear regression models were used for the analysis. The results showed increments of 0.59, 1.40 and 1.85 goals for the periods within the first, third and fifth timeout ball possessions for the teams that requested the timeout. Conversely, significant negative effects on goals scored were found for the opponent teams, with decrements of 0.59, 1.43 and 2.04 goals for the same periods, respectively. The influence of situational variables on the scoring performance was only registered in certain game periods. Finally, in the third study, we analyzed the players’ exclusions temporal effects on teams’ scoring performance, for the teams that suffer the exclusion (numerical inferiority) and for the opponents (numerical superiority). Multiple linear regression models were used for the analysis. The results showed significant negative effects on the number of goals scored for the teams with one less player, with decrements of 0.25, 0.40, 0.61, 0.62, and 0.57 goals for the periods within the previous and post one, two, three, four and five minutes of play. For the opponent teams, the results showed positive effects, with increments of the same magnitude in the same game periods. This trend was not affected by match status, game location, quality of opposition, or game period. The scoring increments were smaller than might be expected from a 2-minute numerical playing superiority. Psychological theories such as choking under pressure situations where good performance is expected could contribute to explain this finding. The final chapters of the thesis enumerate the main conclusions and underline the main practical applications that arise from the three studies. Lastly, limitations and future research directions are described.

Gobernar la complejidad urbana desde la sostenibilidad. Evaluación del gobierno de la gestión visible utilizando indicadores de gobernanza (Venezuela)

Se evalúa con indicadores de gobernanza urbana la sostenibilidad de las formas de hacer ciudad hibrida compleja del gobierno de la gestión visible (GGV). Argumenta que el GGV hace ciudad para legitimarse por desempeño y fortalecer la gobernanza local, en un contexto de mutaciones múltiples y radicales que tienden a diluir y centralizar el poder local y fractalizar la ciudad, profundizando la segregación sociopolítica-territorial y la ingobernabilidad genética de la ciudad hibrida, poniendo en riesgo el Estado federal descentralizado, el derecho a la ciudad, al gobierno local y la gobernanza urbana y multinivel (hipótesis). La estrategia de evaluación de gobernanza innovadora (EEG+i) diseñada para evaluar la relación entre las formas de hacer ciudad hibrida (variables espaciales) y gobernanza (variable a-espacial) es transversal, multidimensional y se construye desde la complejidad, el análisis de escenarios, formulación de constructos, modelos e indicadores de gobernanza, entretejiendo tres campos de conocimiento, gobierno, ciudad y sostenibilidad, en cuatro fases. La Fase 1, contextualiza la gobernanza en la dramática del siglo XXI. La Fase 2, desarrolla la fundamentación teórico-práctica, nuevos conceptos y un abordaje analítico propio ‘genética territorial’, para analizar y comprehender la complejidad de la ciudad hibrida de países en desarrollo, tejiendo ontogenética territorial y el carácter autopoiético del gen informal. En la Fase 3, se caracterizan las formas de hacer ciudad desde la genética del territorio, se formulan modelos e indicadores de gobernanza con los que se evalúan, aplicando un delphi y cuestionarios, los genes tipológicos-formas de hacer ciudad y validan las conclusiones. En la Fase 4, se correlacionan los resultados de los instrumentos aplicados con la praxis urbana del GGV, durante cuatro periodos de gobierno (1996-2010). Concluyendo que, la estrategia de evaluación comprobó las hipótesis y demostró la correlación transversal y multinivel existente entre, las mutaciones en curso que contradicen el modelo de gobernanza constitucional, el paisaje de gobernanza latinoamericano y venezolano, la praxis de los regímenes híbridos ricos en recursos naturales, las perspectivas de desarrollo globales y se expresa sociopolíticamente en déficit de gobernanza, Estado de derecho y cohesión-capital social y, espaciolocalmente, en la ciudad hibrida dispersa y diluida (compleja) y en el gobierno del poder diluido centralizado. La confrontación de flujos de poder centrípetos y centrífugos en la ciudad profundiza la fragmentación socioespacial y política y el deterioro de la calidad de vida, incrementando las protestas ciudadanas e ingobernabilidad que obstaculiza la superación de la pobreza y gobernanza urbana y multinivel. La evaluación de la praxis urbana del GGV evidenció que la correlación entre gobernanza, la producción de genes formales y la ciudad por iniciativa privada tiende a ser positiva y entre gobernanza, genes y producción de ciudad informal negativa, por el carácter autopoiético-autogobernable del gen informal y de los nuevos gobiernos sublocales que dificulta gobernar en gobernanza. La praxis del GGV es contraria al modelo de gobernanza formulado y la disolución centralizada del gobierno local y de la ciudad hibrida-dispersa es socio-espacial y políticamente insostenible. Se proponen estrategias y tácticas de gobernanza multinivel para recuperar la cohesión social y de planificación de la gestión innovadora (EG [PG] +i) para orquestar, desde el Consejo Local de Gobernanza (CLG) y con la participación de los espacios y gobiernos sublocales, un proyecto de ciudad compartido y sostenible. ABSTRACT The sustainability of the forms of making the hybrid-complex city by the visible management government (VMG) is evaluated using urban governance indicators. Argues that the VMG builds city to legitimate itself by performance and to strengthen local governance in a context of multiple and radical mutations that tend to dilute and centralize local power and fractalize the city, deepening the socio-spatial and political segregation, the genetic ingovernability of the hybrid city and placing the decentralized federal State, the right to city, local government and urban governance at risk (hypothesis). The innovative governance evaluation strategy (GES+i) designed to assess the relationship between the forms of making the hybrid city (spatial variables) and governance (a-spatial variable) is transversal, multidimensional; is constructed from complexity, scenario analysis, the formulation of concepts, models and governance indicators, weaving three fields of knowledge, government, city and sustainability in four phases. Phase 1, contextualizes governance in the dramatic of the twenty-first century. Phase 2, develops the theoretical and practical foundations, new concepts and a proper analytical approach to comprehend the complexity of the hybrid city from developing countries, weaving territorial ontogenetic with the autopiethic character of the informal city gen. In Phase 3, the ways of making city are characterized from the genetics of territory; governance indicators and models are formulated to evaluate, using delphi and questionnaires, the ways of making city and validate the conclusions. In Phase 4, the results of the instruments applied are correlated with the urban praxis of the VMG during the four periods of government analyzed (1996-2010). Concluding that, the evaluation strategy proved the hypothesis and showed the transversal and multilevel correlation between, mutations that contradict the constitutional governance model, the governance landscape of Latinamerica and the country, the praxis of the hybrid regimes rich in natural resources, the perspectives of the glocal economy and expresses socio-politically the governance and rule of law and social capital-cohesion deficit and spatial-temporarily the hybrid disperse and diluted city (complex) and the diluted-centralized local government. The confrontation of flows of power centripetal and centrifugal in the city deepens the socio-spatial and political fragmentation and deterioration of the quality of life, increasing citizens' protests and ingovernability which hinders poverty eradication and, multilevel and urban governance. The evaluation of the VMG urban praxis showed the correlation between governance, the production of formal genes and city by private initiative tended to be positive and, between informal genes-city production and governance negative, due to its autopiethic-self governable character that hinders governance. The urban praxis of the VMG contradicts the formulated governance model and thecentralized dissolution of the local government and hybrid city are socio-spatial and politically unsustainable. Multiscale governance strategies are proposed to recreate social cohesion and a management planning innovative method (EG [PG] + i) to orchestrate, from the Local Governance Council (LGC) and with the participation of sublocal governments and spaces, a shared and sustainable city project.

High resolution system for nanoparticles hyperthermia efficiency evaluation

A system to evaluate nanoparticles efficiency in hyperthermia applications is presented. The method allows a direct measurement of the power dissipated by the nanoparticles through the determination of the first harmonic component of the in quadrature magnetic moment induced by the applied field. The magnetic moment is measured by using an induction method. To avoid errors and reduce the noise signal a double in phase demodulation technique is used. To test the system viability we have measured nanowires, nanoparticles and copper samples of different volumes to prove by comparing experimental and modeled results

Coherent excitation of nonlinear oscillators

Coherently driven, dissipative nonlinear oscillators,(driving kept permanently in phase with the oscillators response) are proposed as systems with interesting dynamics. Results for simple, preliminary examples, which do not show chaotic behavior, are briefly discussed.

Análisis biomecánico zancada a zancada de la prueba "60 metros vallas" durante los campeonatos del mundo y de España de pista cubierta Valencia 2008

El principal objetivo del presente trabajo de investigación fue determinar las diferencias en distintas variables relacionadas con el rendimiento físico entre atletas de distinto nivel durante la prueba de los 60 metros vallas. Un total de 59 vallistas masculinos (los 31 participantes en el Campeonato del Mundo Absoluto de Pista Cubierta y los 28 participantes en el Campeonato de España Absoluto de Pista Cubierta, ambos celebrados en Valencia en el año 2008) formaron la muestra del estudio. El análisis biomecánico se realizó mediante un sistema fotogramétrico en dos dimensiones que permitió calcular, aplicando algoritmos basados en el procedimiento de la DLT (Abdel-Aziz y Karara, 1971), las coordenadas (x, y) de los sucesivos apoyos de los pies de los atletas sobre toda la superficie de competición. La filmación de las pruebas se llevó a cabo con seis cámaras de vídeo, ubicadas sobre la gradas, con una frecuencia de muestreo para el tratamiento de los datos de 50 Hz. En la fase de salida, los atletas de nivel superior mostraron una menor longitud (p<0,05) y tiempo de zancada (p<0,001), debido a un menor tiempo de vuelo (p<0,05). En la fase de vallas, los atletas de nivel más elevado presentaron mayores distancia de ataque a la valla (p<0,001), así como menores distancias de caída de la valla (p<0,001), tiempos de zancada (p<0,01-0,001) y de apoyo (p<0,01-0,001 ) en los cuatro pasos que conforman cada ciclo de vallas, así como un menor tiempo de vuelo en el paso de valla (p<0,001) y en el paso de transición (p<0,001). De manera adicional, se encontraron importantes diferencias en el reparto de los pasos entre vallas entre la primera y tercera valla y el resto de obstáculos. En la fase final, se observó una mayor longitud de zancada en los atletas de nivel superior (p<0,001), así como un menor tiempo de zancada (p<0,01) y de apoyo (p<0,01). Los resultados obtenidos en el presente estudio de investigación avalan la utilización de la fotogrametría en dos dimensiones para el análisis biomecánico de la prueba de 60 metros vallas en competición. Su aplicación en competiciones del máximo nivel internacional ha posibilitado conocer las características de los vallistas a lo largo de toda la prueba y determinar posibles implicaciones de cara al proceso de entrenamiento. ABSTRACT The aim of this research was to determine the differences in different variables related to physical performance among athletes of different levels during the race of 60 meter hurdles. A total of 59 male hurdlers (the 31 participants in the World Indoor Championship and the 28 participants in the Spanish Indoor Championship, both held in Valencia in 2008) formed the sample of the study. The biomechanical analysis of athletes was performed using a two-dimensional photogrammetric system which enabled calculation, applying algorithms based on the DLT method (Abdel -Aziz y Karara , 1971), the coordinates (x , y) of the successive supports of the feet on the entire competition surface. Filming test was conducted with six video cameras, located on the bleachers, with a sampling frequency for data processing of 50 Hz. In the approach run phase, the top-level athletes showed a smaller length step (p<0.05), and shorter step time (p<0.001), due to a shorter step flight time (p<0.05). In the hurdle unit phase, the higher level athletes had greater take-off distances (p<0.001), shorter landing distances (p<0.001), smaller step times (p<0.01-0.001), and support times (p<0.01- 0.001) in the four steps that comprised each hurdle unit, and smaller flight times in the hurdle step (p < 0.001), and the recovery step (p<0.001). Additionally, differences in the distribution of hurdle unit steps between the first and third hurdle, and other hurdles were found. In the run-in phase, a greater step length in top-level athletes (p<0.001), and a shorter step time (p<0.01) and contact time (p<0.01) was observed. The results obtained in this study support the use of photogrammetry in two dimensions for biomechanical analysis in 60 meter hurdles competition events. Its application at the highest international level competitions has allowed to know the characteristics of the hurdlers over the entire race and identify possible implications for the training process.

Temporal self-imaging effect for periodically modulated trains of pulses

In this paper, the mathematical description of the temporal selfimaging effect is studied, focusing on the situation in which the train of pulses to be dispersed has been previously periodically modulated in phase and amplitude. It is demonstrated that, for each input pulse and for some specific values of the chromatic dispersion, a subtrain of optical pulses is generated whose envelope is determined by the Discrete Fourier Transform of the modulating coefficients. The mathematical results are confirmed by simulations of various examples and some limits on the realization of the theory are commented.