Asymptotic solution for the two-body problem with constant tangencial acceleration

An analytical solution of the two body problem perturbed by a constant tangential acceleration is derived with the aid of perturbation theory. The solution, which is valid for circular and elliptic orbits with generic eccentricity, describes the instantaneous time variation of all orbital elements. A comparison with high-accuracy numerical results shows that the analytical method can be effectively applied to multiple-revolution low-thrust orbit transfer around planets and in interplanetary space with negligible error.

Asymptotic Description of Flutter Amplitude Saturation by Nonlinear Friction Forces

The computation of the non-linear vibration dynamics of an aerodynamically unstable bladed-disk is a formidable numerical task, even for the simplified case of aerodynamic forces assumed to be linear. The nonlinear friction forces effectively couple dif- ferent travelling waves modes and, in order to properly elucidate the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction microslip regime) is basically a superposition of the linear aeroelastic un- stable travelling waves, which exhibit a slow time modulation that is much longer than the elastic oscillation period. This slow time modulation is due to both, the small aerodynamic effects and the small nonlinear friction forces, and it is crucial to deter- mine the final amplitude of the flutter vibration. In this presenta- tion we apply asymptotic techniques to obtain a new simplified model that captures the slow time dynamics of the amplitudes of the travelling waves. The resulting asymptotic model is very re- duced and extremely cheap to simulate, and it has the advantage that it gives precise information about the characteristics of the nonlinear friction models that actually play a role in the satura- tion of the vibration amplitude.

Ab initio Methodology for Calculating Elastic Constant and Sound Velocity for Hydrogen and Deuterium in Molecular Solid Phase

Hydrogen isotopes play a critical role both in inertial and magnetic confinement Nuclear Fusion. Since the preferent fuel needed for this technology is a mixture of deuterium and tritium. The study of these isotopes particularly at very low temperatures carries a technological interest in other applications. The present line promotes a deep study on the structural configuration that hydrogen and deuterium adopt at cryogenic temperatures and at high pressures. Typical conditions occurring in present Inertial Fusion target designs. Our approach is aims to determine the crystal structure characteristics, phase transitions and other parameters strongly correlated to variations of temperature and pressure. With this results is possible calculated the elastic constant and sound velocity for hydrogen and deuterium in molecular solid phase.

Asymptotic Description of Flutter Amplitude Saturation by Nonlinear Friction Forces

The computation of the non-linear vibration dynamics of an aerodynamically unstable bladed-disk is a formidable numerical task, even for the simplified case of aerodynamic forces assumed to be linear. The nonlinear friction forces effectively couple dif- ferent travelling waves modes and, in order to properly elucidate the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction microslip regime) is basically a superposition of the linear aeroelastic un- stable travelling waves, which exhibit a slow time modulation that is much longer than the elastic oscillation period. This slow time modulation is due to both, the small aerodynamic effects and the small nonlinear friction forces, and it is crucial to deter- mine the final amplitude of the flutter vibration. In this presenta- tion we apply asymptotic techniques to obtain a new simplified model that captures the slow time dynamics of the amplitudes of the travelling waves. The resulting asymptotic model is very re- duced and extremely cheap to simulate, and it has the advantage that it gives precise information about the characteristics of the nonlinear friction models that actually play a role in the satura- tion of the vibration amplitude.

A critical force constant of the structural phase transition in quartz

Long wavelength optical phonons of quartz were analyzed by a Born-Von Karman model not previously used. It was found that only one force constant associated with the turning of the Si-O bonds has a critical effect on the soft-mode frequency and the α-β transition in quartz. The square of the soft-mode frequency was found to depend linearly on this force constant which has the temperature dependence K(T)= -5.33+225.3x10-4(851-T)2/3 in units of 104 dyn/cm2.

Accurate analytical approximation of asteroid deflection with constant tangential thrust

We present analytical formulas to estimate the variation of achieved deflection for an Earth-impacting asteroid following a continuous tangential low-thrust deflection strategy. Relatively simple analytical expressions are obtained with the aid of asymptotic theory and the use of Peláez orbital elements set, an approach that is particularly suitable to the asteroid deflection problem and is not limited to small eccentricities. The accuracy of the proposed formulas is evaluated numerically showing negligible error for both early and late deflection campaigns. The results will be of aid in planning future low-thrust asteroid deflection missions

Pulsating emission of droplets from an electrified meniscus.

A numerical description is given for the pulsating emission of droplets from an electrified meniscus of an inviscid liquid of infinite electrical conductivity which is injected at a constant flow rate into a region of uniform, continuous or time periodic, electric field. Under a continuous field, the meniscus attains a periodic regime in which bursts of tiny droplets are emitted from its tip. At low electric fields this regime consists of sequences of emission bursts interspersed with sequences of meniscus oscillations without droplet emission, while at higher fields the bursts occur periodically. These results are in qualitative agreement with experimental results in the literature. Under a time periodic electric field with square waveform, the electric stress that acts on the surface of the liquid while the field is on may generate a tip that emits tiny droplets or may accelerate part of the meniscus and lead to a second emission mode in which a few large droplets are emitted after the electric field is turned off. Conditions under which each emission mode or a combination of the two are realized are discussed for low frequency oscillatory fields. A simplified model is proposed for high electric field frequencies, of the order of the capillary frequency of the meniscus. This model allows computing the average emission rate as a function of the amplitude, duration and bias of the electric field square wave, and shows that droplet emission fails to follow the applied field above a certain frequency

Jupiter power generation with electrodynamic tethers at constant orbital energy

An electrodynamic tether system for power generation at Jupiter is presented that allows extracting energy from Jupiter's corotating plasmasphere while leaving the system orbital energy unaltered to first order. The spacecraft is placed in a polar orbit with the tether spinning in the orbital plane so that the resulting Lorentz force, neglecting Jupiter's magnetic dipole tilt, is orthogonal to the instantaneous velocity vector and orbital radius, hence affecting orbital inclination rather than orbital energy. In addition, the electrodynamic tether subsystem, which consists of two radial tether arms deployed from the main central spacecraft, is designed in such a way as to extract maximum power while keeping the resulting Lorentz torque constantly null. The power-generation performance of the system and the effect on the orbit inclination is evaluated analytically for different orbital conditions and verified numerically. Finally, a thruster-based inclination-compensation maneuver at apoapsis is added, resulting in an efficient scheme to extract energy from the plasmasphere of the planet with minimum propellant consumption and no inclination change. A tradeoff analysis is conducted showing that, depending on tether size and orbit characteristics, the system performance can be considerably higher than conventional power-generation methods.

Xyloglucan endotransglucosylase/hydrolase (XTH) overexpression affects growth and cell wall mechanics in etiolated Arabidopsis hypocotyls.

Growth and biomechanics of etiolated hypocotyls from Arabidopsis thaliana lines overexpressing xyloglucan endotransglucosylase/hydrolase AtXTH18, AtXTH19, AtXTH20, and PttXET16-34 were studied. Overexpression of AtXTH18, AtXTH19, and AtXTH20 stimulated growth of hypocotyls, while PttXET16-34 overexpression did not show this effect. In vitro extension of frozen/thawed hypocotyls measured by a constant-load extensiometer started from a high-amplitude initial deformation followed by a slow time-dependent creep. Creep of growing XTH-overexpressing (OE) hypocotyls was more linear in time compared with the wild type at pH 5.0, reflecting their higher potential for long-term extension. XTH-OE plants deposited 65?84% more cell wall material per hypocotyl cross-sectional area than wild-type plants. As a result, their wall stress under each external load was lower than in the wild-type. Growing XTH-OE hypocotyls had higher values of initial deformation·stress?1 compared with the wild type. Plotting creep rates for each line under different loads against the respective wall stress values gave straight lines. Their slopes and intercepts with the abscissa correspond to ? (in vitro cell wall extensibility) and y (in vitro cell wall yield threshold) values characterizing cell wall material properties. The wall material in XTH-OE lines was more pliant than in the wild type due to lower y values. In contrast, the acid-induced wall extension in vitro resulted from increasing ? values. Thus, three factors contributed to the XTH-OE-stimulated growth in Arabidopsis hypocotyls: their more linear creep, higher values of initial deformation·stress?1, and lower y values.

Monte Carlo Neutronics and Thermal-hydraulics coupling applied to Fast Reactors

Un escenario habitualmente considerado para el uso sostenible y prolongado de la energía nuclear contempla un parque de reactores rápidos refrigerados por metales líquidos (LMFR) dedicados al reciclado de Pu y la transmutación de actínidos minoritarios (MA). Otra opción es combinar dichos reactores con algunos sistemas subcríticos asistidos por acelerador (ADS), exclusivamente destinados a la eliminación de MA. El diseño y licenciamiento de estos reactores innovadores requiere herramientas computacionales prácticas y precisas, que incorporen el conocimiento obtenido en la investigación experimental de nuevas configuraciones de reactores, materiales y sistemas. A pesar de que se han construido y operado un cierto número de reactores rápidos a nivel mundial, la experiencia operacional es todavía reducida y no todos los transitorios se han podido entender completamente. Por tanto, los análisis de seguridad de nuevos LMFR están basados fundamentalmente en métodos deterministas, al contrario que las aproximaciones modernas para reactores de agua ligera (LWR), que se benefician también de los métodos probabilistas. La aproximación más usada en los estudios de seguridad de LMFR es utilizar una variedad de códigos, desarrollados a base de distintas teorías, en busca de soluciones integrales para los transitorios e incluyendo incertidumbres. En este marco, los nuevos códigos para cálculos de mejor estimación ("best estimate") que no incluyen aproximaciones conservadoras, son de una importancia primordial para analizar estacionarios y transitorios en reactores rápidos. Esta tesis se centra en el desarrollo de un código acoplado para realizar análisis realistas en reactores rápidos críticos aplicando el método de Monte Carlo. Hoy en día, dado el mayor potencial de recursos computacionales, los códigos de transporte neutrónico por Monte Carlo se pueden usar de manera práctica para realizar cálculos detallados de núcleos completos, incluso de elevada heterogeneidad material. Además, los códigos de Monte Carlo se toman normalmente como referencia para los códigos deterministas de difusión en multigrupos en aplicaciones con reactores rápidos, porque usan secciones eficaces punto a punto, un modelo geométrico exacto y tienen en cuenta intrínsecamente la dependencia angular de flujo. En esta tesis se presenta una metodología de acoplamiento entre el conocido código MCNP, que calcula la generación de potencia en el reactor, y el código de termohidráulica de subcanal COBRA-IV, que obtiene las distribuciones de temperatura y densidad en el sistema. COBRA-IV es un código apropiado para aplicaciones en reactores rápidos ya que ha sido validado con resultados experimentales en haces de barras con sodio, incluyendo las correlaciones más apropiadas para metales líquidos. En una primera fase de la tesis, ambos códigos se han acoplado en estado estacionario utilizando un método iterativo con intercambio de archivos externos. El principal problema en el acoplamiento neutrónico y termohidráulico en estacionario con códigos de Monte Carlo es la manipulación de las secciones eficaces para tener en cuenta el ensanchamiento Doppler cuando la temperatura del combustible aumenta. Entre todas las opciones disponibles, en esta tesis se ha escogido la aproximación de pseudo materiales, y se ha comprobado que proporciona resultados aceptables en su aplicación con reactores rápidos. Por otro lado, los cambios geométricos originados por grandes gradientes de temperatura en el núcleo de reactores rápidos resultan importantes para la neutrónica como consecuencia del elevado recorrido libre medio del neutrón en estos sistemas. Por tanto, se ha desarrollado un módulo adicional que simula la geometría del reactor en caliente y permite estimar la reactividad debido a la expansión del núcleo en un transitorio. éste módulo calcula automáticamente la longitud del combustible, el radio de la vaina, la separación de los elementos de combustible y el radio de la placa soporte en función de la temperatura. éste efecto es muy relevante en transitorios sin inserción de bancos de parada. También relacionado con los cambios geométricos, se ha implementado una herramienta que, automatiza el movimiento de las barras de control en busca d la criticidad del reactor, o bien calcula el valor de inserción axial las barras de control. Una segunda fase en la plataforma de cálculo que se ha desarrollado es la simulació dinámica. Puesto que MCNP sólo realiza cálculos estacionarios para sistemas críticos o supercríticos, la solución más directa que se propone sin modificar el código fuente de MCNP es usar la aproximación de factorización de flujo, que resuelve por separado la forma del flujo y la amplitud. En este caso se han estudiado en profundidad dos aproximaciones: adiabática y quasiestática. El método adiabático usa un esquema de acoplamiento que alterna en el tiempo los cálculos neutrónicos y termohidráulicos. MCNP calcula el modo fundamental de la distribución de neutrones y la reactividad al final de cada paso de tiempo, y COBRA-IV calcula las propiedades térmicas en el punto intermedio de los pasos de tiempo. La evolución de la amplitud de flujo se calcula resolviendo las ecuaciones de cinética puntual. Este método calcula la reactividad estática en cada paso de tiempo que, en general, difiere de la reactividad dinámica que se obtendría con la distribución de flujo exacta y dependiente de tiempo. No obstante, para entornos no excesivamente alejados de la criticidad ambas reactividades son similares y el método conduce a resultados prácticos aceptables. Siguiendo esta línea, se ha desarrollado después un método mejorado para intentar tener en cuenta el efecto de la fuente de neutrones retardados en la evolución de la forma del flujo durante el transitorio. El esquema consiste en realizar un cálculo cuasiestacionario por cada paso de tiempo con MCNP. La simulación cuasiestacionaria se basa EN la aproximación de fuente constante de neutrones retardados, y consiste en dar un determinado peso o importancia a cada ciclo computacial del cálculo de criticidad con MCNP para la estimación del flujo final. Ambos métodos se han verificado tomando como referencia los resultados del código de difusión COBAYA3 frente a un ejercicio común y suficientemente significativo. Finalmente, con objeto de demostrar la posibilidad de uso práctico del código, se ha simulado un transitorio en el concepto de reactor crítico en fase de diseño MYRRHA/FASTEF, de 100 MW de potencia térmica y refrigerado por plomo-bismuto. ABSTRACT Long term sustainable nuclear energy scenarios envisage a fleet of Liquid Metal Fast Reactors (LMFR) for the Pu recycling and minor actinides (MAs) transmutation or combined with some accelerator driven systems (ADS) just for MAs elimination. Design and licensing of these innovative reactor concepts require accurate computational tools, implementing the knowledge obtained in experimental research for new reactor configurations, materials and associated systems. Although a number of fast reactor systems have already been built, the operational experience is still reduced, especially for lead reactors, and not all the transients are fully understood. The safety analysis approach for LMFR is therefore based only on deterministic methods, different from modern approach for Light Water Reactors (LWR) which also benefit from probabilistic methods. Usually, the approach adopted in LMFR safety assessments is to employ a variety of codes, somewhat different for the each other, to analyze transients looking for a comprehensive solution and including uncertainties. In this frame, new best estimate simulation codes are of prime importance in order to analyze fast reactors steady state and transients. This thesis is focused on the development of a coupled code system for best estimate analysis in fast critical reactor. Currently due to the increase in the computational resources, Monte Carlo methods for neutrons transport can be used for detailed full core calculations. Furthermore, Monte Carlo codes are usually taken as reference for deterministic diffusion multigroups codes in fast reactors applications because they employ point-wise cross sections in an exact geometry model and intrinsically account for directional dependence of the ux. The coupling methodology presented here uses MCNP to calculate the power deposition within the reactor. The subchannel code COBRA-IV calculates the temperature and density distribution within the reactor. COBRA-IV is suitable for fast reactors applications because it has been validated against experimental results in sodium rod bundles. The proper correlations for liquid metal applications have been added to the thermal-hydraulics program. Both codes are coupled at steady state using an iterative method and external files exchange. The main issue in the Monte Carlo/thermal-hydraulics steady state coupling is the cross section handling to take into account Doppler broadening when temperature rises. Among every available options, the pseudo materials approach has been chosen in this thesis. This approach obtains reasonable results in fast reactor applications. Furthermore, geometrical changes caused by large temperature gradients in the core, are of major importance in fast reactor due to the large neutron mean free path. An additional module has therefore been included in order to simulate the reactor geometry in hot state or to estimate the reactivity due to core expansion in a transient. The module automatically calculates the fuel length, cladding radius, fuel assembly pitch and diagrid radius with the temperature. This effect will be crucial in some unprotected transients. Also related to geometrical changes, an automatic control rod movement feature has been implemented in order to achieve a just critical reactor or to calculate control rod worth. A step forward in the coupling platform is the dynamic simulation. Since MCNP performs only steady state calculations for critical systems, the more straight forward option without modifying MCNP source code, is to use the flux factorization approach solving separately the flux shape and amplitude. In this thesis two options have been studied to tackle time dependent neutronic simulations using a Monte Carlo code: adiabatic and quasistatic methods. The adiabatic methods uses a staggered time coupling scheme for the time advance of neutronics and the thermal-hydraulics calculations. MCNP computes the fundamental mode of the neutron flux distribution and the reactivity at the end of each time step and COBRA-IV the thermal properties at half of the the time steps. To calculate the flux amplitude evolution a solver of the point kinetics equations is used. This method calculates the static reactivity in each time step that in general is different from the dynamic reactivity calculated with the exact flux distribution. Nevertheless, for close to critical situations, both reactivities are similar and the method leads to acceptable practical results. In this line, an improved method as an attempt to take into account the effect of delayed neutron source in the transient flux shape evolutions is developed. The scheme performs a quasistationary calculation per time step with MCNP. This quasistationary simulations is based con the constant delayed source approach, taking into account the importance of each criticality cycle in the final flux estimation. Both adiabatic and quasistatic methods have been verified against the diffusion code COBAYA3, using a theoretical kinetic exercise. Finally, a transient in a critical 100 MWth lead-bismuth-eutectic reactor concept is analyzed using the adiabatic method as an application example in a real system.

On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity

We study a parabolic–elliptic chemotactic system describing the evolution of a population’s density “u” and a chemoattractant’s concentration “v”. The system considers a non-constant chemotactic sensitivity given by “χ(N−u)”, for N≥0, and a source term of logistic type “λu(1−u)”. The existence of global bounded classical solutions is proved for any χ>0, N≥0 and λ≥0. By using a comparison argument we analyze the stability of the constant steady state u=1, v=1, for a range of parameters. – For N>1 and Nλ>2χ, any positive and bounded solution converges to the steady state. – For N≤1 the steady state is locally asymptotically stable and for χN<λ, the steady state is globally asymptotically stable.

Measurement of the intrinsic damping constant in individual nanodisks of Y3Fe5O12 and Y3Fe5O12|Pt

We report on an experimental study on the spin-waves relaxation rate in two series of nanodisks of diameter ϕ=300 , 500, and 700 nm, patterned out of two systems: a 20 nm thick yttrium iron garnet (YIG) film grown by pulsed laser deposition either bare or covered by 13 nm of Pt. Using a magnetic resonance force microscope, we measure precisely the ferromagnetic resonance linewidth of each individual YIG and YIG|Pt nanodisks. We find that the linewidth in the nanostructure is sensibly smaller than the one measured in the extended film. Analysis of the frequency dependence of the spectral linewidth indicates that the improvement is principally due to the suppression of the inhomogeneous part of the broadening due to geometrical confinement, suggesting that only the homogeneous broadening contributes to the linewidth of the nanostructure. For the bare YIG nano-disks, the broadening is associated to a damping constant α=4 × 10−4 . A threefold increase of the linewidth is observed for the series with Pt cap layer, attributed to the spin pumping effect. The measured enhancement allows to extract the spin mixing conductance found to be G↑↓=1.55 × 1014 Ω−1 m−2 for our YIG(20nm)|Pt interface, thus opening large opportunities for the design of YIG based nanostructures with optimized magnetic losses.

Estudio de la dinámica no lineal de vórtices magnéticos en nanodots

En el presente trabajo se ha realizado un estudio sobre el comportamiento dinámico de vórtices magnéticos en su aplicación en osciladores de espín-torque. A partir de los modelos matemáticos elaborados en [4] sobre estos osciladores de espín-torque, se han simulado y estudiado usando MATLAB, entre otras herramientas, para tratar de verificar su concordancia con el comportamiento físico observado en el laboratorio. Es importante señalar que el estudio tiene en cuenta la dinámica no lineal, esencial para describir correctamente un sistema oscilante en la práctica. El análisis matemático del sistema que describe la órbita del núcleo de un vórtice magnético sometido a la acción de un campo magnético externo oscilatorio, muestra la posibilidad de la existencia de hasta tres soluciones especiales, según la geometría del dot y el valor del campo magnético de excitación, tanto de su frecuencia como de su amplitud. Estas soluciones corresponden a estados estacionarios del vórtice caracterizados como una órbita circular, aunque en el caso de existir tres equilibrios uno de ellos es inestable. El modelo matemático ha sido estudiado y analizado para reproducir los resultados obtenidos en [4] y adicionalmente se ha implementado el caso de la energía potencial del vórtice con el término no lineal distinto de [4] (con una constante β negativa). Los resultados obtenidos bajo esta suposición muestran una cierta disparidad respecto al caso de β positiva y reflejan la existencia de comportamientos muy diferentes. En la dinámica del vórtice bajo la suposición de β negativa también surgen bifurcaciones de pliegue (fold-over) en la trayectoria del núcleo del vórtice: siempre se obtienen tres equilibrios a bajas frecuencias y aparecen a veces dos intervalos con tres equilibrios en lugar de uno solo, a diferencia del caso de β positiva. El comportamiento del núcleo del vórtice sigue un proceso de histéresis en ambos casos, cuando se dan ciertas condiciones. ABSTRACT. This work is a study about the dynamic behaviour of magnetic vortex in its application in spin-torque oscillators. Starting from mathematical models developed in [4] on this subject, a further analysis has been performed using MATLAB to simulate the behaviour of vortex-based spin-torque oscillators as different relevant parameters vary. The main aim of the study is to check if the obtained results can explain the observed physical behaviour, and an important observation is that fully nonlinear effects are taken into consideration. The mathematical analysis of the system that describes the orbit of the vortex core under the influence of an external oscillatory magnetic field shows that there are up to three possible special solutions depending on the dot geometry and the magnetic driving field value, both on its amplitude as well as its frequency. These solutions correspond to a stable circular orbit of the vortex core, but when the system has three solutions one of them is unstable. This mathematical model has been analyzed and studied to reproduce the results obtained in [4] and, additionally, the effect of a negative value of the nonlinear part of the vortex potential (constant β). Results derived from this assumption exhibit certain differences with respect to the case of a positive constant (β) and reflect the existence of very different patterns. Vortex dynamics under the supposition of a negative β also yield fold-over bifurcations in the trajectory of the vortex core: there are always three solutions at low frequencies and there may be two different intervals with three solutions as opposed to the case of positive β. The vortex core follows a hysteresis process in both cases, when certain conditions are met.

A Wireless Charging System Applying Phase-Shift and Amplitude Control to Maximize Efficiency and Extractable Power

Wireless power transfer (WPT) is an emerging technology with an increasing number of potential applications to transfer power from a transmitter to a mobile receiver over a relatively large air gap. However, its widespread application is hampered due to the relatively low efficiency of current Wireless power transfer (WPT) systems. This study presents a concept to maximize the efficiency as well as to increase the amount of extractable power of a WPT system operating in nonresonant operation. The proposed method is based on actively modifying the equivalent secondary-side load impedance by controlling the phase-shift of the active rectifier and its output voltage level. The presented hardware prototype represents a complete wireless charging system, including a dc-dc converter which is used to charge a battery at the output of the system. Experimental results are shown for the proposed concept in comparison to a conventional synchronous rectification approach. The presented optimization method clearly outperforms state-of-the-art solutions in terms of efficiency and extractable power.