Rational invariants on the space of all structures of algebras on a two-dimensional vector space

Rational invariants on the space of all structures of algebras on a two-dimensional vector space

Magnetic pumping of whistler waves by tether current modulation

Magnetic excitation of whistlers by a square array of electrodynamic tethers is discussed. The array is made of perpendicular rows of tethers that carry equal, uniform, and time-modulated currents at equal frequency with a 90° phase shift. The array would fly vertical in the orbital equatorial plane, which is perpendicular to the geomagnetic field B0 when its tilt is ignored. The array radiates a whistler wave along B0. A parametric instability due to pumping by the background magnetic field through the radiated wave gives rise to two unstable coupled whistler perturbations. The growth rate is maximum for perturbations with wave vector at angles 38.36° and 75.93° from B0. For an experiment involving a wavefront that moves with the orbiting array, which might serve to study nonlinear wave interactions and turbulence in space plasmas, characteristic values of growth rate and parameters, such as the number of tethers and their dimensions and distances in the array, are discussed for low Earth orbit ambient conditions.

Random-modulation cw lidar system for space-borne carbon dioxide remote sensing based on a high-brightness semiconductor laser

In this paper, we report on the progresses of the BRITESPACE Consortium in order to achieve space-borne LIDAR measurements of atmospheric carbon dioxide concentration based on an all semiconductor laser source at 1.57 ?m. The complete design of the proposed RM-CW IPDA LIDAR has been presented and described in detail. Complete descriptions of the laser module and the FSU have been presented. Two bended MOPAs, emitting at the sounding frequency of the on- and off- IPDA channels, have been proposed as the transmitter optical sources with the required high brightness. Experimental results on the bended MOPAs have been presented showing a high spectral purity and promising expectations on the high output power requirements. Finally, the RM-CW approach has been modelled and an estimation of the expected SNR for the entire system is presented. Preliminary results indicate that a CO2 retrieval precision of 1.5 ppm could be achieved with an average output power of 2 W for each channel.

Vector spaces of entire functions of unbounded type

Let E be an infinite dimensional complex Banach space. We prove the existence of an infinitely generated algebra, an infinite dimensional closed subspace and a dense subspace of entire functions on E whose non-zero elements are functions of unbounded type. We also show that the τδ topology on the space of all holomorphic functions cannot be obtained as a countable inductive limit of Fr´echet spaces. RESUMEN. Sea E un espacio de Banach complejo de dimensión infinita y sea H(E) el espacio de funciones holomorfas definidas en E. En el artículo se demuestra la existencia de un álgebra infinitamente generada en H(E), un subespacio vectorial en H(E) cerrado de dimensión infinita y un subespacio denso en H(E) cuyos elementos no nulos son funciones de tipo no acotado. También se demuestra que el espacio de funciones holomorfas con la topología ? no es un límite inductivo numberable de espacios de Fréchet.

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.

Space-state robust control of a Buck converter with amorphous core coil and variable load

Pulse-width modulation is widely used to control electronic converters. One of the most frequently used topologies for high DC voltage/low DC voltage conversion is the Buck converter. These converters are described by a second order system with an LC filter between the switching subsystem and the load. The use of a coil with an amorphous magnetic material core rather than an air core permits the design of smaller converters. If high switching frequencies are used to obtain high quality voltage output, then the value of the auto inductance L is reduced over time. Robust controllers are thus needed if the accuracy of the converter response must be preserved under auto inductance and payload variations. This paper presents a robust controller for a Buck converter based on a state space feedback control system combined with an additional virtual space variable which minimizes the effects of the inductance and load variations when a switching frequency that is not too high is applied. The system exhibits a null steady-state average error response for the entire range of parameter variations. Simulation results and a comparison with a standard PID controller are also presented.

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.

High-brightness all semiconductor laser at 1.57 µm for space-borne lidar measurements of atmospheric carbon dioxide: device design and analysis of requirements

The availability of suitable laser sources is one of the main challenges in future space missions for accurate measurement of atmospheric CO2. The main objective of the European project BRITESPACE is to demonstrate the feasibility of an all-semiconductor laser source to be used as a space-borne laser transmitter in an Integrated Path Differential Absorption (IPDA) lidar system. We present here the proposed transmitter and system architectures, the initial device design and the results of the simulations performed in order to estimate the source requirements in terms of power, beam quality, and spectral properties to achieve the required measurement accuracy. The laser transmitter is based on two InGaAsP/InP monolithic Master Oscillator Power Amplifiers (MOPAs), providing the ON and OFF wavelengths close to the selected absorption line around 1.57 µm. Each MOPA consists of a frequency stabilized Distributed Feedback (DFB) master oscillator, a modulator section, and a tapered semiconductor amplifier optimized to maximize the optical output power. The design of the space-compliant laser module includes the beam forming optics and the thermoelectric coolers.The proposed system replaces the conventional pulsed source with a modulated continuous wave source using the Random Modulation-Continuous Wave (RM-CW) approach, allowing the designed semiconductor MOPA to be applicable in such applications. The system requirements for obtaining a CO2 retrieval accuracy of 1 ppmv and a spatial resolution of less than 10 meters have been defined. Envelope estimated of the returns indicate that the average power needed is of a few watts and that the main noise source is the ambient noise.