Spacecraft formation flying in the port-Hamiltonian framework

The problem of controlling the relative position and velocity in multi-spacecraft formation flying in the planetary orbits is an enabling technology for current and future research. This paper proposes a family of tracking controllers for different dynamics of Spacecraft Formation Flying (SFF) in the framework of port-Hamiltonian (pH) systems through application of timed Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). The leader–multi-follower architecture is used to address this problem. In this regard, first we model the spacecraft motion in the pH framework in the Earth Centered Inertial frame and then transform it to the Hill frame which is a special local coordinate system. By this technique, we may present a unified structure which encompasses linear/nonlinear dynamics, with/without perturbation. Then, using the timed IDA-PBC method and the contraction analysis, a new method for controlling a family of SFF dynamics is developed. The numerical simulations show the efficiency of the approach in two different cases of missions.

     

Predictive control of uncertain nonlinear parabolic PDE systems using a Galerkin/neural-network-based model

In this paper, a model predictive control (MPC) scheme for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities, arising in the context of transport-reaction processes, is proposed. A spatial operator of a parabolic PDE system is characterized by a spectrum that can be partitioned into a finite slow and an infinite fast complement. In this view, first, Galerkin method is used to derive a set of finite dimensional slow ordinary differential equation (ODE) system that captures the dominant dynamics of the initial PDE system. Then, a Multilayer Neural Network (MNN) is employed to parameterize the unknown nonlinearities in the resulting finite dimensional ODE model. Finally, a Galerkin/neural-network-based ODE model is used to predict future states in the MPC algorithm. The proposed controller is applied to stabilize an unstable steady-state of the temperature profile of a catalytic rod subject to input and state constraints.     

Pool-Frenkel effect and high frequency dielectric constant determination of semiconducting P2O5-Li2MoO4-Li2O and P2O5-Na2MoO4-Na2O bulk glasses

The ternary 70P₂O₅-10Li₂MoO₄-20Li₂O and 70P₂O₅-10Na₂MoO₄-20Na₂O glasses, prepared by the press-melt quenching technique, were studied at temperatures between 298 and 418 K for their high dc electric field properties. For the above purpose, the effect of a strong electric field on the dc conduction of these amorphous bulk samples was investigated using the gap-type electrode configuration. At low electric fields, the current-voltage (I — V) characteristics have a linear shape, while at high electric fields (> 10³ V/cm), bulk samples show nonlinear effects (nonohmic conduction). Current-voltage curves show increasing departure from Ohm’s law with increasing current density, leading to critical phenomena at a maximum voltage (threshold voltage), known as switching (switch from a low-conduction state to a higher-conduction state at threshold voltage). The Pool-Frenkel high-field effect was observed at electrical fields of about 10³–10⁴ V/cm; then the lowering factor of the potential barrier, the high frequency dielectric constant, and the refractive index of these glasses were determined.      

A new approach to calculate the gluon polarization

We derive the Leading-Order (LO) master equation to extract the polarized gluon distribution G(x,Q ²)=xδg(x,Q ²) from polarized proton structure function, g^p₁(x,Q²)g^{p}_{1}(x,Q^{2}). By using a Laplace-transform technique, we solve the master equation and derive the polarized gluon distribution inside the proton. The test of accuracy which is based in our calculations on two different methods, confirms that we achieve to the correct solution for the polarized gluon distribution. To determine the polarized gluon distribution xδg(x,Q ²) more accurately, we only need to have more experimental data on the polarized structure functions, g₁^p(x,Q²)g_{1}^{p}(x,Q^{2}). Our result for polarized gluon distribution is in good agreement with some phenomenological models.     

Derivations into duals of ideals of Banach algebras

We introduce two notions of amenability for a Banach algebra A. LetI be a closed two-sided ideal inA, we sayA is I-weakly amenable if the first cohomology group ofA with coefficients in the dual space I* is zero; i.e.,H ¹(A, I*) = {0}, and,A is ideally amenable ifA isI-weakly amenable for every closed two-sided idealI inA. We relate these concepts to weak amenability of Banach algebras. We also show that ideal amenability is different from amenability and weak amenability. We study theI-weak amenability of a Banach algebraA for some special closed two-sided idealI.     

Target mass correction on the 3He polarized structure function

Target mass correction (TMC) is employed to amend the polarized helium structure functions, ³He . The structure function can be obtained via the convolution of the light cone momentum distribution with the polarized structure of the proton and neutron. The calculation of the polarized structure function of the nucleon is based on the constituent quark model. The analytical result for ³He polarized structure function at low values of Q² is not in good agreement with the available experimental data. The reliability of calculations is increased using TMC effect. New comparison confirms a better agreement with the experimental data.     

The Q<Superscript>2</Superscript> dependence of polarized and unpolarized proton structure functions in the relativistic quark exchange framework

In this article we intend to discuss the evolution of polarized and unpolarized structure functions in the (x,Q²) plane. We analyze the proton data on the spin dependence asymmetry A₁(x,Q²), by making the dynamical assumption that at low resolution energies, the hadrons consist only of valence quarks and the scaling violation of F₂(x,Q²) at low x comes only from the gluons density. While the sea quark and the gluon distributions are calculated using the inverse Mellin technique and the various moments of the valence quarks, the valence quark distribution itself is obtained from the relativistic quark-exchange model. A comparison is made with the corresponding available experimental data. Finally in agreement with the data, it is demonstrated that there is no significant Q²-dependence of asymmetry A₁(x,Q²) for x ranging 0.014 ≤ x ≤ 0.25. Received: 11 September 1999 / Revised version: 8 December 1999     

Quantitative assay of plasma homocysteine thiolactone by gas chromatography/mass spectrometry

Enzymatic cyclization of homocysteine forms a reactive thiolactone that may play an important role in its cardiovascular toxicity, but reliable quantitation of the free thiolactone metabolite in physiological fluids has not been reported. We have therefore used a highly selective gas chromatography/mass spectrometry (GC/MS) technique combined with the sensitivity of negative chemical ionization (NCI) to develop a quantitative method for the detection of homocysteine thiolactone (HcyTL) in plasma. To improve accuracy the deuterated isomer d(4)-HcyTL was synthesized and added to plasma as internal standard. The plasma was then treated with silica solid-phase extraction and derivatized with heptafluorobutyric anhydride. The derivative was analyzed by GC/MS in NCI mode with methane as the reagent gas and quantified by analyzing for the HcyTL ion [M(-)[bond]HF] and its d(4)-HcyTL counterpart in single-ion monitoring mode. The calibration curve showed a dynamic linear range up to 40 nmol/L. Within-day precision (n = 20, nominal concentration 5.2 nmol/L) was 0.96% and between-day precision was 3.9%, with a detection limit of 1.7 nmol/L and quantification limit of 5.2 nmol/L. Two human plasma samples had HcyTL concentrations of 18 and 25 nmol/L. This facile method for quantitation of homocysteine thiolactone opens the way for more detailed clinical studies of its potential role in homocysteine-induced arteriosclerosis and vaso-occlusive disease.