Signal and System Approximation from General Measurements

In this paper we analyze the behavior of system approximation processes for stable linear time-invariant (LTI) systems and signals in the Paley-Wiener space PW_\pi^1. We consider approximation processes, where the input signal is not directly used to generate the system output, but instead a sequence of numbers is used that is generated from the input signal by measurement functionals. We consider classical sampling which corresponds to a pointwise evaluation of the signal, as well as several more general measurement functionals. We show that a stable system approximation is not possible for pointwise sampling, because there exist signals and systems such that the approximation process diverges. This remains true even with oversampling. However, if more general measurement functionals are considered, a stable approximation is possible if oversampling is used. Further, we show that without oversampling we have divergence for a large class of practically relevant measurement procedures.Comment: This paper will be published as part of the book "New Perspectives on Approximation and Sampling Theory - Festschrift in honor of Paul Butzer's 85th birthday" in the Applied and Numerical Harmonic Analysis Series, Birkhauser (Springer-Verlag). Parts of this work have been presented at the IEEE International Conference on Acoustics, Speech, and Signal Processing 2014 (ICASSP 2014

The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros

BICCO-Net II. Final report to the Biological Impacts of Climate Change Observation Network (BICCO-Net) Steering Group

• BICCO-Net Phase II presents the most comprehensive single assessment of climate change impacts on UK biodiversity to date. • The results provide a valuable resource for the CCRA 2018, future LWEC report cards, the National Adaptation Programme and other policy-relevant initiatives linked to climate change impacts on biodiversity

Analysis of false waves in numerical sea simulations

[EN] It is common practice to consider the random sea waves as a succession of discrete waves characterized by individual amplitudes and periods. The zero-up-crossing criterion for discretizing waves, as well as other criteria proposed by different authors, has been found to isolate some discrete waves that do not correspond to physical waves. These false waves alter the wave statistics of random sea waves. A new orbital criterion is proposed to avoid this problem. The orbital criterion has been shown to be consistent and robust with respect to the zero-up-crossing criterion. Furthermore, the new criterion produces a distribution of wave heights in better agreement with the Rayleigh distribution. The mean period of the discrete waves corresponding to the orbital criterion is proved to be T01, while the mean period of the zero-up-crossing waves is T02. A formula relating the Longuet-Higgins spectral bandwidth nu with the relative number of false waves is given.Gimenez Valentin, MH.; Sánchez Carratalá, CR.; Medina, JR. (1994). Analysis of false waves in numerical sea simulations. Ocean Engineering. 21(8):751-764. doi:10.1016/0029-8018(94)90050-7S75176421

Metastability and Transient Effects in Vortex Matter Near a Decoupling Transition

We examine metastable and transient effects both above and below the first-order decoupling line in a 3D simulation of magnetically interacting pancake vortices. We observe pronounced transient and history effects as well as supercooling and superheating between the 3D coupled, ordered and 2D decoupled, disordered phases. In the disordered supercooled state as a function of DC driving, reordering occurs through the formation of growing moving channels of the ordered phase. No channels form in the superheated region; instead the ordered state is homogeneously destroyed. When a sequence of current pulses is applied we observe memory effects. We find a ramp rate dependence of the V(I) curves on both sides of the decoupling transition. The critical current that we obtain depends on how the system is prepared.Comment: 10 pages, 15 postscript figures, version to appear in PR

Spectral analysis and zeta determinant on the deformed spheres

We consider a class of singular Riemannian manifolds, the deformed spheres $S^N_k$, defined as the classical spheres with a one parameter family $g[k]$ of singular Riemannian structures, that reduces for $k=1$ to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian $\Delta_{S^N_k}$, we study the associated zeta functions $\zeta(s,\Delta_{S^N_k})$. We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the ones appearing in $\zeta(s,\Delta_{S^N_k})$. An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and in particular $\zeta(0,\Delta_{S^N_k})$ and $\zeta'(0,\Delta_{S^N_k})$. We give explicit formulas for the zeta regularized determinant in the low dimensional cases, $N=2,3$, thus generalizing a result of Dowker \cite{Dow1}, and we compute the first coefficients in the expansion of these determinants in powers of the deformation parameter $k$.Comment: 1 figur

Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals

We investigate analytically and numerically the mean-field superconducting-normal phase boundaries of two-dimensional superconducting wire networks and Josephson junction arrays immersed in a transverse magnetic field. The geometries we consider include square, honeycomb, triangular, and kagome' lattices. Our approach is based on an analytical study of multiple-loop Aharonov-Bohm effects: the quantum interference between different electron closed paths where each one of them encloses a net magnetic flux. Specifically, we compute exactly the sums of magnetic phase factors, i.e., the lattice path integrals, on all closed lattice paths of different lengths. A very large number, e.g., up to $10^{81}$ for the square lattice, exact lattice path integrals are obtained. Analytic results of these lattice path integrals then enable us to obtain the resistive transition temperature as a continuous function of the field. In particular, we can analyze measurable effects on the superconducting transition temperature, $T_c(B)$, as a function of the magnetic filed $B$, originating from electron trajectories over loops of various lengths. In addition to systematically deriving previously observed features, and understanding the physical origin of the dips in $T_c(B)$ as a result of multiple-loop quantum interference effects, we also find novel results. In particular, we explicitly derive the self-similarity in the phase diagram of square networks. Our approach allows us to analyze the complex structure present in the phase boundaries from the viewpoint of quantum interference effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure

Triggering Threshold Spacecraft Charging with Changes in Electron Emission from Materials

Modest changes in spacecraft charging conditions can lead to abrupt changes in the spacecraft equilibrium, from small positive potentials to large negative potentials relative to the space plasma; this phenomenon is referred to as threshold charging. It is well known that temporal changes of the space plasma environment (electron plasma temperature or density) can cause threshold charging. Threshold charging can also result from by temporal changes in the juxtaposition of the spacecraft to the environment, including spacecraft orbit, orientation, and geometry. This study focuses on the effects of possible changes in electron emission properties of representative spacecraft materials. It is found that for electron-induced emission, the possible threshold scenarios are very rich, since this type of electron emission can cause either positive or negative charging. Alternately, modification of photon- or ion-induced electron emission is found to induce threshold charging only in certain favorable cases. Changes of emission properties discussed include modifications due to: contamination, degradation and roughening of surfaces and layered materials; biasing and charge accumulation; bandstructure occupation and density of states caused by heat, optical or particle radiation; optical reflectivity and absorptivity; and inaccuracies and errors in measurements and parameterization of materials properties. An established method is used here to quantitatively gauge the relative extent to which these various changes in electron emission alter a spacecraft’s charging behavior and possibly lead to threshold charging. The absolute charging behavior of a hypothetical flat, two-dimensional satellite panel of a single material (either polycrystalline conductor Au or the polymeric polyimide Kapton™ H) is modeled as it undergoes modification and concomitant changes in spacecraft charging in three representative geosynchronous orbit environments, from full sunlight to full shade (eclipse) are considered

Percolating Reaction-Diffusion Waves (PERWAVES) — Sounding Rocket Combustion Experiments

Percolating reaction–diffusion waves in disordered random media are encountered in many branches of modern science, ranging from physics and biology to material science and combustion. Most disordered reaction–diffusion systems, however, have complex morphologies and reaction kinetics that complicate the study of the dynamics. Flames in suspensions of heterogeneously reacting metal-fuel particles is a rare example of a reaction–diffusion wave with a simple structure formed by point-like heat sources having well-defined ignition temperature thresholds and combustion times. Particle sedimentation and natural convection can be suppressed in the free-fall conditions of sounding rocket experiments, enabling the properties of percolating flames in suspensions to be observed, studied, and compared with emerging theoretical models. The current paper describes the design of the European Space Agency PERWAVES microgravity combustion apparatus, built by the Airbus Defense and Space team from Bremen in collaboration with the scientific research teams from McGill University and the Technical University of Eindhoven, and discusses the results of two sounding-rocket flight experiments. The apparatus allows multiple flame experiments in quartz glass tubes filled with uniform suspensions of 25-micron iron particles in oxygen/xenon gas mixtures. The experiments performed during the MAXUS-9 (April 2017) and TEXUS-56 (November 2019) sounding rocket flights have confirmed flame propagation in the discrete mode, which is a pre-requisite for percolating-flame behavior, and have allowed observation of the flame structure in the vicinity of the propagation threshold