Points on nodal lines with given direction

We study of the directional distribution function of nodal lines for eigenfunctions of the Laplacian on a planar domain. This quantity counts the number of points where the normal to the nodal line points in a given direction. We give upper bounds for the flat torus, and compute the expected number for arithmetic random waves.Comment: The statement and the proof of Theorem 1.2 correcte

Percolation, statistical topography, and transport in random-media

A review of classical percolation theory is presented, with an emphasis on novel applications to statistical topography, turbulent diffusion, and heterogeneous media. Statistical topography involves the geometrical properties of the isosets (contour lines or surfaces) of a random potential psi(x). For rapidly decaying correlations of psi, the isopotentials fall into the same universality class as the perimeters of percolation clusters. The topography of long-range correlated potentials involves many length scales and is associated either with the correlated percolation problem or with Mandelbrot's fractional Brownian reliefs. In all cases, the concept of fractal dimension is particularly fruitful in characterizing the geometry of random fields. The physical applications of statistical topography include diffusion in random velocity fields, heat and particle transport in turbulent plasmas, quantum Hall effect, magnetoresistance in inhomogeneous conductors with the classical Hall effect, and many others where random isopotentials are relevant. A geometrical approach to studying transport in random media, which captures essential qualitative features of the described phenomena, is advocated.Physic

Statistical assessment on Non-cooperative Target Recognition using the Neyman-Pearson statistical test

Electromagnetic simulations of a X-target were performed in order to obtain its Radar Cross Section (RCS) for several positions and frequencies. The software used is the CST MWS©. A 1 : 5 scale model of the proposed aircraft was created in CATIA© V5 R19 and imported directly into the CST MWS© environment. Simulations on the X-band were made with a variable mesh size due to a considerable wavelength variation. It is intended to evaluate the Neyman-Pearson (NP) simple hypothesis test performance by analyzing its Receiver Operating Characteristics (ROCs) for two different radar detection scenarios - a Radar Absorbent Material (RAM) coated model, and a Perfect Electric Conductor (PEC) model for recognition purposes. In parallel the radar range equation is used to estimate the maximum range detection for the simulated RAM coated cases to compare their shielding effectiveness (SE) and its consequent impact on recognition. The AN/APG-68(V)9’s airborne radar specifications were used to compute these ranges and to simulate an airborne hostile interception for a Non-Cooperative Target Recognition (NCTR) environment. Statistical results showed weak recognition performances using the Neyman-Pearson (NP) statistical test. Nevertheless, good RCS reductions for most of the simulated positions were obtained reflecting in a 50:9% maximum range detection gain for the PAniCo RAM coating, abiding with experimental results taken from the reviewed literature. The best SE was verified for the PAniCo and CFC-Fe RAMs.Simulações electromagnéticas do alvo foram realizadas de modo a obter a assinatura radar (RCS) para várias posições e frequências. O software utilizado é o CST MWS©. O modelo proposto à escala 1:5 foi modelado em CATIA© V5 R19 e importado diretamente para o ambiente de trabalho CST MWS©. Foram efectuadas simulações na banda X com uma malha de tamanho variável devido à considerável variação do comprimento de onda. Pretende-se avaliar estatisticamente o teste de decisão simples de Neyman-Pearson (NP), analisando as Características de Operação do Receptor (ROCs) para dois cenários de detecção distintos - um modelo revestido com material absorvente (RAM), e outro sendo um condutor perfeito (PEC) para fins de detecção. Em paralelo, a equação de alcance para radares foi usada para estimar o alcance máximo de detecção para ambos os casos de modo a comparar a eficiência de blindagem electromagnética (SE) entre os diferentes revestimentos. As especificações do radar AN/APG-68(V)9 do F-16 foram usadas para calcular os alcances para cada material, simulando uma intercepção hostil num ambiente de reconhecimento de alvos não-cooperativos (NCTR). Os resultados mostram performances de detecção fracas usando o teste de decisão simples de Neyman-Pearson como detector e uma boa redução de RCS para todas as posições na gama de frequências selecionada. Um ganho de alcance de detecção máximo 50:9 % foi obtido para o RAM PAniCo, estando de acordo com os resultados experimentais da bibliografia estudada. Já a melhor SE foi verificada para o RAM CFC-Fe e PAniCo

Study of quantitative methods for LEM LANDING-SITE selection Final report

Mathematical, statistical, and optical-Fourier methods for lunar excursion module landing site selectio

The probability of detecting and tracking RADAR targets in clutter at low grazing angles

Modern military acquisition and tracking RADARs are required to operate against aircraft and missiles specifically designed to have minimal radar cross section (RCS) and which fly at very low level to take maximum advantage of terrain screening. A model for predicting system performance is necessary for a range of terrain types in varying precipitation and seasonal cultural conditions. While the main degradation is from surface clutter and denial of sightline due to terrain and other local obstructions, several other factors such as multipath propagation, deliberate jamming and even operator performance contribute to the total model. The possibility that some radars may track obscured targets, however briefly, by using the diffraction path, is of particular interest. Although this report critically examines each of the contributory factors in order to select optimum values for inclusion in an overall computer prediction model; a new surface clutter model is specifically developed for sloped terrain using actual clutter measurements. The model is validated by comparison with an extensive survey of worldwide clutter results from both published and unpublished sources. Certain constraints have been necessary to restrict the study to a manageable size, while meeting the requirements of the sponsors. Attention is therefore focussed upon performance prediction for typical mobile tracking radar systems designed for operation against small RCS low level targets flying overland

Development and performance evaluation of a multistatic radar system

Multistatic radar systems are of emerging interest as they can exploit spatial diversity, enabling improved performance and new applications. Their development is being fuelled by advances in enabling technologies in such fields as communications and Digital Signal Processing (DSP). Such systems differ from typical modern active radar systems through consisting of multiple spatially diverse transmitter and receiver sites. Due to this spatial diversity, these systems present challenges in managing their operation as well as in usefully combining the multiple sources of information to give an output to the radar operator. In this work, a novel digital Commercial Off-The-Shelf (COTS) based coherent multistatic radar system designed at University College London, named ‘NetRad’, has been developed to produce some of the first published experimental results, investigating the challenges of operating such a system, and determining what level of performance might be achievable. Full detail of the various stages involved in the combination of data from the component transmitter-receiver pairs within a multistatic system is investigated, and many of the practical issues inherent are discussed. Simulation and subsequent experimental verification of several centralised and decentralised detection algorithms in terms of localisation (resolution and parameter estimation) of targets was undertaken. The computational cost of the DSP involved in multistatic data fusion is also considered. This gave a clear demonstration of several of the benefits of multistatic radar. Resolution of multiple targets that would have been unresolvable in a conventional monostatic system was shown. Targets were also shown to be plotted as two-dimensional vector position and velocities from use of time delay and Doppler shift information only. A range of targets were used including some such as walking people which were particularly challenging due to the variability of Radar Cross Section (RCS). Performance improvements were found to be dependant on the type of multistatic radar, method of data fusion and target characteristics in question. It is likely that future work will look to further explore the optimisation of multistatic radar for the various measures of performance identified and discussed in this work

Mean conservation of nodal volume and connectivity measures for Gaussian ensembles

We study in depth the nesting graph and volume distribution of the nodal domains of a Gaussian field, which have been shown in previous works to exhibit asymptotic laws. A striking link is established between the asymptotic mean connectivity of a nodal domain (i.e.\ the vertex degree in its nesting graph) and the positivity of the percolation probability of the field, along with a direct dependence of the average nodal volume on the percolation probability. Our results support the prevailing ansatz that the mean connectivity and volume of a nodal domain is conserved for generic random fields in dimension $d=2$ but not in $d \ge 3$, and are applied to a number of concrete motivating examples.Comment: 29 pages, 4 figure

COMBAT SYSTEMS Volume 1. Sensor Elements Part I. Sensor Functional Characteristics

This document includes: CHAPTER 1. SIGNATURES, OBSERVABLES, & PROPAGATORS. CHAPTER 2. PROPAGATION OF ELECTROMAGNETIC RADIATION. I. – FUNDAMENTAL EFFECTS. CHAPTER 3. PROPAGATION OF ELECTROMAGNETIC RADIATION. II. – WEATHER EFFECTS. CHAPTER 4. PROPAGATION OF ELECTROMAGNETIC RADIATION. III. – REFRACTIVE EFFECTS. CHAPTER 5. PROPAGATION OF ELECTROMAGNETIC RADIATION IV. – OTHER ATMOSPHERIC AND UNDERWATER EFFECTS. CHAPTER 6. PROPAGATION OF ACOUSTIC RADIATION. CHAPTER 7. NUCLEAR RADIATION: ITS ORIGIN AND PROPAGATION. CHAPTER 8. RADIOMETRY, PHOTOMETRY, & RADIOMETRIC ANALYSIS. CHAPTER 9. SENSOR FUNCTIONS. CHAPTER 10. SEARCH. CHAPTER 11. DETECTION. CHAPTER 12. ESTIMATION. CHAPTER 13. MODULATION AND DEMODULATION. CHAPTER 14. IMAGING AND IMAGE-BASED PERCEPTION. CHAPTER 15. TRACKING. APPENDIX A. UNITS, PHYSICAL CONSTANTS, AND USEFUL CONVERSION FACTORS. APPENDIX B. FINITE DIFFERENCE AND FINITE ELEMENT TECHNIQUES. APPENDIX C. PROBABILITY AND STATISTICS. INDEX TO VOLUME 1. Note by author: Note: Boldface entries in the table of contents are not yet completed