| Modeling a Temporally Evolving Atmosphere with Zernike Polynomials |
Sep 2012 |
8 pages |
| Authors:
Isaac B Putnam; Stephen C Cain; AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
|
 | This paper develops a new, more accurate temporal model of phase screen generation. The long standing Fourier transform (FT) based method assumes the frozen flow hypothesis holds, where large phase screens are generated and then shifted. The result is a statistically correct screen. Realistically however, the phase changes with time especially when the wind velocity is small or non-existent. The temporal evolution method proposed in this paper is based on ... |
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| Microstructure-Sensitive HCF and VHCF Simulations (Preprint) |
Aug 2012 |
44 pages |
| Authors:
Craig Przybyla; William Musinski; Gustavo Castelluccio; David L McDowell; AIR FORCE RESEARCH LAB WRIGHT-PATTERSON AFB OH MATERIALS AND MANUFACTURING DIRECTORATE
|
| This paper provides some background and historical review of how microstructure-sensitive finite element simulations can play a role in understanding effects of stress amplitude, R-ratio, and microstructure on fatigue crack formation and early growth at notches, including pores and non-metallic inclusions for Ti alloys and Ni-base superalloys. Fatigue indicator parameters (FIPs) are computed over finite volumes that relate to processes of fatigue crack formation and early growth at the scale ... |
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| Axiomatic Analysis of Co-occurrence Similarity Functions |
Feb 2012 |
34 pages |
| Authors:
U Kang; Mikhail Bilenko; Dengyong Zhou; Christos Faloutsos; CARNEGIE-MELLON UNIV PITTSBURGH PA SCHOOL OF COMPUTER SCIENCE
|
| Finding similar items based on co-occurrence data is an important data mining task with applications ranging from recommender systems to keyword based advertising. A number of co-occurrence similarity functions have been proposed based on graph-theoretic, geometric, and statistical abstractions. Despite the variety of existing algorithms, however, there exists no formal methodology for analyzing their properties and comparing their benefits and limitations. At the same time, the wide range of applications ... |
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| On the Correlation Functions Associated with Polynomials of the Diffusion Operator |
Oct 2011 |
7 pages |
| Authors:
Max Yaremchuk; Scott Smith; NAVAL RESEARCH LAB STENNIS DETACHMENT STENNIS SPACE CENTER MS OCEANOGRAPHY DIV
|
| Correlation functions (CFs) associated with the inverse background-error correlations (iBECs) represented by polynomials of the diffusion operator D are obtained analytically for the binomial approximations of the Gaussian BEC and in the general case of a quadratic polynomial of D. The respective analytical expressions for one-, two- and three-dimensional cases have two tuning parameters, which provide enough freedom in adjusting the CFs' shape to, experimental data. The polynomial coefficients of ... |
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| A Novel Empirical Orthogonal Function (EOF)-Based Methodology to Study the Internal Wave Effects on Acoustic Propagation |
Oct 2011 |
16 pages |
| Authors:
Gaelle Casagrande; Yann Stephan; Alex C Warn Varnas; Thomas Folegot; NAVAL RESEARCH LAB STENNIS DETACHMENT STENNIS SPACE CENTER MS OCEANOGRAPHY DIV
|
| This paper presents a novel approach to synthesize realistic environment for ocean-acoustic parametric studies. In its current form, this methodology applies to internal waves and tides. Empirical orthogonal function (EOF) decomposition is applied to a temporal series of temperature profiles. It can be observed that the first two time-dependent expansion coefficients are dynamically linked. When they are plotted one versus another in a scatter diagram, the cloud of points consists ... |
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| On Convergence of the Immersed Boundary Method for Elliptic Interface Problems |
29 Sep 2011 |
13 pages |
| Authors:
Zhilin Li; NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC COMPUTATION
|
| Peskin's Immersed Boundary (IB) method is one of the most popular numerical methods for many years and has been applied to problems in mathematical biology, fluid mechanics material sciences, and many other areas. Peskin's IB method is associated with discrete delta functions. It is believed that the IB method is first order accurate in the L(infinity) norm. But almost none rigorous proof could be found in the literature until recently ... |
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| Efficient Greedy Algorithms for High-Dimensional Parameter Spaces with Applications to Empirical Interpolation and Reduced Basis Methods |
09 Sep 2011 |
24 pages |
| Authors:
Jan S Hesthaven; Benjamin Stamm; Shun Zhang; BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS
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| We propose two new and enhanced algorithms for greedy sampling of high-dimensional functions. While the techniques have a substantial degree of generality, we frame the discussion in the context of methods for empirical interpolation and the development of reduced basis techniques for high-dimensional parametrized functions. The first algorithm, based on a assumption of saturation of error in the greedy algorithm, is shown to result in a significant reduction of the ... |
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| Spectroscopy of Dipolar Fermions in Layered Two-Dimensional and Three-Dimensional Lattices |
06 Sep 2011 |
14 pages |
| Authors:
Kaden R Hazzard; Alexey V Gorshkov; Ana M Rey; COLORADO UNIV AT BOULDER
|
| Motivated by ongoing measurements at JILA, we calculate the recoil-free spectra of dipolar interacting fermions, for example ultracold heteronuclear molecules, in a one-dimensional lattice of two-dimensional layers or pancakes, spectroscopically probing transitions between different internal (e.g., rotational) states. We additionally incorporate p-wave interactions and losses, which are important for reactive molecules such as KRb. Moreover, we consider other sources of spectral broadening: interaction-induced quasiparticle lifetimes and the different polarizabilities of ... |
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| The Restricted Isometry Property for Time-Frequency Structured Random Matrices |
16 Jun 2011 |
26 pages |
| Authors:
Goetz E Pfander; Holger Rauhut; Joel A Tropp; CALIFORNIA INST OF TECH PASADENA DEPT OF COMPUTING AND MATHEMATICAL SCIENCES
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| We establish the restricted isometry property for finite dimensional Gabor systems, that is, for families of time{frequency shifts of a randomly chosen window function. We show that the s-th order restricted isometry constant of the associated n n2 Gabor synthesis matrix is small provided s less or equal to cn2/3 / log2 n. This improves on previous estimates that exhibit quadratic scaling of n in s. Our proof develops bounds ... |
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| Characterizing Cyclostationary Features of Digital Modulated Signals with Empirical Measurements using Spectral Correlation Function |
JUN 2011 |
107 pages |
| Authors:
Mujun Song; AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING AND MANAGEMENT
|
| Signal detection is widely used in many applications. Some examples include Cognitive Radio (CR) and military intelligence. CRs use signal detection to sense spectral occupancy. Without guaranteed signal detection, a CR cannot reliably perform its role. Similarly, signal detection is the first step for garnering an opponent's information. Wireless signal detection can be performed using many different techniques. Some of the most popular include matched filters, energy detectors (which use ... |
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| Numeric Function Generators Using Piecewise Arithmetic Expressions |
MAY 2011 |
7 pages |
| Authors:
Shinobu Nagayama; Tsutomu Sasao; Jon T. Butler; NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
|
| This paper proposes new architectures for numeric function generators (NFGs) using piecewise arithmetic expressions. The proposed architectures are programmable, and they realize a wide range of numeric functions. To design an NFG for a given function, we partition the domain of the function into uniform segments, and transform a subfunction in each segment into an arithmetic spectrum. From this arithmetic spectrum, we derive an arithmetic expression, and realize the arithmetic ... |
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| Multidisciplinary Design Optimization Under Uncertainty: An Information Model Approach (PREPRINT) |
01 MAR 2011 |
39 pages |
| Authors:
James A. Reneke; Margaret M. Wiecek; Georges M. Fadel; Sundeep Samson; CLEMSON UNIV SC DEPT OF MATHEMATICAL SCIENCES
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| Motivated by needs of concurrent multi-disciplinary design of a multi-purpose vehicle, a modeling and methodological approach to handling tradeoffs is presented. Each component has uncertain elements and a random performance which is influenced by the performance of other components. The components may require different knowledge bases and models with different mathematical structures, time and size scales, calling for higher-level coordination. The theory of reproducing kernel Hilbert spaces provides the mathematical ... |
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| Grid-Free Electromagnetic Plasma Simulations |
01 Jan 2011 |
9 pages |
| Authors:
Andrew J Christlieb; MICHIGAN STATE UNIV EAST LANSING DEPT OF MATHEMATICS
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| Basic plasma science plays an increasingly significant role in applications of importance to the United States Air Force. Many of these applications require a fully kinetic description in at least part of the domain. The most common approach is to use a fully Lagrangian framework, where the model is reduced to tracking the evolution of test particles in phase space. Of the many varieties, the most accepted approach is Particle-In-Cell. ... |
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| A Matrix Approach for General Higher Order Linear Recurrences |
Jan 2011 |
18 pages |
| Authors:
Emrah Kilic; Pantelimon Stanica; NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF APPLIED MATHEMATICS
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| We consider k sequences of generalized order-k linear recurrences with arbitrary initial conditions and coefficients, and we give their generalized Binet formulas and generating functions. We also obtain a new matrix method to derive explicit formulas for the sums of terms of the k sequences. Further some relationships between determinants of certain Hessenberg matrices and the terms of these sequences are obtained. |
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| Theoretical Methods in the Non-Equilibrium Quantum Mechanics of Many Bodies |
2011 |
191 pages |
| Authors:
Andrew B. Robertson; MARYLAND UNIV COLLEGE PARK
|
| A toolbox of theoretical methods pertinent to the study of non-equilibrium many-body quantum mechanics is presented with an eye to specific applications in cold atoms systems and solids. We discuss the generalization from unitary quantum mechanics to the non-unitary framework of open quantum systems. Theoretical techniques include the Keldysh close-time-path integral and its associated correlation functions, the quantum kinetic equation, and numerical integration of equations of motion both unitary and ... |
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| Resistance of Concrete Masonry Walls With Membrane Catcher Systems Subjected to Blast Loading |
DEC 2010 |
22 pages |
| Authors:
Lee G. Moradi; Robert J. Dinan; Bryan T. Bewick; James S. Davidson; ALABAMA UNIV IN BIRMINGHAM
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| This paper describes a methodology for analyzing the impulse pressure response of unreinforced concrete masonry walls that have been retrofitted with membranes that are not bonded to the masonry (catcher systems). Membrane catcher systems can be used to protect building occupants from secondary debris resulting from blast pressure, and the effectiveness of systems comprised of polymers, composites, geotextiles, and thin steel and aluminum sheets has been researched extensively over the ... |
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| A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams |
AUG 2010 |
10 pages |
| Authors:
Shinobu Nagayama; Tsutomu Sasao; Jon T. Butler; NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
|
| This paper proposes a high-speed architecture to realize two-variable numeric functions. It represents the given function as an edge-valued multiple-valued decision diagram (EVMDD), and shows a systematic design method based on the EVMDD. To achieve a design, we characterize a numeric function f by the values of l and p for which f is an l-restricted Mp-monotone increasing function. Here, l is a measure of subfunctions of f and p ... |
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| On Vehicle Placement to Intercept Moving Targets (Preprint) |
09 MAR 2010 |
9 pages |
| Authors:
Shaunak D. Bopardikar; Stephen L. Smith; Francesco Bullo; CALIFORNIA UNIV SANTA BARBARA CENTER FOR CONTROL, DYNAMICAL SYSTEMS AND COMPUTATION (CCDC)
|
| We address optimal placement of vehicles with simple motion, to intercept a mobile target that arrives stochastically on a line segment. The optimality of vehicle placement is measured through a cost function associated with intercepting the target. With a single vehicle, we assume that the target either moves with fixed speed and in a fixed direction or moves to maximize the vertical height or intercept time. We show that each ... |
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| Programmable Architectures and Design Methods for Two-Variable Numeric Function Generators |
FEB 2010 |
13 pages |
| Authors:
Shinobu Nagayama; Tsutomu Sasao; Jon T. Butler; NAVAL POSTGRADUATE SCHOOL MONTEREY CA
|
| This paper proposes programmable architectures and design methods for numeric function generators (NFGs) of two-variable functions. To realize a two-variable function in hardware, we partition a given domain of the function into segments, and approximate the function by a polynomial in each segment. This paper introduces two planar segmentation algorithms that efficiently partition a domain of a two-variable function. This paper also introduces a design method for symmetric two-variable functions ... |
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| Numeric Function Generators |
Jul 2009 |
|
| Authors:
J T Butler; T Sasao; S Nagayama; NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
|
| We show the architecture and design of a numeric function generator that realizes, at high speed, arithmetic functions, like log x, sin x, 1 x , etc.. This approach is general; different circuits are not needed for different functions. Further, composite functions, like log (sin ( 1 x )) can be realized as easily as individual functions. A tutorial description of the method is presented, followed by descriptions of the ... |
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| Approximation for the Rayleigh Resolution of a Circular Aperture |
MAY 2009 |
3 pages |
| Authors:
Carl E. Mungan; NAVAL ACADEMY ANNAPOLIS MD DEPT OF PHYSICS
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| Rayleigh's criterion states that a pair of point sources are barely resolved by an optical instrument when the central maximum of the diffraction pattern due to one source coincides with the first minimum of the pattern of the other source. As derived in standard introductory physics textbooks,1 the first minimum for a rectangular slit of width a is located at angular position theta = sin(inverse) (lambda /a) for light of ... |
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| Logic Functions for Cryptography - A Tutorial |
MAY 2009 |
11 pages |
| Authors:
Jon T. Butler; Tsutomu Sasao; NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
|
| Significant research has been done on bent functions, yet researchers in switching theory have paid little attention to this important topic. The goal of this paper to provide a concise exposition. Bent functions are the most nonlinear functions among n-variable switching functions, and are useful in cryptographic applications. This paper discusses three other kinds of cyptographic properties, strict avalanche criterion, propation criterion, and correlation immunity. We discuss known properties, as ... |
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| Numeric Function Generators Using Decision Diagrams for Discrete Functions |
MAY 2009 |
7 pages |
| Authors:
Shinobu Nagayama; Tsutomu Sasao; Jon T. Butler; NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
|
| This paper introduces design methods for numeric function generators (NFGs) using decision diagrams. NFGs are hardware accelerators to compute values of numeric functions such as trigonometric, logarithmic, square root, and reciprocal functions. Most existing design methods for NFGs are intended only for a specific class of numeric functions. However, by using decision diagrams for discrete functions (i.e., word-level decision diagrams), we can systematically design fast and compact NFGs for a ... |
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| On the Use of Transeunt Triangles to Synthesize Fixed-Polarity Reed-Muller Expansions of Functions |
May 2009 |
|
| Authors:
Jon T Butler; Svetlana Yanushkevich; Gerhard W Dueck; Vlad P Shmerko; NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
|
| The transeunt triangle was originally proposed by Suprun [19] as the basis of an algorithm for synthesizing fixed-polarity Reed-Muller (FPRM) expansions of symmetric functions. However, he provided no proof that this technique produced the correct FPRM expansion. We provide such a proof, thus establishing the validity of the transeunt triangle technique. Further, we show the extent to which the transeunt triangle reduces the computational work needed. Because of the efficiency ... |
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| Floating-Point Numerical Function Generators Using EVMDDs for Monotone Elementary Functions |
Jan 2009 |
|
| Authors:
Shinobu Nagayama; Tsutomu Sasao; Jon T Butler; NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
|
| This paper proposes a design method for floating-point numerical function generators (NFGs) using multi-valued decision diagrams (MDDs). Our method applies to monotone elementary functions in which real values are converted into integer values that are represented by edge-valued MDDs (EVMDDs). We show that EVMDDs use fewer nodes by one or two orders of magnitude than two other types of decision diagrams, MTBDDs and BMDs. EVMDDs produce fast and compact floating-point ... |
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| Factorizations and Representations of Second Order Linear Recurrences with Indices in Arithmetic Progressions |
Jan 2009 |
14 pages |
| Authors:
E Kilic; P Stanica; NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF APPLIED MATHEMATICS
|
| In this paper we consider second order recurrences {Vk} and {Un} We give second order linear recurrences for the sequences {V +/- kn} and {U +/-kn}. Using these recurrence relations, we derive relationships between the determinants of certain matrices and these sequences. Further, as generalizations of the earlier results, we give representations and trigonometric factorizations of these sequences by matrix methods and methods relying on Chebyshev polynomials of the first ... |
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| Investigation of 2-Dimensional Isotropy of Under-Ice Roughness in the Beaufort Gyre and Implications for Mixed Layer Ocean Turbulence |
MAR 2008 |
73 pages |
| Authors:
Timothy P. McGeehan; NAVAL POSTGRADUATE SCHOOL MONTEREY CA
|
| The two-dimensional (2D) spectral properties, including the degree of isotropy, of under-ice roughness in the Beaufort Gyre were investigated. Under-ice roughness plays an important role in turbulent ocean heat, salt, and momentum fluxes that determine the delicate balance between surface forcing and the ocean interior that sustains or reduces the perennial ice cover. Accurate characterization of this roughness is important for numerical modeling and prediction of the Arctic air-ice-ocean system, ... |
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| Collaborative Operations for Personnel Recovery |
FEB 2008 |
98 pages |
| Authors:
Austin Tate; Jeff Dalton; Jussi Stader; Gerhard Wickler; Jeffrey Hansberger; EDINBURGH UNIV (UNITED KINGDOM) DEPT OF ARTIFICIAL INTELLIGENCE
|
| The report describes the I-X framework and its application to personnel recovery. When the I-X framework is instantiated with a domain-specific model, it is referred to as an I-X application. Such an application has been developed during the Co-OPR project for the task of personnel recovery and personnel recovery training. The I-X technology was applied to develop a tool that can be used to support collaborative personnel recovery as observed ... |
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| A Wall-Function Approach to Incorporating Knudsen-Layer Effects in Gas Micro Flow Simulations |
13 JUL 2005 |
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| Authors:
D. A. Lockerby; J. M. Reese; M. A. Gallis; KING'S COLL LONDON (UNITED KINGDOM) DEPT OF MECHANICAL ENGINEERING
|
 | For gas flows in microfluidic configurations, the Knudsen layer close to the wall can comprise a substantial part of the entire flowfield and has a major effect on quantities such as the mass flow rate through micro devices. The Knudsen layer itself is characterized by a highly nonlinear relationship between the viscous stress and the strain rate of the gas, so even if the Navier-Stokes equations can be used to ... |
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| On A Theory of Rates |
FEB 2005 |
68 pages |
| Authors:
Bruce W. Fowler; ARMY RESEARCH DEVELOPMENT AND ENGINEERING COMMAND REDSTONE ARSENAL AL
|
| While the concept of Rate is common to many disciplines, there exists no consistent and general mathematical theory of rates in any discipline. In this report, a general theory of rates is developed as a transformation of a discrete or punctuated representation into a continuous representation using functional theory. Stochastic events are represented using Renewal Theory and Order Statistics. Examples of several rate differential equations are presented, in some cases ... |
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| Application of the GSF-1 Algorithm to the Near-Optimal Timescale Prediction of the Hydrogen Maser |
SEP 2004 |
17 pages |
| Authors:
Laurent-Guy Bernier; METAS-SWISS FEDERAL OFFICE OF METROLOGYAND ACCREDITATION BERN-WABERN (SWITZERLAND)
|
| The GSF-1 timescale prediction algorithm is a simple generalization of the second difference prediction. It is close to optimal for combinations of power-law noise processes encountered in practice. By adding a drift parameter, it can be extended for use in presence of frequency drift without loss of optimality. It is applied to the timescale prediction of the hydrogen maser. |
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| Electromagnetic Propagation, Localization and Lasing in Random and Periodic Media |
30 DEC 2003 |
13 pages |
| Authors:
A. Z. Genack; CITY UNIV OF NEW YORK RESEARCH FOUNDATION
|
| Our measurements of the frequency and spatial variation of the microwave field in ensembles of random samples have revealed the underlying structure of wave correlation and photon localization. The intensity correlation was found in terms of displacement and polarization shift of the source and detector can be expressed in terms of the square of the corresponding field correlation function. Nonexponential decay of pulsed transmission through disordered media was found in ... |
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| An Approximate Method for Pitch-Damping Prediction |
JUL 2003 |
44 pages |
| Authors:
James E. Danberg; Paul Weinacht; ARMY RESEARCH LAB ABERDEEN PROVING GROUND MD WEAPONS AND MATERIALS RESEARCH DIRECTORATE
|
| A simple method of estimating the pitch-damping coefficients for axisymmetric flight bodies has been developed. The method is suitable for preliminary design and parametric studies. The procedure is based on concepts from slender body theory, but the method significantly improves the accuracy of the results through the use of correlation functions. To derive the correlation functions, extensive use of a recently developed and validated computational fluid dynamics (CFD) method for ... |
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| Fault Tree Representation and Evaluation |
MAR 2003 |
37 pages |
| Authors:
Richard Saucier; ARMY RESEARCH LAB ABERDEEN PROVING GROUND MD
|
| In order to conduct a vulnerability analysis of a combat vehicle, it is first necessary to perform a criticality analysis, which consists of describing each of its combat functions along with the underlying systems, subsystems, and components required to support the function. The basic building blocks for carrying out this process are the fault trees; they depict the logical arrangement of the components required for the proper functioning of the ... |
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| Applied Computational Electromagnetics Society Journal. Volume 17, Number 3 |
NOV 2002 |
|
| Authors:
Atef Z. Elsherbeni; APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY UNIVERSITY MS
|
| The Applied Computational Electromagnetics Society (ACES) Journal hereinafter known as the ACES Journal is devoted to the exchange of information in computational electromagnetics, to the advancement of the state-of-the art, and the promotion of related technical activities. A primary objective of the information exchange is the elimination of the need to "reinvent the wheel" to solve a previously-solved computational problem in electrical engineering, physics, or related fields of study. The ... |
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| When Are On-Off Sources SIS? Conditions and Applications |
2002 |
29 pages |
| Authors:
Sarut Vanichpun; Armand M. Makowski; MARYLAND UNIV COLLEGE PARK INST FOR SYSTEMS RESEARCH
|
| Recent advances from the theory of multivariate stochastic orderings can be used to formalize the "folk theorem" to the effect that positive correlations lead to larger buffer levels at a discrete-time infinite capacity multiplexer queue. For instance, it is known that if the input traffic is larger than its independent version in the supermodular (sm) ordering, then their corresponding buffer contents are similarly ordered in the increasing convex (icx) ordering. ... |
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| Autocorrelation and Cross-Correlation Analyses of Alpha Waves in Reflection to Subjective Preference of a Flickering Light |
25 OCT 2001 |
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| Authors:
Y. Soeta; S. Uetani; Y. Ando; KOBE UNIV (JAPAN) GRADUATE SCHOOL OF SCIENCE AND TECHNOLOGY
|
| To clarify the relationship between the human brain activity and subjective preference of a flickering light under changing temporal frequency and mean luminance, alpha waves were analyzed by autocorrelation function (ACF) and cross correlation function (CCF). Paired-comparison tests were performed to examine the subjective preference of a flickering light. Electroencephalograms (EEGs) were recorded from 7 electrodes (10-20 system) during presentations of the most preferred and the least preferred flickering-light conditions. ... |
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| An Overview of the Relationship Between Approximation Theory and Filtration |
JUL 2001 |
8 pages |
| Authors:
Paul J. Scott; Xiang Q. Jiang; Liam A. Blunt; HUDDERSFIELD UNIV LEEDS (UNITED KINGDOM)
|
| This paper gives an overview of the similarities and differences between the requirements and techniques used in mathematical approximation theory and filtration in surface metrology. Although the two fields tend to use the same or similar mathematical objects to produce functions that simplify a function in a controlled manner, it is the way that this simplification is achieved which is the main difference between the two. Approximation theory uses norms ... |
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| Applications of Radial Basis Functions: Sobolev-Orthogonal Functions, Radial Basis Functions and Spectral Methods |
JUL 2001 |
14 pages |
| Authors:
M. D. Buhmann; A. Iserles; S. P. Norsett; JUSTUS-LIEBIG-UNIV GIESSEN (GERMANY) MATHEMATICS INST
|
| In this paper we consider an application of Sobolev-orthogonal functions and radial basis function to the numerical solution of partial differential equations. We develop the fundamentals of a spectral method, present examples via reaction-diffusion partial differential equations and discuss briefly some links with theory of wavelets. |
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| Computing with Radial Basic Functions the Beatson-Light Way! |
JUL 2001 |
16 pages |
| Authors:
Will Light; LEICESTER UNIV (UNITED KINGDOM) MATHEMATICS AND COMPUTER SCIENCE DEPT
|
| In this paper we discuss a number of recent developments in the practice of how to compute with radial basic functions. The two main problems addressed are how to develop fast evaluation schemes for radial basic functions, and how to efficiently carry out the solution of the interpolation problem. The approach is to mainly describe work which has involved the author and Professor Rick Beatson as contributors, and to include ... |
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| Application of Orthogonalisation Procedures for Gaussian Radial Basis Functions and Chebyshev Polynomials |
JUL 2001 |
8 pages |
| Authors:
John C. Mason; Andrew Crampton; HUDDERSFIELD UNIV (UNITED KINGDOM) SCHOOL OF COMPUTING AND MATHEMATICS
|
| Procedures for orthogonalisation of Gaussians and B-splines are recalled and it is shown that, provided Gaussians are negligible in appropriate regions, the same recurrence formulae may be adopted in both and render the computation relatively efficient. Chebyshev polynomial collocation is well known to be rapidly defined by discrete orthogonalisation, and similar ideas are commonly applicable to partial differential equations (PDEs) and integral equations (IEs). However, it is shown that the ... |
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| Geometric Knot Selection for Radial Scattered Data Approximation |
JUL 2001 |
8 pages |
| Authors:
Rossana Morandi; Alessandra Sestini; FLORENCE UNIV (ITALY) DEPT OF ENERGETICA
|
| Scattered exact and non-exact data are approximated by means of radial basis functions with compact support and the related knot selection is based on the information given by the discrete Gaussian curvature defined on a data triangulation. In case of non-exact data, a strategy to obtain a sign-reliable estimate of its distribution is given extending an approach already studied by the authors for non-exact 2D data. |
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| On the Boundary Over Distance Preconditioner for Radial Basis Function Interpolation |
JUL 2001 |
8 pages |
| Authors:
C. T. Mouat; R. K. Beatson; CANTERBURY UNIV CHRISTCHURCH (NEW ZEALAND) DEPT OF MATHEMATICS AND STATISTICS
|
| In this paper we consider the boundary over distance preconditioner for radial basis function interpolation problems. We give both theoretical and numerical results indicating that it performs extremely well. |
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| Nonparametric Regression Subject to a Given Number of Local Extreme Value |
JUL 2001 |
8 pages |
| Authors:
Ali Majidi; Laurie Davis; ESSEN UNIV (GERMANY) DEPT OF MATHEMATICS AND COMPUTER SCIENCE
|
| We consider the problem of nonparametric regression. The aim is to get a smooth function which represents the dataset and has a reasonable number of extreme values. An iterative method, the QSOR method is introduced. Problems with the slow convergence of the method are reduced using multigrid techniques. |
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| Accurate Approximation of Functions with Discontinuities, Using Low Order Fourier Coefficients |
JUL 2001 |
8 pages |
| Authors:
R. K. Wright; VERMONT UNIV BURLINGTON DEPT OF MATHEMATICS AND STATISTICS
|
| In previous work we introduced a method of using polynomial splines with appropriate discontinuities to approximate a piecewise smooth function f with jump discontinuities of f and f'. The information used is location of discontinuities, and low order, possibly noisy Fourier coefficients. The number of discontinuities was limited to two at most, and the discontinuities needed to lie at meshpoints in a uniform mesh. We showed that the linear operator ... |
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| Approximation by Perceptron Networks |
JUL 2001 |
7 pages |
| Authors:
Vera Kurkova; CZECH ACADEMY OF SCIENCES PRAGUE INST OF COMPUTER SCIENCE
|
| In this paper we survey our recent results on properties of approximation by linear combinations of characteristic functions of half-spaces. We focus on existence of best approximation, impossibility of choosing among best approximations a continuous one, estimates of rates of approximation by linear combinations of "n" characteristic functions of half-spaces and integral representation as a linear combination of a continuum of half-spaces. |
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| Tomographic Reconstruction using Cesaro-Means and Newman-Shapiro Operators |
JUL 2001 |
8 pages |
| Authors:
Ulrike Maier; JUSTUS-LIEBIG-UNIV GIESSEN (GERMANY) MATHEMATICS INST
|
| Tomography is well known because of its many applications. Although theoretically solved, the numerical implementation of tomographic reconstruction algorithms is still a difficult problem. In this article the numerical implementation of a reconstruction method using Cesaro-means and Newman-Shapiro operators is described. The key point herein is the use of suitable quadrature formulae on the sphere. It turns out that in the context described product Gaussian formulae are best suited. The ... |
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| PSPICE Modelling and Parametric Study of Microbolometer Thermal Detectors |
JUN 2001 |
74 pages |
| Authors:
Scott W. Stetson; NAVAL POSTGRADUATE SCHOOL MONTEREY CA
|
| The operation of a bolometer thermal sensor is analogous to that of a charging capacitor in a generic RC circuit. As such, circuits containing bolometers can be analyzed with standard circuit simulation programs such as PSPICE. This thesis deals with the development of a bolometer model by using PSPICE with the aid of Analogue Behavior Modeling (ABM) capability, which allows the user to program circuit components with basic mathematical functions. ... |
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| Influence of the Integration Limits on the Shape of Pair Correlation Functions of Non-Crystalline Materials |
JUN 2001 |
10 pages |
| Authors:
W. Hoyer; I. Kaban; T. Halm; INSTITUTE OF PHYSICS CHEMNITZ (GERMANY)
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| Influence of the termination effect on the shape of pair correlation functions and values of structural parameters of liquid and amorphous materials has been investigated. It is shown that termination of the diffraction curve at Q(min) > 0 rather strongly affects the region around the first peak of g(r) especially its left flank. On the other hand, presence or absence of a prepeak at low Q-values of the structure factor ... |
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| Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications |
OCT 2000 |
19 pages |
| Authors:
Christopher D. Corte; Mark J. Valco; NATIONAL AERONAUTICS AND SPACE ADMINISTRATION CLEVELAND OH GLENN RESEARCH CENTER
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| This paper introduces a simple 'Rule of Thumb' (ROT) method to estimate the load capacity of foil air journal bearings, which are self-acting compliant-surface hydrodynamic bearings being considered for Oil-Free turbomachinery applications such as gas turbine engines. The ROT is based on first principles and data available in the literature and it relates bearing load capacity to the bearing size and speed through an ... |
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