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Optimizing the Fisher ratio is well established in statistical pattern recognition as a means of discriminating between classes. I show how to optimize that ratio for optical correlation intensity by choice of filter on an arbitrary spatial light modulator (SLM). I include the case of additive noise of known power spectral density.
The presented research deals with the development of a dynamic analysis method for structural systems. The modeling approach is essentially a finite element method in the sense that the structure is divided into n elements. An element is defined as any structural unit whose degree of freedom (dofs) can be categorized as either interface or non-interface dofs. An element could be a fundamental unit such as a rod, a beam, a plate etc., or it could be an entire structural component. Furthermore, the parameters for the element could be distributed or lumped. The choice of elements is totally arbitrary and is a matter of user convenience. In particular, issues of accuracy and convergence do not enter on the level of example that bookkeeping is reduced to a minimum. Each element is modeled using a set of interface constraint modes (ICM) combined with a set of interface restrained normal models (IRNM). The next step is the solution of the system eigenvalue problem. The procedure calls for the sequential solution of a number of small eigenvalue problems based on a truncation principle for IRNM. In addition, the form of these eigenvalue problems is very simple such that an escalator type of eigenvalue problem solver can be used which is extremely cost-effective and fast.
Inverse kinematics (IK) for 6-DOF and 7-DOF revolute robot manipulators may be decomposed into canonical subproblems which find the angles on circles where they intersect with other geometric objects. We present new algebraic solutions and geometric interpretations for six subproblems. We demonstrate significant performance improvements over existing IK methods. 7-DOF manipulators have one redundant DOF to parameterize, so we introduce the general SEW angle, which generalizes the conventional SEW angle but with an arbitrary reference direction function. One special choice, the stereographic SEW angle, has a singularity when the wrist is on a half-line instead of a full line.
An extension of Osher's approximate Riemann solver to include gases with an arbitrary equation of state is presented. By a judicious choice of thermodynamic variables, the Riemann invariats are reduced to quadratures which are then approximated numerically. The extension is rigorous and does not involve any further assumptions or approximations over the ideal gas case. Numerical results are presented to demonstrate the feasibility and accuracy of the proposed method.
Langland and Baker (2004) introduced an approach to assess the impact of observations on the forecasts. In that, a state-space aspect of the forecast is defined and a procedure is derived that relates changes in the aspect with changes in the initial conditions associated with the assimilation of observations) ultimately providing information about the impact of individual observations on the forecast. Some features of the approach are to be noted. The typical choice of forecast aspect employed in related works is rather arbitrary and leads to an incomplete assessment of the observing system. Furthermore, the state-space forecast aspect requires availability of a verification state that should ideally be uncorrelated with the forecast but in practice is not. Lastly, the approach involves the adjoint operator of the entire data assimilation system and as such it is constrained by the validity of this operator. In this presentation, an observation-space metric is used that, for a relatively time-homogeneous observing system, allows inferring observation impact on the forecast without some of the limitations above. Specifically, using observation-minus-forecast residuals leads to an approach with the following features: (i) it suggests a rather natural choice of forecast aspect, directly linked to the analysis system and providing full assessment of the observations; (ii) it naturally avoids introducing undesirable correlations in the forecast aspect by verifying against the observations; and (iii) it does not involve linearization and use of adjoints; therefore being applicable to any length of forecast. The state and observation-space approaches might be complementary to some degree, and involve different limitations and complexities. Illustrations are given using the NASA GEOS-5 data.
The class of all possible formulas for computing arbitrary moments of a region from the region's boundary is derived. The selection of a particular formula depends on the choice of an independent parameter. Several choices of this parameter are explored for region boundaries approximated by polygons. The parameter choice that minimizes computation time for boundaries represented by chain code is derived. Algorithms are presented for computing arbitrary moments for a region from a polygonal approximation of its boundary and for computing low order moments from chain encoded boundaries.
A general definition of squeezed states is proposed and its main features are illustrated through a discussion of the standard optical coherent states represented by 'Gaussian pure states'. The set-up involves representations of groups on Hilbert spaces over homogeneous spaces of the group, and relies on the construction of a square integrable (coherent state) group representation modulo a subgroup. This construction depends upon a choice of a Borel section which has a certain permissible arbitrariness in its selection; this freedom is attributable to a squeezing of the defining coherent states of the representation, and corresponds in this way to a sort of gauging.
The structure modification problem, where the computer model of a structure is to be upgraded on the basis of experimental measurements of normal mode frequencies, is approached by the modal energy concept. The modes for correlation with test data are selected on the basis of relative strain energy participation. The resulting procedure can be viewed as an extension of White's (1972) method. Its advantage lies in that both the number and choice of structural parameters to be varied in the modification are arbitrary.
Computer program helps designers to generate detailed configuration geometry with much flexibility in choices of configurations and details of description. Input requirements, program turnaround time, and costs are kept low. It consists of routines that generate fuselage and planar-surface (winglike) geometries and routine that determines true intersection of all components with fuselage.
We present a high-order finite-element method for moving body and fluid/structure interaction problems. Our solution strategy is based on a space-time discontinuous Galerkin (DG) spectral-element discretization which extends to arbitrary order of accuracy. The space-time DG discretization is a natural choice for moving body and fluid-structure interaction problems as moving surfaces are incorporated simply by considering curved space-time elements whose space-time faces align with the moving body. We present a discontinuous-Galerkin in time discretization for six-degree of motion modeling of rigid bodies, and a continuous-Galerkin discretization for equations of linear elasticity to generate curved space-time meshes. Numerical results for several simple 2D test cases are presented in order to verify the implementation of the different models. Finally we present a preliminary dynamic simulation of a parachute.
The implementation of complete exchange on the circuit switched Intel iPSC-860 hypercube is described. This pattern, also known as all-to-all personalized communication, is the densest requirement that can be imposed on a network. On the iPSC-860, care needs to be taken to avoid edge contention, which can have a disastrous impact on communication time. There are basically two classes of algorithms that achieve contention-free complete exchange. The first contains the classical standard exchange algorithm that is generally useful for small message sizes. The second includes a number of optimal or near-optimal algorithms that are best for large messages. Measurement of communication overhead on the iPSC-860 are given and a notation for analyzing communication link usage is developed. It is shown that for the two classes of algorithms, there is substantial variation in performance with synchronization technique and choice of message protocol. Timings of six implementations are given; each of these is useful over a particular range of message size and cube dimension. Since the complete exchange is a superset of communication patterns, these timings represent upper bounds on the time required by an arbitrary communication requirement. These results indicate that the programmer needs to evaluate several possibilities before finalizing an implementation - a careful choice can lead to very significant savings in time.
Discrete time finite dimensional autonomous linear systems, investigating controllability and pole assignment to closed loop transfer matrix by choice of state variable feedback gain
We discuss the far-ultraviolet upturn phenomenon (UVX) observed in elliptical galaxies and spiral galaxy bulges. Our premise is the UV radiation from these systems emanates primarily from extreme horizontal branch (EHB) stars and their progeny. We derive the broad-band UV colors 1500-V and 2500-V for globular clusters and elliptical galaxies from the available satellite data and investigate color-color and color-line strength correlation. Clusters can be bluer than any galaxy in 15-V and 25-V, implying larger hot star populations, but galaxies are significantly bluer than clusters in 15-25 at a given 15-V. We attribute this primarily to the effect of metal abundance on the mid-UV (2500 A) light. These redder colors of the galaxies also imply that the UVX in galaxies is not produced by metal-poor subpopulations similar to the clusters. We devlop a simple spectral synthesis formulation for all phases of single star evolution from the zero-age main sequence (ZAMS) to the white dwarf cooling track that requires only one or two parameters for each choice of age and abundance. We provide the ingredients necessary for constructing models with arbitrary horizontal branch (HB) morphologies in the age range 2 less than t less than 20 Gyr and for six metallicities in the range -2.26 less than (Fe/H) less than 0.58; we also consider the efect of enhanced Y in metal-rich models. The maximum lifetime UV output is produced by EHB stars with (M(sub env))(sup 0) approximately 0.02 solar mass and can be up to 30 times higher than for post-asymptotic giant branch (P-AGB) stars. The ultraviolet output of old populations is governed primarily by the distribution of (M(sub env))(sup 0)P(M(sub env))(sup 0), on the ZAHB. The UV output is not very sensitive to (Fe/H) or to Y, but it can change very rapidly with (M(sub env))(sup 0). Thus it is extremely sensitive to the precise nature of giant-branch mass loss. Our models use simple descriptions of P(M(sub env))(sup 0) to bracket the colors produced from any real distribution of stars. Our models accurately predict the range of UV colors observed for the globular clusters, given known constraints on their age, abundances, and HB morphologies. We find that models with (Fe/H) greater than or = 0 that do not contain EHB stars cannot reproduce the colors of most of the galaxies. The models also predict that the fraction of the far-UV light from P-AGB stars, which are spatially resolvable in nearby galaxies, is approximately 70% and approximately 20% for moderate UVX and strong UVX systems, respectively. We find that 25-V, but not 15-V, is sensitive to the age and abundance, though these cannot always be cleanly distinguished. The galaxy colors place limits of (Fe/H) greater than -0.5 and less than 15% on the contribution of globular cluster-type populations to the V light. Galaxy colors are consistent with solar-abundance models with ages in the range 6-14 Gyr. We discuss several implications of the observations and the models, including the question of light metal versus iron peak enhancements in galaxies, whether the UV color-Mg(sub 2) correlation is continuous or discrete, effects of helium abundnace on the UVX, and the key question of whether red giant branch mass loss can be large enough to produce the necessary EHB population in the strong UVX galaxies.
Simulation studies on the performance of IR sounders under varying conditions of cloud cover and cloud heights are carried out for Nimbus 6. An analytic function is derived for calculating the relative response to cloud height errors for arbitrary cloud-sensing channels. Based on the values of the response function, the best choice of channels for determining cloud amounts are obtained. An algorithm is described for determining cloud heights, and the sensitivity of cloud-height sensing channels is tested. It is found that for the HIRS instrument, the most transparent channel in the 4.3-micron band is optimal for adjusting cloud heights, while the channel in the 15-micron band peaking closest to the surface is best for determining cloud amounts
The development, validation and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems are discussed. A solution method that combines a finite-volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries was previously developed for fixed-grids. In the present research effort, this solution method is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.
The main goals are the development, validation, and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems. A solution method that combines a finite volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.
Frequency selective surfaces are widely used in the microwave and millimeter wave regions of the spectrum for filtering signals. They are used in telecommunication systems for multi-frequency operation or in instrument detectors for spectroscopy. The frequency selective surface operation depends on a periodic array of elements resonating at prescribed wavelengths producing a filter response. The size of the elements is on the order of half the electrical wavelength, and the array period is typically less than a wavelength for efficient operation. When operating in the optical region, diffraction gratings are used for filtering. In this regime the period of the grating may be several wavelengths producing multiple orders of light in reflection or transmission. In regions between these bands (specifically in the infrared band) frequency selective filters consisting of patterned metal layers fabricated using electron beam lithography are beginning to be developed. The operation is completely analogous to surfaces made in the microwave and millimeter wave region except for the choice of materials used and the fabrication process. In addition, the lithography process allows an arbitrary distribution of patterns corresponding to resonances at various wavelengths to be produced. The design of sub-millimeter filters follows the design methods used in the microwave region. Exacting modal matching, integral equation or finite element methods can be used for design. A major difference though is the introduction of material parameters and thicknesses that may not be important in longer wavelength designs. This paper describes the design of multi- bandwidth filters operating in the 1-5 micrometer wavelength range. This work follows on a previous design. In this paper extensions based on further optimization and an examination of the specific shape of the element in the periodic cell will be reported. Results from the design, manufacture and test of linear wedge filters built using microlithographic techniques and used in spectral imaging applications will be presented.
Frequency selective surfaces are widely used in the microwave and millimeter wave regions of the spectrum for filtering signals. They are used in telecommunication systems for multi-frequency operation or in instrument detectors for spectroscopy. The frequency selective surface operation depends on a periodic array of elements resonating at prescribed wavelengths producing a filter response. The size of the elements is on the order of half the electrical wavelength, and the array period is typically less than a wavelength for efficient operation. When operating in the optical region, diffraction gratings are used for filtering. In this regime the period of the grating may be several wavelengths producing multiple orders of light in reflection or transmission. In regions between these bands (specifically in the infrared band) frequency selective filters consisting of patterned metal layers fabricated using electron beam lithography are beginning to be developed. The operation is completely analogous to surfaces made in the microwave and millimeter wave region except for the choice of materials used and the fabrication process. In addition, the lithography process allows an arbitrary distribution of patterns corresponding to resonances at various wavelengths to be produced. The design of sub-millimeter filters follows the design methods used in the microwave region. Exacting modal matching, integral equation or finite element methods can be used for design. A major difference though is the introduction of material parameters and thicknesses tha_ may not be important in longer wavelength designs. This paper describes the design of multi-bandwidth filters operating in the I-5 micrometer wavelength range. This work follows on previous design [1,2]. In this paper extensions based on further optimization and an examination of the specific shape of the element in the periodic cell will be reported. Results from the design, manufacture and test of linear wedge filters built using micro-lithographic techniques and used ir spectral imaging applications will be presented.