Interest For Many Applications Research Articles

A Method to Enhance Noise Reduction for Data Generated from a Known Differential Equation

In this paper we propose a method to enhance noise reduction for data generated from a known differential equation. We develop a theoretical basis for the procedure and then illustrate it in the case of some data generated using Duffing’s equation. This method consists of embedding the data in higher dimensions and then transforming the data into a lower dimension using a singular matrix. We show that the singular matrix squeezes out some of the noise and leaves the true signal intact. Finally, using a nonlinear function, we reverse the effect of the singular matrix to get closer to the original data. In practice, it turns out that often noise contaminates chaotic signals. This leads to great difficulty in accessing the information carried by the chaotic signal. Thus the problem of cleaning a chaotic signal from external noise is of great interest in many applications. A number of linear and nonlinear noise reduction methods have been proposed. 1)–6) In this paper we demonstrate a method to enhance the noise reduction for data generated from a known differential equation. We assume that the noise is additive. The method consists of embedding data in higher dimensions and then transforming the data into a lower dimension using a singular matrix. We show that the singular matrix squeezes out some of the noise and leaves the true signal intact. Then, using a nonlinear function, we reverse the effect of the singular matrix to get closer to the original data. This function is independent of the initial conditions and can be empirically determined via numerical experiments using the known differential equation.

Synthesis and characterization of nano-biomaterials with potential osteological applications.

The manufacture of high-surface area, un-agglomerated nano-sized (1-100 nm) bioceramic particles are of interest for many applications including injectable/controlled setting bone cements, high strength porous/non-porous synthetic bone grafts, and the reinforcing phase in nano-composites that attempt to mimic the complex structure and superior mechanical properties of bone. In the present study, we report on the manufacture of nano-particle hydroxyapatite powders by several wet chemical methods, which incorporate a freeze-drying step. In particular, it was found that the emulsion-based syntheses yielded powders with high surface areas and small primary particle sizes. Freeze drying rather than oven drying of powders prepared by conventional wet chemical synthesis yielded a nano-sized powder with a comparatively higher surface area of 113 m(2)/g. All powders were calcined in air in a furnace at 900 degrees C to investigate the effects of synthesis method on phase purity and surface area. The materials were characterized by a range of analytical methods including Fourier-transform infrared spectroscopy employing the photo acoustic (PAS-FTIR) sampling technique, BET surface area analysis, X-ray powder diffraction (XRD), and the particles were examined using a transmission electron microscope (TEM).

Error bounds on multivariate Normal approximations for word count statistics

Given a sequence S and a collection Ω of d words, it is of interest in many applications to characterize the multivariate distribution of the vector of counts U = (N(S,w 1), …, N(S,w d )), where N(S,w) is the number of times a word w ∈ Ω appears in the sequence S. We obtain an explicit bound on the error made when approximating the multivariate distribution of U by the normal distribution, when the underlying sequence is i.i.d. or first-order stationary Markov over a finite alphabet. When the limiting covariance matrix of U is nonsingular, the error bounds decay at rate O ((log n) / √n) in the i.i.d. case and O ((log n)3 / √n) in the Markov case. In order for U to have a nondegenerate covariance matrix, it is necessary and sufficient that the counted word set Ω is not full, that is, that Ω is not the collection of all possible words of some length k over the given finite alphabet. To supply the bounds on the error, we use a version of Stein's method.

Error bounds on multivariate Normal approximations for word count statistics

Given a sequence S and a collection Ω of d words, it is of interest in many applications to characterize the multivariate distribution of the vector of counts U = (N(S,w1), …, N(S,wd)), where N(S,w) is the number of times a word w ∈ Ω appears in the sequence S. We obtain an explicit bound on the error made when approximating the multivariate distribution of U by the normal distribution, when the underlying sequence is i.i.d. or first-order stationary Markov over a finite alphabet. When the limiting covariance matrix of U is nonsingular, the error bounds decay at rate O((log n) / √n) in the i.i.d. case and O((log n)3 / √n) in the Markov case. In order for U to have a nondegenerate covariance matrix, it is necessary and sufficient that the counted word set Ω is not full, that is, that Ω is not the collection of all possible words of some length k over the given finite alphabet. To supply the bounds on the error, we use a version of Stein's method.

Zum Verhalten rost- und säurebeständiger Stähle unter Komplexbeanspruchung. Teil 1 Passivität und Lochkorrosionsbeständigkeit

Iron-Chromium-Nickel alloys are of special interest for many applications because of their excellent resistance to corrosion. The nature and composition, of passive films formed on stainless steels depend on the prevailing conditions, viz. steel-composition, passivation potential, aging, pH, electrolyt composition and temperature. Passive films may be damaged by local breakdown. At least two mechanisms are possible for this localisation: mechanical breakdown by slip steps and electrochemical breakdown (for e.g. by the effects of chloride ions). Because of this, steels suffer a degradation of their fatique properties when exposed to an aqueous environment. Passivation of austenitic, ferritic-austenitic and martensitic stainless steels has been studied in different solutions using electrochemical techniques. The results clarified that for two of the investigated alloys the prediction of fracture initiation based on pitting corrosion in chlorid containing solutions is possible.

Can the sample variance estimator be improved by using a covariate?

Variance componentsare quantities of central interest in many applications, e.g., in cultivar yield stability analysis and in the analysis of measurement errors. In some applications, the feasible sample size is rather limited, leading to estimates of variance components that are subject to considerable sampling variation. For example, new crop cultivars are tested in only a few environments before release to the market, so the sample size for the variance across environments is small. Similarly, testing a new measurement instrument for some chemical compound may be costly, allowing only a limited number of replications. This article investigates the potential for improving the usual sample variance estimator by exploiting covariate information. In a cultivartrial, yield data may be available for only a few environments while meteorological data or data on a standard cultivar has been recorded for a very large number of environments. Likewise, in the analysis of measurement errors, there may be long-term data on a standard measurement procedure that can be used as a covariate to improve the variance estimate for a new instrument. It is shown in this article that the gain in accuracy achieved by using a covariate can be considerable, provided there is sufficient correlation between the covariate and the variable of interest.

ROBUSTNESS ANALYSIS OF A RELAY OSCILLATOR

Relaxation oscillators typically consist of a hysteresis element and a dynamic feedback. The robustness of oscillations in such an interconnection is of interest in many applications. In particular, we seek the robustness margin on the component perturbations in the gap metric so that oscillatory behavior of the closed loop is preserved. A new distance measure for oscillatory signals utilizing time scaling is introduced for this purpose. The robustness of a system consisting of an ideal relay with hysteresis and an integrator has been studied in (Georgiou and Smith 2000). Here analogous results are derived for a system consisting of an integrator and a relay whose branches have non-zero slope. This system resembles the classical van der Pol oscillator more closely than the ideal relay system.

An Investigation of the Breakup of an Evaporating Liquid Film, Falling Down a Vertical, Uniformly Heated Wall

The breakup of an evaporating, thin liquid film falling down a vertical, uniformly heated wall is of interest in many applications. Analytical expressions are developed for predicting the thickness of an evaporating liquid film and the corresponding wetting rate at breakup, which are in good agreement with experimental data for water. These expressions, derived from minimizing the total energy of a stable liquid rivulet forming immediately following the film breakup, required solving for the rivulet profile and the two-dimensional velocity field in the rivulet. The total energy of the rivulet is the sum of the kinetics energy of the liquid, the surface energies at the liquid-vapor and the solid-liquid interfaces, and those due to evaporation and the thermocapillary force along the liquid-vapor interface. The liquid film thickness at breakup is a function of Marangoni number, vapor Reynolds number, liquid and vapor properties, equilibrium contact angle of the liquid with underlying wall material, and the wall thermal conductance <3×104 W/m2K. For a wall conductance <3×104 W/m2K, the film thickness at breakup, when the wall is heated uniformly at its inner surface, is higher than when the wall is heated at its outer surface, but both are identical when the wall conductance ⩾3×104 W/m2K. The contribution of the equilibrium contact angle diminishes, but the thickness of the liquid film at breakup increases, as the wall heat flux increases.

Modelling and 3D optimisation of CdTe pixels detector array geometry – Extension to small pixels

CdTe and CdZnTe pixel detectors offer great interest for many applications, especially for medical and industrial imaging. Up to now, the material, generally, used and investigated for pixel arrays was CZT (Hamel et al., IEEE Trans. Nucl. Sci. 43 (3) (1996) 1422; Barrett et al., Phys. Rev. Lett. 75 (1) (1995) 156; Bennett et al., Nucl. Instr. and Meth. A 392 (1997) 260; Eskin et al., J. Appl. Phys. 85 (2) (1999) 647; Brunett et al., J. Appl. Phys. 86 (7) (1999) 3926; Luke, Nucl. Instr. and Meth. A 380 (1996) 232), but cadmium telluride can also be an appropriate choice, as shown here. However, we clearly demonstrate here that the optimal pixel configuration is highly dependent on the electrical transport properties of the material. Depending on the field of primary interest, either energy resolution or counting rate efficiency in the photopeak, the geometry for each case has to be optimised. For that purpose, we have developed a calculation of the signal induced onto the pixel. Two distinct parts are used: after showing our approach for the weighting potential calculation, we present our results performed by a “pseudo-Monte Carlo” simulation. Results are supported by a few experimental comparisons. We argue about the optimum sizes with clarifying the problems caused by too small and too large pixel sizes. The study field is chosen to be vast, i.e. pixel size to detector thickness ratios ( W/ L) of 1/8–1, and detector thickness of 1.0–8.0 mm. In addition, several electrical transport properties are used. Since efficiency is often of primary interest, thick detectors could be very attractive, which are shown to be really feasible even on CdTe.

Atomic size effects in continuum modeling.

Continuum modeling of many physical systems typically assumes that the spatial extent of an atom is small compared to the quantities of interest and can therefore be neglected. We show that this is valid only asymptotically. For many applications of practical interest, the spatial extent of a discrete atom cannot be neglected. We have developed a model for the description of epitaxial growth based on the levelset method, and find that we can accurately predict quantities such as the island densities, if we implement boundary conditions in a region with atomic width, rather than just on a line without any spatial extent. Only in the limit of very large islands and island spacings can this be neglected.

Grouping method for the approximate solution of a kinetic equation describing the evolution of point-defect clusters

Abstract An approximate method for the numerical solution of a kinetic equation describing the nucleation, growth and coarsening of point-defect clusters or second-phase precipitates is of interest for many applications in solid-state physics. In the present paper the validity of a grouping method developed by Kiritani (1973, J. phys. Soc. Japan 35, 95) is examined. In this method, which is the only one proposed up to now, a group of equations is replaced by an ‘averaged’ equation. Significant disagreement between the group kinetic equation and the original kinetic equation is revealed and the reasons for this are specified. A new grouping method based on the original equation is proposed and application of the method for the solution of two problems is demonstrated by comparing the results of numerical and analytical calculations.

Direct numerical simulation of three‐dimensional flame instabilities

AbstractThe evolution of premixed gas flames near extinction and stability limits is of primary interest for many applications in combustion technology. Under such conditions the flames are very sensitive, and exhibit quasi‐steady state behaviour so that they are well‐suited to determine flammability limits. We show three‐dimensional numerical simulation of the transient behaviour of lean H2‐air flames. The thermo‐diffusive equations are solved by means of a parallelized Fourier‐pseudospectral code. We compute the evolution of freely propagating spherical flames, whereby the influence of the initial flame radius is investigated. The results exhibit different behaviour as found in experimental studies under microgravity conditions, i.e. the splitting due to cellular instabilities, extinction, and stationary flame balls.

Partitioning Trimmed Spline Surfaces into NonSelf-Occluding Regions for Visibility Computation

Computing the visible portions of curved surfaces from a given viewpoint is of great interest in many applications. It is closely related to the hidden surface removal problem in computer graphics, and machining applications in manufacturing. Most of the early work has focused on discrete methods based on polygonization or ray-tracing and hidden curve removal. In this paper we present an algorithm for decomposing a given surface into regions so that each region is either completely visible or hidden from a given viewpoint. Initially, it decomposes the domain of each surface based on silhouettes and boundary curves. To compute the exact visibility, we introduce a notion of visibility curves obtained by projection of silhouette and boundary curves and decomposition of the surface into nonoverlapping regions. These curves are computed using marching methods and we present techniques to compute all the components. The nonoverlapping and visible portions of the surface are represented as trimmed surfaces and we present a representation based on polygon trapezoidation algorithms. The algorithms presented use some recently developed algorithms from computational geometry like triangulation of simple polygons and point location. Given the nonoverlapping regions, we use an existing randomized algorithm for visibility computation. We also present results from a preliminary implementation of our algorithm.

Far-Field Pressure Estimation of a Plate from the Interpolated Acceleration Distribution

Prediction methods of noise radiated by vibrating structures are of great interest in many applications. Normal acceleration measurements at the radiatorsurface can be used in combinationwith amethod based on the Rayleigh integral to deduce the far-Ž eld radiation corresponding to the excitation sources. This method is very attractive because it is based mainly on the wave-number spectra computed by two-dimensional discrete Fourier transform. The acceleration distribution data are collected with an array of transducers in most practical cases. The spatial samplingperiod followstheNyquist theorem up to time frequencyFMAX . The acoustic computationfrommeasured data is inaccurate up to FMAX for some observation directions because of the limited domain in which the wavenumber spectra are available. A solution is proposed in this paper to remove this limitation. The wave-number spectra computationaldomain is extended by interpolating the acceleration distribution.This technique is applied in estimation of the far-Ž eld pressure radiated by a steel-baf ed plate tested in an anechoic chamber. Comparisons between experimental measurements and estimated amplitudes carried out with interpolated data are in good agreement in all spatial directions up to FMAX .

On the computational complexity of determining polyatomic structures by X-rays

The problem of recovering the structure of crystalline materials from their discrete X-rays is of fundamental interest in many practical applications. An important special case concerns determining the position of atoms of several different types in the integer lattice, given the number of each type lying on each line parallel to some lattice directions. We show that the corresponding consistency problem is NP -complete for any two (or more) different (fixed) directions when six (or more) types of atoms are involved.

Blind deconvolution of ultrasonic traces accounting for pulse variance

The ability of pulse-echo measurements to resolve closely spaced reflectors is limited by the duration of the ultrasonic pulse. Resolution can be improved by deconvolution, but this often fails because frequency selective attenuation introduces unknown changes in the pulse shape. In this paper we propose a maximum a posteriori algorithm for simultaneous estimation of a time varying pulse and high-resolution deconvolution. A priori information is introduced to encourage estimates where the pulse varies only slowly and the reflectivity sequence is sparse. This adds sufficient regularization to the problem, and no further assumptions on the pulse such as minimum phase or a particular parametric form are needed. The joint pulse and reflectivity estimate are computed iteratively by alternating steps of pulse estimation and reflectivity estimation. The first step amounts to only a linear least squares fit. The second step is a difficult combinatorial optimization problem that we solve by a suboptimal but efficient search procedure. Due to the sparseness assumption, our approach is particularly suited for layered media containing a limited number of abrupt impedance changes. This is a situation of interest in many applications of nondestructive evaluation. Synthetic and real data results show that the algorithm works well.

Depth profiling of residual stress in steel by laser ultrasonics

Depth profiling of residual stress in steel is of great interest in many practical applications. Conventional techniques are either destructive (x-ray diffraction and hole drilling) or with obvious restriction (Barkhausen noise). This paper presents a noncontact and nondestructive laser ultrasonics method for determining the depth profile of the residual stress layer in steel samples. It is known that surface acoustic waves penetrate into solids to a depth proportional to the wavelength. They are expected to be dispersive in the presence of gradients in physical properties such as residual stress. Based on the dispersion theory, the depth dependence of an effective velocity v(z), which is related to the stress profile S(z), can be fitted from the frequency dependence of the phase velocity v(w). Due to the advantage of wide bandwidth, laser-generated and -detected surface acoustic waves (SAW) offer a promising nondestructive stress depth profiling method. The profiles obtained by SAW are compared with the stress data obtained by other techniques. a)Also at Service de Métallurgie Physique, Université Libre de Bruxelles, Belgique.

Vibration of antisymmetric angle-ply laminated cylindrical panels with different boundary conditions

Orthotropic laminated structures have attracted much interest in many applications because of their desirable properties such as improved thermal and mechanical properties, high strength to weight ratio, and high stiffness to weight ratio. In this paper, an improved version of the differential quadrature method, called the generalized differential quadrature (GDQ) method, is used for the first time to study the vibration of antisymmetric angle-ply laminated cylindrical panels with boundary conditions other than the simply supported type on its four edges. The GDQ method has shown computational advantages over the existing differential quadrature methods in that there is no restriction on the number of grid points in the approximation and the weighting coefficients are determined using a recurrence relation. The GDQ method has shown superb accuracy, efficiency and convenience, and great potential in solving the differential equations of structural problems. The present analysis is formulated using Donnell's shell theory and is validated by comparing results with those in the literature.

Measured and predicted properties of laminar premixed methane/air flames at various pressures

Effects of positive flame stretch on the laminar burning velocities of methane/air flames were studied both experimentally and computationally, considering freely (outwardly) propagating spherical laminar premixed flames. Measurements based on motion picture shadowgraphs, and numerical simulations based on typical contemporary chemical reaction mechanisms, were used to find the sensitivities of the laminar burning velocities to flame stretch, characterized as Markstein numbers, and the fundamental laminar burning velocities of unstretched flames. Reactant conditions included methane/air mixtures having fuel-equivalence ratios of 0.60–1.35 and pressures of 0.5–4.0 atm, at normal temperatures. Both measured and predicted ratios of unstretched-to-stretched laminar burning velocities varied significantly from unity (in the range 0.6–2.3) even though present stretch levels did not approach quenching conditions. Absolute values of Markstein numbers increased with increasing pressure, while the transition from unstable to stable preferential-diffusion conditions with increasing fuel-equivalence ratio shifted from an equivalence ratio of 0.6 at 0.5 atm to 1.2 at 4.0 atm, suggesting increased unstable flame behavior due to preferential-diffusion effects at the elevated pressures of interest for many practical applications. Finally, predictions using two contemporary chemical reaction mechanisms were in reasonably good agreement with present measurements of both Markstein numbers and unstretched laminar burning velocities.

Performance analysis of forward-backward matched-filterbank spectral estimators

The problem of complex spectral estimation is of great interest in many applications. This paper studies the general class of the forward-backward matched-filterbank (MAFI) spectral estimators including the widely used Capon as well as the more recently introduced amplitude and phase estimation of a sinusoid (APES) methods. In particular, we show by means of a higher order expansion technique that the one-dimensional (1-D) Capon estimator underestimates the true spectrum, whereas the 1-D APES method is unbiased; we also show that the bias of the forward-backward Capon is half that of the forward-only Capon (to within a second-order approximation). Furthermore. We show that these results can be extended to the two-dimensional (2-D) Capon and APES estimators. Numerical examples are also presented to demonstrate quantitatively the properties of and the relation between these MAFI estimators.