Results 1 - 10 of 143455
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[en] The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, MaIysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873-88.], [MaIysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415-28.], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171-8.]. We prove that trajectories of fractal interpolation stochastic processes converge to the trajectory of the original process. We also show that convergence of the trajectories in fractal interpolation of stochastic processes is equivalent to the convergence of trajectories in linear interpolation
[en] The paper deals with the reliability modeling of the failure process of large and complex repairable equipment whose failure intensity shows a bathtub type non-monotonic behavior. A non-homogeneous Poisson process arising from the superposition of two power law processes is proposed, and the characteristics and mathematical details of the proposed model are illustrated. A graphical approach is also presented, which allows to determine whether the proposed model can adequately describe a given failure data. A graphical method for obtaining crude but easy estimates of the model parameters is then illustrated, as well as more accurate estimates based on the maximum likelihood method are provided. Finally, two numerical applications are given to illustrate the proposed model and the estimation procedures
[en] In this paper we introduce a new construction of the fractal interpolation surface (FIS) using an even more general IFS which can generate self-affine and non self-affine fractal surfaces. Here we present the general types of fractal surfaces that are based on nonlinear IFSs.
[en] High-accuracy electronic structure calculations with correlated wave functions demand the use of large basis sets and complete-basis extrapolation, but the accuracy of fragment-based quantum chemistry methods has most often been evaluated using double-ζ basis sets, with errors evaluated relative to a supersystem calculation using the same basis set. Here, we examine the convergence towards the basis-set limit of two- and three-body expansions of the energy, for water clusters and ion–water clusters, focusing on calculations at the level of second-order Møller-Plesset perturbation theory (MP2). Several different corrections for basis-set superposition error (BSSE), each consistent with a truncated many-body expansion, are examined as well. We present a careful analysis of how the interplay of errors (from all sources) influences the accuracy of the results. We conclude that fragment-based methods often benefit from error cancellation wherein BSSE offsets both incompleteness of the basis set as well as higher-order many-body effects that are neglected in a truncated many-body expansion. An n-body counterpoise correction facilitates smooth extrapolation to the MP2 basis-set limit, and at n = 3 affords accurate results while requiring calculations in subsystems no larger than trimers
[en] The main objective of this paper is to study reduction rate of 2D DEM (digital elevation model) data profile after data reduction by the Douglas-Peucker (DP) linear simplification method and by fractal interpolation to show original terrain reconstruction. In this paper, two-dimensional data of measured geographic profiles are taken as the study object, by using the DP method and the improved Douglas-Peucker (IDP) method to reduce data. Its aim is to retain spatial linear characteristics and variations, then take reduced data points as basic points and use the random fractal interpolation approach to add more data points up to the same as the original data points, in order to reconstruct the terrain, and compare the experimental data with the random point extraction method addressed in related literature. This paper uses tolerance calibration to generate different reduction rates and utilizes four types of evaluation factors, statistical measurement, image measurement, spectral analysis and elevation cumulative probability distribution graph, to make a quantitative analysis of profile variation. The study result indicates that real profile elevation data, manipulated with varied reduction approaches, then reconstructed by means of fractal interpolation can produce data points with a higher resolution than those originally observed, thereby the reconstructed profile gets more natural and real details.
[en] We describe the design and testing of a low-cost optical sensor for monitoring separation of magnetic micro and nanoparticles in low magnetic field gradients. The sample is placed in a vertically aligned test tube, where the magnetic field gradient and the gravitational field are both in the same direction, such that the magnetophoretic velocity can be calibrated against a known value. We describe methods for extracting the magnetophoretic velocity using two different theoretical approaches, one based on linear interpolation and another based on fitting to a physical theory implementing a time-dependent version of Beer's law. We discuss strengths and weaknesses of the two approaches. We show that the sensor can be used to detect particle aggregation in polymer solutions. We also show that the magnetic field gradient may alter the size distribution of the aggregates, which is detected as larger intensity fluctuations and nonlinear response
[en] The advantages of the simultaneous integration of production and time-lapse seismic data for history matching have been demonstrated in a number of previous studies. Production data provide accurate observations at particular spatial locations (wells), while seismic data enable global, though filtered/noisy, estimates of state variables. In this work, we present an efficient computational tool for bi-objective history matching, in which data misfits for both production and seismic measurements are minimized using an adjoint-gradient approach. This enables us to obtain a set of Pareto optimal solutions defining the optimal trade-off between production and seismic data misfits (which are, to some extent, conflicting). The impact of noise structure and noise level on Pareto optimal solutions is investigated in detail. We discuss the existence of the “best” trade-off solution, or least-conflicting posterior model, which corresponds to the history-matched model that is expected to provide the least-conflicting forecast of future reservoir performance. The overall framework is successfully applied in 2D and 3D compositional simulation problems to provide a single least-conflicting posterior model and, for the 2D case, multiple samples from the posterior distribution using the randomized maximum likelihood method.
[en] The classical relation between the flame speed and the stretch, employed in modeling flame-flow interaction, is valid only for positive Markstein lengths (high Lewis numbers). At negative Markstein lengths (low Lewis numbers) the corresponding dynamical system suffers short-wavelength instability, making the associated initial value problem ill-posed. In this study the difficulty is resolved by incorporation of higher-order effects using a geometrically-invariant extrapolation from the linear analysis data. As a result one ends up with a reduced model based on a coupled system of second-order dynamic equations for the flame interface and its temperature. As an illustration the new model is applied for description of diffusively unstable stagnation-point flow flames
[en] Random signals and feedback may facilitate the exchange of shared keys in secure communications systems. In this Letter, the security risk during the initial turn-on is examined. Results indicate that causality plays a critical role. If signals are continuous, the eavesdropper can use extrapolation to breach the security. In digital signaling, however, two parties in communication are in control. They use sampling and set the quantization accuracy to limit the information available to eavesdropper. They can gradually increase the feedback coefficient. By using these countermeasures, they can prevent the eavesdropper from gathering useful information during the transient.