Papers by Keyword: Interpolation

Abstract: The solution of the time-dependent Schrödinger equation for the helium atom in double excited states using the time-dependent Hartree-Fock (TDHF) equation is outlined in this work. Schwartz interpolation is used to derive grid representations that are particularly suitable for problems involving the Coulomb potential. This method allows a non-uniform spatial discretization of grid and provides an accurate description of the excited states, eigenvalues and wave functions with a few numbers of grid points. We have introduced the solution using the Coulomb Wave Function Discrete Variable Representation (CWDVR) which is an economical and promising step towards a more efficient treatment of many-electron systems. The equation is transformed into a diffusion type equation by an imaginary-time evolution method and the solution is obtained numerically. The asymptotic solution of these equations leads to definite energy double excited states. We have shown that the calculated electronic energies for the helium atom agree well with the best available values.

Abstract: Mangrove is an essential coastal vegetation with multiple abilities to protect the land from any hazards that come from the sea, also provides a contribution to combat global climate change by sequestering the carbon in the atmosphere on its stem and root system. Measuring the amount of carbon that can be stored by mangroves using terrestrial surveys is relatively challenging due to the harsh environment. Therefore, an optional method using satellite remote sensing and spatial modeling using Geographic Information Systems (GIS) is needed. This research will combine field sampling and a GIS approach to estimate how much mangroves can store in the research area with spatial interpolation techniques i.e., kriging, spline, topo to raster, and nearest neighbor. To check the accuracy, Root Mean Square Error (RMSE) was used. The most accurate model among others is Spline With Barrier with an RMSE of about 1.82 Mg C Ha-1 with a range of Above-Ground Carbon (AGC) values from 13.94 Mg C Ha-1 to 142.43 Mg C Ha-1. In conclusion, spatial interpolation may assist the mangrove’s carbon spatial modelling with promising accuracy.

Abstract: Ultrasonic signal reconstruction for Structural Health Monitoring is a topic that has been discussed extensively. In this paper, we will apply the techniques of compressed sensing to reconstruct ultrasonic signals that are seriously damaged. To reconstruct the data, the application of conventional interpolation techniques is restricted under the criteria of Nyquist sampling theorem. The newly developed technique - compressed sensing breaks the limitations of Nyquist rate and provides effective results based upon sparse signal reconstruction. Sparse representation is constructed using Fourier transform basis. An l₁-norm optimization is then applied for reconstruction. Signals with temperature characteristics were synthetically created. We seriously corrupted these signals and tested the efficacy of our approach under two different scenarios. Firstly, the signal is randomly sampled at very low rates. Secondly, selected intervals were completely blank out. Simulation results show that the signals are effectively reconstructed. It outperforms conventional Spline interpolation in signal-to-noise ratio (SNR) with low variation, especially under very low data rates. This research demonstrates very promising results of using compressed sensing for ultrasonic signal reconstruction.

Abstract: Background correction is an essential part in LIBS signal analysis. The interpolation method of background correction has major drawbacks. This paper introduces an interpolation method to overcome the shortcomings of linear and cubic spline interpolation methods. Finally, we compare different interpolation methods to verify the proposed interpolation method.

Abstract: A numerical technique for constructing liquidus temperature in quaternary system has been proposed. This technique offers accurate calculations of solidification temperature and demonstrates on the Al-Si-Mg-Fe system. The thermodynamic data is extracted by calling the TQ-interface (Thermodynamic Calculation Interface) and modeled using efficient computational approaches such as polynomial regression and interpolation. Si and Mg are treated as independent variables in regression functions, while Fe is treated as interpolated variable. The validated accuracy of results obtained through this method is compared with those calculated using Thermo-Calc. This technique is useful for quaternary systems.

Abstract: In this paper, a simplified CNC system based on PLC and position controller is introduced. The position controller FX2N-20GM, is a pulse chain output unit, which can control motors to accomplish linear interpolation and circular interpolation. PLC,with the mode of FX_2N-16MR, the logic control unit of system, reads position data from the position controller and determines the operation of the system. Labwindows/CVI,the configuration software on PC, is the upper monitoring system, showing the motors position in real time by monitoring PLC. The system, combined PLC , position controller and configuration software, can draw any kinds of two dimensional graphics and show the trajectory of motors on PC in real time, the linear interpolation and circular interpolation had been perfectly implemented by a series of experiments. Compared with classic CNC system, it did not contain tedious hardware wring or complex software programming, which makes the whole structure a simplified CNC system.

Abstract: This paper extends the polynomial function to double logarithmic function, constructing a class of multi parameters iterative function, and uses this function to calculate the fractal interpolated surface for given interpolation points, and establishes the iterative function mathematical model of multi parameters fractal interpolation. In order to verify the effectiveness and reliability of this proposed model algorithm, this paper uses MATLAB numerical simulation method to calculate, and programs the Newton iterative function of multi parameters fractal interpolation surface, finally gets calculation nephogram of multi parameters fractal interpolation curved surface through calculating. Finally, using iterative method reduces the surface grid size, increasing the smoothness of the surface, so the surface is closer to the actual surface. It provides a new computer method research of fractal interpolation function.

Abstract: Data accuracy and completeness of the wind farm has great significance in wind power research. Because of the wind farm in the process of gathering data and transmission appears distorted and missing, and that leads the accuracy and integrity of data is greatly reduced, so the need for a wind farm data, outlier detection and missing data imputation. This paper outlier detection by statistical method based on 3σ criterion under the normal distribution, and use of the effectiveness of the recently distance interpolation and regression interpolation for missing data, outliers and replacement and interpolation, filled after data and accuracy are improved.

Abstract: Radial Basis Function (RBF) interpolation and trilinear interpolation techniques are compared in the soot particle tracking inside the cylinder of a direct injection engine. The interpolation techniques are used separately in an efficient routine written in Matlab codes which is developed to track the movement or pathline of soot particles in the engine operation cycle ranged from inlet valve closing (IVC) to exhaust valve opening (EVO). Soot particles are treated as a massless body and in spherical shape which will move under the influence of bulk gases flow inside the cylinder. Movement of soot particles are examined through the selection factors of particle's initial coordinate (r,Ɵ,z) and soot concentration level at different instant crack angle. Results obtained from both interpolation techniques are compared and good agreement is achieved with some minor relative difference. However, RBF interpolation has wider applications potential where it can be applied to variety type of mesh geometry as compared to trilinear interpolation which is best used in mesh with hexahedral shape.

Abstract: The paper presents an original method to enhance the productivity of the design activity based on a dimensioning stage which integrates information from various sources: tabular data, diagrams, experimental data and others. The integration of such data in an analytic way is based on an original data processor which interpolates data and outputs diagrams, and outputs information regarding the laws of variation expressed as comma separated values data files, as well as automatically generated source code libraries in C++, Java and MATHLAB/GNU Octave. This automatically generated code is optimized in terms of execution time and it was verified in several applications. The data processor allows the user to visually verify the output data accuracy. The paper also presents some of the applications of the data processor: automatic design, method to enhance the accuracy of computer based calculus for both analytic and numerical methods, conversion of the discontinuous experimental data into laws of variation and experimental data processing in applied elasticity. There are several directions of future research, such as: a more general mathematical approach, development of a more general computer based instrument with increased flexibility and accuracy. Also, a complex software for applied elasticity calculi based on the results of the data processor is under development. Implementation of these applications in commercial CAD/CAE applications is another direction of research.