Search results for: Laplacian eigenvalues

Authors: C. G. Jinimole, A. Harsha

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One of the key problems facing in the analysis of Computed Tomography (CT) images is the poor contrast of the images. Image enhancement can be used to improve the visual clarity and quality of the images or to provide a better transformation representation for further processing. Contrast enhancement of images is one of the acceptable methods used for image enhancement in various applications in the medical field. This will be helpful to visualize and extract details of brain infarctions, tumors, and cancers from the CT image. This paper presents a comparison study of five contrast enhancement techniques suitable for the contrast enhancement of CT images. The types of techniques include Power Law Transformation, Logarithmic Transformation, Histogram Equalization, Contrast Stretching, and Laplacian Transformation. All these techniques are compared with each other to find out which enhancement provides better contrast of CT image. For the comparison of the techniques, the parameters Peak Signal to Noise Ratio (PSNR) and Mean Square Error (MSE) are used. Logarithmic Transformation provided the clearer and best quality image compared to all other techniques studied and has got the highest value of PSNR. Comparison concludes with better approach for its future research especially for mapping abnormalities from CT images resulting from Brain Injuries.

Keywords: computed tomography, enhancement techniques, increasing contrast, PSNR and MSE

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Authors: Ouardi Okkacha, Kaarour Abedlkrim, Meskine Mohamed

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The effective Hamiltonians are widely used in molecular spectroscopy for the interpretation of the vibration-rotation spectra. Their construction is an ambiguous procedure due to the existence of unitary transformations that change the effective Hamiltonian but do not change its eigenvalues. As a consequence of this ambiguity, it may happen that some parameters of effective Hamiltonians cannot be recovered from experimental data in a unique way. The type of admissible transformations which keeps the operator form of the effective Hamiltonian unaltered and the number of empirically determinable parameters strongly depend on the symmetry type of a molecule (asymmetric top, spherical top, and so on) and on the degeneracy of the vibrational state. In this work, we report the study of the ambiguity of effective Hamiltonian for the fundamental degenerate states v3 of the Molecule 12CD4.

Keywords: 12CD4, high-resolution infrared spectra, tetrahedral tensorial formalism, vibrational states, rovibrational line position analysis, XTDS, SPVIEW

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Authors: V. T. Ngo, D. M. Xie

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Frequently, in the design of machines, some of parameters that directly affect the rotor dynamics of the machines are not accurately known. In particular, bearing stiffness support is one such parameter. One of the most basic principles to grasp in rotor dynamics is the influence of the bearing stiffness on the critical speeds and mode shapes associated with a rotor-bearing system. Taking a rig shafting as an example, this paper studies the lateral vibration of the rotor with multi-degree-of-freedom by using Finite Element Method (FEM). The FEM model is created and the eigenvalues and eigenvectors are calculated and analyzed to find natural frequencies, critical speeds, mode shapes. Then critical speeds and mode shapes are analyzed by set bearing stiffness changes. The model permitted to identify the critical speeds and bearings that have an important influence on the vibration behavior.

Keywords: lateral vibration, finite element method, rig shafting, critical speed

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Authors: Septimia Sarbu

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The entropy rate of a stochastic process is a fundamental concept in information theory. It provides a limit to the amount of information that can be transmitted reliably over a communication channel, as stated by Shannon's coding theorems. Recently, researchers have focused on developing new measures of information that generalize Shannon's classical theory. The aim is to design more efficient information encoding and transmission schemes. This paper continues the study of generalized entropy rates, by deriving a closed-form solution to the Sharma-Mittal entropy rate for Gaussian processes. Using the squeeze theorem, we solve the limit in the definition of the entropy rate, for different values of alpha and beta, which are the parameters of the Sharma-Mittal entropy. In the end, we compare it with Shannon and Rényi's entropy rates for Gaussian processes.

Keywords: generalized entropies, Sharma-Mittal entropy rate, Gaussian processes, eigenvalues of the covariance matrix, squeeze theorem

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Authors: Amir Hajian, Sepehr Damavandinejadmonfared

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In this paper the issue of dimensionality reduction is investigated in finger vein recognition systems using kernel Principal Component Analysis (KPCA). One aspect of KPCA is to find the most appropriate kernel function on finger vein recognition as there are several kernel functions which can be used within PCA-based algorithms. In this paper, however, another side of PCA-based algorithms -particularly KPCA- is investigated. The aspect of dimension of feature vector in PCA-based algorithms is of importance especially when it comes to the real-world applications and usage of such algorithms. It means that a fixed dimension of feature vector has to be set to reduce the dimension of the input and output data and extract the features from them. Then a classifier is performed to classify the data and make the final decision. We analyze KPCA (Polynomial, Gaussian, and Laplacian) in details in this paper and investigate the optimal feature extraction dimension in finger vein recognition using KPCA.

Keywords: biometrics, finger vein recognition, principal component analysis (PCA), kernel principal component analysis (KPCA)

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Authors: Theddeus T. Akano, Omotayo A. Fakinlede

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The modelling of physical phenomena, such as the earth’s free oscillations, the vibration of strings, the interaction of atomic particles, or the steady state flow in a bar give rise to Sturm-Liouville (SL) eigenvalue problems. The boundary applications of some systems like the convection-diffusion equation, electromagnetic and heat transfer problems requires the combination of Dirichlet and Neumann boundary conditions. Hence, the incorporation of Robin boundary condition in the analyses of Sturm-Liouville problem. This paper deals with the computation of the eigenvalues and eigenfunction of generalized Sturm-Liouville problems with Robin boundary condition using the finite element method. Numerical solutions of classical Sturm–Liouville problems are presented. The results show an agreement with the exact solution. High results precision is achieved with higher number of elements.

Keywords: Sturm-Liouville problem, Robin boundary condition, finite element method, eigenvalue problems

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Authors: Meet Patel, Darshan Patel, Nilay Shah

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Excess growth of wind-based renewable energy sources is required to identify the optimal location and damping capacity of doubly fed induction-generator-based (DFIG) wind farms while it penetrates into the transmission network. In this analysis, various ratings of DFIG wind farms are penetrated into the Single Machine Infinite Bus (SMIB ) at a different distance of the transmission line. On the basis of detailed examinations, a prime position is evaluated to maximize the stability of overall systems. A damping controller is designed at an optimum location to mitigate the small oscillations. The proposed model was validated using eigenvalue analysis, calculation of the participation factor, and time-domain simulation.

Keywords: DFIG, small signal stability, eigenvalues, time domain simulation

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Authors: Joe Amalraj, M. Arunkumar

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Haze is an atmospheric phenomenon that signicantly degrades the visibility of outdoor scenes. This is mainly due to the atmosphere particles that absorb and scatter the light. This paper introduces a novel single image approach that enhances the visibility of such degraded images. In this method is a fusion-based strategy that derives from two original hazy image inputs by applying a white balance and a contrast enhancing procedure. To blend effectively the information of the derived inputs to preserve the regions with good visibility, we filter their important features by computing three measures (weight maps): luminance, chromaticity, and saliency. To minimize artifacts introduced by the weight maps, our approach is designed in a multiscale fashion, using a Laplacian pyramid representation. This paper demonstrates the utility and effectiveness of a fusion-based technique for de-hazing based on a single degraded image. The method performs in a per-pixel fashion, which is straightforward to implement. The experimental results demonstrate that the method yields results comparative to and even better than the more complex state-of-the-art techniques, having the advantage of being appropriate for real-time applications.

Keywords: single image de-hazing, outdoor images, enhancing, DSP

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Authors: Kazim G. Atman, Hüseyin Sirin

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In theoretical physics, nonlocal phenomena has always been subject of debate. However, in the conventional mathematical approach where the developments of the physical systems are investigated by using the standard mathematical tools, nonlocal effects are not taken into account. In order to investigate the nonlocality in quantum mechanics and fractal property of space, fractional derivative operators are employed in this study. In this manner, fractional creation and annihilation operators are introduced and Einstein coefficients are taken into account as an application of concomitant formalism in quantum field theory. Therefore, each energy mode of photons are considered as fractional quantized harmonic oscillator hereby Einstein coefficients are obtained. Nevertheless, wave function and energy eigenvalues of fractional quantum mechanical harmonic oscillator are obtained via the fractional derivative order α which is a measure of the influence of nonlocal effects. In the case α = 1, where space becomes homogeneous and continuous, standard physical conclusions are recovered.

Keywords: Einstein’s Coefficients, Fractional Calculus, Fractional Quantum Mechanics, Nonlocal Theories

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Authors: Antoni Ivanov, Nikolay Dandanov, Nicole Christoff, Vladimir Poulkov

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Spectrum underutilization has made cognitive radio a promising technology both for current and future telecommunications. This is due to the ability to exploit the unused spectrum in the bands dedicated to other wireless communication systems, and thus, increase their occupancy. The essential function, which allows the cognitive radio device to perceive the occupancy of the spectrum, is spectrum sensing. In this paper, the performance of modern adaptations of the four most widely used spectrum sensing techniques namely, energy detection (ED), cyclostationary feature detection (CSFD), matched filter (MF) and eigenvalues-based detection (EBD) is compared. The implementation has been accomplished through the PlutoSDR hardware platform and the GNU Radio software package in very low Signal-to-Noise Ratio (SNR) conditions. The optimal detection performance of the examined methods in a realistic implementation-oriented model is found for the common relevant parameters (number of observed samples, sensing time and required probability of false alarm).

Keywords: cognitive radio, dynamic spectrum access, GNU Radio, spectrum sensing

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Authors: Zairani Zainol, Zulkiflee Daud

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This study employed 86 respondents representing bank officers of Bank XYX (one of the full-fledged Islamic banks in Malaysia) in the northern region of Malaysia to assess the factors that constitute talent in the Islamic financial industries. To test the discriminant factors for talent among bank officers, a factor analysis was performed. The KMO, Bartlett and MSA tests were executed as the prerequisite before performing the factor analysis. The discriminant factors for talent were extracted via eigenvalues and rotated component matrixes. The results show that five factors, namely (1) self-motivation, (2) leadership, (3) teamwork, (4) interpersonal skills, and (5) creativity/innovation constitute talent in the Islamic financial industries. It is hoped that this study could offer guidelines to education providers, specifically those that conduct the Islamic finance and banking program, as to the areas of emphasis for students before graduating. For the Islamic financial institutions, this study is also vital since they could tackle the areas that need to be improved in managing their talents.

Keywords: talent, Islamic financial industries, talent development, bank’s officers

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Authors: Debjit Dutta, P. Roy, O. Panella

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In recent years, non Hermitian interaction in non relativistic as well as relativistic quantum mechanics have been examined from various aspect. We can observe interesting fact that for such systems a class of potentials, namely the PT symmetric and η-pseudo Hermitian admit real eigenvalues despite being non Hermitian and analogues of those system have been experimentally verified. Point to be noted that relativistic non Hermitian (PT symmetric) interactions can be realized in optical structures and also there exists photonic realization of the (1 + 1) dimensional Dirac oscillator. We have thoroughly studied generalized Dirac oscillators with non Hermitian interactions in (1 + 1) dimensions. To be more specific, we have examined η pseudo Hermitian interactions within the framework of generalized Dirac oscillator in (1 + 1) dimensions. In particular, we have obtained a class of interactions which are η-pseudo Hermitian and the metric operator η could have been also found explicitly. It is possible to have exact solutions of the generalized Dirac oscillator for some choices of the interactions. Subsequently we have employed the mapping between the generalized Dirac oscillator and the Jaynes Cummings (JC) model by spin flip to obtain a class of exactly solvable non Hermitian JC as well as anti Jaynes Cummings (AJC) type models.

Keywords: Dirac oscillator, non-Hermitian quantum system, Hermitian, relativistic

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Authors: F. Amirarfaei, K. Khorasani

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In this paper, reconfigurable consensus achievement of a team of agents with marginally stable linear dynamics and single input channel has been considered. The control algorithm is based on a first order linear protocol. After occurrence of a LOE fault in one of the actuators, using the imperfect information of the effectiveness of the actuators from fault detection and identification module, the control gain is redesigned in a way to still reach consensus. The idea is based on the modeling of change in effectiveness as change of Laplacian matrix. Then as special cases of this class of systems, a team of single integrators as well as double integrators are considered and their behavior subject to a LOE fault is considered. The well-known relative measurements consensus protocol is applied to a leaderless team of single integrator as well as double integrator systems, and Gersgorin disk theorem is employed to determine whether fault occurrence has an effect on system stability and team consensus achievement or not. The analyses show that loss of effectiveness fault in actuator(s) of integrator systems affects neither system stability nor consensus achievement.

Keywords: multi-agent system, actuator fault, stability analysis, consensus achievement

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Authors: Humayun R. H. Kabir

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An analytical solution before used for static and free-vibration response has been extended for thermal buckling response on cylindrical panel with anti-symmetric laminations. The partial differential equations that govern kinematic behavior of shells produce five coupled differential equations. The basic displacement and rotational unknowns are similar to first order shear deformation theory---three displacement in spatial space, and two rotations about in-plane axes. No drilling degree of freedom is considered. Boundary conditions are considered as complete hinge in all edges so that the panel respond on thermal inductions. Two sets of double Fourier series are considered in the analytical solution process. The sets are selected that satisfy mixed type of natural boundary conditions. Numerical results are presented for the first 10 eigenvalues, and first 10 mode shapes for Ux, Uy, and Uz components. The numerical results are compared with a finite element based solution.

Keywords: higher order shear deformation, composite, thermal buckling, angle-ply laminations

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Authors: O. P. Popoola, O. A. Alawode, M. O. Olayiwola, A. M. Oladele

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This research work is based on using discriminant analysis to forecast crime rate in Nigeria between 1996 and 2008. The work is interested in how gender (male and female) relates to offences committed against the government, against other properties, disturbance in public places, murder/robbery offences and other offences. The data used was collected from the National Bureau of Statistics (NBS). SPSS, the statistical package was used to analyse the data. Time plot was plotted on all the 29 offences gotten from the raw data. Eigenvalues and Multivariate tests, Wilks’ Lambda, standardized canonical discriminant function coefficients and the predicted classifications were estimated. The research shows that the distribution of the scores from each function is standardized to have a mean O and a standard deviation of 1. The magnitudes of the coefficients indicate how strongly the discriminating variable affects the score. In the predicted group membership, 172 cases that were predicted to commit crime against Government group, 66 were correctly predicted and 106 were incorrectly predicted. After going through the predicted classifications, we found out that most groups numbers that were correctly predicted were less than those that were incorrectly predicted.

Keywords: discriminant analysis, DA, multivariate analysis of variance, MANOVA, canonical correlation, and Wilks’ Lambda

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Authors: Nadia Ezzat Al-Kirbasee, Ahlam Hussein Hassan, Shatha Raheem Helal Alhimidi, Doaa Ezzat Al-Kirbasee, Muhsen Abood Muhsen Al-Ibadi

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Through DFT/QTAIM calculations, we have provided new insights into the nature of the M-M, M-H, M-O, and M-C bonds of the (Cp*Ru)n(Cp*Os)3−n(μ3-O)2(μ-H)(Cp* = η5-C5Me5, n= 3,2,1,0). The topological analysis of the electron density reveals important details of the chemical bonding interactions in the clusters. Calculations confirm the absence of bond critical points (BCP) and the corresponding bond paths (BP) between Ru-Ru, Ru-Os, and Os-Os. The position of bridging hydrides and Oxo atoms coordinated to Ru-Ru, Ru-Os, and Os-Os determines the distribution of the electron densities and which strongly affects the formation of the bonds between these transition metal atoms. On the other hand, the results confirm that the four clusters contain a 6c–12e and 4c–2e bonding interaction delocalized over M3(μ-H)(μ-O)2 and M3(μ-H), respectively, as revealed by the non-negligible delocalization indexes calculations. The small values for electron density ρ(b) above zero, together with the small values, again above zero, for laplacian ∇2ρ(b) and the small negative values for total energy density H(b) are shown by the Ru-H, Os-H, Ru-O, and Os-O bonds in the four clusters are typical of open shell interactions. Also, the topological data for the bonds between Ru and Os atoms with the C atoms of the pentamethylcyclopentadienyl (Cp*) ring ligands are basically similar and show properties very consistent with open shell interactions in the QTAIM classification.

Keywords: metal-metal and metal-ligand interactions, organometallic complexes, topological analysis, DFT and QTAIM analyses

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Authors: Ping Bo, Meng Yunshan

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Satellite-derived sea surface temperature (SST) is a key parameter for many operational and scientific applications. However, the disadvantage of SST data is a high percentage of missing data which is mainly caused by cloud coverage. Data Interpolating Empirical Orthogonal Function (DINEOF) algorithm is an EOF-based technique for reconstructing the missing data and has been widely used in oceanographic field. The reconstruction of SST images within a long time series using DINEOF can cause large discontinuities and one solution for this problem is to filter the temporal covariance matrix to reduce the spurious variability. Based on the previous researches, an algorithm is presented in this paper to improve the temporal correlations in EOF expansion. Similar with the previous researches, a filter, such as Laplacian filter, is implemented on the temporal covariance matrix, but the temporal relationship between two consecutive images which is used in the filter is considered in the presented algorithm, for example, two images in the same season are more likely correlated than those in the different seasons, hence the latter one is less weighted in the filter. The presented approach is tested for the monthly nighttime 4-km Advanced Very High Resolution Radiometer (AVHRR) Pathfinder SST for the long-term period spanning from 1989 to 2006. The results obtained from the presented algorithm are compared to those from the original DINEOF algorithm without filtering and from the DINEOF algorithm with filtering but without taking temporal relationship into account.

Keywords: data interpolating empirical orthogonal function, image reconstruction, sea surface temperature, temporal filter

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Authors: Mehrnaz Alibeikloo, Hadi Khabbaz, Behzad Fatahi

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The spectral random field method is one of the widely used methods to obtain more reliable and accurate results in geotechnical problems involving material variability. Karhunen-Loeve (K-L) expansion method was applied to perform random field discretization of cross-correlated creep parameters. Karhunen-Loeve expansion method is based on eigenfunctions and eigenvalues of covariance function adopting Kernel integral solution. In this paper, the accuracy of Karhunen-Loeve expansion was investigated to predict long-term settlement of soft soils adopting elastic visco-plastic creep model. For this purpose, a parametric study was carried to evaluate the effect of K-L expansion terms and spatial correlation length on the reliability of results. The results indicate that small values of spatial correlation length require more K-L expansion terms. Moreover, by increasing spatial correlation length, the coefficient of variation (COV) of creep settlement increases, confirming more conservative and safer prediction.

Keywords: Karhunen-Loeve expansion, long-term settlement, reliability analysis, spatial correlation length

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Authors: Nancy Ibrahim Abdalla, Abdelaziz Karamalla Gaiballa

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Rangelands in semi-arid areas provide a good source for feeding huge numbers of animals and serving environmental, economic and social importance; therefore, these areas are considered economically very important for the pastoral sector in Sudan. This paper investigates the means of differentiating between different rangelands sites according to soil types using principal component analysis to assist in monitoring and assessment purposes. Three rangeland sites were identified in the study area as flat sandy sites, sand dune site, and hard clay site. Principal component analysis (PCA) was used to reduce the number of factors needed to distinguish between rangeland sites and produce a new set of data including the most useful spectral information to run satellite image processing. It was performed using selected types of data (two vegetation indices, topographic data and vegetation surface reflectance within the three bands of MODIS data). Analysis with PCA indicated that there is a relatively high correspondence between vegetation and soil of the total variance in the data set. The results showed that the use of the principal component analysis (PCA) with the selected variables showed a high difference, reflected in the variance and eigenvalues and it can be used for differentiation between different range sites.

Keywords: principal component analysis, PCA, rangeland sites, semi-arid areas, soil types

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Authors: Arka Roy, Chandra Prakash Dubey

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Inverse problem generally used for recovering hidden information from outside available data. Vertical component of gravity field we will be going to use for underneath density structure calculation. Ill-posing nature is main obstacle for any inverse problem. Linear regularization using Tikhonov formulation are used for appropriate choice of SVD and GSVD components. For real time data handle, signal to noise ratios should have to be less for reliable solution. In our study, 2D and 3D synthetic model with rectangular grid are used for gravity field calculation and its corresponding inversion for density reconstruction. Fine grid also we have considered to hold any irregular structure. Keeping in mind of algebraic ambiguity factor number of observation point should be more than that of number of data point. Picard plot is represented here for choosing appropriate or main controlling Eigenvalues for a regularized solution. Another important study is depth resolution plot (DRP). DRP are generally used for studying how the inversion is influenced by regularizing or discretizing. Our further study involves real time gravity data inversion of Vredeforte Dome South Africa. We apply our method to this data. The results include density structure is in good agreement with known formation in that region, which puts an additional support of our method.

Keywords: depth resolution plot, gravity inversion, Picard plot, SVD, Tikhonov formulation

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Authors: João Paulo Pascon

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In this work, a mixed 3D finite element formulation is proposed in order to analyze thermoviscoplastic materials under large strain levels and ductile damage. To this end, a tetrahedral element of linear order is employed, considering a thermoviscoplastic constitutive law together with the neo-Hookean hyperelastic relationship and a nonlocal Gurson`s porous plasticity theory The material model is capable of reproducing finite deformations, elastoplastic behavior, void growth, nucleation and coalescence, thermal effects such as plastic work heating and conductivity, strain hardening and strain-rate dependence. The nonlocal character is introduced by means of a nonlocal parameter applied to the Laplacian of the porosity field. The element degrees of freedom are the nodal values of the deformed position, the temperature and the nonlocal porosity field. The internal variables are updated at the Gauss points according to the yield criterion and the evolution laws, including the yield stress of matrix, the equivalent plastic strain, the local porosity and the plastic components of the Cauchy-Green stretch tensor. Two problems involving 3D specimens and ductile damage are numerically analyzed with the developed computational code: the necking problem and a notched sample. The effect of the nonlocal parameter and the mesh refinement is investigated in detail. Results indicate the need of a proper nonlocal parameter. In addition, the numerical formulation can predict ductile fracture, based on the evolution of the fully damaged zone.

Keywords: mixed finite element, large strains, ductile damage, thermoviscoplasticity

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Authors: Meng Su

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High-dimensional data analysis often presents challenges in capturing the complex, nonlinear relationships and manifold structures inherent to the data. This article presents a novel approach that leverages the strengths of two powerful techniques, Diffusion Maps and Diffusion Probabilistic Models (DPMs), to address these challenges. By integrating the dimensionality reduction capability of Diffusion Maps with the data modeling ability of DPMs, the proposed method aims to provide a comprehensive solution for analyzing and generating high-dimensional data. The Diffusion Map technique preserves the nonlinear relationships and manifold structure of the data by mapping it to a lower-dimensional space using the eigenvectors of the graph Laplacian matrix. Meanwhile, DPMs capture the dependencies within the data, enabling effective modeling and generation of new data points in the low-dimensional space. The generated data points can then be mapped back to the original high-dimensional space, ensuring consistency with the underlying manifold structure. Through a detailed example implementation, the article demonstrates the potential of the proposed hybrid approach to achieve more accurate and effective modeling and generation of complex, high-dimensional data. Furthermore, it discusses possible applications in various domains, such as image synthesis, time-series forecasting, and anomaly detection, and outlines future research directions for enhancing the scalability, performance, and integration with other machine learning techniques. By combining the strengths of Diffusion Maps and DPMs, this work paves the way for more advanced and robust data analysis methods.

Keywords: diffusion maps, diffusion probabilistic models (DPMs), manifold learning, high-dimensional data analysis

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Authors: Egor Stadnichuk

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Relativistic runaway electron avalanches (RREA) are a widely accepted source of thunderstorm gamma-radiation. In regions with huge electric field strength, RREA can multiply via relativistic feedback. The relativistic feedback is caused both by positron production and by runaway electron bremsstrahlung gamma-rays reversal. In complex multilayer thunderstorm electric field structures, an additional reactor feedback mechanism appears due to gamma-ray exchange between separate strong electric field regions with different electric field directions. The study of this reactor mechanism in conjunction with the relativistic feedback with Monte Carlo simulations or by direct solution of the kinetic Boltzmann equation requires a significant amount of computational time. In this work, a theoretical approach to study feedback mechanisms in RREA physics is developed. It is based on the matrix of feedback operators construction. With the feedback matrix, the problem of the dynamics of avalanches in complex electric structures is reduced to the problem of finding eigenvectors and eigenvalues. A method of matrix elements calculation is proposed. The proposed concept was used to study the dynamics of RREAs in multilayer thunderclouds.

Keywords: terrestrial Gamma-ray flashes, thunderstorm ground enhancement, relativistic runaway electron avalanches, gamma-rays, high-energy atmospheric physics, TGF, TGE, thunderstorm, relativistic feedback, reactor feedback, reactor model

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Authors: Behnaz Moradijamei, Michael Higgins

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Identifying community structure is a critical task in analyzing social media data sets often modeled by networks. Statistical models such as the stochastic block model have proven to explain the structure of communities in real-world network data. In this work, we develop a goodness-of-fit test to examine community structure's existence by using a distinguishing property in networks: cyclic structures are more prevalent within communities than across them. To better understand how communities are shaped by the cyclic structure of the network rather than just the number of edges, we introduce a novel method for deciding on the existence of communities. We utilize these structures by using renewal non-backtracking random walk (RNBRW) to the existing goodness-of-fit test. RNBRW is an important variant of random walk in which the walk is prohibited from returning back to a node in exactly two steps and terminates and restarts once it completes a cycle. We investigate the use of RNBRW to improve the performance of existing goodness-of-fit tests for community detection algorithms based on the spectral properties of the adjacency matrix. Our proposed test on community structure is based on the probability distribution of eigenvalues of the normalized retracing probability matrix derived by RNBRW. We attempt to make the best use of asymptotic results on such a distribution when there is no community structure, i.e., asymptotic distribution under the null hypothesis. Moreover, we provide a theoretical foundation for our statistic by obtaining the true mean and a tight lower bound for RNBRW edge weights variance.

Keywords: hypothesis testing, RNBRW, network inference, community structure

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Authors: Naser B. Almari, Salem S. Alghamdi, Muhammad Afzal, Mohamed Helmy El Shal

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Wheat landraces are a rich genetic resource for boosting agronomic qualities in breeding programs while also providing diversity and unique adaptation to local environmental conditions. These genotypes have grown increasingly important in the face of recent climate change challenges. This research aimed to look at the genetic diversity of Saudi Durum wheat landraces using morpho-phenological and molecular data. The principal components analysis (PCA) analysis recorded 78.47 % variance and 1.064 eigenvalues for the first six PCs of the total, respectively. The significant characters contributed more to the diversity are the length of owns at the tip relative to the length of the ear, culm: glaucosity of the neck, flag leaf: glaucosity of the sheath, flag leaf: anthocyanin coloration of auricles, plant: frequency of plants with recurved flag leaves, ear: length, and ear: shape in profile in the PC1. The significant wheat genotypes contributed more in the PC1 (8, 14, 497, 650, 569, 590, 594, 598, 600, 601, and 604). The cluster analysis recorded an 85.42 cophenetic correlation among the 22 wheat genotypes and grouped the genotypes into two main groups. Group, I contain 8 genotypes, however, the 2nd group contains 12 wheat genotypes, while two genotypes (13 and 497) are standing alone in the dendrogram and unable to make a group with any one of the genotypes. The second group was subdivided into two subgroups. The genotypes (14, 602, and 600) were present in the second sub-group. The genotypes were grouped into two main groups. The first group contains 17 genotypes, while the second group contains 3 (8, 977, and 594) wheat genotypes. The genotype (602) was standing alone and unable to make a group with any wheat genotype. The genotypes 650 and 13 also stand alone in the first group. Using the Mantel test, the data recorded a significant (R2 = 0.0006) correlation (phenotypic and genetic) among 22 wheat durum genotypes.

Keywords: durum wheat, PCA, cluster analysis, SRAP, genetic diversity

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Authors: Krish Jhurani

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The research paper presents an in-depth analysis of symmetry properties in linear algebraic systems under the operation of non-canonical scalar multiplication structures, specifically semirings, and near-rings. The objective is to unveil the profound alterations that occur in traditional linear algebraic structures when we replace conventional field multiplication with these non-canonical operations. In the methodology, we first establish the theoretical foundations of non-canonical scalar multiplication, followed by a meticulous investigation into the resulting symmetry properties, focusing on eigenvectors, eigenspaces, and invariant subspaces. The methodology involves a combination of rigorous mathematical proofs and derivations, supplemented by illustrative examples that exhibit these discovered symmetry properties in tangible mathematical scenarios. The core findings uncover unique symmetry attributes. For linear algebraic systems with semiring scalar multiplication, we reveal eigenvectors and eigenvalues. Systems operating under near-ring scalar multiplication disclose unique invariant subspaces. These discoveries drastically broaden the traditional landscape of symmetry properties in linear algebraic systems. With the application of these findings, potential practical implications span across various fields such as physics, coding theory, and cryptography. They could enhance error detection and correction codes, devise more secure cryptographic algorithms, and even influence theoretical physics. This expansion of applicability accentuates the significance of the presented research. The research paper thus contributes to the mathematical community by bringing forth perspectives on linear algebraic systems and their symmetry properties through the lens of non-canonical scalar multiplication, coupled with an exploration of practical applications.

Keywords: eigenspaces, eigenvectors, invariant subspaces, near-rings, non-canonical scalar multiplication, semirings, symmetry properties

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Authors: Julie V. Logan, Preston T. Webster, Kevin B. Woller, Christian P. Morath, Michael P. Short

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Semiconductors, as the base of critical electronic systems, are exposed to damaging radiation while operating in space, nuclear reactors, and particle accelerator environments. What innate property allows some semiconductors to sustain little damage while others accumulate defects rapidly with dose is, at present, poorly understood. This limits the extent to which radiation tolerance can be implemented as a design criterion. To address this problem of determining the driver of semiconductor radiation tolerance, the first step is to generate a dataset of the relative radiation tolerance of a large range of semiconductors (exposed to the same radiation damage and characterized in the same way). To accomplish this, Rutherford backscatter channeling experiments are used to compare the displaced lattice atom buildup in InAs, InP, GaP, GaN, ZnO, MgO, and Si as a function of step-wise alpha particle dose. With this experimental information on radiation-induced incorporation of interstitial defects in hand, hybrid density functional theory electron densities (and their derived quantities) are calculated, and their gradient and Laplacian are evaluated to obtain key fundamental information about the interactions in each material. It is shown that simple, undifferentiated values (which are typically used to describe bond strength) are insufficient to predict radiation tolerance. Instead, the curvature of the electron density at bond critical points provides a measure of radiation tolerance consistent with the experimental results obtained. This curvature and associated forces surrounding bond critical points disfavors localization of displaced lattice atoms at these points, favoring their diffusion toward perfect lattice positions. With this criterion to predict radiation tolerance, simple density functional theory simulations can be conducted on potential new materials to gain insight into how they may operate in demanding high radiation environments.

Keywords: density functional theory, GaN, GaP, InAs, InP, MgO, radiation tolerance, rutherford backscatter channeling

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Authors: Jennifer Cuellar, Angie L. Parada, Kevin N. S. Chacon, Sol M. Mejia

Abstract:

The purification of bio-ethanol through distillation methods is an unresolved issue at the biofuel industry because of the ethanol-water azeotrope formation, which increases the steps of the purification process and subsequently increases the production costs. Therefore, understanding the mixture nature at the molecular level could provide new insights for improving the current methods and/or designing new and more efficient purification methods. For that reason, the present study focuses on the evaluation and analysis of (ethanol)₉-water heterodecamers, as the systems with the minimum molecular proportion that represents the azeotropic concentration (96 %m/m in ethanol). The computational modelling was carried out with B3LYP-D3/6-311++G(d,p) in Gaussian 09. Initial explorations of the potential energy surface were done through two methods: annealing simulated runs and molecular dynamics trajectories besides intuitive structures obtained from smaller (ethanol)n-water heteroclusters, n = 7, 8 and 9. The energetic order of the seven stable heterodecamers determines the most stable heterodecamer (Hdec-1) as a structure forming a bicyclic geometry with the O-H---O hydrogen bonds (HBs) where the water is a double proton donor molecule. Hdec-1 combines 1 water molecule and the same quantity of every ethanol conformer; this is, 3 trans, 3 gauche 1 and 3 gauche 2; its abundance is 89%, its decamerization energy is -80.4 kcal/mol, i.e. 13 kcal/mol most stable than the less stable heterodecamer. Besides, a way to understand why methanol does not form an azeotropic mixture with water, analogous systems ((ethanol)10, (methanol)10, and (methanol)9-water)) were optimized. Topologic analysis of the electron density reveals that Hec-1 forms 33 weak interactions in total: 11 O-H---O, 8 C-H---O, 2 C-H---C hydrogen bonds and 12 H---H interactions. The strength and abundance of the most unconventional interactions (H---H, C-H---O and C-H---O) seem to explain the preference of the ethanol for forming heteroclusters instead of clusters. Besides, O-H---O HBs present a significant covalent character according to topologic parameters as the Laplacian of electron density and the relationship between potential and kinetic energy densities evaluated at the bond critical points; obtaining negatives values and values between 1 and 2, for those two topological parameters, respectively.

Keywords: ADMP, DFT, ethanol-water azeotrope, Grimme dispersion correction, simulated annealing, weak interactions

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Authors: H. Jung, N. Kim, B. Kang, J. Choe

Abstract:

History matching is a crucial procedure for predicting reservoir performances and making future decisions. However, it is difficult due to uncertainties of initial reservoir models. Therefore, it is important to have reliable initial models for successful history matching of highly heterogeneous reservoirs such as channel reservoirs. In this paper, we proposed a novel scheme for regenerating geological models using support vector machine (SVM) and principal component analysis (PCA). First, we perform PCA for figuring out main geological characteristics of models. Through the procedure, permeability values of each model are transformed to new parameters by principal components, which have eigenvalues of large magnitude. Secondly, the parameters are projected into two-dimensional plane by multi-dimensional scaling (MDS) based on Euclidean distances. Finally, we train an SVM classifier using 20% models which show the most similar or dissimilar well oil production rates (WOPR) with the true values (10% for each). Then, the other 80% models are classified by trained SVM. We select models on side of low WOPR errors. One hundred channel reservoir models are initially generated by single normal equation simulation. By repeating the classification process, we can select models which have similar geological trend with the true reservoir model. The average field of the selected models is utilized as a probability map for regeneration. Newly generated models can preserve correct channel features and exclude wrong geological properties maintaining suitable uncertainty ranges. History matching with the initial models cannot provide trustworthy results. It fails to find out correct geological features of the true model. However, history matching with the regenerated ensemble offers reliable characterization results by figuring out proper channel trend. Furthermore, it gives dependable prediction of future performances with reduced uncertainties. We propose a novel classification scheme which integrates PCA, MDS, and SVM for regenerating reservoir models. The scheme can easily sort out reliable models which have similar channel trend with the reference in lowered dimension space.

Keywords: history matching, principal component analysis, reservoir modelling, support vector machine

Procedia PDF Downloads 134

Authors: Mancho Manev

Abstract:

The concept of almost paracontact Riemannian manifolds (abbr., apcR manifolds) was introduced by I. Sato in 1976 as an analogue of almost contact Riemannian manifolds. The notion of an apcR manifold of type (p,q) was defined by S. Sasaki in 1980, where p and q are respectively the numbers of the multiplicity of the structure eigenvalues 1 and -1. It also has a simple eigenvalue of 0. In our work, we consider (2n+1)-dimensional apcR manifolds of type (n,n), i.e., the paracontact distribution of the studied manifold can be considered as a 2n-dimensional almost paracomplex Riemannian distribution with almost paracomplex structure and structure group O(n) × O(n). The aim of the present study is to introduce a new class of apcR manifolds. Such a manifold is obtained using the construction of a certain Riemannian cone over it, and the resulting manifold is a paraholomorphic paracomplex Riemannian manifold (abbr., phpcR manifold). We call it a para-Sasaki-like Riemannian manifold (abbr., pSlR manifold) and give some explicit examples. We study the structure of pSlR spaces and find that the paracontact form η is closed and each pSlR manifold locally can be considered as a certain product of the real line with a phpcR manifold, which is locally a Riemannian product of two equidimensional Riemannian spaces. We also obtain that the curvature of the pSlR manifolds is completely determined by the curvature of the underlying local phpcR manifold. Moreover, the ξ-directed Ricci curvature is equal to -2n, while in the Sasaki case, it is 2n. Accordingly, the pSlR manifolds can be interpreted as the counterpart of the Sasaki manifolds; the skew-symmetric part of ∇η vanishes, while in the Sasaki case, the symmetric part vanishes. We define a hyperbolic extension of a (complete) phpcR manifold that resembles a certain warped product, and we indicate that it is a (complete) pSlR manifold. In addition, we consider the hyperbolic extension of a phpcR manifold and prove that if the initial manifold is a complete Einstein manifold with negative scalar curvature, then the resulting manifold is a complete Einstein pSlR manifold with negative scalar curvature. In this way, we produce new examples of a complete Einstein Riemannian manifold with negative scalar curvature. Finally, we define and study para contact conformal/homothetic deformations by deriving a subclass that preserves the para-Sasaki-like condition. We then find that if we apply a paracontact homothetic deformation of a pSlR space, we obtain that the Ricci tensor is invariant.

Keywords: almost paracontact Riemannian manifolds, Einstein manifolds, holomorphic product manifold, warped product manifold

Procedia PDF Downloads 183